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cqrsl (3)
  • >> cqrsl (3) ( Solaris man: Библиотечные вызовы )
  • 
    NAME
         cqrsl - 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 cqrsl(complex *cx, int  ldx,  int  n,  int  k,  complex
                   *qraux,  complex  *cy,  complex *qy, complex *qty,
                   complex *cb, complex *rsd, complex *xb,  int  job,
                   int *info) ;
    
         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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