table of contents
| gelqt(3) | LAPACK | gelqt(3) |
NAME¶
gelqt - gelqt: LQ factor, with T
SYNOPSIS¶
Functions¶
subroutine cgelqt (m, n, mb, a, lda, t, ldt, work, info)
CGELQT subroutine dgelqt (m, n, mb, a, lda, t, ldt, work, info)
DGELQT subroutine sgelqt (m, n, mb, a, lda, t, ldt, work, info)
SGELQT subroutine zgelqt (m, n, mb, a, lda, t, ldt, work, info)
ZGELQT
Detailed Description¶
Function Documentation¶
subroutine cgelqt (integer m, integer n, integer mb, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldt, * ) t, integer ldt, complex, dimension( * ) work, integer info)¶
CGELQT
Purpose:
CGELQT computes a blocked LQ factorization of a complex M-by-N matrix A
using the compact WY representation of Q.
Parameters
M
M is INTEGER
The number of rows of the matrix A. M >= 0.
N
N is INTEGER
The number of columns of the matrix A. N >= 0.
MB
MB is INTEGER
The block size to be used in the blocked QR. MIN(M,N) >= MB >= 1.
A
A is COMPLEX array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, the elements on and below the diagonal of the array
contain the M-by-MIN(M,N) lower trapezoidal matrix L (L is
lower triangular if M <= N); the elements above the diagonal
are the rows of V.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,M).
T
T is COMPLEX array, dimension (LDT,MIN(M,N))
The upper triangular block reflectors stored in compact form
as a sequence of upper triangular blocks. See below
for further details.
LDT
LDT is INTEGER
The leading dimension of the array T. LDT >= MB.
WORK
WORK is COMPLEX array, dimension (MB*N)
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.
Further Details:
The matrix V stores the elementary reflectors H(i) in the i-th row
above the diagonal. For example, if M=5 and N=3, the matrix V is
V = ( 1 v1 v1 v1 v1 )
( 1 v2 v2 v2 )
( 1 v3 v3 )
where the vi's represent the vectors which define H(i), which are returned
in the matrix A. The 1's along the diagonal of V are not stored in A.
Let K=MIN(M,N). The number of blocks is B = ceiling(K/MB), where each
block is of order MB except for the last block, which is of order
IB = K - (B-1)*MB. For each of the B blocks, a upper triangular block
reflector factor is computed: T1, T2, ..., TB. The MB-by-MB (and IB-by-IB
for the last block) T's are stored in the MB-by-K matrix T as
T = (T1 T2 ... TB).
subroutine dgelqt (integer m, integer n, integer mb, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldt, * ) t, integer ldt, double precision, dimension( * ) work, integer info)¶
DGELQT
Purpose:
DGELQT computes a blocked LQ factorization of a real M-by-N matrix A
using the compact WY representation of Q.
Parameters
M
M is INTEGER
The number of rows of the matrix A. M >= 0.
N
N is INTEGER
The number of columns of the matrix A. N >= 0.
MB
MB is INTEGER
The block size to be used in the blocked QR. MIN(M,N) >= MB >= 1.
A
A is DOUBLE PRECISION array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, the elements on and below the diagonal of the array
contain the M-by-MIN(M,N) lower trapezoidal matrix L (L is
lower triangular if M <= N); the elements above the diagonal
are the rows of V.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,M).
T
T is DOUBLE PRECISION array, dimension (LDT,MIN(M,N))
The upper triangular block reflectors stored in compact form
as a sequence of upper triangular blocks. See below
for further details.
LDT
LDT is INTEGER
The leading dimension of the array T. LDT >= MB.
WORK
WORK is DOUBLE PRECISION array, dimension (MB*N)
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.
Further Details:
The matrix V stores the elementary reflectors H(i) in the i-th row
above the diagonal. For example, if M=5 and N=3, the matrix V is
V = ( 1 v1 v1 v1 v1 )
( 1 v2 v2 v2 )
( 1 v3 v3 )
where the vi's represent the vectors which define H(i), which are returned
in the matrix A. The 1's along the diagonal of V are not stored in A.
Let K=MIN(M,N). The number of blocks is B = ceiling(K/MB), where each
block is of order MB except for the last block, which is of order
IB = K - (B-1)*MB. For each of the B blocks, a upper triangular block
reflector factor is computed: T1, T2, ..., TB. The MB-by-MB (and IB-by-IB
for the last block) T's are stored in the MB-by-K matrix T as
T = (T1 T2 ... TB).
subroutine sgelqt (integer m, integer n, integer mb, real, dimension( lda, * ) a, integer lda, real, dimension( ldt, * ) t, integer ldt, real, dimension( * ) work, integer info)¶
SGELQT
Purpose:
DGELQT computes a blocked LQ factorization of a real M-by-N matrix A
using the compact WY representation of Q.
Parameters
M
M is INTEGER
The number of rows of the matrix A. M >= 0.
N
N is INTEGER
The number of columns of the matrix A. N >= 0.
MB
MB is INTEGER
The block size to be used in the blocked QR. MIN(M,N) >= MB >= 1.
A
A is REAL array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, the elements on and below the diagonal of the array
contain the M-by-MIN(M,N) lower trapezoidal matrix L (L is
lower triangular if M <= N); the elements above the diagonal
are the rows of V.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,M).
T
T is REAL array, dimension (LDT,MIN(M,N))
The upper triangular block reflectors stored in compact form
as a sequence of upper triangular blocks. See below
for further details.
LDT
LDT is INTEGER
The leading dimension of the array T. LDT >= MB.
WORK
WORK is REAL array, dimension (MB*N)
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.
Further Details:
The matrix V stores the elementary reflectors H(i) in the i-th row
above the diagonal. For example, if M=5 and N=3, the matrix V is
V = ( 1 v1 v1 v1 v1 )
( 1 v2 v2 v2 )
( 1 v3 v3 )
where the vi's represent the vectors which define H(i), which are returned
in the matrix A. The 1's along the diagonal of V are not stored in A.
Let K=MIN(M,N). The number of blocks is B = ceiling(K/MB), where each
block is of order MB except for the last block, which is of order
IB = K - (B-1)*MB. For each of the B blocks, a upper triangular block
reflector factor is computed: T1, T2, ..., TB. The MB-by-MB (and IB-by-IB
for the last block) T's are stored in the MB-by-K matrix T as
T = (T1 T2 ... TB).
subroutine zgelqt (integer m, integer n, integer mb, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldt, * ) t, integer ldt, complex*16, dimension( * ) work, integer info)¶
ZGELQT
Purpose:
ZGELQT computes a blocked LQ factorization of a complex M-by-N matrix A
using the compact WY representation of Q.
Parameters
M
M is INTEGER
The number of rows of the matrix A. M >= 0.
N
N is INTEGER
The number of columns of the matrix A. N >= 0.
MB
MB is INTEGER
The block size to be used in the blocked QR. MIN(M,N) >= MB >= 1.
A
A is COMPLEX*16 array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, the elements on and below the diagonal of the array
contain the M-by-MIN(M,N) lower trapezoidal matrix L (L is
lower triangular if M <= N); the elements above the diagonal
are the rows of V.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,M).
T
T is COMPLEX*16 array, dimension (LDT,MIN(M,N))
The upper triangular block reflectors stored in compact form
as a sequence of upper triangular blocks. See below
for further details.
LDT
LDT is INTEGER
The leading dimension of the array T. LDT >= MB.
WORK
WORK is COMPLEX*16 array, dimension (MB*N)
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.
Further Details:
The matrix V stores the elementary reflectors H(i) in the i-th row
above the diagonal. For example, if M=5 and N=3, the matrix V is
V = ( 1 v1 v1 v1 v1 )
( 1 v2 v2 v2 )
( 1 v3 v3 )
where the vi's represent the vectors which define H(i), which are returned
in the matrix A. The 1's along the diagonal of V are not stored in A.
Let K=MIN(M,N). The number of blocks is B = ceiling(K/MB), where each
block is of order MB except for the last block, which is of order
IB = K - (B-1)*MB. For each of the B blocks, a upper triangular block
reflector factor is computed: T1, T2, ..., TB. The MB-by-MB (and IB-by-IB
for the last block) T's are stored in the MB-by-K matrix T as
T = (T1 T2 ... TB).
Author¶
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| Wed Feb 7 2024 11:30:40 | Version 3.12.0 |