Eigenvalues and Eigenvectors of a Symmetric Matrix (Simple Driver)

Calling Sequence

CALL DSYEV	(JOBZ, UPLO, N, DA, LDA, DW, DWORK, LDWORK, INFO)
CALL SSYEV	(JOBZ, UPLO, N, SA, LDA, SW, SWORK, LDWORK, INFO)
void dsyev	(char jobz, char uplo, int n, double *da, int lda, double *dw, int *info)
void ssyev	(char jobz, char uplo, int n, float *sa, int lda, float *sw, int *info)

Arguments

JOBZ	Indicates whether to compute eigenvalues only or to compute both eigenvalues and eigenvectors. The legal values for JOBZ are listed below. Any values not listed below are illegal.
	'N' or 'n'	Compute eigenvalues only.
	'V' or 'v'	Compute both eigenvalues and eigenvectors.
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.
xA	On entry, the upper or lower triangle of the matrix A.
	On exit, if JOBZ = 'V' or 'v' then A contains the orthonormal eigenvectors. If JOBZ = 'N' or 'n' then all of A is overwritten.
LDA	Leading dimension of the array A as specified in a dimension or type statement. LDA max(1, N).
xW	On exit, the N eigenvalues in ascending order.
xWORK	Scratch array with a dimension of LDWORK.
LDWORK	Leading dimension of the array WORK as specified in a dimension or type statement. LDWORK max(1, 3 × N - 1).
INFO	On exit:
	INFO = 0	Subroutine completed normally.
	INFO < 0	The ith argument, where i = |INFO|, had an illegal value.
	INFO > 0	Convergence failure.

Sample Program

PROGRAM TEST

IMPLICIT NONE

C

INTEGER LDA, LDWORK, N

PARAMETER (N = 3)

PARAMETER (LDA = N)

PARAMETER (LDWORK = 3 * N - 1)

C

DOUBLE PRECISION A(LDA,N), EVALS(N), WORK(LDWORK)

INTEGER ICOL, INFO, IROW

C

EXTERNAL DSYEV

INTRINSIC ABS

C

C Initialize the array A to store the matrix A shown below.

C

C 9 1 1

C A = 1 9 1

C 1 1 9

C

DATA A / 9.0D0, 8D8, 8D8, 1.0D0, 9.0D0, 8D8, 1.0D0, 1.0D0,

$ 9.0D0 /

C

PRINT 1000

DO 100, IROW = 1, N

PRINT 1010, (A(ICOL,IROW), ICOL = 1, IROW - 1),

$ (A(IROW,ICOL), ICOL = IROW, N)

100 CONTINUE

PRINT 1020

DO 110, IROW = 1, N

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

110 CONTINUE

C

C Compute the eigenvalues and eigenvectors of A.

C

CALL DSYEV ('VALUES AND VECTORS', 'UPPER TRIANGULAR A', N,

$ A, LDA, EVALS, WORK, LDWORK, INFO)

IF (INFO .NE. 0) THEN

IF (INFO .LT. 0) THEN

PRINT 1030, ABS(INFO)

STOP 1

ELSE

PRINT 1040, INFO

STOP 2

END IF

END IF

C

C Print the eigenvalues and eigenvectors.

C

PRINT 1050

DO 120, ICOL = 1, N

PRINT 1060, EVALS(ICOL), (A(IROW,ICOL), IROW = 1, N)

120 CONTINUE

C

1000 FORMAT (1X, 'A in full form:')

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

1020 FORMAT (/1X, 'A in symmetric form: (* in unused elements)')

1030 FORMAT (/1X, 'Illegal argument to DSYEV, argument #', I2)

1040 FORMAT (/1X, 'Convergence failure, INFO = ', I2)

1050 FORMAT (/1X, 'Eigenvalue', 4X, 'Eigenvector**T')

1060 FORMAT (1X, F7.2, 5X, '[', F4.2, ', ', F4.2, ', ',

$ F4.2, ']')

C

END

Sample Output

A in full form:

9.0 1.0 1.0

1.0 9.0 1.0

1.0 1.0 9.0

A in symmetric form: (* in unused elements)

9.0 1.0 1.0

**** 9.0 1.0

**** **** 9.0

Eigenvalue Eigenvector**T

8.00 [0.04, -.73, 0.69]

8.00 [0.82, -.37, -.44]

11.00 [0.58, 0.58, 0.58]