Man page - geqrt2(3)

Packages contains this manual

Manual

geqrt2

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine cgeqrt2 (integer m, integer n, complex, dimension( lda, * ) a,integer lda, complex, dimension( ldt, * ) t, integer ldt, integer info)
subroutine dgeqrt2 (integer m, integer n, double precision, dimension( lda,* ) a, integer lda, double precision, dimension( ldt, * ) t, integerldt, integer info)
subroutine sgeqrt2 (integer m, integer n, real, dimension( lda, * ) a,integer lda, real, dimension( ldt, * ) t, integer ldt, integer info)
subroutine zgeqrt2 (integer m, integer n, complex*16, dimension( lda, * )a, integer lda, complex*16, dimension( ldt, * ) t, integer ldt, integerinfo)
Author

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

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 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 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, integerldt, 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

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 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 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

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 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 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, integerinfo)

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

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 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 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

Generated automatically by Doxygen for LAPACK from the source code.