/// <summary>
/// creates an identity transformation
/// </summary>
/// <param name="D">spatial dimension</param>
/// <returns></returns>
public static AffineTrafo ID(int D)
{
AffineTrafo tr = new AffineTrafo();
tr.Matrix = FullMatrix.Eye(D);
tr.Affine = new double[D];
return(tr);
}
/// <summary>
/// entriesAsColMajor is assumed to be col major form
/// </summary>
public static IMatrix<double> GetMatrix(Guid id, int nodeCount, string entriesAsColMajor)
{
double[] components = null;
if (!MatrixHelper.ParseEntryString(nodeCount, entriesAsColMajor, out components))
throw new ArgumentException(string.Format("Could not parse the matrix entry string: \"{0}\"", entriesAsColMajor), "entriesAsColMajor");
IMatrix<double> target = new FullMatrix<Double>(id, components, nodeCount);
return target;
}
void PlotCell0()
{
BoundingBox BB = new BoundingBox(2);
GridDat.Cells.GetCellBoundingBox(0, BB);
int Nx = 50;
int Ny = 55;
var xNodes = Grid1D.Linspace(BB.Min[0], BB.Max[0], Nx);
var yNodes = Grid1D.Linspace(BB.Min[1], BB.Max[1], Ny);
var GlobalNodes = MultidimensionalArray.Create(Nx, Ny, 2);
for (int i = 0; i < Nx; i++)
{
for (int j = 0; j < Ny; j++)
{
GlobalNodes[i, j, 0] = xNodes[i];
GlobalNodes[i, j, 1] = yNodes[j];
}
}
var GlobalNodes_C = GlobalNodes.ResizeShallow(Nx * Ny, 2);
var LocalNodes = MultidimensionalArray.Create(1, Nx * Ny, 2);
GridDat.TransformGlobal2Local(GlobalNodes_C, LocalNodes, 0, 1, 0);
var Values = MultidimensionalArray.Create(1, Nx, Ny);
var Values_ = Values.ResizeShallow(1, Nx * Ny);
var Gradients = MultidimensionalArray.Create(1, Nx, Ny, 2);
var Gradients_ = Gradients.ResizeShallow(1, Nx * Ny, 2);
var NodeSet = GridDat.NSC.CreateContainer(LocalNodes.ExtractSubArrayShallow(0, -1, -1), 0);
var lh = GridDat.NSC.LockNodeSetFamily(NodeSet);
f1.Evaluate(0, 1, 0, Values_);
f1.EvaluateGradient(0, 1, 0, Gradients_);
GridDat.NSC.UnlockNodeSetFamily(lh);
xNodes.SaveToTextFile("C:\\tmp\\xNodes.txt");
yNodes.SaveToTextFile("C:\\tmp\\yNodes.txt");
FullMatrix output1 = new FullMatrix(Values.ExtractSubArrayShallow(0, -1, -1));
output1.ToTxtFile("C:\\tmp\\f.txt");
FullMatrix output2 = new FullMatrix(Gradients.ExtractSubArrayShallow(0, -1, -1, 0));
output2.ToTxtFile("C:\\tmp\\df.txt");
}
/// <summary>
/// returns a 2D transformation
/// </summary>
public static AffineTrafo Some2DRotation(double angle)
{
AffineTrafo Trafo = new AffineTrafo();
FullMatrix dreh = new FullMatrix(2, 2);
dreh[0, 0] = Math.Cos(angle); dreh[0, 1] = -Math.Sin(angle);
dreh[1, 0] = Math.Sin(angle); dreh[1, 1] = Math.Cos(angle);
Trafo.Affine = new double[2];
Trafo.Matrix = dreh;
return(Trafo);
}
public void BuildEmptyFullMatrix(Int32 nodeCount)
{
var fullMatrix = new FullMatrix<Boolean>(Guid.NewGuid(), nodeCount);
Assert.NotNull(fullMatrix);
Int32 count =
Enumerable.Range(0, nodeCount).AsParallel()
.Select(i =>
Enumerable.Range(i, nodeCount - i).AsParallel()
.Count(j => fullMatrix[i, j] != false)
).Count(v => v != 0);
Assert.Equal(0, count);
}
public void BuildFullMatrixFromDoubleArray()
{
Int32[,] dblArray = new Int32[,] {
{1, 2, 3},
{2, 1, 2},
{3, 2, 1}
};
var fullMatrix = new FullMatrix<Int32>(Guid.NewGuid(), dblArray);
Assert.NotNull(fullMatrix);
Assert.Equal(dblArray[0, 0], fullMatrix[0, 0]);
Assert.Equal(dblArray[0, 1], fullMatrix[0, 1]);
Assert.Equal(dblArray[2, 1], fullMatrix[2, 1]);
}
public static IMatrix<double> GetMatrix(int nodeCount, string entriesAsColMajor, bool symmetric)
{
double[] components = null;
if (!MatrixHelper.ParseEntryString(nodeCount, entriesAsColMajor, out components))
throw new ArgumentException(string.Format("Could not parse the matrix entry string: \"{0}\"", entriesAsColMajor), "entriesAsColMajor");
IMatrix<double> target = null;
if (symmetric)
{
target = new SymmetricMatrix<double>(Guid.NewGuid(), components, nodeCount);
}
else
{
target = new FullMatrix<double>(Guid.NewGuid(), components, nodeCount);
}
return target;
}
public void BuildFullMatrixFromSingleArray()
{
Int32[] sglArray = new Int32[] {
1, 2, 3,
2, 1, 2,
3, 2, 1
};
var fullMatrix = new FullMatrix<Int32>(Guid.NewGuid(), sglArray, 3);
Assert.NotNull(fullMatrix);
Assert.Equal(sglArray[0], fullMatrix[0, 0]);
Assert.Equal(sglArray[2], fullMatrix[0, 2]);
Assert.Equal(sglArray[6], fullMatrix[2, 0]);
Assert.Equal(sglArray[7], fullMatrix[2, 1]);
}
void OrthonormalityTest()
{
Basis B = f1.Basis;
int N = B.Length;
var Mtx = new FullMatrix(N, N);
double TotErrSum = 0.0;
CellQuadrature.GetQuadrature(new int[] { N, N }, this.GridDat,
(new CellQuadratureScheme(true)).Compile(GridDat, Math.Min(B.Degree * 2, 16)),
delegate(MultidimensionalArray NodesUntransformed, int iKref) {
var ret = new NodeSetController.NodeSetContainer[] {
GridDat.NSC.CreateContainer(NodesUntransformed, iKref)
};
return(ret);
},
delegate(int i0, int Length, int NoOfNodes, MultidimensionalArray EvalResult) { // void Del_Evaluate
var BasisVal = B.CellEval(0, i0, Length);
EvalResult.Multiply(1.0, BasisVal, BasisVal, 0.0, "jknm", "jkn", "jkm");
},
delegate(int i0, int Length, MultidimensionalArray ResultsOfIntegration) { // SaveIntegrationResults
for (int i = 0; i < Length; i++)
{
var MassMtx = ResultsOfIntegration.ExtractSubArrayShallow(i, -1, -1);
double errsum = 0;
for (int n = 0; n < N; n++)
{
for (int m = 0; m < N; m++)
{
double soll = (n == m) ? 1.0 : 0.0;
errsum += Math.Abs(MassMtx[m, n] - soll);
}
}
TotErrSum += errsum;
}
}).Execute();
Console.WriteLine("orthonormality error sum:" + TotErrSum);
}
public void IsBinaryReturnsTrueAndFalseForInt32Matrix()
{
Int32[,] dblArray = new Int32[,] {
{0, 0, 1, 0},
{1, 1, 0, 0},
{0, 0, 0, 0},
{1, 0, 0, 1}
};
var fullMatrix = new FullMatrix<Int32>(Guid.NewGuid(), dblArray);
Assert.True(fullMatrix.IsBinary);
fullMatrix.SetEdge(2, 2, 3);
Assert.False(fullMatrix.IsBinary);
}
public void SuccessorsThrowsExceptionIfIndexIsOutOfRange()
{
Int32[,] dblArray = new Int32[,] {
{1, 2, 3},
{2, 1, 2},
{3, 2, 1}
};
var fullMatrix = new FullMatrix<Int32>(Guid.NewGuid(), dblArray);
Assert.Throws<IndexOutOfRangeException>(()
=> fullMatrix.Successors(4));
Assert.Throws<IndexOutOfRangeException>(()
=> fullMatrix.Successors(-1));
}
public void SetUpdatesMatrixEntry(int i, int j, double newValue)
{
Double[,] dblArray = new Double[,] {
{0, 0, 0},
{0, 0, 0},
{0, 0, 0},
};
var fullMatrix = new FullMatrix<Double>(Guid.NewGuid(), dblArray);
fullMatrix.SetEdge(i, j, newValue);
Assert.Equal(newValue, fullMatrix[i, j]);
}
public void SetEdgeThrowsExceptionIfIndexIsOutOfRange()
{
Int32[,] dblArray = new Int32[,] {
{1, 2, 3},
{2, 1, 2},
{3, 2, 1}
};
var fullMatrix = new FullMatrix<Int32>(Guid.NewGuid(), dblArray);
Assert.Throws<IndexOutOfRangeException>(()
=> fullMatrix.SetEdge(4, 0, 3));
Assert.Throws<IndexOutOfRangeException>(()
=> fullMatrix.SetEdge(1, -1, -10));
}
public void IsBinaryReturnsTrueForBooleanMatrix()
{
Boolean[,] dblArray = new Boolean[,] {
{false, false, true, false},
{true, true, false, false},
{false, false, false, false},
{true, true, false, true}
};
var fullMatrix = new FullMatrix<Boolean>(Guid.NewGuid(), dblArray);
Assert.True(fullMatrix.IsBinary);
}
public void IsBinaryReturnsTrueAndFalseForDoubleMatrix()
{
Double[,] dblArray = new Double[,] {
{0, 0, 1, 0},
{1, 1, 0, 0},
{0, 0, 0, 0},
{1, 0, 0, 1}
};
var fullMatrix = new FullMatrix<Double>(Guid.NewGuid(), dblArray);
Assert.True(fullMatrix.IsBinary);
fullMatrix.SetEdge(2, 2, 1.444);
Assert.False(fullMatrix.IsBinary);
}
public void InDegreeThrowsExceptionIfIndexIsOutOfRange()
{
Int32[,] dblArray = new Int32[,] {
{1, 2, 3},
{2, 1, 2},
{3, 2, 1}
};
var fullMatrix = new FullMatrix<Int32>(Guid.NewGuid(), dblArray);
Assert.Throws<AggregateException>(()
=> fullMatrix.InDegree(4));
Assert.Throws<AggregateException>(()
=> fullMatrix.InDegree(-1));
}
/// <summary>
/// computes matrix and affine vector of the affine-linear transformation
/// that maps the vectors in the <paramref name="preimage"/> to <paramref name="image"/>;
/// </summary>
/// <param name="preimage">
/// The preimage: (D+1) vectors of dimension D;
/// <list type="bullet">
/// <item>1st index: vector/vertex index, length is D+1</item>
/// <item>2nd index: spatial dimension, length is D</item>
/// </list>
/// Tip: use <see cref="ilPSP.Utils.ArrayTools.Transpose{t}(t[,],t[,])"/>
/// if the sequence of indices is not appropriate;
/// </param>
/// <param name="image">
/// The image: (D+1) vectors of dimension D;
/// <list type="bullet">
/// <item>1st index: vector/vertex index, length is D+1</item>
/// <item>2nd index: spatial dimension, length is D</item>
/// </list>
/// </param>
/// <returns></returns>
public static AffineTrafo FromPoints(double[,] preimage, double[,] image)
{
int D = preimage.GetLength(1);
if (image.GetLength(1) != D || image.GetLength(0) != D + 1)
{
throw new ArgumentException("wrong size; expecting " + D + "x" + (D + 1) + " - array;", "image");
}
if (preimage.GetLength(0) != D + 1)
{
throw new ArgumentException("wrong size; expecting " + D + "x" + (D + 1) + " - array;", "preimage");
}
FullMatrix M = new FullMatrix(D * (D + 1), D * (D + 1));
double[] rhs = new double[M.NoOfCols];
double[] x = (double[])rhs.Clone();
// gesucht: affine lineare Transformation: "xi -> x"
// preimage = xi, image = x;
//
// x = Tr*xi + o
//
// Sei z.B. D=2 (andere D's ergeben sich analog)
// x1 = (x11,x12)^T, x2 = (x21,x22)^T, x3 seien die Bilder von
// xi1 = (xi11,xi12), xi2, xi3.
//
// gesucht sind die Matrix Tr und der Vektor o = (o1,o2)^T,
//
// [ Tr11 Tr12 ]
// Tr = [ ],
// [ Tr21 Tr22 ]
//
// welche mit einem Glsys. der folgenden Form berechnet werden:
//
// [ 1 0 xi11 xi12 0 0 ] [ o1 ] [ x11 ]
// [ 0 1 0 0 xi11 xi12 ] [ o2 ] [ x12 ]
// [ ] [ 0 ] [ ]
// [ 1 0 xi21 xi22 0 0 ] * [ T11 ] = [ x21 ]
// [ 0 1 0 0 xi21 xi22 ] [ T12 ] [ x22 ]
// [ ] [ ] [ ]
// [ 1 0 xi31 xi32 0 0 ] [ T21 ] [ x31 ]
// [ 0 1 0 0 xi31 xi32 ] [ T22 ] [ x31 ]
//
//
// build rhs
for (int d = 0; d < (D + 1); d++)
{
for (int dd = 0; dd < D; dd++)
{
rhs[d * D + dd] = image[d, dd];
}
}
// build matrix
M.Clear();
for (int d = 0; d < (D + 1); d++)
{
for (int dd = 0; dd < D; dd++)
{
M[d * D + dd, dd] = 1.0;
for (int ddd = 0; ddd < D; ddd++)
{
M[d * D + dd, D + D * dd + ddd] = preimage[d, ddd];
}
}
}
// solve Matrix
M.Solve(x, rhs);
// save results, return
AffineTrafo Trafo = new AffineTrafo();
Trafo.Affine = new double[D];
Trafo.Matrix = new FullMatrix(D, D);
for (int d = 0; d < D; d++)
{
Trafo.Affine[d] = x[d];
for (int dd = 0; dd < D; dd++)
{
Trafo.Matrix[d, dd] = x[D + d * D + dd];
}
}
return(Trafo);
}