SQRDC(3F)

NAME
     SQRDC   - SQRDC uses Householder transformations to compute the QR
     factorization of an N by P matrix X.  Column pivoting based on the 2-
     norms of the reduced columns may be performed at the user's option.


SYNOPSYS
      SUBROUTINE SQRDC(X,LDX,N,P,QRAUX,JPVT,WORK,JOB)

DESCRIPTION
     On Entry

     X REAL(LDX,P), where LDX .GE. N.
        X contains the matrix whose decomposition is to be
        computed.

     LDX INTEGER.
        LDX is the leading dimension of the array X.

     N INTEGER.
        N is the number of rows of the matrix X.

     P INTEGER.
        P is the number of columns of the matrix X.

     JPVT INTEGER(P).
        JPVT contains integers that control the selection
        of the pivot columns.  The K-th column X(K) of X
        is placed in one of three classes according to the
        value of JPVT(K).
        If JPVT(K) .GT. 0, then X(K) is an initial
        column.
        If JPVT(K) .EQ. 0, then X(K) is a free column.
        If JPVT(K) .LT. 0, then X(K) is a final column.
        Before the decomposition is computed, initial columns
        are moved to the beginning of the array X and final
        columns to the end.  Both initial and final columns
        are frozen in place during the computation and only
        free columns are moved.  At the K-th stage of the
        reduction, if X(K) is occupied by a free column,
        it is interchanged with the free column of largest
        reduced norm.  JPVT is not referenced if
        JOB .EQ. 0.

     WORK REAL(P).
        WORK is a work array.  WORK is not referenced if
        JOB .EQ. 0.

     JOB INTEGER.
        JOB is an integer that initiates column pivoting.
        If JOB .EQ. 0, no pivoting is done.
        If JOB .NE. 0, pivoting is done.  On Return
     X X contains in its upper triangle the upper
        triangular matrix R of the QR factorization.
        Below its diagonal X contains information from
        which the orthogonal part of the decomposition
        can be recovered.  Note that if pivoting has
        been requested, the decomposition is not that
        of the original matrix X but that of X
        with its columns permuted as described by JPVT.

     QRAUX REAL(P).
        QRAUX contains further information required to recover
        the orthogonal part of the decomposition.

     JPVT JPVT(K) contains the index of the column of the
        original matrix that has been interchanged into
        the K-th column, if pivoting was requested.  LINPACK.  This version
     dated 08/14/78 .  G. W. Stewart, University of Maryland, Argonne National
     Lab.

     SQRDC uses the following functions and subprograms. BLAS
     SAXPY,SDOT,SSCAL,SSWAP,SNRM2 Fortran ABS,AMAX1,MIN0,SQRT