?feast_syev/?feast_heev

Syntax

call sfeast_syev(uplo, n, a, lda, fpm, epsout, loop, emin, emax, m0, e, x, m, res, info)

call dfeast_syev(uplo, n, a, lda, fpm, epsout, loop, emin, emax, m0, e, x, m, res, info)

call cfeast_heev(uplo, n, a, lda, fpm, epsout, loop, emin, emax, m0, e, x, m, res, info)

call zfeast_heev(uplo, n, a, lda, fpm, epsout, loop, emin, emax, m0, e, x, m, res, info)

Include Files

• mkl.fi

Description

The routines compute all the eigenvalues and eigenvectors for standard eigenvalue problems, Ax = λx, within a given search interval.

Input Parameters

uplo

CHARACTER*1

Must be 'U' or 'L' or 'F' .

If uplo = 'U', a stores the upper triangular parts of A.

If uplo = 'L', a stores the lower triangular parts of A.

If uplo= 'F' , a stores the full matrix A.

n

INTEGER

Sets the size of the problem. n > 0.

a

REAL for sfeast_syev

DOUBLE PRECISION for dfeast_syev

COMPLEX for cfeast_heev

COMPLEX*16 for zfeast_heev

Array of dimension lda by n, contains either full matrix A or upper or lower triangular part of the matrix A, as specified by uplo

lda

INTEGER

The leading dimension of the array a. Must be at least max(1, n).

fpm

INTEGER

Array, dimension of 128. This array is used to pass various parameters to Extended Eigensolver routines. See Extended Eigensolver Input Parameters for a complete description of the parameters and their default values.

emin, emax

REAL for sfeast_syev and cfeast_heev

DOUBLE PRECISION for dfeast_syev and zfeast_heev

The lower and upper bounds of the interval to be searched for eigenvalues; emin ≤ emax.

Note

Users are advised to avoid situations in which eigenvalues nearly coincide with the interval endpoints. This may lead to unpredictable selection or omission of such eigenvalues. Users should instead specify a slightly larger interval than needed and, if required, pick valid eigenvalues and their corresponding eigenvectors for subsequent use.

m0

INTEGER

On entry, specifies the initial guess for subspace dimension to be used, 0 < m0≤n. Set m0 ≥ m where m is the total number of eigenvalues located in the interval [emin, emax]. If the initial guess is wrong, Extended Eigensolver routines return info=3.

x

REAL for sfeast_syev

DOUBLE PRECISION for dfeast_syev

COMPLEX for cfeast_heev

COMPLEX*16 for zfeast_heev

On entry, if fpm(5)=1, the array x(n, m) contains a basis of guess subspace where n is the order of the input matrix.

Output Parameters

epsout

REAL for sfeast_syev and cfeast_heev

DOUBLE PRECISION for dfeast_syev and zfeast_heev

On output, contains the relative error on the trace: |trace_i - trace_i-1| /max(|emin|, |emax|)

loop

INTEGER

On output, contains the number of refinement loop executed. Ignored on input.

e

REAL for sfeast_syev and cfeast_heev

DOUBLE PRECISION for dfeast_syev and zfeast_heev

Array of length m0. On output, the first m entries of e are eigenvalues found in the interval.

x

On output, the first m columns of x contain the orthonormal eigenvectors corresponding to the computed eigenvalues e, with the i-th column of x holding the eigenvector associated with e(i).

m

INTEGER

The total number of eigenvalues found in the interval [emin, emax]: 0 ≤ m ≤ m0.

res

REAL for sfeast_syev and cfeast_heev

DOUBLE PRECISION for dfeast_syev and zfeast_heev

Array of length m0. On exit, the first m components contain the relative residual vector:

for i=1, 2, …, m, and where m is the total number of eigenvalues found in the search interval.

info

INTEGER

If info=0, the execution is successful. If info ≠ 0, see Output Eigensolver info Details.