zunmqr(l) [redhat man page]
ZUNMQR(l) ) ZUNMQR(l) NAME
ZUNMQR - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N' SYNOPSIS
SUBROUTINE ZUNMQR( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO ) CHARACTER SIDE, TRANS INTEGER INFO, K, LDA, LDC, LWORK, M, N COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) PURPOSE
ZUNMQR 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 where Q is a complex unitary matrix defined as the product of k elementary reflectors Q = H(1) H(2) . . . H(k) as returned by ZGEQRF. Q is of order M if SIDE = 'L' and of order N if SIDE = 'R'. ARGUMENTS
SIDE (input) CHARACTER*1 = 'L': apply Q or Q**H from the Left; = 'R': apply Q or Q**H from the Right. TRANS (input) CHARACTER*1 = 'N': No transpose, apply Q; = 'C': Conjugate transpose, apply Q**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 The number of elementary reflectors whose product defines the matrix Q. If SIDE = 'L', M >= K >= 0; if SIDE = 'R', N >= K >= 0. A (input) COMPLEX*16 array, dimension (LDA,K) The i-th column must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by ZGEQRF in the first k columns of its array argument A. A is modified by the routine but restored on exit. LDA (input) INTEGER The leading dimension of the array A. If SIDE = 'L', LDA >= max(1,M); if SIDE = 'R', LDA >= max(1,N). TAU (input) COMPLEX*16 array, dimension (K) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by ZGEQRF. 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. LDC (input) INTEGER The leading dimension of the array C. LDC >= max(1,M). WORK (workspace/output) COMPLEX*16 array, dimension (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). For optimum performance LWORK >= N*NB if SIDE = 'L', and LWORK >= M*NB if SIDE = 'R', where NB is the optimal blocksize. 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 LAPACK version 3.0 15 June 2000 ZUNMQR(l)
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ZUNMTR(l) ) ZUNMTR(l) NAME
ZUNMTR - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N' SYNOPSIS
SUBROUTINE ZUNMTR( SIDE, UPLO, TRANS, M, N, A, LDA, TAU, C, LDC, WORK, LWORK, INFO ) CHARACTER SIDE, TRANS, UPLO INTEGER INFO, LDA, LDC, LWORK, M, N COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) PURPOSE
ZUNMTR 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 where Q is a complex unitary matrix of order nq, with nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of nq-1 elementary reflectors, as returned by ZHETRD: if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1); if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1). ARGUMENTS
SIDE (input) CHARACTER*1 = 'L': apply Q or Q**H from the Left; = 'R': apply Q or Q**H from the Right. UPLO (input) CHARACTER*1 = 'U': Upper triangle of A contains elementary reflectors from ZHETRD; = 'L': Lower triangle of A contains elementary reflectors from ZHETRD. TRANS (input) CHARACTER*1 = 'N': No transpose, apply Q; = 'C': Conjugate transpose, apply Q**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. A (input) COMPLEX*16 array, dimension (LDA,M) if SIDE = 'L' (LDA,N) if SIDE = 'R' The vectors which define the elementary reflectors, as returned by ZHETRD. LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,M) if SIDE = 'L'; LDA >= max(1,N) if SIDE = 'R'. TAU (input) COMPLEX*16 array, dimension (M-1) if SIDE = 'L' (N-1) if SIDE = 'R' TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by ZHETRD. 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. LDC (input) INTEGER The leading dimension of the array C. LDC >= max(1,M). WORK (workspace/output) COMPLEX*16 array, dimension (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). For optimum performance LWORK >= N*NB if SIDE = 'L', and LWORK >=M*NB if SIDE = 'R', where NB is the optimal blocksize. 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 LAPACK version 3.0 15 June 2000 ZUNMTR(l)