Man page - laqp2(3)

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Manual

laqp2

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine claqp2 (integer m, integer n, integer offset, complex,dimension( lda, * ) a, integer lda, integer, dimension( * ) jpvt,complex, dimension( * ) tau, real, dimension( * ) vn1, real, dimension(* ) vn2, complex, dimension( * ) work)
subroutine dlaqp2 (integer m, integer n, integer offset, double precision,dimension( lda, * ) a, integer lda, integer, dimension( * ) jpvt,double precision, dimension( * ) tau, double precision, dimension( * )vn1, double precision, dimension( * ) vn2, double precision, dimension(* ) work)
subroutine slaqp2 (integer m, integer n, integer offset, real, dimension(lda, * ) a, integer lda, integer, dimension( * ) jpvt, real, dimension(* ) tau, real, dimension( * ) vn1, real, dimension( * ) vn2, real,dimension( * ) work)
subroutine zlaqp2 (integer m, integer n, integer offset, complex*16,dimension( lda, * ) a, integer lda, integer, dimension( * ) jpvt,complex*16, dimension( * ) tau, double precision, dimension( * ) vn1,double precision, dimension( * ) vn2, complex*16, dimension( * ) work)
Author

NAME

laqp2 - laqp2: step of geqp3

SYNOPSIS

Functions

subroutine claqp2 (m, n, offset, a, lda, jpvt, tau, vn1, vn2, work)
CLAQP2 computes a QR factorization with column pivoting of the matrix block.
subroutine dlaqp2 (m, n, offset, a, lda, jpvt, tau, vn1, vn2, work)
DLAQP2 computes a QR factorization with column pivoting of the matrix block.
subroutine slaqp2 (m, n, offset, a, lda, jpvt, tau, vn1, vn2, work)
SLAQP2 computes a QR factorization with column pivoting of the matrix block.
subroutine zlaqp2 (m, n, offset, a, lda, jpvt, tau, vn1, vn2, work)
ZLAQP2 computes a QR factorization with column pivoting of the matrix block.

Detailed Description

Function Documentation

subroutine claqp2 (integer m, integer n, integer offset, complex,dimension( lda, * ) a, integer lda, integer, dimension( * ) jpvt,complex, dimension( * ) tau, real, dimension( * ) vn1, real, dimension(* ) vn2, complex, dimension( * ) work)

CLAQP2 computes a QR factorization with column pivoting of the matrix block.

Purpose:

CLAQP2 computes a QR factorization with column pivoting of
the block A(OFFSET+1:M,1:N).
The block A(1:OFFSET,1:N) is accordingly pivoted, but not factorized.

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.

OFFSET

OFFSET is INTEGER
The number of rows of the matrix A that must be pivoted
but no factorized. OFFSET >= 0.

A

A is COMPLEX array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, the upper triangle of block A(OFFSET+1:M,1:N) is
the triangular factor obtained; the elements in block
A(OFFSET+1:M,1:N) below the diagonal, together with the
array TAU, represent the orthogonal matrix Q as a product of
elementary reflectors. Block A(1:OFFSET,1:N) has been
accordingly pivoted, but no factorized.

LDA

LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,M).

JPVT

JPVT is INTEGER array, dimension (N)
On entry, if JPVT(i) .ne. 0, the i-th column of A is permuted
to the front of A*P (a leading column); if JPVT(i) = 0,
the i-th column of A is a free column.
On exit, if JPVT(i) = k, then the i-th column of A*P
was the k-th column of A.

TAU

TAU is COMPLEX array, dimension (min(M,N))
The scalar factors of the elementary reflectors.

VN1

VN1 is REAL array, dimension (N)
The vector with the partial column norms.

VN2

VN2 is REAL array, dimension (N)
The vector with the exact column norms.

WORK

WORK is COMPLEX array, dimension (N)

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Contributors:

G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain X. Sun, Computer Science Dept., Duke University, USA
Partial column norm updating strategy modified on April 2011 Z. Drmac and Z. Bujanovic, Dept. of Mathematics, University of Zagreb, Croatia.

References:

LAPACK Working Note 176

subroutine dlaqp2 (integer m, integer n, integer offset, double precision,dimension( lda, * ) a, integer lda, integer, dimension( * ) jpvt,double precision, dimension( * ) tau, double precision, dimension( * )vn1, double precision, dimension( * ) vn2, double precision, dimension(* ) work)

DLAQP2 computes a QR factorization with column pivoting of the matrix block.

Purpose:

DLAQP2 computes a QR factorization with column pivoting of
the block A(OFFSET+1:M,1:N).
The block A(1:OFFSET,1:N) is accordingly pivoted, but not factorized.

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.

OFFSET

OFFSET is INTEGER
The number of rows of the matrix A that must be pivoted
but no factorized. OFFSET >= 0.

A

A is DOUBLE PRECISION array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, the upper triangle of block A(OFFSET+1:M,1:N) is
the triangular factor obtained; the elements in block
A(OFFSET+1:M,1:N) below the diagonal, together with the
array TAU, represent the orthogonal matrix Q as a product of
elementary reflectors. Block A(1:OFFSET,1:N) has been
accordingly pivoted, but no factorized.

LDA

LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,M).

JPVT

JPVT is INTEGER array, dimension (N)
On entry, if JPVT(i) .ne. 0, the i-th column of A is permuted
to the front of A*P (a leading column); if JPVT(i) = 0,
the i-th column of A is a free column.
On exit, if JPVT(i) = k, then the i-th column of A*P
was the k-th column of A.

TAU

TAU is DOUBLE PRECISION array, dimension (min(M,N))
The scalar factors of the elementary reflectors.

VN1

VN1 is DOUBLE PRECISION array, dimension (N)
The vector with the partial column norms.

VN2

VN2 is DOUBLE PRECISION array, dimension (N)
The vector with the exact column norms.

WORK

WORK is DOUBLE PRECISION array, dimension (N)

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Contributors:

G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain X. Sun, Computer Science Dept., Duke University, USA
Partial column norm updating strategy modified on April 2011 Z. Drmac and Z. Bujanovic, Dept. of Mathematics, University of Zagreb, Croatia.

References:

LAPACK Working Note 176

subroutine slaqp2 (integer m, integer n, integer offset, real, dimension(lda, * ) a, integer lda, integer, dimension( * ) jpvt, real, dimension(* ) tau, real, dimension( * ) vn1, real, dimension( * ) vn2, real,dimension( * ) work)

SLAQP2 computes a QR factorization with column pivoting of the matrix block.

Purpose:

SLAQP2 computes a QR factorization with column pivoting of
the block A(OFFSET+1:M,1:N).
The block A(1:OFFSET,1:N) is accordingly pivoted, but not factorized.

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.

OFFSET

OFFSET is INTEGER
The number of rows of the matrix A that must be pivoted
but no factorized. OFFSET >= 0.

A

A is REAL array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, the upper triangle of block A(OFFSET+1:M,1:N) is
the triangular factor obtained; the elements in block
A(OFFSET+1:M,1:N) below the diagonal, together with the
array TAU, represent the orthogonal matrix Q as a product of
elementary reflectors. Block A(1:OFFSET,1:N) has been
accordingly pivoted, but no factorized.

LDA

LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,M).

JPVT

JPVT is INTEGER array, dimension (N)
On entry, if JPVT(i) .ne. 0, the i-th column of A is permuted
to the front of A*P (a leading column); if JPVT(i) = 0,
the i-th column of A is a free column.
On exit, if JPVT(i) = k, then the i-th column of A*P
was the k-th column of A.

TAU

TAU is REAL array, dimension (min(M,N))
The scalar factors of the elementary reflectors.

VN1

VN1 is REAL array, dimension (N)
The vector with the partial column norms.

VN2

VN2 is REAL array, dimension (N)
The vector with the exact column norms.

WORK

WORK is REAL array, dimension (N)

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Contributors:

G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain X. Sun, Computer Science Dept., Duke University, USA
Partial column norm updating strategy modified on April 2011 Z. Drmac and Z. Bujanovic, Dept. of Mathematics, University of Zagreb, Croatia.

References:

LAPACK Working Note 176

subroutine zlaqp2 (integer m, integer n, integer offset, complex*16,dimension( lda, * ) a, integer lda, integer, dimension( * ) jpvt,complex*16, dimension( * ) tau, double precision, dimension( * ) vn1,double precision, dimension( * ) vn2, complex*16, dimension( * ) work)

ZLAQP2 computes a QR factorization with column pivoting of the matrix block.

Purpose:

ZLAQP2 computes a QR factorization with column pivoting of
the block A(OFFSET+1:M,1:N).
The block A(1:OFFSET,1:N) is accordingly pivoted, but not factorized.

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.

OFFSET

OFFSET is INTEGER
The number of rows of the matrix A that must be pivoted
but no factorized. OFFSET >= 0.

A

A is COMPLEX*16 array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, the upper triangle of block A(OFFSET+1:M,1:N) is
the triangular factor obtained; the elements in block
A(OFFSET+1:M,1:N) below the diagonal, together with the
array TAU, represent the orthogonal matrix Q as a product of
elementary reflectors. Block A(1:OFFSET,1:N) has been
accordingly pivoted, but no factorized.

LDA

LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,M).

JPVT

JPVT is INTEGER array, dimension (N)
On entry, if JPVT(i) .ne. 0, the i-th column of A is permuted
to the front of A*P (a leading column); if JPVT(i) = 0,
the i-th column of A is a free column.
On exit, if JPVT(i) = k, then the i-th column of A*P
was the k-th column of A.

TAU

TAU is COMPLEX*16 array, dimension (min(M,N))
The scalar factors of the elementary reflectors.

VN1

VN1 is DOUBLE PRECISION array, dimension (N)
The vector with the partial column norms.

VN2

VN2 is DOUBLE PRECISION array, dimension (N)
The vector with the exact column norms.

WORK

WORK is COMPLEX*16 array, dimension (N)

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Contributors:

G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain X. Sun, Computer Science Dept., Duke University, USA
Partial column norm updating strategy modified on April 2011 Z. Drmac and Z. Bujanovic, Dept. of Mathematics, University of Zagreb, Croatia.

References:

LAPACK Working Note 176

Author

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