Provided by: liblapack-doc_3.12.0-3build1_all 
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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