Developer Reference for Intel® oneAPI Math Kernel Library for C
?hegvd
Computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian positive-definite eigenproblem using a divide and conquer method.
Syntax
lapack_int LAPACKE_chegvd ( intmatrix_layout , lapack_intitype , charjobz , charuplo , lapack_intn , lapack_complex_float*a , lapack_intlda , lapack_complex_float*b , lapack_intldb , float*w );
lapack_int LAPACKE_zhegvd ( intmatrix_layout , lapack_intitype , charjobz , charuplo , lapack_intn , lapack_complex_double*a , lapack_intlda , lapack_complex_double*b , lapack_intldb , double*w );
Include Files
mkl.h
Description
chegvd zhegvd hegvd
The routine computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian positive-definite eigenproblem, of the form
A*x = λ*B*x, A*B*x = λ*x , or B*A*x = λ*x .
Here A and B are assumed to be Hermitian and B is also positive definite.
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 ).
itype
Must be 1 or 2 or 3. Specifies the problem type to be solved:
if itype = 1 , the problem type is A*x = lambda*B*x ; if itype = 2 , the problem type is A*B*x = lambda*x ; if itype = 3 , the problem type is B*A*x = lambda*x .
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 a and b store the upper triangles of A and B ; If uplo = 'L' , arrays a and b store the lower triangles of A and B .
n
The order of the matrices A and B ( n≥ 0 ).
- a , b , work
-
COMPLEX for chegvd DOUBLE COMPLEX for zhegvd . Arrays:
a (size at least max(1, lda * n )) contains the upper or lower triangle of the Hermitian matrix A , as specified by uplo .
The second dimension of a must be at least max(1, n ).
b (size at least max(1, ldb * n )) contains the upper or lower triangle of the Hermitian positive definite matrix B , as specified by uplo .
The second dimension of b must be at least max(1, n ). work is a workspace array, its dimension max(1, lwork) .
lda
The leading dimension of a ; at least max(1, n ).
ldb
The leading dimension of b ; at least max(1, n ).
lwork
The dimension of the array work . Constraints: If n≤ 1 , lwork≥ 1 ; If jobz = 'N' and n>1 , lwork≥n +1; If jobz = 'V' and n>1 , lwork≥n^{2}+2n . If lwork = -1 , then a workspace query is assumed; the routine only calculates the optimal size of the work , rwork and iwork arrays, returns these values as the first entries of the work , rwork and iwork arrays, and no error message related to lwork or lrwork or liwork is issued by xerbla . See Application Notes for details.
- rwork
-
REAL for chegvd DOUBLE PRECISION for zhegvd . Workspace array, size max(1, lrwork) .
lrwork
The dimension of the array rwork . Constraints: If n≤ 1 , lrwork≥ 1 ; If jobz = 'N' and n>1 , lrwork≥n ; If jobz = 'V' and n>1 , lrwork≥ 2n^{2}+5n+1 . If lrwork = -1 , then a workspace query is assumed; the routine only calculates the optimal size of the work , rwork and iwork arrays, returns these values as the first entries of the work , rwork and iwork arrays, and no error message related to lwork or lrwork or liwork is issued by xerbla . See Application Notes for details.
iwork
Workspace array, size 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 , rwork and iwork arrays, returns these values as the first entries of the work , rwork and iwork arrays, and no error message related to lwork or lrwork or liwork is issued by xerbla . See Application Notes for details.
Output Parameters
- a
-
On exit, if jobz = 'V' , then if info = 0 , a contains the matrix Z of eigenvectors. The eigenvectors are normalized as follows: if itype = 1 or 2, Z^{H}* B*Z = I ; if itype = 3 , Z^{H}*inv(B)*Z = I ; If jobz = 'N' , then on exit the upper triangle (if uplo = 'U' ) or the lower triangle (if uplo = 'L' ) of A , including the diagonal, is destroyed.
- b
-
On exit, if info≤n , the part of b containing the matrix is overwritten by the triangular factor U or L from the Cholesky factorization B = U^{H}*U or B = L*L^{H} .
- w
-
REAL for chegvd DOUBLE PRECISION for zhegvd . Array, size at least max(1, n ). If info = 0 , contains the eigenvalues in ascending order.
- work(1)
-
On exit, if info = 0 , then work(1) returns the required minimal size of lwork .
- rwork(1)
-
On exit, if info = 0 , then rwork(1) returns the required minimal size of lrwork .
- 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 = i , and jobz = 'N' , then the algorithm failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not converge to zero;
if info = i , and jobz = 'V' , then the algorithm failed to compute an eigenvalue while working on the submatrix lying in rows and columns info/(n+1) through mod(info, n+1) .
If info = n + i , for 1 ≤i≤n , then the leading minor of order i of 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 you are in doubt how much workspace to supply, use a generous value of lwork ( liwork or lrwork ) for the first run or set lwork = -1 ( liwork = -1 , lrwork = -1 ).
If you choose the first option and set any of admissible lwork ( liwork or lrwork ) 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 , rwork ) on exit. Use this value ( work(1) , iwork(1) , rwork(1) ) for subsequent runs.
If you set lwork = -1 ( liwork = -1 , lrwork = -1 ), the routine returns immediately and provides the recommended workspace in the first element of the corresponding array ( work , iwork , rwork ). This operation is called a workspace query.
Note that if you set lwork ( liwork , lrwork ) to less than the minimal required value and not -1, the routine returns immediately with an error exit and does not provide any information on the recommended workspace.