Developer Reference for Intel® oneAPI Math Kernel Library for C
?syevd
Computes all eigenvalues and, optionally, all eigenvectors of a real symmetric matrix using divide and conquer algorithm.
Syntax
lapack_intLAPACKE_ssyevd ( intmatrix_layout , charjobz , charuplo , lapack_intn , float*a , lapack_intlda , float*w );
lapack_intLAPACKE_dsyevd ( intmatrix_layout , charjobz , charuplo , lapack_intn , double*a , lapack_intlda , double*w );
Include Files
mkl.h
Description
ssyevd dsyevd syevd
The routine computes all the eigenvalues, and optionally all the eigenvectors, of a real symmetric matrix A . In other words, it can compute the spectral factorization of A as: A = Z*λ*Z^{T} .
Here Λ is a diagonal matrix whose diagonal elements are the eigenvalues λ i , and Z is the orthogonal matrix whose columns are the eigenvectors zi . Thus,
A*z_{i} = λ_{i}*z_{i} for i = 1, 2, ..., n .
If the eigenvectors are requested, then this routine uses a divide and conquer algorithm to compute eigenvalues and eigenvectors. However, if only eigenvalues are required, then it uses the Pal-Walker-Kahan variant of the QL or QR algorithm.
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. ?syevd requires more workspace but is faster in some cases, especially for large matrices.
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
-
REAL for ssyevd DOUBLE PRECISION for dsyevd Array, size ( lda , *).
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 ).
lda
The leading dimension of the array a .
Must be at least max(1, n ).
- work
-
REAL for ssyevd DOUBLE PRECISION for dsyevd . Workspace array, size at least lwork .
lwork
The dimension of the array work . Constraints: if n≤ 1 , then lwork≥ 1 ; if jobz = 'N' and n > 1, then lwork≥ 2*n + 1 ; if jobz = 'V' and n > 1, then lwork≥ 2*n^{2}+ 6*n + 1 . If lwork = -1 , then a workspace query is assumed; the routine only calculates the required sizes of the work and iwork arrays, returns these values as the first entries of the work and iwork arrays, and no error message related to lwork or liwork is issued by xerbla . See Application Notes for details.
iwork
Workspace array, its dimension max(1, liwork) .
liwork
The dimension of the array iwork . Constraints: if n≤ 1 , then liwork≥ 1 ; if jobz = 'N' and n > 1, then liwork≥ 1 ; if jobz = 'V' and n > 1, then liwork≥ 5*n + 3 . If liwork = -1 , then a workspace query is assumed; the routine only calculates the required sizes of the work and iwork arrays, returns these values as the first entries of the work and iwork arrays, and no error message related to lwork or liwork is issued by xerbla . See Application Notes for details.
Output Parameters
- w
-
REAL for ssyevd DOUBLE PRECISION for dsyevd Array, size at least max(1, n ). If info = 0 , contains the eigenvalues of the matrix A in ascending order. See also info .
- a
-
If jobz = 'V' , then on exit this array is overwritten by the orthogonal matrix Z which contains the eigenvectors of A .
- work(1)
-
On exit, if lwork > 0, then work(1) returns the required minimal size of lwork .
- iwork(1)
-
On exit, if liwork > 0, then iwork(1) returns the required minimal size of liwork .
Return Values
This function returns a value info .
If info=0 , the execution is successful.
If info = i , and jobz = 'N' , then the algorithm failed to converge; i indicates the number of off-diagonal elements of an intermediate tridiagonal form which did not converge to zero.
If info = i , and jobz = 'V' , then the algorithm failed to compute an eigenvalue while working on the submatrix lying in rows and columns info/(n+1) through mod(info,n+1) .
If info = -i , the i -th parameter had an illegal value.
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
The computed eigenvalues and eigenvectors are exact for a matrix \(A+E\) such that \(||E||_{2} = O(\varepsilon) ||A||_{2}\) , where \(\varepsilon\) is the machine precision.
The complex analogue of this routine is heevd