SLATEC Routines --- SQRDC ---

*DECK SQRDC
      SUBROUTINE SQRDC (X, LDX, N, P, QRAUX, JPVT, WORK, JOB)
C***BEGIN PROLOGUE  SQRDC
C***PURPOSE  Use Householder transformations to compute the QR
C            factorization of an N by P matrix.  Column pivoting is a
C            users option.
C***LIBRARY   SLATEC (LINPACK)
C***CATEGORY  D5
C***TYPE      SINGLE PRECISION (SQRDC-S, DQRDC-D, CQRDC-C)
C***KEYWORDS  LINEAR ALGEBRA, LINPACK, MATRIX, ORTHOGONAL TRIANGULAR,
C             QR DECOMPOSITION
C***AUTHOR  Stewart, G. W., (U. of Maryland)
C***DESCRIPTION
C
C     SQRDC uses Householder transformations to compute the QR
C     factorization of an N by P matrix X.  Column pivoting
C     based on the 2-norms of the reduced columns may be
C     performed at the user's option.
C
C     On Entry
C
C        X       REAL(LDX,P), where LDX .GE. N.
C                X contains the matrix whose decomposition is to be
C                computed.
C
C        LDX     INTEGER.
C                LDX is the leading dimension of the array X.
C
C        N       INTEGER.
C                N is the number of rows of the matrix X.
C
C        P       INTEGER.
C                P is the number of columns of the matrix X.
C
C        JPVT    INTEGER(P).
C                JPVT contains integers that control the selection
C                of the pivot columns.  The K-th column X(K) of X
C                is placed in one of three classes according to the
C                value of JPVT(K).
C
C                   If JPVT(K) .GT. 0, then X(K) is an initial
C                                      column.
C
C                   If JPVT(K) .EQ. 0, then X(K) is a free column.
C
C                   If JPVT(K) .LT. 0, then X(K) is a final column.
C
C                Before the decomposition is computed, initial columns
C                are moved to the beginning of the array X and final
C                columns to the end.  Both initial and final columns
C                are frozen in place during the computation and only
C                free columns are moved.  At the K-th stage of the
C                reduction, if X(K) is occupied by a free column,
C                it is interchanged with the free column of largest
C                reduced norm.  JPVT is not referenced if
C                JOB .EQ. 0.
C
C        WORK    REAL(P).
C                WORK is a work array.  WORK is not referenced if
C                JOB .EQ. 0.
C
C        JOB     INTEGER.
C                JOB is an integer that initiates column pivoting.
C                If JOB .EQ. 0, no pivoting is done.
C                If JOB .NE. 0, pivoting is done.
C
C     On Return
C
C        X       X contains in its upper triangle the upper
C                triangular matrix R of the QR factorization.
C                Below its diagonal X contains information from
C                which the orthogonal part of the decomposition
C                can be recovered.  Note that if pivoting has
C                been requested, the decomposition is not that
C                of the original matrix X but that of X
C                with its columns permuted as described by JPVT.
C
C        QRAUX   REAL(P).
C                QRAUX contains further information required to recover
C                the orthogonal part of the decomposition.
C
C        JPVT    JPVT(K) contains the index of the column of the
C                original matrix that has been interchanged into
C                the K-th column, if pivoting was requested.
C
C***REFERENCES  J. J. Dongarra, J. R. Bunch, C. B. Moler, and G. W.
C                 Stewart, LINPACK Users' Guide, SIAM, 1979.
C***ROUTINES CALLED  SAXPY, SDOT, SNRM2, SSCAL, SSWAP
C***REVISION HISTORY  (YYMMDD)
C   780814  DATE WRITTEN
C   890531  Changed all specific intrinsics to generic.  (WRB)
C   890831  Modified array declarations.  (WRB)
C   890831  REVISION DATE from Version 3.2
C   891214  Prologue converted to Version 4.0 format.  (BAB)
C   900326  Removed duplicate information from DESCRIPTION section.
C           (WRB)
C   920501  Reformatted the REFERENCES section.  (WRB)
C***END PROLOGUE  SQRDC