Managed
Definition
Namespace: Numerics.NET.LinearAlgebra.Implementation
Assembly: Numerics.NET (in Numerics.NET.dll) Version: 9.0.3
Assembly: Numerics.NET (in Numerics.NET.dll) Version: 9.0.3
Overload List
EigenvalueDecompose(Char, Char, Int32, Span<Complex<Double>>, Int32, Span<Complex<Double>>, Span<Complex<Double>>, Int32, Span<Complex<Double>>, Int32, Int32)
Computes for an N-by-N complex non-symmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors.
public override void EigenvalueDecompose(
char jobvl,
char jobvr,
int n,
Span<Complex<double>> a,
int lda,
Span<Complex<double>> w,
Span<Complex<double>> vl,
int ldvl,
Span<Complex<double>> vr,
int ldvr,
out int info
)Parameters
- jobvl Char
= 'N': left eigenvectors of A are not computed; = 'V': left eigenvectors of are computed.- jobvr Char
= 'N': right eigenvectors of A are not computed; = 'V': right eigenvectors of A are computed.- n Int32
The order of the matrix A. N >= 0.- a Span<Complex<Double>>
A is TComplex array, dimension (LDA,N) On entry, the N-by-N matrix A. On exit, A has been overwritten.- lda Int32
The leading dimension of the array A. LDA >= max(1,N).- w Span<Complex<Double>>
W is TComplex array, dimension (N) W contains the computed eigenvalues.- vl Span<Complex<Double>>
VL is TComplex 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. u(j) = VL(:,j), the j-th column of VL.- ldvl Int32
The leading dimension of the array VL. LDVL >= 1; if JOBVL = 'V', LDVL >= N.- vr Span<Complex<Double>>
VR is TComplex 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. v(j) = VR(:,j), the j-th column of VR.- ldvr Int32
The leading dimension of the array VR. LDVR >= 1; if JOBVR = 'V', LDVR >= N.- info Int32
= 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 and i+1:N of W contain eigenvalues which have converged.
Remarks
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.
Authors: Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver, NAG Ltd.
Date: November 2011
EigenvalueDecompose(Char, Char, Int32, Span<Double>, Int32, Span<Double>, Span<Double>, Span<Double>, Int32, Span<Double>, Int32, Int32)
Computes for an N-by-N real non-symmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors.
public override void EigenvalueDecompose(
char jobvl,
char jobvr,
int n,
Span<double> a,
int lda,
Span<double> wr,
Span<double> wi,
Span<double> vl,
int ldvl,
Span<double> vr,
int ldvr,
out int info
)Parameters
- jobvl Char
= 'N': left eigenvectors of A are not computed; = 'V': left eigenvectors of A are computed.- jobvr Char
= 'N': right eigenvectors of A are not computed; = 'V': right eigenvectors of A are computed.- n Int32
The order of the matrix A. N >= 0.- a Span<Double>
A is TReal array, dimension (LDA,N) On entry, the N-by-N matrix A. On exit, A has been overwritten.- lda Int32
The leading dimension of the array A. LDA >= max(1,N).- wr Span<Double>
WR is TReal array, dimension (N)- wi Span<Double>
WI is TReal 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 Span<Double>
VL is TReal 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).- ldvl Int32
The leading dimension of the array VL. LDVL >= 1; if JOBVL = 'V', LDVL >= N.- vr Span<Double>
VR is TReal 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 Int32
The leading dimension of the array VR. LDVR >= 1; if JOBVR = 'V', LDVR >= N.- info Int32
= 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 WR and WI contain eigenvalues which have converged.
Remarks
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)**T * A = lambda(j) * u(j)**T
where u(j)**T denotes the transpose of u(j).
The computed eigenvectors are normalized to have Euclidean norm
equal to 1 and largest component real.
This method corresponds to the LAPACK routine ?GEEV.