Contents
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(*)
F95 INTERFACE
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
C INTERFACE
#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 posi-
tive 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.
JOBZ (input)
= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors.
UPLO (input)
= 'U': Upper triangles of A and B are stored;
= 'L': Lower triangles of A and B are stored.
N (input) The order of the matrices A and B. N >= 0.
KA (input)
The number of superdiagonals of the matrix A if
UPLO = 'U', or the number of subdiagonals if UPLO
= 'L'. KA >= 0.
KB (input)
The number of superdiagonals of the matrix B if
UPLO = 'U', or the number of subdiagonals if UPLO
= 'L'. KB >= 0.
AB (input/output)
On entry, the upper or lower triangle of the sym-
metric 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 (input)
The leading dimension of the array AB. LDAB >=
KA+1.
BB (input/output)
On entry, the upper or lower triangle of the sym-
metric 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 fac-
torization B = S**T*S, as returned by SPBSTF.
LDBB (input)
The leading dimension of the array BB. LDBB >=
KB+1.
W (output)
If INFO = 0, the eigenvalues in ascending order.
Z (input) 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 (input)
The leading dimension of the array Z. LDZ >= 1,
and if JOBZ = 'V', LDZ >= max(1,N).
WORK (workspace)
On exit, if INFO = 0, WORK(1) returns the optimal
LWORK.
LWORK (input)
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.
IWORK (workspace/output)
On exit, if LIWORK > 0, IWORK(1) returns the
optimal LIWORK.
LIWORK (input)
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.
INFO (output)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille-
gal 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 SPBSTF
returned INFO = i: B is not positive definite.
The factorization of B could not be completed and
no eigenvalues or eigenvectors were computed.
Based on contributions by
Mark Fahey, Department of Mathematics, Univ. of Kentucky,
USA