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cchud (3)
  • >> cchud (3) ( Solaris man: Библиотечные вызовы )
  • 
    NAME
         cchud - update an augmented Cholesky  decomposition  of  the
         triangular part of an augmented QR decomposition.
    
    SYNOPSIS
         SUBROUTINE DCHUD (DA, LDA, N, DX, DZ,  LDZ,  NZ,  DY,  DRHO,
                   DCOS, DSIN)
    
         SUBROUTINE SCHUD (SA, LDA, N, SX, SZ,  LDZ,  NZ,  SY,  SRHO,
                   SCOS, SSIN)
    
         SUBROUTINE ZCHUD (ZA, LDA, N, ZX, ZZ,  LDZ,  NZ,  ZY,  DRHO,
                   DCOS, DSIN)
    
         SUBROUTINE CCHUD (CA, LDA, N, CX, CZ,  LDZ,  NZ,  CY,  SRHO,
                   SCOS, SSIN)
    
    
    
         #include <sunperf.h>
    
         void dchud (double *r, int ldr, int p,  double  *dx,  double
                   *dz,  int  ldz,  int nz, double *dy, double *drho,
                   double *dc, double *s);
    
         void schud (float *r, int ldr, int p, float *sx,  float  *z,
                   int  ldz,  int  nz,  float *sy, float *srho, float
                   *sc, float *s);
    
         void zchud (doublecomplex *r, int ldr, int p,  doublecomplex
                   *zx,  doublecomplex  *zz,  int  ldz, int nz, doub-
                   lecomplex *zy, double  *drho,  double  *dc,  doub-
                   lecomplex *s);
    
         void cchud (complex *r, int ldr, int p, complex *cx, complex
                   *cz,  int  ldz,  int  nz, complex *cy, float *rho,
                   float *sc, complex *s);
    
    ARGUMENTS
         xA        On entry, the upper triangular matrix A.  On exit,
                   A  has been updated.  The strict lower triangle of
                   A is not referenced.
    
         LDA       Leading dimension of the array A as specified in a
                   dimension or type statement.  LDA >= max(1,N).
    
         N         Order of the matrix A.  N >= 0.
    
         xX        Row to be added to A.
    
         xZ        Vectors to be updated with A.
    
         LDZ       Leading dimension on the array Z as specified in a
                   dimension or type statement.  LDZ >= max(1,N).
    
         NZ        Number of vectors to be updated with A.  NZ >=  0.
                   If NZ = 0 then Z, Y, and RHO are not used.
    
         xY        Scalars for updating the vectors in Z.
    
         xRHO      On entry, the norms of the residual  vectors  that
                   are to be updated.  On exit, RHO has been updated.
                   If RHO(i) is negative on  entry  then  it  is  not
                   changed.
    
         xCOS      Cosines of the transforming rotations.
    
         xSIN      Sines of the transforming rotations.
    
    SAMPLE PROGRAM
               PROGRAM TEST
               IMPLICIT NONE
         C
               INTEGER           LDA, N, NOPIV, NZ
               PARAMETER        (N = 4)
               PARAMETER        (NOPIV = 0)
               PARAMETER        (NZ = 0)
               PARAMETER        (LDA = N)
         C
               DOUBLE PRECISION  A(LDA,N), ANULL, C(N), S(N),
              $                  WORK(N), X(N)
               INTEGER           I, ICOL, INFO, IPIVOT(N),
              $                  IROW, JOB, NULL
         C
         C     Initialize the arrays A and Z to store the
         C     matrices A and Z shown below and initialize
         C     X and Y to store the vectors x and y shown below.
         C
         C         4  3  2  1        1
         C     A = 3  4  3  2    x = 1
         C         2  3  4  3        1
         C         1  2  3  4        1
         C
               DATA A / 4.0D0, 3*8D8, 3.0D0, 4.0D0, 2*8D8,
              $         2.0D0, 3.0D0, 4.0D0, 8D8, 1.0D0,
              $         2.0D0, 3.0D0, 4.0D0 /
         C
               PRINT 1000
               PRINT 1010, A(1,1), A(1,2), A(1,3), A(1,4)
               PRINT 1010, A(1,2), A(2,2), A(2,3), A(2,4)
               PRINT 1010, A(1,3), A(2,3), A(3,3), A(3,4)
               PRINT 1010, (A(IROW,4), IROW = 1, N)
               PRINT 1020
               PRINT 1010, ((A(IROW,ICOL), ICOL = 1, N), IROW = 1, N)
               JOB = NOPIV
               CALL DCHDC (A, LDA, N, WORK, IPIVOT, JOB, INFO)
               IF (INFO .EQ. N) THEN
                 PRINT 1030
                 PRINT 1010, A(1,1), A(1,2), A(1,3), A(1,4)
                 PRINT 1040,         A(2,2), A(2,3), A(2,4)
                 PRINT 1050,                 A(3,3), A(3,4)
                 PRINT 1060,                         A(4,4)
                 ANULL = 0.0D0
                 NULL = 1
                 CALL DCHUD (A, LDA, N, X, ANULL, NULL, NZ,
              $              ANULL, ANULL, C, S)
                 PRINT 1070
                 PRINT 1080, (C(I), S(I), I = 1, N)
               ELSE
                 PRINT 1090
               END IF
         C
          1000 FORMAT (1X, 'A in full form:')
          1010 FORMAT (4(3X, F7.3))
          1020 FORMAT (/1X, 'A in symmetric form ',
              $        '(* in unused entries)')
          1030 FORMAT (/1X, 'Upper Cholesky factor:')
          1040 FORMAT (10X, 3(3X, F7.3))
          1050 FORMAT (20X, 2(3X, F7.3))
          1060 FORMAT (30X, 1(3X, F7.3))
          1070 FORMAT (1X, 'Cosine', 3X, '  Sine')
          1080 FORMAT (1X, F6.3, 3X, F6.3)
          1090 FORMAT (/1X, 'A is not positive definite.')
         C
               END
    
    SAMPLE OUTPUT
          A in full form:
              4.000     3.000     2.000     1.000
              3.000     4.000     3.000     2.000
              2.000     3.000     4.000     3.000
              1.000     2.000     3.000     4.000
    
          A in symmetric form (* in unused entries)
              4.000     3.000     2.000     1.000
            *******     4.000     3.000     2.000
            *******   *******     4.000     3.000
            *******   *******   *******     4.000
    
          Upper Cholesky factor:
              2.000     1.500     1.000     0.500
                        1.323     1.134     0.945
                                  1.309     1.091
                                            1.291
          Cosine     Sine
           1.000    0.000
           1.000    0.000
           1.000    0.000
           1.000    0.000
    
    
    
    


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