Developer Reference for Intel® oneAPI Math Kernel Library for C
?hpgvd
Computes all eigenvalues and, optionally, eigenvectors of a complex generalized Hermitian positive-definite eigenproblem with matrices in packed storage using a divide and conquer method.
Syntax
lapack_int LAPACKE_chpgvd ( intmatrix_layout , lapack_intitype , charjobz , charuplo , lapack_intn , lapack_complex_float*ap , lapack_complex_float*bp , float*w , lapack_complex_float*z , lapack_intldz );
lapack_int LAPACKE_zhpgvd ( intmatrix_layout , lapack_intitype , charjobz , charuplo , lapack_intn , lapack_complex_double*ap , lapack_complex_double*bp , double*w , lapack_complex_double*z , lapack_intldz );
Include Files
mkl.h
Description
chpgvd zhpgvd hpgvd
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, stored in packed format, 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 ).
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 ap and bp store the upper triangles of A and B ; If uplo = 'L' , arrays ap and bp store the lower triangles of A and B .
n
The order of the matrices A and B ( n≥ 0 ).
- ap , bp , work
-
COMPLEX for chpgvd DOUBLE COMPLEX for zhpgvd . Arrays:
ap contains the packed upper or lower triangle of the Hermitian matrix A , as specified by uplo .
The dimension of ap must be at least max(1, n *( n +1)/2).
bp contains the packed upper or lower triangle of the Hermitian matrix B , as specified by uplo .
The dimension of bp must be at least max(1, n *( n +1)/2). work is a workspace array, its dimension max(1, lwork) .
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≥n ; If jobz = 'V' and n>1 , lwork≥ 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 chpgvd DOUBLE PRECISION for zhpgvd . Workspace array, its dimension 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, 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 , 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
- ap
-
On exit, the contents of ap are overwritten.
- bp
-
On exit, contains the triangular factor U or L from the Cholesky factorization B = U^{H}*U or B = L*L^{H} , in the same storage format as B .
- w
-
REAL for chpgvd DOUBLE PRECISION for zhpgvd . Array, size at least max(1, n ). If info = 0 , contains the eigenvalues in ascending order.
- z
-
COMPLEX for chpgvd DOUBLE COMPLEX for zhpgvd .
Array 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. 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 z is not referenced.
- 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 > 0 , cpptrf / zpptrf and chpevd / zhpevd returned an error code:
If info = i≤n , chpevd / zhpevd 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 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.