zchdd(3P)

NAME

zchdd - downdate an augmented Cholesky decomposition of the triangular part of an augmented QR decomposition.

SYNOPSIS

SUBROUTINE DCHDD (DA, LDA, N, DX, DZ, LDZ, NZ, DY, DRHO, DCOS, DSIN, INFO)

SUBROUTINE SCHDD (SA, LDA, N, SX, SZ, LDZ, NZ, SY, SRHO, SCOS, SSIN, INFO)

SUBROUTINE ZCHDD (ZA, LDA, N, ZX, ZZ, LDZ, NZ, ZY, DRHO, DCOS, DSIN, INFO)

SUBROUTINE CCHDD (CA, LDA, N, CX, CZ, LDZ, NZ, CY, SRHO, SCOS, SSIN, INFO)

#include <sunperf.h>

void dchdd(double ∗r, int ldr, int p, double ∗dx, double ∗dz, int ldz, int nz, double ∗dy, double ∗drho, double ∗dc, double ∗s, int ∗info)

void schdd(float ∗r, int ldr, int p, float ∗sx, float ∗z, int ldz, int nz, float ∗sy, float ∗srho, float ∗sc, float ∗s, int ∗info)

void zchdd(doublecomplex ∗r, int ldr, int p, doublecomplex ∗x, doublecomplex ∗zz, int ldz, int nz, doublecomplex ∗y, doublecomplex ∗crho, doublecomplex ∗zc, doublecomplex ∗s, int ∗info)

void cchdd(complex ∗r, int ldr, int p, complex ∗cx, complex ∗cz, int ldz, int nz, complex ∗cy, complex ∗rho, complex ∗cc, complex ∗s, int ∗info) ;

ARGUMENTS

xAOn entry, the upper triangular matrix A. On exit, A has been downdated. The strict lower triangle of A is not referenced.

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

NOrder of the matrix A. N >= 0.

xXRow to be added to A.

xZVectors to be downdated with A.

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

NZNumber of vectors to be downdated with A. NZ >= 0. If NZ = 0 then Z, Y, and RHO are not used.

xYScalars for downdating the vectors in Z.

xRHOOn entry, the norms of the residual vectors that are to be downdated. On exit, RHO has been downdated. If RHO(i) is negative on entry then it is not changed.

xCOSCosines of the transforming rotations.

xSINSines of the transforming rotations.

INFOOn exit:
INFO = 0Subroutine completed normally.
INFO = -1A could not be downdated; all values are left unchanged.
INFO = 1Some RHOs could not be downdated; all RHOs that could not be downdated are changed to -1.

SAMPLE PROGRAM

      PROGRAM TEST
      IMPLICIT NONE
C
      INTEGER           LDA, N, NOPIV, NZ
      PARAMETER        (N = 4)
      PARAMETER        (LDA = N)
      PARAMETER        (NOPIV = 0)
      PARAMETER        (NZ = 0)
C
      DOUBLE PRECISION A(LDA,N), ANULL, C(N), S(N), WORK(N), X(N)
      INTEGER           I, INFO, IPIVOT(N), J, JOB, NULL
C
      EXTERNAL          DCHDC, DCHDD
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, I = 1, N
        PRINT 1010, (A(J,I), J = 1, I), (A(I,J), J = I + 1, N)
100 CONTINUE
      PRINT 1020
      PRINT 1010, ((A(I,J), J = 1, N), I = 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 DCHDD (A, LDA, N, X, ANULL, NULL, NZ, ANULL, ANULL, C, S,
     $              INFO)
        IF (INFO .EQ. 0) THEN
          PRINT 1070
          PRINT 1080, (C(I), S(I), I = 1, N)
        ELSE
          PRINT 1090
        END IF
      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, ’Cosine’, 3X, ’ Sine’)
1080 FORMAT (1X, F6.3, 3X, F6.3)
1090 FORMAT (/1X, ’A cannot be downdated.’)
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

Cosine     Sine
1.000    0.000
1.000    0.000
1.000    0.000
1.000    0.000