ssbgvd
ssbgvd - 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 SSBGVD( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z,
* LDZ, WORK, LWORK, IWORK, LIWORK, INFO)
CHARACTER * 1 JOBZ, UPLO
INTEGER N, KA, KB, LDAB, LDBB, LDZ, LWORK, LIWORK, INFO
INTEGER IWORK(*)
REAL AB(LDAB,*), BB(LDBB,*), W(*), Z(LDZ,*), WORK(*)
SUBROUTINE SSBGVD_64( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W,
* Z, LDZ, WORK, LWORK, IWORK, LIWORK, INFO)
CHARACTER * 1 JOBZ, UPLO
INTEGER*8 N, KA, KB, LDAB, LDBB, LDZ, LWORK, LIWORK, INFO
INTEGER*8 IWORK(*)
REAL AB(LDAB,*), BB(LDBB,*), W(*), Z(LDZ,*), WORK(*)
SUBROUTINE SBGVD( JOBZ, UPLO, [N], KA, KB, AB, [LDAB], BB, [LDBB],
* W, Z, [LDZ], [WORK], [LWORK], [IWORK], [LIWORK], [INFO])
CHARACTER(LEN=1) :: JOBZ, UPLO
INTEGER :: N, KA, KB, LDAB, LDBB, LDZ, LWORK, LIWORK, INFO
INTEGER, DIMENSION(:) :: IWORK
REAL, DIMENSION(:) :: W, WORK
REAL, DIMENSION(:,:) :: AB, BB, Z
SUBROUTINE SBGVD_64( JOBZ, UPLO, [N], KA, KB, AB, [LDAB], BB, [LDBB],
* W, Z, [LDZ], [WORK], [LWORK], [IWORK], [LIWORK], [INFO])
CHARACTER(LEN=1) :: JOBZ, UPLO
INTEGER(8) :: N, KA, KB, LDAB, LDBB, LDZ, LWORK, LIWORK, INFO
INTEGER(8), DIMENSION(:) :: IWORK
REAL, DIMENSION(:) :: W, WORK
REAL, DIMENSION(:,:) :: AB, BB, Z
#include <sunperf.h>
void ssbgvd(char jobz, char uplo, int n, int ka, int kb, float *ab, int ldab, float *bb, int ldbb, float *w, float *z, int ldz, int *info);
void ssbgvd_64(char jobz, char uplo, long n, long ka, long kb, float *ab, long ldab, float *bb, long ldbb, float *w, float *z, long ldz, long *info);
ssbgvd 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.
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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(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 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 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 >= max(1,N).
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* WORK (workspace)
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On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
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* LWORK (input)
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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 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.
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* IWORK (workspace)
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On exit, if LIWORK > 0, IWORK(1) returns the optimal LIWORK.
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* LIWORK (input)
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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 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.
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* INFO (output)
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