Developer Reference for Intel® oneAPI Math Kernel Library for C
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?spevd
Uses divide and conquer algorithm to compute all eigenvalues and (optionally) all eigenvectors of a real symmetric matrix held in packed storage.
Syntax
lapack_int LAPACKE_sspevd (int matrix_layout, char jobz, char uplo, lapack_int n, float* ap, float* w, float* z, lapack_int ldz);
lapack_int LAPACKE_dspevd (int matrix_layout, char jobz, char uplo, lapack_int n, double* ap, double* w, double* z, lapack_int ldz);
Include Files
- mkl.h
Description
The routine computes all the eigenvalues, and optionally all the eigenvectors, of a real symmetric matrix A (held in packed storage). In other words, it can compute the spectral factorization of A as:
A = Z*Λ*ZT.
Here Λ is a diagonal matrix whose diagonal elements are the eigenvalues λi, and Z is the orthogonal matrix whose columns are the eigenvectors zi. Thus,
A*zi = λi*zi 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.
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', ap stores the packed upper triangular part of A.
If uplo = 'L', ap stores the packed lower triangular part of A.
- n
-
The order of the matrix A (n≥ 0).
- ap
-
ap contains the packed upper or lower triangle of symmetric matrix A, as specified by uplo.
The dimension of ap must be max(1, n*(n+1)/2)
- ldz
-
The leading dimension of the output array z.
Constraints:
if jobz = 'N', then ldz≥ 1;
if jobz = 'V', then ldz≥ max(1, n).
Output Parameters
- w, z
-
Arrays:
w, size at least max(1, n).
If info = 0, contains the eigenvalues of the matrix A in ascending order. See also info.
z (size max(1, ldz*n)).
If jobz = 'V', then this array is overwritten by the orthogonal matrix Z which contains the eigenvectors of A. If jobz = 'N', then z is not referenced.
- ap
-
On exit, this array is overwritten by the values generated during the reduction to tridiagonal form. The elements of the diagonal and the off-diagonal of the tridiagonal matrix overwrite the corresponding elements of A.
Return Values
This function returns a value info.
If info=0, the execution is successful.
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.
If info = -i, the i-th parameter had an illegal value.