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NAME
     dchex - compute the Cholesky decomposition  of  a  symmetric
     positive definite matrix A.

SYNOPSIS
     SUBROUTINE DCHEX (DA, LDA, N, K, L, DZ, LDZ, NZ, DCOS, DSIN,
               JOB)

     SUBROUTINE SCHEX (SA, LDA, N, K, L, SZ, LDZ, NZ, SCOS, SSIN,
               JOB)

     SUBROUTINE CCHEX (ZA, LDA, N, K, L, ZZ, LDZ, NZ, DCOS, DSIN,
               JOB)

     SUBROUTINE ZCHEX (CA, LDA, N, K, L, CZ, LDZ, NZ, SCOS, SSIN,
               JOB)



     #include <sunperf.h>

     void dchex(double *r, int ldr, int p, int k, int  l,  double
               *dz,  int  ldz, int nz, double *dc, double *s, int
               job) ;

     void schex(float *r, int ldr, int p, int  k,  int  l,  float
               *sz,  int  ldz,  int  nz, float *sc, float *s, int
               job) ;

     void cchex(complex *r, int ldr, int p, int k, int l, complex
               *cz,  int  ldz,  int nz, float *c, complex *s, int
               job) ;

     void zchex(doublecomplex *r, int ldr, int p, int k,  int  l,
               doublecomplex  *zz,  int  ldz, int nz, double *dc,
               doublecomplex *s, int job) ;

ARGUMENTS
     xA        On entry, the upper triangle of the matrix A.   On
               exit,  the  upper triangle of A contains the upper
               triangle of the updated factor.  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.

     K         First column to be permuted.  1 <= K <= L.

     L         Last column  to  be  permuted;  must  be  strictly
               greater than K.  K <= L <= N.

     xZ        Array of vectors into which the  transformation  U
               is multiplied.  Not used if NZ = 0.

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

     NZ        Number of columns in the matrix Z.  NZ >= 0.

     xCOS      Cosines of the transforming rotations.

     xSIN      Sines of the transforming rotations.

     JOB       Determines the type of permutation:
                    1    right circular shift
                    2    left circular shift

SAMPLE PROGRAM
           PROGRAM TEST
           IMPLICIT NONE
     C
           INTEGER           ISHFRT, LDA, N, NULL, NZ
           PARAMETER        (ISHFRT = 1)
           PARAMETER        (N = 4)
           PARAMETER        (LDA = N)
           PARAMETER        (NULL = 1)
           PARAMETER        (NZ = 0)
     C
           DOUBLE PRECISION  A(LDA,N), ANULL, C(N), S(N), WORK(N)
           INTEGER           ICOL, INFO, IPIVOT(N), IROW, JOB, K
     C
           EXTERNAL          DCHDC, DCHEX
     C
     C     Initialize the arrays A and Z to store the matrices A and Z
     C     shown below and initialize X and Y to store the vectors x and y
     C     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
           DO 100, IROW = 1, N
             PRINT 1010, (A(ICOL,IROW), ICOL = 1, IROW),
          $              (A(IROW,ICOL), ICOL = IROW + 1, N)
       100 CONTINUE
           PRINT 1020
           PRINT 1010, ((A(IROW,ICOL), ICOL = 1, N), IROW = 1, N)
           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)
             K = 1
             ANULL = 0.0D0
             JOB = ISHFRT
             CALL DCHEX (A, LDA, N, K, N, ANULL, NULL, NZ, C, S, JOB)
             PRINT 1070
             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)
             PRINT 1080
             PRINT 1090, (C(IROW), S(IROW), IROW = 1, N)
           ELSE
             PRINT 1100
           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, 'Updated Cholesky factor:')
      1080 FORMAT (/1X, 'Cosine', 3X, '  Sine')
      1090 FORMAT (1X, F6.3, 3X, F6.3)
      1100 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
      Updated Cholesky factor:
          2.000     0.500     1.000     1.500
                   -1.936    -1.291    -0.645
                             -1.155    -0.577
                                       -1.000

      Cosine     Sine
       0.645    0.764
       0.488    0.873
       0.250    0.968
       0.000    2.000

Партнёры:

Хостинг: