Man page - geqrt3(3)

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Manual

geqrt3

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
recursive subroutine cgeqrt3 (integer m, integer n, complex, dimension(lda, * ) a, integer lda, complex, dimension( ldt, * ) t, integer ldt,integer info)
recursive subroutine dgeqrt3 (integer m, integer n, double precision,dimension( lda, * ) a, integer lda, double precision, dimension( ldt, *) t, integer ldt, integer info)
recursive subroutine sgeqrt3 (integer m, integer n, real, dimension( lda, *) a, integer lda, real, dimension( ldt, * ) t, integer ldt, integerinfo)
recursive subroutine zgeqrt3 (integer m, integer n, complex*16, dimension(lda, * ) a, integer lda, complex*16, dimension( ldt, * ) t, integerldt, integer info)
Author

NAME

geqrt3 - geqrt3: QR factor, with T, recursive panel

SYNOPSIS

Functions

recursive subroutine cgeqrt3 (m, n, a, lda, t, ldt, info)
CGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.
recursive subroutine dgeqrt3 (m, n, a, lda, t, ldt, info)
DGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.
recursive subroutine sgeqrt3 (m, n, a, lda, t, ldt, info)
SGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.
recursive subroutine zgeqrt3 (m, n, a, lda, t, ldt, info)
ZGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.

Detailed Description

Function Documentation

recursive subroutine cgeqrt3 (integer m, integer n, complex, dimension(lda, * ) a, integer lda, complex, dimension( ldt, * ) t, integer ldt,integer info)

CGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.

Purpose:

CGEQRT3 recursively computes a QR factorization of a complex M-by-N matrix A,
using the compact WY representation of Q.

Based on the algorithm of Elmroth and Gustavson,
IBM J. Res. Develop. Vol 44 No. 4 July 2000.

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.

For details of the algorithm, see Elmroth and Gustavson (cited above).

recursive subroutine dgeqrt3 (integer m, integer n, double precision,dimension( lda, * ) a, integer lda, double precision, dimension( ldt, *) t, integer ldt, integer info)

DGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.

Purpose:

DGEQRT3 recursively computes a QR factorization of a real M-by-N
matrix A, using the compact WY representation of Q.

Based on the algorithm of Elmroth and Gustavson,
IBM J. Res. Develop. Vol 44 No. 4 July 2000.

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.

For details of the algorithm, see Elmroth and Gustavson (cited above).

recursive subroutine sgeqrt3 (integer m, integer n, real, dimension( lda, *) a, integer lda, real, dimension( ldt, * ) t, integer ldt, integerinfo)

SGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.

Purpose:

SGEQRT3 recursively computes a QR factorization of a real M-by-N
matrix A, using the compact WY representation of Q.

Based on the algorithm of Elmroth and Gustavson,
IBM J. Res. Develop. Vol 44 No. 4 July 2000.

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.

For details of the algorithm, see Elmroth and Gustavson (cited above).

recursive subroutine zgeqrt3 (integer m, integer n, complex*16, dimension(lda, * ) a, integer lda, complex*16, dimension( ldt, * ) t, integerldt, integer info)

ZGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.

Purpose:

ZGEQRT3 recursively computes a QR factorization of a complex M-by-N
matrix A, using the compact WY representation of Q.

Based on the algorithm of Elmroth and Gustavson,
IBM J. Res. Develop. Vol 44 No. 4 July 2000.

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.

For details of the algorithm, see Elmroth and Gustavson (cited above).

Author

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