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NAME
     schud - 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 *c, 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 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
           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

Партнёры:

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