DSPGVD (3)  Linux Man Pages
NAME
dspgvd.f 
SYNOPSIS
Functions/Subroutines
subroutine dspgvd (ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK, LWORK, IWORK, LIWORK, INFO)
DSPGST
Function/Subroutine Documentation
subroutine dspgvd (integerITYPE, characterJOBZ, characterUPLO, integerN, double precision, dimension( * )AP, double precision, dimension( * )BP, double precision, dimension( * )W, double precision, dimension( ldz, * )Z, integerLDZ, double precision, dimension( * )WORK, integerLWORK, integer, dimension( * )IWORK, integerLIWORK, integerINFO)
DSPGST
Purpose:

DSPGVD computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetricdefinite 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 symmetric, 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 XMP, Cray YMP, Cray C90, or Cray2. It could conceivably fail on hexadecimal or decimal machines without guard digits, but we know of none.
Parameters:

ITYPE
ITYPE is 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
JOBZJOBZ is CHARACTER*1 = 'N': Compute eigenvalues only; = 'V': Compute eigenvalues and eigenvectors.
UPLOUPLO is CHARACTER*1 = 'U': Upper triangles of A and B are stored; = 'L': Lower triangles of A and B are stored.
NN is INTEGER The order of the matrices A and B. N >= 0.
APAP is DOUBLE PRECISION array, dimension (N*(N+1)/2) On entry, the upper or lower triangle of the symmetric matrix A, packed columnwise in a linear array. The jth column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j1)*(2*nj)/2) = A(i,j) for j<=i<=n. On exit, the contents of AP are destroyed.
BPBP is DOUBLE PRECISION array, dimension (N*(N+1)/2) On entry, the upper or lower triangle of the symmetric matrix B, packed columnwise in a linear array. The jth column of B is stored in the array BP as follows: if UPLO = 'U', BP(i + (j1)*j/2) = B(i,j) for 1<=i<=j; if UPLO = 'L', BP(i + (j1)*(2*nj)/2) = B(i,j) for j<=i<=n. On exit, the triangular factor U or L from the Cholesky factorization B = U**T*U or B = L*L**T, in the same storage format as B.
WW is DOUBLE PRECISION array, dimension (N) If INFO = 0, the eigenvalues in ascending order.
ZZ is DOUBLE PRECISION 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**T*B*Z = I; if ITYPE = 3, Z**T*inv(B)*Z = I. If JOBZ = 'N', then Z is not referenced.
LDZLDZ is INTEGER The leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', LDZ >= max(1,N).
WORKWORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the required LWORK.
LWORKLWORK is INTEGER The dimension of the array WORK. If N <= 1, LWORK >= 1. If JOBZ = 'N' and N > 1, LWORK >= 2*N. If JOBZ = 'V' and N > 1, LWORK >= 1 + 6*N + 2*N**2. If LWORK = 1, then a workspace query is assumed; the routine only calculates the required sizes of the WORK and IWORK arrays, returns these values as the first entries of the WORK and IWORK arrays, and no error message related to LWORK or LIWORK is issued by XERBLA.
IWORKIWORK is INTEGER array, dimension (MAX(1,LIWORK)) On exit, if INFO = 0, IWORK(1) returns the required LIWORK.
LIWORKLIWORK is INTEGER The dimension of the 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 required sizes of the WORK and IWORK arrays, returns these values as the first entries of the WORK and IWORK arrays, and no error message related to LWORK or LIWORK is issued by XERBLA.
INFOINFO is INTEGER = 0: successful exit < 0: if INFO = i, the ith argument had an illegal value > 0: DPPTRF or DSPEVD returned an error code: <= N: if INFO = i, DSPEVD failed to converge; i offdiagonal elements of an intermediate tridiagonal form did not converge to 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.
Author:

Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
 November 2011
Contributors:
 Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
Definition at line 210 of file dspgvd.f.
Author
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