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template<typename T>
void geev(char *jobvl, char *jobvr, integer *n, T *a, integer *lda, T *wr, T *wi, T *vl, integer *ldvl, T *vr, integer *ldvr, T *work, integer *lwork, integer *info)# GEEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices.
Purpose: \verbtatim GEEV computes for an N-by-N real nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors.
The right eigenvector v(j) of A satisfies A * v(j) = lambda(j) * v(j) where lambda(j) is its eigenvalue. The left eigenvector u(j) of A satisfies u(j)**H * A = lambda(j) * u(j)**H where u(j)**H denotes the conjugate-transpose of u(j).
The computed eigenvectors are normalized to have Euclidean norm equal to 1 and largest component real.
- Parameters:
JOBVL – [in]
JOBVL is CHARACTER*1
= ‘N’: left eigenvectors of A are not computed;
= ‘V’: left eigenvectors of A are computed.JOBVR – [in]
JOBVR is CHARACTER*1
= ‘N’: right eigenvectors of A are not computed;
= ‘V’: right eigenvectors of A are computed.N – [in]
N is INTEGER
The order of the matrix A. N >= 0.
A – [inout]
A is REAL array, dimension (LDA,N)
On entry, the N-by-N matrix A.
On exit, A has been overwritten.LDA – [in]
LDA is INTEGER
The leading dimension of the array A. LDA >= fla_max(1,N).
WR – [out] WR is REAL array, dimension (N)
WI – [out]
WI is REAL array, dimension (N)
WR and WI contain the real and imaginary parts, respectively, of the computed eigenvalues. Complex conjugate pairs of eigenvalues appear consecutively with the eigenvalue having the positive imaginary part first.
VL – [out]
VL is REAL array, dimension (LDVL,N)
If JOBVL = ‘V’, the left eigenvectors u(j) are stored one after another in the columns of VL, in the same order as their eigenvalues.
If JOBVL = ‘N’, VL is not referenced.
If the j-th eigenvalue is real, then u(j) = VL(:,j), the j-th column of VL.
If the j-th and (j+1)-st eigenvalues form a complex conjugate pair - computes row and column scaling to reduce condition number of matrixhen u(j@ = VL(:,j) + i*VL(:,j+1) and u(j+1) = VL(:,j)LDVL – [in]
LDVL is INTEGER
The leading dimension of the array VL. LDVL >= 1; if JOBVL = ‘V’, LDVL >= N.
VR – [out]
VR is REAL array, dimension (LDVR,N)
If JOBVR = ‘V’, the right eigenvectors v(j) are stored one after another in the columns of VR, in the same order as their eigenvalues.
If JOBVR = ‘N’, VR is not referenced.
If the j-th eigenvalue is real, then v(j) = VR(:,j), the j-th column of VR.
If the j-th and (j+1)-st eigenvalues form a complex conjugate pair, then v(j) = VR(:,j) + i*VR(:,j+1) and v(j+1) = VR(:,j) - i*VR(:,j+1).LDVR – [in]
LDVR is INTEGER
The leading dimension of the array VR. LDVR >= 1; if JOBVR = ‘V’, LDVR >= N.
WORK – [out]
WORK is COMPLEX array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK – [in]
LWORK is INTEGER
The dimension of the array WORK. LWORK >= fla_max(1,2*N). For good performance, LWORK must generally be larger.
If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.RWORK – [out] RWORK is REAL array, dimension (2*N)
INFO – [out]
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.
> 0: if INFO = i, the QR algorithm failed to compute all the eigenvalues, and no eigenvectors have been computed; elements i+1:N of W contain eigenvalues which have converged.