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NAME
     sqrsl - solve the linear system Ax = b for a general  matrix
     A,  which  has been QR- factored by xQRDC, and vectors b and
     x.

SYNOPSIS
     SUBROUTINE DQRSL (DA, LDA, N, K, DQRAUX, DY, DQY, DQTY,  DB,
               DRESID, DAB, JOB, INFO)

     SUBROUTINE SQRSL (SA, LDA, N, K, SQRAUX, SY, SQY, SQTY,  SB,
               SRESID, SAB, JOB, INFO)

     SUBROUTINE ZQRSL (ZA, LDA, N, K, ZQRAUX, CY, CQY, ZQTY,  ZB,
               ZRESID, ZAB, JOB, INFO)

     SUBROUTINE CQRSL (CA, LDA, N, K, CQRAUX, ZY, ZQY, CQTY,  CB,
               CRESID, CAB, JOB, INFO)



     #include <sunperf.h>

     void dqrsl(double *dx, int ldx, int n, int k, double *qraux,
               double  *dy,  double *qy, double *qty, double *db,
               double *rsd, double *xb, int job, int *info) ;

     void sqrsl(float *sx, int ldx, int n, int k,  float  *qraux,
               float *sy, float *qy, float *qty, float *sb, float
               *rsd, float *xb, int job, int *info) ;

     void zqrsl(doublecomplex *zx, int ldx, int n, int  k,  doub-
               lecomplex *qraux, doublecomplex *zy, doublecomplex
               *qy, doublecomplex *qty, doublecomplex *zb,  doub-
               lecomplex  *rsd,  doublecomplex  *xb, int job, int
               *info) ;

     void cqrsl(complex *cx, int  ldx,  int  n,  int  k,  complex
               *qraux,  complex  *cy,  complex *qy, complex *qty,
               complex *b, complex *rsd, complex  *xb,  int  job,
               int *info) ;

ARGUMENTS
     xA        Part of the QR factorization of matrix A  as  com-
               puted by xSRDC.

     LDA       Leading dimension of the array A as specified in a
               dimension or type statement.  LDA >= max(1,N).

     N         Number of rows  in  the  matrix  AK  where  AK  is
               described below.   N >= 0.

     K         Number of columns in the matrix  AK  where  AK  is
               described below.  K >= 0.

     xQRAUX    Auxiliary output from xQRDC.

     xY        Vector to be manipulated by xQRSL.

     xQY       On exit, QY contains Q * Y if its computation  has
               been requested in JOB; QY is not referenced if its
               computation is not requested.

     xQTY      On exit, QTY contains QT * Y  if  its  computation
               has  been  requested in JOB; QTY is not referenced
               if its computation is not requested.

     xB        On entry, the right-hand side vector b.  On  exit,
               the solution vector x.  B is not referenced if its
               computation is not requested.

     xRESID    On exit, RESID contains the least squares residual
               y  - AK * b if its computation has been requested.
               RESID also is the orthogonal projection of y  onto
               the  orthogonal  complement of the column space of
               AK.  RESID is not referenced if its computation is
               not requested.

     xAB       On exit, AB contains the least squares  approxima-
               tion AK * b if its computation has been requested.
               AB is the orthogonal  projection  of  y  onto  the
               column  space  of  x.  AB is not referenced if its
               computation is not requested.

     JOB       Integer in the form abcde; determines which opera-
               tion or operations the subroutine will perform:
                    a <> 0    compute QY
                    b, c, d, or e <> 0  compute QTY
                    c <> 0    compute B
                    d <> 0    compute RESID
                    e <> 0    compute AB

     INFO      On exit:
               INFO = 0  Subroutine completed normally.
               INFO * 0  Returns a value k if the computation  of
               B  has been requested and R is singular; the value
               of k is then the index of the first  zero  element
               of  R.  The matrix AK is constructed from the fac-
               tored orthogonal matrix  Q  and  upper  triangular
               matrix R from xQRDC.

SAMPLE PROGRAM
           PROGRAM TEST
           IMPLICIT NONE
     C
           INTEGER           IDOB, IDORSD, IDOXB, LDA, N, NCOLA, NOPIV, NROWA
           PARAMETER        (IDOB = 100)
           PARAMETER        (IDORSD = 10)
           PARAMETER        (IDOXB = 1)
           PARAMETER        (N = 3)
           PARAMETER        (LDA = N)
           PARAMETER        (NCOLA = 2)
           PARAMETER        (NOPIV = 0)
           PARAMETER        (NROWA = N)
     C
           DOUBLE PRECISION  A(LDA,NCOLA), B(NCOLA), NULL(N), QRAUX(N)
           DOUBLE PRECISION  RESID(N), WORK(N), Y(N)
           INTEGER           ICOL, INFO, IROW, JOB, JPIVOT
     C
           EXTERNAL          DQRDC, DQRSL
     C
     C      Initialize the array A to store the matrix A shown below.
     C      Initialize the array Y to store the vector y shown below.
     C
     C          1  1         1
     C      A = 1  0    y =  0
     C          0  1        -5
     C
           DATA A / 1.0D0, 1.0D0, 0.0D0, 1.0D0, 0.0D0, 1.0D0 /
           DATA Y / 1.0D0, 0.0D0, -5.0D0 /
     C
           PRINT 1000
           PRINT 1010, ((A(IROW,ICOL), ICOL = 1, NCOLA), IROW = 1, NROWA)
           PRINT 1020
           PRINT 1030, Y
           JOB = NOPIV
           CALL DQRDC (A, LDA, NROWA, NCOLA, QRAUX, JPIVOT, WORK, JOB)
           JOB = IDOB + IDORSD + IDOXB
           CALL DQRSL (A, LDA, NROWA, NCOLA, QRAUX, Y, NULL, NULL, B,
          $            RESID, NULL, JOB, INFO)
           IF (INFO .EQ. 0) THEN
             PRINT 1040
             PRINT 1050, B
             PRINT 1060
             PRINT 1050, RESID
           ELSE
             PRINT 1070
           END IF
     C
      1000 FORMAT (1X, 'A:')
      1010 FORMAT (2(3X, F4.1))
      1020 FORMAT (/1X, 'y:')
      1030 FORMAT (3X, F4.1)
      1040 FORMAT (/1X, 'Least squares solution:')
      1050 FORMAT (3X, F4.1)
      1060 FORMAT (/1X, 'Residual:')
      1070 FORMAT (1X, 'A is singular.')

     C
           END

SAMPLE OUTPUT
      A:
         1.0    1.0
         1.0    0.0
         0.0    1.0

      y:
         1.0
         0.0
        -5.0

      Least squares solution:
         2.0
        -3.0

      Residual:
         2.0
        -2.0
        -2.0

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