Developer Reference for Intel® oneAPI Math Kernel Library for C
?heev
Computes all eigenvalues and, optionally, eigenvectors of a Hermitian matrix.
Syntax
lapack_int LAPACKE_cheev ( intmatrix_layout , charjobz , charuplo , lapack_intn , lapack_complex_float*a , lapack_intlda , float*w );
lapack_int LAPACKE_zheev ( intmatrix_layout , charjobz , charuplo , lapack_intn , lapack_complex_double*a , lapack_intlda , double*w );
Include Files
mkl.h
Description
cheev zheev heev
The routine computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A .
Note that for most cases of complex Hermitian eigenvalue problems the default choice should be heevr function as its underlying algorithm is faster and uses less workspace.
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.
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
-
COMPLEX for cheev DOUBLE COMPLEX for zheev Arrays:
a (size max(1, lda * n )) is an array containing either upper or lower triangular part of the Hermitian 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 ).
lwork
The dimension of the array work . C onstraint: lwork≥ max(1, 2n-1) . 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 .
- rwork
-
REAL for cheev DOUBLE PRECISION for zheev . Workspace array, size at least max(1, 3 n -2).
Output Parameters
- a
-
On exit, if jobz = 'V' , then if info = 0 , array a contains the orthonormal eigenvectors of the matrix A . If jobz = 'N' , then on exit the lower triangle (if uplo = 'L' ) or the upper triangle (if uplo = 'U' ) of A , including the diagonal, is overwritten.
- w
-
REAL for cheev DOUBLE PRECISION for zheev Array, size at least max(1, n ). If info = 0 , contains the eigenvalues of the matrix A in ascending order.
- work(1)
-
On exit, if lwork > 0, then work(1) returns the required minimal size of lwork .
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 the algorithm failed to converge; i indicates the number of elements of an intermediate tridiagonal form which did not converge to zero.
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
For optimum performance use
lwork≥ (nb+1)*n ,
where nb is the blocksize for ?hetrd returned by ilaenv .
If you are in doubt how much workspace to supply, use a generous value of lwork for the first run or set lwork = -1 .
If you choose the first option and set any of admissible lwork sizes, which is no less than the minimal value described, the routine completes the task, though probably not so fast as with a recommended workspace, and provides the recommended workspace in the first element of the corresponding array work on exit. Use this value ( work(1) ) for subsequent runs.
If you set lwork = -1 , the routine returns immediately and provides the recommended workspace in the first element of the corresponding array ( work ). This operation is called a workspace query.
Note that if you set lwork to less than the minimal required value and not -1, the routine returns immediately with an error exit and does not provide any information on the recommended workspace.