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## man page of LAPACK-3

### LAPACK-3: reduces a complex Hermitian-definite generalized eigenproblem to standard form

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## NAME

LAPACK-3 - reduces a complex Hermitian-definite generalized eigenproblem to standard form## SYNOPSIS

SUBROUTINE ZHEGS2( ITYPE, UPLO, N, A, LDA, B, LDB, INFO ) CHARACTER UPLO INTEGER INFO, ITYPE, LDA, LDB, N COMPLEX*16 A( LDA, * ), B( LDB, * )## PURPOSE

ZHEGS2 reduces a complex Hermitian-definite generalized eigenproblem to standard form. If ITYPE = 1, the problem is A*x = lambda*B*x, and A is overwritten by inv(U')*A*inv(U) or inv(L)*A*inv(L') If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or B*A*x = lambda*x, and A is overwritten by U*A*U' or L'*A*L. B must have been previously factorized as U'*U or L*L' by ZPOTRF.## ARGUMENTS

ITYPE (input) INTEGER = 1: compute inv(U')*A*inv(U) or inv(L)*A*inv(L'); = 2 or 3: compute U*A*U' or L'*A*L. UPLO (input) CHARACTER*1 Specifies whether the upper or lower triangular part of the Hermitian matrix A is stored, and how B has been factorized. = 'U': Upper triangular = 'L': Lower triangular N (input) INTEGER The order of the matrices A and B. N >= 0. A (input/output) COMPLEX*16 array, dimension (LDA,N) On entry, the Hermitian matrix A. If UPLO = 'U', the leading n by n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading n by n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, if INFO = 0, the transformed matrix, stored in the same format as A. LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,N). B (input) COMPLEX*16 array, dimension (LDB,N) The triangular factor from the Cholesky factorization of B, as returned by ZPOTRF. LDB (input) INTEGER The leading dimension of the array B. LDB >= max(1,N). INFO (output) INTEGER = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. LAPACK routine (version 3.2) March 2011 LAPACK-3(3)

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