Developer Reference for Intel® oneAPI Math Kernel Library for C
?spgvd
Computes all eigenvalues and, optionally, eigenvectors of a real generalized symmetric definite eigenproblem with matrices in packed storage using a divide and conquer method.
Syntax
lapack_intLAPACKE_sspgvd ( intmatrix_layout , lapack_intitype , charjobz , charuplo , lapack_intn , float*ap , float*bp , float*w , float*z , lapack_intldz );
lapack_intLAPACKE_dspgvd ( intmatrix_layout , lapack_intitype , charjobz , charuplo , lapack_intn , double*ap , double*bp , double*w , double*z , lapack_intldz );
Include Files
mkl.h
Description
sspgvd dspgvd spgvd
The routine computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-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 symmetric, 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
-
REAL for sspgvd DOUBLE PRECISION for dspgvd . Arrays:
ap contains the packed upper or lower triangle of the symmetric 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 symmetric 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≥ 2n ; If jobz = 'V' and n>1 , lwork≥ 2n^{2}+6n+1 . If lwork = -1 , then a workspace query is assumed; the routine only calculates the required sizes 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, dimension max(1, lwork) .
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 required sizes 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
- 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^{T}*U or B = L*L^{T} , in the same storage format as B .
- w , z
-
REAL for sspgv DOUBLE PRECISION for dspgv . 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. The eigenvectors are normalized as follows: if itype = 1 or 2 , Z^{T}*B*Z = I ; if itype = 3 , Z^{T}*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 .
- 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 , spptrf / dpptrf and sspevd / dspevd returned an error code:
If info = i≤n , sspevd / dspevd 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 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, then 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 ), then 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 lwork ( liwork ) is less than the minimal required value and is not equal to -1, then the routine returns immediately with an error exit and does not provide any information on the recommended workspace.