Visible to Intel only — GUID: GUID-094ED6E6-3512-4BAC-B1B6-C723E4F142F4
Visible to Intel only — GUID: GUID-094ED6E6-3512-4BAC-B1B6-C723E4F142F4
?sygst
Reduces a real symmetric-definite generalized eigenvalue problem to the standard form.
Syntax
call ssygst(itype, uplo, n, a, lda, b, ldb, info)
call dsygst(itype, uplo, n, a, lda, b, ldb, info)
call sygst(a, b [,itype] [,uplo] [,info])
Include Files
- mkl.fi, lapack.f90
Description
The routine reduces real symmetric-definite generalized eigenproblems
A*z = λ*B*z, A*B*z = λ*z, or B*A*z = λ*z
to the standard form C*y = λ*y. Here A is a real symmetric matrix, and B is a real symmetric positive-definite matrix. Before calling this routine, call ?potrf to compute the Cholesky factorization: B = UT*U or B = L*LT.
Input Parameters
- itype
-
INTEGER. Must be 1 or 2 or 3.
If itype = 1, the generalized eigenproblem is A*z = lambda*B*z
for uplo = 'U': C = inv(UT)*A*inv(U), z = inv(U)*y;
for uplo = 'L': C = inv(L)*A*inv(LT), z = inv(LT)*y.
If itype = 2, the generalized eigenproblem is A*B*z = lambda*z
for uplo = 'U': C = U*A*UT, z = inv(U)*y;
for uplo = 'L': C = LT*A*L, z = inv(LT)*y.
If itype = 3, the generalized eigenproblem is B*A*z = lambda*z
for uplo = 'U': C = U*A*UT, z = UT*y;
for uplo = 'L': C = LT*A*L, z = L*y.
- uplo
-
CHARACTER*1. Must be 'U' or 'L'.
If uplo = 'U', the array a stores the upper triangle of A; you must supply B in the factored form B = UT*U.
If uplo = 'L', the array a stores the lower triangle of A; you must supply B in the factored form B = L*LT.
- n
-
INTEGER. The order of the matrices A and B (n≥ 0).
- a, b
-
REAL for ssygst
DOUBLE PRECISION for dsygst.
Arrays:
a(lda,*) contains the upper or lower triangle of A.
The second dimension of a must be at least max(1, n).
b(ldb,*) contains the Cholesky-factored matrix B:
B = UT*U or B = L*LT (as returned by ?potrf).
The second dimension of b must be at least max(1, n).
- lda
-
INTEGER. The leading dimension of a; at least max(1, n).
- ldb
-
INTEGER. The leading dimension of b; at least max(1, n).
Output Parameters
- a
-
The upper or lower triangle of A is overwritten by the upper or lower triangle of C, as specified by the arguments itype and uplo.
- info
-
INTEGER.
If info = 0, the execution is successful.
If info = -i, the i-th parameter had an illegal value.
LAPACK 95 Interface Notes
Routines in Fortran 95 interface have fewer arguments in the calling sequence than their FORTRAN 77 counterparts. For general conventions applied to skip redundant or restorable arguments, see LAPACK 95 Interface Conventions.
Specific details for the routine sygst interface are the following:
- a
-
Holds the matrix A of size (n,n).
- b
-
Holds the matrix B of size (n,n).
- itype
-
Must be 1, 2, or 3. The default value is 1.
- uplo
-
Must be 'U' or 'L'. The default value is 'U'.
Application Notes
Forming the reduced matrix C is a stable procedure. However, it involves implicit multiplication by inv(B) (if itype = 1) or B (if itype = 2 or 3). When the routine is used as a step in the computation of eigenvalues and eigenvectors of the original problem, there may be a significant loss of accuracy if B is ill-conditioned with respect to inversion.
The approximate number of floating-point operations is n3.