Visible to Intel only — GUID: GUID-85B6D9A1-D4DA-462E-83D3-4D3AFBFF2CBA
Visible to Intel only — GUID: GUID-85B6D9A1-D4DA-462E-83D3-4D3AFBFF2CBA
?feast_scsrgv/?feast_hcsrgv
Extended Eigensolver interface for generalized eigenvalue problem with sparse matrices.
Syntax
call sfeast_scsrgv(uplo, n, a, ia, ja, b, ib, jb, fpm, epsout, loop, emin, emax, m0, e, x, m, res, info)
call dfeast_scsrgv(uplo, n, a, ia, ja, b, ib, jb, fpm, epsout, loop, emin, emax, m0, e, x, m, res, info)
call cfeast_hcsrgv(uplo, n, a, ia, ja, b, ib, jb, fpm, epsout, loop, emin, emax, m0, e, x, m, res, info)
call zfeast_hcsrgv(uplo, n, a, ia, ja, b, ib, jb, 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 generalized eigenvalue problems, Ax = λBx, within a given search interval.
Both matrices A and B must use the same family of storage format. The position of the non-zero elements can be different (CSR coordinates ib and jb can be different from ia and ja).
Input Parameters
- uplo
-
CHARACTER*1
Must be 'U' or 'L' or 'F' .
If UPLO = 'U', a and b store the upper triangular parts of A and B respectively.
If UPLO = 'L', a and b store the lower triangular parts of A and B respectively.
If UPLO= 'F', a and b store the full matrices A and B respectively.
- n
-
INTEGER
Sets the size of the problem. n > 0.
- a
-
REAL for sfeast_scsrgv
DOUBLE PRECISION for dfeast_scsrgv
COMPLEX for cfeast_hcsrgv
COMPLEX*16 for zfeast_hcsrgv
Array containing the nonzero elements of either the full matrix A or the upper or lower triangular part of the matrix A, as specified by uplo.
- ia
-
INTEGER
Array of length n + 1, containing indices of elements in the array a , such that ia(i) is the index in the array a of the first non-zero element from the row i . The value of the last element ia(n + 1) is equal to the number of non-zeros plus one.
- ja
-
INTEGER
Array containing the column indices for each non-zero element of the matrix A being represented in the array a . Its length is equal to the length of the array a.
- b
-
REAL for sfeast_scsrgv
DOUBLE PRECISION for dfeast_scsrgv
COMPLEX for cfeast_hcsrgv
COMPLEX*16 for zfeast_hcsrgv
Array of dimension ldb by *, contains the nonzero elements of either the full matrix B or the upper or lower triangular part of the matrix B, as specified by uplo.
- ib
-
INTEGER
Array of length n + 1, containing indices of elements in the array b , such that ib(i) is the index in the array b of the first non-zero element from the row i . The value of the last element ib(n + 1) is equal to the number of non-zeros plus one.
- jb
-
INTEGER
Array containing the column indices for each non-zero element of the matrix B being represented in the array b . Its length is equal to the length of the array b.
- 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_scsrgv and cfeast_hcsrgv
DOUBLE PRECISION for dfeast_scsrgv and zfeast_hcsrgv
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_scsrgv
DOUBLE PRECISION for dfeast_scsrgv
COMPLEX for cfeast_hcsrgv
COMPLEX*16 for zfeast_hcsrgv
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
- fpm
-
On output, the last 64 values correspond to Intel® oneAPI Math Kernel Library (oneMKL) PARDISOiparm(1) to iparm(64) (regardless of the value of fpm(64) on input).
- epsout
-
REAL for sfeast_scsrgv and cfeast_hcsrgv
DOUBLE PRECISION for dfeast_scsrgv and zfeast_hcsrgv
On output, contains the relative error on the trace: |tracei - tracei-1| /max(|emin|, |emax|)
- loop
-
INTEGER
On output, contains the number of refinement loop executed. Ignored on input.
- e
-
REAL for sfeast_scsrgv and cfeast_hcsrgv
DOUBLE PRECISION for dfeast_scsrgv and zfeast_hcsrgv
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_scsrgv and cfeast_hcsrgv
DOUBLE PRECISION for dfeast_scsrgv and zfeast_hcsrgv
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.