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

Calling Sequence

CALL ZHBEV	(JOBZ, UPLO, N, NDIAG, ZA, LDA, DW, ZZ, LDZ, ZWORK, DWORK2, INFO)
CALL CHBEV	(JOBZ, UPLO, N, NDIAG, CA, LDA, SW, CZ, LDZ, CWORK, SWORK2, INFO)
void zhbev	(char jobz, char uplo, int n, int ndiag, doublecomplex *za, int lda, double *dw, doublecomplex *zz, int ldz, int *info)
void chbev	(char jobz, char uplo, int n, int ndiag, complex *ca, int lda, float *sw, complex *cz, 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 N.
xWORK2	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

DOUBLE PRECISION ZERO

INTEGER LDA, LDEVAL, LDEVEC, LDWORK, LDWRK2

INTEGER N, NDIAG

PARAMETER (N = 3)

PARAMETER (NDIAG = 1)

PARAMETER (LDA = NDIAG + 1)

PARAMETER (LDEVAL = N)

PARAMETER (LDEVEC = N)

PARAMETER (LDWORK = N)

PARAMETER (LDWRK2 = 3 * N - 2)

PARAMETER (ZERO = 0.0D0)

C

DOUBLE PRECISION EVALS(LDEVAL), WORK2(LDWRK2)

COMPLEX*16 A(LDA,N), EVECS(LDEVEC,N), WORK(LDWORK)

INTEGER ICOL, INFO, IROW

C

EXTERNAL ZHBEV

INTRINSIC ABS, CMPLX, CONJG, DBLE

C

C Initialize the array A to store the coefficient array A

C shown below.

C

C 4 4+4i 0

C A = 4-4i 4 4+4i

C 0 4-4i 4

C

C

DATA A / (8D8,8D8), (4.0D0, 8D8), (4.0D0, 4.0D0),

$ (4.0D0, 8D8), (4.0D0, 4.0D0), (4.0D0, 8D8) /

C

C Print the initial value of A.

C

PRINT 1000

PRINT 1010, CMPLX(DBLE(A(2,1)), ZERO), A(1,2),

$ CMPLX(ZERO, ZERO)

PRINT 1010, CONJG(A(1,2)), CMPLX(DBLE(A(2,2)), ZERO), A(1,3)

PRINT 1010, (ZERO, ZERO), CONJG(A(1,3)), CMPLX(DBLE(A(2,3)),

$ ZERO)

PRINT 1020

DO 100, IROW = 1, LDA

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

100 CONTINUE

C

C Compute the eigenvalues of A.

C

CALL ZHBEV ('VALUES AND VECTORS',

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

$ EVALS, EVECS, LDEVEC, WORK, WORK2, INFO)

IF (INFO .LT. 0) THEN

PRINT 1030, ABS(INFO)

STOP 1

ELSE IF (INFO .GT. 0) THEN

PRINT 1040

STOP 2

END IF

C

C Print the eigenvalues and eigenvectors.

C

PRINT 1050

DO 200, IROW = 1, N

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

200 CONTINUE

C

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

1010 FORMAT (1X, 10(: 2X, '(', F5.1, ',', F5.1, ')'))

1020 FORMAT (/1X, 'A in Hermitian banded form: ',

$ ' (* in unused entries)')

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

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

1050 FORMAT (/1X, 'Eigenvalue', 16X, 'Eigenvector**T')

1060 FORMAT (1X, F8.3, 6X, '[', 3('(', F4.1, ',', F4.1, ') '),

$ ']')

C

END

Sample Output

A in full form:

( 4.0, 0.0) ( 4.0, 4.0) ( 0.0, 0.0)

( 4.0, -4.0) ( 4.0, 0.0) ( 4.0, 4.0)

( 0.0, 0.0) ( 4.0, -4.0) ( 4.0, 0.0)

A in Hermitian banded form: (* in unused entries)

(*****,*****) ( 4.0, 4.0) ( 4.0, 4.0)

( 4.0,*****) ( 4.0,*****) ( 4.0,*****)

Eigenvalue Eigenvector**T

-4.000 [( 0.5, 0.0) (-0.7, 0.0) ( 0.5, 0.0) ]

4.000 [(-0.5, 0.5) ( 0.0, 0.0) ( 0.5,-0.5) ]

12.000 [( 0.0,-0.5) ( 0.0,-0.7) ( 0.0,-0.5) ]