laqp2(3)

NAME
laqp2 - laqp2: step of geqp3

SYNOPSIS

  Functions
subroutine claqp2 (m, n, offset, a, lda, jpvt, tau, vn1, vn2, work)
CLAQP2 computes a QR factorization with column pivoting of the matrix block.
subroutine dlaqp2 (m, n, offset, a, lda, jpvt, tau, vn1, vn2, work)
DLAQP2 computes a QR factorization with column pivoting of the matrix block.
subroutine slaqp2 (m, n, offset, a, lda, jpvt, tau, vn1, vn2, work)
SLAQP2 computes a QR factorization with column pivoting of the matrix block.
subroutine zlaqp2 (m, n, offset, a, lda, jpvt, tau, vn1, vn2, work)
ZLAQP2 computes a QR factorization with column pivoting of the matrix block.

Detailed Description

Function Documentation

  subroutine claqp2 (integer m, integer n, integer offset, complex, dimension( lda, * ) a, integer lda, integer, dimension( * ) jpvt, complex, dimension( * ) tau, real, dimension( * ) vn1, real, dimension( * ) vn2, complex, dimension( * ) work)

CLAQP2 computes a QR factorization with column pivoting of the matrix block.

Purpose:

     CLAQP2 computes a QR factorization with column pivoting of
     the block A(OFFSET+1:M,1:N).
     The 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 the matrix A that must be pivoted
              but no factorized. OFFSET >= 0.

    A

              A is COMPLEX array, dimension (LDA,N)
              On entry, the M-by-N matrix A.
              On exit, the upper triangle of block A(OFFSET+1:M,1:N) is
              the triangular factor obtained; the elements in block
              A(OFFSET+1:M,1:N) below the diagonal, together with the
              array TAU, represent the orthogonal matrix Q as a product of
              elementary reflectors. Block A(1:OFFSET,1:N) has been
              accordingly pivoted, but no factorized.

    LDA

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

    JPVT

              JPVT is INTEGER array, dimension (N)
              On entry, if JPVT(i) .ne. 0, the i-th column of A is permuted
              to the front of A*P (a leading column); if JPVT(i) = 0,
              the i-th column of A is a free column.
              On exit, if JPVT(i) = k, then the i-th column of A*P
              was the k-th column of A.

    TAU

              TAU is COMPLEX array, dimension (min(M,N))
              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.

    WORK

              WORK is COMPLEX array, dimension (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 147 of file claqp2.f.

  subroutine dlaqp2 (integer m, integer n, integer offset, 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( * ) work)

DLAQP2 computes a QR factorization with column pivoting of the matrix block.

Purpose:

     DLAQP2 computes a QR factorization with column pivoting of
     the block A(OFFSET+1:M,1:N).
     The 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 the matrix A that must be pivoted
              but no factorized. OFFSET >= 0.

    A

              A is DOUBLE PRECISION array, dimension (LDA,N)
              On entry, the M-by-N matrix A.
              On exit, the upper triangle of block A(OFFSET+1:M,1:N) is
              the triangular factor obtained; the elements in block
              A(OFFSET+1:M,1:N) below the diagonal, together with the
              array TAU, represent the orthogonal matrix Q as a product of
              elementary reflectors. Block A(1:OFFSET,1:N) has been
              accordingly pivoted, but no factorized.

    LDA

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

    JPVT

              JPVT is INTEGER array, dimension (N)
              On entry, if JPVT(i) .ne. 0, the i-th column of A is permuted
              to the front of A*P (a leading column); if JPVT(i) = 0,
              the i-th column of A is a free column.
              On exit, if JPVT(i) = k, then the i-th column of A*P
              was the k-th column of A.

    TAU

              TAU is DOUBLE PRECISION array, dimension (min(M,N))
              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.

    WORK

              WORK is DOUBLE PRECISION array, dimension (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 147 of file dlaqp2.f.

  subroutine slaqp2 (integer m, integer n, integer offset, real, dimension( lda, * ) a, integer lda, integer, dimension( * ) jpvt, real, dimension( * ) tau, real, dimension( * ) vn1, real, dimension( * ) vn2, real, dimension( * ) work)

SLAQP2 computes a QR factorization with column pivoting of the matrix block.

Purpose:

     SLAQP2 computes a QR factorization with column pivoting of
     the block A(OFFSET+1:M,1:N).
     The 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 the matrix A that must be pivoted
              but no factorized. OFFSET >= 0.

    A

              A is REAL array, dimension (LDA,N)
              On entry, the M-by-N matrix A.
              On exit, the upper triangle of block A(OFFSET+1:M,1:N) is
              the triangular factor obtained; the elements in block
              A(OFFSET+1:M,1:N) below the diagonal, together with the
              array TAU, represent the orthogonal matrix Q as a product of
              elementary reflectors. Block A(1:OFFSET,1:N) has been
              accordingly pivoted, but no factorized.

    LDA

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

    JPVT

              JPVT is INTEGER array, dimension (N)
              On entry, if JPVT(i) .ne. 0, the i-th column of A is permuted
              to the front of A*P (a leading column); if JPVT(i) = 0,
              the i-th column of A is a free column.
              On exit, if JPVT(i) = k, then the i-th column of A*P
              was the k-th column of A.

    TAU

              TAU is REAL array, dimension (min(M,N))
              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.

    WORK

              WORK is REAL array, dimension (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 147 of file slaqp2.f.

  subroutine zlaqp2 (integer m, integer n, integer offset, 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( * ) work)

ZLAQP2 computes a QR factorization with column pivoting of the matrix block.

Purpose:

     ZLAQP2 computes a QR factorization with column pivoting of
     the block A(OFFSET+1:M,1:N).
     The 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 the matrix A that must be pivoted
              but no factorized. OFFSET >= 0.

    A

              A is COMPLEX*16 array, dimension (LDA,N)
              On entry, the M-by-N matrix A.
              On exit, the upper triangle of block A(OFFSET+1:M,1:N) is
              the triangular factor obtained; the elements in block
              A(OFFSET+1:M,1:N) below the diagonal, together with the
              array TAU, represent the orthogonal matrix Q as a product of
              elementary reflectors. Block A(1:OFFSET,1:N) has been
              accordingly pivoted, but no factorized.

    LDA

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

    JPVT

              JPVT is INTEGER array, dimension (N)
              On entry, if JPVT(i) .ne. 0, the i-th column of A is permuted
              to the front of A*P (a leading column); if JPVT(i) = 0,
              the i-th column of A is a free column.
              On exit, if JPVT(i) = k, then the i-th column of A*P
              was the k-th column of A.

    TAU

              TAU is COMPLEX*16 array, dimension (min(M,N))
              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.

    WORK

              WORK is COMPLEX*16 array, dimension (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 147 of file zlaqp2.f.

Author

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