table of contents
| ung2r(3) | LAPACK | ung2r(3) |
NAME¶
ung2r - {un,or}g2r: generate explicit Q from geqrf, level 2
SYNOPSIS¶
Functions¶
subroutine cung2r (m, n, k, a, lda, tau, work, info)
CUNG2R subroutine dorg2r (m, n, k, a, lda, tau, work, info)
DORG2R generates all or part of the orthogonal matrix Q from a QR
factorization determined by sgeqrf (unblocked algorithm). subroutine
sorg2r (m, n, k, a, lda, tau, work, info)
SORG2R generates all or part of the orthogonal matrix Q from a QR
factorization determined by sgeqrf (unblocked algorithm). subroutine
zung2r (m, n, k, a, lda, tau, work, info)
ZUNG2R
Detailed Description¶
Function Documentation¶
subroutine cung2r (integer m, integer n, integer k, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tau, complex, dimension( * ) work, integer info)¶
CUNG2R
Purpose:
CUNG2R generates an m by n complex matrix Q with orthonormal columns,
which is defined as the first n columns of a product of k elementary
reflectors of order m
Q = H(1) H(2) . . . H(k)
as returned by CGEQRF.
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 i-th column must contain the vector which
defines the elementary reflector H(i), for i = 1,2,...,k, as
returned by CGEQRF in the first 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 CGEQRF.
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 dorg2r (integer m, integer n, integer k, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tau, double precision, dimension( * ) work, integer info)¶
DORG2R generates all or part of the orthogonal matrix Q from a QR factorization determined by sgeqrf (unblocked algorithm).
Purpose:
DORG2R generates an m by n real matrix Q with orthonormal columns,
which is defined as the first n columns of a product of k elementary
reflectors of order m
Q = H(1) H(2) . . . H(k)
as returned by DGEQRF.
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 i-th column must contain the vector which
defines the elementary reflector H(i), for i = 1,2,...,k, as
returned by DGEQRF in the first 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 DGEQRF.
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 sorg2r (integer m, integer n, integer k, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( * ) work, integer info)¶
SORG2R generates all or part of the orthogonal matrix Q from a QR factorization determined by sgeqrf (unblocked algorithm).
Purpose:
SORG2R generates an m by n real matrix Q with orthonormal columns,
which is defined as the first n columns of a product of k elementary
reflectors of order m
Q = H(1) H(2) . . . H(k)
as returned by SGEQRF.
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 i-th column must contain the vector which
defines the elementary reflector H(i), for i = 1,2,...,k, as
returned by SGEQRF in the first 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 SGEQRF.
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 zung2r (integer m, integer n, integer k, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * ) work, integer info)¶
ZUNG2R
Purpose:
ZUNG2R generates an m by n complex matrix Q with orthonormal columns,
which is defined as the first n columns of a product of k elementary
reflectors of order m
Q = H(1) H(2) . . . H(k)
as returned by ZGEQRF.
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 i-th column must contain the vector which
defines the elementary reflector H(i), for i = 1,2,...,k, as
returned by ZGEQRF in the first 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 ZGEQRF.
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 |