laqps(3) LAPACK laqps(3)

laqps - laqps: step of geqp3


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.

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

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

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

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

Generated automatically by Doxygen for LAPACK from the source code.

Fri Aug 9 2024 02:33:22 Version 3.12.0