Solution to a Linear System in a General Matrix (Simple Driver)

Calling Sequence

CALL DGESV	(N, NRHS, DA, LDA, IPIVOT, DB, LDB, INFO)
CALL SGESV	(N, NRHS, SA, LDA, IPIVOT, SB, LDB, INFO)
CALL ZGESV	(N, NRHS, ZA, LDA, IPIVOT, ZB, LDB, INFO)
CALL CGESV	(N, NRHS, CA, LDA, IPIVOT, CB, LDB, INFO)
void dgesv	(int n, int nrhs, double *da, int lda, int *ipivot, double *db, int ldb, int *info)
void sgesv	(int n, int nrhs, float *sa, int lda, int *ipivot, float *sb, int ldb, int *info)
void zgesv	(int n, int nrhs, doublecomplex *za, int lda, int *ipivot, doublecomplex *zb, int ldb, int *info)
void cgesv	(int n, int nrhs, complex *ca, int lda, int *ipivot, complex *cb, int ldb, int *info)

Arguments

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 N×N matrix A. On exit, the LU factorization of A as computed by xGETRF.
LDA	Leading dimension of the array A as specified in a dimension or type statement. LDA max(1, N).
IPIVOT	On exit, pivot indices as computed by xGETRF.
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	U(i,i), where i = INFO, is exactly zero and U is therefore singular. The LU factorization has been completed, but the solution could not be computed.

Sample Program

PROGRAM TEST

IMPLICIT NONE

C

INTEGER LDA, LDB, M, N, NRHS

PARAMETER (M = 3)

PARAMETER (N = 3)

PARAMETER (NRHS = 1)

PARAMETER (LDA = M)

PARAMETER (LDB = LDA)

C

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

INTEGER ICOL, INFO, IROW, IPIVOT(N)

C

EXTERNAL DGESV

C

C Initialize the array A to store the coefficient matrix A

C shown below. Initialize the array B to store the right

C hand vector b shown below.

C

C 1 2 2 15

C A = 2 1 2 b = 15

C 2 2 1 15

C

DATA A / 1.0D0, 3*2.0D0, 1.0D0, 3*2.0D0, 1.0D0 /

DATA B / 1.5D1, 1.5D1, 1.5D1 /

C

C Print the initial value of the arrays.

C

PRINT 1000

PRINT 1010, ((A(IROW,ICOL), ICOL = 1, N), IROW = 1, M)

PRINT 1020

PRINT 1030, B

C

C Solve Ax=b and then print the solution.

C

CALL DGESV (N, NRHS, A, LDA, IPIVOT, B, LDB, INFO)

IF (INFO .EQ. 0) THEN

PRINT 1040

PRINT 1030, B

ELSE

PRINT 1050, INFO

END IF

C

1000 FORMAT (1X, 'A:')

1010 FORMAT (3(3X, F4.1))

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

1030 FORMAT (1X, 2X, F4.1)

1040 FORMAT (/1X, 'x:')

1050 FORMAT (1X, 'Solve failed with INFO = ', I6)

C

END

Sample Output

A:
1.0 2.0 2.0
2.0 1.0 2.0
2.0 2.0 1.0
b:
15.0
15.0
15.0
x:
3.0
3.0
3.0