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-- File: Crout.cdl
-- Created: Thu Aug 22 10:57:59 1991
-- Author: Laurent PAINNOT
-- <lpa@topsn3>
---Copyright: Matra Datavision 1991, 1992
class Crout from math
---Purpose: This class implements the Crout algorithm used to solve a
-- system A*X = B where A is a symmetric matrix. It can be used to
-- invert a symmetric matrix.
-- This algorithm is similar to Gauss but is faster than Gauss.
-- Only the inferior triangle of A and the diagonal can be given.
uses Matrix from math,
Vector from math,
OStream from Standard
raises NotDone from StdFail,
NotSquare from math,
DimensionError from Standard
is
Create(A: Matrix; MinPivot: Real = 1.0e-20)
---Purpose: Given an input matrix A, this algorithm inverts A by the
-- Crout algorithm. The user can give only the inferior
-- triangle for the implementation.
-- A can be decomposed like this:
-- A = L * D * T(L) where L is triangular inferior and D is
-- diagonal.
-- If one element of A is less than MinPivot, A is
-- considered as singular.
-- Exception NotSquare is raised if A is not a square matrix.
returns Crout
raises NotSquare;
IsDone(me)
---Purpose: Returns True if all has been correctly done.
---C++: inline
returns Boolean
is static;
Solve(me; B: Vector; X: out Vector)
---Purpose: Given an input vector <B>, this routine returns the
-- solution of the set of linear equations A . X = B.
-- Exception NotDone is raised if the decomposition was not
-- done successfully.
-- Exception DimensionError is raised if the range of B is
-- not equal to the rowrange of A.
raises NotDone,
DimensionError
is static;
Inverse(me)
---Purpose: returns the inverse matrix of A. Only the inferior
-- triangle is returned.
-- Exception NotDone is raised if NotDone.
---C++: inline
---C++: return const&
returns Matrix
raises NotDone
is static;
Invert(me; Inv: out Matrix)
---Purpose: returns in Inv the inverse matrix of A. Only the inferior
-- triangle is returned.
-- Exception NotDone is raised if NotDone.
---C++: inline
raises NotDone
is static;
Determinant(me)
---Purpose: Returns the value of the determinant of the previously LU
-- decomposed matrix A. Zero is returned if the matrix A is considered as singular.
-- Exceptions
-- StdFail_NotDone if the algorithm fails (and IsDone returns false).
---C++: inline
returns Real
raises NotDone
is static;
Dump(me; o: in out OStream)
---Purpose: Prints on the stream o information on the current state
-- of the object.
is static;
fields
InvA: Matrix;
Done: Boolean;
Det: Real;
end Crout;
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