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Diffstat (limited to 'SRC/zunmbr.f')
| -rw-r--r-- | SRC/zunmbr.f | 288 |
1 files changed, 288 insertions, 0 deletions
diff --git a/SRC/zunmbr.f b/SRC/zunmbr.f new file mode 100644 index 00000000..b32ce338 --- /dev/null +++ b/SRC/zunmbr.f @@ -0,0 +1,288 @@ + SUBROUTINE ZUNMBR( VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C, + $ LDC, WORK, LWORK, INFO ) +* +* -- LAPACK routine (version 3.1) -- +* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. +* November 2006 +* +* .. Scalar Arguments .. + CHARACTER SIDE, TRANS, VECT + INTEGER INFO, K, LDA, LDC, LWORK, M, N +* .. +* .. Array Arguments .. + COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) +* .. +* +* Purpose +* ======= +* +* If VECT = 'Q', ZUNMBR overwrites the general complex M-by-N matrix C +* with +* SIDE = 'L' SIDE = 'R' +* TRANS = 'N': Q * C C * Q +* TRANS = 'C': Q**H * C C * Q**H +* +* If VECT = 'P', ZUNMBR overwrites the general complex M-by-N matrix C +* with +* SIDE = 'L' SIDE = 'R' +* TRANS = 'N': P * C C * P +* TRANS = 'C': P**H * C C * P**H +* +* Here Q and P**H are the unitary matrices determined by ZGEBRD when +* reducing a complex matrix A to bidiagonal form: A = Q * B * P**H. Q +* and P**H are defined as products of elementary reflectors H(i) and +* G(i) respectively. +* +* Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the +* order of the unitary matrix Q or P**H that is applied. +* +* If VECT = 'Q', A is assumed to have been an NQ-by-K matrix: +* if nq >= k, Q = H(1) H(2) . . . H(k); +* if nq < k, Q = H(1) H(2) . . . H(nq-1). +* +* If VECT = 'P', A is assumed to have been a K-by-NQ matrix: +* if k < nq, P = G(1) G(2) . . . G(k); +* if k >= nq, P = G(1) G(2) . . . G(nq-1). +* +* Arguments +* ========= +* +* VECT (input) CHARACTER*1 +* = 'Q': apply Q or Q**H; +* = 'P': apply P or P**H. +* +* SIDE (input) CHARACTER*1 +* = 'L': apply Q, Q**H, P or P**H from the Left; +* = 'R': apply Q, Q**H, P or P**H from the Right. +* +* TRANS (input) CHARACTER*1 +* = 'N': No transpose, apply Q or P; +* = 'C': Conjugate transpose, apply Q**H or P**H. +* +* M (input) INTEGER +* The number of rows of the matrix C. M >= 0. +* +* N (input) INTEGER +* The number of columns of the matrix C. N >= 0. +* +* K (input) INTEGER +* If VECT = 'Q', the number of columns in the original +* matrix reduced by ZGEBRD. +* If VECT = 'P', the number of rows in the original +* matrix reduced by ZGEBRD. +* K >= 0. +* +* A (input) COMPLEX*16 array, dimension +* (LDA,min(nq,K)) if VECT = 'Q' +* (LDA,nq) if VECT = 'P' +* The vectors which define the elementary reflectors H(i) and +* G(i), whose products determine the matrices Q and P, as +* returned by ZGEBRD. +* +* LDA (input) INTEGER +* The leading dimension of the array A. +* If VECT = 'Q', LDA >= max(1,nq); +* if VECT = 'P', LDA >= max(1,min(nq,K)). +* +* TAU (input) COMPLEX*16 array, dimension (min(nq,K)) +* TAU(i) must contain the scalar factor of the elementary +* reflector H(i) or G(i) which determines Q or P, as returned +* by ZGEBRD in the array argument TAUQ or TAUP. +* +* C (input/output) COMPLEX*16 array, dimension (LDC,N) +* On entry, the M-by-N matrix C. +* On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q +* or P*C or P**H*C or C*P or C*P**H. +* +* LDC (input) INTEGER +* The leading dimension of the array C. LDC >= max(1,M). +* +* WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK)) +* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. +* +* LWORK (input) INTEGER +* The dimension of the array WORK. +* If SIDE = 'L', LWORK >= max(1,N); +* if SIDE = 'R', LWORK >= max(1,M); +* if N = 0 or M = 0, LWORK >= 1. +* For optimum performance LWORK >= max(1,N*NB) if SIDE = 'L', +* and LWORK >= max(1,M*NB) if SIDE = 'R', where NB is the +* optimal blocksize. (NB = 0 if M = 0 or N = 0.) +* +* 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 +* +* ===================================================================== +* +* .. Local Scalars .. + LOGICAL APPLYQ, LEFT, LQUERY, NOTRAN + CHARACTER TRANST + INTEGER I1, I2, IINFO, LWKOPT, MI, NB, NI, NQ, NW +* .. +* .. External Functions .. + LOGICAL LSAME + INTEGER ILAENV + EXTERNAL LSAME, ILAENV +* .. +* .. External Subroutines .. + EXTERNAL XERBLA, ZUNMLQ, ZUNMQR +* .. +* .. Intrinsic Functions .. + INTRINSIC MAX, MIN +* .. +* .. Executable Statements .. +* +* Test the input arguments +* + INFO = 0 + APPLYQ = LSAME( VECT, 'Q' ) + LEFT = LSAME( SIDE, 'L' ) + NOTRAN = LSAME( TRANS, 'N' ) + LQUERY = ( LWORK.EQ.-1 ) +* +* NQ is the order of Q or P and NW is the minimum dimension of WORK +* + IF( LEFT ) THEN + NQ = M + NW = N + ELSE + NQ = N + NW = M + END IF + IF( M.EQ.0 .OR. N.EQ.0 ) THEN + NW = 0 + END IF + IF( .NOT.APPLYQ .AND. .NOT.LSAME( VECT, 'P' ) ) THEN + INFO = -1 + ELSE IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN + INFO = -2 + ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'C' ) ) THEN + INFO = -3 + ELSE IF( M.LT.0 ) THEN + INFO = -4 + ELSE IF( N.LT.0 ) THEN + INFO = -5 + ELSE IF( K.LT.0 ) THEN + INFO = -6 + ELSE IF( ( APPLYQ .AND. LDA.LT.MAX( 1, NQ ) ) .OR. + $ ( .NOT.APPLYQ .AND. LDA.LT.MAX( 1, MIN( NQ, K ) ) ) ) + $ THEN + INFO = -8 + ELSE IF( LDC.LT.MAX( 1, M ) ) THEN + INFO = -11 + ELSE IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN + INFO = -13 + END IF +* + IF( INFO.EQ.0 ) THEN + IF( NW.GT.0 ) THEN + IF( APPLYQ ) THEN + IF( LEFT ) THEN + NB = ILAENV( 1, 'ZUNMQR', SIDE // TRANS, M-1, N, M-1, + $ -1 ) + ELSE + NB = ILAENV( 1, 'ZUNMQR', SIDE // TRANS, M, N-1, N-1, + $ -1 ) + END IF + ELSE + IF( LEFT ) THEN + NB = ILAENV( 1, 'ZUNMLQ', SIDE // TRANS, M-1, N, M-1, + $ -1 ) + ELSE + NB = ILAENV( 1, 'ZUNMLQ', SIDE // TRANS, M, N-1, N-1, + $ -1 ) + END IF + END IF + LWKOPT = MAX( 1, NW*NB ) + ELSE + LWKOPT = 1 + END IF + WORK( 1 ) = LWKOPT + END IF +* + IF( INFO.NE.0 ) THEN + CALL XERBLA( 'ZUNMBR', -INFO ) + RETURN + ELSE IF( LQUERY ) THEN + RETURN + END IF +* +* Quick return if possible +* + IF( M.EQ.0 .OR. N.EQ.0 ) + $ RETURN +* + IF( APPLYQ ) THEN +* +* Apply Q +* + IF( NQ.GE.K ) THEN +* +* Q was determined by a call to ZGEBRD with nq >= k +* + CALL ZUNMQR( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, + $ WORK, LWORK, IINFO ) + ELSE IF( NQ.GT.1 ) THEN +* +* Q was determined by a call to ZGEBRD with nq < k +* + IF( LEFT ) THEN + MI = M - 1 + NI = N + I1 = 2 + I2 = 1 + ELSE + MI = M + NI = N - 1 + I1 = 1 + I2 = 2 + END IF + CALL ZUNMQR( SIDE, TRANS, MI, NI, NQ-1, A( 2, 1 ), LDA, TAU, + $ C( I1, I2 ), LDC, WORK, LWORK, IINFO ) + END IF + ELSE +* +* Apply P +* + IF( NOTRAN ) THEN + TRANST = 'C' + ELSE + TRANST = 'N' + END IF + IF( NQ.GT.K ) THEN +* +* P was determined by a call to ZGEBRD with nq > k +* + CALL ZUNMLQ( SIDE, TRANST, M, N, K, A, LDA, TAU, C, LDC, + $ WORK, LWORK, IINFO ) + ELSE IF( NQ.GT.1 ) THEN +* +* P was determined by a call to ZGEBRD with nq <= k +* + IF( LEFT ) THEN + MI = M - 1 + NI = N + I1 = 2 + I2 = 1 + ELSE + MI = M + NI = N - 1 + I1 = 1 + I2 = 2 + END IF + CALL ZUNMLQ( SIDE, TRANST, MI, NI, NQ-1, A( 1, 2 ), LDA, + $ TAU, C( I1, I2 ), LDC, WORK, LWORK, IINFO ) + END IF + END IF + WORK( 1 ) = LWKOPT + RETURN +* +* End of ZUNMBR +* + END |