Eigenvalues and Eigenvectors of a Hermitian Matrix (Simple Driver)

Calling Sequence

CALL ZHEEV	(JOBZ, UPLO, N, ZA, LDA, DW, ZWORK, LDWORK, DWORK2, INFO)
CALL CHEEV	(JOBZ, UPLO, N, CA, LDA, SW, CWORK, LDWORK, SWORK2, INFO)
void zheev	(char jobz, char uplo, int n, doublecomplex *za, int lda, double *dw, int *info)
void cheev	(char jobz, char uplo, int n, complex *ca, 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 the upper or lower triangle of A, including the diagonal, 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, 2 × N - 1).
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, LDWORK, LDWRK2, N

PARAMETER (N = 3)

PARAMETER (LDA = N)

PARAMETER (LDEVAL = N)

PARAMETER (LDWORK = 2 * N - 1)

PARAMETER (LDWRK2 = 3 * N - 2)

PARAMETER (ZERO = 0.0D0)

C

DOUBLE PRECISION EVALS(LDEVAL), WORK2(LDWRK2)

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

INTEGER ICOL, INFO, IROW

C

EXTERNAL ZHEEV

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

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

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

$ (0.0D0,0.0D0), (4.0D0,-4.0D0), (4.0D0,8D8) /

C

C Print the initial value of A.

C

PRINT 1000

DO 100, IROW = 1, N

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

$ CMPLX(DBLE(A(IROW,IROW)), ZERO),

$ (A(IROW,ICOL), ICOL = IROW + 1, N)

100 CONTINUE

PRINT 1020

DO 110, IROW = 1, N

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

110 CONTINUE

CALL ZHEEV ('VALUES AND VECTORS',

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

$ EVALS, WORK, LDWORK, WORK2, INFO)

IF (INFO .LT. 0) THEN

PRINT 1040, ABS(INFO)

STOP 1

ELSE IF (INFO .GT. 0) THEN

PRINT 1050

STOP 2

END IF

C

C Print the eigenvalues and eigenvectors.

C

PRINT 1060

DO 200, IROW = 1, N

PRINT 1070, EVALS(IROW), (A(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 form: (* in unused entries)')

1030 FORMAT (/1X, 'b:')

1040 FORMAT (1X, 'Illegal argument to ZHEEV, argument #', I2)

1050 FORMAT (1X, 'Convergence failure, INFO = ', I2)

1060 FORMAT (/1X, 'Eigenvalue', 16X, 'Eigenvector**T')

1070 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 form: (* in unused entries)

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

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

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

Eigenvalue Eigenvector**T

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

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

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