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DGEEVRun Method

Purpose ======= DGEEV 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.

Namespace: DotNumerics.LinearAlgebra.CSLapack
Assembly: DWSIM.MathOps.DotNumerics (in DWSIM.MathOps.DotNumerics.dll) Version: 1.0.0.0 (1.0.0.0)
Syntax
Copy
public void Run(
	string JOBVL,
	string JOBVR,
	int N,
	ref double[] A,
	int offset_a,
	int LDA,
	ref double[] WR,
	int offset_wr,
	ref double[] WI,
	int offset_wi,
	ref double[] VL,
	int offset_vl,
	int LDVL,
	ref double[] VR,
	int offset_vr,
	int LDVR,
	ref double[] WORK,
	int offset_work,
	int LWORK,
	ref int INFO
)
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Parameters

JOBVL  String
(input) CHARACTER*1 = 'N': left eigenvectors of A are not computed; = 'V': left eigenvectors of A are computed.
JOBVR  String
(input) CHARACTER*1 = 'N': right eigenvectors of A are not computed; = 'V': right eigenvectors of A are computed.
N  Int32
(input) INTEGER The order of the matrix A. N .GE. 0.
A  Double
(input/output) DOUBLE PRECISION array, dimension (LDA,N) On entry, the N-by-N matrix A. On exit, A has been overwritten.
offset_a  Int32
 
LDA  Int32
(input) INTEGER The leading dimension of the array A. LDA .GE. max(1,N).
WR  Double
(output) DOUBLE PRECISION array, dimension (N)
offset_wr  Int32
 
WI  Double
(output) DOUBLE PRECISION 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.
offset_wi  Int32
 
VL  Double
(output) DOUBLE PRECISION 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, then u(j) = VL(:,j) + i*VL(:,j+1) and u(j+1) = VL(:,j) - i*VL(:,j+1).
offset_vl  Int32
 
LDVL  Int32
(input) INTEGER The leading dimension of the array VL. LDVL .GE. 1; if JOBVL = 'V', LDVL .GE. N.
VR  Double
(output) DOUBLE PRECISION 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).
offset_vr  Int32
 
LDVR  Int32
(input) INTEGER The leading dimension of the array VR. LDVR .GE. 1; if JOBVR = 'V', LDVR .GE. N.
WORK  Double
(workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
offset_work  Int32
 
LWORK  Int32
(input) INTEGER The dimension of the array WORK. LWORK .GE. max(1,3*N), and if JOBVL = 'V' or JOBVR = 'V', LWORK .GE. 4*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.
INFO  Int32
(output) INTEGER = 0: successful exit .LT. 0: if INFO = -i, the i-th argument had an illegal value. .GT. 0: if INFO = i, the QR algorithm failed to compute all the eigenvalues, and no eigenvectors have been computed; elements i+1:N of WR and WI contain eigenvalues which have converged.
See Also