chpevd man page on IRIX

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CHPEVD(3F)							    CHPEVD(3F)

NAME
     CHPEVD - compute all the eigenvalues and, optionally, eigenvectors of a
     complex Hermitian matrix A in packed storage

SYNOPSIS
     SUBROUTINE CHPEVD( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK, RWORK,
			LRWORK, IWORK, LIWORK, INFO )

	 CHARACTER	JOBZ, UPLO

	 INTEGER	INFO, LDZ, LIWORK, LRWORK, LWORK, N

	 INTEGER	IWORK( * )

	 REAL		RWORK( * ), W( * )

	 COMPLEX	AP( * ), WORK( * ), Z( LDZ, * )

PURPOSE
     CHPEVD computes all the eigenvalues and, optionally, eigenvectors of a
     complex Hermitian matrix A in packed storage.  If eigenvectors are
     desired, it uses a divide and conquer algorithm.

     The divide and conquer algorithm makes very mild assumptions about
     floating point arithmetic. It will work on machines with a guard digit in
     add/subtract, or on those binary machines without guard digits which
     subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could
     conceivably fail on hexadecimal or decimal machines without guard digits,
     but we know of none.

ARGUMENTS
     JOBZ    (input) CHARACTER*1
	     = 'N':  Compute eigenvalues only;
	     = 'V':  Compute eigenvalues and eigenvectors.

     UPLO    (input) CHARACTER*1
	     = 'U':  Upper triangle of A is stored;
	     = 'L':  Lower triangle of A is stored.

     N	     (input) INTEGER
	     The order of the matrix A.	 N >= 0.

     AP	     (input/output) COMPLEX array, dimension (N*(N+1)/2)
	     On entry, the upper or lower triangle of the Hermitian matrix A,
	     packed columnwise in a linear array.  The j-th column of A is
	     stored in the array AP as follows:	 if UPLO = 'U', AP(i + (j-
	     1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2*n-
	     j)/2) = A(i,j) for j<=i<=n.

	     On exit, AP is overwritten by values generated during the
	     reduction to tridiagonal form.  If UPLO = 'U', the diagonal and

									Page 1

CHPEVD(3F)							    CHPEVD(3F)

	     first superdiagonal of the tridiagonal matrix T overwrite the
	     corresponding elements of A, and if UPLO = 'L', the diagonal and
	     first subdiagonal of T overwrite the corresponding elements of A.

     W	     (output) REAL array, dimension (N)
	     If INFO = 0, the eigenvalues in ascending order.

     Z	     (output) COMPLEX array, dimension (LDZ, N)
	     If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
	     eigenvectors of the matrix A, with the i-th column of Z holding
	     the eigenvector associated with W(i).  If JOBZ = 'N', then Z is
	     not referenced.

     LDZ     (input) INTEGER
	     The leading dimension of the array Z.  LDZ >= 1, and if JOBZ =
	     'V', LDZ >= max(1,N).

     WORK    (workspace/output) COMPLEX array, dimension (LWORK)
	     On exit, if LWORK > 0, WORK(1) returns the optimal LWORK.

     LWORK   (input) INTEGER
	     The dimension of array WORK.  If N <= 1,		    LWORK must
	     be at least 1.  If JOBZ = 'N' and N > 1, LWORK must be at least
	     N.	 If JOBZ = 'V' and N > 1, LWORK must be at least 2*N.

     RWORK   (workspace/output) REAL array,
	     dimension (LRWORK) On exit, if LRWORK > 0, RWORK(1) returns the
	     optimal LRWORK.

     LRWORK  (input) INTEGER
	     The dimension of array RWORK.  If N <= 1,		     LRWORK
	     must be at least 1.  If JOBZ = 'N' and N > 1, LRWORK must be at
	     least N.  If JOBZ = 'V' and N > 1, LRWORK must be at least 1 +
	     4*N + 2*N*lg N + 3*N**2 , where lg( N ) = smallest integer k such
	     that 2**k >= N.

     IWORK   (workspace/output) INTEGER array, dimension (LIWORK)
	     On exit, if LIWORK > 0, IWORK(1) returns the optimal LIWORK.

     LIWORK  (input) INTEGER
	     The dimension of array IWORK.  If JOBZ  = 'N' or N <= 1, LIWORK
	     must be at least 1.  If JOBZ  = 'V' and N > 1, LIWORK must be at
	     least 2 + 5*N.

     INFO    (output) INTEGER
	     = 0:  successful exit
	     < 0:  if INFO = -i, the i-th argument had an illegal value.
	     > 0:  if INFO = i, the algorithm failed to converge; i off-
	     diagonal elements of an intermediate tridiagonal form did not
	     converge to zero.

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