Contents
sspgv - 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 SSPGV(ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK, INFO)
CHARACTER * 1 JOBZ, UPLO
INTEGER ITYPE, N, LDZ, INFO
REAL AP(*), BP(*), W(*), Z(LDZ,*), WORK(*)
SUBROUTINE SSPGV_64(ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
INFO)
CHARACTER * 1 JOBZ, UPLO
INTEGER*8 ITYPE, N, LDZ, INFO
REAL AP(*), BP(*), W(*), Z(LDZ,*), WORK(*)
F95 INTERFACE
SUBROUTINE SPGV(ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, [LDZ], [WORK],
[INFO])
CHARACTER(LEN=1) :: JOBZ, UPLO
INTEGER :: ITYPE, N, LDZ, INFO
REAL, DIMENSION(:) :: AP, BP, W, WORK
REAL, DIMENSION(:,:) :: Z
SUBROUTINE SPGV_64(ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, [LDZ], [WORK],
[INFO])
CHARACTER(LEN=1) :: JOBZ, UPLO
INTEGER(8) :: ITYPE, N, LDZ, INFO
REAL, DIMENSION(:) :: AP, BP, W, WORK
REAL, DIMENSION(:,:) :: Z
C INTERFACE
#include <sunperf.h>
void sspgv(int itype, char jobz, char uplo, int n, float
*ap, float *bp, float *w, float *z, int ldz, int
*info);
void sspgv_64(long itype, char jobz, char uplo, long n,
float *ap, float *bp, float *w, float *z, long
ldz, long *info);
sspgv 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.
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)
Real array, dimension(3*N)
INFO (output)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille-
gal value
> 0: SPPTRF or SSPEV returned an error code:
<= N: if INFO = i, SSPEV 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.