table of contents
| gemlq(3) | LAPACK | gemlq(3) |
NAME¶
gemlq - gemlq: multiply by Q from gelq
SYNOPSIS¶
Functions¶
subroutine cgemlq (side, trans, m, n, k, a, lda, t, tsize,
c, ldc, work, lwork, info)
CGEMLQ subroutine dgemlq (side, trans, m, n, k, a, lda, t,
tsize, c, ldc, work, lwork, info)
DGEMLQ subroutine sgemlq (side, trans, m, n, k, a, lda, t,
tsize, c, ldc, work, lwork, info)
SGEMLQ subroutine zgemlq (side, trans, m, n, k, a, lda, t,
tsize, c, ldc, work, lwork, info)
ZGEMLQ
Detailed Description¶
Function Documentation¶
subroutine cgemlq (character side, character trans, integer m, integer n, integer k, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) t, integer tsize, complex, dimension( ldc, * ) c, integer ldc, complex, dimension( * ) work, integer lwork, integer info)¶
CGEMLQ
Purpose:
CGEMLQ overwrites the general real 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 blocked elementary reflectors computed by short wide
LQ factorization (CGELQ)
Parameters
SIDE
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 A. 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'
Part of the data structure to represent Q as returned by CGELQ.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,K).
T
T is COMPLEX array, dimension (MAX(5,TSIZE)).
Part of the data structure to represent Q as returned by CGELQ.
TSIZE
TSIZE is INTEGER
The dimension of the array T. TSIZE >= 5.
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
(workspace) COMPLEX array, dimension (MAX(1,LWORK))
LWORK
LWORK is INTEGER
The dimension of the array WORK.
If LWORK = -1, then a workspace query is assumed. The routine
only calculates the size of the WORK array, returns this
value as WORK(1), and no error message related to WORK
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 Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Further Details
These details are particular for this LAPACK implementation. Users should not
take them for granted. These details may change in the future, and are not likely
true for another LAPACK implementation. These details are relevant if one wants
to try to understand the code. They are not part of the interface.
In this version,
T(2): row block size (MB)
T(3): column block size (NB)
T(6:TSIZE): data structure needed for Q, computed by
CLASWQR or CGELQT
Depending on the matrix dimensions M and N, and row and column
block sizes MB and NB returned by ILAENV, CGELQ will use either
CLASWLQ (if the matrix is wide-and-short) or CGELQT to compute
the LQ factorization.
This version of CGEMLQ will use either CLAMSWLQ or CGEMLQT to
multiply matrix Q by another matrix.
Further Details in CLAMSWLQ or CGEMLQT.
subroutine dgemlq (character side, character trans, integer m, integer n, integer k, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) t, integer tsize, double precision, dimension( ldc, * ) c, integer ldc, double precision, dimension( * ) work, integer lwork, integer info)¶
DGEMLQ
Purpose:
DGEMLQ 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 blocked elementary reflectors computed by short wide LQ
factorization (DGELQ)
Parameters
SIDE
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 A. 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'
Part of the data structure to represent Q as returned by DGELQ.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,K).
T
T is DOUBLE PRECISION array, dimension (MAX(5,TSIZE)).
Part of the data structure to represent Q as returned by DGELQ.
TSIZE
TSIZE is INTEGER
The dimension of the array T. TSIZE >= 5.
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
(workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
LWORK
LWORK is INTEGER
The dimension of the array WORK.
If LWORK = -1, then a workspace query is assumed. The routine
only calculates the size of the WORK array, returns this
value as WORK(1), and no error message related to WORK
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 Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Further Details
These details are particular for this LAPACK implementation. Users should not
take them for granted. These details may change in the future, and are not likely
true for another LAPACK implementation. These details are relevant if one wants
to try to understand the code. They are not part of the interface.
In this version,
T(2): row block size (MB)
T(3): column block size (NB)
T(6:TSIZE): data structure needed for Q, computed by
DLASWLQ or DGELQT
Depending on the matrix dimensions M and N, and row and column
block sizes MB and NB returned by ILAENV, DGELQ will use either
DLASWLQ (if the matrix is wide-and-short) or DGELQT to compute
the LQ factorization.
This version of DGEMLQ will use either DLAMSWLQ or DGEMLQT to
multiply matrix Q by another matrix.
Further Details in DLAMSWLQ or DGEMLQT.
subroutine sgemlq (character side, character trans, integer m, integer n, integer k, real, dimension( lda, * ) a, integer lda, real, dimension( * ) t, integer tsize, real, dimension( ldc, * ) c, integer ldc, real, dimension( * ) work, integer lwork, integer info)¶
SGEMLQ
Purpose:
SGEMLQ 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 blocked elementary reflectors computed by short wide LQ
factorization (SGELQ)
Parameters
SIDE
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 A. 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'
Part of the data structure to represent Q as returned by DGELQ.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,K).
T
T is REAL array, dimension (MAX(5,TSIZE)).
Part of the data structure to represent Q as returned by SGELQ.
TSIZE
TSIZE is INTEGER
The dimension of the array T. TSIZE >= 5.
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
(workspace) REAL array, dimension (MAX(1,LWORK))
LWORK
LWORK is INTEGER
The dimension of the array WORK.
If LWORK = -1, then a workspace query is assumed. The routine
only calculates the size of the WORK array, returns this
value as WORK(1), and no error message related to WORK
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 Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Further Details
These details are particular for this LAPACK implementation. Users should not
take them for granted. These details may change in the future, and are not likely
true for another LAPACK implementation. These details are relevant if one wants
to try to understand the code. They are not part of the interface.
In this version,
T(2): row block size (MB)
T(3): column block size (NB)
T(6:TSIZE): data structure needed for Q, computed by
SLASWLQ or SGELQT
Depending on the matrix dimensions M and N, and row and column
block sizes MB and NB returned by ILAENV, SGELQ will use either
SLASWLQ (if the matrix is wide-and-short) or SGELQT to compute
the LQ factorization.
This version of SGEMLQ will use either SLAMSWLQ or SGEMLQT to
multiply matrix Q by another matrix.
Further Details in SLAMSWLQ or SGEMLQT.
subroutine zgemlq (character side, character trans, integer m, integer n, integer k, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) t, integer tsize, complex*16, dimension( ldc, * ) c, integer ldc, complex*16, dimension( * ) work, integer lwork, integer info)¶
ZGEMLQ
Purpose:
ZGEMLQ overwrites the general real 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 blocked elementary reflectors computed by short wide
LQ factorization (ZGELQ)
Parameters
SIDE
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 A. 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'
Part of the data structure to represent Q as returned by ZGELQ.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,K).
T
T is COMPLEX*16 array, dimension (MAX(5,TSIZE)).
Part of the data structure to represent Q as returned by ZGELQ.
TSIZE
TSIZE is INTEGER
The dimension of the array T. TSIZE >= 5.
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
(workspace) COMPLEX*16 array, dimension (MAX(1,LWORK))
LWORK
LWORK is INTEGER
The dimension of the array WORK.
If LWORK = -1, then a workspace query is assumed. The routine
only calculates the size of the WORK array, returns this
value as WORK(1), and no error message related to WORK
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 Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Further Details
These details are particular for this LAPACK implementation. Users should not
take them for granted. These details may change in the future, and are not likely
true for another LAPACK implementation. These details are relevant if one wants
to try to understand the code. They are not part of the interface.
In this version,
T(2): row block size (MB)
T(3): column block size (NB)
T(6:TSIZE): data structure needed for Q, computed by
ZLASWLQ or ZGELQT
Depending on the matrix dimensions M and N, and row and column
block sizes MB and NB returned by ILAENV, ZGELQ will use either
ZLASWLQ (if the matrix is wide-and-short) or ZGELQT to compute
the LQ factorization.
This version of ZGEMLQ will use either ZLAMSWLQ or ZGEMLQT to
multiply matrix Q by another matrix.
Further Details in ZLAMSWLQ or ZGEMLQT.
Author¶
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| Wed Feb 7 2024 11:30:40 | Version 3.12.0 |