table of contents
| geqrt2(3) | LAPACK | geqrt2(3) |
NAME¶
geqrt2 - geqrt2: QR factor, with T, level 2
SYNOPSIS¶
Functions¶
subroutine cgeqrt2 (m, n, a, lda, t, ldt, info)
CGEQRT2 computes a QR factorization of a general real or complex matrix
using the compact WY representation of Q. subroutine dgeqrt2 (m, n,
a, lda, t, ldt, info)
DGEQRT2 computes a QR factorization of a general real or complex matrix
using the compact WY representation of Q. subroutine sgeqrt2 (m, n,
a, lda, t, ldt, info)
SGEQRT2 computes a QR factorization of a general real or complex matrix
using the compact WY representation of Q. subroutine zgeqrt2 (m, n,
a, lda, t, ldt, info)
ZGEQRT2 computes a QR factorization of a general real or complex matrix
using the compact WY representation of Q.
Detailed Description¶
Function Documentation¶
subroutine cgeqrt2 (integer m, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldt, * ) t, integer ldt, integer info)¶
CGEQRT2 computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.
Purpose:
CGEQRT2 computes a QR factorization of a complex M-by-N matrix A,
using the compact WY representation of Q.
Parameters
M is INTEGER
The number of rows of the matrix A. M >= N.
N
N is INTEGER
The number of columns of the matrix A. N >= 0.
A
A is COMPLEX array, dimension (LDA,N)
On entry, the complex M-by-N matrix A. On exit, the elements on and
above the diagonal contain the N-by-N upper triangular matrix R; the
elements below the diagonal are the columns of V. See below for
further details.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,M).
T
T is COMPLEX array, dimension (LDT,N)
The N-by-N upper triangular factor of the block reflector.
The elements on and above the diagonal contain the block
reflector T; the elements below the diagonal are not used.
See below for further details.
LDT
LDT is INTEGER
The leading dimension of the array T. LDT >= max(1,N).
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.
Further Details:
The matrix V stores the elementary reflectors H(i) in the i-th column
below the diagonal. For example, if M=5 and N=3, the matrix V is
V = ( 1 )
( v1 1 )
( v1 v2 1 )
( v1 v2 v3 )
( v1 v2 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. The
block reflector H is then given by
H = I - V * T * V**H
where V**H is the conjugate transpose of V.
subroutine dgeqrt2 (integer m, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldt, * ) t, integer ldt, integer info)¶
DGEQRT2 computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.
Purpose:
DGEQRT2 computes a QR factorization of a real M-by-N matrix A,
using the compact WY representation of Q.
Parameters
M is INTEGER
The number of rows of the matrix A. M >= N.
N
N is INTEGER
The number of columns of the matrix A. N >= 0.
A
A is DOUBLE PRECISION array, dimension (LDA,N)
On entry, the real M-by-N matrix A. On exit, the elements on and
above the diagonal contain the N-by-N upper triangular matrix R; the
elements below the diagonal are the columns of V. See below for
further details.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,M).
T
T is DOUBLE PRECISION array, dimension (LDT,N)
The N-by-N upper triangular factor of the block reflector.
The elements on and above the diagonal contain the block
reflector T; the elements below the diagonal are not used.
See below for further details.
LDT
LDT is INTEGER
The leading dimension of the array T. LDT >= max(1,N).
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.
Further Details:
The matrix V stores the elementary reflectors H(i) in the i-th column
below the diagonal. For example, if M=5 and N=3, the matrix V is
V = ( 1 )
( v1 1 )
( v1 v2 1 )
( v1 v2 v3 )
( v1 v2 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. The
block reflector H is then given by
H = I - V * T * V**T
where V**T is the transpose of V.
subroutine sgeqrt2 (integer m, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( ldt, * ) t, integer ldt, integer info)¶
SGEQRT2 computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.
Purpose:
SGEQRT2 computes a QR factorization of a real M-by-N matrix A,
using the compact WY representation of Q.
Parameters
M is INTEGER
The number of rows of the matrix A. M >= N.
N
N is INTEGER
The number of columns of the matrix A. N >= 0.
A
A is REAL array, dimension (LDA,N)
On entry, the real M-by-N matrix A. On exit, the elements on and
above the diagonal contain the N-by-N upper triangular matrix R; the
elements below the diagonal are the columns of V. See below for
further details.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,M).
T
T is REAL array, dimension (LDT,N)
The N-by-N upper triangular factor of the block reflector.
The elements on and above the diagonal contain the block
reflector T; the elements below the diagonal are not used.
See below for further details.
LDT
LDT is INTEGER
The leading dimension of the array T. LDT >= max(1,N).
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.
Further Details:
The matrix V stores the elementary reflectors H(i) in the i-th column
below the diagonal. For example, if M=5 and N=3, the matrix V is
V = ( 1 )
( v1 1 )
( v1 v2 1 )
( v1 v2 v3 )
( v1 v2 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. The
block reflector H is then given by
H = I - V * T * V**T
where V**T is the transpose of V.
subroutine zgeqrt2 (integer m, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldt, * ) t, integer ldt, integer info)¶
ZGEQRT2 computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.
Purpose:
ZGEQRT2 computes a QR factorization of a complex M-by-N matrix A,
using the compact WY representation of Q.
Parameters
M is INTEGER
The number of rows of the matrix A. M >= N.
N
N is INTEGER
The number of columns of the matrix A. N >= 0.
A
A is COMPLEX*16 array, dimension (LDA,N)
On entry, the complex M-by-N matrix A. On exit, the elements on and
above the diagonal contain the N-by-N upper triangular matrix R; the
elements below the diagonal are the columns of V. See below for
further details.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,M).
T
T is COMPLEX*16 array, dimension (LDT,N)
The N-by-N upper triangular factor of the block reflector.
The elements on and above the diagonal contain the block
reflector T; the elements below the diagonal are not used.
See below for further details.
LDT
LDT is INTEGER
The leading dimension of the array T. LDT >= max(1,N).
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.
Further Details:
The matrix V stores the elementary reflectors H(i) in the i-th column
below the diagonal. For example, if M=5 and N=3, the matrix V is
V = ( 1 )
( v1 1 )
( v1 v2 1 )
( v1 v2 v3 )
( v1 v2 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. The
block reflector H is then given by
H = I - V * T * V**H
where V**H is the conjugate transpose of V.
Author¶
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| Wed Feb 7 2024 11:30:40 | Version 3.12.0 |