p?hegst

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 3/22/2024

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p?hegst

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

Syntax

void pchegst (MKL_INT *ibtype , char *uplo , MKL_INT *n , MKL_Complex8 *a , MKL_INT *ia , MKL_INT *ja , MKL_INT *desca , MKL_Complex8 *b , MKL_INT *ib , MKL_INT *jb , MKL_INT *descb , float *scale , MKL_INT *info );

void pzhegst (MKL_INT *ibtype , char *uplo , MKL_INT *n , MKL_Complex16 *a , MKL_INT *ia , MKL_INT *ja , MKL_INT *desca , MKL_Complex16 *b , MKL_INT *ib , MKL_INT *jb , MKL_INT *descb , double *scale , MKL_INT *info );

Include Files

mkl_scalapack.h

Description

The p?hegst function reduces complex Hermitian positive-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(U^H)*sub(A)*inv(U), or inv(L)*sub(A)*inv(L^H).

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)*U^H, or L^H*sub(A)*L.

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

Input Parameters

ibtype

(global) Must be 1 or 2 or 3.

If itype = 1, compute inv(U^H)*sub(A)*inv(U), or inv(L)*sub(A)*inv(L^H);

If itype = 2 or 3, compute U*sub(A)*U^H, or L^H*sub(A)*L.

uplo

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

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

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

n

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

a

(local)

Pointer into the local memory to an array of size 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) The row and column indices in the global matrix A indicating the first row and the first column of the submatrix A, respectively.

desca

(global and local) array of size dlen_. The array descriptor for the distributed matrix A.

b

(local)

Pointer into the local memory to an array of size 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) The row and column indices in the global matrix B indicating the first row and the first column of the submatrix B, respectively.

descb

(global and local) array of size 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)

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

info

(global)

If info = 0, the execution is successful. If info <0, if the i-th argument is an array and the j-th entry, indexed j - 1, had an illegal value, then info = -(i*100+j); if the i-th argument is a scalar and had an illegal value, then info = -i.

Parent topic: Generalized Symmetric-Definite Eigenvalue Problems: ScaLAPACK Computational Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for C

p?hegst

Syntax

Include Files

Description

Input Parameters

Output Parameters

See Also