/*
    Triangular.java copyright claim:

    Copyright (C) 1996 by Steve Verrill.

    This class is free software; you can redistribute it and/or 
    modify it under the terms of version 2 of the GNU General 
    Public License as published by the Free Software Foundation.

    This class are distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    GNU General Public License for more details.

    You should have received a copy of the GNU General Public License
    along with these programs in the file COPYING; if not, write to 
    the Free Software Foundation, Inc., 675 Mass Ave, Cambridge, 
    MA 02139, USA.

    The author's mail address is:

    Steve Verrill 
    USDA Forest Products Laboratory
    1 Gifford Pinchot Drive
    Madison, Wisconsin
    53705

    The author's e-mail address is:

    steve@swst.org


***********************************************************************

DISCLAIMER OF WARRANTIES:

THIS SOFTWARE IS PROVIDED "AS IS" WITHOUT WARRANTY OF ANY KIND. 
THE AUTHOR DOES NOT WARRANT, GUARANTEE OR MAKE ANY REPRESENTATIONS 
REGARDING THE SOFTWARE OR DOCUMENTATION IN TERMS OF THEIR CORRECTNESS, 
RELIABILITY, CURRENTNESS, OR OTHERWISE. THE ENTIRE RISK AS TO 
THE RESULTS AND PERFORMANCE OF THE SOFTWARE IS ASSUMED BY YOU. 
IN NO CASE WILL ANY PARTY INVOLVED WITH THE CREATION OR DISTRIBUTION 
OF THE SOFTWARE BE LIABLE FOR ANY DAMAGE THAT MAY RESULT FROM THE USE 
OF THIS SOFTWARE.

Sorry about that.

***********************************************************************

History:

Date        Author            Changes

11/30/96    Steve Verrill     Created

*/


package linear_algebra;


/**
*
*

*This class contains: *

    *
  1. methods to solve Ly = b and Ux = y *where L is a full rank lower triangular matrix and *U is a full rank upper triangular matrix. *
  2. methods to invert upper and lower *triangular full rank matrices. *
* *

*This class was written by a statistician rather than *a numerical analyst. When public domain Java *numerical analysis routines become available from *numerical analysts (e.g., the people who produce *LAPACK), then the code produced by the numerical *analysts should be used. * *

*Meanwhile, if you have suggestions for improving this *code, please contact Steve Verrill at . * *@author Steve Verrill *@version .5 --- November 30, 1996 * */ public class Triangular extends Object { /** * *

*This method obtains the solution, y, of the equation *Ly = b where L is a known full rank lower triangular *n by n matrix, *and b is a known vector of length n. * *@param l[ ][ ] The lower triangular matrix. *@param y The solution vector. *@param b The right hand side of the equation. *@param n The order of l, y, and b. *@throws NotFullRankException if one or more of the diagonal *elements of l[ ][ ] is zero. * */ public void solveLower (double l[][], double y[], double b[], int n) throws NotFullRankException { double sum; int i,j; int err; err = 0; for (i = 0; i < n; i++) { if (l[i][i] == 0.0) { System.out.println("\nTriangular.solveLower error:" + " Diagonal element " + i + " of the L matrix is zero.\n"); err = 1; } } if (err == 1) { throw new NotFullRankException(); } for (i = 0; i < n; i++) { sum = 0.0; for (j = 0; j < i; j++) { sum += l[i][j]*y[j]; } y[i] = (b[i] - sum)/l[i][i]; } return; } /** * *This method obtains the solution, x, of the equation *Ux = y where U is a known full rank upper triangular *n by n matrix, *and y is a known vector of length n. * *@param u[ ][ ] The upper triangular matrix. *@param x The solution vector. *@param y The right hand side of the equation. *@param n The order of u, x, and y. *@throws NotFullRankException if one or more of the diagonal *elements of u[ ][ ] is zero. * */ public void solveUpper (double u[][], double x[], double y[], int n) throws NotFullRankException { double sum; int i,j; int err; err = 0; for (i = 0; i < n; i++) { if (u[i][i] == 0.0) { System.out.println("\nTriangular.solveUpper error:" + " Diagonal element " + i + " of the U matrix is zero.\n"); err = 1; } } if (err == 1) { throw new NotFullRankException(); } for (i = n - 1; i > -1; i--) { sum = 0.0; for (j = i + 1; j < n; j++) { sum += u[i][j]*x[j]; } x[i] = (y[i] - sum)/u[i][i]; } return; } /** * *This method obtains the inverse of a lower *triangular n by n matrix L. L must have non-zero *diagonal elements. On exit L is replaced by its inverse. * *@param l[ ][ ] The lower triangular matrix. *@param n The order of l. *@throws NotFullRankException if one or more of the diagonal *elements of l[ ][ ] is zero. * */ public void invertLower (double l[][], int n) throws NotFullRankException { double sum; int i,j,k; int err; err = 0; for (i = 0; i < n; i++) { if (l[i][i] == 0.0) { System.out.println("\nTriangular.invertLower error:" + " Diagonal element " + i + " of the L matrix is zero.\n"); err = 1; } } if (err == 1) { throw new NotFullRankException(); } for (j = 0; j < n; j++) { l[j][j] = 1.0/l[j][j]; for (i = j + 1; i < n; i++) { sum = 0.0; for (k = j; k < i; k++) { sum -= l[i][k]*l[k][j]; } l[i][j] = sum/l[i][i]; } } return; } /** * *This method obtains the inverse of an upper *triangular n by n matrix U. U must have non-zero *diagonal elements. On exit U is replaced by its inverse. * *@param u[ ][ ] The upper triangular matrix. *@param n The order of u. *@throws NotFullRankException if one or more of the diagonal *elements of u[ ][ ] is zero. * */ public void invertUpper (double u[][], int n) throws NotFullRankException { double sum; int i,j,k; int err; err = 0; for (i = 0; i < n; i++) { if (u[i][i] == 0.0) { System.out.println("\nTriangular.invertUpper error:" + " Diagonal element " + i + " of the U matrix is zero.\n"); err = 1; } } if (err == 1) { throw new NotFullRankException(); } for (j = n - 1; j > -1; j--) { u[j][j] = 1.0/u[j][j]; for (i = j - 1; i > -1; i--) { sum = 0.0; for (k = j; k > i; k--) { sum -= u[i][k]*u[k][j]; } u[i][j] = sum/u[i][i]; } } return; } }