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-- File: Householder.cdl
-- Created: Wed Aug 7 10:24:48 1991
-- Author: Laurent PAINNOT
-- <lpa@topsn3>
---Copyright: Matra Datavision 1991, 1992
class Householder from math
---Purpose: This class implements the least square solution of a set of
-- linear equations of m unknowns (n >= m) using the Householder
-- method. It solves A.X = B.
-- This algorithm has more numerical stability than
-- GaussLeastSquare but is longer.
-- It must be used if the matrix is singular or nearly singular.
-- It is about 16% longer than GaussLeastSquare if there is only
-- one member B to solve.
-- It is about 30% longer if there are twenty B members to solve.
uses Matrix from math,
Vector from math,
OStream from Standard
raises NotDone from StdFail,
OutOfRange from Standard,
DimensionError from Standard,
ConstructionError from Standard
is
Create(A, B: Matrix; EPS: Real = 1.0e-20)
---Purpose: Given an input matrix A with n>= m, given an input matrix B
-- this constructor performs the least square resolution of
-- the set of linear equations A.X = B for each column of B.
-- If a column norm is less than EPS, the resolution can't
-- be done.
-- Exception DimensionError is raised if the row number of B
-- is different from the A row number.
returns Householder
raises DimensionError;
Create(A, B: Matrix; lowerArow, upperArow, lowerAcol, upperAcol: Integer;
EPS: Real = 1.0e-20)
---Purpose: Given an input matrix A with n>= m, given an input matrix B
-- this constructor performs the least square resolution of
-- the set of linear equations A.X = B for each column of B.
-- If a column norm is less than EPS, the resolution can't
-- be done.
-- Exception DimensionError is raised if the row number of B
-- is different from the A row number.
returns Householder
raises DimensionError;
Create(A: Matrix; B: Vector; EPS: Real = 1.0e-20)
---Purpose: Given an input matrix A with n>= m, given an input vector B
-- this constructor performs the least square resolution of
-- the set of linear equations A.X = B.
-- If a column norm is less than EPS, the resolution can't
-- be done.
-- Exception DimensionError is raised if the length of B
-- is different from the A row number.
returns Householder
raises DimensionError;
Perform(me: in out; A, B: Matrix; EPS: Real)
---Purpose: This method is used internally for each constructor
-- above and can't be used directly.
is static protected;
IsDone(me)
---Purpose: Returns true if the computations are successful, otherwise returns false.
---C++: inline
returns Boolean
is static;
Value(me; sol : out Vector; Index: Integer = 1)
---Purpose: Given the integer Index, this routine returns the
-- corresponding least square solution sol.
-- Exception NotDone is raised if the resolution has not be
-- done.
-- Exception OutOfRange is raised if Index <=0 or
-- Index is more than the number of columns of B.
---C++: inline
raises NotDone, OutOfRange
is static;
AllValues(me)
---Purpose: Returns the matrix sol of all the solutions of the system
-- A.X = B.
-- Exception NotDone is raised is the resolution has not be
-- done.
---C++: inline
---C++: return const&
returns Matrix
raises NotDone, ConstructionError
is static;
Dump(me; o: in out OStream)
---Purpose: Prints informations on the current state of the object.
is static;
fields
Sol: Matrix;
Q: Matrix;
Done: Boolean;
mylowerArow: Integer;
myupperArow: Integer;
mylowerAcol: Integer;
myupperAcol: Integer;
end Householder;
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