forum.alglib.nethttp://forum.alglib.net/ Matrix inversion produces unexpected resultshttp://forum.alglib.net/viewtopic.php?f=2&t=4466 Page 1 of 1

 Author: epsPro [ Sun Jun 05, 2022 9:06 pm ] Post subject: Matrix inversion produces unexpected results Please see the first code excerpt below along with an input matrix, Z, and an output matrix, Zinverse. Zinverse is produced by the alglib.rmatrixinverse; and it is obviously wrong. However, in the second code excerpt, alglib.rmatrixinverse produces a correct result. I do not see reason for the difference in the results. As far as I can tell, the problem is occuring within alglib.rmatrixinverse. Can you please help me understand (1) how this results difference is happening, and (2) how to diagnose issues within alglib methods?Thanks in advance. // search for the non-singular scaling matrix with largest termCount termCount = 6; // (m / 4) + 2; while (searching && termCount >= MIN_TERM_COUNT) { matrix.Multiply(Yt, Y, termCount, ref Z); if (alglib.rmatrixdet(Z, termCount) != 0) { File.WriteAllText(Path.Combine(dataPath, \$"Z_{termCount}.txt"), matrix.FormatMatrix(Z, "Z", fieldWidth)); searching = false; // compute inverse alglib.rmatrixinverse(ref Z, termCount, out aglibInfo, out aglibReport); // inverse returns in Z matrix if (aglibInfo == 1) // inversion was successful { File.WriteAllText(Path.Combine(dataPath, \$"Zinverse_{termCount}.txt"), matrix.FormatMatrix(Z, "Zinverse", fieldWidth)); matrix.Multiply(Z, Yt, ref S); matrix.Multiply(S, x, ref a); SetScalingConstants(a); TermCount = termCount; rv = true; break; } else throw new InvalidOperationException(\$"alglib.rmatrixinverse: aglibInfo = {aglibInfo}"); } else { matrix.Initialize(ref Z, Matrix.InitializationTypes.Null); termCount--; } } File.WriteAllText(Path.Combine(dataPath, \$"Y_{termCount}.txt"), matrix.FormatMatrix(Y, "Y", fieldWidth)); File.WriteAllText(Path.Combine(dataPath, \$"Yt_{termCount}.txt"), matrix.FormatMatrix(Yt, "Yt", fieldWidth)); File.WriteAllText(Path.Combine(dataPath, \$"S_{termCount}.txt"), matrix.FormatMatrix(S, "S", fieldWidth)); Z = { 6.00 -9.28 3.21 -1.81 -0.01 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 } { -9.28 17.65 -6.75 3.21 0.01 -0.04 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 } { 3.21 -6.75 2.69 -1.19 -0.01 0.02 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 } { -1.81 3.21 -1.19 0.60 0.00 -0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 } { -0.01 0.01 -0.01 0.00 0.00 -0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 } { 0.01 -0.04 0.02 -0.01 -0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 } { 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 } { 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 } { 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 } { 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 } { 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 } { 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 } { 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 } { 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 } { 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 } { 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 }Zinverse = { 10646.89 201458.61 164016.83 -660336.75 -4243385.60 4725122.52 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 } { 201458.61 3918229.40 3163567.51 -12893771.96 -89957384.22 90987096.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 } { 164016.83 3163567.51 2560885.83 -10397909.15 -70690760.75 73714030.96 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 } { -660336.75 -12893771.96 -10397909.15 42453443.94 299596879.81 -298962625.64 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 } { -4243385.60 -89957384.22 -70690760.75 299596879.82 2674360516.42 -2003109303.81 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 } { 4725122.52 90987096.05 73714030.96 -298962625.64 -2003109303.73 2126085570.33 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 } { 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 } { 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 } { 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 } { 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 } { 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 } { 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 } { 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 } { 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 } { 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 } { 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 } public void Test_ZInverse() { int info; alglib.matinvreport rep; Matrix matrix = new Matrix(); double[,] I; double[,] P = null; int termCount = 6; double[,] X= null; double[,] Z = null; double[,] Zinverse = null; initializeZInputSet(ref Zinverse, ref X); if (alglib.rmatrixdet(Zinverse, termCount) != 0) { //lglib.rmatrixinverse(ref Zinverse, termCount, out info, out rep); alglib.rmatrixinverse(ref Zinverse, termCount, out info, out rep); Assert.True(info == 1); } else Assert.True(false); initializeZInputSet(ref Z, ref X); matrix.Multiply(Z, Zinverse, termCount, ref P); I = matrix.NewMatrix(termCount, termCount, Matrix.InitializationTypes.Identity); Assert.True(matrix.IsEqual(P, I)); }

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