sspgvd(3P) Sun Performance Library sspgvd(3P)NAMEsspgvd - 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 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);
PURPOSEsspgvd 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.
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 dig‐
its, but we know of none.
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)
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 fac‐
torization B = U**T*U or B = L*L**T, in the same storage for‐
mat as B.
W (output)
Real array, dimension (N) If INFO = 0, the eigenvalues in
ascending order.
Z (output)
Real 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/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 + 5*N + 2*N*LGN + 2*N**2, where
LGN = lg2(N) = log(N)/log(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 rou‐
tine 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 illegal value
> 0: SPPTRF or SSPEVD returned an error code:
<= N: if INFO = i, SSPEVD 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.
FURTHER DETAILS
Based on contributions by
Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
6 Mar 2009 sspgvd(3P)
