| gemlqt(3) | LAPACK | gemlqt(3) |
gemlqt - gemlqt: multiply by Q from gelqt
subroutine cgemlqt (side, trans, m, n, k, mb, v, ldv, t,
ldt, c, ldc, work, info)
CGEMLQT subroutine dgemlqt (side, trans, m, n, k, mb, v, ldv, t,
ldt, c, ldc, work, info)
DGEMLQT subroutine sgemlqt (side, trans, m, n, k, mb, v, ldv, t,
ldt, c, ldc, work, info)
SGEMLQT subroutine zgemlqt (side, trans, m, n, k, mb, v, ldv, t,
ldt, c, ldc, work, info)
ZGEMLQT
CGEMLQT
Purpose:
CGEMLQT overwrites the general complex M-by-N matrix C with
SIDE = 'L' SIDE = 'R'
TRANS = 'N': Q C C Q
TRANS = 'C': Q**H C C Q**H
where Q is a complex unitary matrix defined as the product of K
elementary reflectors:
Q = H(1) H(2) . . . H(K) = I - V T V**H
generated using the compact WY representation as returned by CGELQT.
Q is of order M if SIDE = 'L' and of order N if SIDE = 'R'.
Parameters
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': No transpose, apply Q;
= 'C': Conjugate transpose, apply Q**H.
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.
MB
MB is INTEGER
The block size used for the storage of T. K >= MB >= 1.
This must be the same value of MB used to generate T
in CGELQT.
V
V is COMPLEX array, dimension
(LDV,M) if SIDE = 'L',
(LDV,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
CGELQT in the first K rows of its array argument A.
LDV
LDV is INTEGER
The leading dimension of the array V. LDV >= max(1,K).
T
T is COMPLEX array, dimension (LDT,K)
The upper triangular factors of the block reflectors
as returned by CGELQT, stored as a MB-by-K matrix.
LDT
LDT is INTEGER
The leading dimension of the array T. LDT >= MB.
C
C is COMPLEX array, dimension (LDC,N)
On entry, the M-by-N matrix C.
On exit, C is overwritten by Q C, Q**H C, 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. The dimension of
WORK is N*MB if SIDE = 'L', or M*MB 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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
DGEMLQT
Purpose:
DGEMLQT overwrites the general real M-by-N matrix C with
SIDE = 'L' SIDE = 'R'
TRANS = 'N': Q C C Q
TRANS = 'T': Q**T C C Q**T
where Q is a real orthogonal matrix defined as the product of K
elementary reflectors:
Q = H(1) H(2) . . . H(K) = I - V T V**T
generated using the compact WY representation as returned by DGELQT.
Q is of order M if SIDE = 'L' and of order N if SIDE = 'R'.
Parameters
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': No transpose, apply Q;
= 'C': Transpose, apply Q**T.
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.
MB
MB is INTEGER
The block size used for the storage of T. K >= MB >= 1.
This must be the same value of MB used to generate T
in DGELQT.
V
V is DOUBLE PRECISION array, dimension
(LDV,M) if SIDE = 'L',
(LDV,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
DGELQT in the first K rows of its array argument A.
LDV
LDV is INTEGER
The leading dimension of the array V. LDV >= max(1,K).
T
T is DOUBLE PRECISION array, dimension (LDT,K)
The upper triangular factors of the block reflectors
as returned by DGELQT, stored as a MB-by-K matrix.
LDT
LDT is INTEGER
The leading dimension of the array T. LDT >= MB.
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, Q**T C, 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. The dimension of
WORK is N*MB if SIDE = 'L', or M*MB 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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
SGEMLQT
Purpose:
DGEMLQT overwrites the general real M-by-N matrix C with
SIDE = 'L' SIDE = 'R'
TRANS = 'N': Q C C Q
TRANS = 'T': Q**T C C Q**T
where Q is a real orthogonal matrix defined as the product of K
elementary reflectors:
Q = H(1) H(2) . . . H(K) = I - V T V**T
generated using the compact WY representation as returned by SGELQT.
Q is of order M if SIDE = 'L' and of order N if SIDE = 'R'.
Parameters
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': No transpose, apply Q;
= 'C': Transpose, apply Q**T.
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.
MB
MB is INTEGER
The block size used for the storage of T. K >= MB >= 1.
This must be the same value of MB used to generate T
in SGELQT.
V
V is REAL array, dimension
(LDV,M) if SIDE = 'L',
(LDV,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
SGELQT in the first K rows of its array argument A.
LDV
LDV is INTEGER
The leading dimension of the array V. LDV >= max(1,K).
T
T is REAL array, dimension (LDT,K)
The upper triangular factors of the block reflectors
as returned by SGELQT, stored as a MB-by-K matrix.
LDT
LDT is INTEGER
The leading dimension of the array T. LDT >= MB.
C
C is REAL array, dimension (LDC,N)
On entry, the M-by-N matrix C.
On exit, C is overwritten by Q C, Q**T C, 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. The dimension of
WORK is N*MB if SIDE = 'L', or M*MB 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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
ZGEMLQT
Purpose:
ZGEMLQT overwrites the general complex M-by-N matrix C with
SIDE = 'L' SIDE = 'R'
TRANS = 'N': Q C C Q
TRANS = 'C': Q**H C C Q**H
where Q is a complex unitary matrix defined as the product of K
elementary reflectors:
Q = H(1) H(2) . . . H(K) = I - V T V**H
generated using the compact WY representation as returned by ZGELQT.
Q is of order M if SIDE = 'L' and of order N if SIDE = 'R'.
Parameters
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': No transpose, apply Q;
= 'C': Conjugate transpose, apply Q**H.
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.
MB
MB is INTEGER
The block size used for the storage of T. K >= MB >= 1.
This must be the same value of MB used to generate T
in ZGELQT.
V
V is COMPLEX*16 array, dimension
(LDV,M) if SIDE = 'L',
(LDV,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
ZGELQT in the first K rows of its array argument A.
LDV
LDV is INTEGER
The leading dimension of the array V. LDV >= max(1,K).
T
T is COMPLEX*16 array, dimension (LDT,K)
The upper triangular factors of the block reflectors
as returned by ZGELQT, stored as a MB-by-K matrix.
LDT
LDT is INTEGER
The leading dimension of the array T. LDT >= MB.
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, Q**H C, 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. The dimension of
WORK is N*MB if SIDE = 'L', or M*MB 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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
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| Fri Aug 9 2024 02:33:22 | Version 3.12.0 |