# p?hegst

Reduces a Hermitian-definite generalized eigenvalue problem to the standard form.

## Syntax

call pchegst( ibtype, uplo, n, a, ia, ja, desca, b, ib, jb, descb, scale, info)

call pzhegst( ibtype, uplo, n, a, ia, ja, desca, b, ib, jb, descb, scale, info)

## Description

This routine reduces complex Hermitian-definite generalized eigenproblems to the standard form.

In the following `sub(A) denotes A(ia:ia+n-1, ja:ja+n-1) and sub(B) denotes B(ib:ib+n-1, jb:jb+n-1)`.

If `ibtype = 1`, the problem is

`sub(A)*x = λ*sub(B)*x`,

and sub(A) is overwritten by inv(UH)*sub(A)*inv(U), or inv(L)*sub(A)*inv(LH).

If `ibtype = 2 or 3`, the problem is

`sub(A)*sub(B)*x = λ*x,` or `sub(B)*sub(A)*x = λ*x`,

and sub(A) is overwritten by U*sub(A)*UH, or LH*sub(A)*L.

sub(B) must have been previously factorized as UH*U or L*LH by p?potrf.

## Input Parameters

ibtype

  (global) INTEGER. Must be 1 or 2 or 3.

  If `itype = 1`, compute `inv(UH)*sub(A)*inv(U)`, or `inv(L)*sub(A)*inv(LH)`;

  If `itype = 2 or 3`, compute `U*sub(A)*UH`, or `LH*sub(A)*L`.

uplo

  (global) CHARACTER. Must be 'U' or 'L'.

  If `uplo = 'U'`, the upper triangle of sub(A) is stored and sub (B) is factored as `UH*U`.

  If `uplo = 'L'`, the lower triangle of sub(A) is stored and sub (B) is factored as `L*LH`.

n

  (global) INTEGER. The order of the matrices sub (A) and sub (B) `(n≥0)`.

a

  (local)

  COMPLEX for pchegst

  DOUBLE COMPLEX for pzhegst.

  Pointer into the local memory to an array of dimension `(lld_a, LOCc(ja+n-1))`. On entry, the array contains the local pieces of the n-by-n Hermitian distributed matrix sub(A). If `uplo = 'U'`, the leading n-by-n upper triangular part of sub(A) contains the upper triangular part of the matrix, and its strictly lower triangular part is not referenced. If `uplo = 'L'`, the leading n-by-n lower triangular part of sub(A) contains the lower triangular part of the matrix, and its strictly upper triangular part is not referenced.

ia, ja

  (global) INTEGER. The row and column indices in the global array a indicating the first row and the first column of the submatrix A, respectively.

desca

  (global and local) INTEGER array, dimension (dlen_). The array descriptor for the distributed matrix A.

b

  (local)

  COMPLEX for pchegst

  DOUBLE COMPLEX for pzhegst.

  Pointer into the local memory to an array of dimension `(lld_b, LOCc(jb+n-1))`. On entry, the array contains the local pieces of the triangular factor from the Cholesky factorization of sub (B) as returned by p?potrf.

ib, jb

  (global) INTEGER. The row and column indices in the global array b indicating the first row and the first column of the submatrix B, respectively.

descb

  (global and local) INTEGER array, dimension (dlen_). The array descriptor for the distributed matrix B.

## Output Parameters

a

  On exit, if info = 0, the transformed matrix, stored in the same format as sub(A).

scale

  (global)

  REAL for pchegst

  DOUBLE PRECISION for pzhegst.

  Amount by which the eigenvalues should be scaled to compensate for the scaling performed in this routine. At present, scale is always returned as 1.0, it is returned here to allow for future enhancement.

info

  (global) INTEGER.

  If `info = 0`, the execution is successful. If `info <0`, if the i-th argument is an array and the j-entry had an illegal value, then `info = -(i100+j)`, if the i-th argument is a scalar and had an illegal value, then `info = -i`.

Parent topic: Generalized Symmetric-Definite Eigen Problems