LAPACK

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 is INTEGER


          The number of rows of the matrix A. M >= 0.



          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 is INTEGER


          The number of columns to factorize.



          KB is INTEGER


          The number of columns actually factorized.



          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 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 is INTEGER


          The number of rows of the matrix A. M >= 0.



          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 is INTEGER


          The number of columns to factorize.



          KB is INTEGER


          The number of columns actually factorized.



          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 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 is INTEGER


          The number of rows of the matrix A. M >= 0.



          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 is INTEGER


          The number of columns to factorize.



          KB is INTEGER


          The number of columns actually factorized.



          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 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, complex16, dimension( lda, ) a, integer lda, integer, dimension( * ) jpvt, complex16, dimension( ) tau, double precision, dimension( * ) vn1, double precision, dimension( * ) vn2, complex16, dimension( ) auxv, complex16, 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 is INTEGER


          The number of rows of the matrix A. M >= 0.



          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 is INTEGER


          The number of columns to factorize.



          KB is INTEGER


          The number of columns actually factorized.



          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 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:

References:

LAPACK Working Note 176

Author¶

Generated automatically by Doxygen for LAPACK from the source code.

Tue Jan 14 2025 16:19:47

Version 3.12.0

Source file:	laqps.3.en.gz (from liblapack-doc 3.12.1-1)
Source last updated:	2025-01-14T16:19:47Z
Converted to HTML:	2025-01-28T03:17:29Z