dsbgvd.f (3) Linux Manual Page

dsbgvd.f –

Synopsis

Functions/Subroutines

subroutine dsbgvd (JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z, LDZ, WORK, LWORK, IWORK, LIWORK, INFO)
DSBGST

Function/Subroutine Documentation

subroutine dsbgvd (characterJOBZ, characterUPLO, integerN, integerKA, integerKB, double precision, dimension( ldab, * )AB, integerLDAB, double precision, dimension( ldbb, * )BB, integerLDBB, double precision, dimension( * )W, double precision, dimension( ldz, * )Z, integerLDZ, double precision, dimension( * )WORK, integerLWORK, integer, dimension( * )IWORK, integerLIWORK, integerINFO)

DSBGST

Purpose:

 DSBGVD computes all the eigenvalues, and optionally, the eigenvectors

 of a real generalized symmetric-definite banded eigenproblem, of the

 form A*x=(lambda)*B*x. Here A and B are assumed to be symmetric and

 banded, 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.

 

Parameters:

JOBZ

 JOBZ is CHARACTER*1

 = ‘N’: Compute eigenvalues only;

 = ‘V’: Compute eigenvalues and eigenvectors.

UPLO

 UPLO is CHARACTER*1

 = ‘U’: Upper triangles of A and B are stored;

 = ‘L’: Lower triangles of A and B are stored.

N

 N is INTEGER

 The order of the matrices A and B. N >= 0.

KA

 KA is INTEGER

 The number of superdiagonals of the matrix A if UPLO = ‘U’,

 or the number of subdiagonals if UPLO = ‘L’. KA >= 0.

KB

 KB is INTEGER

 The number of superdiagonals of the matrix B if UPLO = ‘U’,

 or the number of subdiagonals if UPLO = ‘L’. KB >= 0.

AB

 AB is DOUBLE PRECISION array, dimension (LDAB, N)

 On entry, the upper or lower triangle of the symmetric band

 matrix A, stored in the first ka+1 rows of the array. The

 j-th column of A is stored in the j-th column of the array AB

 as follows:

 if UPLO = ‘U’, AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j;

 if UPLO = ‘L’, AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka).

 On exit, the contents of AB are destroyed.

LDAB

 LDAB is INTEGER

 The leading dimension of the array AB. LDAB >= KA+1.

BB

 BB is DOUBLE PRECISION array, dimension (LDBB, N)

 On entry, the upper or lower triangle of the symmetric band

 matrix B, stored in the first kb+1 rows of the array. The

 j-th column of B is stored in the j-th column of the array BB

 as follows:

 if UPLO = ‘U’, BB(ka+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j;

 if UPLO = ‘L’, BB(1+i-j,j) = B(i,j) for j<=i<=min(n,j+kb).

 On exit, the factor S from the split Cholesky factorization

 B = S**T*S, as returned by DPBSTF.

LDBB

 LDBB is INTEGER

 The leading dimension of the array BB. LDBB >= KB+1.

W

 W is DOUBLE PRECISION array, dimension (N)

 If INFO = 0, the eigenvalues in ascending order.

Z

 Z is DOUBLE PRECISION array, dimension (LDZ, N)

 If JOBZ = ‘V’, then if INFO = 0, Z contains the matrix Z of

 eigenvectors, with the i-th column of Z holding the

 eigenvector associated with W(i). The eigenvectors are

 normalized so Z**T*B*Z = I.

 If JOBZ = ‘N’, then Z is not referenced.

LDZ

 LDZ is INTEGER

 The leading dimension of the array Z. LDZ >= 1, and if

 JOBZ = ‘V’, LDZ >= max(1,N).

WORK

 WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))

 On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

 LWORK is INTEGER

 The dimension of the array WORK.

 If N <= 1, LWORK >= 1.

 If JOBZ = ‘N’ and N > 1, LWORK >= 3*N.

 If JOBZ = ‘V’ and N > 1, LWORK >= 1 + 5*N + 2*N**2.

 If LWORK = -1, then a workspace query is assumed; the routine

 only calculates the optimal 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.

IWORK

 IWORK is INTEGER array, dimension (MAX(1,LIWORK))

 On exit, if LIWORK > 0, IWORK(1) returns the optimal LIWORK.

LIWORK

 LIWORK 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 optimal 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.

INFO

 INFO is INTEGER

 = 0: successful exit

 < 0: if INFO = -i, the i-th argument had an illegal value

 > 0: if INFO = i, and i is:

 <= N: the algorithm failed to converge:

 i off-diagonal elements of an intermediate

 tridiagonal form did not converge to zero;

 > N: if INFO = N + i, for 1 <= i <= N, then DPBSTF

 returned INFO = i: 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 227 of file dsbgvd.f.

Author

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