| unglq(3) | LAPACK | unglq(3) |
unglq - {un,or}glq: generate explicit Q from gelqf
subroutine cunglq (m, n, k, a, lda, tau, work, lwork, info)
CUNGLQ subroutine dorglq (m, n, k, a, lda, tau, work, lwork,
info)
DORGLQ subroutine sorglq (m, n, k, a, lda, tau, work, lwork,
info)
SORGLQ subroutine zunglq (m, n, k, a, lda, tau, work, lwork,
info)
ZUNGLQ
CUNGLQ
Purpose:
CUNGLQ generates an M-by-N complex matrix Q with orthonormal rows,
which is defined as the first M rows of a product of K elementary
reflectors of order N
Q = H(k)**H . . . H(2)**H H(1)**H
as returned by CGELQF.
Parameters
M is INTEGER
The number of rows of the matrix Q. M >= 0.
N
N is INTEGER
The number of columns of the matrix Q. N >= M.
K
K is INTEGER
The number of elementary reflectors whose product defines the
matrix Q. M >= K >= 0.
A
A is COMPLEX array, dimension (LDA,N)
On entry, the i-th row must contain the vector which defines
the elementary reflector H(i), for i = 1,2,...,k, as returned
by CGELQF in the first k rows of its array argument A.
On exit, the M-by-N matrix Q.
LDA
LDA is INTEGER
The first dimension of the array A. LDA >= max(1,M).
TAU
TAU is COMPLEX array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by CGELQF.
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. LWORK >= max(1,M).
For optimum performance LWORK >= M*NB, 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
INFO is INTEGER
= 0: successful exit;
< 0: if INFO = -i, the i-th argument has an illegal value
Author
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
DORGLQ
Purpose:
DORGLQ generates an M-by-N real matrix Q with orthonormal rows,
which is defined as the first M rows of a product of K elementary
reflectors of order N
Q = H(k) . . . H(2) H(1)
as returned by DGELQF.
Parameters
M is INTEGER
The number of rows of the matrix Q. M >= 0.
N
N is INTEGER
The number of columns of the matrix Q. N >= M.
K
K is INTEGER
The number of elementary reflectors whose product defines the
matrix Q. M >= K >= 0.
A
A is DOUBLE PRECISION array, dimension (LDA,N)
On entry, the i-th row must contain the vector which defines
the elementary reflector H(i), for i = 1,2,...,k, as returned
by DGELQF in the first k rows of its array argument A.
On exit, the M-by-N matrix Q.
LDA
LDA is INTEGER
The first dimension of the array A. LDA >= max(1,M).
TAU
TAU is DOUBLE PRECISION array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by DGELQF.
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. LWORK >= max(1,M).
For optimum performance LWORK >= M*NB, 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
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument has an illegal value
Author
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
SORGLQ
Purpose:
SORGLQ generates an M-by-N real matrix Q with orthonormal rows,
which is defined as the first M rows of a product of K elementary
reflectors of order N
Q = H(k) . . . H(2) H(1)
as returned by SGELQF.
Parameters
M is INTEGER
The number of rows of the matrix Q. M >= 0.
N
N is INTEGER
The number of columns of the matrix Q. N >= M.
K
K is INTEGER
The number of elementary reflectors whose product defines the
matrix Q. M >= K >= 0.
A
A is REAL array, dimension (LDA,N)
On entry, the i-th row must contain the vector which defines
the elementary reflector H(i), for i = 1,2,...,k, as returned
by SGELQF in the first k rows of its array argument A.
On exit, the M-by-N matrix Q.
LDA
LDA is INTEGER
The first dimension of the array A. LDA >= max(1,M).
TAU
TAU is REAL array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by SGELQF.
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. LWORK >= max(1,M).
For optimum performance LWORK >= M*NB, 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
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument has an illegal value
Author
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
ZUNGLQ
Purpose:
ZUNGLQ generates an M-by-N complex matrix Q with orthonormal rows,
which is defined as the first M rows of a product of K elementary
reflectors of order N
Q = H(k)**H . . . H(2)**H H(1)**H
as returned by ZGELQF.
Parameters
M is INTEGER
The number of rows of the matrix Q. M >= 0.
N
N is INTEGER
The number of columns of the matrix Q. N >= M.
K
K is INTEGER
The number of elementary reflectors whose product defines the
matrix Q. M >= K >= 0.
A
A is COMPLEX*16 array, dimension (LDA,N)
On entry, the i-th row must contain the vector which defines
the elementary reflector H(i), for i = 1,2,...,k, as returned
by ZGELQF in the first k rows of its array argument A.
On exit, the M-by-N matrix Q.
LDA
LDA is INTEGER
The first dimension of the array A. LDA >= max(1,M).
TAU
TAU is COMPLEX*16 array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by ZGELQF.
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. LWORK >= max(1,M).
For optimum performance LWORK >= M*NB, 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
INFO is INTEGER
= 0: successful exit;
< 0: if INFO = -i, the i-th argument has an illegal value
Author
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
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| Fri Aug 9 2024 02:33:22 | Version 3.12.0 |