table of contents
| unmr2(3) | LAPACK | unmr2(3) |
NAME¶
unmr2 - {un,or}mr2: step in unmrq
SYNOPSIS¶
Functions¶
subroutine cunmr2 (side, trans, m, n, k, a, lda, tau, c,
ldc, work, info)
CUNMR2 multiplies a general matrix by the unitary matrix from a RQ
factorization determined by cgerqf (unblocked algorithm). subroutine
dormr2 (side, trans, m, n, k, a, lda, tau, c, ldc, work, info)
DORMR2 multiplies a general matrix by the orthogonal matrix from a RQ
factorization determined by sgerqf (unblocked algorithm). subroutine
sormr2 (side, trans, m, n, k, a, lda, tau, c, ldc, work, info)
SORMR2 multiplies a general matrix by the orthogonal matrix from a RQ
factorization determined by sgerqf (unblocked algorithm). subroutine
zunmr2 (side, trans, m, n, k, a, lda, tau, c, ldc, work, info)
ZUNMR2 multiplies a general matrix by the unitary matrix from a RQ
factorization determined by cgerqf (unblocked algorithm).
Detailed Description¶
Function Documentation¶
subroutine cunmr2 (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)¶
CUNMR2 multiplies a general matrix by the unitary matrix from a RQ factorization determined by cgerqf (unblocked algorithm).
Purpose:
CUNMR2 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(1)**H H(2)**H . . . H(k)**H
as returned by CGERQF. 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
CGERQF in the last 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 CGERQF.
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 dormr2 (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)¶
DORMR2 multiplies a general matrix by the orthogonal matrix from a RQ factorization determined by sgerqf (unblocked algorithm).
Purpose:
DORMR2 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(1) H(2) . . . H(k)
as returned by DGERQF. 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' (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
DGERQF in the last 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 DGERQF.
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 sormr2 (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)¶
SORMR2 multiplies a general matrix by the orthogonal matrix from a RQ factorization determined by sgerqf (unblocked algorithm).
Purpose:
SORMR2 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(1) H(2) . . . H(k)
as returned by SGERQF. 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' (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
SGERQF in the last 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 SGERQF.
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 zunmr2 (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)¶
ZUNMR2 multiplies a general matrix by the unitary matrix from a RQ factorization determined by cgerqf (unblocked algorithm).
Purpose:
ZUNMR2 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(1)**H H(2)**H . . . H(k)**H
as returned by ZGERQF. 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
ZGERQF in the last 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 ZGERQF.
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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