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## man page of LAPACK-3

### LAPACK-3: reduces a complex Hermitian-definite generalized eigenproblem to standard form, using packed storage

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## NAME

LAPACK-3 - reduces a complex Hermitian-definite generalized eigenproblem to standard form, using packed storage## SYNOPSIS

SUBROUTINE ZHPGST( ITYPE, UPLO, N, AP, BP, INFO ) CHARACTER UPLO INTEGER INFO, ITYPE, N COMPLEX*16 AP( * ), BP( * )PURPOSE

ZHPGST reduces a complex Hermitian-definite generalized eigenproblem to standard form, using packed storage. If ITYPE = 1, the problem is A*x = lambda*B*x, and A is overwritten by inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H) 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**H or L**H*A*L. B must have been previously factorized as U**H*U or L*L**H by ZPPTRF.## ARGUMENTS

ITYPE (input) INTEGER = 1: compute inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H); = 2 or 3: compute U*A*U**H or L**H*A*L. UPLO (input) CHARACTER*1 = 'U': Upper triangle of A is stored and B is factored as U**H*U; = 'L': Lower triangle of A is stored and B is factored as L*L**H. N (input) INTEGER The order of the matrices A and B. N >= 0. AP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2) On entry, the upper or lower triangle of the Hermitian 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)*(2n-j)/2) = A(i,j) for j<=i<=n. On exit, if INFO = 0, the transformed matrix, stored in the same format as A. BP (input) COMPLEX*16 array, dimension (N*(N+1)/2) The triangular factor from the Cholesky factorization of B, stored in the same format as A, as returned by ZPPTRF. 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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