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Diffstat (limited to 'SRC/sgsvj0.f')
| -rw-r--r-- | SRC/sgsvj0.f | 835 |
1 files changed, 835 insertions, 0 deletions
diff --git a/SRC/sgsvj0.f b/SRC/sgsvj0.f new file mode 100644 index 00000000..975205e3 --- /dev/null +++ b/SRC/sgsvj0.f @@ -0,0 +1,835 @@ + SUBROUTINE SGSVJ0( JOBV, M, N, A, LDA, D, SVA, MV, V, LDV, EPS, + & SFMIN, TOL, NSWEEP, WORK, LWORK, INFO ) +* +* -- LAPACK routine (version 3.2) -- +* +* -- Contributed by Zlatko Drmac of the University of Zagreb and -- +* -- Kresimir Veselic of the Fernuniversitaet Hagen -- +* -- November 2008 -- +* +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* +* This routine is also part of SIGMA (version 1.23, October 23. 2008.) +* SIGMA is a library of algorithms for highly accurate algorithms for +* 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 ) +* .. +* +* 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 +* parameters (marked by [TP]) are available for the implementer. +* +* Further details +* ~~~~~~~~~~~~~~~ +* SGSVJ0 is used just to enable SGESVJ to call a simplified version of +* itself to work on a submatrix of the original matrix. +* +* Contributors +* ~~~~~~~~~~~~ +* Zlatko Drmac (Zagreb, Croatia) and Kresimir Veselic (Hagen, Germany) +* +* Bugs, Examples and Comments +* ~~~~~~~~~~~~~~~~~~~~~~~~~~~ +* Please report all bugs and send interesting test examples and comments to +* drmac@math.hr. Thank you. +* +* Arguments +* ~~~~~~~~~ +* +* JOBV (input) CHARACTER*1 +* Specifies whether the output from this procedure is used +* to compute the matrix V: +* = 'V': the product of the Jacobi rotations is accumulated +* by postmulyiplying the N-by-N array V. +* (See the description of V.) +* = 'A': the product of the Jacobi rotations is accumulated +* by postmulyiplying the MV-by-N array V. +* (See the descriptions of MV and V.) +* = 'N': the Jacobi rotations are not accumulated. +* +* M (input) INTEGER +* The number of rows of the input matrix A. M >= 0. +* +* N (input) INTEGER +* The number of columns of the input matrix A. +* M >= N >= 0. +* +* A (input/output) REAL array, dimension (LDA,N) +* On entry, M-by-N matrix A, such that A*diag(D) represents +* the input matrix. +* On exit, +* A_onexit * D_onexit represents the input matrix A*diag(D) +* post-multiplied by a sequence of Jacobi rotations, where the +* rotation threshold and the total number of sweeps are given in +* TOL and NSWEEP, respectively. +* (See the descriptions of D, TOL and NSWEEP.) +* +* LDA (input) INTEGER +* The leading dimension of the array A. LDA >= max(1,M). +* +* D (input/workspace/output) REAL array, dimension (N) +* The array D accumulates the scaling factors from the fast scaled +* Jacobi rotations. +* On entry, A*diag(D) represents the input matrix. +* On exit, A_onexit*diag(D_onexit) represents the input matrix +* post-multiplied by a sequence of Jacobi rotations, where the +* rotation threshold and the total number of sweeps are given in +* TOL and NSWEEP, respectively. +* (See the descriptions of A, TOL and NSWEEP.) +* +* SVA (input/workspace/output) REAL array, dimension (N) +* On entry, SVA contains the Euclidean norms of the columns of +* the matrix A*diag(D). +* On exit, SVA contains the Euclidean norms of the columns of +* the matrix onexit*diag(D_onexit). +* +* MV (input) INTEGER +* If JOBV .EQ. 'A', then MV rows of V are post-multipled by a +* sequence of Jacobi rotations. +* If JOBV = 'N', then MV is not referenced. +* +* V (input/output) REAL array, dimension (LDV,N) +* If JOBV .EQ. 'V' then N rows of V are post-multipled by a +* sequence of Jacobi rotations. +* If JOBV .EQ. 'A' then MV rows of V are post-multipled by a +* sequence of Jacobi rotations. +* If JOBV = 'N', then V is not referenced. +* +* LDV (input) INTEGER +* The leading dimension of the array V, LDV >= 1. +* If JOBV = 'V', LDV .GE. N. +* If JOBV = 'A', LDV .GE. MV. +* +* EPS (input) INTEGER +* EPS = SLAMCH('Epsilon') +* +* SFMIN (input) INTEGER +* SFMIN = SLAMCH('Safe Minimum') +* +* TOL (input) REAL +* TOL is the threshold for Jacobi rotations. For a pair +* A(:,p), A(:,q) of pivot columns, the Jacobi rotation is +* applied only if ABS(COS(angle(A(:,p),A(:,q)))) .GT. TOL. +* +* NSWEEP (input) INTEGER +* NSWEEP is the number of sweeps of Jacobi rotations to be +* performed. +* +* WORK (workspace) REAL array, dimension LWORK. +* +* LWORK (input) INTEGER +* LWORK is the dimension of WORK. LWORK .GE. M. +* +* INFO (output) INTEGER +* = 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 +* +* ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~| +* + 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 + INFO = -2 + ELSE IF ( ( N .LT. 0 ) .OR. ( N .GT. M )) THEN + INFO = -3 + ELSE IF ( LDA .LT. M ) THEN + INFO = -5 + ELSE IF ( MV .LT. 0 ) THEN + INFO = -8 + ELSE IF ( LDV .LT. M ) THEN + INFO = -10 + ELSE IF ( TOL .LE. EPS ) THEN + INFO = -13 + ELSE IF ( NSWEEP .LT. 0 ) THEN + INFO = -14 + ELSE IF ( LWORK .LT. M ) THEN + INFO = -16 + ELSE + INFO = 0 + END IF +* +* #:( + IF ( INFO .NE. 0 ) THEN + CALL XERBLA( 'SGSVJ0', -INFO ) + RETURN + END IF +* + IF ( RSVEC ) THEN + MVL = N + 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) +* +* +* -#- Row-cyclic Jacobi SVD algorithm with column pivoting -#- +* + EMPTSW = ( N * ( N - 1 ) ) / 2 + NOTROT = 0 + FASTR(1) = ZERO +* +* -#- Row-cyclic pivot strategy with de Rijk's pivoting -#- +* + + SWBAND = 0 +*[TP] SWBAND is a tuning parameter. It is meaningful and effective +* if SGESVJ is used as a computational routine in the preconditioned +* Jacobi SVD algorithm SGESVJ. For sweeps i=1:SWBAND the procedure +* ...... + + KBL = MIN0( 8, N ) +*[TP] KBL is a tuning parameter that defines the tile size in the +* tiling of the p-q loops of pivot pairs. In general, an optimal +* value of KBL depends on the matrix dimensions and on the +* parameters of the computer's memory. +* + NBL = N / KBL + IF ( ( NBL * KBL ) .NE. N ) NBL = NBL + 1 + + BLSKIP = ( KBL**2 ) + 1 +*[TP] BLKSKIP is a tuning parameter that depends on SWBAND and KBL. + + ROWSKIP = MIN0( 5, KBL ) +*[TP] ROWSKIP is a tuning parameter. + + LKAHEAD = 1 +*[TP] LKAHEAD is a tuning parameter. + SWBAND = 0 + PSKIPPED = 0 +* + DO 1993 i = 1, NSWEEP +* .. go go go ... +* + MXAAPQ = ZERO + MXSINJ = ZERO + ISWROT = 0 +* + NOTROT = 0 + PSKIPPED = 0 +* + DO 2000 ibr = 1, NBL + + igl = ( ibr - 1 ) * KBL + 1 +* + DO 1002 ir1 = 0, MIN0( LKAHEAD, NBL - ibr ) +* + igl = igl + ir1 * KBL +* + 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 +* +* Column norms are periodically updated by explicit +* norm computation. +* Caveat: +* Some BLAS implementations compute SNRM2(M,A(1,p),1) +* as SQRT(SDOT(M,A(1,p),1,A(1,p),1)), which may result in +* overflow for ||A(:,p)||_2 > SQRT(overflow_threshold), and +* undeflow for ||A(:,p)||_2 < SQRT(underflow_threshold). +* Hence, SNRM2 cannot be trusted, not even in the case when +* the true norm is far from the under(over)flow boundaries. +* 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 ( 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 ) * + & 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) ) +* +* TO rotate or NOT to rotate, THAT is the question ... +* + 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 ( 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 * 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 +* +* .. 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 +* .. 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 +* 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 +* A(:,p) and A(:,q) already numerically orthogonal + 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 ( ( i .LE. SWBAND ) .AND. ( PSKIPPED .GT. ROWSKIP ) ) THEN + IF ( ir1 .EQ. 0 ) AAPP = - AAPP + NOTROT = 0 + GO TO 2103 + END IF +* + 2002 CONTINUE +* END q-LOOP +* + 2103 CONTINUE +* bailed out of q-loop + + 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 +* + 2001 CONTINUE +* end of the p-loop +* end of doing the block ( ibr, ibr ) + 1002 CONTINUE +* end of ir1-loop +* +*........................................................ +* ... go to the off diagonal blocks +* + igl = ( ibr - 1 ) * KBL + 1 +* + DO 2010 jbc = ibr + 1, NBL +* + 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 +* + MXAAPQ = AMAX1( MXAAPQ, ABS(AAPQ) ) +* +* TO rotate or NOT to rotate, THAT is the question ... +* + 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 +* +* .. 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 +* 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 +* 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 +* + 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 +* end of the q-loop + 2203 CONTINUE +* + 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 + + 2100 CONTINUE +* end of the p-loop + 2010 CONTINUE +* end of the jbc-loop + 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 +* + 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 +* +* Additional steering devices +* + 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 ( NOTROT .GE. EMPTSW ) GO TO 1994 + + 1993 CONTINUE +* end i=1:NSWEEP loop +* #:) Reaching this point means that the procedure has comleted the given +* number of iterations. + INFO = NSWEEP - 1 + GO TO 1995 + 1994 CONTINUE +* #:) Reaching this point means that during the i-th sweep all pivots were +* below the given tolerance, causing early exit. +* + INFO = 0 +* #:) INFO = 0 confirms successful iterations. + 1995 CONTINUE +* +* 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 ) + END IF + 5991 CONTINUE +* + RETURN +* .. +* .. END OF SGSVJ0 +* .. + END +* |