Developer Reference for Intel® oneAPI Math Kernel Library for C
?sbgv
Computes all eigenvalues and, optionally, eigenvectors of a real generalized symmetric definite eigenproblem with banded matrices.
Syntax
lapack_intLAPACKE_ssbgv ( intmatrix_layout , charjobz , charuplo , lapack_intn , lapack_intka , lapack_intkb , float*ab , lapack_intldab , float*bb , lapack_intldbb , float*w , float*z , lapack_intldz );
lapack_intLAPACKE_dsbgv ( intmatrix_layout , charjobz , charuplo , lapack_intn , lapack_intka , lapack_intkb , double*ab , lapack_intldab , double*bb , lapack_intldbb , double*w , double*z , lapack_intldz );
Include Files
mkl.h
Description
ssbgv dsbgv sbgv
The routine computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite banded eigenproblem, of the form A*x = λ*B*x . Here A and B are assumed to be symmetric and banded, and B is also positive definite.
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 compute eigenvalues only. If jobz = 'V' , then compute eigenvalues and eigenvectors.
uplo
Must be ‘U’ or ‘L’ .
If uplo = 'U' , arrays ab and bb store the upper triangles of A and B ; If uplo = 'L' , arrays ab and bb store the lower triangles of A and B .
n
The order of the matrices A and B ( n≥ 0 ).
ka
The number of super- or sub-diagonals in A
( ka≥ 0 ).
kb
The number of super- or sub-diagonals in B ( kb ≥ 0).
- ab , bb , work
-
REAL for ssbgv DOUBLE PRECISION for dsbgv Arrays:
ab (size at least max(1, ldab * n ) for column major layout and max(1, ldab *( ka + 1)) for row major layout) is an array containing either upper or lower triangular part of the symmetric matrix A (as specified by uplo ) in band storage format.
The second dimension of the array ab must be at least max(1, n ).
bb (size at least max(1, ldbb * n ) for column major layout and max(1, ldbb *( kb + 1)) for row major layout) is an array containing either upper or lower triangular part of the symmetric matrix B (as specified by uplo ) in band storage format.
The second dimension of the array bb must be at least max(1, n ). work(*) is a workspace array, dimension at least max(1, 3 n )
ldab
The leading dimension of the array ab ; must be at least ka +1 for column major layout and at least max(1, n ) for row major layout .
ldbb
The leading dimension of the array bb ; must be at least kb +1 for column major layout and at least max(1, n ) for row major layout .
ldz
The leading dimension of the output array z ; ldz≥ 1 . If jobz = 'V' , ldz≥ max(1, n) .
Output Parameters
- ab
-
On exit, the contents of ab are overwritten.
- bb
-
On exit, contains the factor S from the split Cholesky factorization B = S^{T}*S , as returned by pbstf / pbstf .
- w , z
-
REAL for ssbgv DOUBLE PRECISION for dsbgv Arrays:
w , size at least max(1, n ).
If info = 0 , contains the eigenvalues in ascending order.
z (size at least max(1, ldz * n )) .
The second dimension of z must be at least max(1, n ). If jobz = 'V' , then if info = 0 , z contains the matrix Z of eigenvectors, with the i -th column of z holding the eigenvector associated with w(i). The eigenvectors are normalized so that Z^{T}*B*Z = I . If jobz = 'N' , then z 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 > 0 , and
if i≤n , the algorithm failed to converge, and i off-diagonal elements of an intermediate tridiagonal did not converge to zero;
if info = n + i , for 1 ≤i≤n , then pbstf / pbstf returned info = i and B is not positive-definite. The factorization of B could not be completed and no eigenvalues or eigenvectors were computed.
LAPACK 95 Interface Notes
There exist FORTRAN 77 and FORTRAN 95 interfaces for this routine. See the Intel® oneMKL Fortran Developer Reference for details.