DLAQR4Run Method

public void Run(
	bool WANTT,
	bool WANTZ,
	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,
	int ILOZ,
	int IHIZ,
	ref double[] Z,
	int offset_z,
	int LDZ,
	ref double[] WORK,
	int offset_work,
	int LWORK,
	ref int INFO
)

Public Sub Run ( 
	WANTT As Boolean,
	WANTZ As Boolean,
	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,
	ILOZ As Integer,
	IHIZ 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

WANTT  Boolean

(input) LOGICAL = .TRUE. : the full Schur form T is required; = .FALSE.: only eigenvalues are required.

WANTZ  Boolean

(input) LOGICAL = .TRUE. : the matrix of Schur vectors Z is required; = .FALSE.: Schur vectors are not required.

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 and, if ILO.GT.1, H(ILO,ILO-1) is zero. 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 WANTT is .TRUE., 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 WANTT is .FALSE., then 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.) This subroutine may explicitly set 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 (IHI)

offset_wr  Int32

 

WI  Double

(output) DOUBLE PRECISION array, dimension (IHI) The real and imaginary parts, respectively, of the computed eigenvalues of H(ILO:IHI,ILO:IHI) are stored WR(ILO:IHI) and WI(ILO:IHI). 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 WANTT is .TRUE., then 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

 

ILOZ  Int32

(input) INTEGER

IHIZ  Int32

(input) INTEGER Specify the rows of Z to which transformations must be applied if WANTZ is .TRUE.. 1 .LE. ILOZ .LE. ILO; IHI .LE. IHIZ .LE. N.

Z  Double

(input/output) DOUBLE PRECISION array, dimension (LDZ,IHI) If WANTZ is .FALSE., then Z is not referenced. If WANTZ is .TRUE., then Z(ILO:IHI,ILOZ:IHIZ) is replaced by Z(ILO:IHI,ILOZ:IHIZ)*U where U is the orthogonal Schur factor of H(ILO:IHI,ILO:IHI). (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 WANTZ is .TRUE. then LDZ.GE.MAX(1,IHIZ). Otherwize, LDZ.GE.1.

WORK  Double

(workspace/output) DOUBLE PRECISION array, dimension LWORK On exit, if LWORK = -1, 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 DLAQR4 does a workspace query. In this case, DLAQR4 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 .GT. 0: if INFO = i, DLAQR4 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 WANT is .FALSE., 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 WANTT is .TRUE., 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 WANTZ is .TRUE., then on exit (final value of Z(ILO:IHI,ILOZ:IHIZ) = (initial value of Z(ILO:IHI,ILOZ:IHIZ)*U where U is the orthogonal matrix in (*) (regard- less of the value of WANTT.) If INFO .GT. 0 and WANTZ is .FALSE., then Z is not accessed.

Reference