dsbgv
dsbgv - compute all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite banded eigenproblem, of the form A*x=(lambda)*B*x
SUBROUTINE DSBGV( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z,
* LDZ, WORK, INFO)
CHARACTER * 1 JOBZ, UPLO
INTEGER N, KA, KB, LDAB, LDBB, LDZ, INFO
DOUBLE PRECISION AB(LDAB,*), BB(LDBB,*), W(*), Z(LDZ,*), WORK(*)
SUBROUTINE DSBGV_64( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W,
* Z, LDZ, WORK, INFO)
CHARACTER * 1 JOBZ, UPLO
INTEGER*8 N, KA, KB, LDAB, LDBB, LDZ, INFO
DOUBLE PRECISION AB(LDAB,*), BB(LDBB,*), W(*), Z(LDZ,*), WORK(*)
SUBROUTINE SBGV( JOBZ, UPLO, [N], KA, KB, AB, [LDAB], BB, [LDBB], W,
* Z, [LDZ], [WORK], [INFO])
CHARACTER(LEN=1) :: JOBZ, UPLO
INTEGER :: N, KA, KB, LDAB, LDBB, LDZ, INFO
REAL(8), DIMENSION(:) :: W, WORK
REAL(8), DIMENSION(:,:) :: AB, BB, Z
SUBROUTINE SBGV_64( JOBZ, UPLO, [N], KA, KB, AB, [LDAB], BB, [LDBB],
* W, Z, [LDZ], [WORK], [INFO])
CHARACTER(LEN=1) :: JOBZ, UPLO
INTEGER(8) :: N, KA, KB, LDAB, LDBB, LDZ, INFO
REAL(8), DIMENSION(:) :: W, WORK
REAL(8), DIMENSION(:,:) :: AB, BB, Z
#include <sunperf.h>
void dsbgv(char jobz, char uplo, int n, int ka, int kb, double *ab, int ldab, double *bb, int ldbb, double *w, double *z, int ldz, int *info);
void dsbgv_64(char jobz, char uplo, long n, long ka, long kb, double *ab, long ldab, double *bb, long ldbb, double *w, double *z, long ldz, long *info);
dsbgv 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.
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* JOBZ (input)
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* UPLO (input)
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* N (input)
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The order of the matrices A and B. N >= 0.
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* KA (input)
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The number of superdiagonals of the matrix A if UPLO = 'U',
or the number of subdiagonals if UPLO = 'L'. KA >= 0.
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* KB (input)
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The number of superdiagonals of the matrix B if UPLO = 'U',
or the number of subdiagonals if UPLO = 'L'. KB >= 0.
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* AB (input/output)
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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.
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* LDAB (input)
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The leading dimension of the array AB. LDAB >= KA+1.
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* BB (input/output)
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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(kb+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 SPBSTF.
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* LDBB (input)
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The leading dimension of the array BB. LDBB >= KB+1.
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* W (output)
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If INFO = 0, the eigenvalues in ascending order.
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* Z (input)
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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 that Z**T*B*Z = I.
If JOBZ = 'N', then Z is not referenced.
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* LDZ (input)
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The leading dimension of the array Z. LDZ >= 1, and if
JOBZ = 'V', LDZ >= N.
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* WORK (workspace)
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dimension(3*N)
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* INFO (output)
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