diff options
144 files changed, 4988 insertions, 3691 deletions
diff --git a/SRC/cla_gbamv.f b/SRC/cla_gbamv.f index 28dc88a6..9bfbab08 100644 --- a/SRC/cla_gbamv.f +++ b/SRC/cla_gbamv.f @@ -40,7 +40,7 @@ * entry is considered "symbolic" if all multiplications involved * in computing that entry have at least one zero multiplicand. * -* Parameters +* Arguments * ========== * * TRANS - INTEGER @@ -118,7 +118,8 @@ * * Level 2 Blas routine. * -* .. +* ===================================================================== +* * .. Parameters .. COMPLEX ONE, ZERO PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) diff --git a/SRC/cla_gbrcond_c.f b/SRC/cla_gbrcond_c.f index a8de1799..434ebbc5 100644 --- a/SRC/cla_gbrcond_c.f +++ b/SRC/cla_gbrcond_c.f @@ -21,12 +21,25 @@ INTEGER IPIV( * ) COMPLEX AB( LDAB, * ), AFB( LDAFB, * ), WORK( * ) REAL C( * ), RWORK( * ) +* .. +* +* Purpose +* ======= * * CLA_GBRCOND_C Computes the infinity norm condition number of * op(A) * inv(diag(C)) where C is a REAL vector. -* WORK is a COMPLEX workspace of size 2*N, and -* RWORK is a REAL workspace of size 3*N. -* .. +* +* Arguments +* ========= +* +* C REAL vector. +* +* WORK COMPLEX workspace of size 2*N. +* +* RWORK REAL workspace of size 3*N. +* +* ===================================================================== +* * .. Local Scalars .. LOGICAL NOTRANS INTEGER KASE, I, J diff --git a/SRC/cla_gbrcond_x.f b/SRC/cla_gbrcond_x.f index a0e04f33..073cecc4 100644 --- a/SRC/cla_gbrcond_x.f +++ b/SRC/cla_gbrcond_x.f @@ -20,12 +20,25 @@ COMPLEX AB( LDAB, * ), AFB( LDAFB, * ), WORK( * ), $ X( * ) REAL RWORK( * ) +* .. +* +* Purpose +* ======= * * CLA_GBRCOND_X Computes the infinity norm condition number of * op(A) * diag(X) where X is a COMPLEX vector. -* WORK is a COMPLEX workspace of size 2*N, and -* RWORK is a REAL workspace of size 3*N. -* .. +* +* Arguments +* ========= +* +* X COMPLEX vector. +* +* WORK COMPLEX workspace of size 2*N. +* +* RWORK REAL workspace of size 3*N. +* +* ===================================================================== +* * .. Local Scalars .. LOGICAL NOTRANS INTEGER KASE, I, J diff --git a/SRC/cla_gbrfsx_extended.f b/SRC/cla_gbrfsx_extended.f index d5eab504..e1a4e3e9 100644 --- a/SRC/cla_gbrfsx_extended.f +++ b/SRC/cla_gbrfsx_extended.f @@ -29,6 +29,9 @@ REAL C( * ), AYB(*), RCOND, BERR_OUT( * ), $ ERRS_N( NRHS, * ), ERRS_C( NRHS, * ) * .. +* +* ===================================================================== +* * .. Local Scalars .. CHARACTER TRANS INTEGER CNT, I, J, M, X_STATE, Z_STATE, Y_PREC_STATE diff --git a/SRC/cla_gbrpvgrw.f b/SRC/cla_gbrpvgrw.f index f486e1e6..aa85d57f 100644 --- a/SRC/cla_gbrpvgrw.f +++ b/SRC/cla_gbrpvgrw.f @@ -17,6 +17,9 @@ * .. Array Arguments .. COMPLEX AB( LDAB, * ), AFB( LDAFB, * ) * .. +* +* ===================================================================== +* * .. Local Scalars .. INTEGER I, J, KD REAL AMAX, UMAX, RPVGRW diff --git a/SRC/cla_geamv.f b/SRC/cla_geamv.f index 66c962ff..32688aff 100644 --- a/SRC/cla_geamv.f +++ b/SRC/cla_geamv.f @@ -41,7 +41,7 @@ * entry is considered "symbolic" if all multiplications involved * in computing that entry have at least one zero multiplicand. * -* Parameters +* Arguments * ========== * * TRANS - INTEGER @@ -113,7 +113,8 @@ * * Level 2 Blas routine. * -* .. +* ===================================================================== +* * .. Parameters .. COMPLEX ONE, ZERO PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) diff --git a/SRC/cla_gercond_c.f b/SRC/cla_gercond_c.f index e6a16635..7c00bed2 100644 --- a/SRC/cla_gercond_c.f +++ b/SRC/cla_gercond_c.f @@ -20,12 +20,25 @@ INTEGER IPIV( * ) COMPLEX A( LDA, * ), AF( LDAF, * ), WORK( * ) REAL C( * ), RWORK( * ) +* .. * +* Purpose +* ======= +* * CLA_GERCOND_C computes the infinity norm condition number of * op(A) * inv(diag(C)) where C is a REAL vector. -* WORK is a COMPLEX workspace of size 2*N, and -* RWORK is a REAL workspace of size 3*N. -* .. +* +* Arguments +* ========= +* +* C REAL vector. +* +* WORK COMPLEX workspace of size 2*N. +* +* RWORK REAL workspace of size 3*N. +* +* ===================================================================== +* * .. Local Scalars .. LOGICAL NOTRANS INTEGER KASE, I, J diff --git a/SRC/cla_gercond_x.f b/SRC/cla_gercond_x.f index 189322a8..b95a6473 100644 --- a/SRC/cla_gercond_x.f +++ b/SRC/cla_gercond_x.f @@ -19,12 +19,25 @@ INTEGER IPIV( * ) COMPLEX A( LDA, * ), AF( LDAF, * ), WORK( * ), X( * ) REAL RWORK( * ) +* .. * +* Purpose +* ======= +* * CLA_GERCOND_X computes the infinity norm condition number of * op(A) * diag(X) where X is a COMPLEX vector. -* WORK is a COMPLEX workspace of size 2*N, and -* RWORK is a REAL workspace of size 3*N. -* .. +* +* Arguments +* ========= +* +* X COMPLEX vector. +* +* WORK COMPLEX workspace of size 2*N. +* +* RWORK REAL workspace of size 3*N. +* +* ===================================================================== +* * .. Local Scalars .. LOGICAL NOTRANS INTEGER KASE diff --git a/SRC/cla_gerfsx_extended.f b/SRC/cla_gerfsx_extended.f index 90ba5bd9..7231f2cd 100644 --- a/SRC/cla_gerfsx_extended.f +++ b/SRC/cla_gerfsx_extended.f @@ -29,6 +29,9 @@ REAL C( * ), AYB( * ), RCOND, BERR_OUT( * ), $ ERRS_N( NRHS, * ), ERRS_C( NRHS, * ) * .. +* +* ===================================================================== +* * .. Local Scalars .. CHARACTER TRANS INTEGER CNT, I, J, X_STATE, Z_STATE, Y_PREC_STATE diff --git a/SRC/cla_heamv.f b/SRC/cla_heamv.f index 4ffaaca0..08480e03 100644 --- a/SRC/cla_heamv.f +++ b/SRC/cla_heamv.f @@ -39,7 +39,7 @@ * entry is considered "symbolic" if all multiplications involved * in computing that entry have at least one zero multiplicand. * -* Parameters +* Arguments * ========== * * UPLO - INTEGER @@ -102,6 +102,8 @@ * Y. INCY must not be zero. * Unchanged on exit. * +* Further Details +* =============== * * Level 2 Blas routine. * @@ -113,7 +115,8 @@ * -- Modified for the absolute-value product, April 2006 * Jason Riedy, UC Berkeley * -* .. +* ===================================================================== +* * .. Parameters .. REAL ONE, ZERO PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) diff --git a/SRC/cla_hercond_c.f b/SRC/cla_hercond_c.f index 2422b5b4..f4ffda94 100644 --- a/SRC/cla_hercond_c.f +++ b/SRC/cla_hercond_c.f @@ -20,12 +20,25 @@ INTEGER IPIV( * ) COMPLEX A( LDA, * ), AF( LDAF, * ), WORK( * ) REAL C ( * ), RWORK( * ) +* .. +* +* Purpose +* ======= * * CLA_HERCOND_C computes the infinity norm condition number of * op(A) * inv(diag(C)) where C is a REAL vector. -* WORK is a COMPLEX workspace of size 2*N, and -* RWORK is a REAL workspace of size 3*N. -* .. +* +* Arguments +* ========= +* +* C REAL vector. +* +* WORK COMPLEX workspace of size 2*N. +* +* RWORK REAL workspace of size 3*N. +* +* ===================================================================== +* * .. Local Scalars .. INTEGER KASE, I, J REAL AINVNM, ANORM, TMP diff --git a/SRC/cla_hercond_x.f b/SRC/cla_hercond_x.f index 7a042ec8..8ca18eba 100644 --- a/SRC/cla_hercond_x.f +++ b/SRC/cla_hercond_x.f @@ -19,12 +19,25 @@ INTEGER IPIV( * ) COMPLEX A( LDA, * ), AF( LDAF, * ), WORK( * ), X( * ) REAL RWORK( * ) +* .. +* +* Purpose +* ======= * * CLA_HERCOND_X computes the infinity norm condition number of * op(A) * diag(X) where X is a COMPLEX vector. -* WORK is a COMPLEX workspace of size 2*N, and -* RWORK is a REAL workspace of size 3*N. -* .. +* +* Arguments +* ========= +* +* X COMPLEX vector. +* +* WORK COMPLEX workspace of size 2*N. +* +* RWORK REAL workspace of size 3*N. +* +* ===================================================================== +* * .. Local Scalars .. INTEGER KASE, I, J REAL AINVNM, ANORM, TMP diff --git a/SRC/cla_herfsx_extended.f b/SRC/cla_herfsx_extended.f index d0c5a5fa..b79d9708 100644 --- a/SRC/cla_herfsx_extended.f +++ b/SRC/cla_herfsx_extended.f @@ -29,6 +29,9 @@ REAL C( * ), AYB( * ), RCOND, BERR_OUT( * ), $ ERRS_N( NRHS, * ), ERRS_C( NRHS, * ) * .. +* +* ===================================================================== +* * .. Local Scalars .. INTEGER UPLO2, CNT, I, J, X_STATE, Z_STATE, $ Y_PREC_STATE diff --git a/SRC/cla_herpvgrw.f b/SRC/cla_herpvgrw.f index 3f331ee1..10e82fd2 100644 --- a/SRC/cla_herpvgrw.f +++ b/SRC/cla_herpvgrw.f @@ -20,6 +20,9 @@ COMPLEX A( LDA, * ), AF( LDAF, * ) REAL WORK( * ) * .. +* +* ===================================================================== +* * .. Local Scalars .. INTEGER NCOLS, I, J, K, KP REAL AMAX, UMAX, RPVGRW, TMP diff --git a/SRC/cla_lin_berr.f b/SRC/cla_lin_berr.f index b2a9702f..7d1480c6 100644 --- a/SRC/cla_lin_berr.f +++ b/SRC/cla_lin_berr.f @@ -16,13 +16,19 @@ * .. Array Arguments .. REAL AYB( N, NRHS ), BERR( NRHS ) COMPLEX RES( N, NRHS ) +* .. +* +* Purpose +* ======= * -* CLA_LIN_BERR computes componentwise relative backward error from +* CLA_LIN_BERR computes component-wise relative backward error from * the formula * max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) ) -* where abs(Z) is the componentwise absolute value of the matrix +* where abs(Z) is the component-wise absolute value of the matrix * or vector Z. -* .. +* +* ===================================================================== +* * .. Local Scalars .. REAL TMP INTEGER I, J diff --git a/SRC/cla_porcond_c.f b/SRC/cla_porcond_c.f index 24b6be26..d4d8072f 100644 --- a/SRC/cla_porcond_c.f +++ b/SRC/cla_porcond_c.f @@ -19,12 +19,18 @@ * .. Array Arguments .. COMPLEX A( LDA, * ), AF( LDAF, * ), WORK( * ) REAL C( * ), RWORK( * ) +* .. +* +* Purpose +* ======= * * SLA_PORCOND_C Computes the infinity norm condition number of * op(A) * inv(diag(C)) where C is a REAL vector * WORK is a COMPLEX workspace of size 2*N, and * RWORK is a REAL workspace of size 3*N. -* .. +* +* ===================================================================== +* * .. Local Scalars .. INTEGER KASE REAL AINVNM, ANORM, TMP diff --git a/SRC/cla_porcond_x.f b/SRC/cla_porcond_x.f index 036fd43c..5946bb52 100644 --- a/SRC/cla_porcond_x.f +++ b/SRC/cla_porcond_x.f @@ -18,12 +18,18 @@ * .. Array Arguments .. COMPLEX A( LDA, * ), AF( LDAF, * ), WORK( * ), X( * ) REAL RWORK( * ) +* .. +* +* Purpose +* ======= * * CLA_PORCOND_X Computes the infinity norm condition number of * op(A) * diag(X) where X is a COMPLEX vector. * WORK is a COMPLEX workspace of size 2*N, and * RWORK is a REAL workspace of size 3*N. -* .. +* +* ===================================================================== +* * .. Local Scalars .. INTEGER KASE, I, J REAL AINVNM, ANORM, TMP diff --git a/SRC/cla_porfsx_extended.f b/SRC/cla_porfsx_extended.f index 25b073e4..8e05a6bb 100644 --- a/SRC/cla_porfsx_extended.f +++ b/SRC/cla_porfsx_extended.f @@ -28,6 +28,9 @@ REAL C( * ), AYB( * ), RCOND, BERR_OUT( * ), $ ERRS_N( NRHS, * ), ERRS_C( NRHS, * ) * .. +* +* ===================================================================== +* * .. Local Scalars .. INTEGER UPLO2, CNT, I, J, X_STATE, Z_STATE, $ Y_PREC_STATE diff --git a/SRC/cla_porpvgrw.f b/SRC/cla_porpvgrw.f index e2a2eab6..3f01199c 100644 --- a/SRC/cla_porpvgrw.f +++ b/SRC/cla_porpvgrw.f @@ -18,6 +18,9 @@ COMPLEX A( LDA, * ), AF( LDAF, * ) REAL WORK( * ) * .. +* +* ===================================================================== +* * .. Local Scalars .. INTEGER I, J REAL AMAX, UMAX, RPVGRW diff --git a/SRC/cla_rpvgrw.f b/SRC/cla_rpvgrw.f index 9cec26d1..fb481c22 100644 --- a/SRC/cla_rpvgrw.f +++ b/SRC/cla_rpvgrw.f @@ -16,6 +16,9 @@ * .. Array Arguments .. COMPLEX A( LDA, * ), AF( LDAF, * ) * .. +* +* ===================================================================== +* * .. Local Scalars .. INTEGER I, J REAL AMAX, UMAX, RPVGRW diff --git a/SRC/cla_syamv.f b/SRC/cla_syamv.f index 412c5799..00faa2dd 100644 --- a/SRC/cla_syamv.f +++ b/SRC/cla_syamv.f @@ -40,7 +40,7 @@ * entry is considered "symbolic" if all multiplications involved * in computing that entry have at least one zero multiplicand. * -* Parameters +* Arguments * ========== * * UPLO - INTEGER @@ -103,6 +103,8 @@ * Y. INCY must not be zero. * Unchanged on exit. * +* Further Details +* =============== * * Level 2 Blas routine. * @@ -114,7 +116,8 @@ * -- Modified for the absolute-value product, April 2006 * Jason Riedy, UC Berkeley * -* .. +* ===================================================================== +* * .. Parameters .. REAL ONE, ZERO PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) diff --git a/SRC/cla_syrcond_c.f b/SRC/cla_syrcond_c.f index 7784a2d5..bd2ba7ea 100644 --- a/SRC/cla_syrcond_c.f +++ b/SRC/cla_syrcond_c.f @@ -20,12 +20,25 @@ INTEGER IPIV( * ) COMPLEX A( LDA, * ), AF( LDAF, * ), WORK( * ) REAL C( * ), RWORK( * ) +* .. +* +* Purpose +* ======= * * CLA_SYRCOND_C Computes the infinity norm condition number of * op(A) * inv(diag(C)) where C is a REAL vector. -* WORK is a COMPLEX workspace of size 2*N, and -* RWORK is a REAL workspace of size 3*N. -* .. +* +* Arguments +* ========= +* +* C REAL vector. +* +* WORK COMPLEX workspace of size 2*N. +* +* RWORK REAL workspace of size 3*N. +* +* ===================================================================== +* * .. Local Scalars .. INTEGER KASE REAL AINVNM, ANORM, TMP diff --git a/SRC/cla_syrcond_x.f b/SRC/cla_syrcond_x.f index c98c1242..fad3211b 100644 --- a/SRC/cla_syrcond_x.f +++ b/SRC/cla_syrcond_x.f @@ -19,12 +19,25 @@ INTEGER IPIV( * ) COMPLEX A( LDA, * ), AF( LDAF, * ), WORK( * ), X( * ) REAL RWORK( * ) +* .. +* +* Purpose +* ======= * * CLA_SYRCOND_X Computes the infinity norm condition number of * op(A) * diag(X) where X is a COMPLEX vector. -* WORK is a COMPLEX workspace of size 2*N, and -* RWORK is a REAL workspace of size 3*N. -* .. +* +* Arguments +* ========= +* +* X COMPLEX vector. +* +* WORK COMPLEX workspace of size 2*N. +* +* RWORK REAL workspace of size 3*N. +* +* ===================================================================== +* * .. Local Scalars .. INTEGER KASE REAL AINVNM, ANORM, TMP diff --git a/SRC/cla_syrfsx_extended.f b/SRC/cla_syrfsx_extended.f index afe76130..d3df3149 100644 --- a/SRC/cla_syrfsx_extended.f +++ b/SRC/cla_syrfsx_extended.f @@ -29,6 +29,9 @@ REAL C( * ), AYB( * ), RCOND, BERR_OUT( * ), $ ERRS_N( NRHS, * ), ERRS_C( NRHS, * ) * .. +* +* ===================================================================== +* * .. Local Scalars .. INTEGER UPLO2, CNT, I, J, X_STATE, Z_STATE, $ Y_PREC_STATE diff --git a/SRC/cla_syrpvgrw.f b/SRC/cla_syrpvgrw.f index 84e71be9..1c1a6e52 100644 --- a/SRC/cla_syrpvgrw.f +++ b/SRC/cla_syrpvgrw.f @@ -20,6 +20,9 @@ REAL WORK( * ) INTEGER IPIV( * ) * .. +* +* ===================================================================== +* * .. Local Scalars .. INTEGER NCOLS, I, J, K, KP REAL AMAX, UMAX, RPVGRW, TMP diff --git a/SRC/cla_wwaddw.f b/SRC/cla_wwaddw.f index d0a7e88f..ebbe3f0b 100644 --- a/SRC/cla_wwaddw.f +++ b/SRC/cla_wwaddw.f @@ -36,7 +36,9 @@ * * W (input) COMPLEX array, length N * The vector to be added. -* .. +* +* ===================================================================== +* * .. Local Scalars .. COMPLEX S INTEGER I diff --git a/SRC/clanhf.f b/SRC/clanhf.f index a89474e5..46957811 100644 --- a/SRC/clanhf.f +++ b/SRC/clanhf.f @@ -90,8 +90,8 @@ * where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, * WORK is not referenced. * -* Note: -* ===== +* Further Details +* =============== * * We first consider Standard Packed Format when N is even. * We give an example where N = 6. diff --git a/SRC/cpftri.f b/SRC/cpftri.f index 82f97cf8..56b4c581 100644 --- a/SRC/cpftri.f +++ b/SRC/cpftri.f @@ -58,8 +58,8 @@ * > 0: if INFO = i, the (i,i) element of the factor U or L is * zero, and the inverse could not be computed. * -* Note: -* ===== +* Further Details +* =============== * * We first consider Standard Packed Format when N is even. * We give an example where N = 6. diff --git a/SRC/cpftrs.f b/SRC/cpftrs.f index cfddeb6e..8b36d15f 100644 --- a/SRC/cpftrs.f +++ b/SRC/cpftrs.f @@ -57,8 +57,8 @@ * = 0: successful exit * < 0: if INFO = -i, the i-th argument had an illegal value * -* Note: -* ===== +* Further Details +* =============== * * We first consider Standard Packed Format when N is even. * We give an example where N = 6. diff --git a/SRC/cstemr.f b/SRC/cstemr.f index 641591f7..2525e18b 100644 --- a/SRC/cstemr.f +++ b/SRC/cstemr.f @@ -67,7 +67,7 @@ * Computer Science Division Technical Report No. UCB/CSD-97-971, * UC Berkeley, May 1997. * -* Notes: +* Further Details * 1.CSTEMR works only on machines which follow IEEE-754 * floating-point standard in their handling of infinities and NaNs. * This permits the use of efficient inner loops avoiding a check for diff --git a/SRC/ctfsm.f b/SRC/ctfsm.f index e26a769a..9eeee773 100644 --- a/SRC/ctfsm.f +++ b/SRC/ctfsm.f @@ -126,8 +126,8 @@ * max( 1, m ). * Unchanged on exit. * -* Notes: -* ====== +* Further Details +* =============== * * We first consider Standard Packed Format when N is even. * We give an example where N = 6. diff --git a/SRC/ctftri.f b/SRC/ctftri.f index ffa0f014..19470e7e 100644 --- a/SRC/ctftri.f +++ b/SRC/ctftri.f @@ -64,8 +64,8 @@ * > 0: if INFO = i, A(i,i) is exactly zero. The triangular * matrix is singular and its inverse can not be computed. * -* Notes: -* ====== +* Further Details +* =============== * * We first consider Standard Packed Format when N is even. * We give an example where N = 6. diff --git a/SRC/ctfttp.f b/SRC/ctfttp.f index 4af92fd7..c56dfc42 100644 --- a/SRC/ctfttp.f +++ b/SRC/ctfttp.f @@ -52,8 +52,8 @@ * = 0: successful exit * < 0: if INFO = -i, the i-th argument had an illegal value * -* Notes: -* ====== +* Further Details +* =============== * * We first consider Standard Packed Format when N is even. * We give an example where N = 6. diff --git a/SRC/ctfttr.f b/SRC/ctfttr.f index bc23d16d..c1b716ec 100644 --- a/SRC/ctfttr.f +++ b/SRC/ctfttr.f @@ -56,8 +56,8 @@ * = 0: successful exit * < 0: if INFO = -i, the i-th argument had an illegal value * -* Notes: -* ====== +* Further Details +* =============== * * We first consider Standard Packed Format when N is even. * We give an example where N = 6. diff --git a/SRC/ctpttf.f b/SRC/ctpttf.f index 96cff67a..7661f3a0 100644 --- a/SRC/ctpttf.f +++ b/SRC/ctpttf.f @@ -51,8 +51,8 @@ * = 0: successful exit * < 0: if INFO = -i, the i-th argument had an illegal value * -* Notes: -* ====== +* Further Details +* =============== * * We first consider Standard Packed Format when N is even. * We give an example where N = 6. diff --git a/SRC/ctrttf.f b/SRC/ctrttf.f index 3412536f..1c53ed80 100644 --- a/SRC/ctrttf.f +++ b/SRC/ctrttf.f @@ -56,8 +56,8 @@ * = 0: successful exit * < 0: if INFO = -i, the i-th argument had an illegal value * -* Notes -* ===== +* Further Details +* =============== * * We first consider Standard Packed Format when N is even. * We give an example where N = 6. diff --git a/SRC/dgesvj.f b/SRC/dgesvj.f index 22538fe4..b583dfee 100644 --- a/SRC/dgesvj.f +++ b/SRC/dgesvj.f @@ -1,5 +1,5 @@ - SUBROUTINE DGESVJ( JOBA, JOBU, JOBV, M, N, A, LDA, SVA, - & MV, V, LDV, WORK, LWORK, INFO ) + SUBROUTINE DGESVJ( JOBA, JOBU, JOBV, M, N, A, LDA, SVA, MV, V, + + LDV, WORK, LWORK, INFO ) * * -- LAPACK routine (version 3.2) -- * @@ -15,19 +15,20 @@ * computation of SVD, PSVD, QSVD, (H,K)-SVD, and for solution of the * eigenvalue problems Hx = lambda M x, H M x = lambda x with H, M > 0. * -* -#- Scalar Arguments -#- -* - IMPLICIT NONE - INTEGER INFO, LDA, LDV, LWORK, M, MV, N - CHARACTER*1 JOBA, JOBU, JOBV -* -* -#- Array Arguments -#- -* - DOUBLE PRECISION A( LDA, * ), SVA( N ), V( LDV, * ), WORK( LWORK ) + IMPLICIT NONE +* .. +* .. Scalar Arguments .. + INTEGER INFO, LDA, LDV, LWORK, M, MV, N + CHARACTER*1 JOBA, JOBU, JOBV +* .. +* .. Array Arguments .. + DOUBLE PRECISION A( LDA, * ), SVA( N ), V( LDV, * ), + + WORK( LWORK ) * .. * * Purpose -* ~~~~~~~ +* ======= +* * DGESVJ computes the singular value decomposition (SVD) of a real * M-by-N matrix A, where M >= N. The SVD of A is written as * [++] [xx] [x0] [xx] @@ -90,7 +91,7 @@ * drmac@math.hr. Thank you. * * Arguments -* ~~~~~~~~~ +* ========= * * JOBA (input) CHARACTER* 1 * Specifies the structure of A. @@ -101,7 +102,6 @@ * JOBU (input) CHARACTER*1 * Specifies whether to compute the left singular vectors * (columns of U): -* * = 'U': The left singular vectors corresponding to the nonzero * singular values are computed and returned in the leading * columns of A. See more details in the description of A. @@ -141,11 +141,9 @@ * * A (input/output) REAL array, dimension (LDA,N) * On entry, the M-by-N matrix A. -* On exit, -* If JOBU .EQ. 'U' .OR. JOBU .EQ. 'C': -* ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ -* If INFO .EQ. 0, -* ~~~~~~~~~~~~~~~ +* On exit : +* If JOBU .EQ. 'U' .OR. JOBU .EQ. 'C' : +* If INFO .EQ. 0 : * RANKA orthonormal columns of U are returned in the * leading RANKA columns of the array A. Here RANKA <= N * is the number of computed singular values of A that are @@ -157,8 +155,7 @@ * are mutually numerically orthogonal up to approximately * TOL=DSQRT(M)*EPS (default); or TOL=CTOL*EPS (JOBU.EQ.'C'), * see the description of JOBU. -* If INFO .GT. 0, -* ~~~~~~~~~~~~~~~ +* If INFO .GT. 0 : * the procedure DGESVJ did not converge in the given number * of iterations (sweeps). In that case, the computed * columns of U may not be orthogonal up to TOL. The output @@ -167,10 +164,8 @@ * input matrix A in the sense that the residual * ||A-SCALE*U*SIGMA*V^T||_2 / ||A||_2 is small. * -* If JOBU .EQ. 'N': -* ~~~~~~~~~~~~~~~~~ -* If INFO .EQ. 0 -* ~~~~~~~~~~~~~~ +* If JOBU .EQ. 'N' : +* If INFO .EQ. 0 : * Note that the left singular vectors are 'for free' in the * one-sided Jacobi SVD algorithm. However, if only the * singular values are needed, the level of numerical @@ -179,8 +174,7 @@ * numerically orthogonal up to approximately M*EPS. Thus, * on exit, A contains the columns of U scaled with the * corresponding singular values. -* If INFO .GT. 0, -* ~~~~~~~~~~~~~~~ +* If INFO .GT. 0 : * the procedure DGESVJ did not converge in the given number * of iterations (sweeps). * @@ -188,23 +182,18 @@ * The leading dimension of the array A. LDA >= max(1,M). * * SVA (workspace/output) REAL array, dimension (N) -* On exit, -* If INFO .EQ. 0, -* ~~~~~~~~~~~~~~~ +* On exit : +* If INFO .EQ. 0 : * depending on the value SCALE = WORK(1), we have: -* If SCALE .EQ. ONE: -* ~~~~~~~~~~~~~~~~~~ +* If SCALE .EQ. ONE : * SVA(1:N) contains the computed singular values of A. * During the computation SVA contains the Euclidean column * norms of the iterated matrices in the array A. -* If SCALE .NE. ONE: -* ~~~~~~~~~~~~~~~~~~ +* If SCALE .NE. ONE : * The singular values of A are SCALE*SVA(1:N), and this * factored representation is due to the fact that some of the * singular values of A might underflow or overflow. -* -* If INFO .GT. 0, -* ~~~~~~~~~~~~~~~ +* If INFO .GT. 0 : * the procedure DGESVJ did not converge in the given number of * iterations (sweeps) and SCALE*SVA(1:N) may not be accurate. * @@ -226,18 +215,17 @@ * If JOBV .EQ. 'A', then LDV .GE. max(1,MV) . * * WORK (input/workspace/output) REAL array, dimension max(4,M+N). -* On entry, -* If JOBU .EQ. 'C', -* ~~~~~~~~~~~~~~~~~ +* On entry : +* If JOBU .EQ. 'C' : * WORK(1) = CTOL, where CTOL defines the threshold for convergence. * The process stops if all columns of A are mutually * orthogonal up to CTOL*EPS, EPS=DLAMCH('E'). * It is required that CTOL >= ONE, i.e. it is not * allowed to force the routine to obtain orthogonality * below EPSILON. -* On exit, +* On exit : * WORK(1) = SCALE is the scaling factor such that SCALE*SVA(1:N) -* are the computed singular vcalues of A. +* are the computed singular values of A. * (See description of SVA().) * WORK(2) = NINT(WORK(2)) is the number of the computed nonzero * singular values. @@ -262,54 +250,57 @@ * of sweeps. The output may still be useful. See the * description of WORK. * -* Local Parameters -* - DOUBLE PRECISION ZERO, HALF, ONE, TWO - PARAMETER ( ZERO = 0.0D0, HALF = 0.5D0, ONE = 1.0D0, TWO = 2.0D0 ) - INTEGER NSWEEP - PARAMETER ( NSWEEP = 30 ) -* -* Local Scalars +* ===================================================================== * - DOUBLE PRECISION AAPP, AAPP0, AAPQ, AAQQ, APOAQ, AQOAP, - & BIG, BIGTHETA, CS, CTOL, EPSILON, LARGE, - & MXAAPQ, MXSINJ, ROOTBIG, ROOTEPS, ROOTSFMIN, ROOTTOL, - & SCALE, SFMIN, SMALL, SN, T, TEMP1, - & THETA, THSIGN, TOL - INTEGER BLSKIP, EMPTSW, i, ibr, IERR, igl, - & IJBLSK, ir1, ISWROT, jbc, jgl, KBL, - & LKAHEAD, MVL, N2, N34, N4, NBL, - & NOTROT, p, PSKIPPED, q, ROWSKIP, SWBAND - LOGICAL APPLV, GOSCALE, LOWER, LSVEC, NOSCALE, ROTOK, - & RSVEC, UCTOL, UPPER -* -* Local Arrays -* - DOUBLE PRECISION FASTR(5) -* -* Intrinsic Functions -* - INTRINSIC DABS, DMAX1, DMIN1, DBLE, MIN0, DSIGN, DSQRT -* -* External Functions -* .. from BLAS - DOUBLE PRECISION DDOT, DNRM2 - EXTERNAL DDOT, DNRM2 - INTEGER IDAMAX - EXTERNAL IDAMAX -* .. from LAPACK - DOUBLE PRECISION DLAMCH - EXTERNAL DLAMCH - LOGICAL LSAME - EXTERNAL LSAME -* -* External Subroutines -* .. from BLAS - EXTERNAL DAXPY, DCOPY, DROTM, DSCAL, DSWAP -* .. from LAPACK - EXTERNAL DLASCL, DLASET, DLASSQ, XERBLA +* .. Local Parameters .. + DOUBLE PRECISION ZERO, HALF, ONE, TWO + PARAMETER ( ZERO = 0.0D0, HALF = 0.5D0, ONE = 1.0D0, + + TWO = 2.0D0 ) + INTEGER NSWEEP + PARAMETER ( NSWEEP = 30 ) +* .. +* .. Local Scalars .. + DOUBLE PRECISION AAPP, AAPP0, AAPQ, AAQQ, APOAQ, AQOAP, BIG, + + BIGTHETA, CS, CTOL, EPSILON, LARGE, MXAAPQ, + + MXSINJ, ROOTBIG, ROOTEPS, ROOTSFMIN, ROOTTOL, + + SCALE, SFMIN, SMALL, SN, T, TEMP1, THETA, + + THSIGN, TOL + INTEGER BLSKIP, EMPTSW, i, ibr, IERR, igl, IJBLSK, ir1, + + ISWROT, jbc, jgl, KBL, LKAHEAD, MVL, N2, N34, + + N4, NBL, NOTROT, p, PSKIPPED, q, ROWSKIP, + + SWBAND + LOGICAL APPLV, GOSCALE, LOWER, LSVEC, NOSCALE, ROTOK, + + RSVEC, UCTOL, UPPER +* .. +* .. Local Arrays .. + DOUBLE PRECISION FASTR( 5 ) +* .. +* .. Intrinsic Functions .. + INTRINSIC DABS, DMAX1, DMIN1, DBLE, MIN0, DSIGN, DSQRT +* .. +* .. External Functions .. +* .. +* from BLAS + DOUBLE PRECISION DDOT, DNRM2 + EXTERNAL DDOT, DNRM2 + INTEGER IDAMAX + EXTERNAL IDAMAX +* from LAPACK + DOUBLE PRECISION DLAMCH + EXTERNAL DLAMCH + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. External Subroutines .. +* .. +* from BLAS + EXTERNAL DAXPY, DCOPY, DROTM, DSCAL, DSWAP +* from LAPACK + EXTERNAL DLASCL, DLASET, DLASSQ, XERBLA * - EXTERNAL DGSVJ0, DGSVJ1 + EXTERNAL DGSVJ0, DGSVJ1 +* .. +* .. Executable Statements .. * * Test the input arguments * @@ -320,40 +311,40 @@ UPPER = LSAME( JOBA, 'U' ) LOWER = LSAME( JOBA, 'L' ) * - IF ( .NOT.( UPPER .OR. LOWER .OR. LSAME(JOBA,'G') ) ) THEN - INFO = - 1 - ELSE IF ( .NOT.( LSVEC .OR. UCTOL .OR. LSAME(JOBU,'N') ) ) THEN - INFO = - 2 - ELSE IF ( .NOT.( RSVEC .OR. APPLV .OR. LSAME(JOBV,'N') ) ) THEN - INFO = - 3 - ELSE IF ( M .LT. 0 ) THEN - INFO = - 4 - ELSE IF ( ( N .LT. 0 ) .OR. ( N .GT. M ) ) THEN - INFO = - 5 - ELSE IF ( LDA .LT. M ) THEN - INFO = - 7 - ELSE IF ( MV .LT. 0 ) THEN - INFO = - 9 - ELSE IF ( ( RSVEC .AND. (LDV .LT. N ) ) .OR. - & ( APPLV .AND. (LDV .LT. MV) ) ) THEN + IF( .NOT.( UPPER .OR. LOWER .OR. LSAME( JOBA, 'G' ) ) ) THEN + INFO = -1 + ELSE IF( .NOT.( LSVEC .OR. UCTOL .OR. LSAME( JOBU, 'N' ) ) ) THEN + INFO = -2 + ELSE IF( .NOT.( RSVEC .OR. APPLV .OR. LSAME( JOBV, 'N' ) ) ) THEN + INFO = -3 + ELSE IF( M.LT.0 ) THEN + INFO = -4 + ELSE IF( ( N.LT.0 ) .OR. ( N.GT.M ) ) THEN + INFO = -5 + ELSE IF( LDA.LT.M ) THEN + INFO = -7 + ELSE IF( MV.LT.0 ) THEN + INFO = -9 + ELSE IF( ( RSVEC .AND. ( LDV.LT.N ) ) .OR. + + ( APPLV .AND. ( LDV.LT.MV ) ) ) THEN INFO = -11 - ELSE IF ( UCTOL .AND. (WORK(1) .LE. ONE) ) THEN - INFO = - 12 - ELSE IF ( LWORK .LT. MAX0( M + N , 6 ) ) THEN - INFO = - 13 + ELSE IF( UCTOL .AND. ( WORK( 1 ).LE.ONE ) ) THEN + INFO = -12 + ELSE IF( LWORK.LT.MAX0( M+N, 6 ) ) THEN + INFO = -13 ELSE - INFO = 0 + INFO = 0 END IF * * #:( - IF ( INFO .NE. 0 ) THEN + IF( INFO.NE.0 ) THEN CALL XERBLA( 'DGESVJ', -INFO ) RETURN END IF * * #:) Quick return for void matrix * - IF ( ( M .EQ. 0 ) .OR. ( N .EQ. 0 ) ) RETURN + IF( ( M.EQ.0 ) .OR. ( N.EQ.0 ) )RETURN * * Set numerical parameters * The stopping criterion for Jacobi rotations is @@ -362,46 +353,46 @@ * * where EPS is the round-off and CTOL is defined as follows: * - IF ( UCTOL ) THEN + IF( UCTOL ) THEN * ... user controlled - CTOL = WORK(1) + CTOL = WORK( 1 ) ELSE * ... default - IF ( LSVEC .OR. RSVEC .OR. APPLV ) THEN - CTOL = DSQRT(DBLE(M)) + IF( LSVEC .OR. RSVEC .OR. APPLV ) THEN + CTOL = DSQRT( DBLE( M ) ) ELSE - CTOL = DBLE(M) + CTOL = DBLE( M ) END IF END IF * ... and the machine dependent parameters are *[!] (Make sure that DLAMCH() works properly on the target machine.) * - EPSILON = DLAMCH('Epsilon') - ROOTEPS = DSQRT(EPSILON) - SFMIN = DLAMCH('SafeMinimum') - ROOTSFMIN = DSQRT(SFMIN) - SMALL = SFMIN / EPSILON - BIG = DLAMCH('Overflow') + EPSILON = DLAMCH( 'Epsilon' ) + ROOTEPS = DSQRT( EPSILON ) + SFMIN = DLAMCH( 'SafeMinimum' ) + ROOTSFMIN = DSQRT( SFMIN ) + SMALL = SFMIN / EPSILON + BIG = DLAMCH( 'Overflow' ) * BIG = ONE / SFMIN - ROOTBIG = ONE / ROOTSFMIN - LARGE = BIG / DSQRT(DBLE(M*N)) - BIGTHETA = ONE / ROOTEPS + ROOTBIG = ONE / ROOTSFMIN + LARGE = BIG / DSQRT( DBLE( M*N ) ) + BIGTHETA = ONE / ROOTEPS * - TOL = CTOL * EPSILON - ROOTTOL = DSQRT(TOL) + TOL = CTOL*EPSILON + ROOTTOL = DSQRT( TOL ) * - IF ( DBLE(M)*EPSILON .GE. ONE ) THEN - INFO = - 5 + IF( DBLE( M )*EPSILON.GE.ONE ) THEN + INFO = -5 CALL XERBLA( 'DGESVJ', -INFO ) RETURN END IF * * Initialize the right singular vector matrix. * - IF ( RSVEC ) THEN + IF( RSVEC ) THEN MVL = N CALL DLASET( 'A', MVL, N, ZERO, ONE, V, LDV ) - ELSE IF ( APPLV ) THEN + ELSE IF( APPLV ) THEN MVL = MV END IF RSVEC = RSVEC .OR. APPLV @@ -415,56 +406,56 @@ * DSQRT(N)*max_i SVA(i) does not overflow. If INFinite entries * in A are detected, the procedure returns with INFO=-6. * - SCALE = ONE / DSQRT(DBLE(M)*DBLE(N)) - NOSCALE = .TRUE. - GOSCALE = .TRUE. + SCALE = ONE / DSQRT( DBLE( M )*DBLE( N ) ) + NOSCALE = .TRUE. + GOSCALE = .TRUE. * - IF ( LOWER ) THEN + IF( LOWER ) THEN * the input matrix is M-by-N lower triangular (trapezoidal) DO 1874 p = 1, N AAPP = ZERO AAQQ = ZERO - CALL DLASSQ( M-p+1, A(p,p), 1, AAPP, AAQQ ) - IF ( AAPP .GT. BIG ) THEN - INFO = - 6 + CALL DLASSQ( M-p+1, A( p, p ), 1, AAPP, AAQQ ) + IF( AAPP.GT.BIG ) THEN + INFO = -6 CALL XERBLA( 'DGESVJ', -INFO ) RETURN END IF - AAQQ = DSQRT(AAQQ) - IF ( ( AAPP .LT. (BIG / AAQQ) ) .AND. NOSCALE ) THEN - SVA(p) = AAPP * AAQQ + AAQQ = DSQRT( AAQQ ) + IF( ( AAPP.LT.( BIG / AAQQ ) ) .AND. NOSCALE ) THEN + SVA( p ) = AAPP*AAQQ ELSE NOSCALE = .FALSE. - SVA(p) = AAPP * ( AAQQ * SCALE ) - IF ( GOSCALE ) THEN + SVA( p ) = AAPP*( AAQQ*SCALE ) + IF( GOSCALE ) THEN GOSCALE = .FALSE. DO 1873 q = 1, p - 1 - SVA(q) = SVA(q)*SCALE + SVA( q ) = SVA( q )*SCALE 1873 CONTINUE END IF END IF 1874 CONTINUE - ELSE IF ( UPPER ) THEN + ELSE IF( UPPER ) THEN * the input matrix is M-by-N upper triangular (trapezoidal) DO 2874 p = 1, N AAPP = ZERO AAQQ = ZERO - CALL DLASSQ( p, A(1,p), 1, AAPP, AAQQ ) - IF ( AAPP .GT. BIG ) THEN - INFO = - 6 + CALL DLASSQ( p, A( 1, p ), 1, AAPP, AAQQ ) + IF( AAPP.GT.BIG ) THEN + INFO = -6 CALL XERBLA( 'DGESVJ', -INFO ) RETURN END IF - AAQQ = DSQRT(AAQQ) - IF ( ( AAPP .LT. (BIG / AAQQ) ) .AND. NOSCALE ) THEN - SVA(p) = AAPP * AAQQ + AAQQ = DSQRT( AAQQ ) + IF( ( AAPP.LT.( BIG / AAQQ ) ) .AND. NOSCALE ) THEN + SVA( p ) = AAPP*AAQQ ELSE NOSCALE = .FALSE. - SVA(p) = AAPP * ( AAQQ * SCALE ) - IF ( GOSCALE ) THEN + SVA( p ) = AAPP*( AAQQ*SCALE ) + IF( GOSCALE ) THEN GOSCALE = .FALSE. DO 2873 q = 1, p - 1 - SVA(q) = SVA(q)*SCALE + SVA( q ) = SVA( q )*SCALE 2873 CONTINUE END IF END IF @@ -474,29 +465,29 @@ DO 3874 p = 1, N AAPP = ZERO AAQQ = ZERO - CALL DLASSQ( M, A(1,p), 1, AAPP, AAQQ ) - IF ( AAPP .GT. BIG ) THEN - INFO = - 6 + CALL DLASSQ( M, A( 1, p ), 1, AAPP, AAQQ ) + IF( AAPP.GT.BIG ) THEN + INFO = -6 CALL XERBLA( 'DGESVJ', -INFO ) RETURN END IF - AAQQ = DSQRT(AAQQ) - IF ( ( AAPP .LT. (BIG / AAQQ) ) .AND. NOSCALE ) THEN - SVA(p) = AAPP * AAQQ + AAQQ = DSQRT( AAQQ ) + IF( ( AAPP.LT.( BIG / AAQQ ) ) .AND. NOSCALE ) THEN + SVA( p ) = AAPP*AAQQ ELSE NOSCALE = .FALSE. - SVA(p) = AAPP * ( AAQQ * SCALE ) - IF ( GOSCALE ) THEN + SVA( p ) = AAPP*( AAQQ*SCALE ) + IF( GOSCALE ) THEN GOSCALE = .FALSE. DO 3873 q = 1, p - 1 - SVA(q) = SVA(q)*SCALE + SVA( q ) = SVA( q )*SCALE 3873 CONTINUE END IF END IF 3874 CONTINUE END IF * - IF ( NOSCALE ) SCALE = ONE + IF( NOSCALE )SCALE = ONE * * Move the smaller part of the spectrum from the underflow threshold *(!) Start by determining the position of the nonzero entries of the @@ -505,61 +496,61 @@ AAPP = ZERO AAQQ = BIG DO 4781 p = 1, N - IF ( SVA(p) .NE. ZERO ) AAQQ = DMIN1( AAQQ, SVA(p) ) - AAPP = DMAX1( AAPP, SVA(p) ) + IF( SVA( p ).NE.ZERO )AAQQ = DMIN1( AAQQ, SVA( p ) ) + AAPP = DMAX1( AAPP, SVA( p ) ) 4781 CONTINUE * * #:) Quick return for zero matrix * - IF ( AAPP .EQ. ZERO ) THEN - IF ( LSVEC ) CALL DLASET( 'G', M, N, ZERO, ONE, A, LDA ) - WORK(1) = ONE - WORK(2) = ZERO - WORK(3) = ZERO - WORK(4) = ZERO - WORK(5) = ZERO - WORK(6) = ZERO + IF( AAPP.EQ.ZERO ) THEN + IF( LSVEC )CALL DLASET( 'G', M, N, ZERO, ONE, A, LDA ) + WORK( 1 ) = ONE + WORK( 2 ) = ZERO + WORK( 3 ) = ZERO + WORK( 4 ) = ZERO + WORK( 5 ) = ZERO + WORK( 6 ) = ZERO RETURN END IF * * #:) Quick return for one-column matrix * - IF ( N .EQ. 1 ) THEN - IF ( LSVEC ) - & CALL DLASCL( 'G',0,0,SVA(1),SCALE,M,1,A(1,1),LDA,IERR ) - WORK(1) = ONE / SCALE - IF ( SVA(1) .GE. SFMIN ) THEN - WORK(2) = ONE + IF( N.EQ.1 ) THEN + IF( LSVEC )CALL DLASCL( 'G', 0, 0, SVA( 1 ), SCALE, M, 1, + + A( 1, 1 ), LDA, IERR ) + WORK( 1 ) = ONE / SCALE + IF( SVA( 1 ).GE.SFMIN ) THEN + WORK( 2 ) = ONE ELSE - WORK(2) = ZERO + WORK( 2 ) = ZERO END IF - WORK(3) = ZERO - WORK(4) = ZERO - WORK(5) = ZERO - WORK(6) = ZERO + WORK( 3 ) = ZERO + WORK( 4 ) = ZERO + WORK( 5 ) = ZERO + WORK( 6 ) = ZERO RETURN END IF * * Protect small singular values from underflow, and try to * avoid underflows/overflows in computing Jacobi rotations. * - SN = DSQRT( SFMIN / EPSILON ) - TEMP1 = DSQRT( BIG / DBLE(N) ) - IF ( (AAPP.LE.SN).OR.(AAQQ.GE.TEMP1) - & .OR.((SN.LE.AAQQ).AND.(AAPP.LE.TEMP1)) ) THEN - TEMP1 = DMIN1(BIG,TEMP1/AAPP) + SN = DSQRT( SFMIN / EPSILON ) + TEMP1 = DSQRT( BIG / DBLE( N ) ) + IF( ( AAPP.LE.SN ) .OR. ( AAQQ.GE.TEMP1 ) .OR. + + ( ( SN.LE.AAQQ ) .AND. ( AAPP.LE.TEMP1 ) ) ) THEN + TEMP1 = DMIN1( BIG, TEMP1 / AAPP ) * AAQQ = AAQQ*TEMP1 * AAPP = AAPP*TEMP1 - ELSE IF ( (AAQQ.LE.SN).AND.(AAPP.LE.TEMP1) ) THEN - TEMP1 = DMIN1( SN / AAQQ, BIG/(AAPP*DSQRT(DBLE(N))) ) + ELSE IF( ( AAQQ.LE.SN ) .AND. ( AAPP.LE.TEMP1 ) ) THEN + TEMP1 = DMIN1( SN / AAQQ, BIG / ( AAPP*DSQRT( DBLE( N ) ) ) ) * AAQQ = AAQQ*TEMP1 * AAPP = AAPP*TEMP1 - ELSE IF ( (AAQQ.GE.SN).AND.(AAPP.GE.TEMP1) ) THEN + ELSE IF( ( AAQQ.GE.SN ) .AND. ( AAPP.GE.TEMP1 ) ) THEN TEMP1 = DMAX1( SN / AAQQ, TEMP1 / AAPP ) * AAQQ = AAQQ*TEMP1 * AAPP = AAPP*TEMP1 - ELSE IF ( (AAQQ.LE.SN).AND.(AAPP.GE.TEMP1) ) THEN - TEMP1 = DMIN1( SN / AAQQ, BIG / (DSQRT(DBLE(N))*AAPP)) + ELSE IF( ( AAQQ.LE.SN ) .AND. ( AAPP.GE.TEMP1 ) ) THEN + TEMP1 = DMIN1( SN / AAQQ, BIG / ( DSQRT( DBLE( N ) )*AAPP ) ) * AAQQ = AAQQ*TEMP1 * AAPP = AAPP*TEMP1 ELSE @@ -568,27 +559,27 @@ * * Scale, if necessary * - IF ( TEMP1 .NE. ONE ) THEN + IF( TEMP1.NE.ONE ) THEN CALL DLASCL( 'G', 0, 0, ONE, TEMP1, N, 1, SVA, N, IERR ) END IF - SCALE = TEMP1 * SCALE - IF ( SCALE .NE. ONE ) THEN + SCALE = TEMP1*SCALE + IF( SCALE.NE.ONE ) THEN CALL DLASCL( JOBA, 0, 0, ONE, SCALE, M, N, A, LDA, IERR ) SCALE = ONE / SCALE END IF * * Row-cyclic Jacobi SVD algorithm with column pivoting * - EMPTSW = ( N * ( N - 1 ) ) / 2 - NOTROT = 0 - FASTR(1) = ZERO + EMPTSW = ( N*( N-1 ) ) / 2 + NOTROT = 0 + FASTR( 1 ) = ZERO * * A is represented in factored form A = A * diag(WORK), where diag(WORK) * is initialized to identity. WORK is updated during fast scaled * rotations. * DO 1868 q = 1, N - WORK(q) = ONE + WORK( q ) = ONE 1868 CONTINUE * * @@ -607,7 +598,7 @@ * parameters of the computer's memory. * NBL = N / KBL - IF ( ( NBL * KBL ) .NE. N ) NBL = NBL + 1 + IF( ( NBL*KBL ).NE.N )NBL = NBL + 1 * BLSKIP = KBL**2 *[TP] BLKSKIP is a tuning parameter that depends on SWBAND and KBL. @@ -623,19 +614,19 @@ * invokes cubic convergence. Big part of this cycle is done inside * canonical subspaces of dimensions less than M. * - IF ( (LOWER .OR. UPPER) .AND. (N .GT. MAX0(64, 4*KBL)) ) THEN + IF( ( LOWER .OR. UPPER ) .AND. ( N.GT.MAX0( 64, 4*KBL ) ) ) THEN *[TP] The number of partition levels and the actual partition are * tuning parameters. - N4 = N / 4 - N2 = N / 2 - N34 = 3 * N4 - IF ( APPLV ) THEN - q = 0 - ELSE - q = 1 - END IF + N4 = N / 4 + N2 = N / 2 + N34 = 3*N4 + IF( APPLV ) THEN + q = 0 + ELSE + q = 1 + END IF * - IF ( LOWER ) THEN + IF( LOWER ) THEN * * This works very well on lower triangular matrices, in particular * in the framework of the preconditioned Jacobi SVD (xGEJSV). @@ -645,93 +636,104 @@ * [+ + x 0] actually work on [x 0] [x 0] * [+ + x x] [x x]. [x x] * - CALL DGSVJ0(JOBV,M-N34,N-N34,A(N34+1,N34+1),LDA,WORK(N34+1), - & SVA(N34+1),MVL,V(N34*q+1,N34+1),LDV,EPSILON,SFMIN,TOL,2, - & WORK(N+1),LWORK-N,IERR ) + CALL DGSVJ0( JOBV, M-N34, N-N34, A( N34+1, N34+1 ), LDA, + + WORK( N34+1 ), SVA( N34+1 ), MVL, + + V( N34*q+1, N34+1 ), LDV, EPSILON, SFMIN, TOL, + + 2, WORK( N+1 ), LWORK-N, IERR ) * - CALL DGSVJ0( JOBV,M-N2,N34-N2,A(N2+1,N2+1),LDA,WORK(N2+1), - & SVA(N2+1),MVL,V(N2*q+1,N2+1),LDV,EPSILON,SFMIN,TOL,2, - & WORK(N+1),LWORK-N,IERR ) + CALL DGSVJ0( JOBV, M-N2, N34-N2, A( N2+1, N2+1 ), LDA, + + WORK( N2+1 ), SVA( N2+1 ), MVL, + + V( N2*q+1, N2+1 ), LDV, EPSILON, SFMIN, TOL, 2, + + WORK( N+1 ), LWORK-N, IERR ) * - CALL DGSVJ1( JOBV,M-N2,N-N2,N4,A(N2+1,N2+1),LDA,WORK(N2+1), - & SVA(N2+1),MVL,V(N2*q+1,N2+1),LDV,EPSILON,SFMIN,TOL,1, - & WORK(N+1),LWORK-N,IERR ) + CALL DGSVJ1( JOBV, M-N2, N-N2, N4, A( N2+1, N2+1 ), LDA, + + WORK( N2+1 ), SVA( N2+1 ), MVL, + + V( N2*q+1, N2+1 ), LDV, EPSILON, SFMIN, TOL, 1, + + WORK( N+1 ), LWORK-N, IERR ) * - CALL DGSVJ0( JOBV,M-N4,N2-N4,A(N4+1,N4+1),LDA,WORK(N4+1), - & SVA(N4+1),MVL,V(N4*q+1,N4+1),LDV,EPSILON,SFMIN,TOL,1, - & WORK(N+1),LWORK-N,IERR ) + CALL DGSVJ0( JOBV, M-N4, N2-N4, A( N4+1, N4+1 ), LDA, + + WORK( N4+1 ), SVA( N4+1 ), MVL, + + V( N4*q+1, N4+1 ), LDV, EPSILON, SFMIN, TOL, 1, + + WORK( N+1 ), LWORK-N, IERR ) * - CALL DGSVJ0( JOBV,M,N4,A,LDA,WORK,SVA,MVL,V,LDV,EPSILON, - & SFMIN,TOL,1,WORK(N+1),LWORK-N,IERR ) + CALL DGSVJ0( JOBV, M, N4, A, LDA, WORK, SVA, MVL, V, LDV, + + EPSILON, SFMIN, TOL, 1, WORK( N+1 ), LWORK-N, + + IERR ) * - CALL DGSVJ1( JOBV,M,N2,N4,A,LDA,WORK,SVA,MVL,V,LDV,EPSILON, - & SFMIN,TOL,1,WORK(N+1),LWORK-N,IERR ) + CALL DGSVJ1( JOBV, M, N2, N4, A, LDA, WORK, SVA, MVL, V, + + LDV, EPSILON, SFMIN, TOL, 1, WORK( N+1 ), + + LWORK-N, IERR ) * * - ELSE IF ( UPPER ) THEN + ELSE IF( UPPER ) THEN * * - CALL DGSVJ0( JOBV,N4,N4,A,LDA,WORK,SVA,MVL,V,LDV,EPSILON, - & SFMIN,TOL,2,WORK(N+1),LWORK-N,IERR ) + CALL DGSVJ0( JOBV, N4, N4, A, LDA, WORK, SVA, MVL, V, LDV, + + EPSILON, SFMIN, TOL, 2, WORK( N+1 ), LWORK-N, + + IERR ) * - CALL DGSVJ0(JOBV,N2,N4,A(1,N4+1),LDA,WORK(N4+1),SVA(N4+1),MVL, - & V(N4*q+1,N4+1),LDV,EPSILON,SFMIN,TOL,1,WORK(N+1),LWORK-N, - & IERR ) + CALL DGSVJ0( JOBV, N2, N4, A( 1, N4+1 ), LDA, WORK( N4+1 ), + + SVA( N4+1 ), MVL, V( N4*q+1, N4+1 ), LDV, + + EPSILON, SFMIN, TOL, 1, WORK( N+1 ), LWORK-N, + + IERR ) * - CALL DGSVJ1( JOBV,N2,N2,N4,A,LDA,WORK,SVA,MVL,V,LDV,EPSILON, - & SFMIN,TOL,1,WORK(N+1),LWORK-N,IERR ) + CALL DGSVJ1( JOBV, N2, N2, N4, A, LDA, WORK, SVA, MVL, V, + + LDV, EPSILON, SFMIN, TOL, 1, WORK( N+1 ), + + LWORK-N, IERR ) * - CALL DGSVJ0( JOBV,N2+N4,N4,A(1,N2+1),LDA,WORK(N2+1),SVA(N2+1),MVL, - & V(N2*q+1,N2+1),LDV,EPSILON,SFMIN,TOL,1, - & WORK(N+1),LWORK-N,IERR ) + CALL DGSVJ0( JOBV, N2+N4, N4, A( 1, N2+1 ), LDA, + + WORK( N2+1 ), SVA( N2+1 ), MVL, + + V( N2*q+1, N2+1 ), LDV, EPSILON, SFMIN, TOL, 1, + + WORK( N+1 ), LWORK-N, IERR ) - END IF + END IF * END IF * -* -#- Row-cyclic pivot strategy with de Rijk's pivoting -#- +* .. Row-cyclic pivot strategy with de Rijk's pivoting .. * DO 1993 i = 1, NSWEEP * * .. go go go ... * - MXAAPQ = ZERO - MXSINJ = ZERO - ISWROT = 0 + MXAAPQ = ZERO + MXSINJ = ZERO + ISWROT = 0 * - NOTROT = 0 - PSKIPPED = 0 + NOTROT = 0 + PSKIPPED = 0 * * Each sweep is unrolled using KBL-by-KBL tiles over the pivot pairs * 1 <= p < q <= N. This is the first step toward a blocked implementation * of the rotations. New implementation, based on block transformations, * is under development. * - DO 2000 ibr = 1, NBL + DO 2000 ibr = 1, NBL * - igl = ( ibr - 1 ) * KBL + 1 + igl = ( ibr-1 )*KBL + 1 * - DO 1002 ir1 = 0, MIN0( LKAHEAD, NBL - ibr ) + DO 1002 ir1 = 0, MIN0( LKAHEAD, NBL-ibr ) * - igl = igl + ir1 * KBL + igl = igl + ir1*KBL * - DO 2001 p = igl, MIN0( igl + KBL - 1, N - 1) + DO 2001 p = igl, MIN0( igl+KBL-1, N-1 ) * * .. de Rijk's pivoting * - q = IDAMAX( N-p+1, SVA(p), 1 ) + p - 1 - IF ( p .NE. q ) THEN - CALL DSWAP( M, A(1,p), 1, A(1,q), 1 ) - IF ( RSVEC ) CALL DSWAP( MVL, V(1,p), 1, V(1,q), 1 ) - TEMP1 = SVA(p) - SVA(p) = SVA(q) - SVA(q) = TEMP1 - TEMP1 = WORK(p) - WORK(p) = WORK(q) - WORK(q) = TEMP1 - END IF -* - IF ( ir1 .EQ. 0 ) THEN + q = IDAMAX( N-p+1, SVA( p ), 1 ) + p - 1 + IF( p.NE.q ) THEN + CALL DSWAP( M, A( 1, p ), 1, A( 1, q ), 1 ) + IF( RSVEC )CALL DSWAP( MVL, V( 1, p ), 1, + + V( 1, q ), 1 ) + TEMP1 = SVA( p ) + SVA( p ) = SVA( q ) + SVA( q ) = TEMP1 + TEMP1 = WORK( p ) + WORK( p ) = WORK( q ) + WORK( q ) = TEMP1 + END IF +* + IF( ir1.EQ.0 ) THEN * * Column norms are periodically updated by explicit * norm computation. @@ -745,506 +747,669 @@ * If properly implemented DNRM2 is available, the IF-THEN-ELSE * below should read "AAPP = DNRM2( M, A(1,p), 1 ) * WORK(p)". * - IF ((SVA(p) .LT. ROOTBIG) .AND. (SVA(p) .GT. ROOTSFMIN)) THEN - SVA(p) = DNRM2( M, A(1,p), 1 ) * WORK(p) - ELSE - TEMP1 = ZERO - AAPP = ZERO - CALL DLASSQ( M, A(1,p), 1, TEMP1, AAPP ) - SVA(p) = TEMP1 * DSQRT(AAPP) * WORK(p) - END IF - AAPP = SVA(p) - ELSE - AAPP = SVA(p) - END IF -* - IF ( AAPP .GT. ZERO ) THEN -* - PSKIPPED = 0 -* - DO 2002 q = p + 1, MIN0( igl + KBL - 1, N ) -* - AAQQ = SVA(q) -* - IF ( AAQQ .GT. ZERO ) THEN -* - AAPP0 = AAPP - IF ( AAQQ .GE. ONE ) THEN - ROTOK = ( SMALL*AAPP ) .LE. AAQQ - IF ( AAPP .LT. ( BIG / AAQQ ) ) THEN - AAPQ = ( DDOT(M, A(1,p), 1, A(1,q), 1 ) * - & WORK(p) * WORK(q) / AAQQ ) / AAPP - ELSE - CALL DCOPY( M, A(1,p), 1, WORK(N+1), 1 ) - CALL DLASCL( 'G', 0, 0, AAPP, WORK(p), M, - & 1, WORK(N+1), LDA, IERR ) - AAPQ = DDOT( M, WORK(N+1),1, A(1,q),1 )*WORK(q) / AAQQ - END IF - ELSE - ROTOK = AAPP .LE. ( AAQQ / SMALL ) - IF ( AAPP .GT. ( SMALL / AAQQ ) ) THEN - AAPQ = ( DDOT( M, A(1,p), 1, A(1,q), 1 ) * - & WORK(p) * WORK(q) / AAQQ ) / AAPP - ELSE - CALL DCOPY( M, A(1,q), 1, WORK(N+1), 1 ) - CALL DLASCL( 'G', 0, 0, AAQQ, WORK(q), M, - & 1, WORK(N+1), LDA, IERR ) - AAPQ = DDOT( M, WORK(N+1),1, A(1,p),1 )*WORK(p) / AAPP - END IF - END IF + IF( ( SVA( p ).LT.ROOTBIG ) .AND. + + ( SVA( p ).GT.ROOTSFMIN ) ) THEN + SVA( p ) = DNRM2( M, A( 1, p ), 1 )*WORK( p ) + ELSE + TEMP1 = ZERO + AAPP = ZERO + CALL DLASSQ( M, A( 1, p ), 1, TEMP1, AAPP ) + SVA( p ) = TEMP1*DSQRT( AAPP )*WORK( p ) + END IF + AAPP = SVA( p ) + ELSE + AAPP = SVA( p ) + END IF +* + IF( AAPP.GT.ZERO ) THEN +* + PSKIPPED = 0 +* + DO 2002 q = p + 1, MIN0( igl+KBL-1, N ) +* + AAQQ = SVA( q ) +* + IF( AAQQ.GT.ZERO ) THEN +* + AAPP0 = AAPP + IF( AAQQ.GE.ONE ) THEN + ROTOK = ( SMALL*AAPP ).LE.AAQQ + IF( AAPP.LT.( BIG / AAQQ ) ) THEN + AAPQ = ( DDOT( M, A( 1, p ), 1, A( 1, + + q ), 1 )*WORK( p )*WORK( q ) / + + AAQQ ) / AAPP + ELSE + CALL DCOPY( M, A( 1, p ), 1, + + WORK( N+1 ), 1 ) + CALL DLASCL( 'G', 0, 0, AAPP, + + WORK( p ), M, 1, + + WORK( N+1 ), LDA, IERR ) + AAPQ = DDOT( M, WORK( N+1 ), 1, + + A( 1, q ), 1 )*WORK( q ) / AAQQ + END IF + ELSE + ROTOK = AAPP.LE.( AAQQ / SMALL ) + IF( AAPP.GT.( SMALL / AAQQ ) ) THEN + AAPQ = ( DDOT( M, A( 1, p ), 1, A( 1, + + q ), 1 )*WORK( p )*WORK( q ) / + + AAQQ ) / AAPP + ELSE + CALL DCOPY( M, A( 1, q ), 1, + + WORK( N+1 ), 1 ) + CALL DLASCL( 'G', 0, 0, AAQQ, + + WORK( q ), M, 1, + + WORK( N+1 ), LDA, IERR ) + AAPQ = DDOT( M, WORK( N+1 ), 1, + + A( 1, p ), 1 )*WORK( p ) / AAPP + END IF + END IF * - MXAAPQ = DMAX1( MXAAPQ, DABS(AAPQ) ) + MXAAPQ = DMAX1( MXAAPQ, DABS( AAPQ ) ) * * TO rotate or NOT to rotate, THAT is the question ... * - IF ( DABS( AAPQ ) .GT. TOL ) THEN + IF( DABS( AAPQ ).GT.TOL ) THEN * * .. rotate *[RTD] ROTATED = ROTATED + ONE * - IF ( ir1 .EQ. 0 ) THEN - NOTROT = 0 - PSKIPPED = 0 - ISWROT = ISWROT + 1 - END IF -* - IF ( ROTOK ) THEN -* - AQOAP = AAQQ / AAPP - APOAQ = AAPP / AAQQ - THETA = - HALF * DABS( AQOAP - APOAQ ) / AAPQ -* - IF ( DABS( THETA ) .GT. BIGTHETA ) THEN -* - T = HALF / THETA - FASTR(3) = T * WORK(p) / WORK(q) - FASTR(4) = - T * WORK(q) / WORK(p) - CALL DROTM( M, A(1,p), 1, A(1,q), 1, FASTR ) - IF ( RSVEC ) - & CALL DROTM( MVL, V(1,p), 1, V(1,q), 1, FASTR ) - SVA(q) = AAQQ*DSQRT( DMAX1(ZERO,ONE + T*APOAQ*AAPQ) ) - AAPP = AAPP*DSQRT( ONE - T*AQOAP*AAPQ ) - MXSINJ = DMAX1( MXSINJ, DABS(T) ) -* - ELSE + IF( ir1.EQ.0 ) THEN + NOTROT = 0 + PSKIPPED = 0 + ISWROT = ISWROT + 1 + END IF +* + IF( ROTOK ) THEN +* + AQOAP = AAQQ / AAPP + APOAQ = AAPP / AAQQ + THETA = -HALF*DABS( AQOAP-APOAQ ) / + + AAPQ +* + IF( DABS( THETA ).GT.BIGTHETA ) THEN +* + T = HALF / THETA + FASTR( 3 ) = T*WORK( p ) / WORK( q ) + FASTR( 4 ) = -T*WORK( q ) / + + WORK( p ) + CALL DROTM( M, A( 1, p ), 1, + + A( 1, q ), 1, FASTR ) + IF( RSVEC )CALL DROTM( MVL, + + V( 1, p ), 1, + + V( 1, q ), 1, + + FASTR ) + SVA( q ) = AAQQ*DSQRT( DMAX1( ZERO, + + ONE+T*APOAQ*AAPQ ) ) + AAPP = AAPP*DSQRT( ONE-T*AQOAP* + + AAPQ ) + MXSINJ = DMAX1( MXSINJ, DABS( T ) ) +* + ELSE * * .. choose correct signum for THETA and rotate * - THSIGN = - DSIGN(ONE,AAPQ) - T = ONE / ( THETA + THSIGN*DSQRT(ONE+THETA*THETA) ) - CS = DSQRT( ONE / ( ONE + T*T ) ) - SN = T * CS -* - MXSINJ = DMAX1( MXSINJ, DABS(SN) ) - SVA(q) = AAQQ*DSQRT( DMAX1(ZERO, ONE+T*APOAQ*AAPQ) ) - AAPP = AAPP*DSQRT( DMAX1(ZERO, ONE-T*AQOAP*AAPQ) ) -* - APOAQ = WORK(p) / WORK(q) - AQOAP = WORK(q) / WORK(p) - IF ( WORK(p) .GE. ONE ) THEN - IF ( WORK(q) .GE. ONE ) THEN - FASTR(3) = T * APOAQ - FASTR(4) = - T * AQOAP - WORK(p) = WORK(p) * CS - WORK(q) = WORK(q) * CS - CALL DROTM( M, A(1,p),1, A(1,q),1, FASTR ) - IF ( RSVEC ) - & CALL DROTM( MVL, V(1,p),1, V(1,q),1, FASTR ) - ELSE - CALL DAXPY( M, -T*AQOAP, A(1,q),1, A(1,p),1 ) - CALL DAXPY( M, CS*SN*APOAQ, A(1,p),1, A(1,q),1 ) - WORK(p) = WORK(p) * CS - WORK(q) = WORK(q) / CS - IF ( RSVEC ) THEN - CALL DAXPY(MVL, -T*AQOAP, V(1,q),1,V(1,p),1) - CALL DAXPY(MVL,CS*SN*APOAQ, V(1,p),1,V(1,q),1) - END IF - END IF - ELSE - IF ( WORK(q) .GE. ONE ) THEN - CALL DAXPY( M, T*APOAQ, A(1,p),1, A(1,q),1 ) - CALL DAXPY( M,-CS*SN*AQOAP, A(1,q),1, A(1,p),1 ) - WORK(p) = WORK(p) / CS - WORK(q) = WORK(q) * CS - IF ( RSVEC ) THEN - CALL DAXPY(MVL, T*APOAQ, V(1,p),1,V(1,q),1) - CALL DAXPY(MVL,-CS*SN*AQOAP,V(1,q),1,V(1,p),1) - END IF - ELSE - IF ( WORK(p) .GE. WORK(q) ) THEN - CALL DAXPY( M,-T*AQOAP, A(1,q),1,A(1,p),1 ) - CALL DAXPY( M,CS*SN*APOAQ,A(1,p),1,A(1,q),1 ) - WORK(p) = WORK(p) * CS - WORK(q) = WORK(q) / CS - IF ( RSVEC ) THEN - CALL DAXPY(MVL, -T*AQOAP, V(1,q),1,V(1,p),1) - CALL DAXPY(MVL,CS*SN*APOAQ,V(1,p),1,V(1,q),1) - END IF - ELSE - CALL DAXPY( M, T*APOAQ, A(1,p),1,A(1,q),1) - CALL DAXPY( M,-CS*SN*AQOAP,A(1,q),1,A(1,p),1) - WORK(p) = WORK(p) / CS - WORK(q) = WORK(q) * CS - IF ( RSVEC ) THEN - CALL DAXPY(MVL, T*APOAQ, V(1,p),1,V(1,q),1) - CALL DAXPY(MVL,-CS*SN*AQOAP,V(1,q),1,V(1,p),1) - END IF - END IF - END IF - ENDIF - END IF -* - ELSE + THSIGN = -DSIGN( ONE, AAPQ ) + T = ONE / ( THETA+THSIGN* + + DSQRT( ONE+THETA*THETA ) ) + CS = DSQRT( ONE / ( ONE+T*T ) ) + SN = T*CS +* + MXSINJ = DMAX1( MXSINJ, DABS( SN ) ) + SVA( q ) = AAQQ*DSQRT( DMAX1( ZERO, + + ONE+T*APOAQ*AAPQ ) ) + AAPP = AAPP*DSQRT( DMAX1( ZERO, + + ONE-T*AQOAP*AAPQ ) ) +* + APOAQ = WORK( p ) / WORK( q ) + AQOAP = WORK( q ) / WORK( p ) + IF( WORK( p ).GE.ONE ) THEN + IF( WORK( q ).GE.ONE ) THEN + FASTR( 3 ) = T*APOAQ + FASTR( 4 ) = -T*AQOAP + WORK( p ) = WORK( p )*CS + WORK( q ) = WORK( q )*CS + CALL DROTM( M, A( 1, p ), 1, + + A( 1, q ), 1, + + FASTR ) + IF( RSVEC )CALL DROTM( MVL, + + V( 1, p ), 1, V( 1, q ), + + 1, FASTR ) + ELSE + CALL DAXPY( M, -T*AQOAP, + + A( 1, q ), 1, + + A( 1, p ), 1 ) + CALL DAXPY( M, CS*SN*APOAQ, + + A( 1, p ), 1, + + A( 1, q ), 1 ) + WORK( p ) = WORK( p )*CS + WORK( q ) = WORK( q ) / CS + IF( RSVEC ) THEN + CALL DAXPY( MVL, -T*AQOAP, + + V( 1, q ), 1, + + V( 1, p ), 1 ) + CALL DAXPY( MVL, + + CS*SN*APOAQ, + + V( 1, p ), 1, + + V( 1, q ), 1 ) + END IF + END IF + ELSE + IF( WORK( q ).GE.ONE ) THEN + CALL DAXPY( M, T*APOAQ, + + A( 1, p ), 1, + + A( 1, q ), 1 ) + CALL DAXPY( M, -CS*SN*AQOAP, + + A( 1, q ), 1, + + A( 1, p ), 1 ) + WORK( p ) = WORK( p ) / CS + WORK( q ) = WORK( q )*CS + IF( RSVEC ) THEN + CALL DAXPY( MVL, T*APOAQ, + + V( 1, p ), 1, + + V( 1, q ), 1 ) + CALL DAXPY( MVL, + + -CS*SN*AQOAP, + + V( 1, q ), 1, + + V( 1, p ), 1 ) + END IF + ELSE + IF( WORK( p ).GE.WORK( q ) ) + + THEN + CALL DAXPY( M, -T*AQOAP, + + A( 1, q ), 1, + + A( 1, p ), 1 ) + CALL DAXPY( M, CS*SN*APOAQ, + + A( 1, p ), 1, + + A( 1, q ), 1 ) + WORK( p ) = WORK( p )*CS + WORK( q ) = WORK( q ) / CS + IF( RSVEC ) THEN + CALL DAXPY( MVL, + + -T*AQOAP, + + V( 1, q ), 1, + + V( 1, p ), 1 ) + CALL DAXPY( MVL, + + CS*SN*APOAQ, + + V( 1, p ), 1, + + V( 1, q ), 1 ) + END IF + ELSE + CALL DAXPY( M, T*APOAQ, + + A( 1, p ), 1, + + A( 1, q ), 1 ) + CALL DAXPY( M, + + -CS*SN*AQOAP, + + A( 1, q ), 1, + + A( 1, p ), 1 ) + WORK( p ) = WORK( p ) / CS + WORK( q ) = WORK( q )*CS + IF( RSVEC ) THEN + CALL DAXPY( MVL, + + T*APOAQ, V( 1, p ), + + 1, V( 1, q ), 1 ) + CALL DAXPY( MVL, + + -CS*SN*AQOAP, + + V( 1, q ), 1, + + V( 1, p ), 1 ) + END IF + END IF + END IF + END IF + END IF +* + ELSE * .. have to use modified Gram-Schmidt like transformation - CALL DCOPY( M, A(1,p), 1, WORK(N+1), 1 ) - CALL DLASCL( 'G',0,0,AAPP,ONE,M,1,WORK(N+1),LDA,IERR ) - CALL DLASCL( 'G',0,0,AAQQ,ONE,M,1, A(1,q),LDA,IERR ) - TEMP1 = -AAPQ * WORK(p) / WORK(q) - CALL DAXPY ( M, TEMP1, WORK(N+1), 1, A(1,q), 1 ) - CALL DLASCL( 'G',0,0,ONE,AAQQ,M,1, A(1,q),LDA,IERR ) - SVA(q) = AAQQ*DSQRT( DMAX1( ZERO, ONE - AAPQ*AAPQ ) ) - MXSINJ = DMAX1( MXSINJ, SFMIN ) - END IF + CALL DCOPY( M, A( 1, p ), 1, + + WORK( N+1 ), 1 ) + CALL DLASCL( 'G', 0, 0, AAPP, ONE, M, + + 1, WORK( N+1 ), LDA, + + IERR ) + CALL DLASCL( 'G', 0, 0, AAQQ, ONE, M, + + 1, A( 1, q ), LDA, IERR ) + TEMP1 = -AAPQ*WORK( p ) / WORK( q ) + CALL DAXPY( M, TEMP1, WORK( N+1 ), 1, + + A( 1, q ), 1 ) + CALL DLASCL( 'G', 0, 0, ONE, AAQQ, M, + + 1, A( 1, q ), LDA, IERR ) + SVA( q ) = AAQQ*DSQRT( DMAX1( ZERO, + + ONE-AAPQ*AAPQ ) ) + MXSINJ = DMAX1( MXSINJ, SFMIN ) + END IF * END IF ROTOK THEN ... ELSE * * In the case of cancellation in updating SVA(q), SVA(p) * recompute SVA(q), SVA(p). * - IF ( (SVA(q) / AAQQ )**2 .LE. ROOTEPS ) THEN - IF ((AAQQ .LT. ROOTBIG).AND.(AAQQ .GT. ROOTSFMIN)) THEN - SVA(q) = DNRM2( M, A(1,q), 1 ) * WORK(q) - ELSE - T = ZERO - AAQQ = ZERO - CALL DLASSQ( M, A(1,q), 1, T, AAQQ ) - SVA(q) = T * DSQRT(AAQQ) * WORK(q) - END IF - END IF - IF ( ( AAPP / AAPP0) .LE. ROOTEPS ) THEN - IF ((AAPP .LT. ROOTBIG).AND.(AAPP .GT. ROOTSFMIN)) THEN - AAPP = DNRM2( M, A(1,p), 1 ) * WORK(p) - ELSE - T = ZERO - AAPP = ZERO - CALL DLASSQ( M, A(1,p), 1, T, AAPP ) - AAPP = T * DSQRT(AAPP) * WORK(p) - END IF - SVA(p) = AAPP - END IF -* - ELSE + IF( ( SVA( q ) / AAQQ )**2.LE.ROOTEPS ) + + THEN + IF( ( AAQQ.LT.ROOTBIG ) .AND. + + ( AAQQ.GT.ROOTSFMIN ) ) THEN + SVA( q ) = DNRM2( M, A( 1, q ), 1 )* + + WORK( q ) + ELSE + T = ZERO + AAQQ = ZERO + CALL DLASSQ( M, A( 1, q ), 1, T, + + AAQQ ) + SVA( q ) = T*DSQRT( AAQQ )*WORK( q ) + END IF + END IF + IF( ( AAPP / AAPP0 ).LE.ROOTEPS ) THEN + IF( ( AAPP.LT.ROOTBIG ) .AND. + + ( AAPP.GT.ROOTSFMIN ) ) THEN + AAPP = DNRM2( M, A( 1, p ), 1 )* + + WORK( p ) + ELSE + T = ZERO + AAPP = ZERO + CALL DLASSQ( M, A( 1, p ), 1, T, + + AAPP ) + AAPP = T*DSQRT( AAPP )*WORK( p ) + END IF + SVA( p ) = AAPP + END IF +* + ELSE * A(:,p) and A(:,q) already numerically orthogonal - IF ( ir1 .EQ. 0 ) NOTROT = NOTROT + 1 + IF( ir1.EQ.0 )NOTROT = NOTROT + 1 *[RTD] SKIPPED = SKIPPED + 1 - PSKIPPED = PSKIPPED + 1 - END IF - ELSE + PSKIPPED = PSKIPPED + 1 + END IF + ELSE * A(:,q) is zero column - IF ( ir1. EQ. 0 ) NOTROT = NOTROT + 1 - PSKIPPED = PSKIPPED + 1 - END IF + IF( ir1.EQ.0 )NOTROT = NOTROT + 1 + PSKIPPED = PSKIPPED + 1 + END IF * - IF ( ( i .LE. SWBAND ) .AND. ( PSKIPPED .GT. ROWSKIP ) ) THEN - IF ( ir1 .EQ. 0 ) AAPP = - AAPP - NOTROT = 0 - GO TO 2103 - END IF + IF( ( i.LE.SWBAND ) .AND. + + ( PSKIPPED.GT.ROWSKIP ) ) THEN + IF( ir1.EQ.0 )AAPP = -AAPP + NOTROT = 0 + GO TO 2103 + END IF * - 2002 CONTINUE + 2002 CONTINUE * END q-LOOP * - 2103 CONTINUE + 2103 CONTINUE * bailed out of q-loop * - SVA(p) = AAPP + SVA( p ) = AAPP * - ELSE - SVA(p) = AAPP - IF ( ( ir1 .EQ. 0 ) .AND. (AAPP .EQ. ZERO) ) - & NOTROT=NOTROT+MIN0(igl+KBL-1,N)-p - END IF + ELSE + SVA( p ) = AAPP + IF( ( ir1.EQ.0 ) .AND. ( AAPP.EQ.ZERO ) ) + + NOTROT = NOTROT + MIN0( igl+KBL-1, N ) - p + END IF * - 2001 CONTINUE + 2001 CONTINUE * end of the p-loop * end of doing the block ( ibr, ibr ) - 1002 CONTINUE + 1002 CONTINUE * end of ir1-loop * * ... go to the off diagonal blocks * - igl = ( ibr - 1 ) * KBL + 1 + igl = ( ibr-1 )*KBL + 1 * - DO 2010 jbc = ibr + 1, NBL + DO 2010 jbc = ibr + 1, NBL * - jgl = ( jbc - 1 ) * KBL + 1 + jgl = ( jbc-1 )*KBL + 1 * * doing the block at ( ibr, jbc ) * - IJBLSK = 0 - DO 2100 p = igl, MIN0( igl + KBL - 1, N ) + IJBLSK = 0 + DO 2100 p = igl, MIN0( igl+KBL-1, N ) * - AAPP = SVA(p) - IF ( AAPP .GT. ZERO ) THEN + AAPP = SVA( p ) + IF( AAPP.GT.ZERO ) THEN * - PSKIPPED = 0 + PSKIPPED = 0 * - DO 2200 q = jgl, MIN0( jgl + KBL - 1, N ) + DO 2200 q = jgl, MIN0( jgl+KBL-1, N ) * - AAQQ = SVA(q) - IF ( AAQQ .GT. ZERO ) THEN - AAPP0 = AAPP + AAQQ = SVA( q ) + IF( AAQQ.GT.ZERO ) THEN + AAPP0 = AAPP * -* -#- M x 2 Jacobi SVD -#- +* .. M x 2 Jacobi SVD .. * * Safe Gram matrix computation * - IF ( AAQQ .GE. ONE ) THEN - IF ( AAPP .GE. AAQQ ) THEN - ROTOK = ( SMALL*AAPP ) .LE. AAQQ - ELSE - ROTOK = ( SMALL*AAQQ ) .LE. AAPP - END IF - IF ( AAPP .LT. ( BIG / AAQQ ) ) THEN - AAPQ = ( DDOT(M, A(1,p), 1, A(1,q), 1 ) * - & WORK(p) * WORK(q) / AAQQ ) / AAPP - ELSE - CALL DCOPY( M, A(1,p), 1, WORK(N+1), 1 ) - CALL DLASCL( 'G', 0, 0, AAPP, WORK(p), M, - & 1, WORK(N+1), LDA, IERR ) - AAPQ = DDOT( M, WORK(N+1), 1, A(1,q), 1 ) * - & WORK(q) / AAQQ - END IF - ELSE - IF ( AAPP .GE. AAQQ ) THEN - ROTOK = AAPP .LE. ( AAQQ / SMALL ) - ELSE - ROTOK = AAQQ .LE. ( AAPP / SMALL ) - END IF - IF ( AAPP .GT. ( SMALL / AAQQ ) ) THEN - AAPQ = ( DDOT( M, A(1,p), 1, A(1,q), 1 ) * - & WORK(p) * WORK(q) / AAQQ ) / AAPP - ELSE - CALL DCOPY( M, A(1,q), 1, WORK(N+1), 1 ) - CALL DLASCL( 'G', 0, 0, AAQQ, WORK(q), M, 1, - & WORK(N+1), LDA, IERR ) - AAPQ = DDOT(M,WORK(N+1),1,A(1,p),1) * WORK(p) / AAPP - END IF - END IF + IF( AAQQ.GE.ONE ) THEN + IF( AAPP.GE.AAQQ ) THEN + ROTOK = ( SMALL*AAPP ).LE.AAQQ + ELSE + ROTOK = ( SMALL*AAQQ ).LE.AAPP + END IF + IF( AAPP.LT.( BIG / AAQQ ) ) THEN + AAPQ = ( DDOT( M, A( 1, p ), 1, A( 1, + + q ), 1 )*WORK( p )*WORK( q ) / + + AAQQ ) / AAPP + ELSE + CALL DCOPY( M, A( 1, p ), 1, + + WORK( N+1 ), 1 ) + CALL DLASCL( 'G', 0, 0, AAPP, + + WORK( p ), M, 1, + + WORK( N+1 ), LDA, IERR ) + AAPQ = DDOT( M, WORK( N+1 ), 1, + + A( 1, q ), 1 )*WORK( q ) / AAQQ + END IF + ELSE + IF( AAPP.GE.AAQQ ) THEN + ROTOK = AAPP.LE.( AAQQ / SMALL ) + ELSE + ROTOK = AAQQ.LE.( AAPP / SMALL ) + END IF + IF( AAPP.GT.( SMALL / AAQQ ) ) THEN + AAPQ = ( DDOT( M, A( 1, p ), 1, A( 1, + + q ), 1 )*WORK( p )*WORK( q ) / + + AAQQ ) / AAPP + ELSE + CALL DCOPY( M, A( 1, q ), 1, + + WORK( N+1 ), 1 ) + CALL DLASCL( 'G', 0, 0, AAQQ, + + WORK( q ), M, 1, + + WORK( N+1 ), LDA, IERR ) + AAPQ = DDOT( M, WORK( N+1 ), 1, + + A( 1, p ), 1 )*WORK( p ) / AAPP + END IF + END IF * - MXAAPQ = DMAX1( MXAAPQ, DABS(AAPQ) ) + MXAAPQ = DMAX1( MXAAPQ, DABS( AAPQ ) ) * * TO rotate or NOT to rotate, THAT is the question ... * - IF ( DABS( AAPQ ) .GT. TOL ) THEN - NOTROT = 0 + IF( DABS( AAPQ ).GT.TOL ) THEN + NOTROT = 0 *[RTD] ROTATED = ROTATED + 1 - PSKIPPED = 0 - ISWROT = ISWROT + 1 -* - IF ( ROTOK ) THEN -* - AQOAP = AAQQ / AAPP - APOAQ = AAPP / AAQQ - THETA = - HALF * DABS( AQOAP - APOAQ ) / AAPQ - IF ( AAQQ .GT. AAPP0 ) THETA = - THETA -* - IF ( DABS( THETA ) .GT. BIGTHETA ) THEN - T = HALF / THETA - FASTR(3) = T * WORK(p) / WORK(q) - FASTR(4) = -T * WORK(q) / WORK(p) - CALL DROTM( M, A(1,p), 1, A(1,q), 1, FASTR ) - IF ( RSVEC ) - & CALL DROTM( MVL, V(1,p), 1, V(1,q), 1, FASTR ) - SVA(q) = AAQQ*DSQRT( DMAX1(ZERO,ONE + T*APOAQ*AAPQ) ) - AAPP = AAPP*DSQRT( DMAX1(ZERO,ONE - T*AQOAP*AAPQ) ) - MXSINJ = DMAX1( MXSINJ, DABS(T) ) - ELSE + PSKIPPED = 0 + ISWROT = ISWROT + 1 +* + IF( ROTOK ) THEN +* + AQOAP = AAQQ / AAPP + APOAQ = AAPP / AAQQ + THETA = -HALF*DABS( AQOAP-APOAQ ) / + + AAPQ + IF( AAQQ.GT.AAPP0 )THETA = -THETA +* + IF( DABS( THETA ).GT.BIGTHETA ) THEN + T = HALF / THETA + FASTR( 3 ) = T*WORK( p ) / WORK( q ) + FASTR( 4 ) = -T*WORK( q ) / + + WORK( p ) + CALL DROTM( M, A( 1, p ), 1, + + A( 1, q ), 1, FASTR ) + IF( RSVEC )CALL DROTM( MVL, + + V( 1, p ), 1, + + V( 1, q ), 1, + + FASTR ) + SVA( q ) = AAQQ*DSQRT( DMAX1( ZERO, + + ONE+T*APOAQ*AAPQ ) ) + AAPP = AAPP*DSQRT( DMAX1( ZERO, + + ONE-T*AQOAP*AAPQ ) ) + MXSINJ = DMAX1( MXSINJ, DABS( T ) ) + ELSE * * .. choose correct signum for THETA and rotate * - THSIGN = - DSIGN(ONE,AAPQ) - IF ( AAQQ .GT. AAPP0 ) THSIGN = - THSIGN - T = ONE / ( THETA + THSIGN*DSQRT(ONE+THETA*THETA) ) - CS = DSQRT( ONE / ( ONE + T*T ) ) - SN = T * CS - MXSINJ = DMAX1( MXSINJ, DABS(SN) ) - SVA(q) = AAQQ*DSQRT( DMAX1(ZERO, ONE+T*APOAQ*AAPQ) ) - AAPP = AAPP*DSQRT( ONE - T*AQOAP*AAPQ) -* - APOAQ = WORK(p) / WORK(q) - AQOAP = WORK(q) / WORK(p) - IF ( WORK(p) .GE. ONE ) THEN -* - IF ( WORK(q) .GE. ONE ) THEN - FASTR(3) = T * APOAQ - FASTR(4) = - T * AQOAP - WORK(p) = WORK(p) * CS - WORK(q) = WORK(q) * CS - CALL DROTM( M, A(1,p),1, A(1,q),1, FASTR ) - IF ( RSVEC ) - & CALL DROTM( MVL, V(1,p),1, V(1,q),1, FASTR ) - ELSE - CALL DAXPY( M, -T*AQOAP, A(1,q),1, A(1,p),1 ) - CALL DAXPY( M, CS*SN*APOAQ, A(1,p),1, A(1,q),1 ) - IF ( RSVEC ) THEN - CALL DAXPY( MVL, -T*AQOAP, V(1,q),1, V(1,p),1 ) - CALL DAXPY( MVL,CS*SN*APOAQ,V(1,p),1, V(1,q),1 ) - END IF - WORK(p) = WORK(p) * CS - WORK(q) = WORK(q) / CS - END IF - ELSE - IF ( WORK(q) .GE. ONE ) THEN - CALL DAXPY( M, T*APOAQ, A(1,p),1, A(1,q),1 ) - CALL DAXPY( M,-CS*SN*AQOAP, A(1,q),1, A(1,p),1 ) - IF ( RSVEC ) THEN - CALL DAXPY(MVL,T*APOAQ, V(1,p),1, V(1,q),1 ) - CALL DAXPY(MVL,-CS*SN*AQOAP,V(1,q),1, V(1,p),1 ) - END IF - WORK(p) = WORK(p) / CS - WORK(q) = WORK(q) * CS - ELSE - IF ( WORK(p) .GE. WORK(q) ) THEN - CALL DAXPY( M,-T*AQOAP, A(1,q),1,A(1,p),1 ) - CALL DAXPY( M,CS*SN*APOAQ,A(1,p),1,A(1,q),1 ) - WORK(p) = WORK(p) * CS - WORK(q) = WORK(q) / CS - IF ( RSVEC ) THEN - CALL DAXPY( MVL, -T*AQOAP, V(1,q),1,V(1,p),1) - CALL DAXPY(MVL,CS*SN*APOAQ,V(1,p),1,V(1,q),1) - END IF - ELSE - CALL DAXPY(M, T*APOAQ, A(1,p),1,A(1,q),1) - CALL DAXPY(M,-CS*SN*AQOAP,A(1,q),1,A(1,p),1) - WORK(p) = WORK(p) / CS - WORK(q) = WORK(q) * CS - IF ( RSVEC ) THEN - CALL DAXPY(MVL, T*APOAQ, V(1,p),1,V(1,q),1) - CALL DAXPY(MVL,-CS*SN*AQOAP,V(1,q),1,V(1,p),1) - END IF - END IF - END IF - ENDIF - END IF -* - ELSE - IF ( AAPP .GT. AAQQ ) THEN - CALL DCOPY( M, A(1,p), 1, WORK(N+1), 1 ) - CALL DLASCL('G',0,0,AAPP,ONE,M,1,WORK(N+1),LDA,IERR) - CALL DLASCL('G',0,0,AAQQ,ONE,M,1, A(1,q),LDA,IERR) - TEMP1 = -AAPQ * WORK(p) / WORK(q) - CALL DAXPY(M,TEMP1,WORK(N+1),1,A(1,q),1) - CALL DLASCL('G',0,0,ONE,AAQQ,M,1,A(1,q),LDA,IERR) - SVA(q) = AAQQ*DSQRT(DMAX1(ZERO, ONE - AAPQ*AAPQ)) - MXSINJ = DMAX1( MXSINJ, SFMIN ) - ELSE - CALL DCOPY( M, A(1,q), 1, WORK(N+1), 1 ) - CALL DLASCL('G',0,0,AAQQ,ONE,M,1,WORK(N+1),LDA,IERR) - CALL DLASCL('G',0,0,AAPP,ONE,M,1, A(1,p),LDA,IERR) - TEMP1 = -AAPQ * WORK(q) / WORK(p) - CALL DAXPY(M,TEMP1,WORK(N+1),1,A(1,p),1) - CALL DLASCL('G',0,0,ONE,AAPP,M,1,A(1,p),LDA,IERR) - SVA(p) = AAPP*DSQRT(DMAX1(ZERO, ONE - AAPQ*AAPQ)) - MXSINJ = DMAX1( MXSINJ, SFMIN ) - END IF - END IF + THSIGN = -DSIGN( ONE, AAPQ ) + IF( AAQQ.GT.AAPP0 )THSIGN = -THSIGN + T = ONE / ( THETA+THSIGN* + + DSQRT( ONE+THETA*THETA ) ) + CS = DSQRT( ONE / ( ONE+T*T ) ) + SN = T*CS + MXSINJ = DMAX1( MXSINJ, DABS( SN ) ) + SVA( q ) = AAQQ*DSQRT( DMAX1( ZERO, + + ONE+T*APOAQ*AAPQ ) ) + AAPP = AAPP*DSQRT( ONE-T*AQOAP* + + AAPQ ) +* + APOAQ = WORK( p ) / WORK( q ) + AQOAP = WORK( q ) / WORK( p ) + IF( WORK( p ).GE.ONE ) THEN +* + IF( WORK( q ).GE.ONE ) THEN + FASTR( 3 ) = T*APOAQ + FASTR( 4 ) = -T*AQOAP + WORK( p ) = WORK( p )*CS + WORK( q ) = WORK( q )*CS + CALL DROTM( M, A( 1, p ), 1, + + A( 1, q ), 1, + + FASTR ) + IF( RSVEC )CALL DROTM( MVL, + + V( 1, p ), 1, V( 1, q ), + + 1, FASTR ) + ELSE + CALL DAXPY( M, -T*AQOAP, + + A( 1, q ), 1, + + A( 1, p ), 1 ) + CALL DAXPY( M, CS*SN*APOAQ, + + A( 1, p ), 1, + + A( 1, q ), 1 ) + IF( RSVEC ) THEN + CALL DAXPY( MVL, -T*AQOAP, + + V( 1, q ), 1, + + V( 1, p ), 1 ) + CALL DAXPY( MVL, + + CS*SN*APOAQ, + + V( 1, p ), 1, + + V( 1, q ), 1 ) + END IF + WORK( p ) = WORK( p )*CS + WORK( q ) = WORK( q ) / CS + END IF + ELSE + IF( WORK( q ).GE.ONE ) THEN + CALL DAXPY( M, T*APOAQ, + + A( 1, p ), 1, + + A( 1, q ), 1 ) + CALL DAXPY( M, -CS*SN*AQOAP, + + A( 1, q ), 1, + + A( 1, p ), 1 ) + IF( RSVEC ) THEN + CALL DAXPY( MVL, T*APOAQ, + + V( 1, p ), 1, + + V( 1, q ), 1 ) + CALL DAXPY( MVL, + + -CS*SN*AQOAP, + + V( 1, q ), 1, + + V( 1, p ), 1 ) + END IF + WORK( p ) = WORK( p ) / CS + WORK( q ) = WORK( q )*CS + ELSE + IF( WORK( p ).GE.WORK( q ) ) + + THEN + CALL DAXPY( M, -T*AQOAP, + + A( 1, q ), 1, + + A( 1, p ), 1 ) + CALL DAXPY( M, CS*SN*APOAQ, + + A( 1, p ), 1, + + A( 1, q ), 1 ) + WORK( p ) = WORK( p )*CS + WORK( q ) = WORK( q ) / CS + IF( RSVEC ) THEN + CALL DAXPY( MVL, + + -T*AQOAP, + + V( 1, q ), 1, + + V( 1, p ), 1 ) + CALL DAXPY( MVL, + + CS*SN*APOAQ, + + V( 1, p ), 1, + + V( 1, q ), 1 ) + END IF + ELSE + CALL DAXPY( M, T*APOAQ, + + A( 1, p ), 1, + + A( 1, q ), 1 ) + CALL DAXPY( M, + + -CS*SN*AQOAP, + + A( 1, q ), 1, + + A( 1, p ), 1 ) + WORK( p ) = WORK( p ) / CS + WORK( q ) = WORK( q )*CS + IF( RSVEC ) THEN + CALL DAXPY( MVL, + + T*APOAQ, V( 1, p ), + + 1, V( 1, q ), 1 ) + CALL DAXPY( MVL, + + -CS*SN*AQOAP, + + V( 1, q ), 1, + + V( 1, p ), 1 ) + END IF + END IF + END IF + END IF + END IF +* + ELSE + IF( AAPP.GT.AAQQ ) THEN + CALL DCOPY( M, A( 1, p ), 1, + + WORK( N+1 ), 1 ) + CALL DLASCL( 'G', 0, 0, AAPP, ONE, + + M, 1, WORK( N+1 ), LDA, + + IERR ) + CALL DLASCL( 'G', 0, 0, AAQQ, ONE, + + M, 1, A( 1, q ), LDA, + + IERR ) + TEMP1 = -AAPQ*WORK( p ) / WORK( q ) + CALL DAXPY( M, TEMP1, WORK( N+1 ), + + 1, A( 1, q ), 1 ) + CALL DLASCL( 'G', 0, 0, ONE, AAQQ, + + M, 1, A( 1, q ), LDA, + + IERR ) + SVA( q ) = AAQQ*DSQRT( DMAX1( ZERO, + + ONE-AAPQ*AAPQ ) ) + MXSINJ = DMAX1( MXSINJ, SFMIN ) + ELSE + CALL DCOPY( M, A( 1, q ), 1, + + WORK( N+1 ), 1 ) + CALL DLASCL( 'G', 0, 0, AAQQ, ONE, + + M, 1, WORK( N+1 ), LDA, + + IERR ) + CALL DLASCL( 'G', 0, 0, AAPP, ONE, + + M, 1, A( 1, p ), LDA, + + IERR ) + TEMP1 = -AAPQ*WORK( q ) / WORK( p ) + CALL DAXPY( M, TEMP1, WORK( N+1 ), + + 1, A( 1, p ), 1 ) + CALL DLASCL( 'G', 0, 0, ONE, AAPP, + + M, 1, A( 1, p ), LDA, + + IERR ) + SVA( p ) = AAPP*DSQRT( DMAX1( ZERO, + + ONE-AAPQ*AAPQ ) ) + MXSINJ = DMAX1( MXSINJ, SFMIN ) + END IF + END IF * END IF ROTOK THEN ... ELSE * * In the case of cancellation in updating SVA(q) * .. recompute SVA(q) - IF ( (SVA(q) / AAQQ )**2 .LE. ROOTEPS ) THEN - IF ((AAQQ .LT. ROOTBIG).AND.(AAQQ .GT. ROOTSFMIN)) THEN - SVA(q) = DNRM2( M, A(1,q), 1 ) * WORK(q) - ELSE - T = ZERO - AAQQ = ZERO - CALL DLASSQ( M, A(1,q), 1, T, AAQQ ) - SVA(q) = T * DSQRT(AAQQ) * WORK(q) - END IF - END IF - IF ( (AAPP / AAPP0 )**2 .LE. ROOTEPS ) THEN - IF ((AAPP .LT. ROOTBIG).AND.(AAPP .GT. ROOTSFMIN)) THEN - AAPP = DNRM2( M, A(1,p), 1 ) * WORK(p) - ELSE - T = ZERO - AAPP = ZERO - CALL DLASSQ( M, A(1,p), 1, T, AAPP ) - AAPP = T * DSQRT(AAPP) * WORK(p) - END IF - SVA(p) = AAPP - END IF + IF( ( SVA( q ) / AAQQ )**2.LE.ROOTEPS ) + + THEN + IF( ( AAQQ.LT.ROOTBIG ) .AND. + + ( AAQQ.GT.ROOTSFMIN ) ) THEN + SVA( q ) = DNRM2( M, A( 1, q ), 1 )* + + WORK( q ) + ELSE + T = ZERO + AAQQ = ZERO + CALL DLASSQ( M, A( 1, q ), 1, T, + + AAQQ ) + SVA( q ) = T*DSQRT( AAQQ )*WORK( q ) + END IF + END IF + IF( ( AAPP / AAPP0 )**2.LE.ROOTEPS ) THEN + IF( ( AAPP.LT.ROOTBIG ) .AND. + + ( AAPP.GT.ROOTSFMIN ) ) THEN + AAPP = DNRM2( M, A( 1, p ), 1 )* + + WORK( p ) + ELSE + T = ZERO + AAPP = ZERO + CALL DLASSQ( M, A( 1, p ), 1, T, + + AAPP ) + AAPP = T*DSQRT( AAPP )*WORK( p ) + END IF + SVA( p ) = AAPP + END IF * end of OK rotation - ELSE - NOTROT = NOTROT + 1 + ELSE + NOTROT = NOTROT + 1 *[RTD] SKIPPED = SKIPPED + 1 - PSKIPPED = PSKIPPED + 1 - IJBLSK = IJBLSK + 1 - END IF - ELSE - NOTROT = NOTROT + 1 - PSKIPPED = PSKIPPED + 1 - IJBLSK = IJBLSK + 1 - END IF + PSKIPPED = PSKIPPED + 1 + IJBLSK = IJBLSK + 1 + END IF + ELSE + NOTROT = NOTROT + 1 + PSKIPPED = PSKIPPED + 1 + IJBLSK = IJBLSK + 1 + END IF * - IF ( ( i .LE. SWBAND ) .AND. ( IJBLSK .GE. BLSKIP ) ) THEN - SVA(p) = AAPP - NOTROT = 0 - GO TO 2011 - END IF - IF ( ( i .LE. SWBAND ) .AND. ( PSKIPPED .GT. ROWSKIP ) ) THEN - AAPP = -AAPP - NOTROT = 0 - GO TO 2203 - END IF + IF( ( i.LE.SWBAND ) .AND. ( IJBLSK.GE.BLSKIP ) ) + + THEN + SVA( p ) = AAPP + NOTROT = 0 + GO TO 2011 + END IF + IF( ( i.LE.SWBAND ) .AND. + + ( PSKIPPED.GT.ROWSKIP ) ) THEN + AAPP = -AAPP + NOTROT = 0 + GO TO 2203 + END IF * - 2200 CONTINUE + 2200 CONTINUE * end of the q-loop - 2203 CONTINUE + 2203 CONTINUE * - SVA(p) = AAPP + SVA( p ) = AAPP * - ELSE + ELSE * - IF ( AAPP .EQ. ZERO ) NOTROT=NOTROT+MIN0(jgl+KBL-1,N)-jgl+1 - IF ( AAPP .LT. ZERO ) NOTROT = 0 + IF( AAPP.EQ.ZERO )NOTROT = NOTROT + + + MIN0( jgl+KBL-1, N ) - jgl + 1 + IF( AAPP.LT.ZERO )NOTROT = 0 * - END IF + END IF * - 2100 CONTINUE + 2100 CONTINUE * end of the p-loop - 2010 CONTINUE + 2010 CONTINUE * end of the jbc-loop - 2011 CONTINUE + 2011 CONTINUE *2011 bailed out of the jbc-loop - DO 2012 p = igl, MIN0( igl + KBL - 1, N ) - SVA(p) = DABS(SVA(p)) - 2012 CONTINUE + DO 2012 p = igl, MIN0( igl+KBL-1, N ) + SVA( p ) = DABS( SVA( p ) ) + 2012 CONTINUE *** - 2000 CONTINUE + 2000 CONTINUE *2000 :: end of the ibr-loop * * .. update SVA(N) - IF ((SVA(N) .LT. ROOTBIG).AND.(SVA(N) .GT. ROOTSFMIN)) THEN - SVA(N) = DNRM2( M, A(1,N), 1 ) * WORK(N) - ELSE - T = ZERO - AAPP = ZERO - CALL DLASSQ( M, A(1,N), 1, T, AAPP ) - SVA(N) = T * DSQRT(AAPP) * WORK(N) - END IF + IF( ( SVA( N ).LT.ROOTBIG ) .AND. ( SVA( N ).GT.ROOTSFMIN ) ) + + THEN + SVA( N ) = DNRM2( M, A( 1, N ), 1 )*WORK( N ) + ELSE + T = ZERO + AAPP = ZERO + CALL DLASSQ( M, A( 1, N ), 1, T, AAPP ) + SVA( N ) = T*DSQRT( AAPP )*WORK( N ) + END IF * * Additional steering devices * - IF ( ( i.LT.SWBAND ) .AND. ( ( MXAAPQ.LE.ROOTTOL ) .OR. - & ( ISWROT .LE. N ) ) ) - & SWBAND = i + IF( ( i.LT.SWBAND ) .AND. ( ( MXAAPQ.LE.ROOTTOL ) .OR. + + ( ISWROT.LE.N ) ) )SWBAND = i * - IF ( (i .GT. SWBAND+1) .AND. (MXAAPQ .LT. DSQRT(DBLE(N))*TOL) - & .AND. (DBLE(N)*MXAAPQ*MXSINJ .LT. TOL) ) THEN - GO TO 1994 - END IF + IF( ( i.GT.SWBAND+1 ) .AND. ( MXAAPQ.LT.DSQRT( DBLE( N ) )* + + TOL ) .AND. ( DBLE( N )*MXAAPQ*MXSINJ.LT.TOL ) ) THEN + GO TO 1994 + END IF * - IF ( NOTROT .GE. EMPTSW ) GO TO 1994 + IF( NOTROT.GE.EMPTSW )GO TO 1994 * 1993 CONTINUE * end i=1:NSWEEP loop @@ -1267,80 +1432,81 @@ N2 = 0 N4 = 0 DO 5991 p = 1, N - 1 - q = IDAMAX( N-p+1, SVA(p), 1 ) + p - 1 - IF ( p .NE. q ) THEN - TEMP1 = SVA(p) - SVA(p) = SVA(q) - SVA(q) = TEMP1 - TEMP1 = WORK(p) - WORK(p) = WORK(q) - WORK(q) = TEMP1 - CALL DSWAP( M, A(1,p), 1, A(1,q), 1 ) - IF ( RSVEC ) CALL DSWAP( MVL, V(1,p), 1, V(1,q), 1 ) + q = IDAMAX( N-p+1, SVA( p ), 1 ) + p - 1 + IF( p.NE.q ) THEN + TEMP1 = SVA( p ) + SVA( p ) = SVA( q ) + SVA( q ) = TEMP1 + TEMP1 = WORK( p ) + WORK( p ) = WORK( q ) + WORK( q ) = TEMP1 + CALL DSWAP( M, A( 1, p ), 1, A( 1, q ), 1 ) + IF( RSVEC )CALL DSWAP( MVL, V( 1, p ), 1, V( 1, q ), 1 ) END IF - IF ( SVA(p) .NE. ZERO ) THEN + IF( SVA( p ).NE.ZERO ) THEN N4 = N4 + 1 - IF ( SVA(p)*SCALE .GT. SFMIN ) N2 = N2 + 1 + IF( SVA( p )*SCALE.GT.SFMIN )N2 = N2 + 1 END IF 5991 CONTINUE - IF ( SVA(N) .NE. ZERO ) THEN + IF( SVA( N ).NE.ZERO ) THEN N4 = N4 + 1 - IF ( SVA(N)*SCALE .GT. SFMIN ) N2 = N2 + 1 + IF( SVA( N )*SCALE.GT.SFMIN )N2 = N2 + 1 END IF * * Normalize the left singular vectors. * - IF ( LSVEC .OR. UCTOL ) THEN + IF( LSVEC .OR. UCTOL ) THEN DO 1998 p = 1, N2 - CALL DSCAL( M, WORK(p) / SVA(p), A(1,p), 1 ) + CALL DSCAL( M, WORK( p ) / SVA( p ), A( 1, p ), 1 ) 1998 CONTINUE END IF * * Scale the product of Jacobi rotations (assemble the fast rotations). * - IF ( RSVEC ) THEN - IF ( APPLV ) THEN + IF( RSVEC ) THEN + IF( APPLV ) THEN DO 2398 p = 1, N - CALL DSCAL( MVL, WORK(p), V(1,p), 1 ) + CALL DSCAL( MVL, WORK( p ), V( 1, p ), 1 ) 2398 CONTINUE ELSE DO 2399 p = 1, N - TEMP1 = ONE / DNRM2(MVL, V(1,p), 1 ) - CALL DSCAL( MVL, TEMP1, V(1,p), 1 ) + TEMP1 = ONE / DNRM2( MVL, V( 1, p ), 1 ) + CALL DSCAL( MVL, TEMP1, V( 1, p ), 1 ) 2399 CONTINUE END IF END IF * * Undo scaling, if necessary (and possible). - IF ( ((SCALE.GT.ONE).AND.(SVA(1).LT.(BIG/SCALE))) - & .OR.((SCALE.LT.ONE).AND.(SVA(N2).GT.(SFMIN/SCALE))) ) THEN + IF( ( ( SCALE.GT.ONE ) .AND. ( SVA( 1 ).LT.( BIG / + + SCALE ) ) ) .OR. ( ( SCALE.LT.ONE ) .AND. ( SVA( N2 ).GT. + + ( SFMIN / SCALE ) ) ) ) THEN DO 2400 p = 1, N - SVA(p) = SCALE*SVA(p) + SVA( p ) = SCALE*SVA( p ) 2400 CONTINUE SCALE = ONE END IF * - WORK(1) = SCALE + WORK( 1 ) = SCALE * The singular values of A are SCALE*SVA(1:N). If SCALE.NE.ONE * then some of the singular values may overflow or underflow and * the spectrum is given in this factored representation. * - WORK(2) = DBLE(N4) + WORK( 2 ) = DBLE( N4 ) * N4 is the number of computed nonzero singular values of A. * - WORK(3) = DBLE(N2) + WORK( 3 ) = DBLE( N2 ) * N2 is the number of singular values of A greater than SFMIN. * If N2<N, SVA(N2:N) contains ZEROS and/or denormalized numbers * that may carry some information. * - WORK(4) = DBLE(i) + WORK( 4 ) = DBLE( i ) * i is the index of the last sweep before declaring convergence. * - WORK(5) = MXAAPQ + WORK( 5 ) = MXAAPQ * MXAAPQ is the largest absolute value of scaled pivots in the * last sweep * - WORK(6) = MXSINJ + WORK( 6 ) = MXSINJ * MXSINJ is the largest absolute value of the sines of Jacobi angles * in the last sweep * @@ -1349,4 +1515,3 @@ * .. END OF DGESVJ * .. END -* diff --git a/SRC/dgsvj0.f b/SRC/dgsvj0.f index 39ed0542..473aa58a 100644 --- a/SRC/dgsvj0.f +++ b/SRC/dgsvj0.f @@ -1,5 +1,5 @@ SUBROUTINE DGSVJ0( JOBV, M, N, A, LDA, D, SVA, MV, V, LDV, EPS, - & SFMIN, TOL, NSWEEP, WORK, LWORK, INFO ) + + SFMIN, TOL, NSWEEP, WORK, LWORK, INFO ) * * -- LAPACK routine (version 3.2) -- * @@ -15,21 +15,20 @@ * computation of SVD, PSVD, QSVD, (H,K)-SVD, and for solution of the * eigenvalue problems Hx = lambda M x, H M x = lambda x with H, M > 0. * -* Scalar Arguments -* - IMPLICIT NONE - INTEGER INFO, LDA, LDV, LWORK, M, MV, N, NSWEEP - DOUBLE PRECISION EPS, SFMIN, TOL - CHARACTER*1 JOBV -* -* Array Arguments -* - DOUBLE PRECISION A( LDA, * ), SVA( N ), D( N ), V( LDV, * ), - & WORK( LWORK ) + IMPLICIT NONE +* .. Scalar Arguments .. + INTEGER INFO, LDA, LDV, LWORK, M, MV, N, NSWEEP + DOUBLE PRECISION EPS, SFMIN, TOL + CHARACTER*1 JOBV +* .. +* .. Array Arguments .. + DOUBLE PRECISION A( LDA, * ), SVA( N ), D( N ), V( LDV, * ), + + WORK( LWORK ) * .. * * Purpose -* ~~~~~~~ +* ======= +* * DGSVJ0 is called from DGESVJ as a pre-processor and that is its main * purpose. It applies Jacobi rotations in the same way as DGESVJ does, but * it does not check convergence (stopping criterion). Few tuning @@ -50,7 +49,7 @@ * drmac@math.hr. Thank you. * * Arguments -* ~~~~~~~~~ +* ========= * * JOBV (input) CHARACTER*1 * Specifies whether the output from this procedure is used @@ -140,92 +139,91 @@ * = 0 : successful exit. * < 0 : if INFO = -i, then the i-th argument had an illegal value * -* Local Parameters - DOUBLE PRECISION ZERO, HALF, ONE, TWO - PARAMETER ( ZERO = 0.0D0, HALF = 0.5D0, ONE = 1.0D0, TWO = 2.0D0 ) - -* Local Scalars - DOUBLE PRECISION AAPP, AAPP0, AAPQ, AAQQ, APOAQ, AQOAP, - & BIG, BIGTHETA, CS, MXAAPQ, MXSINJ, ROOTBIG, ROOTEPS, - & ROOTSFMIN, ROOTTOL, SMALL, SN, T, TEMP1, THETA, - & THSIGN - INTEGER BLSKIP, EMPTSW, i, ibr, IERR, igl, IJBLSK, ir1, ISWROT, - & jbc, jgl, KBL, LKAHEAD, MVL, NBL, NOTROT, p, PSKIPPED, - & q, ROWSKIP, SWBAND - LOGICAL APPLV, ROTOK, RSVEC - -* Local Arrays -* - DOUBLE PRECISION FASTR(5) -* -* Intrinsic Functions -* - INTRINSIC DABS, DMAX1, DBLE, MIN0, DSIGN, DSQRT -* -* External Functions -* - DOUBLE PRECISION DDOT, DNRM2 - INTEGER IDAMAX - LOGICAL LSAME - EXTERNAL IDAMAX, LSAME, DDOT, DNRM2 -* -* External Subroutines -* - EXTERNAL DAXPY, DCOPY, DLASCL, DLASSQ, DROTM, DSWAP +* ===================================================================== * -* ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~| +* .. Local Parameters .. + DOUBLE PRECISION ZERO, HALF, ONE, TWO + PARAMETER ( ZERO = 0.0D0, HALF = 0.5D0, ONE = 1.0D0, + + TWO = 2.0D0 ) +* .. +* .. Local Scalars .. + DOUBLE PRECISION AAPP, AAPP0, AAPQ, AAQQ, APOAQ, AQOAP, BIG, + + BIGTHETA, CS, MXAAPQ, MXSINJ, ROOTBIG, ROOTEPS, + + ROOTSFMIN, ROOTTOL, SMALL, SN, T, TEMP1, THETA, + + THSIGN + INTEGER BLSKIP, EMPTSW, i, ibr, IERR, igl, IJBLSK, ir1, + + ISWROT, jbc, jgl, KBL, LKAHEAD, MVL, NBL, + + NOTROT, p, PSKIPPED, q, ROWSKIP, SWBAND + LOGICAL APPLV, ROTOK, RSVEC +* .. +* .. Local Arrays .. + DOUBLE PRECISION FASTR( 5 ) +* .. +* .. Intrinsic Functions .. + INTRINSIC DABS, DMAX1, DBLE, MIN0, DSIGN, DSQRT +* .. +* .. External Functions .. + DOUBLE PRECISION DDOT, DNRM2 + INTEGER IDAMAX + LOGICAL LSAME + EXTERNAL IDAMAX, LSAME, DDOT, DNRM2 +* .. +* .. External Subroutines .. + EXTERNAL DAXPY, DCOPY, DLASCL, DLASSQ, DROTM, DSWAP +* .. +* .. Executable Statements .. * - APPLV = LSAME(JOBV,'A') - RSVEC = LSAME(JOBV,'V') - IF ( .NOT.( RSVEC .OR. APPLV .OR. LSAME(JOBV,'N'))) THEN + APPLV = LSAME( JOBV, 'A' ) + RSVEC = LSAME( JOBV, 'V' ) + IF( .NOT.( RSVEC .OR. APPLV .OR. LSAME( JOBV, 'N' ) ) ) THEN INFO = -1 - ELSE IF ( M .LT. 0 ) THEN + ELSE IF( M.LT.0 ) THEN INFO = -2 - ELSE IF ( ( N .LT. 0 ) .OR. ( N .GT. M )) THEN + ELSE IF( ( N.LT.0 ) .OR. ( N.GT.M ) ) THEN INFO = -3 - ELSE IF ( LDA .LT. M ) THEN + ELSE IF( LDA.LT.M ) THEN INFO = -5 - ELSE IF ( MV .LT. 0 ) THEN + ELSE IF( MV.LT.0 ) THEN INFO = -8 - ELSE IF ( LDV .LT. M ) THEN + ELSE IF( LDV.LT.M ) THEN INFO = -10 - ELSE IF ( TOL .LE. EPS ) THEN + ELSE IF( TOL.LE.EPS ) THEN INFO = -13 - ELSE IF ( NSWEEP .LT. 0 ) THEN + ELSE IF( NSWEEP.LT.0 ) THEN INFO = -14 - ELSE IF ( LWORK .LT. M ) THEN + ELSE IF( LWORK.LT.M ) THEN INFO = -16 ELSE INFO = 0 END IF * * #:( - IF ( INFO .NE. 0 ) THEN + IF( INFO.NE.0 ) THEN CALL XERBLA( 'DGSVJ0', -INFO ) RETURN END IF * - IF ( RSVEC ) THEN + IF( RSVEC ) THEN MVL = N - ELSE IF ( APPLV ) THEN + ELSE IF( APPLV ) THEN MVL = MV END IF RSVEC = RSVEC .OR. APPLV - ROOTEPS = DSQRT(EPS) - ROOTSFMIN = DSQRT(SFMIN) - SMALL = SFMIN / EPS - BIG = ONE / SFMIN - ROOTBIG = ONE / ROOTSFMIN - BIGTHETA = ONE / ROOTEPS - ROOTTOL = DSQRT(TOL) + ROOTEPS = DSQRT( EPS ) + ROOTSFMIN = DSQRT( SFMIN ) + SMALL = SFMIN / EPS + BIG = ONE / SFMIN + ROOTBIG = ONE / ROOTSFMIN + BIGTHETA = ONE / ROOTEPS + ROOTTOL = DSQRT( TOL ) * * * -#- Row-cyclic Jacobi SVD algorithm with column pivoting -#- * - EMPTSW = ( N * ( N - 1 ) ) / 2 - NOTROT = 0 - FASTR(1) = ZERO + EMPTSW = ( N*( N-1 ) ) / 2 + NOTROT = 0 + FASTR( 1 ) = ZERO * * -#- Row-cyclic pivot strategy with de Rijk's pivoting -#- * @@ -243,7 +241,7 @@ * parameters of the computer's memory. * NBL = N / KBL - IF ( ( NBL * KBL ) .NE. N ) NBL = NBL + 1 + IF( ( NBL*KBL ).NE.N )NBL = NBL + 1 BLSKIP = ( KBL**2 ) + 1 *[TP] BLKSKIP is a tuning parameter that depends on SWBAND and KBL. @@ -259,37 +257,38 @@ DO 1993 i = 1, NSWEEP * .. go go go ... * - MXAAPQ = ZERO - MXSINJ = ZERO - ISWROT = 0 + MXAAPQ = ZERO + MXSINJ = ZERO + ISWROT = 0 * - NOTROT = 0 - PSKIPPED = 0 + NOTROT = 0 + PSKIPPED = 0 * - DO 2000 ibr = 1, NBL + DO 2000 ibr = 1, NBL - igl = ( ibr - 1 ) * KBL + 1 + igl = ( ibr-1 )*KBL + 1 * - DO 1002 ir1 = 0, MIN0( LKAHEAD, NBL - ibr ) + DO 1002 ir1 = 0, MIN0( LKAHEAD, NBL-ibr ) * - igl = igl + ir1 * KBL + igl = igl + ir1*KBL * - DO 2001 p = igl, MIN0( igl + KBL - 1, N - 1) + DO 2001 p = igl, MIN0( igl+KBL-1, N-1 ) * .. de Rijk's pivoting - q = IDAMAX( N-p+1, SVA(p), 1 ) + p - 1 - IF ( p .NE. q ) THEN - CALL DSWAP( M, A(1,p), 1, A(1,q), 1 ) - IF ( RSVEC ) CALL DSWAP( MVL, V(1,p), 1, V(1,q), 1 ) - TEMP1 = SVA(p) - SVA(p) = SVA(q) - SVA(q) = TEMP1 - TEMP1 = D(p) - D(p) = D(q) - D(q) = TEMP1 - END IF -* - IF ( ir1 .EQ. 0 ) THEN + q = IDAMAX( N-p+1, SVA( p ), 1 ) + p - 1 + IF( p.NE.q ) THEN + CALL DSWAP( M, A( 1, p ), 1, A( 1, q ), 1 ) + IF( RSVEC )CALL DSWAP( MVL, V( 1, p ), 1, + + V( 1, q ), 1 ) + TEMP1 = SVA( p ) + SVA( p ) = SVA( q ) + SVA( q ) = TEMP1 + TEMP1 = D( p ) + D( p ) = D( q ) + D( q ) = TEMP1 + END IF +* + IF( ir1.EQ.0 ) THEN * * Column norms are periodically updated by explicit * norm computation. @@ -303,505 +302,652 @@ * If properly implemented DNRM2 is available, the IF-THEN-ELSE * below should read "AAPP = DNRM2( M, A(1,p), 1 ) * D(p)". * - IF ((SVA(p) .LT. ROOTBIG) .AND. (SVA(p) .GT. ROOTSFMIN)) THEN - SVA(p) = DNRM2( M, A(1,p), 1 ) * D(p) - ELSE - TEMP1 = ZERO - AAPP = ZERO - CALL DLASSQ( M, A(1,p), 1, TEMP1, AAPP ) - SVA(p) = TEMP1 * DSQRT(AAPP) * D(p) - END IF - AAPP = SVA(p) - ELSE - AAPP = SVA(p) - END IF + IF( ( SVA( p ).LT.ROOTBIG ) .AND. + + ( SVA( p ).GT.ROOTSFMIN ) ) THEN + SVA( p ) = DNRM2( M, A( 1, p ), 1 )*D( p ) + ELSE + TEMP1 = ZERO + AAPP = ZERO + CALL DLASSQ( M, A( 1, p ), 1, TEMP1, AAPP ) + SVA( p ) = TEMP1*DSQRT( AAPP )*D( p ) + END IF + AAPP = SVA( p ) + ELSE + AAPP = SVA( p ) + END IF * - IF ( AAPP .GT. ZERO ) THEN + IF( AAPP.GT.ZERO ) THEN * - PSKIPPED = 0 + PSKIPPED = 0 * - DO 2002 q = p + 1, MIN0( igl + KBL - 1, N ) + DO 2002 q = p + 1, MIN0( igl+KBL-1, N ) * - AAQQ = SVA(q) + AAQQ = SVA( q ) - IF ( AAQQ .GT. ZERO ) THEN -* - AAPP0 = AAPP - IF ( AAQQ .GE. ONE ) THEN - ROTOK = ( SMALL*AAPP ) .LE. AAQQ - IF ( AAPP .LT. ( BIG / AAQQ ) ) THEN - AAPQ = ( DDOT(M, A(1,p), 1, A(1,q), 1 ) * - & D(p) * D(q) / AAQQ ) / AAPP - ELSE - CALL DCOPY( M, A(1,p), 1, WORK, 1 ) - CALL DLASCL( 'G', 0, 0, AAPP, D(p), M, - & 1, WORK, LDA, IERR ) - AAPQ = DDOT( M, WORK,1, A(1,q),1 )*D(q) / AAQQ - END IF - ELSE - ROTOK = AAPP .LE. ( AAQQ / SMALL ) - IF ( AAPP .GT. ( SMALL / AAQQ ) ) THEN - AAPQ = ( DDOT( M, A(1,p), 1, A(1,q), 1 ) * - & D(p) * D(q) / AAQQ ) / AAPP - ELSE - CALL DCOPY( M, A(1,q), 1, WORK, 1 ) - CALL DLASCL( 'G', 0, 0, AAQQ, D(q), M, - & 1, WORK, LDA, IERR ) - AAPQ = DDOT( M, WORK,1, A(1,p),1 )*D(p) / AAPP - END IF - END IF + IF( AAQQ.GT.ZERO ) THEN +* + AAPP0 = AAPP + IF( AAQQ.GE.ONE ) THEN + ROTOK = ( SMALL*AAPP ).LE.AAQQ + IF( AAPP.LT.( BIG / AAQQ ) ) THEN + AAPQ = ( DDOT( M, A( 1, p ), 1, A( 1, + + q ), 1 )*D( p )*D( q ) / AAQQ ) + + / AAPP + ELSE + CALL DCOPY( M, A( 1, p ), 1, WORK, 1 ) + CALL DLASCL( 'G', 0, 0, AAPP, D( p ), + + M, 1, WORK, LDA, IERR ) + AAPQ = DDOT( M, WORK, 1, A( 1, q ), + + 1 )*D( q ) / AAQQ + END IF + ELSE + ROTOK = AAPP.LE.( AAQQ / SMALL ) + IF( AAPP.GT.( SMALL / AAQQ ) ) THEN + AAPQ = ( DDOT( M, A( 1, p ), 1, A( 1, + + q ), 1 )*D( p )*D( q ) / AAQQ ) + + / AAPP + ELSE + CALL DCOPY( M, A( 1, q ), 1, WORK, 1 ) + CALL DLASCL( 'G', 0, 0, AAQQ, D( q ), + + M, 1, WORK, LDA, IERR ) + AAPQ = DDOT( M, WORK, 1, A( 1, p ), + + 1 )*D( p ) / AAPP + END IF + END IF * - MXAAPQ = DMAX1( MXAAPQ, DABS(AAPQ) ) + MXAAPQ = DMAX1( MXAAPQ, DABS( AAPQ ) ) * * TO rotate or NOT to rotate, THAT is the question ... * - IF ( DABS( AAPQ ) .GT. TOL ) THEN + IF( DABS( AAPQ ).GT.TOL ) THEN * * .. rotate * ROTATED = ROTATED + ONE * - IF ( ir1 .EQ. 0 ) THEN - NOTROT = 0 - PSKIPPED = 0 - ISWROT = ISWROT + 1 - END IF -* - IF ( ROTOK ) THEN -* - AQOAP = AAQQ / AAPP - APOAQ = AAPP / AAQQ - THETA = - HALF * DABS( AQOAP - APOAQ ) / AAPQ -* - IF ( DABS( THETA ) .GT. BIGTHETA ) THEN -* - T = HALF / THETA - FASTR(3) = T * D(p) / D(q) - FASTR(4) = - T * D(q) / D(p) - CALL DROTM( M, A(1,p), 1, A(1,q), 1, FASTR ) - IF ( RSVEC ) - & CALL DROTM( MVL, V(1,p), 1, V(1,q), 1, FASTR ) - SVA(q) = AAQQ*DSQRT( DMAX1(ZERO,ONE + T*APOAQ*AAPQ) ) - AAPP = AAPP*DSQRT( ONE - T*AQOAP*AAPQ ) - MXSINJ = DMAX1( MXSINJ, DABS(T) ) -* - ELSE + IF( ir1.EQ.0 ) THEN + NOTROT = 0 + PSKIPPED = 0 + ISWROT = ISWROT + 1 + END IF +* + IF( ROTOK ) THEN +* + AQOAP = AAQQ / AAPP + APOAQ = AAPP / AAQQ + THETA = -HALF*DABS( AQOAP-APOAQ ) / + + AAPQ +* + IF( DABS( THETA ).GT.BIGTHETA ) THEN +* + T = HALF / THETA + FASTR( 3 ) = T*D( p ) / D( q ) + FASTR( 4 ) = -T*D( q ) / D( p ) + CALL DROTM( M, A( 1, p ), 1, + + A( 1, q ), 1, FASTR ) + IF( RSVEC )CALL DROTM( MVL, + + V( 1, p ), 1, + + V( 1, q ), 1, + + FASTR ) + SVA( q ) = AAQQ*DSQRT( DMAX1( ZERO, + + ONE+T*APOAQ*AAPQ ) ) + AAPP = AAPP*DSQRT( ONE-T*AQOAP* + + AAPQ ) + MXSINJ = DMAX1( MXSINJ, DABS( T ) ) +* + ELSE * * .. choose correct signum for THETA and rotate * - THSIGN = - DSIGN(ONE,AAPQ) - T = ONE / ( THETA + THSIGN*DSQRT(ONE+THETA*THETA) ) - CS = DSQRT( ONE / ( ONE + T*T ) ) - SN = T * CS -* - MXSINJ = DMAX1( MXSINJ, DABS(SN) ) - SVA(q) = AAQQ*DSQRT( DMAX1(ZERO, ONE+T*APOAQ*AAPQ) ) - AAPP = AAPP*DSQRT( DMAX1(ZERO, ONE-T*AQOAP*AAPQ) ) -* - APOAQ = D(p) / D(q) - AQOAP = D(q) / D(p) - IF ( D(p) .GE. ONE ) THEN - IF ( D(q) .GE. ONE ) THEN - FASTR(3) = T * APOAQ - FASTR(4) = - T * AQOAP - D(p) = D(p) * CS - D(q) = D(q) * CS - CALL DROTM( M, A(1,p),1, A(1,q),1, FASTR ) - IF ( RSVEC ) - & CALL DROTM( MVL, V(1,p),1, V(1,q),1, FASTR ) - ELSE - CALL DAXPY( M, -T*AQOAP, A(1,q),1, A(1,p),1 ) - CALL DAXPY( M, CS*SN*APOAQ, A(1,p),1, A(1,q),1 ) - D(p) = D(p) * CS - D(q) = D(q) / CS - IF ( RSVEC ) THEN - CALL DAXPY(MVL, -T*AQOAP, V(1,q),1,V(1,p),1) - CALL DAXPY(MVL,CS*SN*APOAQ, V(1,p),1,V(1,q),1) - END IF - END IF - ELSE - IF ( D(q) .GE. ONE ) THEN - CALL DAXPY( M, T*APOAQ, A(1,p),1, A(1,q),1 ) - CALL DAXPY( M,-CS*SN*AQOAP, A(1,q),1, A(1,p),1 ) - D(p) = D(p) / CS - D(q) = D(q) * CS - IF ( RSVEC ) THEN - CALL DAXPY(MVL, T*APOAQ, V(1,p),1,V(1,q),1) - CALL DAXPY(MVL,-CS*SN*AQOAP,V(1,q),1,V(1,p),1) - END IF - ELSE - IF ( D(p) .GE. D(q) ) THEN - CALL DAXPY( M,-T*AQOAP, A(1,q),1,A(1,p),1 ) - CALL DAXPY( M,CS*SN*APOAQ,A(1,p),1,A(1,q),1 ) - D(p) = D(p) * CS - D(q) = D(q) / CS - IF ( RSVEC ) THEN - CALL DAXPY(MVL, -T*AQOAP, V(1,q),1,V(1,p),1) - CALL DAXPY(MVL,CS*SN*APOAQ,V(1,p),1,V(1,q),1) - END IF - ELSE - CALL DAXPY( M, T*APOAQ, A(1,p),1,A(1,q),1) - CALL DAXPY( M,-CS*SN*AQOAP,A(1,q),1,A(1,p),1) - D(p) = D(p) / CS - D(q) = D(q) * CS - IF ( RSVEC ) THEN - CALL DAXPY(MVL, T*APOAQ, V(1,p),1,V(1,q),1) - CALL DAXPY(MVL,-CS*SN*AQOAP,V(1,q),1,V(1,p),1) - END IF - END IF - END IF - ENDIF - END IF -* - ELSE + THSIGN = -DSIGN( ONE, AAPQ ) + T = ONE / ( THETA+THSIGN* + + DSQRT( ONE+THETA*THETA ) ) + CS = DSQRT( ONE / ( ONE+T*T ) ) + SN = T*CS +* + MXSINJ = DMAX1( MXSINJ, DABS( SN ) ) + SVA( q ) = AAQQ*DSQRT( DMAX1( ZERO, + + ONE+T*APOAQ*AAPQ ) ) + AAPP = AAPP*DSQRT( DMAX1( ZERO, + + ONE-T*AQOAP*AAPQ ) ) +* + APOAQ = D( p ) / D( q ) + AQOAP = D( q ) / D( p ) + IF( D( p ).GE.ONE ) THEN + IF( D( q ).GE.ONE ) THEN + FASTR( 3 ) = T*APOAQ + FASTR( 4 ) = -T*AQOAP + D( p ) = D( p )*CS + D( q ) = D( q )*CS + CALL DROTM( M, A( 1, p ), 1, + + A( 1, q ), 1, + + FASTR ) + IF( RSVEC )CALL DROTM( MVL, + + V( 1, p ), 1, V( 1, q ), + + 1, FASTR ) + ELSE + CALL DAXPY( M, -T*AQOAP, + + A( 1, q ), 1, + + A( 1, p ), 1 ) + CALL DAXPY( M, CS*SN*APOAQ, + + A( 1, p ), 1, + + A( 1, q ), 1 ) + D( p ) = D( p )*CS + D( q ) = D( q ) / CS + IF( RSVEC ) THEN + CALL DAXPY( MVL, -T*AQOAP, + + V( 1, q ), 1, + + V( 1, p ), 1 ) + CALL DAXPY( MVL, + + CS*SN*APOAQ, + + V( 1, p ), 1, + + V( 1, q ), 1 ) + END IF + END IF + ELSE + IF( D( q ).GE.ONE ) THEN + CALL DAXPY( M, T*APOAQ, + + A( 1, p ), 1, + + A( 1, q ), 1 ) + CALL DAXPY( M, -CS*SN*AQOAP, + + A( 1, q ), 1, + + A( 1, p ), 1 ) + D( p ) = D( p ) / CS + D( q ) = D( q )*CS + IF( RSVEC ) THEN + CALL DAXPY( MVL, T*APOAQ, + + V( 1, p ), 1, + + V( 1, q ), 1 ) + CALL DAXPY( MVL, + + -CS*SN*AQOAP, + + V( 1, q ), 1, + + V( 1, p ), 1 ) + END IF + ELSE + IF( D( p ).GE.D( q ) ) THEN + CALL DAXPY( M, -T*AQOAP, + + A( 1, q ), 1, + + A( 1, p ), 1 ) + CALL DAXPY( M, CS*SN*APOAQ, + + A( 1, p ), 1, + + A( 1, q ), 1 ) + D( p ) = D( p )*CS + D( q ) = D( q ) / CS + IF( RSVEC ) THEN + CALL DAXPY( MVL, + + -T*AQOAP, + + V( 1, q ), 1, + + V( 1, p ), 1 ) + CALL DAXPY( MVL, + + CS*SN*APOAQ, + + V( 1, p ), 1, + + V( 1, q ), 1 ) + END IF + ELSE + CALL DAXPY( M, T*APOAQ, + + A( 1, p ), 1, + + A( 1, q ), 1 ) + CALL DAXPY( M, + + -CS*SN*AQOAP, + + A( 1, q ), 1, + + A( 1, p ), 1 ) + D( p ) = D( p ) / CS + D( q ) = D( q )*CS + IF( RSVEC ) THEN + CALL DAXPY( MVL, + + T*APOAQ, V( 1, p ), + + 1, V( 1, q ), 1 ) + CALL DAXPY( MVL, + + -CS*SN*AQOAP, + + V( 1, q ), 1, + + V( 1, p ), 1 ) + END IF + END IF + END IF + END IF + END IF +* + ELSE * .. have to use modified Gram-Schmidt like transformation - CALL DCOPY( M, A(1,p), 1, WORK, 1 ) - CALL DLASCL( 'G',0,0,AAPP,ONE,M,1,WORK,LDA,IERR ) - CALL DLASCL( 'G',0,0,AAQQ,ONE,M,1, A(1,q),LDA,IERR ) - TEMP1 = -AAPQ * D(p) / D(q) - CALL DAXPY ( M, TEMP1, WORK, 1, A(1,q), 1 ) - CALL DLASCL( 'G',0,0,ONE,AAQQ,M,1, A(1,q),LDA,IERR ) - SVA(q) = AAQQ*DSQRT( DMAX1( ZERO, ONE - AAPQ*AAPQ ) ) - MXSINJ = DMAX1( MXSINJ, SFMIN ) - END IF + CALL DCOPY( M, A( 1, p ), 1, WORK, 1 ) + CALL DLASCL( 'G', 0, 0, AAPP, ONE, M, + + 1, WORK, LDA, IERR ) + CALL DLASCL( 'G', 0, 0, AAQQ, ONE, M, + + 1, A( 1, q ), LDA, IERR ) + TEMP1 = -AAPQ*D( p ) / D( q ) + CALL DAXPY( M, TEMP1, WORK, 1, + + A( 1, q ), 1 ) + CALL DLASCL( 'G', 0, 0, ONE, AAQQ, M, + + 1, A( 1, q ), LDA, IERR ) + SVA( q ) = AAQQ*DSQRT( DMAX1( ZERO, + + ONE-AAPQ*AAPQ ) ) + MXSINJ = DMAX1( MXSINJ, SFMIN ) + END IF * END IF ROTOK THEN ... ELSE * * In the case of cancellation in updating SVA(q), SVA(p) * recompute SVA(q), SVA(p). - IF ( (SVA(q) / AAQQ )**2 .LE. ROOTEPS ) THEN - IF ((AAQQ .LT. ROOTBIG).AND.(AAQQ .GT. ROOTSFMIN)) THEN - SVA(q) = DNRM2( M, A(1,q), 1 ) * D(q) - ELSE - T = ZERO - AAQQ = ZERO - CALL DLASSQ( M, A(1,q), 1, T, AAQQ ) - SVA(q) = T * DSQRT(AAQQ) * D(q) - END IF - END IF - IF ( ( AAPP / AAPP0) .LE. ROOTEPS ) THEN - IF ((AAPP .LT. ROOTBIG).AND.(AAPP .GT. ROOTSFMIN)) THEN - AAPP = DNRM2( M, A(1,p), 1 ) * D(p) - ELSE - T = ZERO - AAPP = ZERO - CALL DLASSQ( M, A(1,p), 1, T, AAPP ) - AAPP = T * DSQRT(AAPP) * D(p) - END IF - SVA(p) = AAPP - END IF -* - ELSE + IF( ( SVA( q ) / AAQQ )**2.LE.ROOTEPS ) + + THEN + IF( ( AAQQ.LT.ROOTBIG ) .AND. + + ( AAQQ.GT.ROOTSFMIN ) ) THEN + SVA( q ) = DNRM2( M, A( 1, q ), 1 )* + + D( q ) + ELSE + T = ZERO + AAQQ = ZERO + CALL DLASSQ( M, A( 1, q ), 1, T, + + AAQQ ) + SVA( q ) = T*DSQRT( AAQQ )*D( q ) + END IF + END IF + IF( ( AAPP / AAPP0 ).LE.ROOTEPS ) THEN + IF( ( AAPP.LT.ROOTBIG ) .AND. + + ( AAPP.GT.ROOTSFMIN ) ) THEN + AAPP = DNRM2( M, A( 1, p ), 1 )* + + D( p ) + ELSE + T = ZERO + AAPP = ZERO + CALL DLASSQ( M, A( 1, p ), 1, T, + + AAPP ) + AAPP = T*DSQRT( AAPP )*D( p ) + END IF + SVA( p ) = AAPP + END IF +* + ELSE * A(:,p) and A(:,q) already numerically orthogonal - IF ( ir1 .EQ. 0 ) NOTROT = NOTROT + 1 - PSKIPPED = PSKIPPED + 1 - END IF - ELSE + IF( ir1.EQ.0 )NOTROT = NOTROT + 1 + PSKIPPED = PSKIPPED + 1 + END IF + ELSE * A(:,q) is zero column - IF ( ir1. EQ. 0 ) NOTROT = NOTROT + 1 - PSKIPPED = PSKIPPED + 1 - END IF + IF( ir1.EQ.0 )NOTROT = NOTROT + 1 + PSKIPPED = PSKIPPED + 1 + END IF * - IF ( ( i .LE. SWBAND ) .AND. ( PSKIPPED .GT. ROWSKIP ) ) THEN - IF ( ir1 .EQ. 0 ) AAPP = - AAPP - NOTROT = 0 - GO TO 2103 - END IF + IF( ( i.LE.SWBAND ) .AND. + + ( PSKIPPED.GT.ROWSKIP ) ) THEN + IF( ir1.EQ.0 )AAPP = -AAPP + NOTROT = 0 + GO TO 2103 + END IF * - 2002 CONTINUE + 2002 CONTINUE * END q-LOOP * - 2103 CONTINUE + 2103 CONTINUE * bailed out of q-loop - SVA(p) = AAPP + SVA( p ) = AAPP - ELSE - SVA(p) = AAPP - IF ( ( ir1 .EQ. 0 ) .AND. (AAPP .EQ. ZERO) ) - & NOTROT=NOTROT+MIN0(igl+KBL-1,N)-p - END IF + ELSE + SVA( p ) = AAPP + IF( ( ir1.EQ.0 ) .AND. ( AAPP.EQ.ZERO ) ) + + NOTROT = NOTROT + MIN0( igl+KBL-1, N ) - p + END IF * - 2001 CONTINUE + 2001 CONTINUE * end of the p-loop * end of doing the block ( ibr, ibr ) - 1002 CONTINUE + 1002 CONTINUE * end of ir1-loop * *........................................................ * ... go to the off diagonal blocks * - igl = ( ibr - 1 ) * KBL + 1 + igl = ( ibr-1 )*KBL + 1 * - DO 2010 jbc = ibr + 1, NBL + DO 2010 jbc = ibr + 1, NBL * - jgl = ( jbc - 1 ) * KBL + 1 + jgl = ( jbc-1 )*KBL + 1 * * doing the block at ( ibr, jbc ) * - IJBLSK = 0 - DO 2100 p = igl, MIN0( igl + KBL - 1, N ) + IJBLSK = 0 + DO 2100 p = igl, MIN0( igl+KBL-1, N ) * - AAPP = SVA(p) + AAPP = SVA( p ) * - IF ( AAPP .GT. ZERO ) THEN + IF( AAPP.GT.ZERO ) THEN * - PSKIPPED = 0 + PSKIPPED = 0 * - DO 2200 q = jgl, MIN0( jgl + KBL - 1, N ) + DO 2200 q = jgl, MIN0( jgl+KBL-1, N ) * - AAQQ = SVA(q) + AAQQ = SVA( q ) * - IF ( AAQQ .GT. ZERO ) THEN - AAPP0 = AAPP + IF( AAQQ.GT.ZERO ) THEN + AAPP0 = AAPP * * -#- M x 2 Jacobi SVD -#- * * -#- Safe Gram matrix computation -#- * - IF ( AAQQ .GE. ONE ) THEN - IF ( AAPP .GE. AAQQ ) THEN - ROTOK = ( SMALL*AAPP ) .LE. AAQQ - ELSE - ROTOK = ( SMALL*AAQQ ) .LE. AAPP - END IF - IF ( AAPP .LT. ( BIG / AAQQ ) ) THEN - AAPQ = ( DDOT(M, A(1,p), 1, A(1,q), 1 ) * - & D(p) * D(q) / AAQQ ) / AAPP - ELSE - CALL DCOPY( M, A(1,p), 1, WORK, 1 ) - CALL DLASCL( 'G', 0, 0, AAPP, D(p), M, - & 1, WORK, LDA, IERR ) - AAPQ = DDOT( M, WORK, 1, A(1,q), 1 ) * - & D(q) / AAQQ - END IF - ELSE - IF ( AAPP .GE. AAQQ ) THEN - ROTOK = AAPP .LE. ( AAQQ / SMALL ) - ELSE - ROTOK = AAQQ .LE. ( AAPP / SMALL ) - END IF - IF ( AAPP .GT. ( SMALL / AAQQ ) ) THEN - AAPQ = ( DDOT( M, A(1,p), 1, A(1,q), 1 ) * - & D(p) * D(q) / AAQQ ) / AAPP - ELSE - CALL DCOPY( M, A(1,q), 1, WORK, 1 ) - CALL DLASCL( 'G', 0, 0, AAQQ, D(q), M, 1, - & WORK, LDA, IERR ) - AAPQ = DDOT(M,WORK,1,A(1,p),1) * D(p) / AAPP - END IF - END IF + IF( AAQQ.GE.ONE ) THEN + IF( AAPP.GE.AAQQ ) THEN + ROTOK = ( SMALL*AAPP ).LE.AAQQ + ELSE + ROTOK = ( SMALL*AAQQ ).LE.AAPP + END IF + IF( AAPP.LT.( BIG / AAQQ ) ) THEN + AAPQ = ( DDOT( M, A( 1, p ), 1, A( 1, + + q ), 1 )*D( p )*D( q ) / AAQQ ) + + / AAPP + ELSE + CALL DCOPY( M, A( 1, p ), 1, WORK, 1 ) + CALL DLASCL( 'G', 0, 0, AAPP, D( p ), + + M, 1, WORK, LDA, IERR ) + AAPQ = DDOT( M, WORK, 1, A( 1, q ), + + 1 )*D( q ) / AAQQ + END IF + ELSE + IF( AAPP.GE.AAQQ ) THEN + ROTOK = AAPP.LE.( AAQQ / SMALL ) + ELSE + ROTOK = AAQQ.LE.( AAPP / SMALL ) + END IF + IF( AAPP.GT.( SMALL / AAQQ ) ) THEN + AAPQ = ( DDOT( M, A( 1, p ), 1, A( 1, + + q ), 1 )*D( p )*D( q ) / AAQQ ) + + / AAPP + ELSE + CALL DCOPY( M, A( 1, q ), 1, WORK, 1 ) + CALL DLASCL( 'G', 0, 0, AAQQ, D( q ), + + M, 1, WORK, LDA, IERR ) + AAPQ = DDOT( M, WORK, 1, A( 1, p ), + + 1 )*D( p ) / AAPP + END IF + END IF * - MXAAPQ = DMAX1( MXAAPQ, DABS(AAPQ) ) + MXAAPQ = DMAX1( MXAAPQ, DABS( AAPQ ) ) * * TO rotate or NOT to rotate, THAT is the question ... * - IF ( DABS( AAPQ ) .GT. TOL ) THEN - NOTROT = 0 + IF( DABS( AAPQ ).GT.TOL ) THEN + NOTROT = 0 * ROTATED = ROTATED + 1 - PSKIPPED = 0 - ISWROT = ISWROT + 1 -* - IF ( ROTOK ) THEN -* - AQOAP = AAQQ / AAPP - APOAQ = AAPP / AAQQ - THETA = - HALF * DABS( AQOAP - APOAQ ) / AAPQ - IF ( AAQQ .GT. AAPP0 ) THETA = - THETA -* - IF ( DABS( THETA ) .GT. BIGTHETA ) THEN - T = HALF / THETA - FASTR(3) = T * D(p) / D(q) - FASTR(4) = -T * D(q) / D(p) - CALL DROTM( M, A(1,p), 1, A(1,q), 1, FASTR ) - IF ( RSVEC ) - & CALL DROTM( MVL, V(1,p), 1, V(1,q), 1, FASTR ) - SVA(q) = AAQQ*DSQRT( DMAX1(ZERO,ONE + T*APOAQ*AAPQ) ) - AAPP = AAPP*DSQRT( DMAX1(ZERO,ONE - T*AQOAP*AAPQ) ) - MXSINJ = DMAX1( MXSINJ, DABS(T) ) - ELSE + PSKIPPED = 0 + ISWROT = ISWROT + 1 +* + IF( ROTOK ) THEN +* + AQOAP = AAQQ / AAPP + APOAQ = AAPP / AAQQ + THETA = -HALF*DABS( AQOAP-APOAQ ) / + + AAPQ + IF( AAQQ.GT.AAPP0 )THETA = -THETA +* + IF( DABS( THETA ).GT.BIGTHETA ) THEN + T = HALF / THETA + FASTR( 3 ) = T*D( p ) / D( q ) + FASTR( 4 ) = -T*D( q ) / D( p ) + CALL DROTM( M, A( 1, p ), 1, + + A( 1, q ), 1, FASTR ) + IF( RSVEC )CALL DROTM( MVL, + + V( 1, p ), 1, + + V( 1, q ), 1, + + FASTR ) + SVA( q ) = AAQQ*DSQRT( DMAX1( ZERO, + + ONE+T*APOAQ*AAPQ ) ) + AAPP = AAPP*DSQRT( DMAX1( ZERO, + + ONE-T*AQOAP*AAPQ ) ) + MXSINJ = DMAX1( MXSINJ, DABS( T ) ) + ELSE * * .. choose correct signum for THETA and rotate * - THSIGN = - DSIGN(ONE,AAPQ) - IF ( AAQQ .GT. AAPP0 ) THSIGN = - THSIGN - T = ONE / ( THETA + THSIGN*DSQRT(ONE+THETA*THETA) ) - CS = DSQRT( ONE / ( ONE + T*T ) ) - SN = T * CS - MXSINJ = DMAX1( MXSINJ, DABS(SN) ) - SVA(q) = AAQQ*DSQRT( DMAX1(ZERO, ONE+T*APOAQ*AAPQ) ) - AAPP = AAPP*DSQRT( ONE - T*AQOAP*AAPQ) -* - APOAQ = D(p) / D(q) - AQOAP = D(q) / D(p) - IF ( D(p) .GE. ONE ) THEN -* - IF ( D(q) .GE. ONE ) THEN - FASTR(3) = T * APOAQ - FASTR(4) = - T * AQOAP - D(p) = D(p) * CS - D(q) = D(q) * CS - CALL DROTM( M, A(1,p),1, A(1,q),1, FASTR ) - IF ( RSVEC ) - & CALL DROTM( MVL, V(1,p),1, V(1,q),1, FASTR ) - ELSE - CALL DAXPY( M, -T*AQOAP, A(1,q),1, A(1,p),1 ) - CALL DAXPY( M, CS*SN*APOAQ, A(1,p),1, A(1,q),1 ) - IF ( RSVEC ) THEN - CALL DAXPY( MVL, -T*AQOAP, V(1,q),1, V(1,p),1 ) - CALL DAXPY( MVL,CS*SN*APOAQ,V(1,p),1, V(1,q),1 ) - END IF - D(p) = D(p) * CS - D(q) = D(q) / CS - END IF - ELSE - IF ( D(q) .GE. ONE ) THEN - CALL DAXPY( M, T*APOAQ, A(1,p),1, A(1,q),1 ) - CALL DAXPY( M,-CS*SN*AQOAP, A(1,q),1, A(1,p),1 ) - IF ( RSVEC ) THEN - CALL DAXPY(MVL,T*APOAQ, V(1,p),1, V(1,q),1 ) - CALL DAXPY(MVL,-CS*SN*AQOAP,V(1,q),1, V(1,p),1 ) - END IF - D(p) = D(p) / CS - D(q) = D(q) * CS - ELSE - IF ( D(p) .GE. D(q) ) THEN - CALL DAXPY( M,-T*AQOAP, A(1,q),1,A(1,p),1 ) - CALL DAXPY( M,CS*SN*APOAQ,A(1,p),1,A(1,q),1 ) - D(p) = D(p) * CS - D(q) = D(q) / CS - IF ( RSVEC ) THEN - CALL DAXPY( MVL, -T*AQOAP, V(1,q),1,V(1,p),1) - CALL DAXPY(MVL,CS*SN*APOAQ,V(1,p),1,V(1,q),1) - END IF - ELSE - CALL DAXPY(M, T*APOAQ, A(1,p),1,A(1,q),1) - CALL DAXPY(M,-CS*SN*AQOAP,A(1,q),1,A(1,p),1) - D(p) = D(p) / CS - D(q) = D(q) * CS - IF ( RSVEC ) THEN - CALL DAXPY(MVL, T*APOAQ, V(1,p),1,V(1,q),1) - CALL DAXPY(MVL,-CS*SN*AQOAP,V(1,q),1,V(1,p),1) - END IF - END IF - END IF - ENDIF - END IF -* - ELSE - IF ( AAPP .GT. AAQQ ) THEN - CALL DCOPY( M, A(1,p), 1, WORK, 1 ) - CALL DLASCL('G',0,0,AAPP,ONE,M,1,WORK,LDA,IERR) - CALL DLASCL('G',0,0,AAQQ,ONE,M,1, A(1,q),LDA,IERR) - TEMP1 = -AAPQ * D(p) / D(q) - CALL DAXPY(M,TEMP1,WORK,1,A(1,q),1) - CALL DLASCL('G',0,0,ONE,AAQQ,M,1,A(1,q),LDA,IERR) - SVA(q) = AAQQ*DSQRT(DMAX1(ZERO, ONE - AAPQ*AAPQ)) - MXSINJ = DMAX1( MXSINJ, SFMIN ) - ELSE - CALL DCOPY( M, A(1,q), 1, WORK, 1 ) - CALL DLASCL('G',0,0,AAQQ,ONE,M,1,WORK,LDA,IERR) - CALL DLASCL('G',0,0,AAPP,ONE,M,1, A(1,p),LDA,IERR) - TEMP1 = -AAPQ * D(q) / D(p) - CALL DAXPY(M,TEMP1,WORK,1,A(1,p),1) - CALL DLASCL('G',0,0,ONE,AAPP,M,1,A(1,p),LDA,IERR) - SVA(p) = AAPP*DSQRT(DMAX1(ZERO, ONE - AAPQ*AAPQ)) - MXSINJ = DMAX1( MXSINJ, SFMIN ) - END IF - END IF + THSIGN = -DSIGN( ONE, AAPQ ) + IF( AAQQ.GT.AAPP0 )THSIGN = -THSIGN + T = ONE / ( THETA+THSIGN* + + DSQRT( ONE+THETA*THETA ) ) + CS = DSQRT( ONE / ( ONE+T*T ) ) + SN = T*CS + MXSINJ = DMAX1( MXSINJ, DABS( SN ) ) + SVA( q ) = AAQQ*DSQRT( DMAX1( ZERO, + + ONE+T*APOAQ*AAPQ ) ) + AAPP = AAPP*DSQRT( ONE-T*AQOAP* + + AAPQ ) +* + APOAQ = D( p ) / D( q ) + AQOAP = D( q ) / D( p ) + IF( D( p ).GE.ONE ) THEN +* + IF( D( q ).GE.ONE ) THEN + FASTR( 3 ) = T*APOAQ + FASTR( 4 ) = -T*AQOAP + D( p ) = D( p )*CS + D( q ) = D( q )*CS + CALL DROTM( M, A( 1, p ), 1, + + A( 1, q ), 1, + + FASTR ) + IF( RSVEC )CALL DROTM( MVL, + + V( 1, p ), 1, V( 1, q ), + + 1, FASTR ) + ELSE + CALL DAXPY( M, -T*AQOAP, + + A( 1, q ), 1, + + A( 1, p ), 1 ) + CALL DAXPY( M, CS*SN*APOAQ, + + A( 1, p ), 1, + + A( 1, q ), 1 ) + IF( RSVEC ) THEN + CALL DAXPY( MVL, -T*AQOAP, + + V( 1, q ), 1, + + V( 1, p ), 1 ) + CALL DAXPY( MVL, + + CS*SN*APOAQ, + + V( 1, p ), 1, + + V( 1, q ), 1 ) + END IF + D( p ) = D( p )*CS + D( q ) = D( q ) / CS + END IF + ELSE + IF( D( q ).GE.ONE ) THEN + CALL DAXPY( M, T*APOAQ, + + A( 1, p ), 1, + + A( 1, q ), 1 ) + CALL DAXPY( M, -CS*SN*AQOAP, + + A( 1, q ), 1, + + A( 1, p ), 1 ) + IF( RSVEC ) THEN + CALL DAXPY( MVL, T*APOAQ, + + V( 1, p ), 1, + + V( 1, q ), 1 ) + CALL DAXPY( MVL, + + -CS*SN*AQOAP, + + V( 1, q ), 1, + + V( 1, p ), 1 ) + END IF + D( p ) = D( p ) / CS + D( q ) = D( q )*CS + ELSE + IF( D( p ).GE.D( q ) ) THEN + CALL DAXPY( M, -T*AQOAP, + + A( 1, q ), 1, + + A( 1, p ), 1 ) + CALL DAXPY( M, CS*SN*APOAQ, + + A( 1, p ), 1, + + A( 1, q ), 1 ) + D( p ) = D( p )*CS + D( q ) = D( q ) / CS + IF( RSVEC ) THEN + CALL DAXPY( MVL, + + -T*AQOAP, + + V( 1, q ), 1, + + V( 1, p ), 1 ) + CALL DAXPY( MVL, + + CS*SN*APOAQ, + + V( 1, p ), 1, + + V( 1, q ), 1 ) + END IF + ELSE + CALL DAXPY( M, T*APOAQ, + + A( 1, p ), 1, + + A( 1, q ), 1 ) + CALL DAXPY( M, + + -CS*SN*AQOAP, + + A( 1, q ), 1, + + A( 1, p ), 1 ) + D( p ) = D( p ) / CS + D( q ) = D( q )*CS + IF( RSVEC ) THEN + CALL DAXPY( MVL, + + T*APOAQ, V( 1, p ), + + 1, V( 1, q ), 1 ) + CALL DAXPY( MVL, + + -CS*SN*AQOAP, + + V( 1, q ), 1, + + V( 1, p ), 1 ) + END IF + END IF + END IF + END IF + END IF +* + ELSE + IF( AAPP.GT.AAQQ ) THEN + CALL DCOPY( M, A( 1, p ), 1, WORK, + + 1 ) + CALL DLASCL( 'G', 0, 0, AAPP, ONE, + + M, 1, WORK, LDA, IERR ) + CALL DLASCL( 'G', 0, 0, AAQQ, ONE, + + M, 1, A( 1, q ), LDA, + + IERR ) + TEMP1 = -AAPQ*D( p ) / D( q ) + CALL DAXPY( M, TEMP1, WORK, 1, + + A( 1, q ), 1 ) + CALL DLASCL( 'G', 0, 0, ONE, AAQQ, + + M, 1, A( 1, q ), LDA, + + IERR ) + SVA( q ) = AAQQ*DSQRT( DMAX1( ZERO, + + ONE-AAPQ*AAPQ ) ) + MXSINJ = DMAX1( MXSINJ, SFMIN ) + ELSE + CALL DCOPY( M, A( 1, q ), 1, WORK, + + 1 ) + CALL DLASCL( 'G', 0, 0, AAQQ, ONE, + + M, 1, WORK, LDA, IERR ) + CALL DLASCL( 'G', 0, 0, AAPP, ONE, + + M, 1, A( 1, p ), LDA, + + IERR ) + TEMP1 = -AAPQ*D( q ) / D( p ) + CALL DAXPY( M, TEMP1, WORK, 1, + + A( 1, p ), 1 ) + CALL DLASCL( 'G', 0, 0, ONE, AAPP, + + M, 1, A( 1, p ), LDA, + + IERR ) + SVA( p ) = AAPP*DSQRT( DMAX1( ZERO, + + ONE-AAPQ*AAPQ ) ) + MXSINJ = DMAX1( MXSINJ, SFMIN ) + END IF + END IF * END IF ROTOK THEN ... ELSE * * In the case of cancellation in updating SVA(q) * .. recompute SVA(q) - IF ( (SVA(q) / AAQQ )**2 .LE. ROOTEPS ) THEN - IF ((AAQQ .LT. ROOTBIG).AND.(AAQQ .GT. ROOTSFMIN)) THEN - SVA(q) = DNRM2( M, A(1,q), 1 ) * D(q) - ELSE - T = ZERO - AAQQ = ZERO - CALL DLASSQ( M, A(1,q), 1, T, AAQQ ) - SVA(q) = T * DSQRT(AAQQ) * D(q) - END IF - END IF - IF ( (AAPP / AAPP0 )**2 .LE. ROOTEPS ) THEN - IF ((AAPP .LT. ROOTBIG).AND.(AAPP .GT. ROOTSFMIN)) THEN - AAPP = DNRM2( M, A(1,p), 1 ) * D(p) - ELSE - T = ZERO - AAPP = ZERO - CALL DLASSQ( M, A(1,p), 1, T, AAPP ) - AAPP = T * DSQRT(AAPP) * D(p) - END IF - SVA(p) = AAPP - END IF + IF( ( SVA( q ) / AAQQ )**2.LE.ROOTEPS ) + + THEN + IF( ( AAQQ.LT.ROOTBIG ) .AND. + + ( AAQQ.GT.ROOTSFMIN ) ) THEN + SVA( q ) = DNRM2( M, A( 1, q ), 1 )* + + D( q ) + ELSE + T = ZERO + AAQQ = ZERO + CALL DLASSQ( M, A( 1, q ), 1, T, + + AAQQ ) + SVA( q ) = T*DSQRT( AAQQ )*D( q ) + END IF + END IF + IF( ( AAPP / AAPP0 )**2.LE.ROOTEPS ) THEN + IF( ( AAPP.LT.ROOTBIG ) .AND. + + ( AAPP.GT.ROOTSFMIN ) ) THEN + AAPP = DNRM2( M, A( 1, p ), 1 )* + + D( p ) + ELSE + T = ZERO + AAPP = ZERO + CALL DLASSQ( M, A( 1, p ), 1, T, + + AAPP ) + AAPP = T*DSQRT( AAPP )*D( p ) + END IF + SVA( p ) = AAPP + END IF * end of OK rotation - ELSE - NOTROT = NOTROT + 1 - PSKIPPED = PSKIPPED + 1 - IJBLSK = IJBLSK + 1 - END IF - ELSE - NOTROT = NOTROT + 1 - PSKIPPED = PSKIPPED + 1 - IJBLSK = IJBLSK + 1 - END IF + ELSE + NOTROT = NOTROT + 1 + PSKIPPED = PSKIPPED + 1 + IJBLSK = IJBLSK + 1 + END IF + ELSE + NOTROT = NOTROT + 1 + PSKIPPED = PSKIPPED + 1 + IJBLSK = IJBLSK + 1 + END IF * - IF ( ( i .LE. SWBAND ) .AND. ( IJBLSK .GE. BLSKIP ) ) THEN - SVA(p) = AAPP - NOTROT = 0 - GO TO 2011 - END IF - IF ( ( i .LE. SWBAND ) .AND. ( PSKIPPED .GT. ROWSKIP ) ) THEN - AAPP = -AAPP - NOTROT = 0 - GO TO 2203 - END IF + IF( ( i.LE.SWBAND ) .AND. ( IJBLSK.GE.BLSKIP ) ) + + THEN + SVA( p ) = AAPP + NOTROT = 0 + GO TO 2011 + END IF + IF( ( i.LE.SWBAND ) .AND. + + ( PSKIPPED.GT.ROWSKIP ) ) THEN + AAPP = -AAPP + NOTROT = 0 + GO TO 2203 + END IF * - 2200 CONTINUE + 2200 CONTINUE * end of the q-loop - 2203 CONTINUE + 2203 CONTINUE * - SVA(p) = AAPP + SVA( p ) = AAPP * - ELSE - IF ( AAPP .EQ. ZERO ) NOTROT=NOTROT+MIN0(jgl+KBL-1,N)-jgl+1 - IF ( AAPP .LT. ZERO ) NOTROT = 0 - END IF + ELSE + IF( AAPP.EQ.ZERO )NOTROT = NOTROT + + + MIN0( jgl+KBL-1, N ) - jgl + 1 + IF( AAPP.LT.ZERO )NOTROT = 0 + END IF - 2100 CONTINUE + 2100 CONTINUE * end of the p-loop - 2010 CONTINUE + 2010 CONTINUE * end of the jbc-loop - 2011 CONTINUE + 2011 CONTINUE *2011 bailed out of the jbc-loop - DO 2012 p = igl, MIN0( igl + KBL - 1, N ) - SVA(p) = DABS(SVA(p)) - 2012 CONTINUE + DO 2012 p = igl, MIN0( igl+KBL-1, N ) + SVA( p ) = DABS( SVA( p ) ) + 2012 CONTINUE * - 2000 CONTINUE + 2000 CONTINUE *2000 :: end of the ibr-loop * * .. update SVA(N) - IF ((SVA(N) .LT. ROOTBIG).AND.(SVA(N) .GT. ROOTSFMIN)) THEN - SVA(N) = DNRM2( M, A(1,N), 1 ) * D(N) - ELSE - T = ZERO - AAPP = ZERO - CALL DLASSQ( M, A(1,N), 1, T, AAPP ) - SVA(N) = T * DSQRT(AAPP) * D(N) - END IF + IF( ( SVA( N ).LT.ROOTBIG ) .AND. ( SVA( N ).GT.ROOTSFMIN ) ) + + THEN + SVA( N ) = DNRM2( M, A( 1, N ), 1 )*D( N ) + ELSE + T = ZERO + AAPP = ZERO + CALL DLASSQ( M, A( 1, N ), 1, T, AAPP ) + SVA( N ) = T*DSQRT( AAPP )*D( N ) + END IF * * Additional steering devices * - IF ( ( i.LT.SWBAND ) .AND. ( ( MXAAPQ.LE.ROOTTOL ) .OR. - & ( ISWROT .LE. N ) ) ) - & SWBAND = i + IF( ( i.LT.SWBAND ) .AND. ( ( MXAAPQ.LE.ROOTTOL ) .OR. + + ( ISWROT.LE.N ) ) )SWBAND = i * - IF ((i.GT.SWBAND+1).AND. (MXAAPQ.LT.DBLE(N)*TOL).AND. - & (DBLE(N)*MXAAPQ*MXSINJ.LT.TOL))THEN - GO TO 1994 - END IF + IF( ( i.GT.SWBAND+1 ) .AND. ( MXAAPQ.LT.DBLE( N )*TOL ) .AND. + + ( DBLE( N )*MXAAPQ*MXSINJ.LT.TOL ) ) THEN + GO TO 1994 + END IF * - IF ( NOTROT .GE. EMPTSW ) GO TO 1994 + IF( NOTROT.GE.EMPTSW )GO TO 1994 1993 CONTINUE * end i=1:NSWEEP loop @@ -819,16 +965,16 @@ * * Sort the vector D. DO 5991 p = 1, N - 1 - q = IDAMAX( N-p+1, SVA(p), 1 ) + p - 1 - IF ( p .NE. q ) THEN - TEMP1 = SVA(p) - SVA(p) = SVA(q) - SVA(q) = TEMP1 - TEMP1 = D(p) - D(p) = D(q) - D(q) = TEMP1 - CALL DSWAP( M, A(1,p), 1, A(1,q), 1 ) - IF ( RSVEC ) CALL DSWAP( MVL, V(1,p), 1, V(1,q), 1 ) + q = IDAMAX( N-p+1, SVA( p ), 1 ) + p - 1 + IF( p.NE.q ) THEN + TEMP1 = SVA( p ) + SVA( p ) = SVA( q ) + SVA( q ) = TEMP1 + TEMP1 = D( p ) + D( p ) = D( q ) + D( q ) = TEMP1 + CALL DSWAP( M, A( 1, p ), 1, A( 1, q ), 1 ) + IF( RSVEC )CALL DSWAP( MVL, V( 1, p ), 1, V( 1, q ), 1 ) END IF 5991 CONTINUE * @@ -837,4 +983,3 @@ * .. END OF DGSVJ0 * .. END -* diff --git a/SRC/dgsvj1.f b/SRC/dgsvj1.f index ddc7a6c0..5f6a102c 100644 --- a/SRC/dgsvj1.f +++ b/SRC/dgsvj1.f @@ -1,5 +1,5 @@ SUBROUTINE DGSVJ1( JOBV, M, N, N1, A, LDA, D, SVA, MV, V, LDV, - & EPS, SFMIN, TOL, NSWEEP, WORK, LWORK, INFO ) + + EPS, SFMIN, TOL, NSWEEP, WORK, LWORK, INFO ) * * -- LAPACK routine (version 3.2) -- * @@ -15,21 +15,21 @@ * computation of SVD, PSVD, QSVD, (H,K)-SVD, and for solution of the * eigenvalue problems Hx = lambda M x, H M x = lambda x with H, M > 0. * -* -#- Scalar Arguments -#- -* - IMPLICIT NONE - DOUBLE PRECISION EPS, SFMIN, TOL - INTEGER INFO, LDA, LDV, LWORK, M, MV, N, N1, NSWEEP - CHARACTER*1 JOBV -* -* -#- Array Arguments -#- -* - DOUBLE PRECISION A( LDA, * ), D( N ), SVA( N ), V( LDV, * ), - & WORK( LWORK ) + IMPLICIT NONE +* .. +* .. Scalar Arguments .. + DOUBLE PRECISION EPS, SFMIN, TOL + INTEGER INFO, LDA, LDV, LWORK, M, MV, N, N1, NSWEEP + CHARACTER*1 JOBV +* .. +* .. Array Arguments .. + DOUBLE PRECISION A( LDA, * ), D( N ), SVA( N ), V( LDV, * ), + + WORK( LWORK ) * .. * * Purpose -* ~~~~~~~ +* ======= +* * DGSVJ1 is called from SGESVJ as a pre-processor and that is its main * purpose. It applies Jacobi rotations in the same way as SGESVJ does, but * it targets only particular pivots and it does not check convergence @@ -63,7 +63,7 @@ * Zlatko Drmac (Zagreb, Croatia) and Kresimir Veselic (Hagen, Germany) * * Arguments -* ~~~~~~~~~ +* ========= * * JOBV (input) CHARACTER*1 * Specifies whether the output from this procedure is used @@ -157,107 +157,108 @@ * = 0 : successful exit. * < 0 : if INFO = -i, then the i-th argument had an illegal value * -* -#- Local Parameters -#- -* - DOUBLE PRECISION ZERO, HALF, ONE, TWO - PARAMETER ( ZERO = 0.0D0, HALF = 0.5D0, ONE = 1.0D0, TWO = 2.0D0 ) - -* -#- Local Scalars -#- -* - DOUBLE PRECISION AAPP, AAPP0, AAPQ, AAQQ, APOAQ, AQOAP, BIG, - & BIGTHETA, CS, LARGE, MXAAPQ, MXSINJ, ROOTBIG, ROOTEPS, - & ROOTSFMIN, ROOTTOL, SMALL, SN, T, TEMP1, THETA, THSIGN - INTEGER BLSKIP, EMPTSW, i, ibr, igl, IERR, IJBLSK, ISWROT, jbc, - & jgl, KBL, MVL, NOTROT, nblc, nblr, p, PSKIPPED, q, - & ROWSKIP, SWBAND - LOGICAL APPLV, ROTOK, RSVEC -* -* Local Arrays -* - DOUBLE PRECISION FASTR(5) -* -* Intrinsic Functions -* - INTRINSIC DABS, DMAX1, DBLE, MIN0, DSIGN, DSQRT -* -* External Functions -* - DOUBLE PRECISION DDOT, DNRM2 - INTEGER IDAMAX - LOGICAL LSAME - EXTERNAL IDAMAX, LSAME, DDOT, DNRM2 +* ===================================================================== * -* External Subroutines -* - EXTERNAL DAXPY, DCOPY, DLASCL, DLASSQ, DROTM, DSWAP +* .. Local Parameters .. + DOUBLE PRECISION ZERO, HALF, ONE, TWO + PARAMETER ( ZERO = 0.0D0, HALF = 0.5D0, ONE = 1.0D0, + + TWO = 2.0D0 ) +* .. +* .. Local Scalars .. + DOUBLE PRECISION AAPP, AAPP0, AAPQ, AAQQ, APOAQ, AQOAP, BIG, + + BIGTHETA, CS, LARGE, MXAAPQ, MXSINJ, ROOTBIG, + + ROOTEPS, ROOTSFMIN, ROOTTOL, SMALL, SN, T, + + TEMP1, THETA, THSIGN + INTEGER BLSKIP, EMPTSW, i, ibr, igl, IERR, IJBLSK, + + ISWROT, jbc, jgl, KBL, MVL, NOTROT, nblc, nblr, + + p, PSKIPPED, q, ROWSKIP, SWBAND + LOGICAL APPLV, ROTOK, RSVEC +* .. +* .. Local Arrays .. + DOUBLE PRECISION FASTR( 5 ) +* .. +* .. Intrinsic Functions .. + INTRINSIC DABS, DMAX1, DBLE, MIN0, DSIGN, DSQRT +* .. +* .. External Functions .. + DOUBLE PRECISION DDOT, DNRM2 + INTEGER IDAMAX + LOGICAL LSAME + EXTERNAL IDAMAX, LSAME, DDOT, DNRM2 +* .. +* .. External Subroutines .. + EXTERNAL DAXPY, DCOPY, DLASCL, DLASSQ, DROTM, DSWAP +* .. +* .. Executable Statements .. * +* Test the input parameters. * - APPLV = LSAME(JOBV,'A') - RSVEC = LSAME(JOBV,'V') - IF ( .NOT.( RSVEC .OR. APPLV .OR. LSAME(JOBV,'N'))) THEN + APPLV = LSAME( JOBV, 'A' ) + RSVEC = LSAME( JOBV, 'V' ) + IF( .NOT.( RSVEC .OR. APPLV .OR. LSAME( JOBV, 'N' ) ) ) THEN INFO = -1 - ELSE IF ( M .LT. 0 ) THEN + ELSE IF( M.LT.0 ) THEN INFO = -2 - ELSE IF ( ( N .LT. 0 ) .OR. ( N .GT. M )) THEN + ELSE IF( ( N.LT.0 ) .OR. ( N.GT.M ) ) THEN INFO = -3 - ELSE IF ( N1 .LT. 0 ) THEN + ELSE IF( N1.LT.0 ) THEN INFO = -4 - ELSE IF ( LDA .LT. M ) THEN + ELSE IF( LDA.LT.M ) THEN INFO = -6 - ELSE IF ( MV .LT. 0 ) THEN + ELSE IF( MV.LT.0 ) THEN INFO = -9 - ELSE IF ( LDV .LT. M ) THEN + ELSE IF( LDV.LT.M ) THEN INFO = -11 - ELSE IF ( TOL .LE. EPS ) THEN + ELSE IF( TOL.LE.EPS ) THEN INFO = -14 - ELSE IF ( NSWEEP .LT. 0 ) THEN + ELSE IF( NSWEEP.LT.0 ) THEN INFO = -15 - ELSE IF ( LWORK .LT. M ) THEN + ELSE IF( LWORK.LT.M ) THEN INFO = -17 ELSE INFO = 0 END IF * * #:( - IF ( INFO .NE. 0 ) THEN + IF( INFO.NE.0 ) THEN CALL XERBLA( 'DGSVJ1', -INFO ) RETURN END IF * - IF ( RSVEC ) THEN + IF( RSVEC ) THEN MVL = N - ELSE IF ( APPLV ) THEN + ELSE IF( APPLV ) THEN MVL = MV END IF RSVEC = RSVEC .OR. APPLV - ROOTEPS = DSQRT(EPS) - ROOTSFMIN = DSQRT(SFMIN) - SMALL = SFMIN / EPS - BIG = ONE / SFMIN - ROOTBIG = ONE / ROOTSFMIN - LARGE = BIG / DSQRT(DBLE(M*N)) - BIGTHETA = ONE / ROOTEPS - ROOTTOL = DSQRT(TOL) + ROOTEPS = DSQRT( EPS ) + ROOTSFMIN = DSQRT( SFMIN ) + SMALL = SFMIN / EPS + BIG = ONE / SFMIN + ROOTBIG = ONE / ROOTSFMIN + LARGE = BIG / DSQRT( DBLE( M*N ) ) + BIGTHETA = ONE / ROOTEPS + ROOTTOL = DSQRT( TOL ) * -* -#- Initialize the right singular vector matrix -#- +* .. Initialize the right singular vector matrix .. * * RSVEC = LSAME( JOBV, 'Y' ) * - EMPTSW = N1 * ( N - N1 ) - NOTROT = 0 - FASTR(1) = ZERO + EMPTSW = N1*( N-N1 ) + NOTROT = 0 + FASTR( 1 ) = ZERO * -* -#- Row-cyclic pivot strategy with de Rijk's pivoting -#- +* .. Row-cyclic pivot strategy with de Rijk's pivoting .. * - KBL = MIN0(8,N) + KBL = MIN0( 8, N ) NBLR = N1 / KBL - IF ( ( NBLR * KBL ) .NE. N1 ) NBLR = NBLR + 1 + IF( ( NBLR*KBL ).NE.N1 )NBLR = NBLR + 1 * .. the tiling is nblr-by-nblc [tiles] - NBLC = ( N - N1 ) / KBL - IF ( ( NBLC * KBL ) .NE. ( N - N1 ) ) NBLC = NBLC + 1 + NBLC = ( N-N1 ) / KBL + IF( ( NBLC*KBL ).NE.( N-N1 ) )NBLC = NBLC + 1 BLSKIP = ( KBL**2 ) + 1 *[TP] BLKSKIP is a tuning parameter that depends on SWBAND and KBL. @@ -280,298 +281,377 @@ DO 1993 i = 1, NSWEEP * .. go go go ... * - MXAAPQ = ZERO - MXSINJ = ZERO - ISWROT = 0 + MXAAPQ = ZERO + MXSINJ = ZERO + ISWROT = 0 * - NOTROT = 0 - PSKIPPED = 0 + NOTROT = 0 + PSKIPPED = 0 * - DO 2000 ibr = 1, NBLR + DO 2000 ibr = 1, NBLR - igl = ( ibr - 1 ) * KBL + 1 + igl = ( ibr-1 )*KBL + 1 * * *........................................................ * ... go to the off diagonal blocks - igl = ( ibr - 1 ) * KBL + 1 + igl = ( ibr-1 )*KBL + 1 - DO 2010 jbc = 1, NBLC + DO 2010 jbc = 1, NBLC - jgl = N1 + ( jbc - 1 ) * KBL + 1 + jgl = N1 + ( jbc-1 )*KBL + 1 * doing the block at ( ibr, jbc ) - IJBLSK = 0 - DO 2100 p = igl, MIN0( igl + KBL - 1, N1 ) + IJBLSK = 0 + DO 2100 p = igl, MIN0( igl+KBL-1, N1 ) - AAPP = SVA(p) + AAPP = SVA( p ) - IF ( AAPP .GT. ZERO ) THEN + IF( AAPP.GT.ZERO ) THEN - PSKIPPED = 0 + PSKIPPED = 0 - DO 2200 q = jgl, MIN0( jgl + KBL - 1, N ) + DO 2200 q = jgl, MIN0( jgl+KBL-1, N ) * - AAQQ = SVA(q) + AAQQ = SVA( q ) - IF ( AAQQ .GT. ZERO ) THEN - AAPP0 = AAPP -* -* -#- M x 2 Jacobi SVD -#- -* -* -#- Safe Gram matrix computation -#- -* - IF ( AAQQ .GE. ONE ) THEN - IF ( AAPP .GE. AAQQ ) THEN - ROTOK = ( SMALL*AAPP ) .LE. AAQQ - ELSE - ROTOK = ( SMALL*AAQQ ) .LE. AAPP - END IF - IF ( AAPP .LT. ( BIG / AAQQ ) ) THEN - AAPQ = ( DDOT(M, A(1,p), 1, A(1,q), 1 ) * - & D(p) * D(q) / AAQQ ) / AAPP - ELSE - CALL DCOPY( M, A(1,p), 1, WORK, 1 ) - CALL DLASCL( 'G', 0, 0, AAPP, D(p), M, - & 1, WORK, LDA, IERR ) - AAPQ = DDOT( M, WORK, 1, A(1,q), 1 ) * - & D(q) / AAQQ - END IF - ELSE - IF ( AAPP .GE. AAQQ ) THEN - ROTOK = AAPP .LE. ( AAQQ / SMALL ) - ELSE - ROTOK = AAQQ .LE. ( AAPP / SMALL ) - END IF - IF ( AAPP .GT. ( SMALL / AAQQ ) ) THEN - AAPQ = ( DDOT( M, A(1,p), 1, A(1,q), 1 ) * - & D(p) * D(q) / AAQQ ) / AAPP - ELSE - CALL DCOPY( M, A(1,q), 1, WORK, 1 ) - CALL DLASCL( 'G', 0, 0, AAQQ, D(q), M, 1, - & WORK, LDA, IERR ) - AAPQ = DDOT(M,WORK,1,A(1,p),1) * D(p) / AAPP - END IF - END IF + IF( AAQQ.GT.ZERO ) THEN + AAPP0 = AAPP +* +* .. M x 2 Jacobi SVD .. +* +* .. Safe Gram matrix computation .. +* + IF( AAQQ.GE.ONE ) THEN + IF( AAPP.GE.AAQQ ) THEN + ROTOK = ( SMALL*AAPP ).LE.AAQQ + ELSE + ROTOK = ( SMALL*AAQQ ).LE.AAPP + END IF + IF( AAPP.LT.( BIG / AAQQ ) ) THEN + AAPQ = ( DDOT( M, A( 1, p ), 1, A( 1, + + q ), 1 )*D( p )*D( q ) / AAQQ ) + + / AAPP + ELSE + CALL DCOPY( M, A( 1, p ), 1, WORK, 1 ) + CALL DLASCL( 'G', 0, 0, AAPP, D( p ), + + M, 1, WORK, LDA, IERR ) + AAPQ = DDOT( M, WORK, 1, A( 1, q ), + + 1 )*D( q ) / AAQQ + END IF + ELSE + IF( AAPP.GE.AAQQ ) THEN + ROTOK = AAPP.LE.( AAQQ / SMALL ) + ELSE + ROTOK = AAQQ.LE.( AAPP / SMALL ) + END IF + IF( AAPP.GT.( SMALL / AAQQ ) ) THEN + AAPQ = ( DDOT( M, A( 1, p ), 1, A( 1, + + q ), 1 )*D( p )*D( q ) / AAQQ ) + + / AAPP + ELSE + CALL DCOPY( M, A( 1, q ), 1, WORK, 1 ) + CALL DLASCL( 'G', 0, 0, AAQQ, D( q ), + + M, 1, WORK, LDA, IERR ) + AAPQ = DDOT( M, WORK, 1, A( 1, p ), + + 1 )*D( p ) / AAPP + END IF + END IF - MXAAPQ = DMAX1( MXAAPQ, DABS(AAPQ) ) + MXAAPQ = DMAX1( MXAAPQ, DABS( AAPQ ) ) * TO rotate or NOT to rotate, THAT is the question ... * - IF ( DABS( AAPQ ) .GT. TOL ) THEN - NOTROT = 0 + IF( DABS( AAPQ ).GT.TOL ) THEN + NOTROT = 0 * ROTATED = ROTATED + 1 - PSKIPPED = 0 - ISWROT = ISWROT + 1 + PSKIPPED = 0 + ISWROT = ISWROT + 1 * - IF ( ROTOK ) THEN + IF( ROTOK ) THEN * - AQOAP = AAQQ / AAPP - APOAQ = AAPP / AAQQ - THETA = - HALF * DABS( AQOAP - APOAQ ) / AAPQ - IF ( AAQQ .GT. AAPP0 ) THETA = - THETA + AQOAP = AAQQ / AAPP + APOAQ = AAPP / AAQQ + THETA = -HALF*DABS( AQOAP-APOAQ ) / + + AAPQ + IF( AAQQ.GT.AAPP0 )THETA = -THETA - IF ( DABS( THETA ) .GT. BIGTHETA ) THEN - T = HALF / THETA - FASTR(3) = T * D(p) / D(q) - FASTR(4) = -T * D(q) / D(p) - CALL DROTM( M, A(1,p), 1, A(1,q), 1, FASTR ) - IF ( RSVEC ) - & CALL DROTM( MVL, V(1,p), 1, V(1,q), 1, FASTR ) - SVA(q) = AAQQ*DSQRT( DMAX1(ZERO,ONE + T*APOAQ*AAPQ) ) - AAPP = AAPP*DSQRT( DMAX1(ZERO,ONE - T*AQOAP*AAPQ) ) - MXSINJ = DMAX1( MXSINJ, DABS(T) ) - ELSE + IF( DABS( THETA ).GT.BIGTHETA ) THEN + T = HALF / THETA + FASTR( 3 ) = T*D( p ) / D( q ) + FASTR( 4 ) = -T*D( q ) / D( p ) + CALL DROTM( M, A( 1, p ), 1, + + A( 1, q ), 1, FASTR ) + IF( RSVEC )CALL DROTM( MVL, + + V( 1, p ), 1, + + V( 1, q ), 1, + + FASTR ) + SVA( q ) = AAQQ*DSQRT( DMAX1( ZERO, + + ONE+T*APOAQ*AAPQ ) ) + AAPP = AAPP*DSQRT( DMAX1( ZERO, + + ONE-T*AQOAP*AAPQ ) ) + MXSINJ = DMAX1( MXSINJ, DABS( T ) ) + ELSE * * .. choose correct signum for THETA and rotate * - THSIGN = - DSIGN(ONE,AAPQ) - IF ( AAQQ .GT. AAPP0 ) THSIGN = - THSIGN - T = ONE / ( THETA + THSIGN*DSQRT(ONE+THETA*THETA) ) - CS = DSQRT( ONE / ( ONE + T*T ) ) - SN = T * CS - MXSINJ = DMAX1( MXSINJ, DABS(SN) ) - SVA(q) = AAQQ*DSQRT( DMAX1(ZERO, ONE+T*APOAQ*AAPQ) ) - AAPP = AAPP*DSQRT( ONE - T*AQOAP*AAPQ) + THSIGN = -DSIGN( ONE, AAPQ ) + IF( AAQQ.GT.AAPP0 )THSIGN = -THSIGN + T = ONE / ( THETA+THSIGN* + + DSQRT( ONE+THETA*THETA ) ) + CS = DSQRT( ONE / ( ONE+T*T ) ) + SN = T*CS + MXSINJ = DMAX1( MXSINJ, DABS( SN ) ) + SVA( q ) = AAQQ*DSQRT( DMAX1( ZERO, + + ONE+T*APOAQ*AAPQ ) ) + AAPP = AAPP*DSQRT( ONE-T*AQOAP* + + AAPQ ) - APOAQ = D(p) / D(q) - AQOAP = D(q) / D(p) - IF ( D(p) .GE. ONE ) THEN -* - IF ( D(q) .GE. ONE ) THEN - FASTR(3) = T * APOAQ - FASTR(4) = - T * AQOAP - D(p) = D(p) * CS - D(q) = D(q) * CS - CALL DROTM( M, A(1,p),1, A(1,q),1, FASTR ) - IF ( RSVEC ) - & CALL DROTM( MVL, V(1,p),1, V(1,q),1, FASTR ) - ELSE - CALL DAXPY( M, -T*AQOAP, A(1,q),1, A(1,p),1 ) - CALL DAXPY( M, CS*SN*APOAQ, A(1,p),1, A(1,q),1 ) - IF ( RSVEC ) THEN - CALL DAXPY( MVL, -T*AQOAP, V(1,q),1, V(1,p),1 ) - CALL DAXPY( MVL,CS*SN*APOAQ,V(1,p),1, V(1,q),1 ) - END IF - D(p) = D(p) * CS - D(q) = D(q) / CS - END IF - ELSE - IF ( D(q) .GE. ONE ) THEN - CALL DAXPY( M, T*APOAQ, A(1,p),1, A(1,q),1 ) - CALL DAXPY( M,-CS*SN*AQOAP, A(1,q),1, A(1,p),1 ) - IF ( RSVEC ) THEN - CALL DAXPY(MVL,T*APOAQ, V(1,p),1, V(1,q),1 ) - CALL DAXPY(MVL,-CS*SN*AQOAP,V(1,q),1, V(1,p),1 ) - END IF - D(p) = D(p) / CS - D(q) = D(q) * CS - ELSE - IF ( D(p) .GE. D(q) ) THEN - CALL DAXPY( M,-T*AQOAP, A(1,q),1,A(1,p),1 ) - CALL DAXPY( M,CS*SN*APOAQ,A(1,p),1,A(1,q),1 ) - D(p) = D(p) * CS - D(q) = D(q) / CS - IF ( RSVEC ) THEN - CALL DAXPY( MVL, -T*AQOAP, V(1,q),1,V(1,p),1) - CALL DAXPY(MVL,CS*SN*APOAQ,V(1,p),1,V(1,q),1) - END IF - ELSE - CALL DAXPY(M, T*APOAQ, A(1,p),1,A(1,q),1) - CALL DAXPY(M,-CS*SN*AQOAP,A(1,q),1,A(1,p),1) - D(p) = D(p) / CS - D(q) = D(q) * CS - IF ( RSVEC ) THEN - CALL DAXPY(MVL, T*APOAQ, V(1,p),1,V(1,q),1) - CALL DAXPY(MVL,-CS*SN*AQOAP,V(1,q),1,V(1,p),1) - END IF - END IF - END IF - ENDIF - END IF + APOAQ = D( p ) / D( q ) + AQOAP = D( q ) / D( p ) + IF( D( p ).GE.ONE ) THEN +* + IF( D( q ).GE.ONE ) THEN + FASTR( 3 ) = T*APOAQ + FASTR( 4 ) = -T*AQOAP + D( p ) = D( p )*CS + D( q ) = D( q )*CS + CALL DROTM( M, A( 1, p ), 1, + + A( 1, q ), 1, + + FASTR ) + IF( RSVEC )CALL DROTM( MVL, + + V( 1, p ), 1, V( 1, q ), + + 1, FASTR ) + ELSE + CALL DAXPY( M, -T*AQOAP, + + A( 1, q ), 1, + + A( 1, p ), 1 ) + CALL DAXPY( M, CS*SN*APOAQ, + + A( 1, p ), 1, + + A( 1, q ), 1 ) + IF( RSVEC ) THEN + CALL DAXPY( MVL, -T*AQOAP, + + V( 1, q ), 1, + + V( 1, p ), 1 ) + CALL DAXPY( MVL, + + CS*SN*APOAQ, + + V( 1, p ), 1, + + V( 1, q ), 1 ) + END IF + D( p ) = D( p )*CS + D( q ) = D( q ) / CS + END IF + ELSE + IF( D( q ).GE.ONE ) THEN + CALL DAXPY( M, T*APOAQ, + + A( 1, p ), 1, + + A( 1, q ), 1 ) + CALL DAXPY( M, -CS*SN*AQOAP, + + A( 1, q ), 1, + + A( 1, p ), 1 ) + IF( RSVEC ) THEN + CALL DAXPY( MVL, T*APOAQ, + + V( 1, p ), 1, + + V( 1, q ), 1 ) + CALL DAXPY( MVL, + + -CS*SN*AQOAP, + + V( 1, q ), 1, + + V( 1, p ), 1 ) + END IF + D( p ) = D( p ) / CS + D( q ) = D( q )*CS + ELSE + IF( D( p ).GE.D( q ) ) THEN + CALL DAXPY( M, -T*AQOAP, + + A( 1, q ), 1, + + A( 1, p ), 1 ) + CALL DAXPY( M, CS*SN*APOAQ, + + A( 1, p ), 1, + + A( 1, q ), 1 ) + D( p ) = D( p )*CS + D( q ) = D( q ) / CS + IF( RSVEC ) THEN + CALL DAXPY( MVL, + + -T*AQOAP, + + V( 1, q ), 1, + + V( 1, p ), 1 ) + CALL DAXPY( MVL, + + CS*SN*APOAQ, + + V( 1, p ), 1, + + V( 1, q ), 1 ) + END IF + ELSE + CALL DAXPY( M, T*APOAQ, + + A( 1, p ), 1, + + A( 1, q ), 1 ) + CALL DAXPY( M, + + -CS*SN*AQOAP, + + A( 1, q ), 1, + + A( 1, p ), 1 ) + D( p ) = D( p ) / CS + D( q ) = D( q )*CS + IF( RSVEC ) THEN + CALL DAXPY( MVL, + + T*APOAQ, V( 1, p ), + + 1, V( 1, q ), 1 ) + CALL DAXPY( MVL, + + -CS*SN*AQOAP, + + V( 1, q ), 1, + + V( 1, p ), 1 ) + END IF + END IF + END IF + END IF + END IF - ELSE - IF ( AAPP .GT. AAQQ ) THEN - CALL DCOPY( M, A(1,p), 1, WORK, 1 ) - CALL DLASCL('G',0,0,AAPP,ONE,M,1,WORK,LDA,IERR) - CALL DLASCL('G',0,0,AAQQ,ONE,M,1, A(1,q),LDA,IERR) - TEMP1 = -AAPQ * D(p) / D(q) - CALL DAXPY(M,TEMP1,WORK,1,A(1,q),1) - CALL DLASCL('G',0,0,ONE,AAQQ,M,1,A(1,q),LDA,IERR) - SVA(q) = AAQQ*DSQRT(DMAX1(ZERO, ONE - AAPQ*AAPQ)) - MXSINJ = DMAX1( MXSINJ, SFMIN ) - ELSE - CALL DCOPY( M, A(1,q), 1, WORK, 1 ) - CALL DLASCL('G',0,0,AAQQ,ONE,M,1,WORK,LDA,IERR) - CALL DLASCL('G',0,0,AAPP,ONE,M,1, A(1,p),LDA,IERR) - TEMP1 = -AAPQ * D(q) / D(p) - CALL DAXPY(M,TEMP1,WORK,1,A(1,p),1) - CALL DLASCL('G',0,0,ONE,AAPP,M,1,A(1,p),LDA,IERR) - SVA(p) = AAPP*DSQRT(DMAX1(ZERO, ONE - AAPQ*AAPQ)) - MXSINJ = DMAX1( MXSINJ, SFMIN ) - END IF - END IF + ELSE + IF( AAPP.GT.AAQQ ) THEN + CALL DCOPY( M, A( 1, p ), 1, WORK, + + 1 ) + CALL DLASCL( 'G', 0, 0, AAPP, ONE, + + M, 1, WORK, LDA, IERR ) + CALL DLASCL( 'G', 0, 0, AAQQ, ONE, + + M, 1, A( 1, q ), LDA, + + IERR ) + TEMP1 = -AAPQ*D( p ) / D( q ) + CALL DAXPY( M, TEMP1, WORK, 1, + + A( 1, q ), 1 ) + CALL DLASCL( 'G', 0, 0, ONE, AAQQ, + + M, 1, A( 1, q ), LDA, + + IERR ) + SVA( q ) = AAQQ*DSQRT( DMAX1( ZERO, + + ONE-AAPQ*AAPQ ) ) + MXSINJ = DMAX1( MXSINJ, SFMIN ) + ELSE + CALL DCOPY( M, A( 1, q ), 1, WORK, + + 1 ) + CALL DLASCL( 'G', 0, 0, AAQQ, ONE, + + M, 1, WORK, LDA, IERR ) + CALL DLASCL( 'G', 0, 0, AAPP, ONE, + + M, 1, A( 1, p ), LDA, + + IERR ) + TEMP1 = -AAPQ*D( q ) / D( p ) + CALL DAXPY( M, TEMP1, WORK, 1, + + A( 1, p ), 1 ) + CALL DLASCL( 'G', 0, 0, ONE, AAPP, + + M, 1, A( 1, p ), LDA, + + IERR ) + SVA( p ) = AAPP*DSQRT( DMAX1( ZERO, + + ONE-AAPQ*AAPQ ) ) + MXSINJ = DMAX1( MXSINJ, SFMIN ) + END IF + END IF * END IF ROTOK THEN ... ELSE * * In the case of cancellation in updating SVA(q) * .. recompute SVA(q) - IF ( (SVA(q) / AAQQ )**2 .LE. ROOTEPS ) THEN - IF ((AAQQ .LT. ROOTBIG).AND.(AAQQ .GT. ROOTSFMIN)) THEN - SVA(q) = DNRM2( M, A(1,q), 1 ) * D(q) - ELSE - T = ZERO - AAQQ = ZERO - CALL DLASSQ( M, A(1,q), 1, T, AAQQ ) - SVA(q) = T * DSQRT(AAQQ) * D(q) - END IF - END IF - IF ( (AAPP / AAPP0 )**2 .LE. ROOTEPS ) THEN - IF ((AAPP .LT. ROOTBIG).AND.(AAPP .GT. ROOTSFMIN)) THEN - AAPP = DNRM2( M, A(1,p), 1 ) * D(p) - ELSE - T = ZERO - AAPP = ZERO - CALL DLASSQ( M, A(1,p), 1, T, AAPP ) - AAPP = T * DSQRT(AAPP) * D(p) - END IF - SVA(p) = AAPP - END IF + IF( ( SVA( q ) / AAQQ )**2.LE.ROOTEPS ) + + THEN + IF( ( AAQQ.LT.ROOTBIG ) .AND. + + ( AAQQ.GT.ROOTSFMIN ) ) THEN + SVA( q ) = DNRM2( M, A( 1, q ), 1 )* + + D( q ) + ELSE + T = ZERO + AAQQ = ZERO + CALL DLASSQ( M, A( 1, q ), 1, T, + + AAQQ ) + SVA( q ) = T*DSQRT( AAQQ )*D( q ) + END IF + END IF + IF( ( AAPP / AAPP0 )**2.LE.ROOTEPS ) THEN + IF( ( AAPP.LT.ROOTBIG ) .AND. + + ( AAPP.GT.ROOTSFMIN ) ) THEN + AAPP = DNRM2( M, A( 1, p ), 1 )* + + D( p ) + ELSE + T = ZERO + AAPP = ZERO + CALL DLASSQ( M, A( 1, p ), 1, T, + + AAPP ) + AAPP = T*DSQRT( AAPP )*D( p ) + END IF + SVA( p ) = AAPP + END IF * end of OK rotation - ELSE - NOTROT = NOTROT + 1 + ELSE + NOTROT = NOTROT + 1 * SKIPPED = SKIPPED + 1 - PSKIPPED = PSKIPPED + 1 - IJBLSK = IJBLSK + 1 - END IF - ELSE - NOTROT = NOTROT + 1 - PSKIPPED = PSKIPPED + 1 - IJBLSK = IJBLSK + 1 - END IF + PSKIPPED = PSKIPPED + 1 + IJBLSK = IJBLSK + 1 + END IF + ELSE + NOTROT = NOTROT + 1 + PSKIPPED = PSKIPPED + 1 + IJBLSK = IJBLSK + 1 + END IF * IF ( NOTROT .GE. EMPTSW ) GO TO 2011 - IF ( ( i .LE. SWBAND ) .AND. ( IJBLSK .GE. BLSKIP ) ) THEN - SVA(p) = AAPP - NOTROT = 0 - GO TO 2011 - END IF - IF ( ( i .LE. SWBAND ) .AND. ( PSKIPPED .GT. ROWSKIP ) ) THEN - AAPP = -AAPP - NOTROT = 0 - GO TO 2203 - END IF + IF( ( i.LE.SWBAND ) .AND. ( IJBLSK.GE.BLSKIP ) ) + + THEN + SVA( p ) = AAPP + NOTROT = 0 + GO TO 2011 + END IF + IF( ( i.LE.SWBAND ) .AND. + + ( PSKIPPED.GT.ROWSKIP ) ) THEN + AAPP = -AAPP + NOTROT = 0 + GO TO 2203 + END IF * - 2200 CONTINUE + 2200 CONTINUE * end of the q-loop - 2203 CONTINUE + 2203 CONTINUE - SVA(p) = AAPP + SVA( p ) = AAPP * - ELSE - IF ( AAPP .EQ. ZERO ) NOTROT=NOTROT+MIN0(jgl+KBL-1,N)-jgl+1 - IF ( AAPP .LT. ZERO ) NOTROT = 0 + ELSE + IF( AAPP.EQ.ZERO )NOTROT = NOTROT + + + MIN0( jgl+KBL-1, N ) - jgl + 1 + IF( AAPP.LT.ZERO )NOTROT = 0 *** IF ( NOTROT .GE. EMPTSW ) GO TO 2011 - END IF + END IF - 2100 CONTINUE + 2100 CONTINUE * end of the p-loop - 2010 CONTINUE + 2010 CONTINUE * end of the jbc-loop - 2011 CONTINUE + 2011 CONTINUE *2011 bailed out of the jbc-loop - DO 2012 p = igl, MIN0( igl + KBL - 1, N ) - SVA(p) = DABS(SVA(p)) - 2012 CONTINUE + DO 2012 p = igl, MIN0( igl+KBL-1, N ) + SVA( p ) = DABS( SVA( p ) ) + 2012 CONTINUE *** IF ( NOTROT .GE. EMPTSW ) GO TO 1994 - 2000 CONTINUE + 2000 CONTINUE *2000 :: end of the ibr-loop * * .. update SVA(N) - IF ((SVA(N) .LT. ROOTBIG).AND.(SVA(N) .GT. ROOTSFMIN)) THEN - SVA(N) = DNRM2( M, A(1,N), 1 ) * D(N) - ELSE - T = ZERO - AAPP = ZERO - CALL DLASSQ( M, A(1,N), 1, T, AAPP ) - SVA(N) = T * DSQRT(AAPP) * D(N) - END IF + IF( ( SVA( N ).LT.ROOTBIG ) .AND. ( SVA( N ).GT.ROOTSFMIN ) ) + + THEN + SVA( N ) = DNRM2( M, A( 1, N ), 1 )*D( N ) + ELSE + T = ZERO + AAPP = ZERO + CALL DLASSQ( M, A( 1, N ), 1, T, AAPP ) + SVA( N ) = T*DSQRT( AAPP )*D( N ) + END IF * * Additional steering devices * - IF ( ( i.LT.SWBAND ) .AND. ( ( MXAAPQ.LE.ROOTTOL ) .OR. - & ( ISWROT .LE. N ) ) ) - & SWBAND = i + IF( ( i.LT.SWBAND ) .AND. ( ( MXAAPQ.LE.ROOTTOL ) .OR. + + ( ISWROT.LE.N ) ) )SWBAND = i - IF ((i.GT.SWBAND+1).AND. (MXAAPQ.LT.DBLE(N)*TOL).AND. - & (DBLE(N)*MXAAPQ*MXSINJ.LT.TOL))THEN - GO TO 1994 - END IF + IF( ( i.GT.SWBAND+1 ) .AND. ( MXAAPQ.LT.DBLE( N )*TOL ) .AND. + + ( DBLE( N )*MXAAPQ*MXSINJ.LT.TOL ) ) THEN + GO TO 1994 + END IF * - IF ( NOTROT .GE. EMPTSW ) GO TO 1994 + IF( NOTROT.GE.EMPTSW )GO TO 1994 1993 CONTINUE * end i=1:NSWEEP loop @@ -590,16 +670,16 @@ * Sort the vector D * DO 5991 p = 1, N - 1 - q = IDAMAX( N-p+1, SVA(p), 1 ) + p - 1 - IF ( p .NE. q ) THEN - TEMP1 = SVA(p) - SVA(p) = SVA(q) - SVA(q) = TEMP1 - TEMP1 = D(p) - D(p) = D(q) - D(q) = TEMP1 - CALL DSWAP( M, A(1,p), 1, A(1,q), 1 ) - IF ( RSVEC ) CALL DSWAP( MVL, V(1,p), 1, V(1,q), 1 ) + q = IDAMAX( N-p+1, SVA( p ), 1 ) + p - 1 + IF( p.NE.q ) THEN + TEMP1 = SVA( p ) + SVA( p ) = SVA( q ) + SVA( q ) = TEMP1 + TEMP1 = D( p ) + D( p ) = D( q ) + D( q ) = TEMP1 + CALL DSWAP( M, A( 1, p ), 1, A( 1, q ), 1 ) + IF( RSVEC )CALL DSWAP( MVL, V( 1, p ), 1, V( 1, q ), 1 ) END IF 5991 CONTINUE * @@ -608,4 +688,3 @@ * .. END OF DGSVJ1 * .. END -* diff --git a/SRC/dla_gbamv.f b/SRC/dla_gbamv.f index 36a223a4..cab0a645 100644 --- a/SRC/dla_gbamv.f +++ b/SRC/dla_gbamv.f @@ -39,7 +39,7 @@ * entry is considered "symbolic" if all multiplications involved * in computing that entry have at least one zero multiplicand. * -* Parameters +* Arguments * ========== * * TRANS - INTEGER @@ -116,7 +116,9 @@ * * * Level 2 Blas routine. -* .. +* +* ===================================================================== +* * .. Parameters .. DOUBLE PRECISION ONE, ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) diff --git a/SRC/dla_gbrcond.f b/SRC/dla_gbrcond.f index fd57665a..904e50af 100644 --- a/SRC/dla_gbrcond.f +++ b/SRC/dla_gbrcond.f @@ -20,6 +20,10 @@ INTEGER IWORK( * ), IPIV( * ) DOUBLE PRECISION AB( LDAB, * ), AFB( LDAFB, * ), WORK( * ), $ C( * ) +* .. +* +* Purpose +* ======= * * DLA_GERCOND Estimates the Skeel condition number of op(A) * op2(C) * where op2 is determined by CMODE as follows @@ -30,9 +34,16 @@ * is computed by computing scaling factors R such that * diag(R)*A*op2(C) is row equilibrated and computing the standard * infinity-norm condition number. -* WORK is a double precision workspace of size 5*N, and -* IWORK is an integer workspace of size N. -* .. +* +* Arguments +* ========= +* +* WORK double precision workspace of size 5*N. +* +* IWORK integer workspace of size N. +* +* ===================================================================== +* * .. Local Scalars .. LOGICAL NOTRANS INTEGER KASE, I, J, KD diff --git a/SRC/dla_gbrfsx_extended.f b/SRC/dla_gbrfsx_extended.f index e747c8a7..e3bb0f1a 100644 --- a/SRC/dla_gbrfsx_extended.f +++ b/SRC/dla_gbrfsx_extended.f @@ -29,6 +29,9 @@ DOUBLE PRECISION C( * ), AYB(*), RCOND, BERR_OUT(*), $ ERRS_N( NRHS, * ), ERRS_C( NRHS, * ) * .. +* +* ===================================================================== +* * .. Local Scalars .. CHARACTER TRANS INTEGER CNT, I, J, M, X_STATE, Z_STATE, Y_PREC_STATE diff --git a/SRC/dla_gbrpvgrw.f b/SRC/dla_gbrpvgrw.f index b233b683..eea53feb 100644 --- a/SRC/dla_gbrpvgrw.f +++ b/SRC/dla_gbrpvgrw.f @@ -17,6 +17,9 @@ * .. Array Arguments .. DOUBLE PRECISION AB( LDAB, * ), AFB( LDAFB, * ) * .. +* +* ===================================================================== +* * .. Local Scalars .. INTEGER I, J, KD DOUBLE PRECISION AMAX, UMAX, RPVGRW diff --git a/SRC/dla_geamv.f b/SRC/dla_geamv.f index 6c042c03..ca82a8e5 100644 --- a/SRC/dla_geamv.f +++ b/SRC/dla_geamv.f @@ -39,7 +39,7 @@ * entry is considered "symbolic" if all multiplications involved * in computing that entry have at least one zero multiplicand. * -* Parameters +* Arguments * ========== * * TRANS - INTEGER @@ -111,7 +111,8 @@ * * Level 2 Blas routine. * -* .. +* ===================================================================== +* * .. Parameters .. DOUBLE PRECISION ONE, ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) diff --git a/SRC/dla_gercond.f b/SRC/dla_gercond.f index cb75a97e..de7ef9d2 100644 --- a/SRC/dla_gercond.f +++ b/SRC/dla_gercond.f @@ -20,6 +20,10 @@ INTEGER IPIV( * ), IWORK( * ) DOUBLE PRECISION A( LDA, * ), AF( LDAF, * ), WORK( * ), $ C( * ) +* .. +* +* Purpose +* ======= * * DLA_GERCOND estimates the Skeel condition number of op(A) * op2(C) * where op2 is determined by CMODE as follows @@ -30,9 +34,16 @@ * is computed by computing scaling factors R such that * diag(R)*A*op2(C) is row equilibrated and computing the standard * infinity-norm condition number. -* WORK is a DOUBLE PRECISION workspace of size 3*N, and -* IWORK is an INTEGER workspace of size N. -* .. +* +* Arguments +* ========== +* +* WORK DOUBLE PRECISION workspace of size 3*N, and +* +* IWORK INTEGER workspace of size N. +* +* ===================================================================== +* * .. Local Scalars .. LOGICAL NOTRANS INTEGER KASE, I, J diff --git a/SRC/dla_gerfsx_extended.f b/SRC/dla_gerfsx_extended.f index c16d7b4a..05daa969 100644 --- a/SRC/dla_gerfsx_extended.f +++ b/SRC/dla_gerfsx_extended.f @@ -28,6 +28,9 @@ DOUBLE PRECISION C( * ), AYB( * ), RCOND, BERR_OUT( * ), $ ERRS_N( NRHS, * ), ERRS_C( NRHS, * ) * .. +* +* ===================================================================== +* * .. Local Scalars .. CHARACTER TRANS INTEGER CNT, I, J, X_STATE, Z_STATE, Y_PREC_STATE diff --git a/SRC/dla_lin_berr.f b/SRC/dla_lin_berr.f index c8f1652a..991dfffd 100644 --- a/SRC/dla_lin_berr.f +++ b/SRC/dla_lin_berr.f @@ -16,13 +16,19 @@ * .. Array Arguments .. DOUBLE PRECISION AYB( N, NRHS ), BERR( NRHS ) DOUBLE PRECISION RES( N, NRHS ) +* .. +* +* Purpose +* ======= * -* DLA_LIN_BERR computes componentwise relative backward error from +* DLA_LIN_BERR computes component-wise relative backward error from * the formula * max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) ) -* where abs(Z) is the componentwise absolute value of the matrix +* where abs(Z) is the component-wise absolute value of the matrix * or vector Z. -* .. +* +* ===================================================================== +* * .. Local Scalars .. DOUBLE PRECISION TMP INTEGER I, J diff --git a/SRC/dla_porcond.f b/SRC/dla_porcond.f index 78a9d948..1a7ac25e 100644 --- a/SRC/dla_porcond.f +++ b/SRC/dla_porcond.f @@ -19,6 +19,10 @@ * .. * .. Array Arguments .. INTEGER IWORK( * ) +* .. +* +* Purpose +* ======= * * DLA_PORCOND Estimates the Skeel condition number of op(A) * op2(C) * where op2 is determined by CMODE as follows @@ -29,9 +33,16 @@ * is computed by computing scaling factors R such that * diag(R)*A*op2(C) is row equilibrated and computing the standard * infinity-norm condition number. -* WORK is a double precision workspace of size 3*N, and -* IWORK is an integer workspace of size N. -* .. +* +* Arguments +* ========== +* +* WORK double precision workspace of size 3*N. +* +* IWORK integer workspace of size N. +* +* ===================================================================== +* * .. Local Scalars .. INTEGER KASE, I, J DOUBLE PRECISION AINVNM, TMP diff --git a/SRC/dla_porfsx_extended.f b/SRC/dla_porfsx_extended.f index 01e3010d..33c16119 100644 --- a/SRC/dla_porfsx_extended.f +++ b/SRC/dla_porfsx_extended.f @@ -28,6 +28,9 @@ DOUBLE PRECISION C( * ), AYB(*), RCOND, BERR_OUT( * ), $ ERRS_N( NRHS, * ), ERRS_C( NRHS, * ) * .. +* +* ===================================================================== +* * .. Local Scalars .. INTEGER UPLO2, CNT, I, J, X_STATE, Z_STATE DOUBLE PRECISION YK, DYK, YMIN, NORMY, NORMX, NORMDX, DXRAT, diff --git a/SRC/dla_porpvgrw.f b/SRC/dla_porpvgrw.f index 535b4e46..06efe3f1 100644 --- a/SRC/dla_porpvgrw.f +++ b/SRC/dla_porpvgrw.f @@ -18,6 +18,9 @@ * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), AF( LDAF, * ), WORK( * ) * .. +* +* ===================================================================== +* * .. Local Scalars .. INTEGER I, J DOUBLE PRECISION AMAX, UMAX, RPVGRW diff --git a/SRC/dla_rpvgrw.f b/SRC/dla_rpvgrw.f index 791bd5a6..47d7ed8b 100644 --- a/SRC/dla_rpvgrw.f +++ b/SRC/dla_rpvgrw.f @@ -16,6 +16,9 @@ * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), AF( LDAF, * ) * .. +* +* ===================================================================== +* * .. Local Scalars .. INTEGER I, J DOUBLE PRECISION AMAX, UMAX, RPVGRW diff --git a/SRC/dla_syamv.f b/SRC/dla_syamv.f index 49c36152..49b2ba00 100644 --- a/SRC/dla_syamv.f +++ b/SRC/dla_syamv.f @@ -38,7 +38,7 @@ * entry is considered "symbolic" if all multiplications involved * in computing that entry have at least one zero multiplicand. * -* Parameters +* Arguments * ========== * * UPLO - INTEGER @@ -101,6 +101,8 @@ * Y. INCY must not be zero. * Unchanged on exit. * +* Further Details +* =============== * * Level 2 Blas routine. * @@ -112,7 +114,8 @@ * -- Modified for the absolute-value product, April 2006 * Jason Riedy, UC Berkeley * -* .. +* ===================================================================== +* * .. Parameters .. DOUBLE PRECISION ONE, ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) diff --git a/SRC/dla_syrcond.f b/SRC/dla_syrcond.f index 751af1a6..2a69e7c0 100644 --- a/SRC/dla_syrcond.f +++ b/SRC/dla_syrcond.f @@ -18,6 +18,10 @@ * .. Array Arguments INTEGER IWORK( * ), IPIV( * ) DOUBLE PRECISION A( LDA, * ), AF( LDAF, * ), WORK( * ), C( * ) +* .. +* +* Purpose +* ======= * * DLA_SYRCOND estimates the Skeel condition number of op(A) * op2(C) * where op2 is determined by CMODE as follows @@ -28,9 +32,16 @@ * is computed by computing scaling factors R such that * diag(R)*A*op2(C) is row equilibrated and computing the standard * infinity-norm condition number. -* WORK is a double precision workspace of size 3*N, and -* IWORK is an integer workspace of size N. -* .. +* +* Arguments +* ========== +* +* WORK double precision workspace of size 3*N. +* +* IWORK integer workspace of size N. +* +* ===================================================================== +* * .. Local Scalars .. CHARACTER NORMIN INTEGER KASE, I, J diff --git a/SRC/dla_syrfsx_extended.f b/SRC/dla_syrfsx_extended.f index 1a75ce8e..6eee0573 100644 --- a/SRC/dla_syrfsx_extended.f +++ b/SRC/dla_syrfsx_extended.f @@ -29,6 +29,9 @@ DOUBLE PRECISION C( * ), AYB( * ), RCOND, BERR_OUT( * ), $ ERRS_N( NRHS, * ), ERRS_C( NRHS, * ) * .. +* +* ===================================================================== +* * .. Local Scalars .. INTEGER UPLO2, CNT, I, J, X_STATE, Z_STATE DOUBLE PRECISION YK, DYK, YMIN, NORMY, NORMX, NORMDX, DXRAT, diff --git a/SRC/dla_syrpvgrw.f b/SRC/dla_syrpvgrw.f index 90a19de4..67adf069 100644 --- a/SRC/dla_syrpvgrw.f +++ b/SRC/dla_syrpvgrw.f @@ -19,6 +19,9 @@ INTEGER IPIV( * ) DOUBLE PRECISION A( LDA, * ), AF( LDAF, * ), WORK( * ) * .. +* +* ===================================================================== +* * .. Local Scalars .. INTEGER NCOLS, I, J, K, KP DOUBLE PRECISION AMAX, UMAX, RPVGRW, TMP diff --git a/SRC/dla_wwaddw.f b/SRC/dla_wwaddw.f index f9cba7e8..5c3d79a7 100644 --- a/SRC/dla_wwaddw.f +++ b/SRC/dla_wwaddw.f @@ -36,7 +36,9 @@ * * W (input) DOUBLE PRECISION array, length N * The vector to be added. -* .. +* +* ===================================================================== +* * .. Local Scalars .. DOUBLE PRECISION S INTEGER I diff --git a/SRC/dlansf.f b/SRC/dlansf.f index 33cd71c1..2e0354bf 100644 --- a/SRC/dlansf.f +++ b/SRC/dlansf.f @@ -74,8 +74,8 @@ * where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, * WORK is not referenced. * -* Notes -* ===== +* Further Details +* =============== * * We first consider Rectangular Full Packed (RFP) Format when N is * even. We give an example where N = 6. diff --git a/SRC/dpftrf.f b/SRC/dpftrf.f index 4451dfb3..d70c9aa5 100644 --- a/SRC/dpftrf.f +++ b/SRC/dpftrf.f @@ -66,8 +66,8 @@ * positive definite, and the factorization could not be * completed. * -* Notes -* ===== +* Further Details +* =============== * * We first consider Rectangular Full Packed (RFP) Format when N is * even. We give an example where N = 6. diff --git a/SRC/dpftri.f b/SRC/dpftri.f index 674d70c0..16a3f5b5 100644 --- a/SRC/dpftri.f +++ b/SRC/dpftri.f @@ -58,8 +58,8 @@ * > 0: if INFO = i, the (i,i) element of the factor U or L is * zero, and the inverse could not be computed. * -* Notes -* ===== +* Further Details +* =============== * * We first consider Rectangular Full Packed (RFP) Format when N is * even. We give an example where N = 6. diff --git a/SRC/dpftrs.f b/SRC/dpftrs.f index 2f1287cc..ee18027d 100644 --- a/SRC/dpftrs.f +++ b/SRC/dpftrs.f @@ -57,8 +57,8 @@ * = 0: successful exit * < 0: if INFO = -i, the i-th argument had an illegal value * -* Notes -* ===== +* Further Details +* =============== * * We first consider Rectangular Full Packed (RFP) Format when N is * even. We give an example where N = 6. diff --git a/SRC/dstemr.f b/SRC/dstemr.f index b8be826e..73dacd75 100644 --- a/SRC/dstemr.f +++ b/SRC/dstemr.f @@ -67,7 +67,7 @@ * Computer Science Division Technical Report No. UCB/CSD-97-971, * UC Berkeley, May 1997. * -* Notes: +* Further Details * 1.DSTEMR works only on machines which follow IEEE-754 * floating-point standard in their handling of infinities and NaNs. * This permits the use of efficient inner loops avoiding a check for diff --git a/SRC/dtfsm.f b/SRC/dtfsm.f index 93dedb7b..7ba96a30 100644 --- a/SRC/dtfsm.f +++ b/SRC/dtfsm.f @@ -126,8 +126,8 @@ * max( 1, m ). * Unchanged on exit. * -* Notes -* ===== +* Further Details +* =============== * * We first consider Rectangular Full Packed (RFP) Format when N is * even. We give an example where N = 6. diff --git a/SRC/dtftri.f b/SRC/dtftri.f index 60eecdd9..29f77567 100644 --- a/SRC/dtftri.f +++ b/SRC/dtftri.f @@ -65,8 +65,8 @@ * > 0: if INFO = i, A(i,i) is exactly zero. The triangular * matrix is singular and its inverse can not be computed. * -* Notes -* ===== +* Further Details +* =============== * * We first consider Rectangular Full Packed (RFP) Format when N is * even. We give an example where N = 6. diff --git a/SRC/dtfttp.f b/SRC/dtfttp.f index 94064d95..be797c5b 100644 --- a/SRC/dtfttp.f +++ b/SRC/dtfttp.f @@ -52,8 +52,8 @@ * = 0: successful exit * < 0: if INFO = -i, the i-th argument had an illegal value * -* Notes -* ===== +* Further Details +* =============== * * We first consider Rectangular Full Packed (RFP) Format when N is * even. We give an example where N = 6. diff --git a/SRC/dtfttr.f b/SRC/dtfttr.f index d1b92dc4..d752a490 100644 --- a/SRC/dtfttr.f +++ b/SRC/dtfttr.f @@ -57,8 +57,8 @@ * = 0: successful exit * < 0: if INFO = -i, the i-th argument had an illegal value * -* Notes -* ===== +* Further Details +* =============== * * We first consider Rectangular Full Packed (RFP) Format when N is * even. We give an example where N = 6. diff --git a/SRC/dtpttf.f b/SRC/dtpttf.f index 7671e7de..89b911f2 100644 --- a/SRC/dtpttf.f +++ b/SRC/dtpttf.f @@ -51,8 +51,8 @@ * = 0: successful exit * < 0: if INFO = -i, the i-th argument had an illegal value * -* Notes -* ===== +* Further Details +* =============== * * We first consider Rectangular Full Packed (RFP) Format when N is * even. We give an example where N = 6. diff --git a/SRC/dtrttf.f b/SRC/dtrttf.f index 866f6a12..42a050f7 100644 --- a/SRC/dtrttf.f +++ b/SRC/dtrttf.f @@ -55,8 +55,8 @@ * = 0: successful exit * < 0: if INFO = -i, the i-th argument had an illegal value * -* Notes -* ===== +* Further Details +* =============== * * We first consider Rectangular Full Packed (RFP) Format when N is * even. We give an example where N = 6. diff --git a/SRC/ilaclc.f b/SRC/ilaclc.f index 0e021afa..0b488da9 100644 --- a/SRC/ilaclc.f +++ b/SRC/ilaclc.f @@ -1,53 +1,55 @@ INTEGER FUNCTION ILACLC(M, N, A, LDA) IMPLICIT NONE -! -! -- LAPACK auxiliary routine (version 3.2) -- -! Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -! December 2007 -! -! .. Scalar Arguments .. +* +* -- LAPACK auxiliary routine (version 3.2) -- +* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. +* December 2007 +* +* .. Scalar Arguments .. INTEGER M, N, LDA -! .. -! .. Array Arguments .. +* .. +* .. Array Arguments .. COMPLEX A( LDA, * ) -! .. -! -! Purpose -! ======= -! -! ILACLC scans A for its last non-zero column. -! -! Arguments -! ========= -! -! M (input) INTEGER -! The number of rows of the matrix A. -! -! N (input) INTEGER -! The number of columns of the matrix A. -! -! A (input) COMPLEX array, dimension (LDA,N) -! The m by n matrix A. -! -! LDA (input) INTEGER -! The leading dimension of the array A. LDA >= max(1,M). -! -! ===================================================================== -! -! .. Parameters .. +* .. +* +* Purpose +* ======= +* +* ILACLC scans A for its last non-zero column. +* +* Arguments +* ========= +* +* M (input) INTEGER +* The number of rows of the matrix A. +* +* N (input) INTEGER +* The number of columns of the matrix A. +* +* A (input) COMPLEX array, dimension (LDA,N) +* The m by n matrix A. +* +* LDA (input) INTEGER +* The leading dimension of the array A. LDA >= max(1,M). +* +* ===================================================================== +* +* .. Parameters .. COMPLEX ZERO PARAMETER ( ZERO = (0.0E+0, 0.0E+0) ) -! .. -! .. Local Scalars .. +* .. +* .. Local Scalars .. INTEGER I -! .. -! .. Executable Statements .. -! -! Quick test for the common case where one corner is non-zero. - IF( N.EQ.0 .OR. A(1, N).NE.ZERO .OR. A(M, N).NE.ZERO ) THEN +* .. +* .. Executable Statements .. +* +* Quick test for the common case where one corner is non-zero. + IF( N.EQ.0 ) THEN + ILACLC = N + ELSE IF( A(1, N).NE.ZERO .OR. A(M, N).NE.ZERO ) THEN ILACLC = N ELSE -! Now scan each column from the end, returning with the first non-zero. +* Now scan each column from the end, returning with the first non-zero. DO ILACLC = N, 1, -1 DO I = 1, M IF( A(I, ILACLC).NE.ZERO ) RETURN diff --git a/SRC/ilaclr.f b/SRC/ilaclr.f index 2a9f9803..fed0653c 100644 --- a/SRC/ilaclr.f +++ b/SRC/ilaclr.f @@ -1,53 +1,55 @@ INTEGER FUNCTION ILACLR(M, N, A, LDA) IMPLICIT NONE -! -! -- LAPACK auxiliary routine (version 3.2) -- -! Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -! December 2007 -! -! .. Scalar Arguments .. +* +* -- LAPACK auxiliary routine (version 3.2) -- +* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. +* December 2007 +* +* .. Scalar Arguments .. INTEGER M, N, LDA -! .. -! .. Array Arguments .. +* .. +* .. Array Arguments .. COMPLEX A( LDA, * ) -! .. -! -! Purpose -! ======= -! -! ILACLR scans A for its last non-zero row. -! -! Arguments -! ========= -! -! M (input) INTEGER -! The number of rows of the matrix A. -! -! N (input) INTEGER -! The number of columns of the matrix A. -! -! A (input) COMPLEX array, dimension (LDA,N) -! The m by n matrix A. -! -! LDA (input) INTEGER -! The leading dimension of the array A. LDA >= max(1,M). -! -! ===================================================================== -! -! .. Parameters .. +* .. +* +* Purpose +* ======= +* +* ILACLR scans A for its last non-zero row. +* +* Arguments +* ========= +* +* M (input) INTEGER +* The number of rows of the matrix A. +* +* N (input) INTEGER +* The number of columns of the matrix A. +* +* A (input) COMPLEX array, dimension (LDA,N) +* The m by n matrix A. +* +* LDA (input) INTEGER +* The leading dimension of the array A. LDA >= max(1,M). +* +* ===================================================================== +* +* .. Parameters .. COMPLEX ZERO PARAMETER ( ZERO = (0.0E+0, 0.0E+0) ) -! .. -! .. Local Scalars .. +* .. +* .. Local Scalars .. INTEGER I, J -! .. -! .. Executable Statements .. -! -! Quick test for the common case where one corner is non-zero. - IF( M.EQ.0 .OR. A(M, 1).NE.ZERO .OR. A(M, N).NE.ZERO ) THEN +* .. +* .. Executable Statements .. +* +* Quick test for the common case where one corner is non-zero. + IF( M.EQ.0 ) THEN + ILACLR = M + ELSE IF( A(M, 1).NE.ZERO .OR. A(M, N).NE.ZERO ) THEN ILACLR = M ELSE -! Scan up each column tracking the last zero row seen. +* Scan up each column tracking the last zero row seen. ILACLR = 0 DO J = 1, N DO I = M, 1, -1 diff --git a/SRC/iladlc.f b/SRC/iladlc.f index 2ef71805..0e5a0a8c 100644 --- a/SRC/iladlc.f +++ b/SRC/iladlc.f @@ -1,53 +1,55 @@ INTEGER FUNCTION ILADLC(M, N, A, LDA) IMPLICIT NONE -! -! -- LAPACK auxiliary routine (version 3.2) -- -! Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -! December 2007 -! -! .. Scalar Arguments .. +* +* -- LAPACK auxiliary routine (version 3.2) -- +* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. +* December 2007 +* +* .. Scalar Arguments .. INTEGER M, N, LDA -! .. -! .. Array Arguments .. +* .. +* .. Array Arguments .. DOUBLE PRECISION A( LDA, * ) -! .. -! -! Purpose -! ======= -! -! ILADLC scans A for its last non-zero column. -! -! Arguments -! ========= -! -! M (input) INTEGER -! The number of rows of the matrix A. -! -! N (input) INTEGER -! The number of columns of the matrix A. -! -! A (input) DOUBLE PRECISION array, dimension (LDA,N) -! The m by n matrix A. -! -! LDA (input) INTEGER -! The leading dimension of the array A. LDA >= max(1,M). -! -! ===================================================================== -! -! .. Parameters .. +* .. +* +* Purpose +* ======= +* +* ILADLC scans A for its last non-zero column. +* +* Arguments +* ========= +* +* M (input) INTEGER +* The number of rows of the matrix A. +* +* N (input) INTEGER +* The number of columns of the matrix A. +* +* A (input) DOUBLE PRECISION array, dimension (LDA,N) +* The m by n matrix A. +* +* LDA (input) INTEGER +* The leading dimension of the array A. LDA >= max(1,M). +* +* ===================================================================== +* +* .. Parameters .. DOUBLE PRECISION ZERO PARAMETER ( ZERO = 0.0D+0 ) -! .. -! .. Local Scalars .. +* .. +* .. Local Scalars .. INTEGER I -! .. -! .. Executable Statements .. -! -! Quick test for the common case where one corner is non-zero. - IF( N.EQ.0 .OR. A(1, N).NE.ZERO .OR. A(M, N).NE.ZERO ) THEN +* .. +* .. Executable Statements .. +* +* Quick test for the common case where one corner is non-zero. + IF( N.EQ.0 ) THEN + ILADLC = N + ELSE IF( A(1, N).NE.ZERO .OR. A(M, N).NE.ZERO ) THEN ILADLC = N ELSE -! Now scan each column from the end, returning with the first non-zero. +* Now scan each column from the end, returning with the first non-zero. DO ILADLC = N, 1, -1 DO I = 1, M IF( A(I, ILADLC).NE.ZERO ) RETURN diff --git a/SRC/iladlr.f b/SRC/iladlr.f index 49aaee19..7b07956d 100644 --- a/SRC/iladlr.f +++ b/SRC/iladlr.f @@ -1,53 +1,55 @@ INTEGER FUNCTION ILADLR(M, N, A, LDA) IMPLICIT NONE -! -! -- LAPACK auxiliary routine (version 3.2) -- -! Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -! December 2007 -! -! .. Scalar Arguments .. +* +* -- LAPACK auxiliary routine (version 3.2) -- +* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. +* December 2007 +* +* .. Scalar Arguments .. INTEGER M, N, LDA -! .. -! .. Array Arguments .. +* .. +* .. Array Arguments .. DOUBLE PRECISION A( LDA, * ) -! .. -! -! Purpose -! ======= -! -! ILADLR scans A for its last non-zero row. -! -! Arguments -! ========= -! -! M (input) INTEGER -! The number of rows of the matrix A. -! -! N (input) INTEGER -! The number of columns of the matrix A. -! -! A (input) DOUBLE PRECISION array, dimension (LDA,N) -! The m by n matrix A. -! -! LDA (input) INTEGER -! The leading dimension of the array A. LDA >= max(1,M). -! -! ===================================================================== -! -! .. Parameters .. +* .. +* +* Purpose +* ======= +* +* ILADLR scans A for its last non-zero row. +* +* Arguments +* ========= +* +* M (input) INTEGER +* The number of rows of the matrix A. +* +* N (input) INTEGER +* The number of columns of the matrix A. +* +* A (input) DOUBLE PRECISION array, dimension (LDA,N) +* The m by n matrix A. +* +* LDA (input) INTEGER +* The leading dimension of the array A. LDA >= max(1,M). +* +* ===================================================================== +* +* .. Parameters .. DOUBLE PRECISION ZERO PARAMETER ( ZERO = 0.0D+0 ) -! .. -! .. Local Scalars .. +* .. +* .. Local Scalars .. INTEGER I, J -! .. -! .. Executable Statements .. -! -! Quick test for the common case where one corner is non-zero. - IF( M.EQ.0 .OR. A(M, 1).NE.ZERO .OR. A(M, N).NE.ZERO ) THEN +* .. +* .. Executable Statements .. +* +* Quick test for the common case where one corner is non-zero. + IF( M.EQ.0 ) THEN + ILADLR = M + ELSE IF( A(M, 1).NE.ZERO .OR. A(M, N).NE.ZERO ) THEN ILADLR = M ELSE -! Scan up each column tracking the last zero row seen. +* Scan up each column tracking the last zero row seen. ILADLR = 0 DO J = 1, N DO I = M, 1, -1 diff --git a/SRC/ilaslc.f b/SRC/ilaslc.f index baa51dba..12c8a294 100644 --- a/SRC/ilaslc.f +++ b/SRC/ilaslc.f @@ -1,53 +1,55 @@ INTEGER FUNCTION ILASLC(M, N, A, LDA) IMPLICIT NONE -! -! -- LAPACK auxiliary routine (version 3.2) -- -! Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -! December 2007 -! -! .. Scalar Arguments .. +* +* -- LAPACK auxiliary routine (version 3.2) -- +* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. +* December 2007 +* +* .. Scalar Arguments .. INTEGER M, N, LDA -! .. -! .. Array Arguments .. +* .. +* .. Array Arguments .. REAL A( LDA, * ) -! .. -! -! Purpose -! ======= -! -! ILASLC scans A for its last non-zero column. -! -! Arguments -! ========= -! -! M (input) INTEGER -! The number of rows of the matrix A. -! -! N (input) INTEGER -! The number of columns of the matrix A. -! -! A (input) REAL array, dimension (LDA,N) -! The m by n matrix A. -! -! LDA (input) INTEGER -! The leading dimension of the array A. LDA >= max(1,M). -! -! ===================================================================== -! -! .. Parameters .. +* .. +* +* Purpose +* ======= +* +* ILASLC scans A for its last non-zero column. +* +* Arguments +* ========= +* +* M (input) INTEGER +* The number of rows of the matrix A. +* +* N (input) INTEGER +* The number of columns of the matrix A. +* +* A (input) REAL array, dimension (LDA,N) +* The m by n matrix A. +* +* LDA (input) INTEGER +* The leading dimension of the array A. LDA >= max(1,M). +* +* ===================================================================== +* +* .. Parameters .. REAL ZERO PARAMETER ( ZERO = 0.0D+0 ) -! .. -! .. Local Scalars .. +* .. +* .. Local Scalars .. INTEGER I -! .. -! .. Executable Statements .. -! -! Quick test for the common case where one corner is non-zero. - IF( N.EQ.0 .OR. A(1, N).NE.ZERO .OR. A(M, N).NE.ZERO ) THEN +* .. +* .. Executable Statements .. +* +* Quick test for the common case where one corner is non-zero. + IF( N.EQ.0 ) THEN + ILASLC = N + ELSE IF( A(1, N).NE.ZERO .OR. A(M, N).NE.ZERO ) THEN ILASLC = N ELSE -! Now scan each column from the end, returning with the first non-zero. +* Now scan each column from the end, returning with the first non-zero. DO ILASLC = N, 1, -1 DO I = 1, M IF( A(I, ILASLC).NE.ZERO ) RETURN diff --git a/SRC/ilaslr.f b/SRC/ilaslr.f index 80e8780e..8b2cba48 100644 --- a/SRC/ilaslr.f +++ b/SRC/ilaslr.f @@ -1,53 +1,55 @@ INTEGER FUNCTION ILASLR(M, N, A, LDA) IMPLICIT NONE -! -! -- LAPACK auxiliary routine (version 3.2) -- -! Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -! December 2007 -! -! .. Scalar Arguments .. +* +* -- LAPACK auxiliary routine (version 3.2) -- +* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. +* December 2007 +* +* .. Scalar Arguments .. INTEGER M, N, LDA -! .. -! .. Array Arguments .. +* .. +* .. Array Arguments .. REAL A( LDA, * ) -! .. -! -! Purpose -! ======= -! -! ILASLR scans A for its last non-zero row. -! -! Arguments -! ========= -! -! M (input) INTEGER -! The number of rows of the matrix A. -! -! N (input) INTEGER -! The number of columns of the matrix A. -! -! A (input) REAL array, dimension (LDA,N) -! The m by n matrix A. -! -! LDA (input) INTEGER -! The leading dimension of the array A. LDA >= max(1,M). -! -! ===================================================================== -! -! .. Parameters .. +* .. +* +* Purpose +* ======= +* +* ILASLR scans A for its last non-zero row. +* +* Arguments +* ========= +* +* M (input) INTEGER +* The number of rows of the matrix A. +* +* N (input) INTEGER +* The number of columns of the matrix A. +* +* A (input) REAL array, dimension (LDA,N) +* The m by n matrix A. +* +* LDA (input) INTEGER +* The leading dimension of the array A. LDA >= max(1,M). +* +* ===================================================================== +* +* .. Parameters .. REAL ZERO PARAMETER ( ZERO = 0.0E+0 ) -! .. -! .. Local Scalars .. +* .. +* .. Local Scalars .. INTEGER I, J -! .. -! .. Executable Statements .. -! -! Quick test for the common case where one corner is non-zero. - IF( M.EQ.0 .OR. A(M, 1).NE.ZERO .OR. A(M, N).NE.ZERO ) THEN +* .. +* .. Executable Statements .. +* +* Quick test for the common case where one corner is non-zero. + IF( M.EQ.0 ) THEN + ILASLR = M + ELSEIF( A(M, 1).NE.ZERO .OR. A(M, N).NE.ZERO ) THEN ILASLR = M ELSE -! Scan up each column tracking the last zero row seen. +* Scan up each column tracking the last zero row seen. ILASLR = 0 DO J = 1, N DO I = M, 1, -1 diff --git a/SRC/ilaver.f b/SRC/ilaver.f index 80ee5d93..f00313d9 100644 --- a/SRC/ilaver.f +++ b/SRC/ilaver.f @@ -23,8 +23,8 @@ INTEGER VERS_MAJOR, VERS_MINOR, VERS_PATCH * ===================================================================== VERS_MAJOR = 3 - VERS_MINOR = 1 - VERS_PATCH = 1 + VERS_MINOR = 2 + VERS_PATCH = 0 * ===================================================================== * RETURN diff --git a/SRC/ilazlc.f b/SRC/ilazlc.f index 794959b1..4c8bc7a3 100644 --- a/SRC/ilazlc.f +++ b/SRC/ilazlc.f @@ -1,53 +1,55 @@ INTEGER FUNCTION ILAZLC(M, N, A, LDA) IMPLICIT NONE -! -! -- LAPACK auxiliary routine (version 3.2) -- -! Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -! December 2007 -! -! .. Scalar Arguments .. +* +* -- LAPACK auxiliary routine (version 3.2) -- +* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. +* December 2007 +* +* .. Scalar Arguments .. INTEGER M, N, LDA -! .. -! .. Array Arguments .. +* .. +* .. Array Arguments .. COMPLEX*16 A( LDA, * ) -! .. -! -! Purpose -! ======= -! -! ILAZLC scans A for its last non-zero column. -! -! Arguments -! ========= -! -! M (input) INTEGER -! The number of rows of the matrix A. -! -! N (input) INTEGER -! The number of columns of the matrix A. -! -! A (input) COMPLEX*16 array, dimension (LDA,N) -! The m by n matrix A. -! -! LDA (input) INTEGER -! The leading dimension of the array A. LDA >= max(1,M). -! -! ===================================================================== -! -! .. Parameters .. +* .. +* +* Purpose +* ======= +* +* ILAZLC scans A for its last non-zero column. +* +* Arguments +* ========= +* +* M (input) INTEGER +* The number of rows of the matrix A. +* +* N (input) INTEGER +* The number of columns of the matrix A. +* +* A (input) COMPLEX*16 array, dimension (LDA,N) +* The m by n matrix A. +* +* LDA (input) INTEGER +* The leading dimension of the array A. LDA >= max(1,M). +* +* ===================================================================== +* +* .. Parameters .. COMPLEX*16 ZERO PARAMETER ( ZERO = (0.0D+0, 0.0D+0) ) -! .. -! .. Local Scalars .. +* .. +* .. Local Scalars .. INTEGER I -! .. -! .. Executable Statements .. -! -! Quick test for the common case where one corner is non-zero. - IF( N.EQ.0 .OR. A(1, N).NE.ZERO .OR. A(M, N).NE.ZERO ) THEN +* .. +* .. Executable Statements .. +* +* Quick test for the common case where one corner is non-zero. + IF( N.EQ.0 ) THEN + ILAZLC = N + ELSE IF( A(1, N).NE.ZERO .OR. A(M, N).NE.ZERO ) THEN ILAZLC = N ELSE -! Now scan each column from the end, returning with the first non-zero. +* Now scan each column from the end, returning with the first non-zero. DO ILAZLC = N, 1, -1 DO I = 1, M IF( A(I, ILAZLC).NE.ZERO ) RETURN diff --git a/SRC/ilazlr.f b/SRC/ilazlr.f index 71cb462e..c3e415e9 100644 --- a/SRC/ilazlr.f +++ b/SRC/ilazlr.f @@ -1,53 +1,55 @@ INTEGER FUNCTION ILAZLR(M, N, A, LDA) IMPLICIT NONE -! -! -- LAPACK auxiliary routine (version 3.2) -- -! Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -! December 2007 -! -! .. Scalar Arguments .. +* +* -- LAPACK auxiliary routine (version 3.2) -- +* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. +* December 2007 +* +* .. Scalar Arguments .. INTEGER M, N, LDA -! .. -! .. Array Arguments .. +* .. +* .. Array Arguments .. COMPLEX*16 A( LDA, * ) -! .. -! -! Purpose -! ======= -! -! ILAZLR scans A for its last non-zero row. -! -! Arguments -! ========= -! -! M (input) INTEGER -! The number of rows of the matrix A. -! -! N (input) INTEGER -! The number of columns of the matrix A. -! -! A (input) COMPLEX*16 array, dimension (LDA,N) -! The m by n matrix A. -! -! LDA (input) INTEGER -! The leading dimension of the array A. LDA >= max(1,M). -! -! ===================================================================== -! -! .. Parameters .. +* .. +* +* Purpose +* ======= +* +* ILAZLR scans A for its last non-zero row. +* +* Arguments +* ========= +* +* M (input) INTEGER +* The number of rows of the matrix A. +* +* N (input) INTEGER +* The number of columns of the matrix A. +* +* A (input) COMPLEX*16 array, dimension (LDA,N) +* The m by n matrix A. +* +* LDA (input) INTEGER +* The leading dimension of the array A. LDA >= max(1,M). +* +* ===================================================================== +* +* .. Parameters .. COMPLEX*16 ZERO PARAMETER ( ZERO = (0.0D+0, 0.0D+0) ) -! .. -! .. Local Scalars .. +* .. +* .. Local Scalars .. INTEGER I, J -! .. -! .. Executable Statements .. -! -! Quick test for the common case where one corner is non-zero. - IF( M.EQ.0 .OR. A(M, 1).NE.ZERO .OR. A(M, N).NE.ZERO ) THEN +* .. +* .. Executable Statements .. +* +* Quick test for the common case where one corner is non-zero. + IF( M.EQ.0 ) THEN + ILAZLR = M + ELSE IF( A(M, 1).NE.ZERO .OR. A(M, N).NE.ZERO ) THEN ILAZLR = M ELSE -! Scan up each column tracking the last zero row seen. +* Scan up each column tracking the last zero row seen. ILAZLR = 0 DO J = 1, N DO I = M, 1, -1 diff --git a/SRC/sgesvj.f b/SRC/sgesvj.f index 71193ee1..197c4038 100644 --- a/SRC/sgesvj.f +++ b/SRC/sgesvj.f @@ -1,5 +1,5 @@ - SUBROUTINE SGESVJ( JOBA, JOBU, JOBV, M, N, A, LDA, SVA, - & MV, V, LDV, WORK, LWORK, INFO ) + SUBROUTINE SGESVJ( JOBA, JOBU, JOBV, M, N, A, LDA, SVA, MV, V, + + LDV, WORK, LWORK, INFO ) * * -- LAPACK routine (version 3.2) -- * @@ -15,19 +15,20 @@ * computation of SVD, PSVD, QSVD, (H,K)-SVD, and for solution of the * eigenvalue problems Hx = lambda M x, H M x = lambda x with H, M > 0. * -* -#- Scalar Arguments -#- -* - IMPLICIT NONE - INTEGER INFO, LDA, LDV, LWORK, M, MV, N - CHARACTER*1 JOBA, JOBU, JOBV -* -* -#- Array Arguments -#- -* - REAL A( LDA, * ), SVA( N ), V( LDV, * ), WORK( LWORK ) + IMPLICIT NONE +* .. +* .. Scalar Arguments .. + INTEGER INFO, LDA, LDV, LWORK, M, MV, N + CHARACTER*1 JOBA, JOBU, JOBV +* .. +* .. Array Arguments .. + REAL A( LDA, * ), SVA( N ), V( LDV, * ), + + WORK( LWORK ) * .. * * Purpose -* ~~~~~~~ +* ======= +* * SGESVJ computes the singular value decomposition (SVD) of a real * M-by-N matrix A, where M >= N. The SVD of A is written as * [++] [xx] [x0] [xx] @@ -90,7 +91,7 @@ * drmac@math.hr. Thank you. * * Arguments -* ~~~~~~~~~ +* ========= * * JOBA (input) CHARACTER* 1 * Specifies the structure of A. @@ -101,7 +102,6 @@ * JOBU (input) CHARACTER*1 * Specifies whether to compute the left singular vectors * (columns of U): -* * = 'U': The left singular vectors corresponding to the nonzero * singular values are computed and returned in the leading * columns of A. See more details in the description of A. @@ -143,9 +143,7 @@ * On entry, the M-by-N matrix A. * On exit, * If JOBU .EQ. 'U' .OR. JOBU .EQ. 'C': -* ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ -* If INFO .EQ. 0, -* ~~~~~~~~~~~~~~~ +* If INFO .EQ. 0 : * RANKA orthonormal columns of U are returned in the * leading RANKA columns of the array A. Here RANKA <= N * is the number of computed singular values of A that are @@ -158,7 +156,6 @@ * TOL=SQRT(M)*EPS (default); or TOL=CTOL*EPS (JOBU.EQ.'C'), * see the description of JOBU. * If INFO .GT. 0, -* ~~~~~~~~~~~~~~~ * the procedure SGESVJ did not converge in the given number * of iterations (sweeps). In that case, the computed * columns of U may not be orthogonal up to TOL. The output @@ -166,11 +163,8 @@ * values in SVA(1:N)) and V is still a decomposition of the * input matrix A in the sense that the residual * ||A-SCALE*U*SIGMA*V^T||_2 / ||A||_2 is small. -* * If JOBU .EQ. 'N': -* ~~~~~~~~~~~~~~~~~ -* If INFO .EQ. 0 -* ~~~~~~~~~~~~~~ +* If INFO .EQ. 0 : * Note that the left singular vectors are 'for free' in the * one-sided Jacobi SVD algorithm. However, if only the * singular values are needed, the level of numerical @@ -179,8 +173,7 @@ * numerically orthogonal up to approximately M*EPS. Thus, * on exit, A contains the columns of U scaled with the * corresponding singular values. -* If INFO .GT. 0, -* ~~~~~~~~~~~~~~~ +* If INFO .GT. 0 : * the procedure SGESVJ did not converge in the given number * of iterations (sweeps). * @@ -189,22 +182,18 @@ * * SVA (workspace/output) REAL array, dimension (N) * On exit, -* If INFO .EQ. 0, -* ~~~~~~~~~~~~~~~ +* If INFO .EQ. 0 : * depending on the value SCALE = WORK(1), we have: * If SCALE .EQ. ONE: -* ~~~~~~~~~~~~~~~~~~ * SVA(1:N) contains the computed singular values of A. * During the computation SVA contains the Euclidean column * norms of the iterated matrices in the array A. * If SCALE .NE. ONE: -* ~~~~~~~~~~~~~~~~~~ * The singular values of A are SCALE*SVA(1:N), and this * factored representation is due to the fact that some of the * singular values of A might underflow or overflow. * -* If INFO .GT. 0, -* ~~~~~~~~~~~~~~~ +* If INFO .GT. 0 : * the procedure SGESVJ did not converge in the given number of * iterations (sweeps) and SCALE*SVA(1:N) may not be accurate. * @@ -227,8 +216,7 @@ * * WORK (input/workspace/output) REAL array, dimension max(4,M+N). * On entry, -* If JOBU .EQ. 'C', -* ~~~~~~~~~~~~~~~~~ +* If JOBU .EQ. 'C' : * WORK(1) = CTOL, where CTOL defines the threshold for convergence. * The process stops if all columns of A are mutually * orthogonal up to CTOL*EPS, EPS=SLAMCH('E'). @@ -261,55 +249,55 @@ * > 0 : SGESVJ did not converge in the maximal allowed number (30) * of sweeps. The output may still be useful. See the * description of WORK. +* ===================================================================== +* +* .. Local Parameters .. + REAL ZERO, HALF, ONE, TWO + PARAMETER ( ZERO = 0.0E0, HALF = 0.5E0, ONE = 1.0E0, + + TWO = 2.0E0 ) + INTEGER NSWEEP + PARAMETER ( NSWEEP = 30 ) +* .. +* .. Local Scalars .. + REAL AAPP, AAPP0, AAPQ, AAQQ, APOAQ, AQOAP, BIG, + + BIGTHETA, CS, CTOL, EPSILON, LARGE, MXAAPQ, + + MXSINJ, ROOTBIG, ROOTEPS, ROOTSFMIN, ROOTTOL, + + SCALE, SFMIN, SMALL, SN, T, TEMP1, THETA, + + THSIGN, TOL + INTEGER BLSKIP, EMPTSW, i, ibr, IERR, igl, IJBLSK, ir1, + + ISWROT, jbc, jgl, KBL, LKAHEAD, MVL, N2, N34, + + N4, NBL, NOTROT, p, PSKIPPED, q, ROWSKIP, + + SWBAND + LOGICAL APPLV, GOSCALE, LOWER, LSVEC, NOSCALE, ROTOK, + + RSVEC, UCTOL, UPPER +* .. +* .. Local Arrays .. + REAL FASTR( 5 ) +* .. +* .. Intrinsic Functions .. + INTRINSIC ABS, AMAX1, AMIN1, FLOAT, MIN0, SIGN, SQRT +* .. +* .. External Functions .. +* from BLAS + REAL SDOT, SNRM2 + EXTERNAL SDOT, SNRM2 + INTEGER ISAMAX + EXTERNAL ISAMAX +* from LAPACK + REAL SLAMCH + EXTERNAL SLAMCH + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. External Subroutines .. +* from BLAS + EXTERNAL SAXPY, SCOPY, SROTM, SSCAL, SSWAP +* from LAPACK + EXTERNAL SLASCL, SLASET, SLASSQ, XERBLA * -* Local Parameters -* - REAL ZERO, HALF, ONE, TWO - PARAMETER ( ZERO = 0.0E0, HALF = 0.5E0, ONE = 1.0E0, TWO = 2.0E0 ) - INTEGER NSWEEP - PARAMETER ( NSWEEP = 30 ) -* -* Local Scalars -* - REAL AAPP, AAPP0, AAPQ, AAQQ, APOAQ, AQOAP, - & BIG, BIGTHETA, CS, CTOL, EPSILON, LARGE, - & MXAAPQ, MXSINJ, ROOTBIG, ROOTEPS, ROOTSFMIN, ROOTTOL, - & SCALE, SFMIN, SMALL, SN, T, TEMP1, - & THETA, THSIGN, TOL - INTEGER BLSKIP, EMPTSW, i, ibr, IERR, igl, - & IJBLSK, ir1, ISWROT, jbc, jgl, KBL, - & LKAHEAD, MVL, N2, N34, N4, NBL, - & NOTROT, p, PSKIPPED, q, ROWSKIP, SWBAND - LOGICAL APPLV, GOSCALE, LOWER, LSVEC, NOSCALE, ROTOK, - & RSVEC, UCTOL, UPPER -* -* Local Arrays -* - REAL FASTR(5) -* -* Intrinsic Functions -* - INTRINSIC ABS, AMAX1, AMIN1, FLOAT, MIN0, SIGN, SQRT -* -* External Functions -* .. from BLAS - REAL SDOT, SNRM2 - EXTERNAL SDOT, SNRM2 - INTEGER ISAMAX - EXTERNAL ISAMAX -* .. from LAPACK - REAL SLAMCH - EXTERNAL SLAMCH - LOGICAL LSAME - EXTERNAL LSAME -* -* External Subroutines -* .. from BLAS - EXTERNAL SAXPY, SCOPY, SROTM, SSCAL, SSWAP -* .. from LAPACK - EXTERNAL SLASCL, SLASET, SLASSQ, XERBLA -* - EXTERNAL SGSVJ0, SGSVJ1 + EXTERNAL SGSVJ0, SGSVJ1 +* .. +* .. Executable Statements .. * * Test the input arguments * @@ -320,40 +308,40 @@ UPPER = LSAME( JOBA, 'U' ) LOWER = LSAME( JOBA, 'L' ) * - IF ( .NOT.( UPPER .OR. LOWER .OR. LSAME(JOBA,'G') ) ) THEN - INFO = - 1 - ELSE IF ( .NOT.( LSVEC .OR. UCTOL .OR. LSAME(JOBU,'N') ) ) THEN - INFO = - 2 - ELSE IF ( .NOT.( RSVEC .OR. APPLV .OR. LSAME(JOBV,'N') ) ) THEN - INFO = - 3 - ELSE IF ( M .LT. 0 ) THEN - INFO = - 4 - ELSE IF ( ( N .LT. 0 ) .OR. ( N .GT. M ) ) THEN - INFO = - 5 - ELSE IF ( LDA .LT. M ) THEN - INFO = - 7 - ELSE IF ( MV .LT. 0 ) THEN - INFO = - 9 - ELSE IF ( ( RSVEC .AND. (LDV .LT. N ) ) .OR. - & ( APPLV .AND. (LDV .LT. MV) ) ) THEN + IF( .NOT.( UPPER .OR. LOWER .OR. LSAME( JOBA, 'G' ) ) ) THEN + INFO = -1 + ELSE IF( .NOT.( LSVEC .OR. UCTOL .OR. LSAME( JOBU, 'N' ) ) ) THEN + INFO = -2 + ELSE IF( .NOT.( RSVEC .OR. APPLV .OR. LSAME( JOBV, 'N' ) ) ) THEN + INFO = -3 + ELSE IF( M.LT.0 ) THEN + INFO = -4 + ELSE IF( ( N.LT.0 ) .OR. ( N.GT.M ) ) THEN + INFO = -5 + ELSE IF( LDA.LT.M ) THEN + INFO = -7 + ELSE IF( MV.LT.0 ) THEN + INFO = -9 + ELSE IF( ( RSVEC .AND. ( LDV.LT.N ) ) .OR. + + ( APPLV .AND. ( LDV.LT.MV ) ) ) THEN INFO = -11 - ELSE IF ( UCTOL .AND. (WORK(1) .LE. ONE) ) THEN - INFO = - 12 - ELSE IF ( LWORK .LT. MAX0( M + N , 6 ) ) THEN - INFO = - 13 + ELSE IF( UCTOL .AND. ( WORK( 1 ).LE.ONE ) ) THEN + INFO = -12 + ELSE IF( LWORK.LT.MAX0( M+N, 6 ) ) THEN + INFO = -13 ELSE - INFO = 0 + INFO = 0 END IF * * #:( - IF ( INFO .NE. 0 ) THEN + IF( INFO.NE.0 ) THEN CALL XERBLA( 'SGESVJ', -INFO ) RETURN END IF * * #:) Quick return for void matrix * - IF ( ( M .EQ. 0 ) .OR. ( N .EQ. 0 ) ) RETURN + IF( ( M.EQ.0 ) .OR. ( N.EQ.0 ) )RETURN * * Set numerical parameters * The stopping criterion for Jacobi rotations is @@ -362,45 +350,45 @@ * * where EPS is the round-off and CTOL is defined as follows: * - IF ( UCTOL ) THEN + IF( UCTOL ) THEN * ... user controlled - CTOL = WORK(1) + CTOL = WORK( 1 ) ELSE * ... default - IF ( LSVEC .OR. RSVEC .OR. APPLV ) THEN - CTOL = SQRT(FLOAT(M)) + IF( LSVEC .OR. RSVEC .OR. APPLV ) THEN + CTOL = SQRT( FLOAT( M ) ) ELSE - CTOL = FLOAT(M) + CTOL = FLOAT( M ) END IF END IF * ... and the machine dependent parameters are *[!] (Make sure that SLAMCH() works properly on the target machine.) * - EPSILON = SLAMCH('Epsilon') - ROOTEPS = SQRT(EPSILON) - SFMIN = SLAMCH('SafeMinimum') - ROOTSFMIN = SQRT(SFMIN) - SMALL = SFMIN / EPSILON - BIG = SLAMCH('Overflow') - ROOTBIG = ONE / ROOTSFMIN - LARGE = BIG / SQRT(FLOAT(M*N)) - BIGTHETA = ONE / ROOTEPS -* - TOL = CTOL * EPSILON - ROOTTOL = SQRT(TOL) -* - IF ( FLOAT(M)*EPSILON .GE. ONE ) THEN - INFO = - 5 + EPSILON = SLAMCH( 'Epsilon' ) + ROOTEPS = SQRT( EPSILON ) + SFMIN = SLAMCH( 'SafeMinimum' ) + ROOTSFMIN = SQRT( SFMIN ) + SMALL = SFMIN / EPSILON + BIG = SLAMCH( 'Overflow' ) + ROOTBIG = ONE / ROOTSFMIN + LARGE = BIG / SQRT( FLOAT( M*N ) ) + BIGTHETA = ONE / ROOTEPS +* + TOL = CTOL*EPSILON + ROOTTOL = SQRT( TOL ) +* + IF( FLOAT( M )*EPSILON.GE.ONE ) THEN + INFO = -5 CALL XERBLA( 'SGESVJ', -INFO ) RETURN END IF * * Initialize the right singular vector matrix. * - IF ( RSVEC ) THEN + IF( RSVEC ) THEN MVL = N CALL SLASET( 'A', MVL, N, ZERO, ONE, V, LDV ) - ELSE IF ( APPLV ) THEN + ELSE IF( APPLV ) THEN MVL = MV END IF RSVEC = RSVEC .OR. APPLV @@ -414,56 +402,56 @@ * SQRT(N)*max_i SVA(i) does not overflow. If INFinite entries * in A are detected, the procedure returns with INFO=-6. * - SCALE = ONE / SQRT(FLOAT(M)*FLOAT(N)) - NOSCALE = .TRUE. - GOSCALE = .TRUE. + SCALE = ONE / SQRT( FLOAT( M )*FLOAT( N ) ) + NOSCALE = .TRUE. + GOSCALE = .TRUE. * - IF ( LOWER ) THEN + IF( LOWER ) THEN * the input matrix is M-by-N lower triangular (trapezoidal) DO 1874 p = 1, N AAPP = ZERO AAQQ = ZERO - CALL SLASSQ( M-p+1, A(p,p), 1, AAPP, AAQQ ) - IF ( AAPP .GT. BIG ) THEN - INFO = - 6 + CALL SLASSQ( M-p+1, A( p, p ), 1, AAPP, AAQQ ) + IF( AAPP.GT.BIG ) THEN + INFO = -6 CALL XERBLA( 'SGESVJ', -INFO ) RETURN END IF - AAQQ = SQRT(AAQQ) - IF ( ( AAPP .LT. (BIG / AAQQ) ) .AND. NOSCALE ) THEN - SVA(p) = AAPP * AAQQ + AAQQ = SQRT( AAQQ ) + IF( ( AAPP.LT.( BIG / AAQQ ) ) .AND. NOSCALE ) THEN + SVA( p ) = AAPP*AAQQ ELSE NOSCALE = .FALSE. - SVA(p) = AAPP * ( AAQQ * SCALE ) - IF ( GOSCALE ) THEN + SVA( p ) = AAPP*( AAQQ*SCALE ) + IF( GOSCALE ) THEN GOSCALE = .FALSE. DO 1873 q = 1, p - 1 - SVA(q) = SVA(q)*SCALE + SVA( q ) = SVA( q )*SCALE 1873 CONTINUE END IF END IF 1874 CONTINUE - ELSE IF ( UPPER ) THEN + ELSE IF( UPPER ) THEN * the input matrix is M-by-N upper triangular (trapezoidal) DO 2874 p = 1, N AAPP = ZERO AAQQ = ZERO - CALL SLASSQ( p, A(1,p), 1, AAPP, AAQQ ) - IF ( AAPP .GT. BIG ) THEN - INFO = - 6 + CALL SLASSQ( p, A( 1, p ), 1, AAPP, AAQQ ) + IF( AAPP.GT.BIG ) THEN + INFO = -6 CALL XERBLA( 'SGESVJ', -INFO ) RETURN END IF - AAQQ = SQRT(AAQQ) - IF ( ( AAPP .LT. (BIG / AAQQ) ) .AND. NOSCALE ) THEN - SVA(p) = AAPP * AAQQ + AAQQ = SQRT( AAQQ ) + IF( ( AAPP.LT.( BIG / AAQQ ) ) .AND. NOSCALE ) THEN + SVA( p ) = AAPP*AAQQ ELSE NOSCALE = .FALSE. - SVA(p) = AAPP * ( AAQQ * SCALE ) - IF ( GOSCALE ) THEN + SVA( p ) = AAPP*( AAQQ*SCALE ) + IF( GOSCALE ) THEN GOSCALE = .FALSE. DO 2873 q = 1, p - 1 - SVA(q) = SVA(q)*SCALE + SVA( q ) = SVA( q )*SCALE 2873 CONTINUE END IF END IF @@ -473,29 +461,29 @@ DO 3874 p = 1, N AAPP = ZERO AAQQ = ZERO - CALL SLASSQ( M, A(1,p), 1, AAPP, AAQQ ) - IF ( AAPP .GT. BIG ) THEN - INFO = - 6 + CALL SLASSQ( M, A( 1, p ), 1, AAPP, AAQQ ) + IF( AAPP.GT.BIG ) THEN + INFO = -6 CALL XERBLA( 'SGESVJ', -INFO ) RETURN END IF - AAQQ = SQRT(AAQQ) - IF ( ( AAPP .LT. (BIG / AAQQ) ) .AND. NOSCALE ) THEN - SVA(p) = AAPP * AAQQ + AAQQ = SQRT( AAQQ ) + IF( ( AAPP.LT.( BIG / AAQQ ) ) .AND. NOSCALE ) THEN + SVA( p ) = AAPP*AAQQ ELSE NOSCALE = .FALSE. - SVA(p) = AAPP * ( AAQQ * SCALE ) - IF ( GOSCALE ) THEN + SVA( p ) = AAPP*( AAQQ*SCALE ) + IF( GOSCALE ) THEN GOSCALE = .FALSE. DO 3873 q = 1, p - 1 - SVA(q) = SVA(q)*SCALE + SVA( q ) = SVA( q )*SCALE 3873 CONTINUE END IF END IF 3874 CONTINUE END IF * - IF ( NOSCALE ) SCALE = ONE + IF( NOSCALE )SCALE = ONE * * Move the smaller part of the spectrum from the underflow threshold *(!) Start by determining the position of the nonzero entries of the @@ -504,61 +492,61 @@ AAPP = ZERO AAQQ = BIG DO 4781 p = 1, N - IF ( SVA(p) .NE. ZERO ) AAQQ = AMIN1( AAQQ, SVA(p) ) - AAPP = AMAX1( AAPP, SVA(p) ) + IF( SVA( p ).NE.ZERO )AAQQ = AMIN1( AAQQ, SVA( p ) ) + AAPP = AMAX1( AAPP, SVA( p ) ) 4781 CONTINUE * * #:) Quick return for zero matrix * - IF ( AAPP .EQ. ZERO ) THEN - IF ( LSVEC ) CALL SLASET( 'G', M, N, ZERO, ONE, A, LDA ) - WORK(1) = ONE - WORK(2) = ZERO - WORK(3) = ZERO - WORK(4) = ZERO - WORK(5) = ZERO - WORK(6) = ZERO + IF( AAPP.EQ.ZERO ) THEN + IF( LSVEC )CALL SLASET( 'G', M, N, ZERO, ONE, A, LDA ) + WORK( 1 ) = ONE + WORK( 2 ) = ZERO + WORK( 3 ) = ZERO + WORK( 4 ) = ZERO + WORK( 5 ) = ZERO + WORK( 6 ) = ZERO RETURN END IF * * #:) Quick return for one-column matrix * - IF ( N .EQ. 1 ) THEN - IF ( LSVEC ) - & CALL SLASCL( 'G',0,0,SVA(1),SCALE,M,1,A(1,1),LDA,IERR ) - WORK(1) = ONE / SCALE - IF ( SVA(1) .GE. SFMIN ) THEN - WORK(2) = ONE + IF( N.EQ.1 ) THEN + IF( LSVEC )CALL SLASCL( 'G', 0, 0, SVA( 1 ), SCALE, M, 1, + + A( 1, 1 ), LDA, IERR ) + WORK( 1 ) = ONE / SCALE + IF( SVA( 1 ).GE.SFMIN ) THEN + WORK( 2 ) = ONE ELSE - WORK(2) = ZERO + WORK( 2 ) = ZERO END IF - WORK(3) = ZERO - WORK(4) = ZERO - WORK(5) = ZERO - WORK(6) = ZERO + WORK( 3 ) = ZERO + WORK( 4 ) = ZERO + WORK( 5 ) = ZERO + WORK( 6 ) = ZERO RETURN END IF * * Protect small singular values from underflow, and try to * avoid underflows/overflows in computing Jacobi rotations. * - SN = SQRT( SFMIN / EPSILON ) - TEMP1 = SQRT( BIG / FLOAT(N) ) - IF ( (AAPP.LE.SN).OR.(AAQQ.GE.TEMP1) - & .OR.((SN.LE.AAQQ).AND.(AAPP.LE.TEMP1)) ) THEN - TEMP1 = AMIN1(BIG,TEMP1/AAPP) + SN = SQRT( SFMIN / EPSILON ) + TEMP1 = SQRT( BIG / FLOAT( N ) ) + IF( ( AAPP.LE.SN ) .OR. ( AAQQ.GE.TEMP1 ) .OR. + + ( ( SN.LE.AAQQ ) .AND. ( AAPP.LE.TEMP1 ) ) ) THEN + TEMP1 = AMIN1( BIG, TEMP1 / AAPP ) * AAQQ = AAQQ*TEMP1 * AAPP = AAPP*TEMP1 - ELSE IF ( (AAQQ.LE.SN).AND.(AAPP.LE.TEMP1) ) THEN - TEMP1 = AMIN1( SN / AAQQ, BIG/(AAPP*SQRT(FLOAT(N))) ) + ELSE IF( ( AAQQ.LE.SN ) .AND. ( AAPP.LE.TEMP1 ) ) THEN + TEMP1 = AMIN1( SN / AAQQ, BIG / ( AAPP*SQRT( FLOAT( N ) ) ) ) * AAQQ = AAQQ*TEMP1 * AAPP = AAPP*TEMP1 - ELSE IF ( (AAQQ.GE.SN).AND.(AAPP.GE.TEMP1) ) THEN + ELSE IF( ( AAQQ.GE.SN ) .AND. ( AAPP.GE.TEMP1 ) ) THEN TEMP1 = AMAX1( SN / AAQQ, TEMP1 / AAPP ) * AAQQ = AAQQ*TEMP1 * AAPP = AAPP*TEMP1 - ELSE IF ( (AAQQ.LE.SN).AND.(AAPP.GE.TEMP1) ) THEN - TEMP1 = AMIN1( SN / AAQQ, BIG / (SQRT(FLOAT(N))*AAPP)) + ELSE IF( ( AAQQ.LE.SN ) .AND. ( AAPP.GE.TEMP1 ) ) THEN + TEMP1 = AMIN1( SN / AAQQ, BIG / ( SQRT( FLOAT( N ) )*AAPP ) ) * AAQQ = AAQQ*TEMP1 * AAPP = AAPP*TEMP1 ELSE @@ -567,27 +555,27 @@ * * Scale, if necessary * - IF ( TEMP1 .NE. ONE ) THEN + IF( TEMP1.NE.ONE ) THEN CALL SLASCL( 'G', 0, 0, ONE, TEMP1, N, 1, SVA, N, IERR ) END IF - SCALE = TEMP1 * SCALE - IF ( SCALE .NE. ONE ) THEN + SCALE = TEMP1*SCALE + IF( SCALE.NE.ONE ) THEN CALL SLASCL( JOBA, 0, 0, ONE, SCALE, M, N, A, LDA, IERR ) SCALE = ONE / SCALE END IF * * Row-cyclic Jacobi SVD algorithm with column pivoting * - EMPTSW = ( N * ( N - 1 ) ) / 2 - NOTROT = 0 - FASTR(1) = ZERO + EMPTSW = ( N*( N-1 ) ) / 2 + NOTROT = 0 + FASTR( 1 ) = ZERO * * A is represented in factored form A = A * diag(WORK), where diag(WORK) * is initialized to identity. WORK is updated during fast scaled * rotations. * DO 1868 q = 1, N - WORK(q) = ONE + WORK( q ) = ONE 1868 CONTINUE * * @@ -606,7 +594,7 @@ * parameters of the computer's memory. * NBL = N / KBL - IF ( ( NBL * KBL ) .NE. N ) NBL = NBL + 1 + IF( ( NBL*KBL ).NE.N )NBL = NBL + 1 * BLSKIP = KBL**2 *[TP] BLKSKIP is a tuning parameter that depends on SWBAND and KBL. @@ -622,19 +610,19 @@ * invokes cubic convergence. Big part of this cycle is done inside * canonical subspaces of dimensions less than M. * - IF ( (LOWER .OR. UPPER) .AND. (N .GT. MAX0(64, 4*KBL)) ) THEN + IF( ( LOWER .OR. UPPER ) .AND. ( N.GT.MAX0( 64, 4*KBL ) ) ) THEN *[TP] The number of partition levels and the actual partition are * tuning parameters. - N4 = N / 4 - N2 = N / 2 - N34 = 3 * N4 - IF ( APPLV ) THEN - q = 0 - ELSE - q = 1 - END IF + N4 = N / 4 + N2 = N / 2 + N34 = 3*N4 + IF( APPLV ) THEN + q = 0 + ELSE + q = 1 + END IF * - IF ( LOWER ) THEN + IF( LOWER ) THEN * * This works very well on lower triangular matrices, in particular * in the framework of the preconditioned Jacobi SVD (xGEJSV). @@ -644,92 +632,103 @@ * [+ + x 0] actually work on [x 0] [x 0] * [+ + x x] [x x]. [x x] * - CALL SGSVJ0(JOBV,M-N34,N-N34,A(N34+1,N34+1),LDA,WORK(N34+1), - & SVA(N34+1),MVL,V(N34*q+1,N34+1),LDV,EPSILON,SFMIN,TOL,2, - & WORK(N+1),LWORK-N,IERR ) + CALL SGSVJ0( JOBV, M-N34, N-N34, A( N34+1, N34+1 ), LDA, + + WORK( N34+1 ), SVA( N34+1 ), MVL, + + V( N34*q+1, N34+1 ), LDV, EPSILON, SFMIN, TOL, + + 2, WORK( N+1 ), LWORK-N, IERR ) * - CALL SGSVJ0( JOBV,M-N2,N34-N2,A(N2+1,N2+1),LDA,WORK(N2+1), - & SVA(N2+1),MVL,V(N2*q+1,N2+1),LDV,EPSILON,SFMIN,TOL,2, - & WORK(N+1),LWORK-N,IERR ) + CALL SGSVJ0( JOBV, M-N2, N34-N2, A( N2+1, N2+1 ), LDA, + + WORK( N2+1 ), SVA( N2+1 ), MVL, + + V( N2*q+1, N2+1 ), LDV, EPSILON, SFMIN, TOL, 2, + + WORK( N+1 ), LWORK-N, IERR ) * - CALL SGSVJ1( JOBV,M-N2,N-N2,N4,A(N2+1,N2+1),LDA,WORK(N2+1), - & SVA(N2+1),MVL,V(N2*q+1,N2+1),LDV,EPSILON,SFMIN,TOL,1, - & WORK(N+1),LWORK-N,IERR ) + CALL SGSVJ1( JOBV, M-N2, N-N2, N4, A( N2+1, N2+1 ), LDA, + + WORK( N2+1 ), SVA( N2+1 ), MVL, + + V( N2*q+1, N2+1 ), LDV, EPSILON, SFMIN, TOL, 1, + + WORK( N+1 ), LWORK-N, IERR ) * - CALL SGSVJ0( JOBV,M-N4,N2-N4,A(N4+1,N4+1),LDA,WORK(N4+1), - & SVA(N4+1),MVL,V(N4*q+1,N4+1),LDV,EPSILON,SFMIN,TOL,1, - & WORK(N+1),LWORK-N,IERR ) + CALL SGSVJ0( JOBV, M-N4, N2-N4, A( N4+1, N4+1 ), LDA, + + WORK( N4+1 ), SVA( N4+1 ), MVL, + + V( N4*q+1, N4+1 ), LDV, EPSILON, SFMIN, TOL, 1, + + WORK( N+1 ), LWORK-N, IERR ) * - CALL SGSVJ0( JOBV,M,N4,A,LDA,WORK,SVA,MVL,V,LDV,EPSILON, - & SFMIN,TOL,1,WORK(N+1),LWORK-N,IERR ) + CALL SGSVJ0( JOBV, M, N4, A, LDA, WORK, SVA, MVL, V, LDV, + + EPSILON, SFMIN, TOL, 1, WORK( N+1 ), LWORK-N, + + IERR ) * - CALL SGSVJ1( JOBV,M,N2,N4,A,LDA,WORK,SVA,MVL,V,LDV,EPSILON, - & SFMIN,TOL,1,WORK(N+1),LWORK-N,IERR ) + CALL SGSVJ1( JOBV, M, N2, N4, A, LDA, WORK, SVA, MVL, V, + + LDV, EPSILON, SFMIN, TOL, 1, WORK( N+1 ), + + LWORK-N, IERR ) * * - ELSE IF ( UPPER ) THEN + ELSE IF( UPPER ) THEN * * - CALL SGSVJ0( JOBV,N4,N4,A,LDA,WORK,SVA,MVL,V,LDV,EPSILON, - & SFMIN,TOL,2,WORK(N+1),LWORK-N,IERR ) + CALL SGSVJ0( JOBV, N4, N4, A, LDA, WORK, SVA, MVL, V, LDV, + + EPSILON, SFMIN, TOL, 2, WORK( N+1 ), LWORK-N, + + IERR ) * - CALL SGSVJ0(JOBV,N2,N4,A(1,N4+1),LDA,WORK(N4+1),SVA(N4+1),MVL, - & V(N4*q+1,N4+1),LDV,EPSILON,SFMIN,TOL,1,WORK(N+1),LWORK-N, - & IERR ) + CALL SGSVJ0( JOBV, N2, N4, A( 1, N4+1 ), LDA, WORK( N4+1 ), + + SVA( N4+1 ), MVL, V( N4*q+1, N4+1 ), LDV, + + EPSILON, SFMIN, TOL, 1, WORK( N+1 ), LWORK-N, + + IERR ) * - CALL SGSVJ1( JOBV,N2,N2,N4,A,LDA,WORK,SVA,MVL,V,LDV,EPSILON, - & SFMIN,TOL,1,WORK(N+1),LWORK-N,IERR ) + CALL SGSVJ1( JOBV, N2, N2, N4, A, LDA, WORK, SVA, MVL, V, + + LDV, EPSILON, SFMIN, TOL, 1, WORK( N+1 ), + + LWORK-N, IERR ) * - CALL SGSVJ0( JOBV,N2+N4,N4,A(1,N2+1),LDA,WORK(N2+1),SVA(N2+1),MVL, - & V(N2*q+1,N2+1),LDV,EPSILON,SFMIN,TOL,1, - & WORK(N+1),LWORK-N,IERR ) + CALL SGSVJ0( JOBV, N2+N4, N4, A( 1, N2+1 ), LDA, + + WORK( N2+1 ), SVA( N2+1 ), MVL, + + V( N2*q+1, N2+1 ), LDV, EPSILON, SFMIN, TOL, 1, + + WORK( N+1 ), LWORK-N, IERR ) - END IF + END IF * END IF * -* -#- Row-cyclic pivot strategy with de Rijk's pivoting -#- +* .. Row-cyclic pivot strategy with de Rijk's pivoting .. * DO 1993 i = 1, NSWEEP * .. go go go ... * - MXAAPQ = ZERO - MXSINJ = ZERO - ISWROT = 0 + MXAAPQ = ZERO + MXSINJ = ZERO + ISWROT = 0 * - NOTROT = 0 - PSKIPPED = 0 + NOTROT = 0 + PSKIPPED = 0 * * Each sweep is unrolled using KBL-by-KBL tiles over the pivot pairs * 1 <= p < q <= N. This is the first step toward a blocked implementation * of the rotations. New implementation, based on block transformations, * is under development. * - DO 2000 ibr = 1, NBL + DO 2000 ibr = 1, NBL * - igl = ( ibr - 1 ) * KBL + 1 + igl = ( ibr-1 )*KBL + 1 * - DO 1002 ir1 = 0, MIN0( LKAHEAD, NBL - ibr ) + DO 1002 ir1 = 0, MIN0( LKAHEAD, NBL-ibr ) * - igl = igl + ir1 * KBL + igl = igl + ir1*KBL * - DO 2001 p = igl, MIN0( igl + KBL - 1, N - 1) + DO 2001 p = igl, MIN0( igl+KBL-1, N-1 ) * * .. de Rijk's pivoting * - q = ISAMAX( N-p+1, SVA(p), 1 ) + p - 1 - IF ( p .NE. q ) THEN - CALL SSWAP( M, A(1,p), 1, A(1,q), 1 ) - IF ( RSVEC ) CALL SSWAP( MVL, V(1,p), 1, V(1,q), 1 ) - TEMP1 = SVA(p) - SVA(p) = SVA(q) - SVA(q) = TEMP1 - TEMP1 = WORK(p) - WORK(p) = WORK(q) - WORK(q) = TEMP1 - END IF -* - IF ( ir1 .EQ. 0 ) THEN + q = ISAMAX( N-p+1, SVA( p ), 1 ) + p - 1 + IF( p.NE.q ) THEN + CALL SSWAP( M, A( 1, p ), 1, A( 1, q ), 1 ) + IF( RSVEC )CALL SSWAP( MVL, V( 1, p ), 1, + + V( 1, q ), 1 ) + TEMP1 = SVA( p ) + SVA( p ) = SVA( q ) + SVA( q ) = TEMP1 + TEMP1 = WORK( p ) + WORK( p ) = WORK( q ) + WORK( q ) = TEMP1 + END IF +* + IF( ir1.EQ.0 ) THEN * * Column norms are periodically updated by explicit * norm computation. @@ -743,506 +742,665 @@ * If properly implemented SNRM2 is available, the IF-THEN-ELSE * below should read "AAPP = SNRM2( M, A(1,p), 1 ) * WORK(p)". * - IF ((SVA(p) .LT. ROOTBIG) .AND. (SVA(p) .GT. ROOTSFMIN)) THEN - SVA(p) = SNRM2( M, A(1,p), 1 ) * WORK(p) - ELSE - TEMP1 = ZERO - AAPP = ZERO - CALL SLASSQ( M, A(1,p), 1, TEMP1, AAPP ) - SVA(p) = TEMP1 * SQRT(AAPP) * WORK(p) - END IF - AAPP = SVA(p) - ELSE - AAPP = SVA(p) - END IF -* - IF ( AAPP .GT. ZERO ) THEN -* - PSKIPPED = 0 -* - DO 2002 q = p + 1, MIN0( igl + KBL - 1, N ) -* - AAQQ = SVA(q) -* - IF ( AAQQ .GT. ZERO ) THEN -* - AAPP0 = AAPP - IF ( AAQQ .GE. ONE ) THEN - ROTOK = ( SMALL*AAPP ) .LE. AAQQ - IF ( AAPP .LT. ( BIG / AAQQ ) ) THEN - AAPQ = ( SDOT(M, A(1,p), 1, A(1,q), 1 ) * - & WORK(p) * WORK(q) / AAQQ ) / AAPP - ELSE - CALL SCOPY( M, A(1,p), 1, WORK(N+1), 1 ) - CALL SLASCL( 'G', 0, 0, AAPP, WORK(p), M, - & 1, WORK(N+1), LDA, IERR ) - AAPQ = SDOT( M, WORK(N+1),1, A(1,q),1 )*WORK(q) / AAQQ - END IF - ELSE - ROTOK = AAPP .LE. ( AAQQ / SMALL ) - IF ( AAPP .GT. ( SMALL / AAQQ ) ) THEN - AAPQ = ( SDOT( M, A(1,p), 1, A(1,q), 1 ) * - & WORK(p) * WORK(q) / AAQQ ) / AAPP - ELSE - CALL SCOPY( M, A(1,q), 1, WORK(N+1), 1 ) - CALL SLASCL( 'G', 0, 0, AAQQ, WORK(q), M, - & 1, WORK(N+1), LDA, IERR ) - AAPQ = SDOT( M, WORK(N+1),1, A(1,p),1 )*WORK(p) / AAPP - END IF - END IF + IF( ( SVA( p ).LT.ROOTBIG ) .AND. + + ( SVA( p ).GT.ROOTSFMIN ) ) THEN + SVA( p ) = SNRM2( M, A( 1, p ), 1 )*WORK( p ) + ELSE + TEMP1 = ZERO + AAPP = ZERO + CALL SLASSQ( M, A( 1, p ), 1, TEMP1, AAPP ) + SVA( p ) = TEMP1*SQRT( AAPP )*WORK( p ) + END IF + AAPP = SVA( p ) + ELSE + AAPP = SVA( p ) + END IF +* + IF( AAPP.GT.ZERO ) THEN +* + PSKIPPED = 0 +* + DO 2002 q = p + 1, MIN0( igl+KBL-1, N ) +* + AAQQ = SVA( q ) +* + IF( AAQQ.GT.ZERO ) THEN +* + AAPP0 = AAPP + IF( AAQQ.GE.ONE ) THEN + ROTOK = ( SMALL*AAPP ).LE.AAQQ + IF( AAPP.LT.( BIG / AAQQ ) ) THEN + AAPQ = ( SDOT( M, A( 1, p ), 1, A( 1, + + q ), 1 )*WORK( p )*WORK( q ) / + + AAQQ ) / AAPP + ELSE + CALL SCOPY( M, A( 1, p ), 1, + + WORK( N+1 ), 1 ) + CALL SLASCL( 'G', 0, 0, AAPP, + + WORK( p ), M, 1, + + WORK( N+1 ), LDA, IERR ) + AAPQ = SDOT( M, WORK( N+1 ), 1, + + A( 1, q ), 1 )*WORK( q ) / AAQQ + END IF + ELSE + ROTOK = AAPP.LE.( AAQQ / SMALL ) + IF( AAPP.GT.( SMALL / AAQQ ) ) THEN + AAPQ = ( SDOT( M, A( 1, p ), 1, A( 1, + + q ), 1 )*WORK( p )*WORK( q ) / + + AAQQ ) / AAPP + ELSE + CALL SCOPY( M, A( 1, q ), 1, + + WORK( N+1 ), 1 ) + CALL SLASCL( 'G', 0, 0, AAQQ, + + WORK( q ), M, 1, + + WORK( N+1 ), LDA, IERR ) + AAPQ = SDOT( M, WORK( N+1 ), 1, + + A( 1, p ), 1 )*WORK( p ) / AAPP + END IF + END IF * - MXAAPQ = AMAX1( MXAAPQ, ABS(AAPQ) ) + MXAAPQ = AMAX1( MXAAPQ, ABS( AAPQ ) ) * * TO rotate or NOT to rotate, THAT is the question ... * - IF ( ABS( AAPQ ) .GT. TOL ) THEN + IF( ABS( AAPQ ).GT.TOL ) THEN * * .. rotate *[RTD] ROTATED = ROTATED + ONE * - IF ( ir1 .EQ. 0 ) THEN - NOTROT = 0 - PSKIPPED = 0 - ISWROT = ISWROT + 1 - END IF -* - IF ( ROTOK ) THEN -* - AQOAP = AAQQ / AAPP - APOAQ = AAPP / AAQQ - THETA = - HALF * ABS( AQOAP - APOAQ ) / AAPQ -* - IF ( ABS( THETA ) .GT. BIGTHETA ) THEN -* - T = HALF / THETA - FASTR(3) = T * WORK(p) / WORK(q) - FASTR(4) = - T * WORK(q) / WORK(p) - CALL SROTM( M, A(1,p), 1, A(1,q), 1, FASTR ) - IF ( RSVEC ) - & CALL SROTM( MVL, V(1,p), 1, V(1,q), 1, FASTR ) - SVA(q) = AAQQ*SQRT( AMAX1(ZERO,ONE + T*APOAQ*AAPQ) ) - AAPP = AAPP*SQRT( ONE - T*AQOAP*AAPQ ) - MXSINJ = AMAX1( MXSINJ, ABS(T) ) -* - ELSE + IF( ir1.EQ.0 ) THEN + NOTROT = 0 + PSKIPPED = 0 + ISWROT = ISWROT + 1 + END IF +* + IF( ROTOK ) THEN +* + AQOAP = AAQQ / AAPP + APOAQ = AAPP / AAQQ + THETA = -HALF*ABS( AQOAP-APOAQ ) / AAPQ +* + IF( ABS( THETA ).GT.BIGTHETA ) THEN +* + T = HALF / THETA + FASTR( 3 ) = T*WORK( p ) / WORK( q ) + FASTR( 4 ) = -T*WORK( q ) / + + WORK( p ) + CALL SROTM( M, A( 1, p ), 1, + + A( 1, q ), 1, FASTR ) + IF( RSVEC )CALL SROTM( MVL, + + V( 1, p ), 1, + + V( 1, q ), 1, + + FASTR ) + SVA( q ) = AAQQ*SQRT( AMAX1( ZERO, + + ONE+T*APOAQ*AAPQ ) ) + AAPP = AAPP*SQRT( ONE-T*AQOAP*AAPQ ) + MXSINJ = AMAX1( MXSINJ, ABS( T ) ) +* + ELSE * * .. choose correct signum for THETA and rotate * - THSIGN = - SIGN(ONE,AAPQ) - T = ONE / ( THETA + THSIGN*SQRT(ONE+THETA*THETA) ) - CS = SQRT( ONE / ( ONE + T*T ) ) - SN = T * CS -* - MXSINJ = AMAX1( MXSINJ, ABS(SN) ) - SVA(q) = AAQQ*SQRT( AMAX1(ZERO, ONE+T*APOAQ*AAPQ) ) - AAPP = AAPP*SQRT( AMAX1(ZERO, ONE-T*AQOAP*AAPQ) ) -* - APOAQ = WORK(p) / WORK(q) - AQOAP = WORK(q) / WORK(p) - IF ( WORK(p) .GE. ONE ) THEN - IF ( WORK(q) .GE. ONE ) THEN - FASTR(3) = T * APOAQ - FASTR(4) = - T * AQOAP - WORK(p) = WORK(p) * CS - WORK(q) = WORK(q) * CS - CALL SROTM( M, A(1,p),1, A(1,q),1, FASTR ) - IF ( RSVEC ) - & CALL SROTM( MVL, V(1,p),1, V(1,q),1, FASTR ) - ELSE - CALL SAXPY( M, -T*AQOAP, A(1,q),1, A(1,p),1 ) - CALL SAXPY( M, CS*SN*APOAQ, A(1,p),1, A(1,q),1 ) - WORK(p) = WORK(p) * CS - WORK(q) = WORK(q) / CS - IF ( RSVEC ) THEN - CALL SAXPY(MVL, -T*AQOAP, V(1,q),1,V(1,p),1) - CALL SAXPY(MVL,CS*SN*APOAQ, V(1,p),1,V(1,q),1) - END IF - END IF - ELSE - IF ( WORK(q) .GE. ONE ) THEN - CALL SAXPY( M, T*APOAQ, A(1,p),1, A(1,q),1 ) - CALL SAXPY( M,-CS*SN*AQOAP, A(1,q),1, A(1,p),1 ) - WORK(p) = WORK(p) / CS - WORK(q) = WORK(q) * CS - IF ( RSVEC ) THEN - CALL SAXPY(MVL, T*APOAQ, V(1,p),1,V(1,q),1) - CALL SAXPY(MVL,-CS*SN*AQOAP,V(1,q),1,V(1,p),1) - END IF - ELSE - IF ( WORK(p) .GE. WORK(q) ) THEN - CALL SAXPY( M,-T*AQOAP, A(1,q),1,A(1,p),1 ) - CALL SAXPY( M,CS*SN*APOAQ,A(1,p),1,A(1,q),1 ) - WORK(p) = WORK(p) * CS - WORK(q) = WORK(q) / CS - IF ( RSVEC ) THEN - CALL SAXPY(MVL, -T*AQOAP, V(1,q),1,V(1,p),1) - CALL SAXPY(MVL,CS*SN*APOAQ,V(1,p),1,V(1,q),1) - END IF - ELSE - CALL SAXPY( M, T*APOAQ, A(1,p),1,A(1,q),1) - CALL SAXPY( M,-CS*SN*AQOAP,A(1,q),1,A(1,p),1) - WORK(p) = WORK(p) / CS - WORK(q) = WORK(q) * CS - IF ( RSVEC ) THEN - CALL SAXPY(MVL, T*APOAQ, V(1,p),1,V(1,q),1) - CALL SAXPY(MVL,-CS*SN*AQOAP,V(1,q),1,V(1,p),1) - END IF - END IF - END IF - ENDIF - END IF -* - ELSE + THSIGN = -SIGN( ONE, AAPQ ) + T = ONE / ( THETA+THSIGN* + + SQRT( ONE+THETA*THETA ) ) + CS = SQRT( ONE / ( ONE+T*T ) ) + SN = T*CS +* + MXSINJ = AMAX1( MXSINJ, ABS( SN ) ) + SVA( q ) = AAQQ*SQRT( AMAX1( ZERO, + + ONE+T*APOAQ*AAPQ ) ) + AAPP = AAPP*SQRT( AMAX1( ZERO, + + ONE-T*AQOAP*AAPQ ) ) +* + APOAQ = WORK( p ) / WORK( q ) + AQOAP = WORK( q ) / WORK( p ) + IF( WORK( p ).GE.ONE ) THEN + IF( WORK( q ).GE.ONE ) THEN + FASTR( 3 ) = T*APOAQ + FASTR( 4 ) = -T*AQOAP + WORK( p ) = WORK( p )*CS + WORK( q ) = WORK( q )*CS + CALL SROTM( M, A( 1, p ), 1, + + A( 1, q ), 1, + + FASTR ) + IF( RSVEC )CALL SROTM( MVL, + + V( 1, p ), 1, V( 1, q ), + + 1, FASTR ) + ELSE + CALL SAXPY( M, -T*AQOAP, + + A( 1, q ), 1, + + A( 1, p ), 1 ) + CALL SAXPY( M, CS*SN*APOAQ, + + A( 1, p ), 1, + + A( 1, q ), 1 ) + WORK( p ) = WORK( p )*CS + WORK( q ) = WORK( q ) / CS + IF( RSVEC ) THEN + CALL SAXPY( MVL, -T*AQOAP, + + V( 1, q ), 1, + + V( 1, p ), 1 ) + CALL SAXPY( MVL, + + CS*SN*APOAQ, + + V( 1, p ), 1, + + V( 1, q ), 1 ) + END IF + END IF + ELSE + IF( WORK( q ).GE.ONE ) THEN + CALL SAXPY( M, T*APOAQ, + + A( 1, p ), 1, + + A( 1, q ), 1 ) + CALL SAXPY( M, -CS*SN*AQOAP, + + A( 1, q ), 1, + + A( 1, p ), 1 ) + WORK( p ) = WORK( p ) / CS + WORK( q ) = WORK( q )*CS + IF( RSVEC ) THEN + CALL SAXPY( MVL, T*APOAQ, + + V( 1, p ), 1, + + V( 1, q ), 1 ) + CALL SAXPY( MVL, + + -CS*SN*AQOAP, + + V( 1, q ), 1, + + V( 1, p ), 1 ) + END IF + ELSE + IF( WORK( p ).GE.WORK( q ) ) + + THEN + CALL SAXPY( M, -T*AQOAP, + + A( 1, q ), 1, + + A( 1, p ), 1 ) + CALL SAXPY( M, CS*SN*APOAQ, + + A( 1, p ), 1, + + A( 1, q ), 1 ) + WORK( p ) = WORK( p )*CS + WORK( q ) = WORK( q ) / CS + IF( RSVEC ) THEN + CALL SAXPY( MVL, + + -T*AQOAP, + + V( 1, q ), 1, + + V( 1, p ), 1 ) + CALL SAXPY( MVL, + + CS*SN*APOAQ, + + V( 1, p ), 1, + + V( 1, q ), 1 ) + END IF + ELSE + CALL SAXPY( M, T*APOAQ, + + A( 1, p ), 1, + + A( 1, q ), 1 ) + CALL SAXPY( M, + + -CS*SN*AQOAP, + + A( 1, q ), 1, + + A( 1, p ), 1 ) + WORK( p ) = WORK( p ) / CS + WORK( q ) = WORK( q )*CS + IF( RSVEC ) THEN + CALL SAXPY( MVL, + + T*APOAQ, V( 1, p ), + + 1, V( 1, q ), 1 ) + CALL SAXPY( MVL, + + -CS*SN*AQOAP, + + V( 1, q ), 1, + + V( 1, p ), 1 ) + END IF + END IF + END IF + END IF + END IF +* + ELSE * .. have to use modified Gram-Schmidt like transformation - CALL SCOPY( M, A(1,p), 1, WORK(N+1), 1 ) - CALL SLASCL( 'G',0,0,AAPP,ONE,M,1,WORK(N+1),LDA,IERR ) - CALL SLASCL( 'G',0,0,AAQQ,ONE,M,1, A(1,q),LDA,IERR ) - TEMP1 = -AAPQ * WORK(p) / WORK(q) - CALL SAXPY ( M, TEMP1, WORK(N+1), 1, A(1,q), 1 ) - CALL SLASCL( 'G',0,0,ONE,AAQQ,M,1, A(1,q),LDA,IERR ) - SVA(q) = AAQQ*SQRT( AMAX1( ZERO, ONE - AAPQ*AAPQ ) ) - MXSINJ = AMAX1( MXSINJ, SFMIN ) - END IF + CALL SCOPY( M, A( 1, p ), 1, + + WORK( N+1 ), 1 ) + CALL SLASCL( 'G', 0, 0, AAPP, ONE, M, + + 1, WORK( N+1 ), LDA, + + IERR ) + CALL SLASCL( 'G', 0, 0, AAQQ, ONE, M, + + 1, A( 1, q ), LDA, IERR ) + TEMP1 = -AAPQ*WORK( p ) / WORK( q ) + CALL SAXPY( M, TEMP1, WORK( N+1 ), 1, + + A( 1, q ), 1 ) + CALL SLASCL( 'G', 0, 0, ONE, AAQQ, M, + + 1, A( 1, q ), LDA, IERR ) + SVA( q ) = AAQQ*SQRT( AMAX1( ZERO, + + ONE-AAPQ*AAPQ ) ) + MXSINJ = AMAX1( MXSINJ, SFMIN ) + END IF * END IF ROTOK THEN ... ELSE * * In the case of cancellation in updating SVA(q), SVA(p) * recompute SVA(q), SVA(p). * - IF ( (SVA(q) / AAQQ )**2 .LE. ROOTEPS ) THEN - IF ((AAQQ .LT. ROOTBIG).AND.(AAQQ .GT. ROOTSFMIN)) THEN - SVA(q) = SNRM2( M, A(1,q), 1 ) * WORK(q) - ELSE - T = ZERO - AAQQ = ZERO - CALL SLASSQ( M, A(1,q), 1, T, AAQQ ) - SVA(q) = T * SQRT(AAQQ) * WORK(q) - END IF - END IF - IF ( ( AAPP / AAPP0) .LE. ROOTEPS ) THEN - IF ((AAPP .LT. ROOTBIG).AND.(AAPP .GT. ROOTSFMIN)) THEN - AAPP = SNRM2( M, A(1,p), 1 ) * WORK(p) - ELSE - T = ZERO - AAPP = ZERO - CALL SLASSQ( M, A(1,p), 1, T, AAPP ) - AAPP = T * SQRT(AAPP) * WORK(p) - END IF - SVA(p) = AAPP - END IF -* - ELSE + IF( ( SVA( q ) / AAQQ )**2.LE.ROOTEPS ) + + THEN + IF( ( AAQQ.LT.ROOTBIG ) .AND. + + ( AAQQ.GT.ROOTSFMIN ) ) THEN + SVA( q ) = SNRM2( M, A( 1, q ), 1 )* + + WORK( q ) + ELSE + T = ZERO + AAQQ = ZERO + CALL SLASSQ( M, A( 1, q ), 1, T, + + AAQQ ) + SVA( q ) = T*SQRT( AAQQ )*WORK( q ) + END IF + END IF + IF( ( AAPP / AAPP0 ).LE.ROOTEPS ) THEN + IF( ( AAPP.LT.ROOTBIG ) .AND. + + ( AAPP.GT.ROOTSFMIN ) ) THEN + AAPP = SNRM2( M, A( 1, p ), 1 )* + + WORK( p ) + ELSE + T = ZERO + AAPP = ZERO + CALL SLASSQ( M, A( 1, p ), 1, T, + + AAPP ) + AAPP = T*SQRT( AAPP )*WORK( p ) + END IF + SVA( p ) = AAPP + END IF +* + ELSE * A(:,p) and A(:,q) already numerically orthogonal - IF ( ir1 .EQ. 0 ) NOTROT = NOTROT + 1 + IF( ir1.EQ.0 )NOTROT = NOTROT + 1 *[RTD] SKIPPED = SKIPPED + 1 - PSKIPPED = PSKIPPED + 1 - END IF - ELSE + PSKIPPED = PSKIPPED + 1 + END IF + ELSE * A(:,q) is zero column - IF ( ir1. EQ. 0 ) NOTROT = NOTROT + 1 - PSKIPPED = PSKIPPED + 1 - END IF + IF( ir1.EQ.0 )NOTROT = NOTROT + 1 + PSKIPPED = PSKIPPED + 1 + END IF * - IF ( ( i .LE. SWBAND ) .AND. ( PSKIPPED .GT. ROWSKIP ) ) THEN - IF ( ir1 .EQ. 0 ) AAPP = - AAPP - NOTROT = 0 - GO TO 2103 - END IF + IF( ( i.LE.SWBAND ) .AND. + + ( PSKIPPED.GT.ROWSKIP ) ) THEN + IF( ir1.EQ.0 )AAPP = -AAPP + NOTROT = 0 + GO TO 2103 + END IF * - 2002 CONTINUE + 2002 CONTINUE * END q-LOOP * - 2103 CONTINUE + 2103 CONTINUE * bailed out of q-loop * - SVA(p) = AAPP + SVA( p ) = AAPP * - ELSE - SVA(p) = AAPP - IF ( ( ir1 .EQ. 0 ) .AND. (AAPP .EQ. ZERO) ) - & NOTROT=NOTROT+MIN0(igl+KBL-1,N)-p - END IF + ELSE + SVA( p ) = AAPP + IF( ( ir1.EQ.0 ) .AND. ( AAPP.EQ.ZERO ) ) + + NOTROT = NOTROT + MIN0( igl+KBL-1, N ) - p + END IF * - 2001 CONTINUE + 2001 CONTINUE * end of the p-loop * end of doing the block ( ibr, ibr ) - 1002 CONTINUE + 1002 CONTINUE * end of ir1-loop * * ... go to the off diagonal blocks * - igl = ( ibr - 1 ) * KBL + 1 + igl = ( ibr-1 )*KBL + 1 * - DO 2010 jbc = ibr + 1, NBL + DO 2010 jbc = ibr + 1, NBL * - jgl = ( jbc - 1 ) * KBL + 1 + jgl = ( jbc-1 )*KBL + 1 * * doing the block at ( ibr, jbc ) * - IJBLSK = 0 - DO 2100 p = igl, MIN0( igl + KBL - 1, N ) + IJBLSK = 0 + DO 2100 p = igl, MIN0( igl+KBL-1, N ) * - AAPP = SVA(p) - IF ( AAPP .GT. ZERO ) THEN + AAPP = SVA( p ) + IF( AAPP.GT.ZERO ) THEN * - PSKIPPED = 0 + PSKIPPED = 0 * - DO 2200 q = jgl, MIN0( jgl + KBL - 1, N ) + DO 2200 q = jgl, MIN0( jgl+KBL-1, N ) * - AAQQ = SVA(q) - IF ( AAQQ .GT. ZERO ) THEN - AAPP0 = AAPP + AAQQ = SVA( q ) + IF( AAQQ.GT.ZERO ) THEN + AAPP0 = AAPP * -* -#- M x 2 Jacobi SVD -#- +* .. M x 2 Jacobi SVD .. * * Safe Gram matrix computation * - IF ( AAQQ .GE. ONE ) THEN - IF ( AAPP .GE. AAQQ ) THEN - ROTOK = ( SMALL*AAPP ) .LE. AAQQ - ELSE - ROTOK = ( SMALL*AAQQ ) .LE. AAPP - END IF - IF ( AAPP .LT. ( BIG / AAQQ ) ) THEN - AAPQ = ( SDOT(M, A(1,p), 1, A(1,q), 1 ) * - & WORK(p) * WORK(q) / AAQQ ) / AAPP - ELSE - CALL SCOPY( M, A(1,p), 1, WORK(N+1), 1 ) - CALL SLASCL( 'G', 0, 0, AAPP, WORK(p), M, - & 1, WORK(N+1), LDA, IERR ) - AAPQ = SDOT( M, WORK(N+1), 1, A(1,q), 1 ) * - & WORK(q) / AAQQ - END IF - ELSE - IF ( AAPP .GE. AAQQ ) THEN - ROTOK = AAPP .LE. ( AAQQ / SMALL ) - ELSE - ROTOK = AAQQ .LE. ( AAPP / SMALL ) - END IF - IF ( AAPP .GT. ( SMALL / AAQQ ) ) THEN - AAPQ = ( SDOT( M, A(1,p), 1, A(1,q), 1 ) * - & WORK(p) * WORK(q) / AAQQ ) / AAPP - ELSE - CALL SCOPY( M, A(1,q), 1, WORK(N+1), 1 ) - CALL SLASCL( 'G', 0, 0, AAQQ, WORK(q), M, 1, - & WORK(N+1), LDA, IERR ) - AAPQ = SDOT(M,WORK(N+1),1,A(1,p),1) * WORK(p) / AAPP - END IF - END IF + IF( AAQQ.GE.ONE ) THEN + IF( AAPP.GE.AAQQ ) THEN + ROTOK = ( SMALL*AAPP ).LE.AAQQ + ELSE + ROTOK = ( SMALL*AAQQ ).LE.AAPP + END IF + IF( AAPP.LT.( BIG / AAQQ ) ) THEN + AAPQ = ( SDOT( M, A( 1, p ), 1, A( 1, + + q ), 1 )*WORK( p )*WORK( q ) / + + AAQQ ) / AAPP + ELSE + CALL SCOPY( M, A( 1, p ), 1, + + WORK( N+1 ), 1 ) + CALL SLASCL( 'G', 0, 0, AAPP, + + WORK( p ), M, 1, + + WORK( N+1 ), LDA, IERR ) + AAPQ = SDOT( M, WORK( N+1 ), 1, + + A( 1, q ), 1 )*WORK( q ) / AAQQ + END IF + ELSE + IF( AAPP.GE.AAQQ ) THEN + ROTOK = AAPP.LE.( AAQQ / SMALL ) + ELSE + ROTOK = AAQQ.LE.( AAPP / SMALL ) + END IF + IF( AAPP.GT.( SMALL / AAQQ ) ) THEN + AAPQ = ( SDOT( M, A( 1, p ), 1, A( 1, + + q ), 1 )*WORK( p )*WORK( q ) / + + AAQQ ) / AAPP + ELSE + CALL SCOPY( M, A( 1, q ), 1, + + WORK( N+1 ), 1 ) + CALL SLASCL( 'G', 0, 0, AAQQ, + + WORK( q ), M, 1, + + WORK( N+1 ), LDA, IERR ) + AAPQ = SDOT( M, WORK( N+1 ), 1, + + A( 1, p ), 1 )*WORK( p ) / AAPP + END IF + END IF * - MXAAPQ = AMAX1( MXAAPQ, ABS(AAPQ) ) + MXAAPQ = AMAX1( MXAAPQ, ABS( AAPQ ) ) * * TO rotate or NOT to rotate, THAT is the question ... * - IF ( ABS( AAPQ ) .GT. TOL ) THEN - NOTROT = 0 + IF( ABS( AAPQ ).GT.TOL ) THEN + NOTROT = 0 *[RTD] ROTATED = ROTATED + 1 - PSKIPPED = 0 - ISWROT = ISWROT + 1 -* - IF ( ROTOK ) THEN -* - AQOAP = AAQQ / AAPP - APOAQ = AAPP / AAQQ - THETA = - HALF * ABS( AQOAP - APOAQ ) / AAPQ - IF ( AAQQ .GT. AAPP0 ) THETA = - THETA -* - IF ( ABS( THETA ) .GT. BIGTHETA ) THEN - T = HALF / THETA - FASTR(3) = T * WORK(p) / WORK(q) - FASTR(4) = -T * WORK(q) / WORK(p) - CALL SROTM( M, A(1,p), 1, A(1,q), 1, FASTR ) - IF ( RSVEC ) - & CALL SROTM( MVL, V(1,p), 1, V(1,q), 1, FASTR ) - SVA(q) = AAQQ*SQRT( AMAX1(ZERO,ONE + T*APOAQ*AAPQ) ) - AAPP = AAPP*SQRT( AMAX1(ZERO,ONE - T*AQOAP*AAPQ) ) - MXSINJ = AMAX1( MXSINJ, ABS(T) ) - ELSE + PSKIPPED = 0 + ISWROT = ISWROT + 1 +* + IF( ROTOK ) THEN +* + AQOAP = AAQQ / AAPP + APOAQ = AAPP / AAQQ + THETA = -HALF*ABS( AQOAP-APOAQ ) / AAPQ + IF( AAQQ.GT.AAPP0 )THETA = -THETA +* + IF( ABS( THETA ).GT.BIGTHETA ) THEN + T = HALF / THETA + FASTR( 3 ) = T*WORK( p ) / WORK( q ) + FASTR( 4 ) = -T*WORK( q ) / + + WORK( p ) + CALL SROTM( M, A( 1, p ), 1, + + A( 1, q ), 1, FASTR ) + IF( RSVEC )CALL SROTM( MVL, + + V( 1, p ), 1, + + V( 1, q ), 1, + + FASTR ) + SVA( q ) = AAQQ*SQRT( AMAX1( ZERO, + + ONE+T*APOAQ*AAPQ ) ) + AAPP = AAPP*SQRT( AMAX1( ZERO, + + ONE-T*AQOAP*AAPQ ) ) + MXSINJ = AMAX1( MXSINJ, ABS( T ) ) + ELSE * * .. choose correct signum for THETA and rotate * - THSIGN = - SIGN(ONE,AAPQ) - IF ( AAQQ .GT. AAPP0 ) THSIGN = - THSIGN - T = ONE / ( THETA + THSIGN*SQRT(ONE+THETA*THETA) ) - CS = SQRT( ONE / ( ONE + T*T ) ) - SN = T * CS - MXSINJ = AMAX1( MXSINJ, ABS(SN) ) - SVA(q) = AAQQ*SQRT( AMAX1(ZERO, ONE+T*APOAQ*AAPQ) ) - AAPP = AAPP*SQRT( ONE - T*AQOAP*AAPQ) -* - APOAQ = WORK(p) / WORK(q) - AQOAP = WORK(q) / WORK(p) - IF ( WORK(p) .GE. ONE ) THEN -* - IF ( WORK(q) .GE. ONE ) THEN - FASTR(3) = T * APOAQ - FASTR(4) = - T * AQOAP - WORK(p) = WORK(p) * CS - WORK(q) = WORK(q) * CS - CALL SROTM( M, A(1,p),1, A(1,q),1, FASTR ) - IF ( RSVEC ) - & CALL SROTM( MVL, V(1,p),1, V(1,q),1, FASTR ) - ELSE - CALL SAXPY( M, -T*AQOAP, A(1,q),1, A(1,p),1 ) - CALL SAXPY( M, CS*SN*APOAQ, A(1,p),1, A(1,q),1 ) - IF ( RSVEC ) THEN - CALL SAXPY( MVL, -T*AQOAP, V(1,q),1, V(1,p),1 ) - CALL SAXPY( MVL,CS*SN*APOAQ,V(1,p),1, V(1,q),1 ) - END IF - WORK(p) = WORK(p) * CS - WORK(q) = WORK(q) / CS - END IF - ELSE - IF ( WORK(q) .GE. ONE ) THEN - CALL SAXPY( M, T*APOAQ, A(1,p),1, A(1,q),1 ) - CALL SAXPY( M,-CS*SN*AQOAP, A(1,q),1, A(1,p),1 ) - IF ( RSVEC ) THEN - CALL SAXPY(MVL,T*APOAQ, V(1,p),1, V(1,q),1 ) - CALL SAXPY(MVL,-CS*SN*AQOAP,V(1,q),1, V(1,p),1 ) - END IF - WORK(p) = WORK(p) / CS - WORK(q) = WORK(q) * CS - ELSE - IF ( WORK(p) .GE. WORK(q) ) THEN - CALL SAXPY( M,-T*AQOAP, A(1,q),1,A(1,p),1 ) - CALL SAXPY( M,CS*SN*APOAQ,A(1,p),1,A(1,q),1 ) - WORK(p) = WORK(p) * CS - WORK(q) = WORK(q) / CS - IF ( RSVEC ) THEN - CALL SAXPY( MVL, -T*AQOAP, V(1,q),1,V(1,p),1) - CALL SAXPY(MVL,CS*SN*APOAQ,V(1,p),1,V(1,q),1) - END IF - ELSE - CALL SAXPY(M, T*APOAQ, A(1,p),1,A(1,q),1) - CALL SAXPY(M,-CS*SN*AQOAP,A(1,q),1,A(1,p),1) - WORK(p) = WORK(p) / CS - WORK(q) = WORK(q) * CS - IF ( RSVEC ) THEN - CALL SAXPY(MVL, T*APOAQ, V(1,p),1,V(1,q),1) - CALL SAXPY(MVL,-CS*SN*AQOAP,V(1,q),1,V(1,p),1) - END IF - END IF - END IF - ENDIF - END IF -* - ELSE - IF ( AAPP .GT. AAQQ ) THEN - CALL SCOPY( M, A(1,p), 1, WORK(N+1), 1 ) - CALL SLASCL('G',0,0,AAPP,ONE,M,1,WORK(N+1),LDA,IERR) - CALL SLASCL('G',0,0,AAQQ,ONE,M,1, A(1,q),LDA,IERR) - TEMP1 = -AAPQ * WORK(p) / WORK(q) - CALL SAXPY(M,TEMP1,WORK(N+1),1,A(1,q),1) - CALL SLASCL('G',0,0,ONE,AAQQ,M,1,A(1,q),LDA,IERR) - SVA(q) = AAQQ*SQRT(AMAX1(ZERO, ONE - AAPQ*AAPQ)) - MXSINJ = AMAX1( MXSINJ, SFMIN ) - ELSE - CALL SCOPY( M, A(1,q), 1, WORK(N+1), 1 ) - CALL SLASCL('G',0,0,AAQQ,ONE,M,1,WORK(N+1),LDA,IERR) - CALL SLASCL('G',0,0,AAPP,ONE,M,1, A(1,p),LDA,IERR) - TEMP1 = -AAPQ * WORK(q) / WORK(p) - CALL SAXPY(M,TEMP1,WORK(N+1),1,A(1,p),1) - CALL SLASCL('G',0,0,ONE,AAPP,M,1,A(1,p),LDA,IERR) - SVA(p) = AAPP*SQRT(AMAX1(ZERO, ONE - AAPQ*AAPQ)) - MXSINJ = AMAX1( MXSINJ, SFMIN ) - END IF - END IF + THSIGN = -SIGN( ONE, AAPQ ) + IF( AAQQ.GT.AAPP0 )THSIGN = -THSIGN + T = ONE / ( THETA+THSIGN* + + SQRT( ONE+THETA*THETA ) ) + CS = SQRT( ONE / ( ONE+T*T ) ) + SN = T*CS + MXSINJ = AMAX1( MXSINJ, ABS( SN ) ) + SVA( q ) = AAQQ*SQRT( AMAX1( ZERO, + + ONE+T*APOAQ*AAPQ ) ) + AAPP = AAPP*SQRT( ONE-T*AQOAP*AAPQ ) +* + APOAQ = WORK( p ) / WORK( q ) + AQOAP = WORK( q ) / WORK( p ) + IF( WORK( p ).GE.ONE ) THEN +* + IF( WORK( q ).GE.ONE ) THEN + FASTR( 3 ) = T*APOAQ + FASTR( 4 ) = -T*AQOAP + WORK( p ) = WORK( p )*CS + WORK( q ) = WORK( q )*CS + CALL SROTM( M, A( 1, p ), 1, + + A( 1, q ), 1, + + FASTR ) + IF( RSVEC )CALL SROTM( MVL, + + V( 1, p ), 1, V( 1, q ), + + 1, FASTR ) + ELSE + CALL SAXPY( M, -T*AQOAP, + + A( 1, q ), 1, + + A( 1, p ), 1 ) + CALL SAXPY( M, CS*SN*APOAQ, + + A( 1, p ), 1, + + A( 1, q ), 1 ) + IF( RSVEC ) THEN + CALL SAXPY( MVL, -T*AQOAP, + + V( 1, q ), 1, + + V( 1, p ), 1 ) + CALL SAXPY( MVL, + + CS*SN*APOAQ, + + V( 1, p ), 1, + + V( 1, q ), 1 ) + END IF + WORK( p ) = WORK( p )*CS + WORK( q ) = WORK( q ) / CS + END IF + ELSE + IF( WORK( q ).GE.ONE ) THEN + CALL SAXPY( M, T*APOAQ, + + A( 1, p ), 1, + + A( 1, q ), 1 ) + CALL SAXPY( M, -CS*SN*AQOAP, + + A( 1, q ), 1, + + A( 1, p ), 1 ) + IF( RSVEC ) THEN + CALL SAXPY( MVL, T*APOAQ, + + V( 1, p ), 1, + + V( 1, q ), 1 ) + CALL SAXPY( MVL, + + -CS*SN*AQOAP, + + V( 1, q ), 1, + + V( 1, p ), 1 ) + END IF + WORK( p ) = WORK( p ) / CS + WORK( q ) = WORK( q )*CS + ELSE + IF( WORK( p ).GE.WORK( q ) ) + + THEN + CALL SAXPY( M, -T*AQOAP, + + A( 1, q ), 1, + + A( 1, p ), 1 ) + CALL SAXPY( M, CS*SN*APOAQ, + + A( 1, p ), 1, + + A( 1, q ), 1 ) + WORK( p ) = WORK( p )*CS + WORK( q ) = WORK( q ) / CS + IF( RSVEC ) THEN + CALL SAXPY( MVL, + + -T*AQOAP, + + V( 1, q ), 1, + + V( 1, p ), 1 ) + CALL SAXPY( MVL, + + CS*SN*APOAQ, + + V( 1, p ), 1, + + V( 1, q ), 1 ) + END IF + ELSE + CALL SAXPY( M, T*APOAQ, + + A( 1, p ), 1, + + A( 1, q ), 1 ) + CALL SAXPY( M, + + -CS*SN*AQOAP, + + A( 1, q ), 1, + + A( 1, p ), 1 ) + WORK( p ) = WORK( p ) / CS + WORK( q ) = WORK( q )*CS + IF( RSVEC ) THEN + CALL SAXPY( MVL, + + T*APOAQ, V( 1, p ), + + 1, V( 1, q ), 1 ) + CALL SAXPY( MVL, + + -CS*SN*AQOAP, + + V( 1, q ), 1, + + V( 1, p ), 1 ) + END IF + END IF + END IF + END IF + END IF +* + ELSE + IF( AAPP.GT.AAQQ ) THEN + CALL SCOPY( M, A( 1, p ), 1, + + WORK( N+1 ), 1 ) + CALL SLASCL( 'G', 0, 0, AAPP, ONE, + + M, 1, WORK( N+1 ), LDA, + + IERR ) + CALL SLASCL( 'G', 0, 0, AAQQ, ONE, + + M, 1, A( 1, q ), LDA, + + IERR ) + TEMP1 = -AAPQ*WORK( p ) / WORK( q ) + CALL SAXPY( M, TEMP1, WORK( N+1 ), + + 1, A( 1, q ), 1 ) + CALL SLASCL( 'G', 0, 0, ONE, AAQQ, + + M, 1, A( 1, q ), LDA, + + IERR ) + SVA( q ) = AAQQ*SQRT( AMAX1( ZERO, + + ONE-AAPQ*AAPQ ) ) + MXSINJ = AMAX1( MXSINJ, SFMIN ) + ELSE + CALL SCOPY( M, A( 1, q ), 1, + + WORK( N+1 ), 1 ) + CALL SLASCL( 'G', 0, 0, AAQQ, ONE, + + M, 1, WORK( N+1 ), LDA, + + IERR ) + CALL SLASCL( 'G', 0, 0, AAPP, ONE, + + M, 1, A( 1, p ), LDA, + + IERR ) + TEMP1 = -AAPQ*WORK( q ) / WORK( p ) + CALL SAXPY( M, TEMP1, WORK( N+1 ), + + 1, A( 1, p ), 1 ) + CALL SLASCL( 'G', 0, 0, ONE, AAPP, + + M, 1, A( 1, p ), LDA, + + IERR ) + SVA( p ) = AAPP*SQRT( AMAX1( ZERO, + + ONE-AAPQ*AAPQ ) ) + MXSINJ = AMAX1( MXSINJ, SFMIN ) + END IF + END IF * END IF ROTOK THEN ... ELSE * * In the case of cancellation in updating SVA(q) * .. recompute SVA(q) - IF ( (SVA(q) / AAQQ )**2 .LE. ROOTEPS ) THEN - IF ((AAQQ .LT. ROOTBIG).AND.(AAQQ .GT. ROOTSFMIN)) THEN - SVA(q) = SNRM2( M, A(1,q), 1 ) * WORK(q) - ELSE - T = ZERO - AAQQ = ZERO - CALL SLASSQ( M, A(1,q), 1, T, AAQQ ) - SVA(q) = T * SQRT(AAQQ) * WORK(q) - END IF - END IF - IF ( (AAPP / AAPP0 )**2 .LE. ROOTEPS ) THEN - IF ((AAPP .LT. ROOTBIG).AND.(AAPP .GT. ROOTSFMIN)) THEN - AAPP = SNRM2( M, A(1,p), 1 ) * WORK(p) - ELSE - T = ZERO - AAPP = ZERO - CALL SLASSQ( M, A(1,p), 1, T, AAPP ) - AAPP = T * SQRT(AAPP) * WORK(p) - END IF - SVA(p) = AAPP - END IF + IF( ( SVA( q ) / AAQQ )**2.LE.ROOTEPS ) + + THEN + IF( ( AAQQ.LT.ROOTBIG ) .AND. + + ( AAQQ.GT.ROOTSFMIN ) ) THEN + SVA( q ) = SNRM2( M, A( 1, q ), 1 )* + + WORK( q ) + ELSE + T = ZERO + AAQQ = ZERO + CALL SLASSQ( M, A( 1, q ), 1, T, + + AAQQ ) + SVA( q ) = T*SQRT( AAQQ )*WORK( q ) + END IF + END IF + IF( ( AAPP / AAPP0 )**2.LE.ROOTEPS ) THEN + IF( ( AAPP.LT.ROOTBIG ) .AND. + + ( AAPP.GT.ROOTSFMIN ) ) THEN + AAPP = SNRM2( M, A( 1, p ), 1 )* + + WORK( p ) + ELSE + T = ZERO + AAPP = ZERO + CALL SLASSQ( M, A( 1, p ), 1, T, + + AAPP ) + AAPP = T*SQRT( AAPP )*WORK( p ) + END IF + SVA( p ) = AAPP + END IF * end of OK rotation - ELSE - NOTROT = NOTROT + 1 + ELSE + NOTROT = NOTROT + 1 *[RTD] SKIPPED = SKIPPED + 1 - PSKIPPED = PSKIPPED + 1 - IJBLSK = IJBLSK + 1 - END IF - ELSE - NOTROT = NOTROT + 1 - PSKIPPED = PSKIPPED + 1 - IJBLSK = IJBLSK + 1 - END IF + PSKIPPED = PSKIPPED + 1 + IJBLSK = IJBLSK + 1 + END IF + ELSE + NOTROT = NOTROT + 1 + PSKIPPED = PSKIPPED + 1 + IJBLSK = IJBLSK + 1 + END IF * - IF ( ( i .LE. SWBAND ) .AND. ( IJBLSK .GE. BLSKIP ) ) THEN - SVA(p) = AAPP - NOTROT = 0 - GO TO 2011 - END IF - IF ( ( i .LE. SWBAND ) .AND. ( PSKIPPED .GT. ROWSKIP ) ) THEN - AAPP = -AAPP - NOTROT = 0 - GO TO 2203 - END IF + IF( ( i.LE.SWBAND ) .AND. ( IJBLSK.GE.BLSKIP ) ) + + THEN + SVA( p ) = AAPP + NOTROT = 0 + GO TO 2011 + END IF + IF( ( i.LE.SWBAND ) .AND. + + ( PSKIPPED.GT.ROWSKIP ) ) THEN + AAPP = -AAPP + NOTROT = 0 + GO TO 2203 + END IF * - 2200 CONTINUE + 2200 CONTINUE * end of the q-loop - 2203 CONTINUE + 2203 CONTINUE * - SVA(p) = AAPP + SVA( p ) = AAPP * - ELSE + ELSE * - IF ( AAPP .EQ. ZERO ) NOTROT=NOTROT+MIN0(jgl+KBL-1,N)-jgl+1 - IF ( AAPP .LT. ZERO ) NOTROT = 0 + IF( AAPP.EQ.ZERO )NOTROT = NOTROT + + + MIN0( jgl+KBL-1, N ) - jgl + 1 + IF( AAPP.LT.ZERO )NOTROT = 0 * - END IF + END IF * - 2100 CONTINUE + 2100 CONTINUE * end of the p-loop - 2010 CONTINUE + 2010 CONTINUE * end of the jbc-loop - 2011 CONTINUE + 2011 CONTINUE *2011 bailed out of the jbc-loop - DO 2012 p = igl, MIN0( igl + KBL - 1, N ) - SVA(p) = ABS(SVA(p)) - 2012 CONTINUE + DO 2012 p = igl, MIN0( igl+KBL-1, N ) + SVA( p ) = ABS( SVA( p ) ) + 2012 CONTINUE *** - 2000 CONTINUE + 2000 CONTINUE *2000 :: end of the ibr-loop * * .. update SVA(N) - IF ((SVA(N) .LT. ROOTBIG).AND.(SVA(N) .GT. ROOTSFMIN)) THEN - SVA(N) = SNRM2( M, A(1,N), 1 ) * WORK(N) - ELSE - T = ZERO - AAPP = ZERO - CALL SLASSQ( M, A(1,N), 1, T, AAPP ) - SVA(N) = T * SQRT(AAPP) * WORK(N) - END IF + IF( ( SVA( N ).LT.ROOTBIG ) .AND. ( SVA( N ).GT.ROOTSFMIN ) ) + + THEN + SVA( N ) = SNRM2( M, A( 1, N ), 1 )*WORK( N ) + ELSE + T = ZERO + AAPP = ZERO + CALL SLASSQ( M, A( 1, N ), 1, T, AAPP ) + SVA( N ) = T*SQRT( AAPP )*WORK( N ) + END IF * * Additional steering devices * - IF ( ( i.LT.SWBAND ) .AND. ( ( MXAAPQ.LE.ROOTTOL ) .OR. - & ( ISWROT .LE. N ) ) ) - & SWBAND = i + IF( ( i.LT.SWBAND ) .AND. ( ( MXAAPQ.LE.ROOTTOL ) .OR. + + ( ISWROT.LE.N ) ) )SWBAND = i * - IF ( (i .GT. SWBAND+1) .AND. (MXAAPQ .LT. SQRT(FLOAT(N))*TOL) - & .AND. (FLOAT(N)*MXAAPQ*MXSINJ .LT. TOL) ) THEN - GO TO 1994 - END IF + IF( ( i.GT.SWBAND+1 ) .AND. ( MXAAPQ.LT.SQRT( FLOAT( N ) )* + + TOL ) .AND. ( FLOAT( N )*MXAAPQ*MXSINJ.LT.TOL ) ) THEN + GO TO 1994 + END IF * - IF ( NOTROT .GE. EMPTSW ) GO TO 1994 + IF( NOTROT.GE.EMPTSW )GO TO 1994 * 1993 CONTINUE * end i=1:NSWEEP loop @@ -1265,80 +1423,81 @@ N2 = 0 N4 = 0 DO 5991 p = 1, N - 1 - q = ISAMAX( N-p+1, SVA(p), 1 ) + p - 1 - IF ( p .NE. q ) THEN - TEMP1 = SVA(p) - SVA(p) = SVA(q) - SVA(q) = TEMP1 - TEMP1 = WORK(p) - WORK(p) = WORK(q) - WORK(q) = TEMP1 - CALL SSWAP( M, A(1,p), 1, A(1,q), 1 ) - IF ( RSVEC ) CALL SSWAP( MVL, V(1,p), 1, V(1,q), 1 ) + q = ISAMAX( N-p+1, SVA( p ), 1 ) + p - 1 + IF( p.NE.q ) THEN + TEMP1 = SVA( p ) + SVA( p ) = SVA( q ) + SVA( q ) = TEMP1 + TEMP1 = WORK( p ) + WORK( p ) = WORK( q ) + WORK( q ) = TEMP1 + CALL SSWAP( M, A( 1, p ), 1, A( 1, q ), 1 ) + IF( RSVEC )CALL SSWAP( MVL, V( 1, p ), 1, V( 1, q ), 1 ) END IF - IF ( SVA(p) .NE. ZERO ) THEN + IF( SVA( p ).NE.ZERO ) THEN N4 = N4 + 1 - IF ( SVA(p)*SCALE .GT. SFMIN ) N2 = N2 + 1 + IF( SVA( p )*SCALE.GT.SFMIN )N2 = N2 + 1 END IF 5991 CONTINUE - IF ( SVA(N) .NE. ZERO ) THEN + IF( SVA( N ).NE.ZERO ) THEN N4 = N4 + 1 - IF ( SVA(N)*SCALE .GT. SFMIN ) N2 = N2 + 1 + IF( SVA( N )*SCALE.GT.SFMIN )N2 = N2 + 1 END IF * * Normalize the left singular vectors. * - IF ( LSVEC .OR. UCTOL ) THEN + IF( LSVEC .OR. UCTOL ) THEN DO 1998 p = 1, N2 - CALL SSCAL( M, WORK(p) / SVA(p), A(1,p), 1 ) + CALL SSCAL( M, WORK( p ) / SVA( p ), A( 1, p ), 1 ) 1998 CONTINUE END IF * * Scale the product of Jacobi rotations (assemble the fast rotations). * - IF ( RSVEC ) THEN - IF ( APPLV ) THEN + IF( RSVEC ) THEN + IF( APPLV ) THEN DO 2398 p = 1, N - CALL SSCAL( MVL, WORK(p), V(1,p), 1 ) + CALL SSCAL( MVL, WORK( p ), V( 1, p ), 1 ) 2398 CONTINUE ELSE DO 2399 p = 1, N - TEMP1 = ONE / SNRM2(MVL, V(1,p), 1 ) - CALL SSCAL( MVL, TEMP1, V(1,p), 1 ) + TEMP1 = ONE / SNRM2( MVL, V( 1, p ), 1 ) + CALL SSCAL( MVL, TEMP1, V( 1, p ), 1 ) 2399 CONTINUE END IF END IF * * Undo scaling, if necessary (and possible). - IF ( ((SCALE.GT.ONE).AND.(SVA(1).LT.(BIG/SCALE))) - & .OR.((SCALE.LT.ONE).AND.(SVA(N2).GT.(SFMIN/SCALE))) ) THEN + IF( ( ( SCALE.GT.ONE ) .AND. ( SVA( 1 ).LT.( BIG / + + SCALE ) ) ) .OR. ( ( SCALE.LT.ONE ) .AND. ( SVA( N2 ).GT. + + ( SFMIN / SCALE ) ) ) ) THEN DO 2400 p = 1, N - SVA(p) = SCALE*SVA(p) + SVA( p ) = SCALE*SVA( p ) 2400 CONTINUE SCALE = ONE END IF * - WORK(1) = SCALE + WORK( 1 ) = SCALE * The singular values of A are SCALE*SVA(1:N). If SCALE.NE.ONE * then some of the singular values may overflow or underflow and * the spectrum is given in this factored representation. * - WORK(2) = FLOAT(N4) + WORK( 2 ) = FLOAT( N4 ) * N4 is the number of computed nonzero singular values of A. * - WORK(3) = FLOAT(N2) + WORK( 3 ) = FLOAT( N2 ) * N2 is the number of singular values of A greater than SFMIN. * If N2<N, SVA(N2:N) contains ZEROS and/or denormalized numbers * that may carry some information. * - WORK(4) = FLOAT(i) + WORK( 4 ) = FLOAT( i ) * i is the index of the last sweep before declaring convergence. * - WORK(5) = MXAAPQ + WORK( 5 ) = MXAAPQ * MXAAPQ is the largest absolute value of scaled pivots in the * last sweep * - WORK(6) = MXSINJ + WORK( 6 ) = MXSINJ * MXSINJ is the largest absolute value of the sines of Jacobi angles * in the last sweep * @@ -1347,4 +1506,3 @@ * .. END OF SGESVJ * .. END -* diff --git a/SRC/sgsvj0.f b/SRC/sgsvj0.f index 975205e3..a7cb80b9 100644 --- a/SRC/sgsvj0.f +++ b/SRC/sgsvj0.f @@ -1,5 +1,5 @@ SUBROUTINE SGSVJ0( JOBV, M, N, A, LDA, D, SVA, MV, V, LDV, EPS, - & SFMIN, TOL, NSWEEP, WORK, LWORK, INFO ) + + SFMIN, TOL, NSWEEP, WORK, LWORK, INFO ) * * -- LAPACK routine (version 3.2) -- * @@ -15,21 +15,21 @@ * computation of SVD, PSVD, QSVD, (H,K)-SVD, and for solution of the * eigenvalue problems Hx = lambda M x, H M x = lambda x with H, M > 0. * -* Scalar Arguments -* - IMPLICIT NONE - INTEGER INFO, LDA, LDV, LWORK, M, MV, N, NSWEEP - REAL EPS, SFMIN, TOL - CHARACTER*1 JOBV -* -* Array Arguments -* - REAL A( LDA, * ), SVA( N ), D( N ), V( LDV, * ), - & WORK( LWORK ) + IMPLICIT NONE +* .. +* .. Scalar Arguments .. + INTEGER INFO, LDA, LDV, LWORK, M, MV, N, NSWEEP + REAL EPS, SFMIN, TOL + CHARACTER*1 JOBV +* .. +* .. Array Arguments .. + REAL A( LDA, * ), SVA( N ), D( N ), V( LDV, * ), + + WORK( LWORK ) * .. * * Purpose -* ~~~~~~~ +* ======= +* * SGSVJ0 is called from SGESVJ as a pre-processor and that is its main * purpose. It applies Jacobi rotations in the same way as SGESVJ does, but * it does not check convergence (stopping criterion). Few tuning @@ -50,7 +50,7 @@ * drmac@math.hr. Thank you. * * Arguments -* ~~~~~~~~~ +* ========= * * JOBV (input) CHARACTER*1 * Specifies whether the output from this procedure is used @@ -140,89 +140,95 @@ * = 0 : successful exit. * < 0 : if INFO = -i, then the i-th argument had an illegal value * -* Local Parameters - REAL ZERO, HALF, ONE, TWO - PARAMETER ( ZERO = 0.0E0, HALF = 0.5E0, ONE = 1.0E0, TWO = 2.0E0 ) - -* Local Scalars - REAL AAPP, AAPP0, AAPQ, AAQQ, APOAQ, AQOAP, BIG, BIGTHETA, - & CS, MXAAPQ, MXSINJ, ROOTBIG, ROOTEPS, ROOTSFMIN, - & ROOTTOL, SMALL, SN, T, TEMP1, THETA, THSIGN - INTEGER BLSKIP, EMPTSW, i, ibr, IERR, igl, IJBLSK, ir1, ISWROT, - & jbc, jgl, KBL, LKAHEAD, MVL, NBL, NOTROT, p, PSKIPPED, - & q, ROWSKIP, SWBAND - LOGICAL APPLV, ROTOK, RSVEC - -* Local Arrays - REAL FASTR(5) -* -* Intrinsic Functions - INTRINSIC ABS, AMAX1, AMIN1, FLOAT, MIN0, SIGN, SQRT -* -* External Functions - REAL SDOT, SNRM2 - INTEGER ISAMAX - LOGICAL LSAME - EXTERNAL ISAMAX, LSAME, SDOT, SNRM2 +* ===================================================================== * -* External Subroutines - EXTERNAL SAXPY, SCOPY, SLASCL, SLASSQ, SROTM, SSWAP +* .. Local Parameters .. + REAL ZERO, HALF, ONE, TWO + PARAMETER ( ZERO = 0.0E0, HALF = 0.5E0, ONE = 1.0E0, + + TWO = 2.0E0 ) +* .. +* .. Local Scalars .. + REAL AAPP, AAPP0, AAPQ, AAQQ, APOAQ, AQOAP, BIG, + + BIGTHETA, CS, MXAAPQ, MXSINJ, ROOTBIG, ROOTEPS, + + ROOTSFMIN, ROOTTOL, SMALL, SN, T, TEMP1, THETA, + + THSIGN + INTEGER BLSKIP, EMPTSW, i, ibr, IERR, igl, IJBLSK, ir1, + + ISWROT, jbc, jgl, KBL, LKAHEAD, MVL, NBL, + + NOTROT, p, PSKIPPED, q, ROWSKIP, SWBAND + LOGICAL APPLV, ROTOK, RSVEC +* .. +* .. Local Arrays .. + REAL FASTR( 5 ) +* .. +* .. Intrinsic Functions .. + INTRINSIC ABS, AMAX1, AMIN1, FLOAT, MIN0, SIGN, SQRT +* .. +* .. External Functions .. + REAL SDOT, SNRM2 + INTEGER ISAMAX + LOGICAL LSAME + EXTERNAL ISAMAX, LSAME, SDOT, SNRM2 +* .. +* .. External Subroutines .. + EXTERNAL SAXPY, SCOPY, SLASCL, SLASSQ, SROTM, SSWAP +* .. +* .. Executable Statements .. * -* ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~| +* Test the input parameters. * - APPLV = LSAME(JOBV,'A') - RSVEC = LSAME(JOBV,'V') - IF ( .NOT.( RSVEC .OR. APPLV .OR. LSAME(JOBV,'N'))) THEN + APPLV = LSAME( JOBV, 'A' ) + RSVEC = LSAME( JOBV, 'V' ) + IF( .NOT.( RSVEC .OR. APPLV .OR. LSAME( JOBV, 'N' ) ) ) THEN INFO = -1 - ELSE IF ( M .LT. 0 ) THEN + ELSE IF( M.LT.0 ) THEN INFO = -2 - ELSE IF ( ( N .LT. 0 ) .OR. ( N .GT. M )) THEN + ELSE IF( ( N.LT.0 ) .OR. ( N.GT.M ) ) THEN INFO = -3 - ELSE IF ( LDA .LT. M ) THEN + ELSE IF( LDA.LT.M ) THEN INFO = -5 - ELSE IF ( MV .LT. 0 ) THEN + ELSE IF( MV.LT.0 ) THEN INFO = -8 - ELSE IF ( LDV .LT. M ) THEN + ELSE IF( LDV.LT.M ) THEN INFO = -10 - ELSE IF ( TOL .LE. EPS ) THEN + ELSE IF( TOL.LE.EPS ) THEN INFO = -13 - ELSE IF ( NSWEEP .LT. 0 ) THEN + ELSE IF( NSWEEP.LT.0 ) THEN INFO = -14 - ELSE IF ( LWORK .LT. M ) THEN + ELSE IF( LWORK.LT.M ) THEN INFO = -16 ELSE INFO = 0 END IF * * #:( - IF ( INFO .NE. 0 ) THEN + IF( INFO.NE.0 ) THEN CALL XERBLA( 'SGSVJ0', -INFO ) RETURN END IF * - IF ( RSVEC ) THEN + IF( RSVEC ) THEN MVL = N - ELSE IF ( APPLV ) THEN + ELSE IF( APPLV ) THEN MVL = MV END IF RSVEC = RSVEC .OR. APPLV - ROOTEPS = SQRT(EPS) - ROOTSFMIN = SQRT(SFMIN) - SMALL = SFMIN / EPS - BIG = ONE / SFMIN - ROOTBIG = ONE / ROOTSFMIN - BIGTHETA = ONE / ROOTEPS - ROOTTOL = SQRT(TOL) + ROOTEPS = SQRT( EPS ) + ROOTSFMIN = SQRT( SFMIN ) + SMALL = SFMIN / EPS + BIG = ONE / SFMIN + ROOTBIG = ONE / ROOTSFMIN + BIGTHETA = ONE / ROOTEPS + ROOTTOL = SQRT( TOL ) * * -* -#- Row-cyclic Jacobi SVD algorithm with column pivoting -#- +* .. Row-cyclic Jacobi SVD algorithm with column pivoting .. * - EMPTSW = ( N * ( N - 1 ) ) / 2 - NOTROT = 0 - FASTR(1) = ZERO + EMPTSW = ( N*( N-1 ) ) / 2 + NOTROT = 0 + FASTR( 1 ) = ZERO * -* -#- Row-cyclic pivot strategy with de Rijk's pivoting -#- +* .. Row-cyclic pivot strategy with de Rijk's pivoting .. * SWBAND = 0 @@ -238,7 +244,7 @@ * parameters of the computer's memory. * NBL = N / KBL - IF ( ( NBL * KBL ) .NE. N ) NBL = NBL + 1 + IF( ( NBL*KBL ).NE.N )NBL = NBL + 1 BLSKIP = ( KBL**2 ) + 1 *[TP] BLKSKIP is a tuning parameter that depends on SWBAND and KBL. @@ -254,37 +260,38 @@ DO 1993 i = 1, NSWEEP * .. go go go ... * - MXAAPQ = ZERO - MXSINJ = ZERO - ISWROT = 0 + MXAAPQ = ZERO + MXSINJ = ZERO + ISWROT = 0 * - NOTROT = 0 - PSKIPPED = 0 + NOTROT = 0 + PSKIPPED = 0 * - DO 2000 ibr = 1, NBL + DO 2000 ibr = 1, NBL - igl = ( ibr - 1 ) * KBL + 1 + igl = ( ibr-1 )*KBL + 1 * - DO 1002 ir1 = 0, MIN0( LKAHEAD, NBL - ibr ) + DO 1002 ir1 = 0, MIN0( LKAHEAD, NBL-ibr ) * - igl = igl + ir1 * KBL + igl = igl + ir1*KBL * - DO 2001 p = igl, MIN0( igl + KBL - 1, N - 1) + DO 2001 p = igl, MIN0( igl+KBL-1, N-1 ) * .. de Rijk's pivoting - q = ISAMAX( N-p+1, SVA(p), 1 ) + p - 1 - IF ( p .NE. q ) THEN - CALL SSWAP( M, A(1,p), 1, A(1,q), 1 ) - IF ( RSVEC ) CALL SSWAP( MVL, V(1,p), 1, V(1,q), 1 ) - TEMP1 = SVA(p) - SVA(p) = SVA(q) - SVA(q) = TEMP1 - TEMP1 = D(p) - D(p) = D(q) - D(q) = TEMP1 - END IF -* - IF ( ir1 .EQ. 0 ) THEN + q = ISAMAX( N-p+1, SVA( p ), 1 ) + p - 1 + IF( p.NE.q ) THEN + CALL SSWAP( M, A( 1, p ), 1, A( 1, q ), 1 ) + IF( RSVEC )CALL SSWAP( MVL, V( 1, p ), 1, + + V( 1, q ), 1 ) + TEMP1 = SVA( p ) + SVA( p ) = SVA( q ) + SVA( q ) = TEMP1 + TEMP1 = D( p ) + D( p ) = D( q ) + D( q ) = TEMP1 + END IF +* + IF( ir1.EQ.0 ) THEN * * Column norms are periodically updated by explicit * norm computation. @@ -298,505 +305,648 @@ * If properly implemented SNRM2 is available, the IF-THEN-ELSE * below should read "AAPP = SNRM2( M, A(1,p), 1 ) * D(p)". * - IF ((SVA(p) .LT. ROOTBIG) .AND. (SVA(p) .GT. ROOTSFMIN)) THEN - SVA(p) = SNRM2( M, A(1,p), 1 ) * D(p) - ELSE - TEMP1 = ZERO - AAPP = ZERO - CALL SLASSQ( M, A(1,p), 1, TEMP1, AAPP ) - SVA(p) = TEMP1 * SQRT(AAPP) * D(p) - END IF - AAPP = SVA(p) - ELSE - AAPP = SVA(p) - END IF + IF( ( SVA( p ).LT.ROOTBIG ) .AND. + + ( SVA( p ).GT.ROOTSFMIN ) ) THEN + SVA( p ) = SNRM2( M, A( 1, p ), 1 )*D( p ) + ELSE + TEMP1 = ZERO + AAPP = ZERO + CALL SLASSQ( M, A( 1, p ), 1, TEMP1, AAPP ) + SVA( p ) = TEMP1*SQRT( AAPP )*D( p ) + END IF + AAPP = SVA( p ) + ELSE + AAPP = SVA( p ) + END IF * - IF ( AAPP .GT. ZERO ) THEN + IF( AAPP.GT.ZERO ) THEN * - PSKIPPED = 0 + PSKIPPED = 0 * - DO 2002 q = p + 1, MIN0( igl + KBL - 1, N ) + DO 2002 q = p + 1, MIN0( igl+KBL-1, N ) * - AAQQ = SVA(q) + AAQQ = SVA( q ) - IF ( AAQQ .GT. ZERO ) THEN -* - AAPP0 = AAPP - IF ( AAQQ .GE. ONE ) THEN - ROTOK = ( SMALL*AAPP ) .LE. AAQQ - IF ( AAPP .LT. ( BIG / AAQQ ) ) THEN - AAPQ = ( SDOT(M, A(1,p), 1, A(1,q), 1 ) * - & D(p) * D(q) / AAQQ ) / AAPP - ELSE - CALL SCOPY( M, A(1,p), 1, WORK, 1 ) - CALL SLASCL( 'G', 0, 0, AAPP, D(p), M, - & 1, WORK, LDA, IERR ) - AAPQ = SDOT( M, WORK,1, A(1,q),1 )*D(q) / AAQQ - END IF - ELSE - ROTOK = AAPP .LE. ( AAQQ / SMALL ) - IF ( AAPP .GT. ( SMALL / AAQQ ) ) THEN - AAPQ = ( SDOT( M, A(1,p), 1, A(1,q), 1 ) * - & D(p) * D(q) / AAQQ ) / AAPP - ELSE - CALL SCOPY( M, A(1,q), 1, WORK, 1 ) - CALL SLASCL( 'G', 0, 0, AAQQ, D(q), M, - & 1, WORK, LDA, IERR ) - AAPQ = SDOT( M, WORK,1, A(1,p),1 )*D(p) / AAPP - END IF - END IF + IF( AAQQ.GT.ZERO ) THEN +* + AAPP0 = AAPP + IF( AAQQ.GE.ONE ) THEN + ROTOK = ( SMALL*AAPP ).LE.AAQQ + IF( AAPP.LT.( BIG / AAQQ ) ) THEN + AAPQ = ( SDOT( M, A( 1, p ), 1, A( 1, + + q ), 1 )*D( p )*D( q ) / AAQQ ) + + / AAPP + ELSE + CALL SCOPY( M, A( 1, p ), 1, WORK, 1 ) + CALL SLASCL( 'G', 0, 0, AAPP, D( p ), + + M, 1, WORK, LDA, IERR ) + AAPQ = SDOT( M, WORK, 1, A( 1, q ), + + 1 )*D( q ) / AAQQ + END IF + ELSE + ROTOK = AAPP.LE.( AAQQ / SMALL ) + IF( AAPP.GT.( SMALL / AAQQ ) ) THEN + AAPQ = ( SDOT( M, A( 1, p ), 1, A( 1, + + q ), 1 )*D( p )*D( q ) / AAQQ ) + + / AAPP + ELSE + CALL SCOPY( M, A( 1, q ), 1, WORK, 1 ) + CALL SLASCL( 'G', 0, 0, AAQQ, D( q ), + + M, 1, WORK, LDA, IERR ) + AAPQ = SDOT( M, WORK, 1, A( 1, p ), + + 1 )*D( p ) / AAPP + END IF + END IF * - MXAAPQ = AMAX1( MXAAPQ, ABS(AAPQ) ) + MXAAPQ = AMAX1( MXAAPQ, ABS( AAPQ ) ) * * TO rotate or NOT to rotate, THAT is the question ... * - IF ( ABS( AAPQ ) .GT. TOL ) THEN + IF( ABS( AAPQ ).GT.TOL ) THEN * * .. rotate * ROTATED = ROTATED + ONE * - IF ( ir1 .EQ. 0 ) THEN - NOTROT = 0 - PSKIPPED = 0 - ISWROT = ISWROT + 1 - END IF + IF( ir1.EQ.0 ) THEN + NOTROT = 0 + PSKIPPED = 0 + ISWROT = ISWROT + 1 + END IF * - IF ( ROTOK ) THEN + IF( ROTOK ) THEN * - AQOAP = AAQQ / AAPP - APOAQ = AAPP / AAQQ - THETA = - HALF * ABS( AQOAP - APOAQ ) / AAPQ + AQOAP = AAQQ / AAPP + APOAQ = AAPP / AAQQ + THETA = -HALF*ABS( AQOAP-APOAQ ) / AAPQ * - IF ( ABS( THETA ) .GT. BIGTHETA ) THEN + IF( ABS( THETA ).GT.BIGTHETA ) THEN * - T = HALF / THETA - FASTR(3) = T * D(p) / D(q) - FASTR(4) = - T * D(q) / D(p) - CALL SROTM( M, A(1,p), 1, A(1,q), 1, FASTR ) - IF ( RSVEC ) - & CALL SROTM( MVL, V(1,p), 1, V(1,q), 1, FASTR ) - SVA(q) = AAQQ*SQRT( AMAX1(ZERO,ONE + T*APOAQ*AAPQ) ) - AAPP = AAPP*SQRT( ONE - T*AQOAP*AAPQ ) - MXSINJ = AMAX1( MXSINJ, ABS(T) ) + T = HALF / THETA + FASTR( 3 ) = T*D( p ) / D( q ) + FASTR( 4 ) = -T*D( q ) / D( p ) + CALL SROTM( M, A( 1, p ), 1, + + A( 1, q ), 1, FASTR ) + IF( RSVEC )CALL SROTM( MVL, + + V( 1, p ), 1, + + V( 1, q ), 1, + + FASTR ) + SVA( q ) = AAQQ*SQRT( AMAX1( ZERO, + + ONE+T*APOAQ*AAPQ ) ) + AAPP = AAPP*SQRT( ONE-T*AQOAP*AAPQ ) + MXSINJ = AMAX1( MXSINJ, ABS( T ) ) * - ELSE + ELSE * * .. choose correct signum for THETA and rotate * - THSIGN = - SIGN(ONE,AAPQ) - T = ONE / ( THETA + THSIGN*SQRT(ONE+THETA*THETA) ) - CS = SQRT( ONE / ( ONE + T*T ) ) - SN = T * CS -* - MXSINJ = AMAX1( MXSINJ, ABS(SN) ) - SVA(q) = AAQQ*SQRT( AMAX1(ZERO, ONE+T*APOAQ*AAPQ) ) - AAPP = AAPP*SQRT( AMAX1(ZERO, ONE-T*AQOAP*AAPQ) ) -* - APOAQ = D(p) / D(q) - AQOAP = D(q) / D(p) - IF ( D(p) .GE. ONE ) THEN - IF ( D(q) .GE. ONE ) THEN - FASTR(3) = T * APOAQ - FASTR(4) = - T * AQOAP - D(p) = D(p) * CS - D(q) = D(q) * CS - CALL SROTM( M, A(1,p),1, A(1,q),1, FASTR ) - IF ( RSVEC ) - & CALL SROTM( MVL, V(1,p),1, V(1,q),1, FASTR ) - ELSE - CALL SAXPY( M, -T*AQOAP, A(1,q),1, A(1,p),1 ) - CALL SAXPY( M, CS*SN*APOAQ, A(1,p),1, A(1,q),1 ) - D(p) = D(p) * CS - D(q) = D(q) / CS - IF ( RSVEC ) THEN - CALL SAXPY(MVL, -T*AQOAP, V(1,q),1,V(1,p),1) - CALL SAXPY(MVL,CS*SN*APOAQ, V(1,p),1,V(1,q),1) - END IF - END IF - ELSE - IF ( D(q) .GE. ONE ) THEN - CALL SAXPY( M, T*APOAQ, A(1,p),1, A(1,q),1 ) - CALL SAXPY( M,-CS*SN*AQOAP, A(1,q),1, A(1,p),1 ) - D(p) = D(p) / CS - D(q) = D(q) * CS - IF ( RSVEC ) THEN - CALL SAXPY(MVL, T*APOAQ, V(1,p),1,V(1,q),1) - CALL SAXPY(MVL,-CS*SN*AQOAP,V(1,q),1,V(1,p),1) - END IF - ELSE - IF ( D(p) .GE. D(q) ) THEN - CALL SAXPY( M,-T*AQOAP, A(1,q),1,A(1,p),1 ) - CALL SAXPY( M,CS*SN*APOAQ,A(1,p),1,A(1,q),1 ) - D(p) = D(p) * CS - D(q) = D(q) / CS - IF ( RSVEC ) THEN - CALL SAXPY(MVL, -T*AQOAP, V(1,q),1,V(1,p),1) - CALL SAXPY(MVL,CS*SN*APOAQ,V(1,p),1,V(1,q),1) - END IF - ELSE - CALL SAXPY( M, T*APOAQ, A(1,p),1,A(1,q),1) - CALL SAXPY( M,-CS*SN*AQOAP,A(1,q),1,A(1,p),1) - D(p) = D(p) / CS - D(q) = D(q) * CS - IF ( RSVEC ) THEN - CALL SAXPY(MVL, T*APOAQ, V(1,p),1,V(1,q),1) - CALL SAXPY(MVL,-CS*SN*AQOAP,V(1,q),1,V(1,p),1) - END IF - END IF - END IF - ENDIF - END IF -* - ELSE + THSIGN = -SIGN( ONE, AAPQ ) + T = ONE / ( THETA+THSIGN* + + SQRT( ONE+THETA*THETA ) ) + CS = SQRT( ONE / ( ONE+T*T ) ) + SN = T*CS +* + MXSINJ = AMAX1( MXSINJ, ABS( SN ) ) + SVA( q ) = AAQQ*SQRT( AMAX1( ZERO, + + ONE+T*APOAQ*AAPQ ) ) + AAPP = AAPP*SQRT( AMAX1( ZERO, + + ONE-T*AQOAP*AAPQ ) ) +* + APOAQ = D( p ) / D( q ) + AQOAP = D( q ) / D( p ) + IF( D( p ).GE.ONE ) THEN + IF( D( q ).GE.ONE ) THEN + FASTR( 3 ) = T*APOAQ + FASTR( 4 ) = -T*AQOAP + D( p ) = D( p )*CS + D( q ) = D( q )*CS + CALL SROTM( M, A( 1, p ), 1, + + A( 1, q ), 1, + + FASTR ) + IF( RSVEC )CALL SROTM( MVL, + + V( 1, p ), 1, V( 1, q ), + + 1, FASTR ) + ELSE + CALL SAXPY( M, -T*AQOAP, + + A( 1, q ), 1, + + A( 1, p ), 1 ) + CALL SAXPY( M, CS*SN*APOAQ, + + A( 1, p ), 1, + + A( 1, q ), 1 ) + D( p ) = D( p )*CS + D( q ) = D( q ) / CS + IF( RSVEC ) THEN + CALL SAXPY( MVL, -T*AQOAP, + + V( 1, q ), 1, + + V( 1, p ), 1 ) + CALL SAXPY( MVL, + + CS*SN*APOAQ, + + V( 1, p ), 1, + + V( 1, q ), 1 ) + END IF + END IF + ELSE + IF( D( q ).GE.ONE ) THEN + CALL SAXPY( M, T*APOAQ, + + A( 1, p ), 1, + + A( 1, q ), 1 ) + CALL SAXPY( M, -CS*SN*AQOAP, + + A( 1, q ), 1, + + A( 1, p ), 1 ) + D( p ) = D( p ) / CS + D( q ) = D( q )*CS + IF( RSVEC ) THEN + CALL SAXPY( MVL, T*APOAQ, + + V( 1, p ), 1, + + V( 1, q ), 1 ) + CALL SAXPY( MVL, + + -CS*SN*AQOAP, + + V( 1, q ), 1, + + V( 1, p ), 1 ) + END IF + ELSE + IF( D( p ).GE.D( q ) ) THEN + CALL SAXPY( M, -T*AQOAP, + + A( 1, q ), 1, + + A( 1, p ), 1 ) + CALL SAXPY( M, CS*SN*APOAQ, + + A( 1, p ), 1, + + A( 1, q ), 1 ) + D( p ) = D( p )*CS + D( q ) = D( q ) / CS + IF( RSVEC ) THEN + CALL SAXPY( MVL, + + -T*AQOAP, + + V( 1, q ), 1, + + V( 1, p ), 1 ) + CALL SAXPY( MVL, + + CS*SN*APOAQ, + + V( 1, p ), 1, + + V( 1, q ), 1 ) + END IF + ELSE + CALL SAXPY( M, T*APOAQ, + + A( 1, p ), 1, + + A( 1, q ), 1 ) + CALL SAXPY( M, + + -CS*SN*AQOAP, + + A( 1, q ), 1, + + A( 1, p ), 1 ) + D( p ) = D( p ) / CS + D( q ) = D( q )*CS + IF( RSVEC ) THEN + CALL SAXPY( MVL, + + T*APOAQ, V( 1, p ), + + 1, V( 1, q ), 1 ) + CALL SAXPY( MVL, + + -CS*SN*AQOAP, + + V( 1, q ), 1, + + V( 1, p ), 1 ) + END IF + END IF + END IF + END IF + END IF +* + ELSE * .. have to use modified Gram-Schmidt like transformation - CALL SCOPY( M, A(1,p), 1, WORK, 1 ) - CALL SLASCL( 'G',0,0,AAPP,ONE,M,1,WORK,LDA,IERR ) - CALL SLASCL( 'G',0,0,AAQQ,ONE,M,1, A(1,q),LDA,IERR ) - TEMP1 = -AAPQ * D(p) / D(q) - CALL SAXPY ( M, TEMP1, WORK, 1, A(1,q), 1 ) - CALL SLASCL( 'G',0,0,ONE,AAQQ,M,1, A(1,q),LDA,IERR ) - SVA(q) = AAQQ*SQRT( AMAX1( ZERO, ONE - AAPQ*AAPQ ) ) - MXSINJ = AMAX1( MXSINJ, SFMIN ) - END IF + CALL SCOPY( M, A( 1, p ), 1, WORK, 1 ) + CALL SLASCL( 'G', 0, 0, AAPP, ONE, M, + + 1, WORK, LDA, IERR ) + CALL SLASCL( 'G', 0, 0, AAQQ, ONE, M, + + 1, A( 1, q ), LDA, IERR ) + TEMP1 = -AAPQ*D( p ) / D( q ) + CALL SAXPY( M, TEMP1, WORK, 1, + + A( 1, q ), 1 ) + CALL SLASCL( 'G', 0, 0, ONE, AAQQ, M, + + 1, A( 1, q ), LDA, IERR ) + SVA( q ) = AAQQ*SQRT( AMAX1( ZERO, + + ONE-AAPQ*AAPQ ) ) + MXSINJ = AMAX1( MXSINJ, SFMIN ) + END IF * END IF ROTOK THEN ... ELSE * * In the case of cancellation in updating SVA(q), SVA(p) * recompute SVA(q), SVA(p). - IF ( (SVA(q) / AAQQ )**2 .LE. ROOTEPS ) THEN - IF ((AAQQ .LT. ROOTBIG).AND.(AAQQ .GT. ROOTSFMIN)) THEN - SVA(q) = SNRM2( M, A(1,q), 1 ) * D(q) - ELSE - T = ZERO - AAQQ = ZERO - CALL SLASSQ( M, A(1,q), 1, T, AAQQ ) - SVA(q) = T * SQRT(AAQQ) * D(q) - END IF - END IF - IF ( ( AAPP / AAPP0) .LE. ROOTEPS ) THEN - IF ((AAPP .LT. ROOTBIG).AND.(AAPP .GT. ROOTSFMIN)) THEN - AAPP = SNRM2( M, A(1,p), 1 ) * D(p) - ELSE - T = ZERO - AAPP = ZERO - CALL SLASSQ( M, A(1,p), 1, T, AAPP ) - AAPP = T * SQRT(AAPP) * D(p) - END IF - SVA(p) = AAPP - END IF -* - ELSE + IF( ( SVA( q ) / AAQQ )**2.LE.ROOTEPS ) + + THEN + IF( ( AAQQ.LT.ROOTBIG ) .AND. + + ( AAQQ.GT.ROOTSFMIN ) ) THEN + SVA( q ) = SNRM2( M, A( 1, q ), 1 )* + + D( q ) + ELSE + T = ZERO + AAQQ = ZERO + CALL SLASSQ( M, A( 1, q ), 1, T, + + AAQQ ) + SVA( q ) = T*SQRT( AAQQ )*D( q ) + END IF + END IF + IF( ( AAPP / AAPP0 ).LE.ROOTEPS ) THEN + IF( ( AAPP.LT.ROOTBIG ) .AND. + + ( AAPP.GT.ROOTSFMIN ) ) THEN + AAPP = SNRM2( M, A( 1, p ), 1 )* + + D( p ) + ELSE + T = ZERO + AAPP = ZERO + CALL SLASSQ( M, A( 1, p ), 1, T, + + AAPP ) + AAPP = T*SQRT( AAPP )*D( p ) + END IF + SVA( p ) = AAPP + END IF +* + ELSE * A(:,p) and A(:,q) already numerically orthogonal - IF ( ir1 .EQ. 0 ) NOTROT = NOTROT + 1 - PSKIPPED = PSKIPPED + 1 - END IF - ELSE + IF( ir1.EQ.0 )NOTROT = NOTROT + 1 + PSKIPPED = PSKIPPED + 1 + END IF + ELSE * A(:,q) is zero column - IF ( ir1. EQ. 0 ) NOTROT = NOTROT + 1 - PSKIPPED = PSKIPPED + 1 - END IF + IF( ir1.EQ.0 )NOTROT = NOTROT + 1 + PSKIPPED = PSKIPPED + 1 + END IF * - IF ( ( i .LE. SWBAND ) .AND. ( PSKIPPED .GT. ROWSKIP ) ) THEN - IF ( ir1 .EQ. 0 ) AAPP = - AAPP - NOTROT = 0 - GO TO 2103 - END IF + IF( ( i.LE.SWBAND ) .AND. + + ( PSKIPPED.GT.ROWSKIP ) ) THEN + IF( ir1.EQ.0 )AAPP = -AAPP + NOTROT = 0 + GO TO 2103 + END IF * - 2002 CONTINUE + 2002 CONTINUE * END q-LOOP * - 2103 CONTINUE + 2103 CONTINUE * bailed out of q-loop - SVA(p) = AAPP + SVA( p ) = AAPP - ELSE - SVA(p) = AAPP - IF ( ( ir1 .EQ. 0 ) .AND. (AAPP .EQ. ZERO) ) - & NOTROT=NOTROT+MIN0(igl+KBL-1,N)-p - END IF + ELSE + SVA( p ) = AAPP + IF( ( ir1.EQ.0 ) .AND. ( AAPP.EQ.ZERO ) ) + + NOTROT = NOTROT + MIN0( igl+KBL-1, N ) - p + END IF * - 2001 CONTINUE + 2001 CONTINUE * end of the p-loop * end of doing the block ( ibr, ibr ) - 1002 CONTINUE + 1002 CONTINUE * end of ir1-loop * *........................................................ * ... go to the off diagonal blocks * - igl = ( ibr - 1 ) * KBL + 1 + igl = ( ibr-1 )*KBL + 1 * - DO 2010 jbc = ibr + 1, NBL + DO 2010 jbc = ibr + 1, NBL * - jgl = ( jbc - 1 ) * KBL + 1 + jgl = ( jbc-1 )*KBL + 1 * * doing the block at ( ibr, jbc ) * - IJBLSK = 0 - DO 2100 p = igl, MIN0( igl + KBL - 1, N ) -* - AAPP = SVA(p) -* - IF ( AAPP .GT. ZERO ) THEN -* - PSKIPPED = 0 -* - DO 2200 q = jgl, MIN0( jgl + KBL - 1, N ) -* - AAQQ = SVA(q) -* - IF ( AAQQ .GT. ZERO ) THEN - AAPP0 = AAPP -* -* -#- M x 2 Jacobi SVD -#- -* -* -#- Safe Gram matrix computation -#- -* - IF ( AAQQ .GE. ONE ) THEN - IF ( AAPP .GE. AAQQ ) THEN - ROTOK = ( SMALL*AAPP ) .LE. AAQQ - ELSE - ROTOK = ( SMALL*AAQQ ) .LE. AAPP - END IF - IF ( AAPP .LT. ( BIG / AAQQ ) ) THEN - AAPQ = ( SDOT(M, A(1,p), 1, A(1,q), 1 ) * - & D(p) * D(q) / AAQQ ) / AAPP - ELSE - CALL SCOPY( M, A(1,p), 1, WORK, 1 ) - CALL SLASCL( 'G', 0, 0, AAPP, D(p), M, - & 1, WORK, LDA, IERR ) - AAPQ = SDOT( M, WORK, 1, A(1,q), 1 ) * - & D(q) / AAQQ - END IF - ELSE - IF ( AAPP .GE. AAQQ ) THEN - ROTOK = AAPP .LE. ( AAQQ / SMALL ) - ELSE - ROTOK = AAQQ .LE. ( AAPP / SMALL ) - END IF - IF ( AAPP .GT. ( SMALL / AAQQ ) ) THEN - AAPQ = ( SDOT( M, A(1,p), 1, A(1,q), 1 ) * - & D(p) * D(q) / AAQQ ) / AAPP - ELSE - CALL SCOPY( M, A(1,q), 1, WORK, 1 ) - CALL SLASCL( 'G', 0, 0, AAQQ, D(q), M, 1, - & WORK, LDA, IERR ) - AAPQ = SDOT(M,WORK,1,A(1,p),1) * D(p) / AAPP - END IF - END IF + IJBLSK = 0 + DO 2100 p = igl, MIN0( igl+KBL-1, N ) +* + AAPP = SVA( p ) +* + IF( AAPP.GT.ZERO ) THEN +* + PSKIPPED = 0 +* + DO 2200 q = jgl, MIN0( jgl+KBL-1, N ) +* + AAQQ = SVA( q ) +* + IF( AAQQ.GT.ZERO ) THEN + AAPP0 = AAPP +* +* .. M x 2 Jacobi SVD .. +* +* .. Safe Gram matrix computation .. +* + IF( AAQQ.GE.ONE ) THEN + IF( AAPP.GE.AAQQ ) THEN + ROTOK = ( SMALL*AAPP ).LE.AAQQ + ELSE + ROTOK = ( SMALL*AAQQ ).LE.AAPP + END IF + IF( AAPP.LT.( BIG / AAQQ ) ) THEN + AAPQ = ( SDOT( M, A( 1, p ), 1, A( 1, + + q ), 1 )*D( p )*D( q ) / AAQQ ) + + / AAPP + ELSE + CALL SCOPY( M, A( 1, p ), 1, WORK, 1 ) + CALL SLASCL( 'G', 0, 0, AAPP, D( p ), + + M, 1, WORK, LDA, IERR ) + AAPQ = SDOT( M, WORK, 1, A( 1, q ), + + 1 )*D( q ) / AAQQ + END IF + ELSE + IF( AAPP.GE.AAQQ ) THEN + ROTOK = AAPP.LE.( AAQQ / SMALL ) + ELSE + ROTOK = AAQQ.LE.( AAPP / SMALL ) + END IF + IF( AAPP.GT.( SMALL / AAQQ ) ) THEN + AAPQ = ( SDOT( M, A( 1, p ), 1, A( 1, + + q ), 1 )*D( p )*D( q ) / AAQQ ) + + / AAPP + ELSE + CALL SCOPY( M, A( 1, q ), 1, WORK, 1 ) + CALL SLASCL( 'G', 0, 0, AAQQ, D( q ), + + M, 1, WORK, LDA, IERR ) + AAPQ = SDOT( M, WORK, 1, A( 1, p ), + + 1 )*D( p ) / AAPP + END IF + END IF * - MXAAPQ = AMAX1( MXAAPQ, ABS(AAPQ) ) + MXAAPQ = AMAX1( MXAAPQ, ABS( AAPQ ) ) * * TO rotate or NOT to rotate, THAT is the question ... * - IF ( ABS( AAPQ ) .GT. TOL ) THEN - NOTROT = 0 + IF( ABS( AAPQ ).GT.TOL ) THEN + NOTROT = 0 * ROTATED = ROTATED + 1 - PSKIPPED = 0 - ISWROT = ISWROT + 1 -* - IF ( ROTOK ) THEN -* - AQOAP = AAQQ / AAPP - APOAQ = AAPP / AAQQ - THETA = - HALF * ABS( AQOAP - APOAQ ) / AAPQ - IF ( AAQQ .GT. AAPP0 ) THETA = - THETA -* - IF ( ABS( THETA ) .GT. BIGTHETA ) THEN - T = HALF / THETA - FASTR(3) = T * D(p) / D(q) - FASTR(4) = -T * D(q) / D(p) - CALL SROTM( M, A(1,p), 1, A(1,q), 1, FASTR ) - IF ( RSVEC ) - & CALL SROTM( MVL, V(1,p), 1, V(1,q), 1, FASTR ) - SVA(q) = AAQQ*SQRT( AMAX1(ZERO,ONE + T*APOAQ*AAPQ) ) - AAPP = AAPP*SQRT( AMAX1(ZERO,ONE - T*AQOAP*AAPQ) ) - MXSINJ = AMAX1( MXSINJ, ABS(T) ) - ELSE + PSKIPPED = 0 + ISWROT = ISWROT + 1 +* + IF( ROTOK ) THEN +* + AQOAP = AAQQ / AAPP + APOAQ = AAPP / AAQQ + THETA = -HALF*ABS( AQOAP-APOAQ ) / AAPQ + IF( AAQQ.GT.AAPP0 )THETA = -THETA +* + IF( ABS( THETA ).GT.BIGTHETA ) THEN + T = HALF / THETA + FASTR( 3 ) = T*D( p ) / D( q ) + FASTR( 4 ) = -T*D( q ) / D( p ) + CALL SROTM( M, A( 1, p ), 1, + + A( 1, q ), 1, FASTR ) + IF( RSVEC )CALL SROTM( MVL, + + V( 1, p ), 1, + + V( 1, q ), 1, + + FASTR ) + SVA( q ) = AAQQ*SQRT( AMAX1( ZERO, + + ONE+T*APOAQ*AAPQ ) ) + AAPP = AAPP*SQRT( AMAX1( ZERO, + + ONE-T*AQOAP*AAPQ ) ) + MXSINJ = AMAX1( MXSINJ, ABS( T ) ) + ELSE * * .. choose correct signum for THETA and rotate * - THSIGN = - SIGN(ONE,AAPQ) - IF ( AAQQ .GT. AAPP0 ) THSIGN = - THSIGN - T = ONE / ( THETA + THSIGN*SQRT(ONE+THETA*THETA) ) - CS = SQRT( ONE / ( ONE + T*T ) ) - SN = T * CS - MXSINJ = AMAX1( MXSINJ, ABS(SN) ) - SVA(q) = AAQQ*SQRT( AMAX1(ZERO, ONE+T*APOAQ*AAPQ) ) - AAPP = AAPP*SQRT( ONE - T*AQOAP*AAPQ) -* - APOAQ = D(p) / D(q) - AQOAP = D(q) / D(p) - IF ( D(p) .GE. ONE ) THEN -* - IF ( D(q) .GE. ONE ) THEN - FASTR(3) = T * APOAQ - FASTR(4) = - T * AQOAP - D(p) = D(p) * CS - D(q) = D(q) * CS - CALL SROTM( M, A(1,p),1, A(1,q),1, FASTR ) - IF ( RSVEC ) - & CALL SROTM( MVL, V(1,p),1, V(1,q),1, FASTR ) - ELSE - CALL SAXPY( M, -T*AQOAP, A(1,q),1, A(1,p),1 ) - CALL SAXPY( M, CS*SN*APOAQ, A(1,p),1, A(1,q),1 ) - IF ( RSVEC ) THEN - CALL SAXPY( MVL, -T*AQOAP, V(1,q),1, V(1,p),1 ) - CALL SAXPY( MVL,CS*SN*APOAQ,V(1,p),1, V(1,q),1 ) - END IF - D(p) = D(p) * CS - D(q) = D(q) / CS - END IF - ELSE - IF ( D(q) .GE. ONE ) THEN - CALL SAXPY( M, T*APOAQ, A(1,p),1, A(1,q),1 ) - CALL SAXPY( M,-CS*SN*AQOAP, A(1,q),1, A(1,p),1 ) - IF ( RSVEC ) THEN - CALL SAXPY(MVL,T*APOAQ, V(1,p),1, V(1,q),1 ) - CALL SAXPY(MVL,-CS*SN*AQOAP,V(1,q),1, V(1,p),1 ) - END IF - D(p) = D(p) / CS - D(q) = D(q) * CS - ELSE - IF ( D(p) .GE. D(q) ) THEN - CALL SAXPY( M,-T*AQOAP, A(1,q),1,A(1,p),1 ) - CALL SAXPY( M,CS*SN*APOAQ,A(1,p),1,A(1,q),1 ) - D(p) = D(p) * CS - D(q) = D(q) / CS - IF ( RSVEC ) THEN - CALL SAXPY( MVL, -T*AQOAP, V(1,q),1,V(1,p),1) - CALL SAXPY(MVL,CS*SN*APOAQ,V(1,p),1,V(1,q),1) - END IF - ELSE - CALL SAXPY(M, T*APOAQ, A(1,p),1,A(1,q),1) - CALL SAXPY(M,-CS*SN*AQOAP,A(1,q),1,A(1,p),1) - D(p) = D(p) / CS - D(q) = D(q) * CS - IF ( RSVEC ) THEN - CALL SAXPY(MVL, T*APOAQ, V(1,p),1,V(1,q),1) - CALL SAXPY(MVL,-CS*SN*AQOAP,V(1,q),1,V(1,p),1) - END IF - END IF - END IF - ENDIF - END IF -* - ELSE - IF ( AAPP .GT. AAQQ ) THEN - CALL SCOPY( M, A(1,p), 1, WORK, 1 ) - CALL SLASCL('G',0,0,AAPP,ONE,M,1,WORK,LDA,IERR) - CALL SLASCL('G',0,0,AAQQ,ONE,M,1, A(1,q),LDA,IERR) - TEMP1 = -AAPQ * D(p) / D(q) - CALL SAXPY(M,TEMP1,WORK,1,A(1,q),1) - CALL SLASCL('G',0,0,ONE,AAQQ,M,1,A(1,q),LDA,IERR) - SVA(q) = AAQQ*SQRT(AMAX1(ZERO, ONE - AAPQ*AAPQ)) - MXSINJ = AMAX1( MXSINJ, SFMIN ) - ELSE - CALL SCOPY( M, A(1,q), 1, WORK, 1 ) - CALL SLASCL('G',0,0,AAQQ,ONE,M,1,WORK,LDA,IERR) - CALL SLASCL('G',0,0,AAPP,ONE,M,1, A(1,p),LDA,IERR) - TEMP1 = -AAPQ * D(q) / D(p) - CALL SAXPY(M,TEMP1,WORK,1,A(1,p),1) - CALL SLASCL('G',0,0,ONE,AAPP,M,1,A(1,p),LDA,IERR) - SVA(p) = AAPP*SQRT(AMAX1(ZERO, ONE - AAPQ*AAPQ)) - MXSINJ = AMAX1( MXSINJ, SFMIN ) - END IF - END IF + THSIGN = -SIGN( ONE, AAPQ ) + IF( AAQQ.GT.AAPP0 )THSIGN = -THSIGN + T = ONE / ( THETA+THSIGN* + + SQRT( ONE+THETA*THETA ) ) + CS = SQRT( ONE / ( ONE+T*T ) ) + SN = T*CS + MXSINJ = AMAX1( MXSINJ, ABS( SN ) ) + SVA( q ) = AAQQ*SQRT( AMAX1( ZERO, + + ONE+T*APOAQ*AAPQ ) ) + AAPP = AAPP*SQRT( ONE-T*AQOAP*AAPQ ) +* + APOAQ = D( p ) / D( q ) + AQOAP = D( q ) / D( p ) + IF( D( p ).GE.ONE ) THEN +* + IF( D( q ).GE.ONE ) THEN + FASTR( 3 ) = T*APOAQ + FASTR( 4 ) = -T*AQOAP + D( p ) = D( p )*CS + D( q ) = D( q )*CS + CALL SROTM( M, A( 1, p ), 1, + + A( 1, q ), 1, + + FASTR ) + IF( RSVEC )CALL SROTM( MVL, + + V( 1, p ), 1, V( 1, q ), + + 1, FASTR ) + ELSE + CALL SAXPY( M, -T*AQOAP, + + A( 1, q ), 1, + + A( 1, p ), 1 ) + CALL SAXPY( M, CS*SN*APOAQ, + + A( 1, p ), 1, + + A( 1, q ), 1 ) + IF( RSVEC ) THEN + CALL SAXPY( MVL, -T*AQOAP, + + V( 1, q ), 1, + + V( 1, p ), 1 ) + CALL SAXPY( MVL, + + CS*SN*APOAQ, + + V( 1, p ), 1, + + V( 1, q ), 1 ) + END IF + D( p ) = D( p )*CS + D( q ) = D( q ) / CS + END IF + ELSE + IF( D( q ).GE.ONE ) THEN + CALL SAXPY( M, T*APOAQ, + + A( 1, p ), 1, + + A( 1, q ), 1 ) + CALL SAXPY( M, -CS*SN*AQOAP, + + A( 1, q ), 1, + + A( 1, p ), 1 ) + IF( RSVEC ) THEN + CALL SAXPY( MVL, T*APOAQ, + + V( 1, p ), 1, + + V( 1, q ), 1 ) + CALL SAXPY( MVL, + + -CS*SN*AQOAP, + + V( 1, q ), 1, + + V( 1, p ), 1 ) + END IF + D( p ) = D( p ) / CS + D( q ) = D( q )*CS + ELSE + IF( D( p ).GE.D( q ) ) THEN + CALL SAXPY( M, -T*AQOAP, + + A( 1, q ), 1, + + A( 1, p ), 1 ) + CALL SAXPY( M, CS*SN*APOAQ, + + A( 1, p ), 1, + + A( 1, q ), 1 ) + D( p ) = D( p )*CS + D( q ) = D( q ) / CS + IF( RSVEC ) THEN + CALL SAXPY( MVL, + + -T*AQOAP, + + V( 1, q ), 1, + + V( 1, p ), 1 ) + CALL SAXPY( MVL, + + CS*SN*APOAQ, + + V( 1, p ), 1, + + V( 1, q ), 1 ) + END IF + ELSE + CALL SAXPY( M, T*APOAQ, + + A( 1, p ), 1, + + A( 1, q ), 1 ) + CALL SAXPY( M, + + -CS*SN*AQOAP, + + A( 1, q ), 1, + + A( 1, p ), 1 ) + D( p ) = D( p ) / CS + D( q ) = D( q )*CS + IF( RSVEC ) THEN + CALL SAXPY( MVL, + + T*APOAQ, V( 1, p ), + + 1, V( 1, q ), 1 ) + CALL SAXPY( MVL, + + -CS*SN*AQOAP, + + V( 1, q ), 1, + + V( 1, p ), 1 ) + END IF + END IF + END IF + END IF + END IF +* + ELSE + IF( AAPP.GT.AAQQ ) THEN + CALL SCOPY( M, A( 1, p ), 1, WORK, + + 1 ) + CALL SLASCL( 'G', 0, 0, AAPP, ONE, + + M, 1, WORK, LDA, IERR ) + CALL SLASCL( 'G', 0, 0, AAQQ, ONE, + + M, 1, A( 1, q ), LDA, + + IERR ) + TEMP1 = -AAPQ*D( p ) / D( q ) + CALL SAXPY( M, TEMP1, WORK, 1, + + A( 1, q ), 1 ) + CALL SLASCL( 'G', 0, 0, ONE, AAQQ, + + M, 1, A( 1, q ), LDA, + + IERR ) + SVA( q ) = AAQQ*SQRT( AMAX1( ZERO, + + ONE-AAPQ*AAPQ ) ) + MXSINJ = AMAX1( MXSINJ, SFMIN ) + ELSE + CALL SCOPY( M, A( 1, q ), 1, WORK, + + 1 ) + CALL SLASCL( 'G', 0, 0, AAQQ, ONE, + + M, 1, WORK, LDA, IERR ) + CALL SLASCL( 'G', 0, 0, AAPP, ONE, + + M, 1, A( 1, p ), LDA, + + IERR ) + TEMP1 = -AAPQ*D( q ) / D( p ) + CALL SAXPY( M, TEMP1, WORK, 1, + + A( 1, p ), 1 ) + CALL SLASCL( 'G', 0, 0, ONE, AAPP, + + M, 1, A( 1, p ), LDA, + + IERR ) + SVA( p ) = AAPP*SQRT( AMAX1( ZERO, + + ONE-AAPQ*AAPQ ) ) + MXSINJ = AMAX1( MXSINJ, SFMIN ) + END IF + END IF * END IF ROTOK THEN ... ELSE * * In the case of cancellation in updating SVA(q) * .. recompute SVA(q) - IF ( (SVA(q) / AAQQ )**2 .LE. ROOTEPS ) THEN - IF ((AAQQ .LT. ROOTBIG).AND.(AAQQ .GT. ROOTSFMIN)) THEN - SVA(q) = SNRM2( M, A(1,q), 1 ) * D(q) - ELSE - T = ZERO - AAQQ = ZERO - CALL SLASSQ( M, A(1,q), 1, T, AAQQ ) - SVA(q) = T * SQRT(AAQQ) * D(q) - END IF - END IF - IF ( (AAPP / AAPP0 )**2 .LE. ROOTEPS ) THEN - IF ((AAPP .LT. ROOTBIG).AND.(AAPP .GT. ROOTSFMIN)) THEN - AAPP = SNRM2( M, A(1,p), 1 ) * D(p) - ELSE - T = ZERO - AAPP = ZERO - CALL SLASSQ( M, A(1,p), 1, T, AAPP ) - AAPP = T * SQRT(AAPP) * D(p) - END IF - SVA(p) = AAPP - END IF + IF( ( SVA( q ) / AAQQ )**2.LE.ROOTEPS ) + + THEN + IF( ( AAQQ.LT.ROOTBIG ) .AND. + + ( AAQQ.GT.ROOTSFMIN ) ) THEN + SVA( q ) = SNRM2( M, A( 1, q ), 1 )* + + D( q ) + ELSE + T = ZERO + AAQQ = ZERO + CALL SLASSQ( M, A( 1, q ), 1, T, + + AAQQ ) + SVA( q ) = T*SQRT( AAQQ )*D( q ) + END IF + END IF + IF( ( AAPP / AAPP0 )**2.LE.ROOTEPS ) THEN + IF( ( AAPP.LT.ROOTBIG ) .AND. + + ( AAPP.GT.ROOTSFMIN ) ) THEN + AAPP = SNRM2( M, A( 1, p ), 1 )* + + D( p ) + ELSE + T = ZERO + AAPP = ZERO + CALL SLASSQ( M, A( 1, p ), 1, T, + + AAPP ) + AAPP = T*SQRT( AAPP )*D( p ) + END IF + SVA( p ) = AAPP + END IF * end of OK rotation - ELSE - NOTROT = NOTROT + 1 - PSKIPPED = PSKIPPED + 1 - IJBLSK = IJBLSK + 1 - END IF - ELSE - NOTROT = NOTROT + 1 - PSKIPPED = PSKIPPED + 1 - IJBLSK = IJBLSK + 1 - END IF + ELSE + NOTROT = NOTROT + 1 + PSKIPPED = PSKIPPED + 1 + IJBLSK = IJBLSK + 1 + END IF + ELSE + NOTROT = NOTROT + 1 + PSKIPPED = PSKIPPED + 1 + IJBLSK = IJBLSK + 1 + END IF * - IF ( ( i .LE. SWBAND ) .AND. ( IJBLSK .GE. BLSKIP ) ) THEN - SVA(p) = AAPP - NOTROT = 0 - GO TO 2011 - END IF - IF ( ( i .LE. SWBAND ) .AND. ( PSKIPPED .GT. ROWSKIP ) ) THEN - AAPP = -AAPP - NOTROT = 0 - GO TO 2203 - END IF + IF( ( i.LE.SWBAND ) .AND. ( IJBLSK.GE.BLSKIP ) ) + + THEN + SVA( p ) = AAPP + NOTROT = 0 + GO TO 2011 + END IF + IF( ( i.LE.SWBAND ) .AND. + + ( PSKIPPED.GT.ROWSKIP ) ) THEN + AAPP = -AAPP + NOTROT = 0 + GO TO 2203 + END IF * - 2200 CONTINUE + 2200 CONTINUE * end of the q-loop - 2203 CONTINUE + 2203 CONTINUE * - SVA(p) = AAPP + SVA( p ) = AAPP * - ELSE - IF ( AAPP .EQ. ZERO ) NOTROT=NOTROT+MIN0(jgl+KBL-1,N)-jgl+1 - IF ( AAPP .LT. ZERO ) NOTROT = 0 - END IF + ELSE + IF( AAPP.EQ.ZERO )NOTROT = NOTROT + + + MIN0( jgl+KBL-1, N ) - jgl + 1 + IF( AAPP.LT.ZERO )NOTROT = 0 + END IF - 2100 CONTINUE + 2100 CONTINUE * end of the p-loop - 2010 CONTINUE + 2010 CONTINUE * end of the jbc-loop - 2011 CONTINUE + 2011 CONTINUE *2011 bailed out of the jbc-loop - DO 2012 p = igl, MIN0( igl + KBL - 1, N ) - SVA(p) = ABS(SVA(p)) - 2012 CONTINUE + DO 2012 p = igl, MIN0( igl+KBL-1, N ) + SVA( p ) = ABS( SVA( p ) ) + 2012 CONTINUE * - 2000 CONTINUE + 2000 CONTINUE *2000 :: end of the ibr-loop * * .. update SVA(N) - IF ((SVA(N) .LT. ROOTBIG).AND.(SVA(N) .GT. ROOTSFMIN)) THEN - SVA(N) = SNRM2( M, A(1,N), 1 ) * D(N) - ELSE - T = ZERO - AAPP = ZERO - CALL SLASSQ( M, A(1,N), 1, T, AAPP ) - SVA(N) = T * SQRT(AAPP) * D(N) - END IF + IF( ( SVA( N ).LT.ROOTBIG ) .AND. ( SVA( N ).GT.ROOTSFMIN ) ) + + THEN + SVA( N ) = SNRM2( M, A( 1, N ), 1 )*D( N ) + ELSE + T = ZERO + AAPP = ZERO + CALL SLASSQ( M, A( 1, N ), 1, T, AAPP ) + SVA( N ) = T*SQRT( AAPP )*D( N ) + END IF * * Additional steering devices * - IF ( ( i.LT.SWBAND ) .AND. ( ( MXAAPQ.LE.ROOTTOL ) .OR. - & ( ISWROT .LE. N ) ) ) - & SWBAND = i + IF( ( i.LT.SWBAND ) .AND. ( ( MXAAPQ.LE.ROOTTOL ) .OR. + + ( ISWROT.LE.N ) ) )SWBAND = i * - IF ((i.GT.SWBAND+1).AND. (MXAAPQ.LT.FLOAT(N)*TOL).AND. - & (FLOAT(N)*MXAAPQ*MXSINJ.LT.TOL))THEN - GO TO 1994 - END IF + IF( ( i.GT.SWBAND+1 ) .AND. ( MXAAPQ.LT.FLOAT( N )*TOL ) .AND. + + ( FLOAT( N )*MXAAPQ*MXSINJ.LT.TOL ) ) THEN + GO TO 1994 + END IF * - IF ( NOTROT .GE. EMPTSW ) GO TO 1994 + IF( NOTROT.GE.EMPTSW )GO TO 1994 1993 CONTINUE * end i=1:NSWEEP loop @@ -814,16 +964,16 @@ * * Sort the vector D. DO 5991 p = 1, N - 1 - q = ISAMAX( N-p+1, SVA(p), 1 ) + p - 1 - IF ( p .NE. q ) THEN - TEMP1 = SVA(p) - SVA(p) = SVA(q) - SVA(q) = TEMP1 - TEMP1 = D(p) - D(p) = D(q) - D(q) = TEMP1 - CALL SSWAP( M, A(1,p), 1, A(1,q), 1 ) - IF ( RSVEC ) CALL SSWAP( MVL, V(1,p), 1, V(1,q), 1 ) + q = ISAMAX( N-p+1, SVA( p ), 1 ) + p - 1 + IF( p.NE.q ) THEN + TEMP1 = SVA( p ) + SVA( p ) = SVA( q ) + SVA( q ) = TEMP1 + TEMP1 = D( p ) + D( p ) = D( q ) + D( q ) = TEMP1 + CALL SSWAP( M, A( 1, p ), 1, A( 1, q ), 1 ) + IF( RSVEC )CALL SSWAP( MVL, V( 1, p ), 1, V( 1, q ), 1 ) END IF 5991 CONTINUE * @@ -832,4 +982,3 @@ * .. END OF SGSVJ0 * .. END -* diff --git a/SRC/sgsvj1.f b/SRC/sgsvj1.f index 010f4fb0..aa965f29 100644 --- a/SRC/sgsvj1.f +++ b/SRC/sgsvj1.f @@ -1,5 +1,5 @@ SUBROUTINE SGSVJ1( JOBV, M, N, N1, A, LDA, D, SVA, MV, V, LDV, - & EPS, SFMIN, TOL, NSWEEP, WORK, LWORK, INFO ) + + EPS, SFMIN, TOL, NSWEEP, WORK, LWORK, INFO ) * * -- LAPACK routine (version 3.2) -- * @@ -15,21 +15,21 @@ * computation of SVD, PSVD, QSVD, (H,K)-SVD, and for solution of the * eigenvalue problems Hx = lambda M x, H M x = lambda x with H, M > 0. * -* -#- Scalar Arguments -#- -* - IMPLICIT NONE - REAL EPS, SFMIN, TOL - INTEGER INFO, LDA, LDV, LWORK, M, MV, N, N1, NSWEEP - CHARACTER*1 JOBV -* -* -#- Array Arguments -#- -* - REAL A( LDA, * ), D( N ), SVA( N ), V( LDV, * ), - & WORK( LWORK ) + IMPLICIT NONE +* .. +* .. Scalar Arguments .. + REAL EPS, SFMIN, TOL + INTEGER INFO, LDA, LDV, LWORK, M, MV, N, N1, NSWEEP + CHARACTER*1 JOBV +* .. +* .. Array Arguments .. + REAL A( LDA, * ), D( N ), SVA( N ), V( LDV, * ), + + WORK( LWORK ) * .. * * Purpose -* ~~~~~~~ +* ======= +* * SGSVJ1 is called from SGESVJ as a pre-processor and that is its main * purpose. It applies Jacobi rotations in the same way as SGESVJ does, but * it targets only particular pivots and it does not check convergence @@ -63,7 +63,7 @@ * Zlatko Drmac (Zagreb, Croatia) and Kresimir Veselic (Hagen, Germany) * * Arguments -* ~~~~~~~~~ +* ========= * * JOBV (input) CHARACTER*1 * Specifies whether the output from this procedure is used @@ -157,103 +157,108 @@ * = 0 : successful exit. * < 0 : if INFO = -i, then the i-th argument had an illegal value * -* -#- Local Parameters -#- -* - REAL ZERO, HALF, ONE, TWO - PARAMETER ( ZERO = 0.0E0, HALF = 0.5E0, ONE = 1.0E0, TWO = 2.0E0 ) - -* -#- Local Scalars -#- -* - REAL AAPP, AAPP0, AAPQ, AAQQ, APOAQ, AQOAP, BIG, BIGTHETA, - & CS, LARGE, MXAAPQ, MXSINJ, ROOTBIG,ROOTEPS, ROOTSFMIN, - & ROOTTOL, SMALL, SN, T, TEMP1, THETA, THSIGN - INTEGER BLSKIP, EMPTSW, i, ibr, igl, IERR, IJBLSK, ISWROT, jbc, - & jgl, KBL, MVL, NOTROT, nblc, nblr, p, PSKIPPED, q, - & ROWSKIP, SWBAND - LOGICAL APPLV, ROTOK, RSVEC -* -* Local Arrays - REAL FASTR(5) -* -* Intrinsic Functions - INTRINSIC ABS, AMAX1, FLOAT, MIN0, SIGN, SQRT +* ===================================================================== * -* External Functions - REAL SDOT, SNRM2 - INTEGER ISAMAX - LOGICAL LSAME - EXTERNAL ISAMAX, LSAME, SDOT, SNRM2 -* -* External Subroutines - EXTERNAL SAXPY, SCOPY, SLASCL, SLASSQ, SROTM, SSWAP +* .. Local Parameters .. + REAL ZERO, HALF, ONE, TWO + PARAMETER ( ZERO = 0.0E0, HALF = 0.5E0, ONE = 1.0E0, + + TWO = 2.0E0 ) +* .. +* .. Local Scalars .. + REAL AAPP, AAPP0, AAPQ, AAQQ, APOAQ, AQOAP, BIG, + + BIGTHETA, CS, LARGE, MXAAPQ, MXSINJ, ROOTBIG, + + ROOTEPS, ROOTSFMIN, ROOTTOL, SMALL, SN, T, + + TEMP1, THETA, THSIGN + INTEGER BLSKIP, EMPTSW, i, ibr, igl, IERR, IJBLSK, + + ISWROT, jbc, jgl, KBL, MVL, NOTROT, nblc, nblr, + + p, PSKIPPED, q, ROWSKIP, SWBAND + LOGICAL APPLV, ROTOK, RSVEC +* .. +* .. Local Arrays .. + REAL FASTR( 5 ) +* .. +* .. Intrinsic Functions .. + INTRINSIC ABS, AMAX1, FLOAT, MIN0, SIGN, SQRT +* .. +* .. External Functions .. + REAL SDOT, SNRM2 + INTEGER ISAMAX + LOGICAL LSAME + EXTERNAL ISAMAX, LSAME, SDOT, SNRM2 +* .. +* .. External Subroutines .. + EXTERNAL SAXPY, SCOPY, SLASCL, SLASSQ, SROTM, SSWAP +* .. +* .. Executable Statements .. * +* Test the input parameters. * - APPLV = LSAME(JOBV,'A') - RSVEC = LSAME(JOBV,'V') - IF ( .NOT.( RSVEC .OR. APPLV .OR. LSAME(JOBV,'N'))) THEN + APPLV = LSAME( JOBV, 'A' ) + RSVEC = LSAME( JOBV, 'V' ) + IF( .NOT.( RSVEC .OR. APPLV .OR. LSAME( JOBV, 'N' ) ) ) THEN INFO = -1 - ELSE IF ( M .LT. 0 ) THEN + ELSE IF( M.LT.0 ) THEN INFO = -2 - ELSE IF ( ( N .LT. 0 ) .OR. ( N .GT. M )) THEN + ELSE IF( ( N.LT.0 ) .OR. ( N.GT.M ) ) THEN INFO = -3 - ELSE IF ( N1 .LT. 0 ) THEN + ELSE IF( N1.LT.0 ) THEN INFO = -4 - ELSE IF ( LDA .LT. M ) THEN + ELSE IF( LDA.LT.M ) THEN INFO = -6 - ELSE IF ( MV .LT. 0 ) THEN + ELSE IF( MV.LT.0 ) THEN INFO = -9 - ELSE IF ( LDV .LT. M ) THEN + ELSE IF( LDV.LT.M ) THEN INFO = -11 - ELSE IF ( TOL .LE. EPS ) THEN + ELSE IF( TOL.LE.EPS ) THEN INFO = -14 - ELSE IF ( NSWEEP .LT. 0 ) THEN + ELSE IF( NSWEEP.LT.0 ) THEN INFO = -15 - ELSE IF ( LWORK .LT. M ) THEN + ELSE IF( LWORK.LT.M ) THEN INFO = -17 ELSE INFO = 0 END IF * * #:( - IF ( INFO .NE. 0 ) THEN + IF( INFO.NE.0 ) THEN CALL XERBLA( 'SGSVJ1', -INFO ) RETURN END IF * - IF ( RSVEC ) THEN + IF( RSVEC ) THEN MVL = N - ELSE IF ( APPLV ) THEN + ELSE IF( APPLV ) THEN MVL = MV END IF RSVEC = RSVEC .OR. APPLV - ROOTEPS = SQRT(EPS) - ROOTSFMIN = SQRT(SFMIN) - SMALL = SFMIN / EPS - BIG = ONE / SFMIN - ROOTBIG = ONE / ROOTSFMIN - LARGE = BIG / SQRT(FLOAT(M*N)) - BIGTHETA = ONE / ROOTEPS - ROOTTOL = SQRT(TOL) + ROOTEPS = SQRT( EPS ) + ROOTSFMIN = SQRT( SFMIN ) + SMALL = SFMIN / EPS + BIG = ONE / SFMIN + ROOTBIG = ONE / ROOTSFMIN + LARGE = BIG / SQRT( FLOAT( M*N ) ) + BIGTHETA = ONE / ROOTEPS + ROOTTOL = SQRT( TOL ) * -* -#- Initialize the right singular vector matrix -#- +* .. Initialize the right singular vector matrix .. * * RSVEC = LSAME( JOBV, 'Y' ) * - EMPTSW = N1 * ( N - N1 ) - NOTROT = 0 - FASTR(1) = ZERO + EMPTSW = N1*( N-N1 ) + NOTROT = 0 + FASTR( 1 ) = ZERO * -* -#- Row-cyclic pivot strategy with de Rijk's pivoting -#- +* .. Row-cyclic pivot strategy with de Rijk's pivoting .. * - KBL = MIN0(8,N) + KBL = MIN0( 8, N ) NBLR = N1 / KBL - IF ( ( NBLR * KBL ) .NE. N1 ) NBLR = NBLR + 1 + IF( ( NBLR*KBL ).NE.N1 )NBLR = NBLR + 1 * .. the tiling is nblr-by-nblc [tiles] - NBLC = ( N - N1 ) / KBL - IF ( ( NBLC * KBL ) .NE. ( N - N1 ) ) NBLC = NBLC + 1 + NBLC = ( N-N1 ) / KBL + IF( ( NBLC*KBL ).NE.( N-N1 ) )NBLC = NBLC + 1 BLSKIP = ( KBL**2 ) + 1 *[TP] BLKSKIP is a tuning parameter that depends on SWBAND and KBL. @@ -276,298 +281,375 @@ DO 1993 i = 1, NSWEEP * .. go go go ... * - MXAAPQ = ZERO - MXSINJ = ZERO - ISWROT = 0 + MXAAPQ = ZERO + MXSINJ = ZERO + ISWROT = 0 * - NOTROT = 0 - PSKIPPED = 0 + NOTROT = 0 + PSKIPPED = 0 * - DO 2000 ibr = 1, NBLR + DO 2000 ibr = 1, NBLR - igl = ( ibr - 1 ) * KBL + 1 + igl = ( ibr-1 )*KBL + 1 * * *........................................................ * ... go to the off diagonal blocks - igl = ( ibr - 1 ) * KBL + 1 + igl = ( ibr-1 )*KBL + 1 - DO 2010 jbc = 1, NBLC + DO 2010 jbc = 1, NBLC - jgl = N1 + ( jbc - 1 ) * KBL + 1 + jgl = N1 + ( jbc-1 )*KBL + 1 * doing the block at ( ibr, jbc ) - IJBLSK = 0 - DO 2100 p = igl, MIN0( igl + KBL - 1, N1 ) + IJBLSK = 0 + DO 2100 p = igl, MIN0( igl+KBL-1, N1 ) - AAPP = SVA(p) + AAPP = SVA( p ) - IF ( AAPP .GT. ZERO ) THEN + IF( AAPP.GT.ZERO ) THEN - PSKIPPED = 0 + PSKIPPED = 0 - DO 2200 q = jgl, MIN0( jgl + KBL - 1, N ) + DO 2200 q = jgl, MIN0( jgl+KBL-1, N ) * - AAQQ = SVA(q) + AAQQ = SVA( q ) - IF ( AAQQ .GT. ZERO ) THEN - AAPP0 = AAPP -* -* -#- M x 2 Jacobi SVD -#- -* -* -#- Safe Gram matrix computation -#- -* - IF ( AAQQ .GE. ONE ) THEN - IF ( AAPP .GE. AAQQ ) THEN - ROTOK = ( SMALL*AAPP ) .LE. AAQQ - ELSE - ROTOK = ( SMALL*AAQQ ) .LE. AAPP - END IF - IF ( AAPP .LT. ( BIG / AAQQ ) ) THEN - AAPQ = ( SDOT(M, A(1,p), 1, A(1,q), 1 ) * - & D(p) * D(q) / AAQQ ) / AAPP - ELSE - CALL SCOPY( M, A(1,p), 1, WORK, 1 ) - CALL SLASCL( 'G', 0, 0, AAPP, D(p), M, - & 1, WORK, LDA, IERR ) - AAPQ = SDOT( M, WORK, 1, A(1,q), 1 ) * - & D(q) / AAQQ - END IF - ELSE - IF ( AAPP .GE. AAQQ ) THEN - ROTOK = AAPP .LE. ( AAQQ / SMALL ) - ELSE - ROTOK = AAQQ .LE. ( AAPP / SMALL ) - END IF - IF ( AAPP .GT. ( SMALL / AAQQ ) ) THEN - AAPQ = ( SDOT( M, A(1,p), 1, A(1,q), 1 ) * - & D(p) * D(q) / AAQQ ) / AAPP - ELSE - CALL SCOPY( M, A(1,q), 1, WORK, 1 ) - CALL SLASCL( 'G', 0, 0, AAQQ, D(q), M, 1, - & WORK, LDA, IERR ) - AAPQ = SDOT(M,WORK,1,A(1,p),1) * D(p) / AAPP - END IF - END IF + IF( AAQQ.GT.ZERO ) THEN + AAPP0 = AAPP +* +* .. M x 2 Jacobi SVD .. +* +* .. Safe Gram matrix computation .. +* + IF( AAQQ.GE.ONE ) THEN + IF( AAPP.GE.AAQQ ) THEN + ROTOK = ( SMALL*AAPP ).LE.AAQQ + ELSE + ROTOK = ( SMALL*AAQQ ).LE.AAPP + END IF + IF( AAPP.LT.( BIG / AAQQ ) ) THEN + AAPQ = ( SDOT( M, A( 1, p ), 1, A( 1, + + q ), 1 )*D( p )*D( q ) / AAQQ ) + + / AAPP + ELSE + CALL SCOPY( M, A( 1, p ), 1, WORK, 1 ) + CALL SLASCL( 'G', 0, 0, AAPP, D( p ), + + M, 1, WORK, LDA, IERR ) + AAPQ = SDOT( M, WORK, 1, A( 1, q ), + + 1 )*D( q ) / AAQQ + END IF + ELSE + IF( AAPP.GE.AAQQ ) THEN + ROTOK = AAPP.LE.( AAQQ / SMALL ) + ELSE + ROTOK = AAQQ.LE.( AAPP / SMALL ) + END IF + IF( AAPP.GT.( SMALL / AAQQ ) ) THEN + AAPQ = ( SDOT( M, A( 1, p ), 1, A( 1, + + q ), 1 )*D( p )*D( q ) / AAQQ ) + + / AAPP + ELSE + CALL SCOPY( M, A( 1, q ), 1, WORK, 1 ) + CALL SLASCL( 'G', 0, 0, AAQQ, D( q ), + + M, 1, WORK, LDA, IERR ) + AAPQ = SDOT( M, WORK, 1, A( 1, p ), + + 1 )*D( p ) / AAPP + END IF + END IF - MXAAPQ = AMAX1( MXAAPQ, ABS(AAPQ) ) + MXAAPQ = AMAX1( MXAAPQ, ABS( AAPQ ) ) * TO rotate or NOT to rotate, THAT is the question ... * - IF ( ABS( AAPQ ) .GT. TOL ) THEN - NOTROT = 0 + IF( ABS( AAPQ ).GT.TOL ) THEN + NOTROT = 0 * ROTATED = ROTATED + 1 - PSKIPPED = 0 - ISWROT = ISWROT + 1 + PSKIPPED = 0 + ISWROT = ISWROT + 1 * - IF ( ROTOK ) THEN + IF( ROTOK ) THEN * - AQOAP = AAQQ / AAPP - APOAQ = AAPP / AAQQ - THETA = - HALF * ABS( AQOAP - APOAQ ) / AAPQ - IF ( AAQQ .GT. AAPP0 ) THETA = - THETA + AQOAP = AAQQ / AAPP + APOAQ = AAPP / AAQQ + THETA = -HALF*ABS( AQOAP-APOAQ ) / AAPQ + IF( AAQQ.GT.AAPP0 )THETA = -THETA - IF ( ABS( THETA ) .GT. BIGTHETA ) THEN - T = HALF / THETA - FASTR(3) = T * D(p) / D(q) - FASTR(4) = -T * D(q) / D(p) - CALL SROTM( M, A(1,p), 1, A(1,q), 1, FASTR ) - IF ( RSVEC ) - & CALL SROTM( MVL, V(1,p), 1, V(1,q), 1, FASTR ) - SVA(q) = AAQQ*SQRT( AMAX1(ZERO,ONE + T*APOAQ*AAPQ) ) - AAPP = AAPP*SQRT( AMAX1(ZERO,ONE - T*AQOAP*AAPQ) ) - MXSINJ = AMAX1( MXSINJ, ABS(T) ) - ELSE + IF( ABS( THETA ).GT.BIGTHETA ) THEN + T = HALF / THETA + FASTR( 3 ) = T*D( p ) / D( q ) + FASTR( 4 ) = -T*D( q ) / D( p ) + CALL SROTM( M, A( 1, p ), 1, + + A( 1, q ), 1, FASTR ) + IF( RSVEC )CALL SROTM( MVL, + + V( 1, p ), 1, + + V( 1, q ), 1, + + FASTR ) + SVA( q ) = AAQQ*SQRT( AMAX1( ZERO, + + ONE+T*APOAQ*AAPQ ) ) + AAPP = AAPP*SQRT( AMAX1( ZERO, + + ONE-T*AQOAP*AAPQ ) ) + MXSINJ = AMAX1( MXSINJ, ABS( T ) ) + ELSE * * .. choose correct signum for THETA and rotate * - THSIGN = - SIGN(ONE,AAPQ) - IF ( AAQQ .GT. AAPP0 ) THSIGN = - THSIGN - T = ONE / ( THETA + THSIGN*SQRT(ONE+THETA*THETA) ) - CS = SQRT( ONE / ( ONE + T*T ) ) - SN = T * CS - MXSINJ = AMAX1( MXSINJ, ABS(SN) ) - SVA(q) = AAQQ*SQRT( AMAX1(ZERO, ONE+T*APOAQ*AAPQ) ) - AAPP = AAPP*SQRT( ONE - T*AQOAP*AAPQ) + THSIGN = -SIGN( ONE, AAPQ ) + IF( AAQQ.GT.AAPP0 )THSIGN = -THSIGN + T = ONE / ( THETA+THSIGN* + + SQRT( ONE+THETA*THETA ) ) + CS = SQRT( ONE / ( ONE+T*T ) ) + SN = T*CS + MXSINJ = AMAX1( MXSINJ, ABS( SN ) ) + SVA( q ) = AAQQ*SQRT( AMAX1( ZERO, + + ONE+T*APOAQ*AAPQ ) ) + AAPP = AAPP*SQRT( ONE-T*AQOAP*AAPQ ) - APOAQ = D(p) / D(q) - AQOAP = D(q) / D(p) - IF ( D(p) .GE. ONE ) THEN -* - IF ( D(q) .GE. ONE ) THEN - FASTR(3) = T * APOAQ - FASTR(4) = - T * AQOAP - D(p) = D(p) * CS - D(q) = D(q) * CS - CALL SROTM( M, A(1,p),1, A(1,q),1, FASTR ) - IF ( RSVEC ) - & CALL SROTM( MVL, V(1,p),1, V(1,q),1, FASTR ) - ELSE - CALL SAXPY( M, -T*AQOAP, A(1,q),1, A(1,p),1 ) - CALL SAXPY( M, CS*SN*APOAQ, A(1,p),1, A(1,q),1 ) - IF ( RSVEC ) THEN - CALL SAXPY( MVL, -T*AQOAP, V(1,q),1, V(1,p),1 ) - CALL SAXPY( MVL,CS*SN*APOAQ,V(1,p),1, V(1,q),1 ) - END IF - D(p) = D(p) * CS - D(q) = D(q) / CS - END IF - ELSE - IF ( D(q) .GE. ONE ) THEN - CALL SAXPY( M, T*APOAQ, A(1,p),1, A(1,q),1 ) - CALL SAXPY( M,-CS*SN*AQOAP, A(1,q),1, A(1,p),1 ) - IF ( RSVEC ) THEN - CALL SAXPY(MVL,T*APOAQ, V(1,p),1, V(1,q),1 ) - CALL SAXPY(MVL,-CS*SN*AQOAP,V(1,q),1, V(1,p),1 ) - END IF - D(p) = D(p) / CS - D(q) = D(q) * CS - ELSE - IF ( D(p) .GE. D(q) ) THEN - CALL SAXPY( M,-T*AQOAP, A(1,q),1,A(1,p),1 ) - CALL SAXPY( M,CS*SN*APOAQ,A(1,p),1,A(1,q),1 ) - D(p) = D(p) * CS - D(q) = D(q) / CS - IF ( RSVEC ) THEN - CALL SAXPY( MVL, -T*AQOAP, V(1,q),1,V(1,p),1) - CALL SAXPY(MVL,CS*SN*APOAQ,V(1,p),1,V(1,q),1) - END IF - ELSE - CALL SAXPY(M, T*APOAQ, A(1,p),1,A(1,q),1) - CALL SAXPY(M,-CS*SN*AQOAP,A(1,q),1,A(1,p),1) - D(p) = D(p) / CS - D(q) = D(q) * CS - IF ( RSVEC ) THEN - CALL SAXPY(MVL, T*APOAQ, V(1,p),1,V(1,q),1) - CALL SAXPY(MVL,-CS*SN*AQOAP,V(1,q),1,V(1,p),1) - END IF - END IF - END IF - ENDIF - END IF + APOAQ = D( p ) / D( q ) + AQOAP = D( q ) / D( p ) + IF( D( p ).GE.ONE ) THEN +* + IF( D( q ).GE.ONE ) THEN + FASTR( 3 ) = T*APOAQ + FASTR( 4 ) = -T*AQOAP + D( p ) = D( p )*CS + D( q ) = D( q )*CS + CALL SROTM( M, A( 1, p ), 1, + + A( 1, q ), 1, + + FASTR ) + IF( RSVEC )CALL SROTM( MVL, + + V( 1, p ), 1, V( 1, q ), + + 1, FASTR ) + ELSE + CALL SAXPY( M, -T*AQOAP, + + A( 1, q ), 1, + + A( 1, p ), 1 ) + CALL SAXPY( M, CS*SN*APOAQ, + + A( 1, p ), 1, + + A( 1, q ), 1 ) + IF( RSVEC ) THEN + CALL SAXPY( MVL, -T*AQOAP, + + V( 1, q ), 1, + + V( 1, p ), 1 ) + CALL SAXPY( MVL, + + CS*SN*APOAQ, + + V( 1, p ), 1, + + V( 1, q ), 1 ) + END IF + D( p ) = D( p )*CS + D( q ) = D( q ) / CS + END IF + ELSE + IF( D( q ).GE.ONE ) THEN + CALL SAXPY( M, T*APOAQ, + + A( 1, p ), 1, + + A( 1, q ), 1 ) + CALL SAXPY( M, -CS*SN*AQOAP, + + A( 1, q ), 1, + + A( 1, p ), 1 ) + IF( RSVEC ) THEN + CALL SAXPY( MVL, T*APOAQ, + + V( 1, p ), 1, + + V( 1, q ), 1 ) + CALL SAXPY( MVL, + + -CS*SN*AQOAP, + + V( 1, q ), 1, + + V( 1, p ), 1 ) + END IF + D( p ) = D( p ) / CS + D( q ) = D( q )*CS + ELSE + IF( D( p ).GE.D( q ) ) THEN + CALL SAXPY( M, -T*AQOAP, + + A( 1, q ), 1, + + A( 1, p ), 1 ) + CALL SAXPY( M, CS*SN*APOAQ, + + A( 1, p ), 1, + + A( 1, q ), 1 ) + D( p ) = D( p )*CS + D( q ) = D( q ) / CS + IF( RSVEC ) THEN + CALL SAXPY( MVL, + + -T*AQOAP, + + V( 1, q ), 1, + + V( 1, p ), 1 ) + CALL SAXPY( MVL, + + CS*SN*APOAQ, + + V( 1, p ), 1, + + V( 1, q ), 1 ) + END IF + ELSE + CALL SAXPY( M, T*APOAQ, + + A( 1, p ), 1, + + A( 1, q ), 1 ) + CALL SAXPY( M, + + -CS*SN*AQOAP, + + A( 1, q ), 1, + + A( 1, p ), 1 ) + D( p ) = D( p ) / CS + D( q ) = D( q )*CS + IF( RSVEC ) THEN + CALL SAXPY( MVL, + + T*APOAQ, V( 1, p ), + + 1, V( 1, q ), 1 ) + CALL SAXPY( MVL, + + -CS*SN*AQOAP, + + V( 1, q ), 1, + + V( 1, p ), 1 ) + END IF + END IF + END IF + END IF + END IF - ELSE - IF ( AAPP .GT. AAQQ ) THEN - CALL SCOPY( M, A(1,p), 1, WORK, 1 ) - CALL SLASCL('G',0,0,AAPP,ONE,M,1,WORK,LDA,IERR) - CALL SLASCL('G',0,0,AAQQ,ONE,M,1, A(1,q),LDA,IERR) - TEMP1 = -AAPQ * D(p) / D(q) - CALL SAXPY(M,TEMP1,WORK,1,A(1,q),1) - CALL SLASCL('G',0,0,ONE,AAQQ,M,1,A(1,q),LDA,IERR) - SVA(q) = AAQQ*SQRT(AMAX1(ZERO, ONE - AAPQ*AAPQ)) - MXSINJ = AMAX1( MXSINJ, SFMIN ) - ELSE - CALL SCOPY( M, A(1,q), 1, WORK, 1 ) - CALL SLASCL('G',0,0,AAQQ,ONE,M,1,WORK,LDA,IERR) - CALL SLASCL('G',0,0,AAPP,ONE,M,1, A(1,p),LDA,IERR) - TEMP1 = -AAPQ * D(q) / D(p) - CALL SAXPY(M,TEMP1,WORK,1,A(1,p),1) - CALL SLASCL('G',0,0,ONE,AAPP,M,1,A(1,p),LDA,IERR) - SVA(p) = AAPP*SQRT(AMAX1(ZERO, ONE - AAPQ*AAPQ)) - MXSINJ = AMAX1( MXSINJ, SFMIN ) - END IF - END IF + ELSE + IF( AAPP.GT.AAQQ ) THEN + CALL SCOPY( M, A( 1, p ), 1, WORK, + + 1 ) + CALL SLASCL( 'G', 0, 0, AAPP, ONE, + + M, 1, WORK, LDA, IERR ) + CALL SLASCL( 'G', 0, 0, AAQQ, ONE, + + M, 1, A( 1, q ), LDA, + + IERR ) + TEMP1 = -AAPQ*D( p ) / D( q ) + CALL SAXPY( M, TEMP1, WORK, 1, + + A( 1, q ), 1 ) + CALL SLASCL( 'G', 0, 0, ONE, AAQQ, + + M, 1, A( 1, q ), LDA, + + IERR ) + SVA( q ) = AAQQ*SQRT( AMAX1( ZERO, + + ONE-AAPQ*AAPQ ) ) + MXSINJ = AMAX1( MXSINJ, SFMIN ) + ELSE + CALL SCOPY( M, A( 1, q ), 1, WORK, + + 1 ) + CALL SLASCL( 'G', 0, 0, AAQQ, ONE, + + M, 1, WORK, LDA, IERR ) + CALL SLASCL( 'G', 0, 0, AAPP, ONE, + + M, 1, A( 1, p ), LDA, + + IERR ) + TEMP1 = -AAPQ*D( q ) / D( p ) + CALL SAXPY( M, TEMP1, WORK, 1, + + A( 1, p ), 1 ) + CALL SLASCL( 'G', 0, 0, ONE, AAPP, + + M, 1, A( 1, p ), LDA, + + IERR ) + SVA( p ) = AAPP*SQRT( AMAX1( ZERO, + + ONE-AAPQ*AAPQ ) ) + MXSINJ = AMAX1( MXSINJ, SFMIN ) + END IF + END IF * END IF ROTOK THEN ... ELSE * * In the case of cancellation in updating SVA(q) * .. recompute SVA(q) - IF ( (SVA(q) / AAQQ )**2 .LE. ROOTEPS ) THEN - IF ((AAQQ .LT. ROOTBIG).AND.(AAQQ .GT. ROOTSFMIN)) THEN - SVA(q) = SNRM2( M, A(1,q), 1 ) * D(q) - ELSE - T = ZERO - AAQQ = ZERO - CALL SLASSQ( M, A(1,q), 1, T, AAQQ ) - SVA(q) = T * SQRT(AAQQ) * D(q) - END IF - END IF - IF ( (AAPP / AAPP0 )**2 .LE. ROOTEPS ) THEN - IF ((AAPP .LT. ROOTBIG).AND.(AAPP .GT. ROOTSFMIN)) THEN - AAPP = SNRM2( M, A(1,p), 1 ) * D(p) - ELSE - T = ZERO - AAPP = ZERO - CALL SLASSQ( M, A(1,p), 1, T, AAPP ) - AAPP = T * SQRT(AAPP) * D(p) - END IF - SVA(p) = AAPP - END IF + IF( ( SVA( q ) / AAQQ )**2.LE.ROOTEPS ) + + THEN + IF( ( AAQQ.LT.ROOTBIG ) .AND. + + ( AAQQ.GT.ROOTSFMIN ) ) THEN + SVA( q ) = SNRM2( M, A( 1, q ), 1 )* + + D( q ) + ELSE + T = ZERO + AAQQ = ZERO + CALL SLASSQ( M, A( 1, q ), 1, T, + + AAQQ ) + SVA( q ) = T*SQRT( AAQQ )*D( q ) + END IF + END IF + IF( ( AAPP / AAPP0 )**2.LE.ROOTEPS ) THEN + IF( ( AAPP.LT.ROOTBIG ) .AND. + + ( AAPP.GT.ROOTSFMIN ) ) THEN + AAPP = SNRM2( M, A( 1, p ), 1 )* + + D( p ) + ELSE + T = ZERO + AAPP = ZERO + CALL SLASSQ( M, A( 1, p ), 1, T, + + AAPP ) + AAPP = T*SQRT( AAPP )*D( p ) + END IF + SVA( p ) = AAPP + END IF * end of OK rotation - ELSE - NOTROT = NOTROT + 1 + ELSE + NOTROT = NOTROT + 1 * SKIPPED = SKIPPED + 1 - PSKIPPED = PSKIPPED + 1 - IJBLSK = IJBLSK + 1 - END IF - ELSE - NOTROT = NOTROT + 1 - PSKIPPED = PSKIPPED + 1 - IJBLSK = IJBLSK + 1 - END IF + PSKIPPED = PSKIPPED + 1 + IJBLSK = IJBLSK + 1 + END IF + ELSE + NOTROT = NOTROT + 1 + PSKIPPED = PSKIPPED + 1 + IJBLSK = IJBLSK + 1 + END IF * IF ( NOTROT .GE. EMPTSW ) GO TO 2011 - IF ( ( i .LE. SWBAND ) .AND. ( IJBLSK .GE. BLSKIP ) ) THEN - SVA(p) = AAPP - NOTROT = 0 - GO TO 2011 - END IF - IF ( ( i .LE. SWBAND ) .AND. ( PSKIPPED .GT. ROWSKIP ) ) THEN - AAPP = -AAPP - NOTROT = 0 - GO TO 2203 - END IF + IF( ( i.LE.SWBAND ) .AND. ( IJBLSK.GE.BLSKIP ) ) + + THEN + SVA( p ) = AAPP + NOTROT = 0 + GO TO 2011 + END IF + IF( ( i.LE.SWBAND ) .AND. + + ( PSKIPPED.GT.ROWSKIP ) ) THEN + AAPP = -AAPP + NOTROT = 0 + GO TO 2203 + END IF * - 2200 CONTINUE + 2200 CONTINUE * end of the q-loop - 2203 CONTINUE + 2203 CONTINUE - SVA(p) = AAPP + SVA( p ) = AAPP * - ELSE - IF ( AAPP .EQ. ZERO ) NOTROT=NOTROT+MIN0(jgl+KBL-1,N)-jgl+1 - IF ( AAPP .LT. ZERO ) NOTROT = 0 + ELSE + IF( AAPP.EQ.ZERO )NOTROT = NOTROT + + + MIN0( jgl+KBL-1, N ) - jgl + 1 + IF( AAPP.LT.ZERO )NOTROT = 0 *** IF ( NOTROT .GE. EMPTSW ) GO TO 2011 - END IF + END IF - 2100 CONTINUE + 2100 CONTINUE * end of the p-loop - 2010 CONTINUE + 2010 CONTINUE * end of the jbc-loop - 2011 CONTINUE + 2011 CONTINUE *2011 bailed out of the jbc-loop - DO 2012 p = igl, MIN0( igl + KBL - 1, N ) - SVA(p) = ABS(SVA(p)) - 2012 CONTINUE + DO 2012 p = igl, MIN0( igl+KBL-1, N ) + SVA( p ) = ABS( SVA( p ) ) + 2012 CONTINUE *** IF ( NOTROT .GE. EMPTSW ) GO TO 1994 - 2000 CONTINUE + 2000 CONTINUE *2000 :: end of the ibr-loop * * .. update SVA(N) - IF ((SVA(N) .LT. ROOTBIG).AND.(SVA(N) .GT. ROOTSFMIN)) THEN - SVA(N) = SNRM2( M, A(1,N), 1 ) * D(N) - ELSE - T = ZERO - AAPP = ZERO - CALL SLASSQ( M, A(1,N), 1, T, AAPP ) - SVA(N) = T * SQRT(AAPP) * D(N) - END IF + IF( ( SVA( N ).LT.ROOTBIG ) .AND. ( SVA( N ).GT.ROOTSFMIN ) ) + + THEN + SVA( N ) = SNRM2( M, A( 1, N ), 1 )*D( N ) + ELSE + T = ZERO + AAPP = ZERO + CALL SLASSQ( M, A( 1, N ), 1, T, AAPP ) + SVA( N ) = T*SQRT( AAPP )*D( N ) + END IF * * Additional steering devices * - IF ( ( i.LT.SWBAND ) .AND. ( ( MXAAPQ.LE.ROOTTOL ) .OR. - & ( ISWROT .LE. N ) ) ) - & SWBAND = i + IF( ( i.LT.SWBAND ) .AND. ( ( MXAAPQ.LE.ROOTTOL ) .OR. + + ( ISWROT.LE.N ) ) )SWBAND = i - IF ((i.GT.SWBAND+1).AND. (MXAAPQ.LT.FLOAT(N)*TOL).AND. - & (FLOAT(N)*MXAAPQ*MXSINJ.LT.TOL))THEN - GO TO 1994 - END IF + IF( ( i.GT.SWBAND+1 ) .AND. ( MXAAPQ.LT.FLOAT( N )*TOL ) .AND. + + ( FLOAT( N )*MXAAPQ*MXSINJ.LT.TOL ) ) THEN + GO TO 1994 + END IF * - IF ( NOTROT .GE. EMPTSW ) GO TO 1994 + IF( NOTROT.GE.EMPTSW )GO TO 1994 1993 CONTINUE * end i=1:NSWEEP loop @@ -586,16 +668,16 @@ * Sort the vector D * DO 5991 p = 1, N - 1 - q = ISAMAX( N-p+1, SVA(p), 1 ) + p - 1 - IF ( p .NE. q ) THEN - TEMP1 = SVA(p) - SVA(p) = SVA(q) - SVA(q) = TEMP1 - TEMP1 = D(p) - D(p) = D(q) - D(q) = TEMP1 - CALL SSWAP( M, A(1,p), 1, A(1,q), 1 ) - IF ( RSVEC ) CALL SSWAP( MVL, V(1,p), 1, V(1,q), 1 ) + q = ISAMAX( N-p+1, SVA( p ), 1 ) + p - 1 + IF( p.NE.q ) THEN + TEMP1 = SVA( p ) + SVA( p ) = SVA( q ) + SVA( q ) = TEMP1 + TEMP1 = D( p ) + D( p ) = D( q ) + D( q ) = TEMP1 + CALL SSWAP( M, A( 1, p ), 1, A( 1, q ), 1 ) + IF( RSVEC )CALL SSWAP( MVL, V( 1, p ), 1, V( 1, q ), 1 ) END IF 5991 CONTINUE * @@ -604,4 +686,3 @@ * .. END OF SGSVJ1 * .. END -* diff --git a/SRC/sla_gbamv.f b/SRC/sla_gbamv.f index 600c0ad4..fb8ff49d 100644 --- a/SRC/sla_gbamv.f +++ b/SRC/sla_gbamv.f @@ -39,7 +39,7 @@ * entry is considered "symbolic" if all multiplications involved * in computing that entry have at least one zero multiplicand. * -* Parameters +* Arguments * ========== * * TRANS - INTEGER @@ -116,7 +116,9 @@ * * * Level 2 Blas routine. -* .. +* +* ===================================================================== +* * .. Parameters .. REAL ONE, ZERO PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) diff --git a/SRC/sla_gbrcond.f b/SRC/sla_gbrcond.f index bf2eda3d..eba7841d 100644 --- a/SRC/sla_gbrcond.f +++ b/SRC/sla_gbrcond.f @@ -19,6 +19,10 @@ INTEGER IWORK( * ), IPIV( * ) REAL AB( LDAB, * ), AFB( LDAFB, * ), WORK( * ), $ C( * ) +* .. +* +* Purpose +* ======= * * SLA_GERCOND Estimates the Skeel condition number of op(A) * op2(C) * where op2 is determined by CMODE as follows @@ -29,9 +33,16 @@ * is computed by computing scaling factors R such that * diag(R)*A*op2(C) is row equilibrated and computing the standard * infinity-norm condition number. -* WORK is a real workspace of size 5*N, and -* IWORK is an integer workspace of size N. -* .. +* +* Arguments +* ========== +* +* WORK real workspace of size 5*N. +* +* IWORK integer workspace of size N. +* +* ===================================================================== +* * .. Local Scalars .. LOGICAL NOTRANS INTEGER KASE, I, J, KD diff --git a/SRC/sla_gbrfsx_extended.f b/SRC/sla_gbrfsx_extended.f index 2ed2d222..93261517 100644 --- a/SRC/sla_gbrfsx_extended.f +++ b/SRC/sla_gbrfsx_extended.f @@ -29,6 +29,9 @@ REAL C( * ), AYB(*), RCOND, BERR_OUT(*), $ ERRS_N( NRHS, * ), ERRS_C( NRHS, * ) * .. +* +* ===================================================================== +* * .. Local Scalars .. CHARACTER TRANS INTEGER CNT, I, J, M, X_STATE, Z_STATE, Y_PREC_STATE diff --git a/SRC/sla_gbrpvgrw.f b/SRC/sla_gbrpvgrw.f index 2c623aad..67985e0e 100644 --- a/SRC/sla_gbrpvgrw.f +++ b/SRC/sla_gbrpvgrw.f @@ -17,6 +17,9 @@ * .. Array Arguments .. REAL AB( LDAB, * ), AFB( LDAFB, * ) * .. +* +* ===================================================================== +* * .. Local Scalars .. INTEGER I, J, KD REAL AMAX, UMAX, RPVGRW diff --git a/SRC/sla_geamv.f b/SRC/sla_geamv.f index 45360469..c70febe2 100644 --- a/SRC/sla_geamv.f +++ b/SRC/sla_geamv.f @@ -39,7 +39,7 @@ * entry is considered "symbolic" if all multiplications involved * in computing that entry have at least one zero multiplicand. * -* Parameters +* Arguments * ========== * * TRANS - INTEGER @@ -111,7 +111,8 @@ * * Level 2 Blas routine. * -* .. +* ===================================================================== +* * .. Parameters .. REAL ONE, ZERO PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) diff --git a/SRC/sla_gercond.f b/SRC/sla_gercond.f index 6279273a..776d4900 100644 --- a/SRC/sla_gercond.f +++ b/SRC/sla_gercond.f @@ -19,6 +19,10 @@ INTEGER IPIV( * ), IWORK( * ) REAL A( LDA, * ), AF( LDAF, * ), WORK( * ), $ C( * ) +* .. +* +* Purpose +* ======= * * SLA_GERCOND estimates the Skeel condition number of op(A) * op2(C) * where op2 is determined by CMODE as follows @@ -29,9 +33,16 @@ * is computed by computing scaling factors R such that * diag(R)*A*op2(C) is row equilibrated and computing the standard * infinity-norm condition number. -* WORK is a REAL workspace of size 3*N, and -* IWORK is an INTEGER workspace of size N. -* .. +* +* Arguments +* ========== +* +* WORK REAL workspace of size 3*N. +* +* IWORK INTEGER workspace of size N. +* +* ===================================================================== +* * .. Local Scalars .. LOGICAL NOTRANS INTEGER KASE, I, J diff --git a/SRC/sla_gerfsx_extended.f b/SRC/sla_gerfsx_extended.f index d7494fd3..8d2c8419 100644 --- a/SRC/sla_gerfsx_extended.f +++ b/SRC/sla_gerfsx_extended.f @@ -28,6 +28,9 @@ REAL C( * ), AYB( * ), RCOND, BERR_OUT( * ), $ ERRS_N( NRHS, * ), ERRS_C( NRHS, * ) * .. +* +* ===================================================================== +* * .. Local Scalars .. CHARACTER TRANS INTEGER CNT, I, J, X_STATE, Z_STATE, Y_PREC_STATE diff --git a/SRC/sla_lin_berr.f b/SRC/sla_lin_berr.f index 2ef69af3..74cb2c9f 100644 --- a/SRC/sla_lin_berr.f +++ b/SRC/sla_lin_berr.f @@ -16,13 +16,19 @@ * .. Array Arguments .. REAL AYB( N, NRHS ), BERR( NRHS ) REAL RES( N, NRHS ) +* .. +* +* Purpose +* ======= * -* SLA_LIN_BERR computes componentwise relative backward error from +* SLA_LIN_BERR computes component-wise relative backward error from * the formula * max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) ) -* where abs(Z) is the componentwise absolute value of the matrix +* where abs(Z) is the component-wise absolute value of the matrix * or vector Z. -* .. +* +* ===================================================================== +* * .. Local Scalars .. REAL TMP INTEGER I, J diff --git a/SRC/sla_porcond.f b/SRC/sla_porcond.f index 4cbc6fef..65134d9d 100644 --- a/SRC/sla_porcond.f +++ b/SRC/sla_porcond.f @@ -19,6 +19,10 @@ * .. * .. Array Arguments .. INTEGER IWORK( * ) +* .. +* +* Purpose +* ======= * * SLA_PORCOND Estimates the Skeel condition number of op(A) * op2(C) * where op2 is determined by CMODE as follows @@ -29,9 +33,16 @@ * is computed by computing scaling factors R such that * diag(R)*A*op2(C) is row equilibrated and computing the standard * infinity-norm condition number. -* WORK is a real workspace of size 3*N, and -* IWORK is an integer workspace of size N. -* .. +* +* Arguments +* ========== +* +* WORK real workspace of size 3*N, and +* +* IWORK integer workspace of size N. +* +* ===================================================================== +* * .. Local Scalars .. INTEGER KASE, I, J REAL AINVNM, TMP diff --git a/SRC/sla_porfsx_extended.f b/SRC/sla_porfsx_extended.f index beff66a8..2d1a1244 100644 --- a/SRC/sla_porfsx_extended.f +++ b/SRC/sla_porfsx_extended.f @@ -28,6 +28,9 @@ REAL C( * ), AYB(*), RCOND, BERR_OUT( * ), $ ERRS_N( NRHS, * ), ERRS_C( NRHS, * ) * .. +* +* ===================================================================== +* * .. Local Scalars .. INTEGER UPLO2, CNT, I, J, X_STATE, Z_STATE REAL YK, DYK, YMIN, NORMY, NORMX, NORMDX, DXRAT, diff --git a/SRC/sla_porpvgrw.f b/SRC/sla_porpvgrw.f index 186a60a0..9174aa5e 100644 --- a/SRC/sla_porpvgrw.f +++ b/SRC/sla_porpvgrw.f @@ -17,6 +17,9 @@ * .. Array Arguments .. REAL A( LDA, * ), AF( LDAF, * ), WORK( * ) * .. +* +* ===================================================================== +* * .. Local Scalars .. INTEGER I, J REAL AMAX, UMAX, RPVGRW diff --git a/SRC/sla_rpvgrw.f b/SRC/sla_rpvgrw.f index 161c9f4b..e58f582c 100644 --- a/SRC/sla_rpvgrw.f +++ b/SRC/sla_rpvgrw.f @@ -16,6 +16,9 @@ * .. Array Arguments .. REAL A( LDA, * ), AF( LDAF, * ) * .. +* +* ===================================================================== +* * .. Local Scalars .. INTEGER I, J REAL AMAX, UMAX, RPVGRW diff --git a/SRC/sla_syamv.f b/SRC/sla_syamv.f index 280cd86f..66465658 100644 --- a/SRC/sla_syamv.f +++ b/SRC/sla_syamv.f @@ -38,7 +38,7 @@ * entry is considered "symbolic" if all multiplications involved * in computing that entry have at least one zero multiplicand. * -* Parameters +* Arguments * ========== * * UPLO - INTEGER @@ -101,6 +101,8 @@ * Y. INCY must not be zero. * Unchanged on exit. * +* Further Details +* =============== * * Level 2 Blas routine. * @@ -112,7 +114,8 @@ * -- Modified for the absolute-value product, April 2006 * Jason Riedy, UC Berkeley * -* .. +* ===================================================================== +* * .. Parameters .. REAL ONE, ZERO PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) diff --git a/SRC/sla_syrcond.f b/SRC/sla_syrcond.f index d410831f..564b6578 100644 --- a/SRC/sla_syrcond.f +++ b/SRC/sla_syrcond.f @@ -18,6 +18,10 @@ * .. Array Arguments INTEGER IWORK( * ), IPIV( * ) REAL A( LDA, * ), AF( LDAF, * ), WORK( * ), C( * ) +* .. +* +* Purpose +* ======= * * SLA_SYRCOND estimates the Skeel condition number of op(A) * op2(C) * where op2 is determined by CMODE as follows @@ -28,9 +32,16 @@ * is computed by computing scaling factors R such that * diag(R)*A*op2(C) is row equilibrated and computing the standard * infinity-norm condition number. -* WORK is a real workspace of size 3*N, and -* IWORK is an integer workspace of size N. -* .. +* +* Arguments +* ========== +* +* WORK real workspace of size 3*N. +* +* IWORK integer workspace of size N. +* +* ===================================================================== +* * .. Local Scalars .. CHARACTER NORMIN INTEGER KASE, I, J diff --git a/SRC/sla_syrfsx_extended.f b/SRC/sla_syrfsx_extended.f index 5671bebf..ce0911d5 100644 --- a/SRC/sla_syrfsx_extended.f +++ b/SRC/sla_syrfsx_extended.f @@ -29,6 +29,9 @@ REAL C( * ), AYB( * ), RCOND, BERR_OUT( * ), $ ERRS_N( NRHS, * ), ERRS_C( NRHS, * ) * .. +* +* ===================================================================== +* * .. Local Scalars .. INTEGER UPLO2, CNT, I, J, X_STATE, Z_STATE REAL YK, DYK, YMIN, NORMY, NORMX, NORMDX, DXRAT, diff --git a/SRC/sla_syrpvgrw.f b/SRC/sla_syrpvgrw.f index d10cab9e..a56cfd17 100644 --- a/SRC/sla_syrpvgrw.f +++ b/SRC/sla_syrpvgrw.f @@ -19,6 +19,9 @@ INTEGER IPIV( * ) REAL A( LDA, * ), AF( LDAF, * ), WORK( * ) * .. +* +* ===================================================================== +* * .. Local Scalars .. INTEGER NCOLS, I, J, K, KP REAL AMAX, UMAX, RPVGRW, TMP diff --git a/SRC/sla_wwaddw.f b/SRC/sla_wwaddw.f index e173d2c2..6312b134 100644 --- a/SRC/sla_wwaddw.f +++ b/SRC/sla_wwaddw.f @@ -36,7 +36,9 @@ * * W (input) REAL array, length N * The vector to be added. -* .. +* +* ===================================================================== +* * .. Local Scalars .. REAL S INTEGER I diff --git a/SRC/slansf.f b/SRC/slansf.f index 98272fb8..84955504 100644 --- a/SRC/slansf.f +++ b/SRC/slansf.f @@ -74,8 +74,8 @@ * where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, * WORK is not referenced. * -* Notes -* ===== +* Further Details +* =============== * * We first consider Rectangular Full Packed (RFP) Format when N is * even. We give an example where N = 6. diff --git a/SRC/spftrf.f b/SRC/spftrf.f index 54083656..5ae38200 100644 --- a/SRC/spftrf.f +++ b/SRC/spftrf.f @@ -66,8 +66,8 @@ * positive definite, and the factorization could not be * completed. * -* Notes -* ===== +* Further Details +* =============== * * We first consider Rectangular Full Packed (RFP) Format when N is * even. We give an example where N = 6. diff --git a/SRC/spftri.f b/SRC/spftri.f index a7dce352..d95ea6ca 100644 --- a/SRC/spftri.f +++ b/SRC/spftri.f @@ -58,8 +58,8 @@ * > 0: if INFO = i, the (i,i) element of the factor U or L is * zero, and the inverse could not be computed. * -* Notes -* ===== +* Further Details +* =============== * * We first consider Rectangular Full Packed (RFP) Format when N is * even. We give an example where N = 6. diff --git a/SRC/spftrs.f b/SRC/spftrs.f index 5bde02ec..ec33add8 100644 --- a/SRC/spftrs.f +++ b/SRC/spftrs.f @@ -57,8 +57,8 @@ * = 0: successful exit * < 0: if INFO = -i, the i-th argument had an illegal value * -* Notes -* ===== +* Further Details +* =============== * * We first consider Rectangular Full Packed (RFP) Format when N is * even. We give an example where N = 6. diff --git a/SRC/sstemr.f b/SRC/sstemr.f index 9d209335..70fa1431 100644 --- a/SRC/sstemr.f +++ b/SRC/sstemr.f @@ -67,7 +67,7 @@ * Computer Science Division Technical Report No. UCB/CSD-97-971, * UC Berkeley, May 1997. * -* Notes: +* Further Details * 1.SSTEMR works only on machines which follow IEEE-754 * floating-point standard in their handling of infinities and NaNs. * This permits the use of efficient inner loops avoiding a check for diff --git a/SRC/stfsm.f b/SRC/stfsm.f index 3c6438e8..2ca36fb0 100644 --- a/SRC/stfsm.f +++ b/SRC/stfsm.f @@ -126,8 +126,8 @@ * max( 1, m ). * Unchanged on exit. * -* Notes -* ===== +* Further Details +* =============== * * We first consider Rectangular Full Packed (RFP) Format when N is * even. We give an example where N = 6. diff --git a/SRC/stftri.f b/SRC/stftri.f index e75727b4..59af8a9a 100644 --- a/SRC/stftri.f +++ b/SRC/stftri.f @@ -65,8 +65,8 @@ * > 0: if INFO = i, A(i,i) is exactly zero. The triangular * matrix is singular and its inverse can not be computed. * -* Notes -* ===== +* Further Details +* =============== * * We first consider Rectangular Full Packed (RFP) Format when N is * even. We give an example where N = 6. diff --git a/SRC/stfttp.f b/SRC/stfttp.f index e582ff86..3ccb5881 100644 --- a/SRC/stfttp.f +++ b/SRC/stfttp.f @@ -52,8 +52,8 @@ * = 0: successful exit * < 0: if INFO = -i, the i-th argument had an illegal value * -* Notes -* ===== +* Further Details +* =============== * * We first consider Rectangular Full Packed (RFP) Format when N is * even. We give an example where N = 6. diff --git a/SRC/stfttr.f b/SRC/stfttr.f index c198b478..dcadbef5 100644 --- a/SRC/stfttr.f +++ b/SRC/stfttr.f @@ -57,8 +57,8 @@ * = 0: successful exit * < 0: if INFO = -i, the i-th argument had an illegal value * -* Notes -* ===== +* Further Details +* =============== * * We first consider Rectangular Full Packed (RFP) Format when N is * even. We give an example where N = 6. diff --git a/SRC/stpttf.f b/SRC/stpttf.f index be98d07e..6fe95433 100644 --- a/SRC/stpttf.f +++ b/SRC/stpttf.f @@ -51,8 +51,8 @@ * = 0: successful exit * < 0: if INFO = -i, the i-th argument had an illegal value * -* Notes -* ===== +* Further Details +* =============== * * We first consider Rectangular Full Packed (RFP) Format when N is * even. We give an example where N = 6. diff --git a/SRC/strttf.f b/SRC/strttf.f index 04db17b0..ec3e9c1b 100644 --- a/SRC/strttf.f +++ b/SRC/strttf.f @@ -55,8 +55,8 @@ * = 0: successful exit * < 0: if INFO = -i, the i-th argument had an illegal value * -* Notes -* ===== +* Further Details +* =============== * * We first consider Rectangular Full Packed (RFP) Format when N is * even. We give an example where N = 6. diff --git a/SRC/xerbla_array.f b/SRC/xerbla_array.f index 57cd98a9..350b59bc 100644 --- a/SRC/xerbla_array.f +++ b/SRC/xerbla_array.f @@ -1,68 +1,68 @@ SUBROUTINE XERBLA_ARRAY(SRNAME_ARRAY, SRNAME_LEN, INFO) -! -! -- LAPACK auxiliary routine (version 3.0) -- -! Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., -! September 19, 2006 -! +* +* -- LAPACK auxiliary routine (version 3.0) -- +* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., +* September 19, 2006 +* IMPLICIT NONE -! .. Scalar Arguments .. +* .. Scalar Arguments .. INTEGER SRNAME_LEN, INFO -! .. -! .. Array Arguments .. +* .. +* .. Array Arguments .. CHARACTER(1) SRNAME_ARRAY(SRNAME_LEN) -! .. -! -! Purpose -! ======= -! -! XERBLA_ARRAY assists other languages in calling XERBLA, the LAPACK -! and BLAS error handler. Rather than taking a Fortran string argument -! as the function's name, XERBLA_ARRAY takes an array of single -! characters along with the array's length. XERBLA_ARRAY then copies -! up to 32 characters of that array into a Fortran string and passes -! that to XERBLA. If called with a non-positive SRNAME_LEN, -! XERBLA_ARRAY will call XERBLA with a string of all blank characters. -! -! Say some macro or other device makes XERBLA_ARRAY available to C99 -! by a name lapack_xerbla and with a common Fortran calling convention. -! Then a C99 program could invoke XERBLA via: -! { -! int flen = strlen(__func__); -! lapack_xerbla(__func__, &flen, &info); -! } -! -! Providing XERBLA_ARRAY is not necessary for intercepting LAPACK -! errors. XERBLA_ARRAY calls XERBLA. -! -! Arguments -! ========= -! -! SRNAME_ARRAY (input) CHARACTER(1) array, dimension (SRNAME_LEN) -! The name of the routine which called XERBLA_ARRAY. -! -! SRNAME_LEN (input) INTEGER -! The length of the name in SRNAME_ARRAY. -! -! INFO (input) INTEGER -! The position of the invalid parameter in the parameter list -! of the calling routine. -! -! ===================================================================== -! -! .. -! .. Local Scalars .. +* .. +* +* Purpose +* ======= +* +* XERBLA_ARRAY assists other languages in calling XERBLA, the LAPACK +* and BLAS error handler. Rather than taking a Fortran string argument +* as the function's name, XERBLA_ARRAY takes an array of single +* characters along with the array's length. XERBLA_ARRAY then copies +* up to 32 characters of that array into a Fortran string and passes +* that to XERBLA. If called with a non-positive SRNAME_LEN, +* XERBLA_ARRAY will call XERBLA with a string of all blank characters. +* +* Say some macro or other device makes XERBLA_ARRAY available to C99 +* by a name lapack_xerbla and with a common Fortran calling convention. +* Then a C99 program could invoke XERBLA via: +* { +* int flen = strlen(__func__); +* lapack_xerbla(__func__, &flen, &info); +* } +* +* Providing XERBLA_ARRAY is not necessary for intercepting LAPACK +* errors. XERBLA_ARRAY calls XERBLA. +* +* Arguments +* ========= +* +* SRNAME_ARRAY (input) CHARACTER(1) array, dimension (SRNAME_LEN) +* The name of the routine which called XERBLA_ARRAY. +* +* SRNAME_LEN (input) INTEGER +* The length of the name in SRNAME_ARRAY. +* +* INFO (input) INTEGER +* The position of the invalid parameter in the parameter list +* of the calling routine. +* +* ===================================================================== +* +* .. +* .. Local Scalars .. INTEGER I -! .. -! .. Local Arrays .. +* .. +* .. Local Arrays .. CHARACTER*32 SRNAME -! .. -! .. Intrinsic Functions .. +* .. +* .. Intrinsic Functions .. INTRINSIC MIN, LEN -! .. -! .. External Functions .. +* .. +* .. External Functions .. EXTERNAL XERBLA -! .. -! .. Executable Statements .. +* .. +* .. Executable Statements .. SRNAME = '' DO I = 1, MIN( SRNAME_LEN, LEN( SRNAME ) ) SRNAME( I:I ) = SRNAME_ARRAY( I ) diff --git a/SRC/zla_gbamv.f b/SRC/zla_gbamv.f index 9bc101fb..fb252014 100644 --- a/SRC/zla_gbamv.f +++ b/SRC/zla_gbamv.f @@ -40,7 +40,7 @@ * entry is considered "symbolic" if all multiplications involved * in computing that entry have at least one zero multiplicand. * -* Parameters +* Arguments * ========== * * TRANS - INTEGER @@ -118,7 +118,9 @@ * * Level 2 Blas routine. * -* .. +* +* ===================================================================== +* * .. Parameters .. COMPLEX*16 ONE, ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) diff --git a/SRC/zla_gbrcond_c.f b/SRC/zla_gbrcond_c.f index 92162f2f..6765e591 100644 --- a/SRC/zla_gbrcond_c.f +++ b/SRC/zla_gbrcond_c.f @@ -22,11 +22,24 @@ COMPLEX*16 AB( LDAB, * ), AFB( LDAFB, * ), WORK( * ) DOUBLE PRECISION C( * ), RWORK( * ) * +* +* Purpose +* ======= +* * ZLA_GBRCOND_C Computes the infinity norm condition number of * op(A) * inv(diag(C)) where C is a DOUBLE PRECISION vector. -* WORK is a COMPLEX*16 workspace of size 2*N, and -* RWORK is a DOUBLE PRECISION workspace of size 3*N. -* .. +* +* Arguments +* ========= +* +* C DOUBLE PRECISION vector. +* +* WORK COMPLEX*16 workspace of size 2*N. +* +* RWORK DOUBLE PRECISION workspace of size 3*N. +* +* ===================================================================== +* * .. Local Scalars .. LOGICAL NOTRANS INTEGER KASE, I, J diff --git a/SRC/zla_gbrcond_x.f b/SRC/zla_gbrcond_x.f index f2decc47..7bc1aa3c 100644 --- a/SRC/zla_gbrcond_x.f +++ b/SRC/zla_gbrcond_x.f @@ -22,11 +22,24 @@ $ X( * ) DOUBLE PRECISION RWORK( * ) * +* +* Purpose +* ======= +* * ZLA_GBRCOND_X Computes the infinity norm condition number of * op(A) * diag(X) where X is a COMPLEX*16 vector. -* WORK is a COMPLEX*16 workspace of size 2*N, and -* RWORK is a DOUBLE PRECISION workspace of size 3*N. -* .. +* +* Arguments +* ========= +* +* X COMPLEX*16 vector. +* +* WORK COMPLEX*16 workspace of size 2*N. +* +* RWORK DOUBLE PRECISION workspace of size 3*N. +* +* ===================================================================== +* * .. Local Scalars .. LOGICAL NOTRANS INTEGER KASE, I, J diff --git a/SRC/zla_gbrfsx_extended.f b/SRC/zla_gbrfsx_extended.f index 33b3c42a..a3096707 100644 --- a/SRC/zla_gbrfsx_extended.f +++ b/SRC/zla_gbrfsx_extended.f @@ -29,6 +29,9 @@ DOUBLE PRECISION C( * ), AYB(*), RCOND, BERR_OUT( * ), $ ERRS_N( NRHS, * ), ERRS_C( NRHS, * ) * .. +* +* ===================================================================== +* * .. Local Scalars .. CHARACTER TRANS INTEGER CNT, I, J, M, X_STATE, Z_STATE, Y_PREC_STATE diff --git a/SRC/zla_gbrpvgrw.f b/SRC/zla_gbrpvgrw.f index d6366c93..49d50f1b 100644 --- a/SRC/zla_gbrpvgrw.f +++ b/SRC/zla_gbrpvgrw.f @@ -17,6 +17,9 @@ * .. Array Arguments .. COMPLEX*16 AB( LDAB, * ), AFB( LDAFB, * ) * .. +* +* ===================================================================== +* * .. Local Scalars .. INTEGER I, J, KD DOUBLE PRECISION AMAX, UMAX, RPVGRW diff --git a/SRC/zla_geamv.f b/SRC/zla_geamv.f index 135ee5e6..e28f7488 100644 --- a/SRC/zla_geamv.f +++ b/SRC/zla_geamv.f @@ -41,7 +41,7 @@ * entry is considered "symbolic" if all multiplications involved * in computing that entry have at least one zero multiplicand. * -* Parameters +* Arguments * ========== * * TRANS - INTEGER @@ -113,7 +113,9 @@ * * Level 2 Blas routine. * -* .. +* +* ===================================================================== +* * .. Parameters .. COMPLEX*16 ONE, ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) diff --git a/SRC/zla_gercond_c.f b/SRC/zla_gercond_c.f index a4cf0926..b141bd24 100644 --- a/SRC/zla_gercond_c.f +++ b/SRC/zla_gercond_c.f @@ -21,12 +21,25 @@ INTEGER IPIV( * ) COMPLEX*16 A( LDA, * ), AF( LDAF, * ), WORK( * ) DOUBLE PRECISION C( * ), RWORK( * ) +* .. +* +* Purpose +* ======= * * ZLA_GERCOND_C computes the infinity norm condition number of * op(A) * inv(diag(C)) where C is a DOUBLE PRECISION vector. -* WORK is a COMPLEX*16 workspace of size 2*N, and -* RWORK is a DOUBLE PRECISION workspace of size 3*N. -* .. +* +* Arguments +* ========= +* +* C DOUBLE PRECISION vector. +* +* WORK COMPLEX*16 workspace of size 2*N. +* +* RWORK DOUBLE PRECISION workspace of size 3*N. +* +* ===================================================================== +* * .. Local Scalars .. LOGICAL NOTRANS INTEGER KASE, I, J diff --git a/SRC/zla_gercond_x.f b/SRC/zla_gercond_x.f index 4ed6faa0..93a1635f 100644 --- a/SRC/zla_gercond_x.f +++ b/SRC/zla_gercond_x.f @@ -19,12 +19,25 @@ INTEGER IPIV( * ) COMPLEX*16 A( LDA, * ), AF( LDAF, * ), WORK( * ), X( * ) DOUBLE PRECISION RWORK( * ) +* .. +* +* Purpose +* ======= * * ZLA_GERCOND_X computes the infinity norm condition number of * op(A) * diag(X) where X is a COMPLEX*16 vector. -* WORK is a COMPLEX*16 workspace of size 2*N, and -* RWORK is a DOUBLE PRECISION workspace of size 3*N. -* .. +* +* Arguments +* ========= +* +* C COMPLEX*16 vector. +* +* WORK COMPLEX*16 workspace of size 2*N. +* +* RWORK DOUBLE PRECISION workspace of size 3*N. +* +* ===================================================================== +* * .. Local Scalars .. LOGICAL NOTRANS INTEGER KASE diff --git a/SRC/zla_gerfsx_extended.f b/SRC/zla_gerfsx_extended.f index 2953878d..d1848e15 100644 --- a/SRC/zla_gerfsx_extended.f +++ b/SRC/zla_gerfsx_extended.f @@ -29,6 +29,9 @@ DOUBLE PRECISION C( * ), AYB( * ), RCOND, BERR_OUT( * ), $ ERRS_N( NRHS, * ), ERRS_C( NRHS, * ) * .. +* +* ===================================================================== +* * .. Local Scalars .. CHARACTER TRANS INTEGER CNT, I, J, X_STATE, Z_STATE, Y_PREC_STATE diff --git a/SRC/zla_heamv.f b/SRC/zla_heamv.f index d9181914..466027be 100644 --- a/SRC/zla_heamv.f +++ b/SRC/zla_heamv.f @@ -39,7 +39,7 @@ * entry is considered "symbolic" if all multiplications involved * in computing that entry have at least one zero multiplicand. * -* Parameters +* Arguments * ========== * * UPLO - INTEGER @@ -102,6 +102,8 @@ * Y. INCY must not be zero. * Unchanged on exit. * +* Further Details +* =============== * * Level 2 Blas routine. * @@ -113,7 +115,8 @@ * -- Modified for the absolute-value product, April 2006 * Jason Riedy, UC Berkeley * -* .. +* ===================================================================== +* * .. Parameters .. DOUBLE PRECISION ONE, ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) diff --git a/SRC/zla_hercond_c.f b/SRC/zla_hercond_c.f index 474a6d7b..bef3c663 100644 --- a/SRC/zla_hercond_c.f +++ b/SRC/zla_hercond_c.f @@ -21,12 +21,25 @@ INTEGER IPIV( * ) COMPLEX*16 A( LDA, * ), AF( LDAF, * ), WORK( * ) DOUBLE PRECISION C ( * ), RWORK( * ) +* .. +* +* Purpose +* ======= * * ZLA_HERCOND_C computes the infinity norm condition number of * op(A) * inv(diag(C)) where C is a DOUBLE PRECISION vector. -* WORK is a COMPLEX*16 workspace of size 2*N, and -* RWORK is a DOUBLE PRECISION workspace of size 3*N. -* .. +* +* Arguments +* ========= +* +* C DOUBLE PRECISION vector. +* +* WORK COMPLEX*16 workspace of size 2*N. +* +* RWORK DOUBLE PRECISION workspace of size 3*N. +* +* ===================================================================== +* * .. Local Scalars .. INTEGER KASE, I, J DOUBLE PRECISION AINVNM, ANORM, TMP diff --git a/SRC/zla_hercond_x.f b/SRC/zla_hercond_x.f index fb7b3c9f..ea031ced 100644 --- a/SRC/zla_hercond_x.f +++ b/SRC/zla_hercond_x.f @@ -19,12 +19,25 @@ INTEGER IPIV( * ) COMPLEX*16 A( LDA, * ), AF( LDAF, * ), WORK( * ), X( * ) DOUBLE PRECISION RWORK( * ) +* .. +* +* Purpose +* ======= * * ZLA_HERCOND_X computes the infinity norm condition number of * op(A) * diag(X) where X is a COMPLEX*16 vector. -* WORK is a COMPLEX*16 workspace of size 2*N, and -* RWORK is a DOUBLE PRECISION workspace of size 3*N. -* .. +* +* Arguments +* ========= +* +* C COMPLEX*16 vector. +* +* WORK COMPLEX*16 workspace of size 2*N. +* +* RWORK DOUBLE PRECISION workspace of size 3*N. +* +* ===================================================================== +* * .. Local Scalars .. INTEGER KASE, I, J DOUBLE PRECISION AINVNM, ANORM, TMP diff --git a/SRC/zla_herfsx_extended.f b/SRC/zla_herfsx_extended.f index 8d3e56bf..84a71c1c 100644 --- a/SRC/zla_herfsx_extended.f +++ b/SRC/zla_herfsx_extended.f @@ -29,6 +29,9 @@ DOUBLE PRECISION C( * ), AYB( * ), RCOND, BERR_OUT( * ), $ ERRS_N( NRHS, * ), ERRS_C( NRHS, * ) * .. +* +* ===================================================================== +* * .. Local Scalars .. INTEGER UPLO2, CNT, I, J, X_STATE, Z_STATE, $ Y_PREC_STATE diff --git a/SRC/zla_herpvgrw.f b/SRC/zla_herpvgrw.f index e0e63f46..35dc69bf 100644 --- a/SRC/zla_herpvgrw.f +++ b/SRC/zla_herpvgrw.f @@ -20,6 +20,9 @@ COMPLEX*16 A( LDA, * ), AF( LDAF, * ) DOUBLE PRECISION WORK( * ) * .. +* +* ===================================================================== +* * .. Local Scalars .. INTEGER NCOLS, I, J, K, KP DOUBLE PRECISION AMAX, UMAX, RPVGRW, TMP diff --git a/SRC/zla_lin_berr.f b/SRC/zla_lin_berr.f index 6246c45a..02a81f5b 100644 --- a/SRC/zla_lin_berr.f +++ b/SRC/zla_lin_berr.f @@ -16,13 +16,19 @@ * .. Array Arguments .. DOUBLE PRECISION AYB( N, NRHS ), BERR( NRHS ) COMPLEX*16 RES( N, NRHS ) +* .. +* +* Purpose +* ======= * * ZLA_LIN_BERR computes componentwise relative backward error from * the formula * max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) ) * where abs(Z) is the componentwise absolute value of the matrix * or vector Z. -* .. +* +* ===================================================================== +* * .. Local Scalars .. DOUBLE PRECISION TMP INTEGER I, J diff --git a/SRC/zla_porcond_c.f b/SRC/zla_porcond_c.f index 5ab1fdfc..81e38b02 100644 --- a/SRC/zla_porcond_c.f +++ b/SRC/zla_porcond_c.f @@ -19,12 +19,25 @@ * .. Array Arguments .. COMPLEX*16 A( LDA, * ), AF( LDAF, * ), WORK( * ) DOUBLE PRECISION C( * ), RWORK( * ) +* .. +* +* Purpose +* ======= * * DLA_PORCOND_C Computes the infinity norm condition number of * op(A) * inv(diag(C)) where C is a DOUBLE PRECISION vector -* WORK is a COMPLEX*16 workspace of size 2*N, and -* RWORK is a DOUBLE PRECISION workspace of size 3*N. -* .. +* +* Arguments +* ========= +* +* C DOUBLE PRECISION vector. +* +* WORK COMPLEX*16 workspace of size 2*N. +* +* RWORK DOUBLE PRECISION workspace of size 3*N. +* +* ===================================================================== +* * .. Local Scalars .. INTEGER KASE DOUBLE PRECISION AINVNM, ANORM, TMP diff --git a/SRC/zla_porcond_x.f b/SRC/zla_porcond_x.f index 95a366d9..aa31f0a3 100644 --- a/SRC/zla_porcond_x.f +++ b/SRC/zla_porcond_x.f @@ -18,12 +18,25 @@ * .. Array Arguments .. COMPLEX*16 A( LDA, * ), AF( LDAF, * ), WORK( * ), X( * ) DOUBLE PRECISION RWORK( * ) +* .. +* +* Purpose +* ======= * * ZLA_PORCOND_X Computes the infinity norm condition number of * op(A) * diag(X) where X is a COMPLEX*16 vector. -* WORK is a COMPLEX*16 workspace of size 2*N, and -* RWORK is a DOUBLE PRECISION workspace of size 3*N. -* .. +* +* Arguments +* ========= +* +* C COMPLEX*16 vector. +* +* WORK COMPLEX*16 workspace of size 2*N. +* +* RWORK DOUBLE PRECISION workspace of size 3*N. +* +* ===================================================================== +* * .. Local Scalars .. INTEGER KASE, I, J DOUBLE PRECISION AINVNM, ANORM, TMP diff --git a/SRC/zla_porfsx_extended.f b/SRC/zla_porfsx_extended.f index e614b578..b9afd66e 100644 --- a/SRC/zla_porfsx_extended.f +++ b/SRC/zla_porfsx_extended.f @@ -28,6 +28,9 @@ DOUBLE PRECISION C( * ), AYB( * ), RCOND, BERR_OUT( * ), $ ERRS_N( NRHS, * ), ERRS_C( NRHS, * ) * .. +* +* ===================================================================== +* * .. Local Scalars .. INTEGER UPLO2, CNT, I, J, X_STATE, Z_STATE, $ Y_PREC_STATE diff --git a/SRC/zla_porpvgrw.f b/SRC/zla_porpvgrw.f index 3ae8ae56..c6a06023 100644 --- a/SRC/zla_porpvgrw.f +++ b/SRC/zla_porpvgrw.f @@ -19,6 +19,9 @@ COMPLEX*16 A( LDA, * ), AF( LDAF, * ) DOUBLE PRECISION WORK( * ) * .. +* +* ===================================================================== +* * .. Local Scalars .. INTEGER I, J DOUBLE PRECISION AMAX, UMAX, RPVGRW diff --git a/SRC/zla_rpvgrw.f b/SRC/zla_rpvgrw.f index 68de32be..1d5546e8 100644 --- a/SRC/zla_rpvgrw.f +++ b/SRC/zla_rpvgrw.f @@ -16,6 +16,9 @@ * .. Array Arguments .. COMPLEX*16 A( LDA, * ), AF( LDAF, * ) * .. +* +* ===================================================================== +* * .. Local Scalars .. INTEGER I, J DOUBLE PRECISION AMAX, UMAX, RPVGRW diff --git a/SRC/zla_syamv.f b/SRC/zla_syamv.f index e400d6a5..da8a1268 100644 --- a/SRC/zla_syamv.f +++ b/SRC/zla_syamv.f @@ -40,7 +40,7 @@ * entry is considered "symbolic" if all multiplications involved * in computing that entry have at least one zero multiplicand. * -* Parameters +* Arguments * ========== * * UPLO - INTEGER @@ -103,6 +103,8 @@ * Y. INCY must not be zero. * Unchanged on exit. * +* Further Details +* =============== * * Level 2 Blas routine. * @@ -114,7 +116,8 @@ * -- Modified for the absolute-value product, April 2006 * Jason Riedy, UC Berkeley * -* .. +* ===================================================================== +* * .. Parameters .. DOUBLE PRECISION ONE, ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) diff --git a/SRC/zla_syrcond_c.f b/SRC/zla_syrcond_c.f index ee10f8e6..12ccdf26 100644 --- a/SRC/zla_syrcond_c.f +++ b/SRC/zla_syrcond_c.f @@ -21,12 +21,25 @@ INTEGER IPIV( * ) COMPLEX*16 A( LDA, * ), AF( LDAF, * ), WORK( * ) DOUBLE PRECISION C( * ), RWORK( * ) +* .. +* +* Purpose +* ======= * * ZLA_SYRCOND_C Computes the infinity norm condition number of * op(A) * inv(diag(C)) where C is a DOUBLE PRECISION vector. -* WORK is a COMPLEX*16 workspace of size 2*N, and -* RWORK is a DOUBLE PRECISION workspace of size 3*N. -* .. +* +* Arguments +* ========= +* +* C DOUBLE PRECISION vector. +* +* WORK COMPLEX*16 workspace of size 2*N. +* +* RWORK DOUBLE PRECISION workspace of size 3*N. +* +* ===================================================================== +* * .. Local Scalars .. INTEGER KASE DOUBLE PRECISION AINVNM, ANORM, TMP diff --git a/SRC/zla_syrcond_x.f b/SRC/zla_syrcond_x.f index 539853f7..8a2fe8e2 100644 --- a/SRC/zla_syrcond_x.f +++ b/SRC/zla_syrcond_x.f @@ -19,12 +19,25 @@ INTEGER IPIV( * ) COMPLEX*16 A( LDA, * ), AF( LDAF, * ), WORK( * ), X( * ) DOUBLE PRECISION RWORK( * ) +* .. +* +* Purpose +* ======= * * ZLA_SYRCOND_X Computes the infinity norm condition number of * op(A) * diag(X) where X is a COMPLEX*16 vector. -* WORK is a COMPLEX*16 workspace of size 2*N, and -* RWORK is a DOUBLE PRECISION workspace of size 3*N. -* .. +* +* Arguments +* ========= +* +* C COMPLEX*16 vector. +* +* WORK COMPLEX*16 workspace of size 2*N. +* +* RWORK DOUBLE PRECISION workspace of size 3*N. +* +* ===================================================================== +* * .. Local Scalars .. INTEGER KASE DOUBLE PRECISION AINVNM, ANORM, TMP diff --git a/SRC/zla_syrfsx_extended.f b/SRC/zla_syrfsx_extended.f index 91f8bd29..2621ddff 100644 --- a/SRC/zla_syrfsx_extended.f +++ b/SRC/zla_syrfsx_extended.f @@ -29,6 +29,9 @@ DOUBLE PRECISION C( * ), AYB( * ), RCOND, BERR_OUT( * ), $ ERRS_N( NRHS, * ), ERRS_C( NRHS, * ) * .. +* +* ===================================================================== +* * .. Local Scalars .. INTEGER UPLO2, CNT, I, J, X_STATE, Z_STATE, $ Y_PREC_STATE diff --git a/SRC/zla_syrpvgrw.f b/SRC/zla_syrpvgrw.f index 2a358b3a..892d216b 100644 --- a/SRC/zla_syrpvgrw.f +++ b/SRC/zla_syrpvgrw.f @@ -20,6 +20,9 @@ DOUBLE PRECISION WORK( * ) INTEGER IPIV( * ) * .. +* +* ===================================================================== +* * .. Local Scalars .. INTEGER NCOLS, I, J, K, KP DOUBLE PRECISION AMAX, UMAX, RPVGRW, TMP diff --git a/SRC/zla_wwaddw.f b/SRC/zla_wwaddw.f index cd4c7e78..ff449e5d 100644 --- a/SRC/zla_wwaddw.f +++ b/SRC/zla_wwaddw.f @@ -36,7 +36,9 @@ * * W (input) COMPLEX*16 array, length N * The vector to be added. -* .. +* +* ===================================================================== +* * .. Local Scalars .. COMPLEX*16 S INTEGER I diff --git a/SRC/zlanhf.f b/SRC/zlanhf.f index 40409936..42b5c91e 100644 --- a/SRC/zlanhf.f +++ b/SRC/zlanhf.f @@ -90,8 +90,8 @@ * where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, * WORK is not referenced. * -* Note: -* ===== +* Further Details +* =============== * * We first consider Standard Packed Format when N is even. * We give an example where N = 6. diff --git a/SRC/zpftri.f b/SRC/zpftri.f index c986a43d..46566614 100644 --- a/SRC/zpftri.f +++ b/SRC/zpftri.f @@ -58,8 +58,8 @@ * > 0: if INFO = i, the (i,i) element of the factor U or L is * zero, and the inverse could not be computed. * -* Note: -* ===== +* Further Details +* =============== * * We first consider Standard Packed Format when N is even. * We give an example where N = 6. diff --git a/SRC/zpftrs.f b/SRC/zpftrs.f index 3fea6b1e..6cd0e88b 100644 --- a/SRC/zpftrs.f +++ b/SRC/zpftrs.f @@ -57,8 +57,8 @@ * = 0: successful exit * < 0: if INFO = -i, the i-th argument had an illegal value * -* Note: -* ===== +* Further Details +* =============== * * We first consider Standard Packed Format when N is even. * We give an example where N = 6. diff --git a/SRC/zstemr.f b/SRC/zstemr.f index fddd97e5..76f36b98 100644 --- a/SRC/zstemr.f +++ b/SRC/zstemr.f @@ -67,7 +67,7 @@ * Computer Science Division Technical Report No. UCB/CSD-97-971, * UC Berkeley, May 1997. * -* Notes: +* Further Details * 1.ZSTEMR works only on machines which follow IEEE-754 * floating-point standard in their handling of infinities and NaNs. * This permits the use of efficient inner loops avoiding a check for diff --git a/SRC/ztfsm.f b/SRC/ztfsm.f index ab409b28..fa9ce767 100644 --- a/SRC/ztfsm.f +++ b/SRC/ztfsm.f @@ -126,8 +126,8 @@ * max( 1, m ). * Unchanged on exit. * -* Notes: -* ====== +* Further Details +* =============== * * We first consider Standard Packed Format when N is even. * We give an example where N = 6. diff --git a/SRC/ztftri.f b/SRC/ztftri.f index 1fc7c304..a63cf9c9 100644 --- a/SRC/ztftri.f +++ b/SRC/ztftri.f @@ -64,8 +64,8 @@ * > 0: if INFO = i, A(i,i) is exactly zero. The triangular * matrix is singular and its inverse can not be computed. * -* Notes: -* ====== +* Further Details +* =============== * * We first consider Standard Packed Format when N is even. * We give an example where N = 6. diff --git a/SRC/ztfttp.f b/SRC/ztfttp.f index bafd0abf..bf46facc 100644 --- a/SRC/ztfttp.f +++ b/SRC/ztfttp.f @@ -51,8 +51,8 @@ * = 0: successful exit * < 0: if INFO = -i, the i-th argument had an illegal value * -* Notes: -* ====== +* Further Details +* =============== * * We first consider Standard Packed Format when N is even. * We give an example where N = 6. diff --git a/SRC/ztfttr.f b/SRC/ztfttr.f index 384c41d1..6ebe0958 100644 --- a/SRC/ztfttr.f +++ b/SRC/ztfttr.f @@ -56,8 +56,8 @@ * = 0: successful exit * < 0: if INFO = -i, the i-th argument had an illegal value * -* Notes: -* ====== +* Further Details +* =============== * * We first consider Standard Packed Format when N is even. * We give an example where N = 6. diff --git a/SRC/ztpttf.f b/SRC/ztpttf.f index 9e49eae6..89dc0d5c 100644 --- a/SRC/ztpttf.f +++ b/SRC/ztpttf.f @@ -51,8 +51,8 @@ * = 0: successful exit * < 0: if INFO = -i, the i-th argument had an illegal value * -* Notes: -* ====== +* Further Details +* =============== * * We first consider Standard Packed Format when N is even. * We give an example where N = 6. diff --git a/SRC/ztrttf.f b/SRC/ztrttf.f index 61c6a82c..f2c24753 100644 --- a/SRC/ztrttf.f +++ b/SRC/ztrttf.f @@ -56,8 +56,8 @@ * = 0: successful exit * < 0: if INFO = -i, the i-th argument had an illegal value * -* Notes -* ===== +* Further Details +* =============== * * We first consider Standard Packed Format when N is even. * We give an example where N = 6. |