I've been noodling with the javax.vecmath.GMatrix and javax.vecmath.GVector classes. I believe I've found a problem in the javax.vecmath.GMatrix.SVD() and javax.vecmath.GVector.SVDBackSolve() methods.
There's a discussion thread at the Java3D Forum that traces out the history: http://forum.java.sun.com/thread.jsp? forum=21&thread=454002&tstart=0&trange=15 I downloaded the Java3D implementation from the Sun Java site. I'm running JDK 1.4.1_03 on a Windows 2000 version 5.0 SP 4 PC. I tested using two classes: SVDTest.java and LUTest.java. Both can be compiled and run by typing "javac *.java" and "java SVDTest" or "java LUTest" - no packages. All the data they need are hardwired inside for all test cases. SVDTest.java: [code] import javax.vecmath.* ; public class SVDTest { // From http://web.mit.edu/18.06/www/Fall03/ps1.pdf, problem 3 // Gil Strang's course Web site. /* public static final int nrows = 3; public static final int ncols = 3; public static final double [] aInput = { 1, 1, 0, 4, 6, 1, -2, 2, 0, }; public static final double [] bInput = { 1, 4, -10, }; */ // From http://www.bluebit.gr/matrix/reference/SVD-Example.htm // Solution vector: x = { 4.089, 3.066, 2.163, } /* public static final int nrows = 20; public static final int ncols = 3; public static final double[] aInput = { 6, 5, 5, 3, 3, 7, 0, 7, 7, 6, 0, 4, 8, 7, 3, 9, 8, 1, 9, 3, 5, 7, 0, 5, 4, 3, 6, 6, 2, 3, 7, 7, 5, 9, 8, 2, 6, 9, 2, 5, 1, 9, 6, 0, 5, 1, 1, 7, 3, 0, 3, 3, 3, 9, 9, 4, 3, 1, 1, 6, }; public static final double[] bInput = { 51, 37, 37, 33, 60, 64, 55, 40, 39, 38, 59, 65, 58, 43, 35, 24, 21, 39, 57, 20, }; */ // From http://cs.uakron.edu/~quesada/Courses/LinAlg/Projects/svdpaper.pdf public static final int nrows = 2; public static final int ncols = 3; public static final double [] aInput = { 3, 2, 2, 2, 3, -2, }; public static final double [] bInput = { 3, 2, }; public static void main(String[] args) { try { // Create the A matrix GMatrix a = new GMatrix(nrows, ncols, aInput); System.out.println("a:"); System.out.println(a); // Perform the SVD GMatrix u = new GMatrix(nrows, nrows); GMatrix w = new GMatrix(nrows, ncols); GMatrix v = new GMatrix(ncols, ncols); int rank = a.SVD(u,w,v); System.out.println("rank: " + rank); System.out.println("u:"); System.out.println(u); System.out.println("v:"); System.out.println(v); System.out.println("w:"); System.out.println(w); // Check to make sure that transpose(U)*U = identity GMatrix utranspose = new GMatrix(u); utranspose.transpose(); GMatrix udelta = new GMatrix(ncols, ncols); udelta.mul(utranspose, u); System.out.println("udelta:"); System.out.println(udelta); // Check to make sure that transpose(V)*V = identity GMatrix vtranspose = new GMatrix(v); vtranspose.transpose(); GMatrix vdelta = new GMatrix(ncols, ncols); vdelta.mul(vtranspose, v); System.out.println("vdelta:"); System.out.println(vdelta); // Create the RHS vector GVector b = new GVector(bInput); System.out.println("b:"); System.out.println(b); // Perform back substitution GVector x = new GVector(nrows); x.SVDBackSolve(u, w, v, b); System.out.println("result:"); System.out.println(x); } catch (Exception e) { e.printStackTrace(System.err); } } } [/code] LUTest.java: [code] import javax.vecmath.* ; public class LUTest { // See http://web.mit.edu/18.06/www/Fall03/ps1.pdf, problem 3 public static final int nrows = 3; public static final int ncols = 3; public static final double [] aInput = { 1, 1, 0, 4, 6, 1, -2, 2, 0, }; public static final double [] bInput = { 1, 4, -10, }; public static void main (String[] args) { try { // Create the A matrix GMatrix a = new GMatrix(nrows, ncols, aInput); System.out.println("a: "); System.out.println(a); // Perform LU decomposition GVector permutation = new GVector(nrows); int numExchanges = a.LUD(a, permutation); // Create the RHS vector GVector b = new GVector(bInput); System.out.println("b:"); System.out.println(b); // Perform back substitution GVector x = new GVector(nrows); x.LUDBackSolve(a, b, permutation); System.out.println("result:"); System.out.println(x); } catch (Exception e) { e.printStackTrace(System.err); } } } [/code] I used two problems to test the algorithms. The first is a homework problem from Gil Strang's linear algebra class at MIT: http://web.mit.edu/18.06/www/Fall03/ps1.pdf, problem 3 The second is from an SVD site that Google found for me: http://cs.uakron.edu/~quesada/Courses/LinAlg/Projects/svdpaper.pdf I ran the Strang problem first because it was a non-singular, square matrix with a solution that was easily available using LU decomposition. The LU decomposition routines in javax.vecmath worked perfectly and gave me the correct, expected answer: x = { 3.0, -2.0, 4.0, } Unfortunately, the SVD routines did not. They gave me: x = { -9.519991330217254, 1.1446425543705807, -5.005952306535923, } When I tried running the Univ. of Akron case with m > n, I got this exception instead of an answer: java.lang.ArrayIndexOutOfBoundsException: 2 at javax.vecmath.GMatrix.computeSVD(GMatrix.java:2055) at javax.vecmath.GMatrix.SVD(GMatrix.java:1574) at SVDTest.main(SVDTest.java:107) Also, I am mystified by the javadocs. When I look at the SVD algorithm in "Numerical Recipes" and at http://kwon3d.com/theory/jkinem/svd.html, both say that if A is an m x n matrix, then U is m x n, W is n x n, and V is n x n. But the javadocs for javax.vecmath say that U is m x m, W is m x n, and V is n x n. Why the difference? Please let me know if this is a bug or pilot error. It's my first foray into Java3D, so perhaps I'm mistaken. Thanks - MOD __________________________________ Do you Yahoo!? The New Yahoo! Shopping - with improved product search http://shopping.yahoo.com =========================================================================== To unsubscribe, send email to [EMAIL PROTECTED] and include in the body of the message "signoff JAVA3D-INTEREST". For general help, send email to [EMAIL PROTECTED] and include in the body of the message "help".
