Developer Reference for Intel® oneAPI Math Kernel Library for C
?spevx
Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix in packed storage.
Syntax
lapack_intLAPACKE_sspevx ( intmatrix_layout , charjobz , charrange , charuplo , lapack_intn , float*ap , floatvl , floatvu , lapack_intil , lapack_intiu , floatabstol , lapack_int*m , float*w , float*z , lapack_intldz , lapack_int*ifail );
lapack_intLAPACKE_dspevx ( intmatrix_layout , charjobz , charrange , charuplo , lapack_intn , double*ap , doublevl , doublevu , lapack_intil , lapack_intiu , doubleabstol , lapack_int*m , double*w , double*z , lapack_intldz , lapack_int*ifail );
Include Files
mkl.h
Description
sspevx dspevx spevx
The routine computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage. 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 .
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 , work
-
REAL for sspevx DOUBLE PRECISION for dspevx Arrays:
Array ap contains the packed upper or lower triangle of the symmetric matrix A , as specified by uplo .
The size of ap must be at least max(1, n *( n +1)/2). work(*) is a workspace array, size at least max(1, 8 n ).
- vl , vu
-
REAL for sspevx DOUBLE PRECISION for dspevx 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 sspevx DOUBLE PRECISION for dspevx The absolute error tolerance to which each eigenvalue is required. See Application notes for details on error tolerance.
ldz
The leading dimension of the output array z .
Constraints: if jobz = 'N' , then 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
- 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 .
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 not known in advance..
- w , z
-
REAL for sspevx DOUBLE PRECISION for dspevx Arrays:
w , size at least max(1, n ).
If info = 0 , contains the selected eigenvalues of the matrix A in ascending order.
z (size 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.
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 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 \(\varepsilon ||T||_{1}\) will be used in its place, where \(T\) is the tridiagonal matrix obtained by reducing \(A\) to tridiagonal form. Eigenvalues will be 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, try setting abstol to 2* ?lamch (‘S’).