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

  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

  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

  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

Author

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