-- File:        SVD.cdl
-- Created:     Mon May 13 14:35:56 1991
-- Author:      Laurent PAINNOT
--              <lpa@topsn3>
---Copyright:    Matra Datavision 1991, 1992


class SVD from math
    	---Purpose: SVD implements the solution of a set of N linear equations
    	-- of M unknowns without condition on N or M. The Singular
    	-- Value Decomposition algorithm is used. For singular or
    	-- nearly singular matrices SVD is a better choice than Gauss
    	-- or GaussLeastSquare.

uses Matrix from math, 
     Vector from math,
     OStream from Standard

raises NotDone from StdFail,
       DimensionError from Standard

is

    Create(A: Matrix)
    	---Purpose: 
        -- Given as input an n X m matrix A with n < m, n = m or n > m 
        -- this constructor performs the Singular Value Decomposition.

    returns SVD;
    
    
    IsDone(me)
    	---Purpose: Returns true if the computations are successful, otherwise returns false.
      	---C++: inline
    returns Boolean
    is static;
    
    
    Solve(me; B: Vector; X: out Vector; Eps: Real = 1.0e-6)    
    	---Purpose:
    	-- Given the input Vector B this routine solves the set of linear 
    	-- equations A . X = B. 
    	-- Exception NotDone is raised if the decomposition of A was not done
    	-- successfully.
    	-- Exception DimensionError is raised if the range of B is not 
    	-- equal to the rowrange of A.
    	-- Exception DimensionError is raised if the range of X is not 
    	-- equal to the colrange of A.
    
    raises NotDone,
    	   DimensionError
    is static;


    PseudoInverse(me; Inv : out Matrix; Eps: Real= 1.0e-6)
    	---Purpose: Computes the inverse Inv of matrix A such as A * Inverse = Identity.
    	-- Exceptions
    	-- StdFail_NotDone if the algorithm fails (and IsDone returns false).
    	-- Standard_DimensionError if the ranges of Inv are
    	-- compatible with the ranges of A.

    raises NotDone
    is static;
    

    Dump(me; o: in out OStream)
    	---Purpose: Prints information on the current state of the object.
    	--          Is used to redefine the operator <<.

    is static;


fields

Done:       Boolean;
Singular:   Boolean;
U:          Matrix;
V:          Matrix;
Diag:       Vector;
RowA:       Integer;

end SVD;