dspgv(3P) Sun Performance Library dspgv(3P)NAMEdspgv - compute all the eigenvalues and, optionally, the eigenvectors
of a real generalized symmetric-definite eigenproblem, of the form
A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x
SYNOPSIS
SUBROUTINE DSPGV(ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK, INFO)
CHARACTER * 1 JOBZ, UPLO
INTEGER ITYPE, N, LDZ, INFO
DOUBLE PRECISION AP(*), BP(*), W(*), Z(LDZ,*), WORK(*)
SUBROUTINE DSPGV_64(ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
INFO)
CHARACTER * 1 JOBZ, UPLO
INTEGER*8 ITYPE, N, LDZ, INFO
DOUBLE PRECISION 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(8), DIMENSION(:) :: AP, BP, W, WORK
REAL(8), 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(8), DIMENSION(:) :: AP, BP, W, WORK
REAL(8), DIMENSION(:,:) :: Z
C INTERFACE
#include <sunperf.h>
void dspgv(int itype, char jobz, char uplo, int n, double *ap, double
*bp, double *w, double *z, int ldz, int *info);
void dspgv_64(long itype, char jobz, char uplo, long n, double *ap,
double *bp, double *w, double *z, long ldz, long *info);
PURPOSEdspgv computes all the eigenvalues and, optionally, the eigenvectors of
a real generalized symmetric-definite eigenproblem, 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.
ARGUMENTS
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)
Double precision 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 A are destroyed.
BP (input/output)
Double precision 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 fac‐
torization B = U**T*U or B = L*L**T, in the same storage for‐
mat as B.
W (output)
Double precision array, dimension (N) If INFO = 0, the eigen‐
values in ascending order.
Z (output)
Double precision array, dimension (LDZ, N) If JOBZ = 'V',
then if INFO = 0, Z contains the matrix Z of eigenvectors.
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)
Double precision array, dimension(3*N)
INFO (output)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: DPPTRF or DSPEV returned an error code:
<= N: if INFO = i, DSPEV 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 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.
6 Mar 2009 dspgv(3P)
