unmrq(3) | Library Functions Manual | unmrq(3) |
NAME
unmrq - {un,or}mrq: multiply by Q from gerqf
SYNOPSIS
Functions
subroutine cunmrq (side, trans, m, n, k, a, lda, tau, c,
ldc, work, lwork, info)
CUNMRQ subroutine dormrq (side, trans, m, n, k, a, lda, tau, c,
ldc, work, lwork, info)
DORMRQ subroutine sormrq (side, trans, m, n, k, a, lda, tau, c,
ldc, work, lwork, info)
SORMRQ subroutine zunmrq (side, trans, m, n, k, a, lda, tau, c,
ldc, work, lwork, info)
ZUNMRQ
Detailed Description
Function Documentation
subroutine cunmrq (character side, character trans, integer m, integer n, integer k, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tau, complex, dimension( ldc, * ) c, integer ldc, complex, dimension( * ) work, integer lwork, integer info)
CUNMRQ
Purpose:
!> !> CUNMRQ 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 H(2)**H . . . H(k)**H !> !> as returned by CGERQF. Q is of order M if SIDE = 'L' and of order N !> if SIDE = 'R'. !>
Parameters
!> SIDE is CHARACTER*1 !> = 'L': apply Q or Q**H from the Left; !> = 'R': apply Q or Q**H from the Right. !>
TRANS
!> TRANS is CHARACTER*1 !> = 'N': No transpose, apply Q; !> = 'C': Conjugate transpose, apply Q**H. !>
M
!> M is INTEGER !> The number of rows of the matrix C. M >= 0. !>
N
!> N is INTEGER !> The number of columns of the matrix C. N >= 0. !>
K
!> K is 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
!> A is COMPLEX array, dimension !> (LDA,M) if SIDE = 'L', !> (LDA,N) if SIDE = 'R' !> The i-th row must contain the vector which defines the !> elementary reflector H(i), for i = 1,2,...,k, as returned by !> CGERQF in the last k rows of its array argument A. !>
LDA
!> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,K). !>
TAU
!> TAU is COMPLEX array, dimension (K) !> TAU(i) must contain the scalar factor of the elementary !> reflector H(i), as returned by CGERQF. !>
C
!> C is COMPLEX 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
!> LDC is INTEGER !> The leading dimension of the array C. LDC >= max(1,M). !>
WORK
!> WORK is COMPLEX array, dimension (MAX(1,LWORK)) !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. !>
LWORK
!> LWORK is INTEGER !> The dimension of the array WORK. !> If SIDE = 'L', LWORK >= max(1,N); !> if SIDE = 'R', LWORK >= max(1,M). !> For good performance, LWORK should generally be larger. !> !> 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
!> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !>
Author
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Definition at line 166 of file cunmrq.f.
subroutine dormrq (character side, character trans, integer m, integer n, integer k, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tau, double precision, dimension( ldc, * ) c, integer ldc, double precision, dimension( * ) work, integer lwork, integer info)
DORMRQ
Purpose:
!> !> DORMRQ overwrites the general real M-by-N matrix C with !> !> SIDE = 'L' SIDE = 'R' !> TRANS = 'N': Q * C C * Q !> TRANS = 'T': Q**T * C C * Q**T !> !> where Q is a real orthogonal matrix defined as the product of k !> elementary reflectors !> !> Q = H(1) H(2) . . . H(k) !> !> as returned by DGERQF. Q is of order M if SIDE = 'L' and of order N !> if SIDE = 'R'. !>
Parameters
!> SIDE is CHARACTER*1 !> = 'L': apply Q or Q**T from the Left; !> = 'R': apply Q or Q**T from the Right. !>
TRANS
!> TRANS is CHARACTER*1 !> = 'N': No transpose, apply Q; !> = 'T': Transpose, apply Q**T. !>
M
!> M is INTEGER !> The number of rows of the matrix C. M >= 0. !>
N
!> N is INTEGER !> The number of columns of the matrix C. N >= 0. !>
K
!> K is 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
!> A is DOUBLE PRECISION array, dimension !> (LDA,M) if SIDE = 'L', !> (LDA,N) if SIDE = 'R' !> The i-th row must contain the vector which defines the !> elementary reflector H(i), for i = 1,2,...,k, as returned by !> DGERQF in the last k rows of its array argument A. !>
LDA
!> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,K). !>
TAU
!> TAU is DOUBLE PRECISION array, dimension (K) !> TAU(i) must contain the scalar factor of the elementary !> reflector H(i), as returned by DGERQF. !>
C
!> C is DOUBLE PRECISION array, dimension (LDC,N) !> On entry, the M-by-N matrix C. !> On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q. !>
LDC
!> LDC is INTEGER !> The leading dimension of the array C. LDC >= max(1,M). !>
WORK
!> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. !>
LWORK
!> LWORK is INTEGER !> The dimension of the array WORK. !> If SIDE = 'L', LWORK >= max(1,N); !> if SIDE = 'R', LWORK >= max(1,M). !> For good performance, LWORK should generally be larger. !> !> 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
!> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !>
Author
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Definition at line 165 of file dormrq.f.
subroutine sormrq (character side, character trans, integer m, integer n, integer k, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( ldc, * ) c, integer ldc, real, dimension( * ) work, integer lwork, integer info)
SORMRQ
Purpose:
!> !> SORMRQ overwrites the general real M-by-N matrix C with !> !> SIDE = 'L' SIDE = 'R' !> TRANS = 'N': Q * C C * Q !> TRANS = 'T': Q**T * C C * Q**T !> !> where Q is a real orthogonal matrix defined as the product of k !> elementary reflectors !> !> Q = H(1) H(2) . . . H(k) !> !> as returned by SGERQF. Q is of order M if SIDE = 'L' and of order N !> if SIDE = 'R'. !>
Parameters
!> SIDE is CHARACTER*1 !> = 'L': apply Q or Q**T from the Left; !> = 'R': apply Q or Q**T from the Right. !>
TRANS
!> TRANS is CHARACTER*1 !> = 'N': No transpose, apply Q; !> = 'T': Transpose, apply Q**T. !>
M
!> M is INTEGER !> The number of rows of the matrix C. M >= 0. !>
N
!> N is INTEGER !> The number of columns of the matrix C. N >= 0. !>
K
!> K is 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
!> A is REAL array, dimension !> (LDA,M) if SIDE = 'L', !> (LDA,N) if SIDE = 'R' !> The i-th row must contain the vector which defines the !> elementary reflector H(i), for i = 1,2,...,k, as returned by !> SGERQF in the last k rows of its array argument A. !>
LDA
!> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,K). !>
TAU
!> TAU is REAL array, dimension (K) !> TAU(i) must contain the scalar factor of the elementary !> reflector H(i), as returned by SGERQF. !>
C
!> C is REAL array, dimension (LDC,N) !> On entry, the M-by-N matrix C. !> On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q. !>
LDC
!> LDC is INTEGER !> The leading dimension of the array C. LDC >= max(1,M). !>
WORK
!> WORK is REAL array, dimension (MAX(1,LWORK)) !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. !>
LWORK
!> LWORK is INTEGER !> The dimension of the array WORK. !> If SIDE = 'L', LWORK >= max(1,N); !> if SIDE = 'R', LWORK >= max(1,M). !> For good performance, LWORK should generally be larger. !> !> 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
!> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !>
Author
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Definition at line 166 of file sormrq.f.
subroutine zunmrq (character side, character trans, integer m, integer n, integer k, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( ldc, * ) c, integer ldc, complex*16, dimension( * ) work, integer lwork, integer info)
ZUNMRQ
Purpose:
!> !> ZUNMRQ 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 H(2)**H . . . H(k)**H !> !> as returned by ZGERQF. Q is of order M if SIDE = 'L' and of order N !> if SIDE = 'R'. !>
Parameters
!> SIDE is CHARACTER*1 !> = 'L': apply Q or Q**H from the Left; !> = 'R': apply Q or Q**H from the Right. !>
TRANS
!> TRANS is CHARACTER*1 !> = 'N': No transpose, apply Q; !> = 'C': Conjugate transpose, apply Q**H. !>
M
!> M is INTEGER !> The number of rows of the matrix C. M >= 0. !>
N
!> N is INTEGER !> The number of columns of the matrix C. N >= 0. !>
K
!> K is 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
!> A is COMPLEX*16 array, dimension !> (LDA,M) if SIDE = 'L', !> (LDA,N) if SIDE = 'R' !> The i-th row must contain the vector which defines the !> elementary reflector H(i), for i = 1,2,...,k, as returned by !> ZGERQF in the last k rows of its array argument A. !>
LDA
!> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,K). !>
TAU
!> TAU is COMPLEX*16 array, dimension (K) !> TAU(i) must contain the scalar factor of the elementary !> reflector H(i), as returned by ZGERQF. !>
C
!> C is 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
!> LDC is INTEGER !> The leading dimension of the array C. LDC >= max(1,M). !>
WORK
!> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. !>
LWORK
!> LWORK is INTEGER !> The dimension of the array WORK. !> If SIDE = 'L', LWORK >= max(1,N); !> if SIDE = 'R', LWORK >= max(1,M). !> For good performance, LWORK should generally be larger. !> !> 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
!> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !>
Author
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Definition at line 165 of file zunmrq.f.
Author
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