IRIX Base Documentation 2002 November/SGI IRIX Base Documentation 2002 November.iso/usr/share/catman/p_man/cat3/SCSL/zhpgv.z/zhpgv

Text File | 2002-10-03 | 5.8 KB | 199 lines

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     ZHPGV - 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

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     SUBROUTINE ZHPGV( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK, RWORK,
                       INFO )

         CHARACTER     JOBZ, UPLO

         INTEGER       INFO, ITYPE, LDZ, N

         DOUBLE        PRECISION RWORK( * ), W( * )

         COMPLEX*16    AP( * ), BP( * ), WORK( * ), Z( LDZ, * )

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     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.

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     ZHPGV 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.


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     ITYPE   (input) INTEGER
             Specifies the problem type to be solved:
             = 1:  A*x = (lambda)*B*x
             = 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.



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     N       (input) INTEGER
             The order of the matrices A and B.  N >= 0.

     AP      (input/output) COMPLEX*16 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*16 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) DOUBLE PRECISION array, dimension (N)
             If INFO = 0, the eigenvalues in ascending order.

     Z       (output) COMPLEX*16 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*16 array, dimension (max(1, 2*N-1))

     RWORK   (workspace) DOUBLE PRECISION array, dimension (max(1, 3*N-2))

     INFO    (output) INTEGER
             = 0:  successful exit
             < 0:  if INFO = -i, the i-th argument had an illegal value
             > 0:  ZPPTRF or ZHPEV returned an error code:
             <= N:  if INFO = i, ZHPEV 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.





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     INTRO_LAPACK(3S), INTRO_SCSL(3S)

     This man page is available only online.



















































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