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CHPGVD(3S)							    CHPGVD(3S)

NAME
     CHPGVD - compute all the eigenvalues and, optionally, the eigenvectors of
     a complex generalized Hermitian-definite eigenproblem, of the form
     A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x

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

	 CHARACTER	JOBZ, UPLO

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

	 INTEGER	IWORK( * )

	 REAL		RWORK( * ), W( * )

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

IMPLEMENTATION
     These routines are part of the SCSL Scientific Library and can be loaded
     using either the -lscs or the -lscs_mp option.  The -lscs_mp option
     directs the linker to use the multi-processor version of the library.

     When linking to SCSL with -lscs or -lscs_mp, the default integer size is
     4 bytes (32 bits). Another version of SCSL is available in which integers
     are 8 bytes (64 bits).  This version allows the user access to larger
     memory sizes and helps when porting legacy Cray codes.  It can be loaded
     by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
     only one of the two versions; 4-byte integer and 8-byte integer library
     calls cannot be mixed.

PURPOSE
     CHPGVD computes all the eigenvalues and, optionally, the eigenvectors of
     a complex generalized Hermitian-definite eigenproblem, of the form
     A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and B are
     assumed to be Hermitian, stored in packed format, and B is also positive
     definite.
     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
     ITYPE   (input) INTEGER
	     Specifies the problem type to be solved:
	     = 1:  A*x = (lambda)*B*x

									Page 1

CHPGVD(3S)							    CHPGVD(3S)

	     = 2:  A*B*x = (lambda)*x
	     = 3:  B*A*x = (lambda)*x

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

     UPLO    (input) CHARACTER*1
	     = 'U':  Upper triangles of A and B are stored;
	     = 'L':  Lower triangles of A and B are stored.

     N	     (input) INTEGER
	     The order of the matrices A and B.	 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, the contents of AP are destroyed.

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

	     On exit, the triangular factor U or L from the Cholesky
	     factorization B = U**H*U or B = L*L**H, in the same storage
	     format as B.

     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 matrix Z of
	     eigenvectors.  The eigenvectors are normalized as follows:	 if
	     ITYPE = 1 or 2, Z**H*B*Z = I; if ITYPE = 3, Z**H*inv(B)*Z = 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) COMPLEX array, dimension (LWORK)
	     On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

									Page 2

CHPGVD(3S)							    CHPGVD(3S)

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

	     If LWORK = -1, then a workspace query is assumed; the routine
	     only calculates the optimal size of the WORK array, returns this
	     value as the first entry of the WORK array, and no error message
	     related to LWORK is issued by XERBLA.

     RWORK   (workspace) REAL array, dimension (LRWORK)
	     On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.

     LRWORK  (input) INTEGER
	     The dimension of array RWORK.  If N <= 1,		     LRWORK >=
	     1.	 If JOBZ = 'N' and N > 1, LRWORK >= N.	If JOBZ = 'V' and N >
	     1, LRWORK >= 1 + 5*N + 2*N**2.

	     If LRWORK = -1, then a workspace query is assumed; the routine
	     only calculates the optimal size of the RWORK array, returns this
	     value as the first entry of the RWORK array, and no error message
	     related to LRWORK is issued by XERBLA.

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

     LIWORK  (input) INTEGER
	     The dimension of array IWORK.  If JOBZ  = 'N' or N <= 1, LIWORK
	     >= 1.  If JOBZ  = 'V' and N > 1, LIWORK >= 3 + 5*N.

	     If LIWORK = -1, then a workspace query is assumed; the routine
	     only calculates the optimal size of the IWORK array, returns this
	     value as the first entry of the IWORK array, and no error message
	     related to LIWORK is issued by XERBLA.

     INFO    (output) INTEGER
	     = 0:  successful exit
	     < 0:  if INFO = -i, the i-th argument had an illegal value
	     > 0:  CPPTRF or CHPEVD returned an error code:
	     <= N:  if INFO = i, CHPEVD failed to converge; i off-diagonal
	     elements of an intermediate tridiagonal form did not convergeto
	     zero; > N:	  if INFO = N + i, for 1 <= i <= n, then the leading
	     minor of order i of B is not positive definite.  The
	     factorization of B could not be completed and no eigenvalues or
	     eigenvectors were computed.

FURTHER DETAILS
     Based on contributions by
	Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA

									Page 3

CHPGVD(3S)							    CHPGVD(3S)

SEE ALSO
     INTRO_LAPACK(3S), INTRO_SCSL(3S)

     This man page is available only online.

									Page 4

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