Man page - laqps(3)

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Manual

laqps

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine claqps (integer m, integer n, integer offset, integer nb,integer kb, complex, dimension( lda, * ) a, integer lda, integer,dimension( * ) jpvt, complex, dimension( * ) tau, real, dimension( * )vn1, real, dimension( * ) vn2, complex, dimension( * ) auxv, complex,dimension( ldf, * ) f, integer ldf)
subroutine dlaqps (integer m, integer n, integer offset, integer nb,integer kb, 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( * ) auxv, double precision,dimension( ldf, * ) f, integer ldf)
subroutine slaqps (integer m, integer n, integer offset, integer nb,integer kb, real, dimension( lda, * ) a, integer lda, integer,dimension( * ) jpvt, real, dimension( * ) tau, real, dimension( * )vn1, real, dimension( * ) vn2, real, dimension( * ) auxv, real,dimension( ldf, * ) f, integer ldf)
subroutine zlaqps (integer m, integer n, integer offset, integer nb,integer kb, 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( * ) auxv, complex*16, dimension( ldf, * ) f, integer ldf)
Author

NAME

laqps - laqps: step of geqp3

SYNOPSIS

Functions

subroutine claqps (m, n, offset, nb, kb, a, lda, jpvt, tau, vn1, vn2, auxv, f, ldf)
CLAQPS computes a step of QR factorization with column pivoting of a real m-by-n matrix A by using BLAS level 3.
subroutine dlaqps (m, n, offset, nb, kb, a, lda, jpvt, tau, vn1, vn2, auxv, f, ldf)
DLAQPS computes a step of QR factorization with column pivoting of a real m-by-n matrix A by using BLAS level 3.
subroutine slaqps (m, n, offset, nb, kb, a, lda, jpvt, tau, vn1, vn2, auxv, f, ldf)
SLAQPS computes a step of QR factorization with column pivoting of a real m-by-n matrix A by using BLAS level 3.
subroutine zlaqps (m, n, offset, nb, kb, a, lda, jpvt, tau, vn1, vn2, auxv, f, ldf)
ZLAQPS computes a step of QR factorization with column pivoting of a real m-by-n matrix A by using BLAS level 3.

Detailed Description

Function Documentation

subroutine claqps (integer m, integer n, integer offset, integer nb,integer kb, complex, dimension( lda, * ) a, integer lda, integer,dimension( * ) jpvt, complex, dimension( * ) tau, real, dimension( * )vn1, real, dimension( * ) vn2, complex, dimension( * ) auxv, complex,dimension( ldf, * ) f, integer ldf)

CLAQPS computes a step of QR factorization with column pivoting of a real m-by-n matrix A by using BLAS level 3.

Purpose:

CLAQPS computes a step of QR factorization with column pivoting
of a complex M-by-N matrix A by using Blas-3. It tries to factorize
NB columns from A starting from the row OFFSET+1, and updates all
of the matrix with Blas-3 xGEMM.

In some cases, due to catastrophic cancellations, it cannot
factorize NB columns. Hence, the actual number of factorized
columns is returned in KB.

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 A that have been factorized in
previous steps.

NB

NB is INTEGER
The number of columns to factorize.

KB

KB is INTEGER
The number of columns actually factorized.

A

A is COMPLEX array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, block A(OFFSET+1:M,1:KB) is the triangular
factor obtained and block A(1:OFFSET,1:N) has been
accordingly pivoted, but no factorized.
The rest of the matrix, block A(OFFSET+1:M,KB+1:N) has
been updated.

LDA

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

JPVT

JPVT is INTEGER array, dimension (N)
JPVT(I) = K <==> Column K of the full matrix A has been
permuted into position I in AP.

TAU

TAU is COMPLEX array, dimension (KB)
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.

AUXV

AUXV is COMPLEX array, dimension (NB)
Auxiliary vector.

F

F is COMPLEX array, dimension (LDF,NB)
Matrix F**H = L * Y**H * A.

LDF

LDF is INTEGER
The leading dimension of the array F. LDF >= max(1,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 dlaqps (integer m, integer n, integer offset, integer nb,integer kb, 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( * ) auxv, double precision,dimension( ldf, * ) f, integer ldf)

DLAQPS computes a step of QR factorization with column pivoting of a real m-by-n matrix A by using BLAS level 3.

Purpose:

DLAQPS computes a step of QR factorization with column pivoting
of a real M-by-N matrix A by using Blas-3. It tries to factorize
NB columns from A starting from the row OFFSET+1, and updates all
of the matrix with Blas-3 xGEMM.

In some cases, due to catastrophic cancellations, it cannot
factorize NB columns. Hence, the actual number of factorized
columns is returned in KB.

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 A that have been factorized in
previous steps.

NB

NB is INTEGER
The number of columns to factorize.

KB

KB is INTEGER
The number of columns actually factorized.

A

A is DOUBLE PRECISION array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, block A(OFFSET+1:M,1:KB) is the triangular
factor obtained and block A(1:OFFSET,1:N) has been
accordingly pivoted, but no factorized.
The rest of the matrix, block A(OFFSET+1:M,KB+1:N) has
been updated.

LDA

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

JPVT

JPVT is INTEGER array, dimension (N)
JPVT(I) = K <==> Column K of the full matrix A has been
permuted into position I in AP.

TAU

TAU is DOUBLE PRECISION array, dimension (KB)
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.

AUXV

AUXV is DOUBLE PRECISION array, dimension (NB)
Auxiliary vector.

F

F is DOUBLE PRECISION array, dimension (LDF,NB)
Matrix F**T = L*Y**T*A.

LDF

LDF is INTEGER
The leading dimension of the array F. LDF >= max(1,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 slaqps (integer m, integer n, integer offset, integer nb,integer kb, real, dimension( lda, * ) a, integer lda, integer,dimension( * ) jpvt, real, dimension( * ) tau, real, dimension( * )vn1, real, dimension( * ) vn2, real, dimension( * ) auxv, real,dimension( ldf, * ) f, integer ldf)

SLAQPS computes a step of QR factorization with column pivoting of a real m-by-n matrix A by using BLAS level 3.

Purpose:

SLAQPS computes a step of QR factorization with column pivoting
of a real M-by-N matrix A by using Blas-3. It tries to factorize
NB columns from A starting from the row OFFSET+1, and updates all
of the matrix with Blas-3 xGEMM.

In some cases, due to catastrophic cancellations, it cannot
factorize NB columns. Hence, the actual number of factorized
columns is returned in KB.

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 A that have been factorized in
previous steps.

NB

NB is INTEGER
The number of columns to factorize.

KB

KB is INTEGER
The number of columns actually factorized.

A

A is REAL array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, block A(OFFSET+1:M,1:KB) is the triangular
factor obtained and block A(1:OFFSET,1:N) has been
accordingly pivoted, but no factorized.
The rest of the matrix, block A(OFFSET+1:M,KB+1:N) has
been updated.

LDA

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

JPVT

JPVT is INTEGER array, dimension (N)
JPVT(I) = K <==> Column K of the full matrix A has been
permuted into position I in AP.

TAU

TAU is REAL array, dimension (KB)
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.

AUXV

AUXV is REAL array, dimension (NB)
Auxiliary vector.

F

F is REAL array, dimension (LDF,NB)
Matrix F**T = L*Y**T*A.

LDF

LDF is INTEGER
The leading dimension of the array F. LDF >= max(1,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 zlaqps (integer m, integer n, integer offset, integer nb,integer kb, 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( * ) auxv, complex*16, dimension( ldf, * ) f, integer ldf)

ZLAQPS computes a step of QR factorization with column pivoting of a real m-by-n matrix A by using BLAS level 3.

Purpose:

ZLAQPS computes a step of QR factorization with column pivoting
of a complex M-by-N matrix A by using Blas-3. It tries to factorize
NB columns from A starting from the row OFFSET+1, and updates all
of the matrix with Blas-3 xGEMM.

In some cases, due to catastrophic cancellations, it cannot
factorize NB columns. Hence, the actual number of factorized
columns is returned in KB.

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 A that have been factorized in
previous steps.

NB

NB is INTEGER
The number of columns to factorize.

KB

KB is INTEGER
The number of columns actually factorized.

A

A is COMPLEX*16 array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, block A(OFFSET+1:M,1:KB) is the triangular
factor obtained and block A(1:OFFSET,1:N) has been
accordingly pivoted, but no factorized.
The rest of the matrix, block A(OFFSET+1:M,KB+1:N) has
been updated.

LDA

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

JPVT

JPVT is INTEGER array, dimension (N)
JPVT(I) = K <==> Column K of the full matrix A has been
permuted into position I in AP.

TAU

TAU is COMPLEX*16 array, dimension (KB)
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.

AUXV

AUXV is COMPLEX*16 array, dimension (NB)
Auxiliary vector.

F

F is COMPLEX*16 array, dimension (LDF,NB)
Matrix F**H = L * Y**H * A.

LDF

LDF is INTEGER
The leading dimension of the array F. LDF >= max(1,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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