Developer Reference for Intel® oneAPI Math Kernel Library for C
?sbgvd
Computes all eigenvalues and, optionally, eigenvectors of a real generalized symmetric definite eigenproblem with banded matrices. If eigenvectors are desired, it uses a divide and conquer method.
Syntax
lapack_intLAPACKE_ssbgvd ( 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_dsbgvd ( 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
ssbgvd dsbgvd sbgvd
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.
If eigenvectors are desired, it uses a divide and conquer 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 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 ssbgvd DOUBLE PRECISION for dsbgvd 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, its dimension max(1, lwork) .
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) .
lwork
The dimension of the array work . Constraints: If n≤ 1 , lwork≥ 1 ; If jobz = 'N' and n>1 , lwork ≥ 3 n ; If jobz = 'V' and n>1 , lwork≥ 2n^{2}+5n+1 . If lwork = -1 , then a workspace query is assumed; the routine only calculates the optimal size of the work and iwork arrays, returns these values as the first entries of the work and iwork arrays, and no error message related to lwork or liwork is issued by xerbla . See Application Notes for details.
iwork
Workspace array, its dimension max(1, liwork) .
liwork
The dimension of the array iwork . Constraints: If n≤ 1 , liwork≥ 1 ; If jobz = 'N' and n>1 , liwork≥ 1 ; If jobz = 'V' and n>1 , liwork≥ 5n+3 . If liwork = -1 , then a workspace query is assumed; the routine only calculates the optimal size of the work and iwork arrays, returns these values as the first entries of the work and iwork arrays, and no error message related to lwork or liwork is issued by xerbla . See Application Notes for details.
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 ssbgvd DOUBLE PRECISION for dsbgvd 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)[i - 1] . The eigenvectors are normalized so that Z:code:`T`*B * Z = I. If jobz = 'N' , then z is not referenced.
- work(1)
-
On exit, if info = 0 , then work(1) returns the required minimal size of lwork .
- iwork(1)
-
On exit, if info = 0 , then iwork(1) returns the required minimal size of liwork .
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.
Application Notes
If it is not clear how much workspace to supply, use a generous value of lwork (or liwork ) for the first run or set lwork = -1 ( liwork = -1 ).
If lwork (or liwork ) has any of admissible sizes, which is no less than the minimal value described, the routine completes the task, though probably not so fast as with a recommended workspace, and provides the recommended workspace in the first element of the corresponding array ( work , iwork ) on exit. Use this value ( work(1) , iwork(1) ) for subsequent runs.
If lwork = -1 ( liwork = -1 ), the routine returns immediately and provides the recommended workspace in the first element of the corresponding array ( work , iwork ). This operation is called a workspace query.
Note that if work ( liwork ) is less than the minimal required value and is not equal to -1, the routine returns immediately with an error exit and does not provide any information on the recommended workspace.