DTREVCRun Method

Purpose ======= DTREVC computes some or all of the right and/or left eigenvectors of a real upper quasi-triangular matrix T. Matrices of this type are produced by the Schur factorization of a real general matrix: A = Q*T*Q**T, as computed by DHSEQR. The right eigenvector x and the left eigenvector y of T corresponding to an eigenvalue w are defined by: T*x = w*x, (y**H)*T = w*(y**H) where y**H denotes the conjugate transpose of y. The eigenvalues are not input to this routine, but are read directly from the diagonal blocks of T. This routine returns the matrices X and/or Y of right and left eigenvectors of T, or the products Q*X and/or Q*Y, where Q is an input matrix. If Q is the orthogonal factor that reduces a matrix A to Schur form T, then Q*X and Q*Y are the matrices of right and left eigenvectors of A.

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 SIDE,
	string HOWMNY,
	ref bool[] SELECT,
	int offset_select,
	int N,
	double[] T,
	int offset_t,
	int LDT,
	ref double[] VL,
	int offset_vl,
	int LDVL,
	ref double[] VR,
	int offset_vr,
	int LDVR,
	int MM,
	ref int M,
	ref double[] WORK,
	int offset_work,
	ref int INFO
)

Public Sub Run ( 
	SIDE As String,
	HOWMNY As String,
	ByRef SELECT As Boolean(),
	offset_select As Integer,
	N As Integer,
	T As Double(),
	offset_t As Integer,
	LDT As Integer,
	ByRef VL As Double(),
	offset_vl As Integer,
	LDVL As Integer,
	ByRef VR As Double(),
	offset_vr As Integer,
	LDVR As Integer,
	MM As Integer,
	ByRef M As Integer,
	ByRef WORK As Double(),
	offset_work As Integer,
	ByRef INFO As Integer
)

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Parameters

SIDE String: (input) CHARACTER*1 = 'R': compute right eigenvectors only; = 'L': compute left eigenvectors only; = 'B': compute both right and left eigenvectors.
HOWMNY String: (input) CHARACTER*1 = 'A': compute all right and/or left eigenvectors; = 'B': compute all right and/or left eigenvectors, backtransformed by the matrices in VR and/or VL; = 'S': compute selected right and/or left eigenvectors, as indicated by the logical array SELECT.
SELECT Boolean: (input/output) LOGICAL array, dimension (N) If HOWMNY = 'S', SELECT specifies the eigenvectors to be computed. If w(j) is a real eigenvalue, the corresponding real eigenvector is computed if SELECT(j) is .TRUE.. If w(j) and w(j+1) are the real and imaginary parts of a complex eigenvalue, the corresponding complex eigenvector is computed if either SELECT(j) or SELECT(j+1) is .TRUE., and on exit SELECT(j) is set to .TRUE. and SELECT(j+1) is set to .FALSE.. Not referenced if HOWMNY = 'A' or 'B'.
offset_select Int32
N Int32: (input) INTEGER The order of the matrix T. N .GE. 0.
T Double: (input) DOUBLE PRECISION array, dimension (LDT,N) The upper quasi-triangular matrix T in Schur canonical form.
offset_t Int32
LDT Int32: (input) INTEGER The leading dimension of the array T. LDT .GE. max(1,N).
VL Double: (input/output) DOUBLE PRECISION array, dimension (LDVL,MM) On entry, if SIDE = 'L' or 'B' and HOWMNY = 'B', VL must contain an N-by-N matrix Q (usually the orthogonal matrix Q of Schur vectors returned by DHSEQR). On exit, if SIDE = 'L' or 'B', VL contains: if HOWMNY = 'A', the matrix Y of left eigenvectors of T; if HOWMNY = 'B', the matrix Q*Y; if HOWMNY = 'S', the left eigenvectors of T specified by SELECT, stored consecutively in the columns of VL, in the same order as their eigenvalues. A complex eigenvector corresponding to a complex eigenvalue is stored in two consecutive columns, the first holding the real part, and the second the imaginary part. Not referenced if SIDE = 'R'.
offset_vl Int32
LDVL Int32: (input) INTEGER The leading dimension of the array VL. LDVL .GE. 1, and if SIDE = 'L' or 'B', LDVL .GE. N.
VR Double: (input/output) DOUBLE PRECISION array, dimension (LDVR,MM) On entry, if SIDE = 'R' or 'B' and HOWMNY = 'B', VR must contain an N-by-N matrix Q (usually the orthogonal matrix Q of Schur vectors returned by DHSEQR). On exit, if SIDE = 'R' or 'B', VR contains: if HOWMNY = 'A', the matrix X of right eigenvectors of T; if HOWMNY = 'B', the matrix Q*X; if HOWMNY = 'S', the right eigenvectors of T specified by SELECT, stored consecutively in the columns of VR, in the same order as their eigenvalues. A complex eigenvector corresponding to a complex eigenvalue is stored in two consecutive columns, the first holding the real part and the second the imaginary part. Not referenced if SIDE = 'L'.
offset_vr Int32
LDVR Int32: (input) INTEGER The leading dimension of the array VR. LDVR .GE. 1, and if SIDE = 'R' or 'B', LDVR .GE. N.
MM Int32: (input) INTEGER The number of columns in the arrays VL and/or VR. MM .GE. M.
M Int32: (output) INTEGER The number of columns in the arrays VL and/or VR actually used to store the eigenvectors. If HOWMNY = 'A' or 'B', M is set to N. Each selected real eigenvector occupies one column and each selected complex eigenvector occupies two columns.
WORK Double: (workspace) DOUBLE PRECISION array, dimension (3*N)
offset_work Int32
INFO Int32: (output) INTEGER = 0: successful exit .LT. 0: if INFO = -i, the i-th argument had an illegal value

Reference

DTREVC Class

DotNumerics.LinearAlgebra.CSLapack Namespace