laqps(3)

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

Definition at line 176 of file claqps.f.

  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

Definition at line 175 of file dlaqps.f.

  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

Definition at line 176 of file slaqps.f.

  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

Definition at line 175 of file zlaqps.f.

Author

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