claqp2(3S)

NAME
     CLAQP2 - compute a QR factorization with column pivoting of the block
     A(OFFSET+1:M,1:N)

SYNOPSIS
     SUBROUTINE CLAQP2( M, N, OFFSET, A, LDA, JPVT, TAU, VN1, VN2, WORK )

         INTEGER        LDA, M, N, OFFSET

         INTEGER        JPVT( * )

         REAL           VN1( * ), VN2( * )

         COMPLEX        A( LDA, * ), TAU( * ), WORK( * )

IMPLEMENTATION
     These routines are part of the SCSL Scientific Library and can be loaded
     using either the -lscs or the -lscs_mp option.  The -lscs_mp option
     directs the linker to use the multi-processor version of the library.

     When linking to SCSL with -lscs or -lscs_mp, the default integer size is
     4 bytes (32 bits). Another version of SCSL is available in which integers
     are 8 bytes (64 bits).  This version allows the user access to larger
     memory sizes and helps when porting legacy Cray codes.  It can be loaded
     by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
     only one of the two versions; 4-byte integer and 8-byte integer library
     calls cannot be mixed.

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.


ARGUMENTS
     M       (input) INTEGER
             The number of rows of the matrix A. M >= 0.

     N       (input) INTEGER
             The number of columns of the matrix A. N >= 0.

     OFFSET  (input) INTEGER
             The number of rows of the matrix A that must be pivoted but no
             factorized. OFFSET >= 0.

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

     JPVT    (input/output) 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     (output) COMPLEX array, dimension (min(M,N))
             The scalar factors of the elementary reflectors.

     VN1     (input/output) REAL array, dimension (N)
             The vector with the partial column norms.

     VN2     (input/output) REAL array, dimension (N)
             The vector with the exact column norms.

     WORK    (workspace) COMPLEX array, dimension (N)

FURTHER DETAILS
     Based on contributions by
       G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
       X. Sun, Computer Science Dept., Duke University, USA


SEE ALSO
     INTRO_LAPACK(3S), INTRO_SCSL(3S)

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