Update an Augmented Cholesky Decomposition with Permutations

Calling Sequence

CALL DCHEX	(DA, LDA, N, K, L, DZ, LDZ, NZ, DCOS, DSIN, JOB)
CALL SCHEX	(SA, LDA, N, K, L, SZ, LDZ, NZ, SCOS, SSIN, JOB)
CALL CCHEX	(ZA, LDA, N, K, L, ZZ, LDZ, NZ, DCOS, ZSIN, JOB)
CALL ZCHEX	(CA, LDA, N, K, L, CZ, LDZ, NZ, SCOS, CSIN, JOB)
void dchex	(double *da, int lda, int n, int k, int l, double *dz, int ldz, int nz, double *dcos, double *dsin, int job)
void schex	(float *da, int lda, int n, int k, int l, float *sz, int ldz, int nz, float *scos, float *ssin, int job)
void zchex	(doublecomplex *za, int lda, int n, int k, int l, doublecomplex *zz, int ldz, int nz, double *dcos, doublecomplex *zsin, int job)
void cchex	(complex*r, int lda, int n, int k, int l, complex *cz, int ldz, int nz, float *scos, complex *csin, 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

C 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

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