Solution to a Linear System in a Symmetric Matrix in Packed Storage (Simple Driver)

Calling Sequence

CALL DSPSV	(UPLO, N, NRHS, DA, IPIVOT, DB, LDB, INFO)
CALL SSPSV	(UPLO, N, NRHS, SA, IPIVOT, SB, LDB, INFO)
CALL ZSPSV	(UPLO, N, NRHS, ZA, IPIVOT, ZB, LDB, INFO)
CALL CSPSV	(UPLO, N, NRHS, CA, IPIVOT, CB, LDB, INFO)
void dspsv	(char uplo, int n, int nrhs, double *da, int *ipivot, double *db, int ldb, int *info)
void sspsv	(char uplo, int n, int nrhs, float *sa, int *ipivot, float *sb, int ldb, int *info)
void zspsv	(char uplo, int n, int nrhs, doublecomplex *za, int *ipivot, doublecomplex *zb, int ldb, int *info)
void cspsv	(char uplo, int n, int nrhs, complex *ca, int *ipivot, complex *cb, int ldb, int *info)

Arguments

UPLO	Indicates whether xA contains the upper or lower triangle of the matrix. The legal values for UPLO are listed below. Any values not listed below are illegal.
	'U' or 'u'	xA contains the upper triangle.
	'L' or 'l'	xA contains the lower triangle.
N	Order of the matrix A. N 0.
NRHS	Number of right-hand sides, equal to the number of columns of the matrix B. NRHS 0.
xA	On entry, the upper or lower triangle of the matrix A. The dimension of xA is (N × N + N) / 2. On exit, the UDU or LDL factorization of the matrix A as computed by xSPTRF.
IPIVOT	On exit, pivot indices as computed by xSPTRF.
xB	On entry, the N×NRHS right-hand side matrix B. On exit, the N×NRHS solution matrix X.
LDB	Leading dimension of the array B as specified in a dimension or type statement. LDB max(1, N).
INFO	On exit:
	INFO = 0	Subroutine completed normally.
	INFO < 0	The ith argument, where i = |INFO|, had an illegal value.
	INFO > 0	D(i,i), where i = INFO, is exactly zero and D is therefore singular. The factorization has been completed, but the solution could not be computed.

Sample Program

PROGRAM TEST

IMPLICIT NONE

C

INTEGER LDA, LDB, N, NRHS

PARAMETER (N = 4)

PARAMETER (LDA = (N * (N + 1)) / 2)

PARAMETER (LDB = N)

PARAMETER (NRHS = 1)

C

DOUBLE PRECISION A(LDA), B(LDB,NRHS)

INTEGER INFO, IPIVOT(N)

C

EXTERNAL DSPSV

C

C Initialize the array A to store in packed symmetric form

C the 4x4 symmetric positive definite matrix A shown below.

C Initialize the array B to store the right hand side

C vector b shown below.

C

C 2 -1 0 0 6

C A = -1 2 -1 0 b = 12

C 0 -1 2 -1 12

C 0 0 -1 2 6

C

DATA A / 2.0D0, -1.0D0, 2.0D0, 0.0D0, -1.0D0, 2.0D0,

$ 0.0D0, 0.0D0, -1.0D0, 2.0D0 /

DATA B / 6.0D0, 1.2D1, 1.2D1, 6.0D0 /

C

C Print the initial values of the arrays.

C

PRINT 1000

PRINT 1010, A(1), A(2), A(4), A(7)

PRINT 1010, A(2), A(3), A(5), A(8)

PRINT 1010, A(4), A(5), A(6), A(9)

PRINT 1010, A(7), A(8), A(9), A(10)

PRINT 1020

PRINT 1030, B

C

C Solve Ax=b and print the solution.

C

CALL DSPSV ('UPPER TRIANGLE OF A STORED', N, NRHS, A,

$ IPIVOT, B, LDB, INFO)

IF (INFO .NE. 0) THEN

PRINT 1040, INFO

STOP 1

END IF

PRINT 1050

PRINT 1030, B

C

1000 FORMAT (1X, 'A:')

1010 FORMAT (4(3X, F6.3))

1020 FORMAT (/1X, 'b:')

1030 FORMAT (1X, F6.3)

1040 FORMAT (1X, 'Error solving Ax=b, INFO = ', I5)

1050 FORMAT (/1X, 'x:')

C

END

Sample Output

A:
2.000 -1.000 0.000 0.000
-1.000 2.000 -1.000 0.000
0.000 -1.000 2.000 -1.000
0.000 0.000 -1.000 2.000
b:
6.000
12.000
12.000
6.000
x:
18.000
30.000
30.000
18.000