Developer Reference for Intel® oneAPI Math Kernel Library for C
?syevx
Computes selected eigenvalues and, optionally, eigenvectors of a symmetric matrix.
Syntax
lapack_intLAPACKE_ssyevx ( intmatrix_layout , charjobz , charrange , charuplo , lapack_intn , float*a , lapack_intlda , floatvl , floatvu , lapack_intil , lapack_intiu , floatabstol , lapack_int*m , float*w , float*z , lapack_intldz , lapack_int*ifail );
lapack_intLAPACKE_dsyevx ( intmatrix_layout , charjobz , charrange , charuplo , lapack_intn , double*a , lapack_intlda , doublevl , doublevu , lapack_intil , lapack_intiu , doubleabstol , lapack_int*m , double*w , double*z , lapack_intldz , lapack_int*ifail );
Include Files
mkl.h
Description
ssyevx dsyevx syevx
The routine computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A . Eigenvalues and eigenvectors can be selected by specifying either a range of values or a range of indices for the desired eigenvalues.
Note that for most cases of real symmetric eigenvalue problems the default choice should be syevr function as its underlying algorithm is faster and uses less workspace. ?syevx is faster for a few selected eigenvalues.
Input Parameters
- matrix_layout
-
Specifies whether matrix storage layout is row major ( LAPACK_ROW_MAJOR ) or column major ( LAPACK_COL_MAJOR ).
jobz
Must be ‘N’ or ‘V’ .
If jobz = 'N' , then only eigenvalues are computed. If jobz = 'V' , then eigenvalues and eigenvectors are computed.
range
Must be ‘A’ , ‘V’ , or ‘I’ .
If range = 'A' , all eigenvalues will be found. If range = 'V' , all eigenvalues in the half-open interval ( vl , vu ] will be found. If range = 'I' , the eigenvalues with indices il through iu will be found.
uplo
Must be ‘U’ or ‘L’ .
If uplo = 'U' , a stores the upper triangular part of A . If uplo = 'L' , a stores the lower triangular part of A .
n
The order of the matrix A ( n≥ 0 ).
- a , work
-
REAL for ssyevx DOUBLE PRECISION for dsyevx . Arrays:
a (size max(1, lda * n )) is an array containing either upper or lower triangular part of the symmetric matrix A , as specified by uplo .
The second dimension of a must be at least max(1, n ). work is a workspace array, its dimension max(1, lwork) .
lda
The leading dimension of the array a . Must be at least max(1, n ) .
- vl , vu
-
REAL for ssyevx DOUBLE PRECISION for dsyevx . If range = 'V' , the lower and upper bounds of the interval to be searched for eigenvalues; vl ≤ vu . Not referenced if range = 'A' or ‘I’ .
il , iu
If range = 'I' , the indices of the smallest and largest eigenvalues to be returned. Constraints: 1 ≤il≤iu≤n , if n > 0 ; il = 1 and iu = 0 , if n = 0 . Not referenced if range = 'A' or ‘V’ .
- abstol
-
REAL for ssyevx DOUBLE PRECISION for dsyevx . The absolute error tolerance for the eigenvalues. See Application Notes for more information.
ldz
The leading dimension of the output array z ; ldz≥ 1 .
If jobz = 'V' , then ldz≥ max(1, n) for column major layout and lda ≥ max(1, m ) for row major layout .
lwork
The dimension of the array work . If n≤ 1 then lwork≥ 1 , otherwise lwork=8*n . If lwork = -1 , then a workspace query is assumed; the routine only calculates the optimal size of the work array, returns this value as the first entry of the work array, and no error message related to lwork is issued by xerbla . See Application Notes for the suggested value of lwork .
iwork
Workspace array, size at least max(1, 5 n ).
Output Parameters
- a
-
On exit, the lower triangle (if uplo = 'L' ) or the upper triangle (if uplo = 'U' ) of A , including the diagonal, is overwritten.
m
The total number of eigenvalues found;
0 ≤m≤n . If range = 'A' , m = n , and if range = 'I' , m = iu-il+1 .
- w
-
REAL for ssyevx DOUBLE PRECISION for dsyevx Array, size at least max(1, n ). The first m elements contain the selected eigenvalues of the matrix A in ascending order.
- z
-
REAL for ssyevx DOUBLE PRECISION for dsyevx .
Array z (size max(1, ldz * m ) for column major layout and max(1, ldz * n ) for row major layout) contains eigenvectors.
The second dimension of z must be at least max(1, m ). If jobz = 'V' , then if info = 0 , the first m columns of z contain the orthonormal eigenvectors of the matrix A corresponding to the selected eigenvalues, with the i-th column of z holding the eigenvector associated with w (i). If an eigenvector fails to converge, then that column of z contains the latest approximation to the eigenvector, and the index of the eigenvector is returned in ifail . If jobz = 'N' , then z is not referenced. Note: you must ensure that at least max(1, m ) columns are supplied in the array z ; if range = 'V' , the exact value of m is not known in advance and an upper bound must be used.
- work(1)
-
On exit, if lwork > 0 , then work(1) returns the required minimal size of lwork .
ifail
Array, size at least max(1, n ). If jobz = 'V' , then if info = 0 , the first m elements of ifail are zero; if info > 0 , then ifail contains the indices of the eigenvectors that failed to converge. If jobz = 'V' , then ifail is not referenced.
Return Values
This function returns a value info .
If info=0 , the execution is successful.
If info = -i , the i -th parameter had an illegal value.
If info = i , then i eigenvectors failed to converge; their indices are stored in the array ifail .
LAPACK 95 Interface Notes
There exist FORTRAN 77 and FORTRAN 95 interfaces for this routine. See the Intel® oneMKL Fortran Developer Reference for details.
Application Notes
An approximate eigenvalue is accepted as converged when it is determined to lie in an interval [a,b] of width less than or equal to \(\text{abstol}+\varepsilon\max(|a|,|b|)\) , where \(\varepsilon\) is the machine precision.
If abstol is less than or equal to zero, then \(\varepsilon||T||\) is used as tolerance, where || \(T\) || is the 1-norm of the tridiagonal matrix obtained by reducing \(A\) to tridiagonal form. Eigenvalues are computed most accurately when abstol is set to twice the underflow threshold 2* ?lamch (‘S’), not zero.
If this routine returns with info > 0 , indicating that some eigenvectors did not converge, try setting abstol to 2* ?lamch (‘S’).