Developer Reference for Intel® oneAPI Math Kernel Library for C
?stevx
Computes selected eigenvalues and eigenvectors of a real symmetric tridiagonal matrix.
Syntax
lapack_intLAPACKE_sstevx ( intmatrix_layout , charjobz , charrange , lapack_intn , float*d , float*e , floatvl , floatvu , lapack_intil , lapack_intiu , floatabstol , lapack_int*m , float*w , float*z , lapack_intldz , lapack_int*ifail );
lapack_intLAPACKE_dstevx ( intmatrix_layout , charjobz , charrange , lapack_intn , double*d , double*e , doublevl , doublevu , lapack_intil , lapack_intiu , doubleabstol , lapack_int*m , double*w , double*z , lapack_intldz , lapack_int*ifail );
Include Files
mkl.h
Description
sstevx dstevx stevx
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.
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 job = 'N' , then only eigenvalues are computed. If job = 'V' , then eigenvalues and eigenvectors are computed.
range
Must be ‘A’ or ‘V’ or ‘I’ .
If range = 'A' , the routine computes all eigenvalues. If range = 'V' , the routine computes eigenvalues w(i)w[i] in the half-open interval: vl<w(i)w[i]≤vu . If range = 'I' , the routine computes eigenvalues with indices il to iu .
n
The order of the matrix A ( n≥ 0 ).
- d , e , work
-
REAL for sstevx DOUBLE PRECISION for dstevx . Arrays: 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. work (*) is a workspace array. The dimension of work must be at least max(1, 5 n ).
- vl , vu
-
REAL for sstevx DOUBLE PRECISION for dstevx . 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.
- abstol
-
REAL for sstevx DOUBLE PRECISION for dstevx . The absolute error tolerance to which each eigenvalue is required. See Application notes for details on error tolerance.
ldz
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 .
iwork
Workspace array, size at least max(1, 5 n ).
Output Parameters
m
The total number of eigenvalues found,
0 ≤m≤n . 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
-
REAL for sstevx DOUBLE PRECISION for dstevx . Arrays: 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) .
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)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. 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.
- d , e
-
On exit, these arrays may be multiplied by a constant factor chosen to avoid overflow or underflow in computing the eigenvalues.
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 , the ifail contains the indices of the eigenvectors that failed to converge. If jobz = 'N' , 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 \(\varepsilon |A|_{1}\) 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’).