Developer Reference for Intel® oneAPI Math Kernel Library for C
?spgv
Computes all eigenvalues and, optionally, eigenvectors of a real generalized symmetric definite eigenproblem with matrices in packed storage.
Syntax
lapack_intLAPACKE_sspgv ( intmatrix_layout , lapack_intitype , charjobz , charuplo , lapack_intn , float*ap , float*bp , float*w , float*z , lapack_intldz );
lapack_intLAPACKE_dspgv ( intmatrix_layout , lapack_intitype , charjobz , charuplo , lapack_intn , double*ap , double*bp , double*w , double*z , lapack_intldz );
Include Files
mkl.h
Description
sspgv dspgv spgv
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.
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 sspgv DOUBLE PRECISION for dspgv . 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, size at least max(1, 3 n ).
ldz
The leading dimension of the output array z ; ldz≥ 1 . If jobz = 'V' , ldz≥ max(1, n) .
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 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.
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 sspev / dspev returned an error code:
If info = i≤n , sspev / dspev 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.