Contents
sspgvd - compute all the eigenvalues, and optionally, the
eigenvectors of a real generalized symmetric-definite eigen-
problem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or
B*A*x=(lambda)*x
SUBROUTINE SSPGVD(ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
LWORK, IWORK, LIWORK, INFO)
CHARACTER * 1 JOBZ, UPLO
INTEGER ITYPE, N, LDZ, LWORK, LIWORK, INFO
INTEGER IWORK(*)
REAL AP(*), BP(*), W(*), Z(LDZ,*), WORK(*)
SUBROUTINE SSPGVD_64(ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
LWORK, IWORK, LIWORK, INFO)
CHARACTER * 1 JOBZ, UPLO
INTEGER*8 ITYPE, N, LDZ, LWORK, LIWORK, INFO
INTEGER*8 IWORK(*)
REAL AP(*), BP(*), W(*), Z(LDZ,*), WORK(*)
F95 INTERFACE
SUBROUTINE SPGVD(ITYPE, JOBZ, UPLO, [N], AP, BP, W, Z, [LDZ], [WORK],
[LWORK], [IWORK], [LIWORK], [INFO])
CHARACTER(LEN=1) :: JOBZ, UPLO
INTEGER :: ITYPE, N, LDZ, LWORK, LIWORK, INFO
INTEGER, DIMENSION(:) :: IWORK
REAL, DIMENSION(:) :: AP, BP, W, WORK
REAL, DIMENSION(:,:) :: Z
SUBROUTINE SPGVD_64(ITYPE, JOBZ, UPLO, [N], AP, BP, W, Z, [LDZ],
[WORK], [LWORK], [IWORK], [LIWORK], [INFO])
CHARACTER(LEN=1) :: JOBZ, UPLO
INTEGER(8) :: ITYPE, N, LDZ, LWORK, LIWORK, INFO
INTEGER(8), DIMENSION(:) :: IWORK
REAL, DIMENSION(:) :: AP, BP, W, WORK
REAL, DIMENSION(:,:) :: Z
C INTERFACE
#include <sunperf.h>
void sspgvd(int itype, char jobz, char uplo, int n, float
*ap, float *bp, float *w, float *z, int ldz, int
*info);
void sspgvd_64(long itype, char jobz, char uplo, long n,
float *ap, float *bp, float *w, float *z, long
ldz, long *info);
sspgvd computes all the eigenvalues, and optionally, the
eigenvectors of a real generalized symmetric-definite eigen-
problem, 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
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.
ITYPE (input)
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
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.
AP (input/output)
Real 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 j-th
column of A is stored in the array AP as follows:
if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for
1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) =
A(i,j) for j<=i<=n.
On exit, the contents of AP are destroyed.
BP (input/output)
Real 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 j-th
column of B is stored in the array BP as follows:
if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for
1<=i<=j; if UPLO = 'L', BP(i + (j-1)*(2*n-j)/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.
W (output)
Real array, dimension (N) If INFO = 0, the eigen-
values in ascending order.
Z (output)
Real array, dimension (LDZ, N) If JOBZ = 'V', then
if INFO = 0, Z contains the matrix Z of eigenvec-
tors. 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.
LDZ (input)
The leading dimension of the array Z. LDZ >= 1,
and if JOBZ = 'V', LDZ >= max(1,N).
WORK (workspace/output)
Real array, dimension (LWORK) 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 >=
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 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)
Integer array, dimension (LIWORK) On exit, if INFO
= 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: SPPTRF or SSPEVD returned an error code:
<= N: if INFO = i, SSPEVD failed to converge; i
off-diagonal elements of an intermediate tridiago-
nal 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.
Based on contributions by
Mark Fahey, Department of Mathematics, Univ. of Kentucky,
USA