unmrz(3) | Library Functions Manual | unmrz(3) |
NAME
unmrz - {un,or}mrz: multiply by Z from tzrzf
SYNOPSIS
Functions
subroutine cunmrz (side, trans, m, n, k, l, a, lda, tau, c,
ldc, work, lwork, info)
CUNMRZ subroutine dormrz (side, trans, m, n, k, l, a, lda, tau,
c, ldc, work, lwork, info)
DORMRZ subroutine sormrz (side, trans, m, n, k, l, a, lda, tau,
c, ldc, work, lwork, info)
SORMRZ subroutine zunmrz (side, trans, m, n, k, l, a, lda, tau,
c, ldc, work, lwork, info)
ZUNMRZ
Detailed Description
Function Documentation
subroutine cunmrz (character side, character trans, integer m, integer n, integer k, integer l, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tau, complex, dimension( ldc, * ) c, integer ldc, complex, dimension( * ) work, integer lwork, integer info)
CUNMRZ
Purpose:
!> !> CUNMRZ 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 CTZRZF. 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. !>
L
!> L is INTEGER !> The number of columns of the matrix A containing !> the meaningful part of the Householder reflectors. !> If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 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 !> CTZRZF in the last k rows of its array argument A. !> A is modified by the routine but restored on exit. !>
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 CTZRZF. !>
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.
Contributors:
Further Details:
!>
Definition at line 185 of file cunmrz.f.
subroutine dormrz (character side, character trans, integer m, integer n, integer k, integer l, 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)
DORMRZ
Purpose:
!> !> DORMRZ 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 DTZRZF. 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. !>
L
!> L is INTEGER !> The number of columns of the matrix A containing !> the meaningful part of the Householder reflectors. !> If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 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 !> DTZRZF in the last k rows of its array argument A. !> A is modified by the routine but restored on exit. !>
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 DTZRZF. !>
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**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 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.
Contributors:
Further Details:
!>
Definition at line 185 of file dormrz.f.
subroutine sormrz (character side, character trans, integer m, integer n, integer k, integer l, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( ldc, * ) c, integer ldc, real, dimension( * ) work, integer lwork, integer info)
SORMRZ
Purpose:
!> !> SORMRZ 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 STZRZF. 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. !>
L
!> L is INTEGER !> The number of columns of the matrix A containing !> the meaningful part of the Householder reflectors. !> If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 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 !> STZRZF in the last k rows of its array argument A. !> A is modified by the routine but restored on exit. !>
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 STZRZF. !>
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**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 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.
Contributors:
Further Details:
!>
Definition at line 185 of file sormrz.f.
subroutine zunmrz (character side, character trans, integer m, integer n, integer k, integer l, 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)
ZUNMRZ
Purpose:
!> !> ZUNMRZ 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 ZTZRZF. 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. !>
L
!> L is INTEGER !> The number of columns of the matrix A containing !> the meaningful part of the Householder reflectors. !> If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 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 !> ZTZRZF in the last k rows of its array argument A. !> A is modified by the routine but restored on exit. !>
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 ZTZRZF. !>
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.
Contributors:
Further Details:
!>
Definition at line 185 of file zunmrz.f.
Author
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