table of contents
| ung2l(3) | LAPACK | ung2l(3) |
NAME¶
ung2l - {un,or}g2l: step in ungql
SYNOPSIS¶
Functions¶
subroutine cung2l (m, n, k, a, lda, tau, work, info)
CUNG2L generates all or part of the unitary matrix Q from a QL
factorization determined by cgeqlf (unblocked algorithm). subroutine
dorg2l (m, n, k, a, lda, tau, work, info)
DORG2L generates all or part of the orthogonal matrix Q from a QL
factorization determined by sgeqlf (unblocked algorithm). subroutine
sorg2l (m, n, k, a, lda, tau, work, info)
SORG2L generates all or part of the orthogonal matrix Q from a QL
factorization determined by sgeqlf (unblocked algorithm). subroutine
zung2l (m, n, k, a, lda, tau, work, info)
ZUNG2L generates all or part of the unitary matrix Q from a QL
factorization determined by cgeqlf (unblocked algorithm).
Detailed Description¶
Function Documentation¶
subroutine cung2l (integer m, integer n, integer k, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tau, complex, dimension( * ) work, integer info)¶
CUNG2L generates all or part of the unitary matrix Q from a QL factorization determined by cgeqlf (unblocked algorithm).
Purpose:
CUNG2L generates an m by n complex matrix Q with orthonormal columns,
which is defined as the last n columns of a product of k elementary
reflectors of order m
Q = H(k) . . . H(2) H(1)
as returned by CGEQLF.
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. M >= N >= 0.
K
K is INTEGER
The number of elementary reflectors whose product defines the
matrix Q. N >= K >= 0.
A
A is COMPLEX array, dimension (LDA,N)
On entry, the (n-k+i)-th column must contain the vector which
defines the elementary reflector H(i), for i = 1,2,...,k, as
returned by CGEQLF in the last k columns 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 CGEQLF.
WORK
WORK is COMPLEX array, dimension (N)
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.
subroutine dorg2l (integer m, integer n, integer k, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tau, double precision, dimension( * ) work, integer info)¶
DORG2L generates all or part of the orthogonal matrix Q from a QL factorization determined by sgeqlf (unblocked algorithm).
Purpose:
DORG2L generates an m by n real matrix Q with orthonormal columns,
which is defined as the last n columns of a product of k elementary
reflectors of order m
Q = H(k) . . . H(2) H(1)
as returned by DGEQLF.
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. M >= N >= 0.
K
K is INTEGER
The number of elementary reflectors whose product defines the
matrix Q. N >= K >= 0.
A
A is DOUBLE PRECISION array, dimension (LDA,N)
On entry, the (n-k+i)-th column must contain the vector which
defines the elementary reflector H(i), for i = 1,2,...,k, as
returned by DGEQLF in the last k columns 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 DGEQLF.
WORK
WORK is DOUBLE PRECISION array, dimension (N)
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.
subroutine sorg2l (integer m, integer n, integer k, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( * ) work, integer info)¶
SORG2L generates all or part of the orthogonal matrix Q from a QL factorization determined by sgeqlf (unblocked algorithm).
Purpose:
SORG2L generates an m by n real matrix Q with orthonormal columns,
which is defined as the last n columns of a product of k elementary
reflectors of order m
Q = H(k) . . . H(2) H(1)
as returned by SGEQLF.
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. M >= N >= 0.
K
K is INTEGER
The number of elementary reflectors whose product defines the
matrix Q. N >= K >= 0.
A
A is REAL array, dimension (LDA,N)
On entry, the (n-k+i)-th column must contain the vector which
defines the elementary reflector H(i), for i = 1,2,...,k, as
returned by SGEQLF in the last k columns 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 SGEQLF.
WORK
WORK is REAL array, dimension (N)
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.
subroutine zung2l (integer m, integer n, integer k, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * ) work, integer info)¶
ZUNG2L generates all or part of the unitary matrix Q from a QL factorization determined by cgeqlf (unblocked algorithm).
Purpose:
ZUNG2L generates an m by n complex matrix Q with orthonormal columns,
which is defined as the last n columns of a product of k elementary
reflectors of order m
Q = H(k) . . . H(2) H(1)
as returned by ZGEQLF.
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. M >= N >= 0.
K
K is INTEGER
The number of elementary reflectors whose product defines the
matrix Q. N >= K >= 0.
A
A is COMPLEX*16 array, dimension (LDA,N)
On entry, the (n-k+i)-th column must contain the vector which
defines the elementary reflector H(i), for i = 1,2,...,k, as
returned by ZGEQLF in the last k columns 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 ZGEQLF.
WORK
WORK is COMPLEX*16 array, dimension (N)
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.
Author¶
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| Wed Feb 7 2024 11:30:40 | Version 3.12.0 |