table of contents
| unml2(3) | LAPACK | unml2(3) |
NAME¶
unml2 - {un,or}ml2: multiply by Q, level 2, step in unmlq
SYNOPSIS¶
Functions¶
subroutine cunml2 (side, trans, m, n, k, a, lda, tau, c,
ldc, work, info)
CUNML2 multiplies a general matrix by the unitary matrix from a LQ
factorization determined by cgelqf (unblocked algorithm). subroutine
dorml2 (side, trans, m, n, k, a, lda, tau, c, ldc, work, info)
DORML2 multiplies a general matrix by the orthogonal matrix from a LQ
factorization determined by sgelqf (unblocked algorithm). subroutine
sorml2 (side, trans, m, n, k, a, lda, tau, c, ldc, work, info)
SORML2 multiplies a general matrix by the orthogonal matrix from a LQ
factorization determined by sgelqf (unblocked algorithm). subroutine
zunml2 (side, trans, m, n, k, a, lda, tau, c, ldc, work, info)
ZUNML2 multiplies a general matrix by the unitary matrix from a LQ
factorization determined by cgelqf (unblocked algorithm).
Detailed Description¶
Function Documentation¶
subroutine cunml2 (character side, character trans, integer m, integer n, integer k, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tau, complex, dimension( ldc, * ) c, integer ldc, complex, dimension( * ) work, integer info)¶
CUNML2 multiplies a general matrix by the unitary matrix from a LQ factorization determined by cgelqf (unblocked algorithm).
Purpose:
CUNML2 overwrites the general complex m-by-n matrix C with
Q * C if SIDE = 'L' and TRANS = 'N', or
Q**H* C if SIDE = 'L' and TRANS = 'C', or
C * Q if SIDE = 'R' and TRANS = 'N', or
C * Q**H if SIDE = 'R' and TRANS = 'C',
where Q is a complex unitary matrix defined as the product of k
elementary reflectors
Q = H(k)**H . . . H(2)**H H(1)**H
as returned by CGELQF. Q is of order m if SIDE = 'L' and of order n
if SIDE = 'R'.
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': apply Q (No transpose)
= 'C': apply Q**H (Conjugate transpose)
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.
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
CGELQF in the first 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 CGELQF.
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
(N) if SIDE = 'L',
(M) if SIDE = 'R'
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.
subroutine dorml2 (character side, character trans, integer m, integer n, integer k, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tau, double precision, dimension( ldc, * ) c, integer ldc, double precision, dimension( * ) work, integer info)¶
DORML2 multiplies a general matrix by the orthogonal matrix from a LQ factorization determined by sgelqf (unblocked algorithm).
Purpose:
DORML2 overwrites the general real m by n matrix C with
Q * C if SIDE = 'L' and TRANS = 'N', or
Q**T* C if SIDE = 'L' and TRANS = 'T', or
C * Q if SIDE = 'R' and TRANS = 'N', or
C * Q**T if SIDE = 'R' and TRANS = 'T',
where Q is a real orthogonal matrix defined as the product of k
elementary reflectors
Q = H(k) . . . H(2) H(1)
as returned by DGELQF. Q is of order m if SIDE = 'L' and of order n
if SIDE = 'R'.
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': apply Q (No transpose)
= 'T': apply Q**T (Transpose)
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.
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
DGELQF in the first 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 DGELQF.
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
WORK is DOUBLE PRECISION array, dimension
(N) if SIDE = 'L',
(M) if SIDE = 'R'
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.
subroutine sorml2 (character side, character trans, integer m, integer n, integer k, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( ldc, * ) c, integer ldc, real, dimension( * ) work, integer info)¶
SORML2 multiplies a general matrix by the orthogonal matrix from a LQ factorization determined by sgelqf (unblocked algorithm).
Purpose:
SORML2 overwrites the general real m by n matrix C with
Q * C if SIDE = 'L' and TRANS = 'N', or
Q**T* C if SIDE = 'L' and TRANS = 'T', or
C * Q if SIDE = 'R' and TRANS = 'N', or
C * Q**T if SIDE = 'R' and TRANS = 'T',
where Q is a real orthogonal matrix defined as the product of k
elementary reflectors
Q = H(k) . . . H(2) H(1)
as returned by SGELQF. Q is of order m if SIDE = 'L' and of order n
if SIDE = 'R'.
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': apply Q (No transpose)
= 'T': apply Q**T (Transpose)
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.
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
SGELQF in the first 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 SGELQF.
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
WORK is REAL array, dimension
(N) if SIDE = 'L',
(M) if SIDE = 'R'
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.
subroutine zunml2 (character side, character trans, integer m, integer n, integer k, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( ldc, * ) c, integer ldc, complex*16, dimension( * ) work, integer info)¶
ZUNML2 multiplies a general matrix by the unitary matrix from a LQ factorization determined by cgelqf (unblocked algorithm).
Purpose:
ZUNML2 overwrites the general complex m-by-n matrix C with
Q * C if SIDE = 'L' and TRANS = 'N', or
Q**H* C if SIDE = 'L' and TRANS = 'C', or
C * Q if SIDE = 'R' and TRANS = 'N', or
C * Q**H if SIDE = 'R' and TRANS = 'C',
where Q is a complex unitary matrix defined as the product of k
elementary reflectors
Q = H(k)**H . . . H(2)**H H(1)**H
as returned by ZGELQF. Q is of order m if SIDE = 'L' and of order n
if SIDE = 'R'.
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': apply Q (No transpose)
= 'C': apply Q**H (Conjugate transpose)
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.
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
ZGELQF in the first 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 ZGELQF.
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
(N) if SIDE = 'L',
(M) if SIDE = 'R'
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.
Author¶
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| Wed Feb 7 2024 11:30:40 | Version 3.12.0 |