/**
* Computes the Moore–Penrose pseudoinverse using the SVD method.
*
* Modified version of the original implementation by Kim van der Linde.
*/
public static GeneralMatrix pinv(GeneralMatrix x)
{
if (x.Rank() < 1)
return null;
if (x.ColumnDimension > x.RowDimension)
return pinv(x.Transpose()).Transpose();
SingularValueDecomposition svdX = new SingularValueDecomposition(x);
double[] singularValues = svdX.SingularValues;
double tol = Math.Max(x.ColumnDimension, x.RowDimension)
* singularValues[0] * 2E-16;
double[] singularValueReciprocals = new double[singularValues.Count()];
for (int i = 0; i < singularValues.Count(); i++)
singularValueReciprocals[i] = Math.Abs(singularValues[i]) < tol ? 0
: (1.0 / singularValues[i]);
double[][] u = svdX.GetU().Array;
double[][] v = svdX.GetV().Array;
int min = Math.Min(x.ColumnDimension, u[0].Count());
double[][] inverse = new double[x.ColumnDimension][];
for (int i = 0; i < x.ColumnDimension; i++) {
inverse[i] = new double[x.RowDimension];
for (int j = 0; j < u.Count(); j++)
for (int k = 0; k < min; k++)
inverse[i][j] += v[i][k] * singularValueReciprocals[k] * u[j][k];
}
return new GeneralMatrix(inverse);
}
public void DEF()
{
double[][] rankdef = {new double[]{1.0, 4.0, 7.0, 10.0}, new double[]{2.0, 5.0, 8.0, 11.0}, new double[]{3.0, 6.0, 9.0, 12.0}};
GeneralMatrix def = new GeneralMatrix(rankdef);
Assert.IsTrue(GeneralTests.Check(def.Rank(), System.Math.Min(def.RowDimension, def.ColumnDimension) - 1));
}
public static void Main(System.String[] argv)
{
GeneralMatrix A, B, C, Z, O, I, R, S, X, SUB, M, T, SQ, DEF, SOL;
int errorCount = 0;
int warningCount = 0;
double tmp;
double[] columnwise = new double[]{1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0, 11.0, 12.0};
double[] rowwise = new double[]{1.0, 4.0, 7.0, 10.0, 2.0, 5.0, 8.0, 11.0, 3.0, 6.0, 9.0, 12.0};
double[][] avals = {new double[]{1.0, 4.0, 7.0, 10.0}, new double[]{2.0, 5.0, 8.0, 11.0}, new double[]{3.0, 6.0, 9.0, 12.0}};
double[][] rankdef = avals;
double[][] tvals = {new double[]{1.0, 2.0, 3.0}, new double[]{4.0, 5.0, 6.0}, new double[]{7.0, 8.0, 9.0}, new double[]{10.0, 11.0, 12.0}};
double[][] subavals = {new double[]{5.0, 8.0, 11.0}, new double[]{6.0, 9.0, 12.0}};
double[][] rvals = {new double[]{1.0, 4.0, 7.0}, new double[]{2.0, 5.0, 8.0, 11.0}, new double[]{3.0, 6.0, 9.0, 12.0}};
double[][] pvals = {new double[]{1.0, 1.0, 1.0}, new double[]{1.0, 2.0, 3.0}, new double[]{1.0, 3.0, 6.0}};
double[][] ivals = {new double[]{1.0, 0.0, 0.0, 0.0}, new double[]{0.0, 1.0, 0.0, 0.0}, new double[]{0.0, 0.0, 1.0, 0.0}};
double[][] evals = {new double[]{0.0, 1.0, 0.0, 0.0}, new double[]{1.0, 0.0, 2e-7, 0.0}, new double[]{0.0, - 2e-7, 0.0, 1.0}, new double[]{0.0, 0.0, 1.0, 0.0}};
double[][] square = {new double[]{166.0, 188.0, 210.0}, new double[]{188.0, 214.0, 240.0}, new double[]{210.0, 240.0, 270.0}};
double[][] sqSolution = {new double[]{13.0}, new double[]{15.0}};
double[][] condmat = {new double[]{1.0, 3.0}, new double[]{7.0, 9.0}};
int rows = 3, cols = 4;
int invalidld = 5; /* should trigger bad shape for construction with val */
int raggedr = 0; /* (raggedr,raggedc) should be out of bounds in ragged array */
int raggedc = 4;
int validld = 3; /* leading dimension of intended test Matrices */
int nonconformld = 4; /* leading dimension which is valid, but nonconforming */
int ib = 1, ie = 2, jb = 1, je = 3; /* index ranges for sub GeneralMatrix */
int[] rowindexset = new int[]{1, 2};
int[] badrowindexset = new int[]{1, 3};
int[] columnindexset = new int[]{1, 2, 3};
int[] badcolumnindexset = new int[]{1, 2, 4};
double columnsummax = 33.0;
double rowsummax = 30.0;
double sumofdiagonals = 15;
double sumofsquares = 650;
/// <summary>Constructors and constructor-like methods:
/// double[], int
/// double[][]
/// int, int
/// int, int, double
/// int, int, double[][]
/// Create(double[][])
/// Random(int,int)
/// Identity(int)
///
/// </summary>
print("\nTesting constructors and constructor-like methods...\n");
try
{
/// <summary>check that exception is thrown in packed constructor with invalid length *</summary>
A = new GeneralMatrix(columnwise, invalidld);
errorCount = try_failure(errorCount, "Catch invalid length in packed constructor... ", "exception not thrown for invalid input");
}
catch (System.ArgumentException e)
{
try_success("Catch invalid length in packed constructor... ", e.Message);
}
try
{
/// <summary>check that exception is thrown in default constructor
/// if input array is 'ragged' *
/// </summary>
A = new GeneralMatrix(rvals);
tmp = A.GetElement(raggedr, raggedc);
}
catch (System.ArgumentException e)
{
try_success("Catch ragged input to default constructor... ", e.Message);
}
catch (System.IndexOutOfRangeException e)
{
errorCount = try_failure(errorCount, "Catch ragged input to constructor... ", "exception not thrown in construction...ArrayIndexOutOfBoundsException thrown later");
System.Console.Out.WriteLine(e.Message);
}
try
{
/// <summary>check that exception is thrown in Create
/// if input array is 'ragged' *
/// </summary>
A = GeneralMatrix.Create(rvals);
tmp = A.GetElement(raggedr, raggedc);
}
catch (System.ArgumentException e)
{
try_success("Catch ragged input to Create... ", e.Message);
System.Console.Out.WriteLine(e.Message);
}
catch (System.IndexOutOfRangeException e)
{
errorCount = try_failure(errorCount, "Catch ragged input to Create... ", "exception not thrown in construction...ArrayIndexOutOfBoundsException thrown later");
System.Console.Out.WriteLine(e.Message);
}
A = new GeneralMatrix(columnwise, validld);
B = new GeneralMatrix(avals);
tmp = B.GetElement(0, 0);
avals[0][0] = 0.0;
C = B.Subtract(A);
avals[0][0] = tmp;
B = GeneralMatrix.Create(avals);
tmp = B.GetElement(0, 0);
avals[0][0] = 0.0;
if ((tmp - B.GetElement(0, 0)) != 0.0)
{
/// <summary>check that Create behaves properly *</summary>
errorCount = try_failure(errorCount, "Create... ", "Copy not effected... data visible outside");
}
else
{
try_success("Create... ", "");
}
avals[0][0] = columnwise[0];
I = new GeneralMatrix(ivals);
try
{
check(I, GeneralMatrix.Identity(3, 4));
try_success("Identity... ", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "Identity... ", "Identity GeneralMatrix not successfully created");
System.Console.Out.WriteLine(e.Message);
}
/// <summary>Access Methods:
/// getColumnDimension()
/// getRowDimension()
/// getArray()
/// getArrayCopy()
/// getColumnPackedCopy()
/// getRowPackedCopy()
/// get(int,int)
/// GetMatrix(int,int,int,int)
/// GetMatrix(int,int,int[])
/// GetMatrix(int[],int,int)
/// GetMatrix(int[],int[])
/// set(int,int,double)
/// SetMatrix(int,int,int,int,GeneralMatrix)
/// SetMatrix(int,int,int[],GeneralMatrix)
/// SetMatrix(int[],int,int,GeneralMatrix)
/// SetMatrix(int[],int[],GeneralMatrix)
///
/// </summary>
print("\nTesting access methods...\n");
/// <summary>Various get methods:
///
/// </summary>
B = new GeneralMatrix(avals);
if (B.RowDimension != rows)
{
errorCount = try_failure(errorCount, "getRowDimension... ", "");
}
else
{
try_success("getRowDimension... ", "");
}
if (B.ColumnDimension != cols)
{
errorCount = try_failure(errorCount, "getColumnDimension... ", "");
}
else
{
try_success("getColumnDimension... ", "");
}
B = new GeneralMatrix(avals);
double[][] barray = B.Array;
if (barray != avals)
{
errorCount = try_failure(errorCount, "getArray... ", "");
}
else
{
try_success("getArray... ", "");
}
barray = B.ArrayCopy;
if (barray == avals)
{
errorCount = try_failure(errorCount, "getArrayCopy... ", "data not (deep) copied");
}
try
{
check(barray, avals);
try_success("getArrayCopy... ", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "getArrayCopy... ", "data not successfully (deep) copied");
System.Console.Out.WriteLine(e.Message);
}
double[] bpacked = B.ColumnPackedCopy;
try
{
check(bpacked, columnwise);
try_success("getColumnPackedCopy... ", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "getColumnPackedCopy... ", "data not successfully (deep) copied by columns");
System.Console.Out.WriteLine(e.Message);
}
bpacked = B.RowPackedCopy;
try
{
check(bpacked, rowwise);
try_success("getRowPackedCopy... ", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "getRowPackedCopy... ", "data not successfully (deep) copied by rows");
System.Console.Out.WriteLine(e.Message);
}
try
{
tmp = B.GetElement(B.RowDimension, B.ColumnDimension - 1);
errorCount = try_failure(errorCount, "get(int,int)... ", "OutOfBoundsException expected but not thrown");
}
catch (System.IndexOutOfRangeException e)
{
System.Console.Out.WriteLine(e.Message);
try
{
tmp = B.GetElement(B.RowDimension - 1, B.ColumnDimension);
errorCount = try_failure(errorCount, "get(int,int)... ", "OutOfBoundsException expected but not thrown");
}
catch (System.IndexOutOfRangeException e1)
{
try_success("get(int,int)... OutofBoundsException... ", "");
System.Console.Out.WriteLine(e1.Message);
}
}
catch (System.ArgumentException e1)
{
errorCount = try_failure(errorCount, "get(int,int)... ", "OutOfBoundsException expected but not thrown");
System.Console.Out.WriteLine(e1.Message);
}
try
{
if (B.GetElement(B.RowDimension - 1, B.ColumnDimension - 1) != avals[B.RowDimension - 1][B.ColumnDimension - 1])
{
errorCount = try_failure(errorCount, "get(int,int)... ", "GeneralMatrix entry (i,j) not successfully retreived");
}
else
{
try_success("get(int,int)... ", "");
}
}
catch (System.IndexOutOfRangeException e)
{
errorCount = try_failure(errorCount, "get(int,int)... ", "Unexpected ArrayIndexOutOfBoundsException");
System.Console.Out.WriteLine(e.Message);
}
SUB = new GeneralMatrix(subavals);
try
{
M = B.GetMatrix(ib, ie + B.RowDimension + 1, jb, je);
errorCount = try_failure(errorCount, "GetMatrix(int,int,int,int)... ", "ArrayIndexOutOfBoundsException expected but not thrown");
}
catch (System.IndexOutOfRangeException e)
{
System.Console.Out.WriteLine(e.Message);
try
{
M = B.GetMatrix(ib, ie, jb, je + B.ColumnDimension + 1);
errorCount = try_failure(errorCount, "GetMatrix(int,int,int,int)... ", "ArrayIndexOutOfBoundsException expected but not thrown");
}
catch (System.IndexOutOfRangeException e1)
{
try_success("GetMatrix(int,int,int,int)... ArrayIndexOutOfBoundsException... ", "");
System.Console.Out.WriteLine(e1.Message);
}
}
catch (System.ArgumentException e1)
{
errorCount = try_failure(errorCount, "GetMatrix(int,int,int,int)... ", "ArrayIndexOutOfBoundsException expected but not thrown");
System.Console.Out.WriteLine(e1.Message);
}
try
{
M = B.GetMatrix(ib, ie, jb, je);
try
{
check(SUB, M);
try_success("GetMatrix(int,int,int,int)... ", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "GetMatrix(int,int,int,int)... ", "submatrix not successfully retreived");
System.Console.Out.WriteLine(e.Message);
}
}
catch (System.IndexOutOfRangeException e)
{
errorCount = try_failure(errorCount, "GetMatrix(int,int,int,int)... ", "Unexpected ArrayIndexOutOfBoundsException");
System.Console.Out.WriteLine(e.Message);
}
try
{
M = B.GetMatrix(ib, ie, badcolumnindexset);
errorCount = try_failure(errorCount, "GetMatrix(int,int,int[])... ", "ArrayIndexOutOfBoundsException expected but not thrown");
}
catch (System.IndexOutOfRangeException e)
{
System.Console.Out.WriteLine(e.Message);
try
{
M = B.GetMatrix(ib, ie + B.RowDimension + 1, columnindexset);
errorCount = try_failure(errorCount, "GetMatrix(int,int,int[])... ", "ArrayIndexOutOfBoundsException expected but not thrown");
}
catch (System.IndexOutOfRangeException e1)
{
try_success("GetMatrix(int,int,int[])... ArrayIndexOutOfBoundsException... ", "");
System.Console.Out.WriteLine(e1.Message);
}
}
catch (System.ArgumentException e1)
{
errorCount = try_failure(errorCount, "GetMatrix(int,int,int[])... ", "ArrayIndexOutOfBoundsException expected but not thrown");
System.Console.Out.WriteLine(e1.Message);
}
try
{
M = B.GetMatrix(ib, ie, columnindexset);
try
{
check(SUB, M);
try_success("GetMatrix(int,int,int[])... ", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "GetMatrix(int,int,int[])... ", "submatrix not successfully retreived");
System.Console.Out.WriteLine(e.Message);
}
}
catch (System.IndexOutOfRangeException e)
{
errorCount = try_failure(errorCount, "GetMatrix(int,int,int[])... ", "Unexpected ArrayIndexOutOfBoundsException");
System.Console.Out.WriteLine(e.Message);
}
try
{
M = B.GetMatrix(badrowindexset, jb, je);
errorCount = try_failure(errorCount, "GetMatrix(int[],int,int)... ", "ArrayIndexOutOfBoundsException expected but not thrown");
}
catch (System.IndexOutOfRangeException e)
{
System.Console.Out.WriteLine(e.Message);
try
{
M = B.GetMatrix(rowindexset, jb, je + B.ColumnDimension + 1);
errorCount = try_failure(errorCount, "GetMatrix(int[],int,int)... ", "ArrayIndexOutOfBoundsException expected but not thrown");
}
catch (System.IndexOutOfRangeException e1)
{
try_success("GetMatrix(int[],int,int)... ArrayIndexOutOfBoundsException... ", "");
System.Console.Out.WriteLine(e1.Message);
}
}
catch (System.ArgumentException e1)
{
errorCount = try_failure(errorCount, "GetMatrix(int[],int,int)... ", "ArrayIndexOutOfBoundsException expected but not thrown");
System.Console.Out.WriteLine(e1.Message);
}
try
{
M = B.GetMatrix(rowindexset, jb, je);
try
{
check(SUB, M);
try_success("GetMatrix(int[],int,int)... ", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "GetMatrix(int[],int,int)... ", "submatrix not successfully retreived");
System.Console.Out.WriteLine(e.Message);
}
}
catch (System.IndexOutOfRangeException e)
{
errorCount = try_failure(errorCount, "GetMatrix(int[],int,int)... ", "Unexpected ArrayIndexOutOfBoundsException");
System.Console.Out.WriteLine(e.Message);
}
try
{
M = B.GetMatrix(badrowindexset, columnindexset);
errorCount = try_failure(errorCount, "GetMatrix(int[],int[])... ", "ArrayIndexOutOfBoundsException expected but not thrown");
}
catch (System.IndexOutOfRangeException e)
{
System.Console.Out.WriteLine(e.Message);
try
{
M = B.GetMatrix(rowindexset, badcolumnindexset);
errorCount = try_failure(errorCount, "GetMatrix(int[],int[])... ", "ArrayIndexOutOfBoundsException expected but not thrown");
}
catch (System.IndexOutOfRangeException e1)
{
try_success("GetMatrix(int[],int[])... ArrayIndexOutOfBoundsException... ", "");
System.Console.Out.WriteLine(e1.Message);
}
}
catch (System.ArgumentException e1)
{
errorCount = try_failure(errorCount, "GetMatrix(int[],int[])... ", "ArrayIndexOutOfBoundsException expected but not thrown");
System.Console.Out.WriteLine(e1.Message);
}
try
{
M = B.GetMatrix(rowindexset, columnindexset);
try
{
check(SUB, M);
try_success("GetMatrix(int[],int[])... ", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "GetMatrix(int[],int[])... ", "submatrix not successfully retreived");
System.Console.Out.WriteLine(e.Message);
}
}
catch (System.IndexOutOfRangeException e)
{
errorCount = try_failure(errorCount, "GetMatrix(int[],int[])... ", "Unexpected ArrayIndexOutOfBoundsException");
System.Console.Out.WriteLine(e.Message);
}
/// <summary>Various set methods:
///
/// </summary>
try
{
B.SetElement(B.RowDimension, B.ColumnDimension - 1, 0.0);
errorCount = try_failure(errorCount, "set(int,int,double)... ", "OutOfBoundsException expected but not thrown");
}
catch (System.IndexOutOfRangeException e)
{
System.Console.Out.WriteLine(e.Message);
try
{
B.SetElement(B.RowDimension - 1, B.ColumnDimension, 0.0);
errorCount = try_failure(errorCount, "set(int,int,double)... ", "OutOfBoundsException expected but not thrown");
}
catch (System.IndexOutOfRangeException e1)
{
try_success("set(int,int,double)... OutofBoundsException... ", "");
System.Console.Out.WriteLine(e1.Message);
}
}
catch (System.ArgumentException e1)
{
errorCount = try_failure(errorCount, "set(int,int,double)... ", "OutOfBoundsException expected but not thrown");
System.Console.Out.WriteLine(e1.Message);
}
try
{
B.SetElement(ib, jb, 0.0);
tmp = B.GetElement(ib, jb);
try
{
check(tmp, 0.0);
try_success("set(int,int,double)... ", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "set(int,int,double)... ", "GeneralMatrix element not successfully set");
System.Console.Out.WriteLine(e.Message);
}
}
catch (System.IndexOutOfRangeException e1)
{
errorCount = try_failure(errorCount, "set(int,int,double)... ", "Unexpected ArrayIndexOutOfBoundsException");
System.Console.Out.WriteLine(e1.Message);
}
M = new GeneralMatrix(2, 3, 0.0);
try
{
B.SetMatrix(ib, ie + B.RowDimension + 1, jb, je, M);
errorCount = try_failure(errorCount, "SetMatrix(int,int,int,int,GeneralMatrix)... ", "ArrayIndexOutOfBoundsException expected but not thrown");
}
catch (System.IndexOutOfRangeException e)
{
System.Console.Out.WriteLine(e.Message);
try
{
B.SetMatrix(ib, ie, jb, je + B.ColumnDimension + 1, M);
errorCount = try_failure(errorCount, "SetMatrix(int,int,int,int,GeneralMatrix)... ", "ArrayIndexOutOfBoundsException expected but not thrown");
}
catch (System.IndexOutOfRangeException e1)
{
try_success("SetMatrix(int,int,int,int,GeneralMatrix)... ArrayIndexOutOfBoundsException... ", "");
System.Console.Out.WriteLine(e1.Message);
}
}
catch (System.ArgumentException e1)
{
errorCount = try_failure(errorCount, "SetMatrix(int,int,int,int,GeneralMatrix)... ", "ArrayIndexOutOfBoundsException expected but not thrown");
System.Console.Out.WriteLine(e1.Message);
}
try
{
B.SetMatrix(ib, ie, jb, je, M);
try
{
check(M.Subtract(B.GetMatrix(ib, ie, jb, je)), M);
try_success("SetMatrix(int,int,int,int,GeneralMatrix)... ", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "SetMatrix(int,int,int,int,GeneralMatrix)... ", "submatrix not successfully set");
System.Console.Out.WriteLine(e.Message);
}
B.SetMatrix(ib, ie, jb, je, SUB);
}
catch (System.IndexOutOfRangeException e1)
{
errorCount = try_failure(errorCount, "SetMatrix(int,int,int,int,GeneralMatrix)... ", "Unexpected ArrayIndexOutOfBoundsException");
System.Console.Out.WriteLine(e1.Message);
}
try
{
B.SetMatrix(ib, ie + B.RowDimension + 1, columnindexset, M);
errorCount = try_failure(errorCount, "SetMatrix(int,int,int[],GeneralMatrix)... ", "ArrayIndexOutOfBoundsException expected but not thrown");
}
catch (System.IndexOutOfRangeException e)
{
System.Console.Out.WriteLine(e.Message);
try
{
B.SetMatrix(ib, ie, badcolumnindexset, M);
errorCount = try_failure(errorCount, "SetMatrix(int,int,int[],GeneralMatrix)... ", "ArrayIndexOutOfBoundsException expected but not thrown");
}
catch (System.IndexOutOfRangeException e1)
{
try_success("SetMatrix(int,int,int[],GeneralMatrix)... ArrayIndexOutOfBoundsException... ", "");
System.Console.Out.WriteLine(e1.Message);
}
}
catch (System.ArgumentException e1)
{
errorCount = try_failure(errorCount, "SetMatrix(int,int,int[],GeneralMatrix)... ", "ArrayIndexOutOfBoundsException expected but not thrown");
System.Console.Out.WriteLine(e1.Message);
}
try
{
B.SetMatrix(ib, ie, columnindexset, M);
try
{
check(M.Subtract(B.GetMatrix(ib, ie, columnindexset)), M);
try_success("SetMatrix(int,int,int[],GeneralMatrix)... ", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "SetMatrix(int,int,int[],GeneralMatrix)... ", "submatrix not successfully set");
System.Console.Out.WriteLine(e.Message);
}
B.SetMatrix(ib, ie, jb, je, SUB);
}
catch (System.IndexOutOfRangeException e1)
{
errorCount = try_failure(errorCount, "SetMatrix(int,int,int[],GeneralMatrix)... ", "Unexpected ArrayIndexOutOfBoundsException");
System.Console.Out.WriteLine(e1.Message);
}
try
{
B.SetMatrix(rowindexset, jb, je + B.ColumnDimension + 1, M);
errorCount = try_failure(errorCount, "SetMatrix(int[],int,int,GeneralMatrix)... ", "ArrayIndexOutOfBoundsException expected but not thrown");
}
catch (System.IndexOutOfRangeException e)
{
System.Console.Out.WriteLine(e.Message);
try
{
B.SetMatrix(badrowindexset, jb, je, M);
errorCount = try_failure(errorCount, "SetMatrix(int[],int,int,GeneralMatrix)... ", "ArrayIndexOutOfBoundsException expected but not thrown");
}
catch (System.IndexOutOfRangeException e1)
{
try_success("SetMatrix(int[],int,int,GeneralMatrix)... ArrayIndexOutOfBoundsException... ", "");
System.Console.Out.WriteLine(e1.Message);
}
}
catch (System.ArgumentException e1)
{
errorCount = try_failure(errorCount, "SetMatrix(int[],int,int,GeneralMatrix)... ", "ArrayIndexOutOfBoundsException expected but not thrown");
System.Console.Out.WriteLine(e1.Message);
}
try
{
B.SetMatrix(rowindexset, jb, je, M);
try
{
check(M.Subtract(B.GetMatrix(rowindexset, jb, je)), M);
try_success("SetMatrix(int[],int,int,GeneralMatrix)... ", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "SetMatrix(int[],int,int,GeneralMatrix)... ", "submatrix not successfully set");
System.Console.Out.WriteLine(e.Message);
}
B.SetMatrix(ib, ie, jb, je, SUB);
}
catch (System.IndexOutOfRangeException e1)
{
errorCount = try_failure(errorCount, "SetMatrix(int[],int,int,GeneralMatrix)... ", "Unexpected ArrayIndexOutOfBoundsException");
System.Console.Out.WriteLine(e1.Message);
}
try
{
B.SetMatrix(rowindexset, badcolumnindexset, M);
errorCount = try_failure(errorCount, "SetMatrix(int[],int[],GeneralMatrix)... ", "ArrayIndexOutOfBoundsException expected but not thrown");
}
catch (System.IndexOutOfRangeException e)
{
System.Console.Out.WriteLine(e.Message);
try
{
B.SetMatrix(badrowindexset, columnindexset, M);
errorCount = try_failure(errorCount, "SetMatrix(int[],int[],GeneralMatrix)... ", "ArrayIndexOutOfBoundsException expected but not thrown");
}
catch (System.IndexOutOfRangeException e1)
{
try_success("SetMatrix(int[],int[],GeneralMatrix)... ArrayIndexOutOfBoundsException... ", "");
System.Console.Out.WriteLine(e1.Message);
}
}
catch (System.ArgumentException e1)
{
errorCount = try_failure(errorCount, "SetMatrix(int[],int[],GeneralMatrix)... ", "ArrayIndexOutOfBoundsException expected but not thrown");
System.Console.Out.WriteLine(e1.Message);
}
try
{
B.SetMatrix(rowindexset, columnindexset, M);
try
{
check(M.Subtract(B.GetMatrix(rowindexset, columnindexset)), M);
try_success("SetMatrix(int[],int[],GeneralMatrix)... ", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "SetMatrix(int[],int[],GeneralMatrix)... ", "submatrix not successfully set");
System.Console.Out.WriteLine(e.Message);
}
}
catch (System.IndexOutOfRangeException e1)
{
errorCount = try_failure(errorCount, "SetMatrix(int[],int[],GeneralMatrix)... ", "Unexpected ArrayIndexOutOfBoundsException");
System.Console.Out.WriteLine(e1.Message);
}
/// <summary>Array-like methods:
/// Subtract
/// SubtractEquals
/// Add
/// AddEquals
/// ArrayLeftDivide
/// ArrayLeftDivideEquals
/// ArrayRightDivide
/// ArrayRightDivideEquals
/// arrayTimes
/// ArrayMultiplyEquals
/// uminus
///
/// </summary>
print("\nTesting array-like methods...\n");
S = new GeneralMatrix(columnwise, nonconformld);
R = GeneralMatrix.Random(A.RowDimension, A.ColumnDimension);
A = R;
try
{
S = A.Subtract(S);
errorCount = try_failure(errorCount, "Subtract conformance check... ", "nonconformance not raised");
}
catch (System.ArgumentException e)
{
try_success("Subtract conformance check... ", "");
System.Console.Out.WriteLine(e.Message);
}
if (A.Subtract(R).Norm1() != 0.0)
{
errorCount = try_failure(errorCount, "Subtract... ", "(difference of identical Matrices is nonzero,\nSubsequent use of Subtract should be suspect)");
}
else
{
try_success("Subtract... ", "");
}
A = R.Copy();
A.SubtractEquals(R);
Z = new GeneralMatrix(A.RowDimension, A.ColumnDimension);
try
{
A.SubtractEquals(S);
errorCount = try_failure(errorCount, "SubtractEquals conformance check... ", "nonconformance not raised");
}
catch (System.ArgumentException e)
{
try_success("SubtractEquals conformance check... ", "");
System.Console.Out.WriteLine(e.Message);
}
if (A.Subtract(Z).Norm1() != 0.0)
{
errorCount = try_failure(errorCount, "SubtractEquals... ", "(difference of identical Matrices is nonzero,\nSubsequent use of Subtract should be suspect)");
}
else
{
try_success("SubtractEquals... ", "");
}
A = R.Copy();
B = GeneralMatrix.Random(A.RowDimension, A.ColumnDimension);
C = A.Subtract(B);
try
{
S = A.Add(S);
errorCount = try_failure(errorCount, "Add conformance check... ", "nonconformance not raised");
}
catch (System.ArgumentException e)
{
try_success("Add conformance check... ", "");
System.Console.Out.WriteLine(e.Message);
}
try
{
check(C.Add(B), A);
try_success("Add... ", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "Add... ", "(C = A - B, but C + B != A)");
System.Console.Out.WriteLine(e.Message);
}
C = A.Subtract(B);
C.AddEquals(B);
try
{
A.AddEquals(S);
errorCount = try_failure(errorCount, "AddEquals conformance check... ", "nonconformance not raised");
}
catch (System.ArgumentException e)
{
try_success("AddEquals conformance check... ", "");
System.Console.Out.WriteLine(e.Message);
}
try
{
check(C, A);
try_success("AddEquals... ", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "AddEquals... ", "(C = A - B, but C = C + B != A)");
System.Console.Out.WriteLine(e.Message);
}
A = R.UnaryMinus();
try
{
check(A.Add(R), Z);
try_success("UnaryMinus... ", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "uminus... ", "(-A + A != zeros)");
System.Console.Out.WriteLine(e.Message);
}
A = R.Copy();
O = new GeneralMatrix(A.RowDimension, A.ColumnDimension, 1.0);
C = A.ArrayLeftDivide(R);
try
{
S = A.ArrayLeftDivide(S);
errorCount = try_failure(errorCount, "ArrayLeftDivide conformance check... ", "nonconformance not raised");
}
catch (System.ArgumentException e)
{
try_success("ArrayLeftDivide conformance check... ", "");
System.Console.Out.WriteLine(e.Message);
}
try
{
check(C, O);
try_success("ArrayLeftDivide... ", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "ArrayLeftDivide... ", "(M.\\M != ones)");
System.Console.Out.WriteLine(e.Message);
}
try
{
A.ArrayLeftDivideEquals(S);
errorCount = try_failure(errorCount, "ArrayLeftDivideEquals conformance check... ", "nonconformance not raised");
}
catch (System.ArgumentException e)
{
try_success("ArrayLeftDivideEquals conformance check... ", "");
System.Console.Out.WriteLine(e.Message);
}
A.ArrayLeftDivideEquals(R);
try
{
check(A, O);
try_success("ArrayLeftDivideEquals... ", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "ArrayLeftDivideEquals... ", "(M.\\M != ones)");
System.Console.Out.WriteLine(e.Message);
}
A = R.Copy();
try
{
A.ArrayRightDivide(S);
errorCount = try_failure(errorCount, "ArrayRightDivide conformance check... ", "nonconformance not raised");
}
catch (System.ArgumentException e)
{
try_success("ArrayRightDivide conformance check... ", "");
System.Console.Out.WriteLine(e.Message);
}
C = A.ArrayRightDivide(R);
try
{
check(C, O);
try_success("ArrayRightDivide... ", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "ArrayRightDivide... ", "(M./M != ones)");
System.Console.Out.WriteLine(e.Message);
}
try
{
A.ArrayRightDivideEquals(S);
errorCount = try_failure(errorCount, "ArrayRightDivideEquals conformance check... ", "nonconformance not raised");
}
catch (System.ArgumentException e)
{
try_success("ArrayRightDivideEquals conformance check... ", "");
System.Console.Out.WriteLine(e.Message);
}
A.ArrayRightDivideEquals(R);
try
{
check(A, O);
try_success("ArrayRightDivideEquals... ", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "ArrayRightDivideEquals... ", "(M./M != ones)");
System.Console.Out.WriteLine(e.Message);
}
A = R.Copy();
B = GeneralMatrix.Random(A.RowDimension, A.ColumnDimension);
try
{
S = A.ArrayMultiply(S);
errorCount = try_failure(errorCount, "arrayTimes conformance check... ", "nonconformance not raised");
}
catch (System.ArgumentException e)
{
try_success("arrayTimes conformance check... ", "");
System.Console.Out.WriteLine(e.Message);
}
C = A.ArrayMultiply(B);
try
{
check(C.ArrayRightDivideEquals(B), A);
try_success("arrayTimes... ", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "arrayTimes... ", "(A = R, C = A.*B, but C./B != A)");
System.Console.Out.WriteLine(e.Message);
}
try
{
A.ArrayMultiplyEquals(S);
errorCount = try_failure(errorCount, "ArrayMultiplyEquals conformance check... ", "nonconformance not raised");
}
catch (System.ArgumentException e)
{
try_success("ArrayMultiplyEquals conformance check... ", "");
System.Console.Out.WriteLine(e.Message);
}
A.ArrayMultiplyEquals(B);
try
{
check(A.ArrayRightDivideEquals(B), R);
try_success("ArrayMultiplyEquals... ", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "ArrayMultiplyEquals... ", "(A = R, A = A.*B, but A./B != R)");
System.Console.Out.WriteLine(e.Message);
}
/// <summary>LA methods:
/// Transpose
/// Multiply
/// Condition
/// Rank
/// Determinant
/// trace
/// Norm1
/// norm2
/// normF
/// normInf
/// Solve
/// solveTranspose
/// Inverse
/// chol
/// Eigen
/// lu
/// qr
/// svd
///
/// </summary>
print("\nTesting linear algebra methods...\n");
A = new GeneralMatrix(columnwise, 3);
T = new GeneralMatrix(tvals);
T = A.Transpose();
try
{
check(A.Transpose(), T);
try_success("Transpose...", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "Transpose()...", "Transpose unsuccessful");
System.Console.Out.WriteLine(e.Message);
}
A.Transpose();
try
{
check(A.Norm1(), columnsummax);
try_success("Norm1...", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "Norm1()...", "incorrect norm calculation");
System.Console.Out.WriteLine(e.Message);
}
try
{
check(A.NormInf(), rowsummax);
try_success("normInf()...", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "normInf()...", "incorrect norm calculation");
System.Console.Out.WriteLine(e.Message);
}
try
{
check(A.NormF(), System.Math.Sqrt(sumofsquares));
try_success("normF...", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "normF()...", "incorrect norm calculation");
System.Console.Out.WriteLine(e.Message);
}
try
{
check(A.Trace(), sumofdiagonals);
try_success("trace()...", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "trace()...", "incorrect trace calculation");
System.Console.Out.WriteLine(e.Message);
}
try
{
check(A.GetMatrix(0, A.RowDimension - 1, 0, A.RowDimension - 1).Determinant(), 0.0);
try_success("Determinant()...", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "Determinant()...", "incorrect determinant calculation");
System.Console.Out.WriteLine(e.Message);
}
SQ = new GeneralMatrix(square);
try
{
check(A.Multiply(A.Transpose()), SQ);
try_success("Multiply(GeneralMatrix)...", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "Multiply(GeneralMatrix)...", "incorrect GeneralMatrix-GeneralMatrix product calculation");
System.Console.Out.WriteLine(e.Message);
}
try
{
check(A.Multiply(0.0), Z);
try_success("Multiply(double)...", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "Multiply(double)...", "incorrect GeneralMatrix-scalar product calculation");
System.Console.Out.WriteLine(e.Message);
}
A = new GeneralMatrix(columnwise, 4);
QRDecomposition QR = A.QRD();
R = QR.R;
try
{
check(A, QR.Q.Multiply(R));
try_success("QRDecomposition...", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "QRDecomposition...", "incorrect QR decomposition calculation");
System.Console.Out.WriteLine(e.Message);
}
SingularValueDecomposition SVD = A.SVD();
try
{
check(A, SVD.GetU().Multiply(SVD.S.Multiply(SVD.GetV().Transpose())));
try_success("SingularValueDecomposition...", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "SingularValueDecomposition...", "incorrect singular value decomposition calculation");
System.Console.Out.WriteLine(e.Message);
}
DEF = new GeneralMatrix(rankdef);
try
{
check(DEF.Rank(), System.Math.Min(DEF.RowDimension, DEF.ColumnDimension) - 1);
try_success("Rank()...", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "Rank()...", "incorrect Rank calculation");
System.Console.Out.WriteLine(e.Message);
}
B = new GeneralMatrix(condmat);
SVD = B.SVD();
double[] singularvalues = SVD.SingularValues;
try
{
check(B.Condition(), singularvalues[0] / singularvalues[System.Math.Min(B.RowDimension, B.ColumnDimension) - 1]);
try_success("Condition()...", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "Condition()...", "incorrect condition number calculation");
System.Console.Out.WriteLine(e.Message);
}
int n = A.ColumnDimension;
A = A.GetMatrix(0, n - 1, 0, n - 1);
A.SetElement(0, 0, 0.0);
LUDecomposition LU = A.LUD();
try
{
check(A.GetMatrix(LU.Pivot, 0, n - 1), LU.L.Multiply(LU.U));
try_success("LUDecomposition...", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "LUDecomposition...", "incorrect LU decomposition calculation");
System.Console.Out.WriteLine(e.Message);
}
X = A.Inverse();
try
{
check(A.Multiply(X), GeneralMatrix.Identity(3, 3));
try_success("Inverse()...", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "Inverse()...", "incorrect Inverse calculation");
System.Console.Out.WriteLine(e.Message);
}
O = new GeneralMatrix(SUB.RowDimension, 1, 1.0);
SOL = new GeneralMatrix(sqSolution);
SQ = SUB.GetMatrix(0, SUB.RowDimension - 1, 0, SUB.RowDimension - 1);
try
{
check(SQ.Solve(SOL), O);
try_success("Solve()...", "");
}
catch (System.ArgumentException e1)
{
errorCount = try_failure(errorCount, "Solve()...", e1.Message);
System.Console.Out.WriteLine(e1.Message);
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "Solve()...", e.Message);
System.Console.Out.WriteLine(e.Message);
}
A = new GeneralMatrix(pvals);
CholeskyDecomposition Chol = A.chol();
GeneralMatrix L = Chol.GetL();
try
{
check(A, L.Multiply(L.Transpose()));
try_success("CholeskyDecomposition...", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "CholeskyDecomposition...", "incorrect Cholesky decomposition calculation");
System.Console.Out.WriteLine(e.Message);
}
X = Chol.Solve(GeneralMatrix.Identity(3, 3));
try
{
check(A.Multiply(X), GeneralMatrix.Identity(3, 3));
try_success("CholeskyDecomposition Solve()...", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "CholeskyDecomposition Solve()...", "incorrect Choleskydecomposition Solve calculation");
System.Console.Out.WriteLine(e.Message);
}
EigenvalueDecomposition Eig = A.Eigen();
GeneralMatrix D = Eig.D;
GeneralMatrix V = Eig.GetV();
try
{
check(A.Multiply(V), V.Multiply(D));
try_success("EigenvalueDecomposition (symmetric)...", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "EigenvalueDecomposition (symmetric)...", "incorrect symmetric Eigenvalue decomposition calculation");
System.Console.Out.WriteLine(e.Message);
}
A = new GeneralMatrix(evals);
Eig = A.Eigen();
D = Eig.D;
V = Eig.GetV();
try
{
check(A.Multiply(V), V.Multiply(D));
try_success("EigenvalueDecomposition (nonsymmetric)...", "");
}
catch (System.SystemException e)
{
errorCount = try_failure(errorCount, "EigenvalueDecomposition (nonsymmetric)...", "incorrect nonsymmetric Eigenvalue decomposition calculation");
System.Console.Out.WriteLine(e.Message);
}
print("\nTestMatrix completed.\n");
print("Total errors reported: " + System.Convert.ToString(errorCount) + "\n");
print("Total warnings reported: " + System.Convert.ToString(warningCount) + "\n");
}