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author | brian <brian@8a072113-8704-0410-8d35-dd094bca7971> | 2010-11-03 23:02:29 +0000 |
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committer | brian <brian@8a072113-8704-0410-8d35-dd094bca7971> | 2010-11-03 23:02:29 +0000 |
commit | 4ca2feaf79883558f849f792f6813819da97a821 (patch) | |
tree | 7079f3949a0356cd2914ab4984e928ef2ebf1b8e /SRC/zunbdb.f | |
parent | 1237a0d5b7f033a117062f78bf055026928af9ec (diff) | |
download | lapack-4ca2feaf79883558f849f792f6813819da97a821.tar.gz lapack-4ca2feaf79883558f849f792f6813819da97a821.tar.bz2 lapack-4ca2feaf79883558f849f792f6813819da97a821.zip |
Added CS decomposition source files to SRC/
Diffstat (limited to 'SRC/zunbdb.f')
-rw-r--r-- | SRC/zunbdb.f | 520 |
1 files changed, 520 insertions, 0 deletions
diff --git a/SRC/zunbdb.f b/SRC/zunbdb.f new file mode 100644 index 00000000..08298387 --- /dev/null +++ b/SRC/zunbdb.f @@ -0,0 +1,520 @@ + SUBROUTINE ZUNBDB( TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12, + $ X21, LDX21, X22, LDX22, THETA, PHI, TAUP1, + $ TAUP2, TAUQ1, TAUQ2, WORK, LWORK, INFO ) + IMPLICIT NONE +* +* Brian Sutton +* Randolph-Macon College +* July 2010 +* +* .. Scalar Arguments .. + CHARACTER SIGNS, TRANS + INTEGER INFO, LDX11, LDX12, LDX21, LDX22, LWORK, M, P, + $ Q +* .. +* .. Array Arguments .. + DOUBLE PRECISION PHI( * ), THETA( * ) + COMPLEX*16 TAUP1( * ), TAUP2( * ), TAUQ1( * ), TAUQ2( * ), + $ WORK( * ), X11( LDX11, * ), X12( LDX12, * ), + $ X21( LDX21, * ), X22( LDX22, * ) +* .. +* +* Purpose +* ======= +* +* ZUNBDB simultaneously bidiagonalizes the blocks of an M-by-M +* partitioned unitary matrix X: +* +* [ B11 | B12 0 0 ] +* [ X11 | X12 ] [ P1 | ] [ 0 | 0 -I 0 ] [ Q1 | ]**H +* X = [-----------] = [---------] [----------------] [---------] . +* [ X21 | X22 ] [ | P2 ] [ B21 | B22 0 0 ] [ | Q2 ] +* [ 0 | 0 0 I ] +* +* X11 is P-by-Q. Q must be no larger than P, M-P, or M-Q. (If this is +* not the case, then X must be transposed and/or permuted. This can be +* done in constant time using the TRANS and SIGNS options. See ZUNCSD +* for details.) +* +* The unitary matrices P1, P2, Q1, and Q2 are P-by-P, (M-P)-by- +* (M-P), Q-by-Q, and (M-Q)-by-(M-Q), respectively. They are +* represented implicitly by Householder vectors. +* +* B11, B12, B21, and B22 are Q-by-Q bidiagonal matrices represented +* implicitly by angles THETA, PHI. +* +* Arguments +* ========= +* +* TRANS (input) CHARACTER +* = 'T': X, U1, U2, V1T, and V2T are stored in row-major +* order; +* otherwise: X, U1, U2, V1T, and V2T are stored in column- +* major order. +* +* SIGNS (input) CHARACTER +* = 'O': The lower-left block is made nonpositive (the +* "other" convention); +* otherwise: The upper-right block is made nonpositive (the +* "default" convention). +* +* M (input) INTEGER +* The number of rows and columns in X. +* +* P (input) INTEGER +* The number of rows in X11 and X12. 0 <= P <= M. +* +* Q (input) INTEGER +* The number of columns in X11 and X21. 0 <= Q <= +* MIN(P,M-P,M-Q). +* +* X11 (input/output) COMPLEX*16 array, dimension (LDX11,Q) +* On entry, the top-left block of the unitary matrix to be +* reduced. On exit, the form depends on TRANS: +* If TRANS = 'N', then +* the columns of tril(X11) specify reflectors for P1, +* the rows of triu(X11,1) specify reflectors for Q1; +* else TRANS = 'T', and +* the rows of triu(X11) specify reflectors for P1, +* the columns of tril(X11,-1) specify reflectors for Q1. +* +* LDX11 (input) INTEGER +* The leading dimension of X11. If TRANS = 'N', then LDX11 >= +* P; else LDX11 >= Q. +* +* X12 (input/output) COMPLEX*16 array, dimension (LDX12,M-Q) +* On entry, the top-right block of the unitary matrix to +* be reduced. On exit, the form depends on TRANS: +* If TRANS = 'N', then +* the rows of triu(X12) specify the first P reflectors for +* Q2; +* else TRANS = 'T', and +* the columns of tril(X12) specify the first P reflectors +* for Q2. +* +* LDX12 (input) INTEGER +* The leading dimension of X12. If TRANS = 'N', then LDX12 >= +* P; else LDX11 >= M-Q. +* +* X21 (input/output) COMPLEX*16 array, dimension (LDX21,Q) +* On entry, the bottom-left block of the unitary matrix to +* be reduced. On exit, the form depends on TRANS: +* If TRANS = 'N', then +* the columns of tril(X21) specify reflectors for P2; +* else TRANS = 'T', and +* the rows of triu(X21) specify reflectors for P2. +* +* LDX21 (input) INTEGER +* The leading dimension of X21. If TRANS = 'N', then LDX21 >= +* M-P; else LDX21 >= Q. +* +* X22 (input/output) COMPLEX*16 array, dimension (LDX22,M-Q) +* On entry, the bottom-right block of the unitary matrix to +* be reduced. On exit, the form depends on TRANS: +* If TRANS = 'N', then +* the rows of triu(X22(Q+1:M-P,P+1:M-Q)) specify the last +* M-P-Q reflectors for Q2, +* else TRANS = 'T', and +* the columns of tril(X22(P+1:M-Q,Q+1:M-P)) specify the last +* M-P-Q reflectors for P2. +* +* LDX22 (input) INTEGER +* The leading dimension of X22. If TRANS = 'N', then LDX22 >= +* M-P; else LDX22 >= M-Q. +* +* THETA (output) DOUBLE PRECISION array, dimension (Q) +* The entries of the bidiagonal blocks B11, B12, B21, B22 can +* be computed from the angles THETA and PHI. See Further +* Details. +* +* PHI (output) DOUBLE PRECISION array, dimension (Q-1) +* The entries of the bidiagonal blocks B11, B12, B21, B22 can +* be computed from the angles THETA and PHI. See Further +* Details. +* +* TAUP1 (output) COMPLEX*16 array, dimension (P) +* The scalar factors of the elementary reflectors that define +* P1. +* +* TAUP2 (output) COMPLEX*16 array, dimension (M-P) +* The scalar factors of the elementary reflectors that define +* P2. +* +* TAUQ1 (output) COMPLEX*16 array, dimension (Q) +* The scalar factors of the elementary reflectors that define +* Q1. +* +* TAUQ2 (output) COMPLEX*16 array, dimension (M-Q) +* The scalar factors of the elementary reflectors that define +* Q2. +* +* WORK (workspace) COMPLEX*16 array, dimension (LWORK) +* +* LWORK (input) INTEGER +* The dimension of the array WORK. LWORK >= M-Q. +* +* If LWORK = -1, then a workspace query is assumed; the routine +* only calculates the optimal size of the WORK array, returns +* this value as the first entry of the WORK array, and no error +* message related to LWORK is issued by XERBLA. +* +* INFO (output) INTEGER +* = 0: successful exit. +* < 0: if INFO = -i, the i-th argument had an illegal value. +* +* Further Details +* =============== +* +* The bidiagonal blocks B11, B12, B21, and B22 are represented +* implicitly by angles THETA(1), ..., THETA(Q) and PHI(1), ..., +* PHI(Q-1). B11 and B21 are upper bidiagonal, while B21 and B22 are +* lower bidiagonal. Every entry in each bidiagonal band is a product +* of a sine or cosine of a THETA with a sine or cosine of a PHI. See +* [1] or ZUNCSD for details. +* +* P1, P2, Q1, and Q2 are represented as products of elementary +* reflectors. See ZUNCSD for details on generating P1, P2, Q1, and Q2 +* using ZUNGQR and ZUNGLQ. +* +* Reference +* ========= +* +* [1] Brian D. Sutton. Computing the complete CS decomposition. Numer. +* Algorithms, 50(1):33-65, 2009. +* +* ==================================================================== +* +* .. Parameters .. + DOUBLE PRECISION REALONE + PARAMETER ( REALONE = 1.0D0 ) + COMPLEX*16 NEGONE, ONE + PARAMETER ( NEGONE = (-1.0D0,0.0D0), + $ ONE = (1.0D0,0.0D0) ) +* .. +* .. Local Scalars .. + LOGICAL COLMAJOR, LQUERY + INTEGER I, LWORKMIN, LWORKOPT + DOUBLE PRECISION Z1, Z2, Z3, Z4 +* .. +* .. External Subroutines .. + EXTERNAL ZAXPY, ZLARF, ZLARFGP, ZSCAL, XERBLA + EXTERNAL ZLACGV +* +* .. +* .. External Functions .. + DOUBLE PRECISION DZNRM2 + LOGICAL LSAME + EXTERNAL DZNRM2, LSAME +* .. +* .. Intrinsic Functions + INTRINSIC ATAN2, COS, MAX, MIN, SIN + INTRINSIC COMPLEX, DCONJG +* .. +* .. Executable Statements .. +* +* Test input arguments +* + INFO = 0 + COLMAJOR = .NOT. LSAME( TRANS, 'T' ) + IF( .NOT. LSAME( SIGNS, 'O' ) ) THEN + Z1 = REALONE + Z2 = REALONE + Z3 = REALONE + Z4 = REALONE + ELSE + Z1 = REALONE + Z2 = -REALONE + Z3 = REALONE + Z4 = -REALONE + END IF + LQUERY = LWORK .EQ. -1 +* + IF( M .LT. 0 ) THEN + INFO = -3 + ELSE IF( P .LT. 0 .OR. P .GT. M ) THEN + INFO = -4 + ELSE IF( Q .LT. 0 .OR. Q .GT. P .OR. Q .GT. M-P .OR. + $ Q .GT. M-Q ) THEN + INFO = -5 + ELSE IF( COLMAJOR .AND. LDX11 .LT. MAX( 1, P ) ) THEN + INFO = -7 + ELSE IF( .NOT.COLMAJOR .AND. LDX11 .LT. MAX( 1, Q ) ) THEN + INFO = -7 + ELSE IF( COLMAJOR .AND. LDX12 .LT. MAX( 1, P ) ) THEN + INFO = -9 + ELSE IF( .NOT.COLMAJOR .AND. LDX12 .LT. MAX( 1, M-Q ) ) THEN + INFO = -9 + ELSE IF( COLMAJOR .AND. LDX21 .LT. MAX( 1, M-P ) ) THEN + INFO = -11 + ELSE IF( .NOT.COLMAJOR .AND. LDX21 .LT. MAX( 1, Q ) ) THEN + INFO = -11 + ELSE IF( COLMAJOR .AND. LDX22 .LT. MAX( 1, M-P ) ) THEN + INFO = -13 + ELSE IF( .NOT.COLMAJOR .AND. LDX22 .LT. MAX( 1, M-Q ) ) THEN + INFO = -13 + END IF +* +* Compute workspace +* + IF( INFO .EQ. 0 ) THEN + LWORKOPT = M - Q + LWORKMIN = M - Q + WORK(1) = LWORKOPT + IF( LWORK .LT. LWORKMIN .AND. .NOT. LQUERY ) THEN + INFO = -21 + END IF + END IF + IF( INFO .NE. 0 ) THEN + CALL XERBLA( 'xORBDB', -INFO ) + RETURN + ELSE IF( LQUERY ) THEN + RETURN + END IF +* +* Handle column-major and row-major separately +* + IF( COLMAJOR ) THEN +* +* Reduce columns 1, ..., Q of X11, X12, X21, and X22 +* + DO I = 1, Q +* + IF( I .EQ. 1 ) THEN + CALL ZSCAL( P-I+1, COMPLEX( Z1, 0.0D0 ), X11(I,I), 1 ) + ELSE + CALL ZSCAL( P-I+1, COMPLEX( Z1*COS(PHI(I-1)), 0.0D0 ), + $ X11(I,I), 1 ) + CALL ZAXPY( P-I+1, COMPLEX( -Z1*Z3*Z4*SIN(PHI(I-1)), + $ 0.0D0 ), X12(I,I-1), 1, X11(I,I), 1 ) + END IF + IF( I .EQ. 1 ) THEN + CALL ZSCAL( M-P-I+1, COMPLEX( Z2, 0.0D0 ), X21(I,I), 1 ) + ELSE + CALL ZSCAL( M-P-I+1, COMPLEX( Z2*COS(PHI(I-1)), 0.0D0 ), + $ X21(I,I), 1 ) + CALL ZAXPY( M-P-I+1, COMPLEX( -Z2*Z3*Z4*SIN(PHI(I-1)), + $ 0.0D0 ), X22(I,I-1), 1, X21(I,I), 1 ) + END IF +* + THETA(I) = ATAN2( DZNRM2( M-P-I+1, X21(I,I), 1 ), + $ DZNRM2( P-I+1, X11(I,I), 1 ) ) +* + CALL ZLARFGP( P-I+1, X11(I,I), X11(I+1,I), 1, TAUP1(I) ) + X11(I,I) = ONE + CALL ZLARFGP( M-P-I+1, X21(I,I), X21(I+1,I), 1, TAUP2(I) ) + X21(I,I) = ONE +* + CALL ZLARF( 'L', P-I+1, Q-I, X11(I,I), 1, DCONJG(TAUP1(I)), + $ X11(I,I+1), LDX11, WORK ) + CALL ZLARF( 'L', P-I+1, M-Q-I+1, X11(I,I), 1, + $ DCONJG(TAUP1(I)), X12(I,I), LDX12, WORK ) + CALL ZLARF( 'L', M-P-I+1, Q-I, X21(I,I), 1, + $ DCONJG(TAUP2(I)), X21(I,I+1), LDX21, WORK ) + CALL ZLARF( 'L', M-P-I+1, M-Q-I+1, X21(I,I), 1, + $ DCONJG(TAUP2(I)), X22(I,I), LDX22, WORK ) +* + IF( I .LT. Q ) THEN + CALL ZSCAL( Q-I, COMPLEX( -Z1*Z3*SIN(THETA(I)), 0.0D0 ), + $ X11(I,I+1), LDX11 ) + CALL ZAXPY( Q-I, COMPLEX( Z2*Z3*COS(THETA(I)), 0.0D0 ), + $ X21(I,I+1), LDX21, X11(I,I+1), LDX11 ) + END IF + CALL ZSCAL( M-Q-I+1, COMPLEX( -Z1*Z4*SIN(THETA(I)), 0.0D0 ), + $ X12(I,I), LDX12 ) + CALL ZAXPY( M-Q-I+1, COMPLEX( Z2*Z4*COS(THETA(I)), 0.0D0 ), + $ X22(I,I), LDX22, X12(I,I), LDX12 ) +* + IF( I .LT. Q ) + $ PHI(I) = ATAN2( DZNRM2( Q-I, X11(I,I+1), LDX11 ), + $ DZNRM2( M-Q-I+1, X12(I,I), LDX12 ) ) +* + IF( I .LT. Q ) THEN + CALL ZLACGV( Q-I, X11(I,I+1), LDX11 ) + CALL ZLARFGP( Q-I, X11(I,I+1), X11(I,I+2), LDX11, + $ TAUQ1(I) ) + X11(I,I+1) = ONE + END IF + CALL ZLACGV( M-Q-I+1, X12(I,I), LDX12 ) + CALL ZLARFGP( M-Q-I+1, X12(I,I), X12(I,I+1), LDX12, + $ TAUQ2(I) ) + X12(I,I) = ONE +* + IF( I .LT. Q ) THEN + CALL ZLARF( 'R', P-I, Q-I, X11(I,I+1), LDX11, TAUQ1(I), + $ X11(I+1,I+1), LDX11, WORK ) + CALL ZLARF( 'R', M-P-I, Q-I, X11(I,I+1), LDX11, TAUQ1(I), + $ X21(I+1,I+1), LDX21, WORK ) + END IF + CALL ZLARF( 'R', P-I, M-Q-I+1, X12(I,I), LDX12, TAUQ2(I), + $ X12(I+1,I), LDX12, WORK ) + CALL ZLARF( 'R', M-P-I, M-Q-I+1, X12(I,I), LDX12, TAUQ2(I), + $ X22(I+1,I), LDX22, WORK ) +* + IF( I .LT. Q ) + $ CALL ZLACGV( Q-I, X11(I,I+1), LDX11 ) + CALL ZLACGV( M-Q-I+1, X12(I,I), LDX12 ) +* + END DO +* +* Reduce columns Q + 1, ..., P of X12, X22 +* + DO I = Q + 1, P +* + CALL ZSCAL( M-Q-I+1, COMPLEX( -Z1*Z4, 0.0D0 ), X12(I,I), + $ LDX12 ) + CALL ZLACGV( M-Q-I+1, X12(I,I), LDX12 ) + CALL ZLARFGP( M-Q-I+1, X12(I,I), X12(I,I+1), LDX12, + $ TAUQ2(I) ) + X12(I,I) = ONE +* + CALL ZLARF( 'R', P-I, M-Q-I+1, X12(I,I), LDX12, TAUQ2(I), + $ X12(I+1,I), LDX12, WORK ) + IF( M-P-Q .GE. 1 ) + $ CALL ZLARF( 'R', M-P-Q, M-Q-I+1, X12(I,I), LDX12, + $ TAUQ2(I), X22(Q+1,I), LDX22, WORK ) +* + CALL ZLACGV( M-Q-I+1, X12(I,I), LDX12 ) +* + END DO +* +* Reduce columns P + 1, ..., M - Q of X12, X22 +* + DO I = 1, M - P - Q +* + CALL ZSCAL( M-P-Q-I+1, COMPLEX( Z2*Z4, 0.0D0 ), + $ X22(Q+I,P+I), LDX22 ) + CALL ZLACGV( M-P-Q-I+1, X22(Q+I,P+I), LDX22 ) + CALL ZLARFGP( M-P-Q-I+1, X22(Q+I,P+I), X22(Q+I,P+I+1), + $ LDX22, TAUQ2(P+I) ) + X22(Q+I,P+I) = ONE + CALL ZLARF( 'R', M-P-Q-I, M-P-Q-I+1, X22(Q+I,P+I), LDX22, + $ TAUQ2(P+I), X22(Q+I+1,P+I), LDX22, WORK ) +* + CALL ZLACGV( M-P-Q-I+1, X22(Q+I,P+I), LDX22 ) +* + END DO +* + ELSE +* +* Reduce columns 1, ..., Q of X11, X12, X21, X22 +* + DO I = 1, Q +* + IF( I .EQ. 1 ) THEN + CALL ZSCAL( P-I+1, COMPLEX( Z1, 0.0D0 ), X11(I,I), + $ LDX11 ) + ELSE + CALL ZSCAL( P-I+1, COMPLEX( Z1*COS(PHI(I-1)), 0.0D0 ), + $ X11(I,I), LDX11 ) + CALL ZAXPY( P-I+1, COMPLEX( -Z1*Z3*Z4*SIN(PHI(I-1)), + $ 0.0D0 ), X12(I-1,I), LDX12, X11(I,I), LDX11 ) + END IF + IF( I .EQ. 1 ) THEN + CALL ZSCAL( M-P-I+1, COMPLEX( Z2, 0.0D0 ), X21(I,I), + $ LDX21 ) + ELSE + CALL ZSCAL( M-P-I+1, COMPLEX( Z2*COS(PHI(I-1)), 0.0D0 ), + $ X21(I,I), LDX21 ) + CALL ZAXPY( M-P-I+1, COMPLEX( -Z2*Z3*Z4*SIN(PHI(I-1)), + $ 0.0D0 ), X22(I-1,I), LDX22, X21(I,I), LDX21 ) + END IF +* + THETA(I) = ATAN2( DZNRM2( M-P-I+1, X21(I,I), LDX21 ), + $ DZNRM2( P-I+1, X11(I,I), LDX11 ) ) +* + CALL ZLACGV( P-I+1, X11(I,I), LDX11 ) + CALL ZLACGV( M-P-I+1, X21(I,I), LDX21 ) +* + CALL ZLARFGP( P-I+1, X11(I,I), X11(I,I+1), LDX11, TAUP1(I) ) + X11(I,I) = ONE + CALL ZLARFGP( M-P-I+1, X21(I,I), X21(I,I+1), LDX21, + $ TAUP2(I) ) + X21(I,I) = ONE +* + CALL ZLARF( 'R', Q-I, P-I+1, X11(I,I), LDX11, TAUP1(I), + $ X11(I+1,I), LDX11, WORK ) + CALL ZLARF( 'R', M-Q-I+1, P-I+1, X11(I,I), LDX11, TAUP1(I), + $ X12(I,I), LDX12, WORK ) + CALL ZLARF( 'R', Q-I, M-P-I+1, X21(I,I), LDX21, TAUP2(I), + $ X21(I+1,I), LDX21, WORK ) + CALL ZLARF( 'R', M-Q-I+1, M-P-I+1, X21(I,I), LDX21, + $ TAUP2(I), X22(I,I), LDX22, WORK ) +* + CALL ZLACGV( P-I+1, X11(I,I), LDX11 ) + CALL ZLACGV( M-P-I+1, X21(I,I), LDX21 ) +* + IF( I .LT. Q ) THEN + CALL ZSCAL( Q-I, COMPLEX( -Z1*Z3*SIN(THETA(I)), 0.0D0 ), + $ X11(I+1,I), 1 ) + CALL ZAXPY( Q-I, COMPLEX( Z2*Z3*COS(THETA(I)), 0.0D0 ), + $ X21(I+1,I), 1, X11(I+1,I), 1 ) + END IF + CALL ZSCAL( M-Q-I+1, COMPLEX( -Z1*Z4*SIN(THETA(I)), 0.0D0 ), + $ X12(I,I), 1 ) + CALL ZAXPY( M-Q-I+1, COMPLEX( Z2*Z4*COS(THETA(I)), 0.0D0 ), + $ X22(I,I), 1, X12(I,I), 1 ) +* + IF( I .LT. Q ) + $ PHI(I) = ATAN2( DZNRM2( Q-I, X11(I+1,I), 1 ), + $ DZNRM2( M-Q-I+1, X12(I,I), 1 ) ) +* + IF( I .LT. Q ) THEN + CALL ZLARFGP( Q-I, X11(I+1,I), X11(I+2,I), 1, TAUQ1(I) ) + X11(I+1,I) = ONE + END IF + CALL ZLARFGP( M-Q-I+1, X12(I,I), X12(I+1,I), 1, TAUQ2(I) ) + X12(I,I) = ONE +* + IF( I .LT. Q ) THEN + CALL ZLARF( 'L', Q-I, P-I, X11(I+1,I), 1, + $ DCONJG(TAUQ1(I)), X11(I+1,I+1), LDX11, WORK ) + CALL ZLARF( 'L', Q-I, M-P-I, X11(I+1,I), 1, + $ DCONJG(TAUQ1(I)), X21(I+1,I+1), LDX21, WORK ) + END IF + CALL ZLARF( 'L', M-Q-I+1, P-I, X12(I,I), 1, + $ DCONJG(TAUQ2(I)), X12(I,I+1), LDX12, WORK ) + CALL ZLARF( 'L', M-Q-I+1, M-P-I, X12(I,I), 1, + $ DCONJG(TAUQ2(I)), X22(I,I+1), LDX22, WORK ) +* + END DO +* +* Reduce columns Q + 1, ..., P of X12, X22 +* + DO I = Q + 1, P +* + CALL ZSCAL( M-Q-I+1, COMPLEX( -Z1*Z4, 0.0D0 ), X12(I,I), 1 ) + CALL ZLARFGP( M-Q-I+1, X12(I,I), X12(I+1,I), 1, TAUQ2(I) ) + X12(I,I) = ONE +* + CALL ZLARF( 'L', M-Q-I+1, P-I, X12(I,I), 1, + $ DCONJG(TAUQ2(I)), X12(I,I+1), LDX12, WORK ) + IF( M-P-Q .GE. 1 ) + $ CALL ZLARF( 'L', M-Q-I+1, M-P-Q, X12(I,I), 1, + $ DCONJG(TAUQ2(I)), X22(I,Q+1), LDX22, WORK ) +* + END DO +* +* Reduce columns P + 1, ..., M - Q of X12, X22 +* + DO I = 1, M - P - Q +* + CALL ZSCAL( M-P-Q-I+1, COMPLEX( Z2*Z4, 0.0D0 ), + $ X22(P+I,Q+I), 1 ) + CALL ZLARFGP( M-P-Q-I+1, X22(P+I,Q+I), X22(P+I+1,Q+I), 1, + $ TAUQ2(P+I) ) + X22(P+I,Q+I) = ONE +* + CALL ZLARF( 'L', M-P-Q-I+1, M-P-Q-I, X22(P+I,Q+I), 1, + $ DCONJG(TAUQ2(P+I)), X22(P+I,Q+I+1), LDX22, + $ WORK ) +* + END DO +* + END IF +* + RETURN +* +* End of ZUNBDB +* + END + |