Scroll to navigation

laqp2(3) LAPACK 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

Generated automatically by Doxygen for LAPACK from the source code.

Tue Jan 28 2025 00:54:31 Version 3.12.0