DHSEQRRun Method

public void Run(
	string JOB,
	string COMPZ,
	int N,
	int ILO,
	int IHI,
	ref double[] H,
	int offset_h,
	int LDH,
	ref double[] WR,
	int offset_wr,
	ref double[] WI,
	int offset_wi,
	ref double[] Z,
	int offset_z,
	int LDZ,
	ref double[] WORK,
	int offset_work,
	int LWORK,
	ref int INFO
)

Public Sub Run ( 
	JOB As String,
	COMPZ As String,
	N As Integer,
	ILO As Integer,
	IHI As Integer,
	ByRef H As Double(),
	offset_h As Integer,
	LDH As Integer,
	ByRef WR As Double(),
	offset_wr As Integer,
	ByRef WI As Double(),
	offset_wi As Integer,
	ByRef Z As Double(),
	offset_z As Integer,
	LDZ As Integer,
	ByRef WORK As Double(),
	offset_work As Integer,
	LWORK As Integer,
	ByRef INFO As Integer
)

Parameters

JOB  String

(input) CHARACTER*1 = 'E': compute eigenvalues only; = 'S': compute eigenvalues and the Schur form T.

COMPZ  String

(input) CHARACTER*1 = 'N': no Schur vectors are computed; = 'I': Z is initialized to the unit matrix and the matrix Z of Schur vectors of H is returned; = 'V': Z must contain an orthogonal matrix Q on entry, and the product Q*Z is returned.

N  Int32

(input) INTEGER The order of the matrix H. N .GE. 0.

ILO  Int32

(input) INTEGER

IHI  Int32

(input) INTEGER It is assumed that H is already upper triangular in rows and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally set by a previous call to DGEBAL, and then passed to DGEHRD when the matrix output by DGEBAL is reduced to Hessenberg form. Otherwise ILO and IHI should be set to 1 and N respectively. If N.GT.0, then 1.LE.ILO.LE.IHI.LE.N. If N = 0, then ILO = 1 and IHI = 0.

H  Double

(input/output) DOUBLE PRECISION array, dimension (LDH,N) On entry, the upper Hessenberg matrix H. On exit, if INFO = 0 and JOB = 'S', then H contains the upper quasi-triangular matrix T from the Schur decomposition (the Schur form); 2-by-2 diagonal blocks (corresponding to complex conjugate pairs of eigenvalues) are returned in standard form, with H(i,i) = H(i+1,i+1) and H(i+1,i)*H(i,i+1).LT.0. If INFO = 0 and JOB = 'E', the contents of H are unspecified on exit. (The output value of H when INFO.GT.0 is given under the description of INFO below.) Unlike earlier versions of DHSEQR, this subroutine may explicitly H(i,j) = 0 for i.GT.j and j = 1, 2, ... ILO-1 or j = IHI+1, IHI+2, ... N.

offset_h  Int32

 

LDH  Int32

(input) INTEGER The leading dimension of the array H. LDH .GE. max(1,N).

WR  Double

(output) DOUBLE PRECISION array, dimension (N)

offset_wr  Int32

 

WI  Double

(output) DOUBLE PRECISION array, dimension (N) The real and imaginary parts, respectively, of the computed eigenvalues. If two eigenvalues are computed as a complex conjugate pair, they are stored in consecutive elements of WR and WI, say the i-th and (i+1)th, with WI(i) .GT. 0 and WI(i+1) .LT. 0. If JOB = 'S', the eigenvalues are stored in the same order as on the diagonal of the Schur form returned in H, with WR(i) = H(i,i) and, if H(i:i+1,i:i+1) is a 2-by-2 diagonal block, WI(i) = sqrt(-H(i+1,i)*H(i,i+1)) and WI(i+1) = -WI(i).

offset_wi  Int32

 

Z  Double

(input/output) DOUBLE PRECISION array, dimension (LDZ,N) If COMPZ = 'N', Z is not referenced. If COMPZ = 'I', on entry Z need not be set and on exit, if INFO = 0, Z contains the orthogonal matrix Z of the Schur vectors of H. If COMPZ = 'V', on entry Z must contain an N-by-N matrix Q, which is assumed to be equal to the unit matrix except for the submatrix Z(ILO:IHI,ILO:IHI). On exit, if INFO = 0, Z contains Q*Z. Normally Q is the orthogonal matrix generated by DORGHR after the call to DGEHRD which formed the Hessenberg matrix H. (The output value of Z when INFO.GT.0 is given under the description of INFO below.)

offset_z  Int32

 

LDZ  Int32

(input) INTEGER The leading dimension of the array Z. if COMPZ = 'I' or COMPZ = 'V', then LDZ.GE.MAX(1,N). Otherwize, LDZ.GE.1.

WORK  Double

(workspace/output) DOUBLE PRECISION array, dimension (LWORK) On exit, if INFO = 0, WORK(1) returns an estimate of the optimal value for LWORK.

offset_work  Int32

 

LWORK  Int32

(input) INTEGER The dimension of the array WORK. LWORK .GE. max(1,N) is sufficient, but LWORK typically as large as 6*N may be required for optimal performance. A workspace query to determine the optimal workspace size is recommended. If LWORK = -1, then DHSEQR does a workspace query. In this case, DHSEQR checks the input parameters and estimates the optimal workspace size for the given values of N, ILO and IHI. The estimate is returned in WORK(1). No error message related to LWORK is issued by XERBLA. Neither H nor Z are accessed.

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, DHSEQR failed to compute all of the eigenvalues. Elements 1:ilo-1 and i+1:n of WR and WI contain those eigenvalues which have been successfully computed. (Failures are rare.) If INFO .GT. 0 and JOB = 'E', then on exit, the remaining unconverged eigenvalues are the eigen- values of the upper Hessenberg matrix rows and columns ILO through INFO of the final, output value of H. If INFO .GT. 0 and JOB = 'S', then on exit (*) (initial value of H)*U = U*(final value of H) where U is an orthogonal matrix. The final value of H is upper Hessenberg and quasi-triangular in rows and columns INFO+1 through IHI. If INFO .GT. 0 and COMPZ = 'V', then on exit (final value of Z) = (initial value of Z)*U where U is the orthogonal matrix in (*) (regard- less of the value of JOB.) If INFO .GT. 0 and COMPZ = 'I', then on exit (final value of Z) = U where U is the orthogonal matrix in (*) (regard- less of the value of JOB.) If INFO .GT. 0 and COMPZ = 'N', then Z is not accessed.

Reference