Computes selected eigenvalues and eigenvectors of a real symmetric tridiagonal matrix.
lapack_int LAPACKE_sstevx (int matrix_layout, char jobz, char range, lapack_int n, float* d, float* e, float vl, float vu, lapack_int il, lapack_int iu, float abstol, lapack_int* m, float* w, float* z, lapack_int ldz, lapack_int* ifail);
lapack_int LAPACKE_dstevx (int matrix_layout, char jobz, char range, lapack_int n, double* d, double* e, double vl, double vu, lapack_int il, lapack_int iu, double abstol, lapack_int* m, double* w, double* z, lapack_int ldz, lapack_int* ifail);
The routine computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix A. Eigenvalues and eigenvectors can be selected by specifying either a range of values or a range of indices for the desired eigenvalues.
Specifies whether matrix storage layout is row major (LAPACK_ROW_MAJOR) or column major (LAPACK_COL_MAJOR).
Must be 'N' or 'V'.
If job = 'N', then only eigenvalues are computed.
If job = 'V', then eigenvalues and eigenvectors are computed.
Must be 'A' or 'V' or 'I'.
If range = 'A', the routine computes all eigenvalues.
If range = 'V', the routine computes eigenvalues w[i] in the half-open interval: vl<w[i]≤vu.
If range = 'I', the routine computes eigenvalues with indices il to iu.
The order of the matrix A (n≥ 0).
- d, e
d contains the n diagonal elements of the tridiagonal matrix A.
The dimension of d must be at least max(1, n).
e contains the n-1 subdiagonal elements of A.
The dimension of e must be at least max(1, n-1). The n-th element of this array is used as workspace.
- vl, vu
If range = 'V', the lower and upper bounds of the interval to be searched for eigenvalues.
Constraint: vl< vu.
If range = 'A' or 'I', vl and vu are not referenced.
- il, iu
If range = 'I', the indices in ascending order of the smallest and largest eigenvalues to be returned.
Constraint: 1 ≤il≤iu≤n, if n > 0; il=1 and iu=0 if n = 0.
If range = 'A' or 'V', il and iu are not referenced.
The leading dimensions of the output array z; ldz≥ 1. If jobz = 'V', then ldz≥ max(1, n) for column major layout and ldz≥ max(1, m) for row major layout.
The total number of eigenvalues found,
If range = 'A', m = n, if range = 'I', m = iu-il+1, and if range = 'V' the exact value of m is unknown.
- w, z
w, size at least max(1, n).
The first m elements of w contain the selected eigenvalues of the matrix A in ascending order.
z(size at least max(1, ldz*m) for column major layout and max(1, ldz*n) for row major layout) .
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 - 1].
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.
- d, e
On exit, these arrays may be multiplied by a constant factor chosen to avoid overflow or underflow in computing the eigenvalues.
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, the ifail contains the indices of the eigenvectors that failed to converge.
If jobz = 'N', then ifail is not referenced.
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.
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 abstol+ε*max(|a|,|b|), where ε is the machine precision.
If abstol is less than or equal to zero, then ε*|A|1 is used instead. 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, set abstol to 2*?lamch('S').