Eigenvalues and Eigenvectors of a Symmetric Matrix in Banded Storage (Simple Driver)

Calling Sequence

CALL DSBEV	(JOBZ, UPLO, N, NDIAG, DA, LDA, DW, DZ, LDZ, DWORK, INFO)
CALL SSBEV	(JOBZ, UPLO, N, NDIAG, SA, LDA, SW, SZ, LDZ, SWORK, INFO)
void dsbev	(char jobz, char uplo, int n, int ndiag, double *da, int lda, double *dw, double *dz, int ldz, int *info)
void ssbev	(char jobz, char uplo, int n, int ndiag, float *sa, int lda, float *sw, float *sz, int ldz, 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.
NDIAG	Number of superdiagonals or subdiagonals of the matrix A. N-1 NDIAG 0 but if N = 0 then NDIAG = 0.
	If UPLO = 'U' or 'u', NDIAG is the number of superdiagonals.
	If UPLO = 'L' or 'l', NDIAG is the number of subdiagonals.
xA	On entry, the upper or lower triangle of the matrix A. On exit, A is overwritten.
LDA	Leading dimension of the array A as specified in a dimension or type statement. LDA NDIAG + 1.
xW	On exit, the N eigenvalues in ascending order.
xZ	On exit, if JOBZ = 'V' or 'v' then Z contains the orthonormal eigenvectors. If JOBZ = 'N' or 'n' then Z is not used.
LDZ	Leading dimension of the array Z as specified in a dimension or type statement. LDZ 1. If JOBZ = 'V' or 'v' then LDZ max(1, N).
xWORK	Scratch array with a dimension of max(1, 3 × N - 2).
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, LDEVEC, LDWORK, N, NDIAG

PARAMETER (N = 4)

PARAMETER (NDIAG = 1)

PARAMETER (LDA = NDIAG + 1)

PARAMETER (LDEVEC = N)

PARAMETER (LDWORK = 3 * N - 2)

C

DOUBLE PRECISION A(LDA,N), EVALS(N), EVECS(LDEVEC,N)

DOUBLE PRECISION WORK(LDWORK)

INTEGER ICOL, INFO, IROW

C

EXTERNAL DSBEV

INTRINSIC ABS

C

C Initialize the array A to store the symmetric tridiagonal

C matrix A shown below.

C

C 1 0 0 0

C A = 0 2 1 0

C 0 1 2 0

C 0 0 0 1

C

DATA A / 8D8, 1.0D0, 0.0D0, 2.0D0, 1.0D0, 2.0D0, 0.0D0,

$ 1.0D0 /

C

C Print the initial values of the arrays.

C

PRINT 1000

PRINT 1010, A(2,1), A(1,2), 0.0D0, 0.0D0

PRINT 1010, A(1,2), A(2,2), A(1,3), 0.0D0

PRINT 1010, 0.0D0, A(1,3), A(2,3), A(1,4)

PRINT 1010, 0.0D0, 0.0D0, A(1,4), A(2,4)

PRINT 1020

DO 100, IROW = 1, LDA

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

100 CONTINUE

C

C Compute the eigenvalues and right eigenvectors of A.

C

CALL DSBEV ('VECTORS AND EIGENVALUES',

$ 'UPPER TRIANGLE A STORED', N, NDIAG, A, LDA,

$ EVALS, EVECS, LDEVEC, WORK, 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), (EVECS(IROW,ICOL), IROW = 1, N)

120 CONTINUE

C

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

1010 FORMAT (4(3X, F9.6))

1020 FORMAT (/1X,

$ 'A in symmetric banded form: ',

$ ' (* in unused elements)')

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

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

1050 FORMAT (/1X, 'Eigenvalue', 10X, 'Eigenvector**T')

1060 FORMAT (1X, F7.2, 6X, '[', 3(F5.3, ', '), F5.3, ']')

C

END

Sample Output

A in full form:

1.000000 0.000000 0.000000 0.000000

0.000000 2.000000 1.000000 0.000000

0.000000 1.000000 2.000000 0.000000

0.000000 0.000000 0.000000 1.000000

A in symmetric banded form: (* in unused elements)

********* 0.000000 1.000000 0.000000

1.000000 2.000000 2.000000 1.000000

Eigenvalue Eigenvector**T

1.00 [1.000, 0.000, 0.000, 0.000]

1.00 [0.000, -.707, 0.707, 0.000]

1.00 [0.000, 0.000, 0.000, 1.000]

3.00 [0.000, 0.707, 0.707, 0.000]