/// <summary>
/// Constructs the image from selection.
/// </summary>
/// <param name="theSelection">The selection.</param>
/// <returns>imageConditionAndData.</returns>
public imageConditionAndData SelectedImageData(PictureBoxSelection theSelection = null)
{
if ((theSelection == null) && (selection != null))
{
theSelection = selection;
}
if (theSelection == null)
{
return(this);
}
Rectangle theSelectionRectangle = (Rectangle)theSelection.SelectionRectReal;
DenseMatrix subMatrix = (DenseMatrix)dmSourceData.SubMatrix(
theSelectionRectangle.Location.Y,
theSelectionRectangle.Height,
theSelectionRectangle.Location.X,
theSelectionRectangle.Width);
Image <Gray, Byte> img = ImageProcessing.grayscaleImageFromDenseMatrix(subMatrix);
DenseMatrix maskMatrix = ImageProcessing.DenseMatrixFromImage(maskImageBinary);
maskMatrix = (DenseMatrix)maskMatrix.SubMatrix(
theSelectionRectangle.Location.Y,
theSelectionRectangle.Height,
theSelectionRectangle.Location.X,
theSelectionRectangle.Width);
//Image<Gray, Byte> maskSubImageBinary = maskImageBinary.GetSubRect(theSelectionRectangle);
Image <Gray, Byte> maskSubImageBinary = ImageProcessing.grayscaleImageFromDenseMatrixWithFixedValuesBounds(maskMatrix, 0.0d, 1.0d);// maskImageBinary.GetSubRect(theSelectionRectangle);
maskSubImageBinary = maskSubImageBinary / 255;
//Image<Gray, double> tmpHighlightingImage = img.CopyBlank();
//tmpHighlightingImage.Draw((Rectangle)theSelection.SelectionRectReal, new Gray(255), -1);
//img = img.AddWeighted(tmpHighlightingImage, 1.0, 0.15, 0.0);
//img.Draw((Rectangle)theSelection.SelectionRectReal, new Gray(255), 1);
//ImageProcessing imgPr = new ImageProcessing(img.Bitmap, false);
//imgPr.significantMaskImageBinary = maskSubImageBinary;
//imgPr.significantMaskImage = maskSubImageBinary*255;
imageConditionAndData retImageData = new imageConditionAndData(subMatrix, maskSubImageBinary);
retImageData.currentColorScheme = currentColorScheme;
retImageData.currentColorSchemeRuler = new ColorSchemeRuler(currentColorSchemeRuler);
retImageData.currentColorSchemeRuler.imgToRule = retImageData;
retImageData.currentColorSchemeRuler.IsMarginsFixed = false;
//retImageData.UpdateColorSchemeRuler();
return(retImageData);
}
/// <summary>
/// Run example
/// </summary>
public void Run()
{
// Format vector output to console
var formatProvider = (CultureInfo)CultureInfo.InvariantCulture.Clone();
formatProvider.TextInfo.ListSeparator = " ";
// Create new empty square matrix
var matrix = new DenseMatrix(10);
Console.WriteLine(@"Empty matrix");
Console.WriteLine(matrix.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// 1. Fill matrix by data using indexer []
var k = 0;
for (var i = 0; i < matrix.RowCount; i++)
{
for (var j = 0; j < matrix.ColumnCount; j++)
{
matrix[i, j] = k++;
}
}
Console.WriteLine(@"1. Fill matrix by data using indexer []");
Console.WriteLine(matrix.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// 2. Fill matrix by data using At. The element is set without range checking.
for (var i = 0; i < matrix.RowCount; i++)
{
for (var j = 0; j < matrix.ColumnCount; j++)
{
matrix.At(i, j, k--);
}
}
Console.WriteLine(@"2. Fill matrix by data using At");
Console.WriteLine(matrix.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// 3. Clone matrix
var clone = matrix.Clone();
Console.WriteLine(@"3. Clone matrix");
Console.WriteLine(clone.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// 4. Clear matrix
clone.Clear();
Console.WriteLine(@"4. Clear matrix");
Console.WriteLine(clone.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// 5. Copy matrix into another matrix
matrix.CopyTo(clone);
Console.WriteLine(@"5. Copy matrix into another matrix");
Console.WriteLine(clone.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// 6. Get submatrix into another matrix
var submatrix = matrix.SubMatrix(2, 2, 3, 3);
Console.WriteLine(@"6. Copy submatrix into another matrix");
Console.WriteLine(submatrix.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// 7. Get part of the row as vector. In this example: get 4 elements from row 5 starting from column 3
var row = matrix.Row(5, 3, 4);
Console.WriteLine(@"7. Get part of the row as vector");
Console.WriteLine(row.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// 8. Get part of the column as vector. In this example: get 3 elements from column 2 starting from row 6
var column = matrix.Column(2, 6, 3);
Console.WriteLine(@"8. Get part of the column as vector");
Console.WriteLine(column.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// 9. Get columns using column enumerator. If you need all columns you may use ColumnEnumerator without parameters
Console.WriteLine(@"9. Get columns using column enumerator");
foreach (var keyValuePair in matrix.ColumnEnumerator(2, 4))
{
Console.WriteLine(@"Column {0}: {1}", keyValuePair.Item1, keyValuePair.Item2.ToString("#0.00\t", formatProvider));
}
Console.WriteLine();
// 10. Get rows using row enumerator. If you need all rows you may use RowEnumerator without parameters
Console.WriteLine(@"10. Get rows using row enumerator");
foreach (var keyValuePair in matrix.RowEnumerator(4, 3))
{
Console.WriteLine(@"Row {0}: {1}", keyValuePair.Item1, keyValuePair.Item2.ToString("#0.00\t", formatProvider));
}
Console.WriteLine();
// 11. Convert matrix into multidimensional array
var data = matrix.ToArray();
Console.WriteLine(@"11. Convert matrix into multidimensional array");
for (var i = 0; i < data.GetLongLength(0); i++)
{
for (var j = 0; j < data.GetLongLength(1); j++)
{
Console.Write(data[i, j].ToString("#0.00\t"));
}
Console.WriteLine();
}
Console.WriteLine();
// 12. Convert matrix into row-wise array
var rowwise = matrix.ToRowWiseArray();
Console.WriteLine(@"12. Convert matrix into row-wise array");
for (var i = 0; i < matrix.RowCount; i++)
{
for (var j = 0; j < matrix.ColumnCount; j++)
{
Console.Write(rowwise[(i * matrix.ColumnCount) + j].ToString("#0.00\t"));
}
Console.WriteLine();
}
Console.WriteLine();
// 13. Convert matrix into column-wise array
var columnise = matrix.ToColumnWiseArray();
Console.WriteLine(@"13. Convert matrix into column-wise array");
for (var i = 0; i < matrix.RowCount; i++)
{
for (var j = 0; j < matrix.ColumnCount; j++)
{
Console.Write(columnise[(j * matrix.RowCount) + i].ToString("#0.00\t"));
}
Console.WriteLine();
}
Console.WriteLine();
// 14. Get matrix diagonal as vector
var diagonal = matrix.Diagonal();
Console.WriteLine(@"14. Get matrix diagonal as vector");
Console.WriteLine(diagonal.ToString("#0.00\t", formatProvider));
Console.WriteLine();
}
/// <summary>
/// Generate a random n-class classification problem.
/// </summary>
/// <param name="nSamples">The number of samples.</param>
/// <param name="nFeatures">The total number of features. These comprise <paramref name="nInformative"/>
/// informative features, <paramref name="nRedundant"/> redundant features, <paramref name="nRepeated"/>
/// dupplicated features and `<paramref name="nFeatures"/>-<paramref name="nInformative"/>-<paramref name="nRedundant"/>-
/// <paramref name="nRepeated"/>` useless features drawn at random.</param>
/// <param name="nInformative">The number of informative features. Each class is composed of a number
/// of gaussian clusters each located around the vertices of a hypercube
/// in a subspace of dimension <paramref name="nInformative"/>. For each cluster,
/// informative features are drawn independently from N(0, 1) and then
/// randomly linearly combined in order to add covariance. The clusters
/// are then placed on the vertices of the hypercube.</param>
/// <param name="nRedundant">The number of redundant features. These features are generated as
/// random linear combinations of the informative features.</param>
/// <param name="nRepeated"> The number of dupplicated features, drawn randomly from the informative
/// and the redundant features.
/// </param>
/// <param name="nClasses">The number of classes (or labels) of the classification problem.</param>
/// <param name="nClustersPerClass">The number of clusters per class.</param>
/// <param name="weights">The proportions of samples assigned to each class. If None, then
/// classes are balanced. Note that if `len(weights) == n_classes - 1`,
/// then the last class weight is automatically inferred.
/// </param>
/// <param name="flipY">The fraction of samples whose class are randomly exchanged.</param>
/// <param name="classSep">The factor multiplying the hypercube dimension.</param>
/// <param name="hypercube">If True, the clusters are put on the vertices of a hypercube. If
/// False, the clusters are put on the vertices of a random polytope.</param>
/// <param name="shift">Shift all features by the specified value. If None, then features
/// are shifted by a random value drawn in [-class_sep, class_sep].</param>
/// <param name="scale">Multiply all features by the specified value. If None, then features
/// are scaled by a random value drawn in [1, 100]. Note that scaling
/// happens after shifting.
/// </param>
/// <param name="shuffle">Shuffle the samples and the features.</param>
/// <param name="randomState">Random generator.</param>
/// <returns>array of shape [n_samples]
/// The integer labels for class membership of each sample.</returns>
/// <remarks>
/// The algorithm is adapted from Guyon [1] and was designed to generate
/// the "Madelon" dataset.
/// References
/// ----------
/// .. [1] I. Guyon, "Design of experiments for the NIPS 2003 variable
/// selection benchmark", 2003.
/// </remarks>
public static Classification MakeClassification(
int nSamples = 100,
int nFeatures = 20,
int nInformative = 2,
int nRedundant = 2,
int nRepeated = 0,
int nClasses = 2,
int nClustersPerClass = 2,
List<double> weights = null,
double flipY = 0.01,
double classSep = 1.0,
bool hypercube = true,
double? shift = 0.0,
double? scale = 1.0,
bool shuffle = true,
Random randomState = null)
{
var generator = randomState ?? new Random();
// Count features, clusters and samples
if (nInformative + nRedundant + nRepeated > nFeatures)
{
throw new ArgumentException("Number of informative, redundant and repeated " +
"features must sum to less than the number of total" +
" features");
}
if (nInformative * nInformative < nClasses * nClustersPerClass)
{
throw new ArgumentException(
"n_classes * n_clusters_per_class must" +
"be smaller or equal 2 ** n_informative");
}
if (weights != null && !new[] { nClasses, nClasses - 1 }.Contains(weights.Count))
{
throw new ArgumentException("Weights specified but incompatible with number of classes.");
}
int nUseless = nFeatures - nInformative - nRedundant - nRepeated;
int nClusters = nClasses * nClustersPerClass;
if (weights != null && weights.Count == nClasses - 1)
{
weights.Add(1.0 - weights.Sum());
}
if (weights == null)
{
weights = Enumerable.Repeat(1.0 / nClasses, nClasses).ToList();
weights[weights.Count - 1] = 1.0 - weights.Take(weights.Count - 1).Sum();
}
var nSamplesPerCluster = new List<int>();
for (int k = 0; k < nClusters; k++)
{
nSamplesPerCluster.Add(
(int)(nSamples * weights[k % nClasses] / nClustersPerClass));
}
for (int i = 0; i < nSamples - nSamplesPerCluster.Sum(); i++)
{
nSamplesPerCluster[i % nClusters] += 1;
}
// Intialize X and y
Matrix x = new DenseMatrix(nSamples, nFeatures);
int[] y = new int[nSamples];
// Build the polytope
Matrix c = new DenseMatrix(1 << nInformative, nInformative);
for (int i = 0; i < 1 << nInformative; i++)
{
var row = new DenseVector(nInformative);
for (int bitN = 0; bitN < nInformative; bitN++)
{
row[bitN] = (i & (1 << bitN)) == 1 ? classSep : -classSep;
}
c.SetRow(i, row);
}
if (!hypercube)
{
for (int k = 0; k < nClusters; k++)
{
c.SetRow(k, c.Row(k) * generator.NextDouble());
}
for (int f = 0; f < nInformative; f++)
{
c.SetColumn(f, c.Column(f) * generator.NextDouble());
}
}
// todo:
// generator.shuffle(C)
// Loop over all clusters
int pos = 0;
int posEnd = 0;
for (int k = 0; k < nClusters; k++)
{
// Number of samples in cluster k
int nSamplesK = nSamplesPerCluster[k];
// Define the range of samples
pos = posEnd;
posEnd = pos + nSamplesK;
// Assign labels
for (int l = pos; l < posEnd; l++)
{
y[l] = k % nClasses;
}
// Draw features at random
var subMatrix = DenseMatrix.CreateRandom(
nSamplesK,
nInformative,
new Normal { RandomSource = generator });
x.SetSubMatrix(pos, nSamplesK, 0, nInformative, subMatrix);
// Multiply by a random matrix to create co-variance of the features
var uniform = new ContinuousUniform(-1, 1) { RandomSource = generator };
Matrix a = DenseMatrix.CreateRandom(nInformative, nInformative, uniform);
x.SetSubMatrix(
pos,
nSamplesK,
0,
nInformative,
x.SubMatrix(pos, nSamplesK, 0, nInformative) * a);
// Shift the cluster to a vertice
var v = x.SubMatrix(pos, nSamplesK, 0, nInformative).AddRowVector(c.Row(k));
x.SetSubMatrix(pos, nSamplesK, 0, nInformative, v);
}
// Create redundant features
if (nRedundant > 0)
{
var uniform = new ContinuousUniform(-1, 1) { RandomSource = generator };
Matrix b = DenseMatrix.CreateRandom(nInformative, nRedundant, uniform);
x.SetSubMatrix(
0,
x.RowCount,
nInformative,
nRedundant,
x.SubMatrix(0, x.RowCount, 0, nInformative) * b);
}
// Repeat some features
if (nRepeated > 0)
{
int n = nInformative + nRedundant;
for (int i = 0; i < nRepeated; i++)
{
int r = (int)((generator.Next(nRepeated) * (n - 1)) + 0.5);
x.SetColumn(i, x.Column(r));
}
}
// Fill useless features
var denseMatrix = DenseMatrix.CreateRandom(nSamples, nUseless, new Normal { RandomSource = generator });
x.SetSubMatrix(0, nSamples, nFeatures - nUseless, nUseless, denseMatrix);
// Randomly flip labels
if (flipY >= 0.0)
{
for (int i = 0; i < nSamples; i++)
{
if (generator.NextDouble() < flipY)
{
y[i] = generator.Next(nClasses);
}
}
}
// Randomly shift and scale
bool constantShift = shift != null;
bool constantScale = scale != null;
for (int f = 0; f < nFeatures; f++)
{
if (!constantShift)
{
shift = ((2 * generator.NextDouble()) - 1) * classSep;
}
if (!constantScale)
{
scale = 1 + (100 * generator.NextDouble());
}
x.SetColumn(f, (x.Column(f) + shift.Value) * scale.Value);
}
// Randomly permute samples and features
// todo:
/*
if (shuffle)
{
X, y = util_shuffle(X, y, random_state=generator)
indices = np.arange(n_features)
generator.shuffle(indices)
X[:, :] = X[:, indices]
}*/
return new Classification { X = x, Y = y };
}
public DenseMatrix createMatrix(Model model)
{
int numConstraints = model.Constraints.Count;
int numDecisionVars = model.Goal.Coefficients.Length;
int varCounter = numDecisionVars;
// matrix(rows, columns)
DenseMatrix coefficients = new DenseMatrix(numConstraints, numDecisionVars);
DenseMatrix artificialVars = new DenseMatrix(numConstraints, 1);
var constraintCounter = 0;
this.rhsValues = new DenseVector(numConstraints);
this.basics = new List<int>();
this.artificialRows = new List<int>();
foreach (var constraint in model.Constraints) {
rhsValues[constraintCounter] = constraint.Value;
// if the constraint RHS is negative, invert the coefficients and flip the inequality sign
if (constraint.Value < 0)
{
for (int i = 0; i< model.Goal.Coefficients.Length; i++) {
model.Goal.Coefficients[i] = model.Goal.Coefficients[i] * -1;
}
if (constraint.Relationship == Relationship.LessThanOrEquals)
{
constraint.Relationship = Relationship.GreaterThanOrEquals;
}
else if (constraint.Relationship == Relationship.GreaterThanOrEquals)
{
constraint.Relationship = Relationship.LessThanOrEquals;
}
// also flip the rhs value which we already put in the array for the simplex setup
rhsValues[constraintCounter] = rhsValues[constraintCounter] * -1;
}
coefficients.SetRow(constraintCounter, 0, constraint.Coefficients.Length, new DenseVector(constraint.Coefficients));
// if it's a less than, add a slack column to the coefs matrix
if (constraint.Relationship == Relationship.LessThanOrEquals)
{
DenseVector slack = DenseVector.Create(model.Constraints.Count, delegate(int s) { return 0; });
slack.At(constraintCounter, 1);
coefficients = (DenseMatrix)coefficients.Append(slack.ToColumnMatrix());
this.basics.Add(varCounter);
}
else
{
// Need to add an artificial variable for >= and = constraints
DenseVector surplus = DenseVector.Create(model.Constraints.Count, delegate(int s) { return 0; });
surplus.At(constraintCounter, -1);
coefficients = (DenseMatrix)coefficients.Append(surplus.ToColumnMatrix());
DenseVector artificial = DenseVector.Create(model.Constraints.Count, delegate(int s) { return 0; });
artificial.At(constraintCounter, 1);
artificialVars = (DenseMatrix)artificialVars.Append(artificial.ToColumnMatrix());
// Keeps track of the rows with artificial variable, for setting w
artificialRows.Add(constraintCounter);
}
varCounter++;
constraintCounter++;
}
// put the constraints and stuff into the matrix
if (artificialVars.ColumnCount > 1)
{
artificialVars = (DenseMatrix)artificialVars.SubMatrix(0, artificialVars.RowCount, 1, artificialVars.ColumnCount - 1);
for (int i = coefficients.ColumnCount; i < coefficients.ColumnCount + artificialVars.ColumnCount; i++)
{
this.basics.Add(i);
}
coefficients = (DenseMatrix)coefficients.Append(artificialVars);
numArtificial = artificialVars.ColumnCount;
}
else
{
numArtificial = 0;
}
return coefficients;
}
private void optimize(DenseMatrix coefficients, DenseVector objFunValues, bool artifical)
{
//for calculations on the optimal solution row
int cCounter,
width = coefficients.ColumnCount;
DenseVector cBVect = new DenseVector(basics.Count);
//Sets up the b matrix
DenseMatrix b = new DenseMatrix(basics.Count, 1);
//basics will have values greater than coefficients.ColumnCount - 1 if there are still artificial variables
//or if Nathan is bad and didn't get rid of them correctly
foreach (int index in basics)
{
b = (DenseMatrix)b.Append(DenseVector.OfVector(coefficients.Column(index)).ToColumnMatrix());
}
// removes the first column
b = (DenseMatrix)b.SubMatrix(0, b.RowCount, 1, b.ColumnCount - 1);
double[] cPrimes = new double[width];
double[] rhsOverPPrime;
DenseMatrix[] pPrimes = new DenseMatrix[width];
DenseMatrix bInverse;
int newEntering, exitingRow;
bool optimal = false;
if(artifical)
{
rhsOverPPrime = new double[numConstraints + 1];
}
else
{
rhsOverPPrime = new double[numConstraints];
}
while (!optimal)
{
//calculates the inverse of b for this iteration
bInverse = (DenseMatrix)b.Inverse();
//updates the C vector with the most recent basic variables
cCounter = 0;
foreach (int index in basics)
{
cBVect[cCounter++] = objFunValues.At(index);
}
//calculates the pPrimes and cPrimes
for (int i = 0; i < coefficients.ColumnCount; i++)
{
if (!basics.Contains(i))
{
pPrimes[i] = (DenseMatrix)bInverse.Multiply((DenseMatrix)coefficients.Column(i).ToColumnMatrix());
//c' = objFunVals - cB * P'n
//At(0) to turn it into a double
cPrimes[i] = objFunValues.At(i) - (pPrimes[i].LeftMultiply(cBVect)).At(0);
}
else
{
pPrimes[i] = null;
}
}
//RHS'
xPrime = (DenseMatrix)bInverse.Multiply((DenseMatrix)rhsValues.ToColumnMatrix());
//Starts newEntering as the first nonbasic
newEntering = -1;
int iter = 0;
while(newEntering == -1)
{
if(!basics.Contains(iter))
{
newEntering = iter;
}
iter++;
}
//new entering becomes the small cPrime that corresponds to a non-basic value
for (int i = 0; i < cPrimes.Length; i++)
{
if (cPrimes[i] < cPrimes[newEntering] && !basics.Contains(i))
{
newEntering = i;
}
}
//if the smallest cPrime is >= 0, ie they are all positive
if (cPrimes[newEntering] >= 0)
{
optimal = true;
}
else
{
//fix me to deal with if all these values are negative
exitingRow = 0;
for (int i = 0; i < xPrime.RowCount; i++)
{
double[,] pPrime = pPrimes[newEntering].ToArray();
rhsOverPPrime[i] = xPrime.ToArray()[i, 0] / pPrime[i, 0];
if (rhsOverPPrime[i] < rhsOverPPrime[exitingRow] && rhsOverPPrime[i] > 0 )
{
exitingRow = i;
}
}
//translates from the index in the basics list to the actual row
exitingRow = basics[exitingRow];
//make sure you're not being stupid here!!!!
int tempIndex = basics.IndexOf(exitingRow);
basics.Remove(exitingRow);
basics.Insert(tempIndex, newEntering);
b.SetColumn(basics.IndexOf(newEntering), coefficients.Column(newEntering));
}
}
}
/// <summary>
/// Adaptive Cross Approximation (ACA) matrix compression
/// the result is stored in U and V matrices like U*V
/// </summary>
/// <param name="acaThres">Relative error threshold to stop adding rows and columns in ACA iteration</param>
/// <param name="m">Row indices of Z submatrix to compress</param>
/// <param name="n">Column indices of Z submatrix to compress</param>
/// <param name="U">to store result</param>
/// <param name="V">to store result</param>
/// <returns>pair with matrix U and V</returns>
public static Tuple<Matrix, Matrix> Aca(double acaThres, List<int> m, List<int> n, Matrix U, Matrix V)
{
int M = m.Count;
int N = n.Count;
int Min = Math.Min(M, N);
U = new DenseMatrix(Min, Min);
V = new DenseMatrix(Min, Min);
//if Z is a vector, there is nothing to compress
if (M == 1 || N == 1)
{
U = UserImpedance(m, n);
V = new DenseMatrix(1, 1);
V[0, 0] = 1.0;
return new Tuple<Matrix,Matrix>(U,V);
}
//Indices of columns picked up from Z
//Vector J = new DenseVector(N);
//List<int> J = new List<int>(N);
List<int> J = new List<int>(new int [N]);
//int[] J = new int[N];
//Indices of rows picked up from Z
//Vector I = new DenseVector(M);
List<int> I = new List<int>(new int [M]);
//int[] I = new int[M];
//Row indices to search for maximum in R
//Vector i = new DenseVector(M);
List<int> i = new List<int>();
//int[] i = new int[M];
//Column indices to search for maximum in R
//Vector j = new DenseVector(N);
List<int> j = new List<int>();
//int[] j = new int[N];
for (int k = 1; k < M; k++)
{
i.Add(k);
}
for (int k = 0; k < N; k++)
{
j.Add(k);
}
//Initialization
//Initialize the 1st row index I(1) = 1
I[0] = 0;
//Initialize the 1st row of the approximate error matrix
List<int> m0 = new List<int>();
m0.Add(m[I[0]]);
Matrix Rik = UserImpedance(m0, n);
//Find the 1st column index J(0)
double max = -1.0;
int col = 0;
foreach (int ind in j)
{
if (Math.Abs(Rik[0, ind]) > max)
{
max = Math.Abs(Rik[0, ind]);
col = ind;
}
}
//J[0] = j[col];
J[0] = col;
j.Remove(J[0]);
//First row of V
V = new DenseMatrix(1, Rik.ColumnCount);
V.SetRow(0, Rik.Row(0).Divide(Rik[0, J[0]]));
//Initialize the 1st column of the approximate error matrix
List<int> n0 = new List<int>();
n0.Add(n[J[0]]);
Matrix Rjk = UserImpedance(m, n0);
//First column of U
U = new DenseMatrix(Rjk.RowCount, 1);
U.SetColumn(0, Rjk.Column(0));
// Norm of (approximate) Z, to test error
double d1 = U.L2Norm();
double d2 = V.L2Norm();
double normZ = d1 * d1 * d2 * d2;
//Find 2nd row index I(2)
int row = 0;
max = -1.0;
foreach (int ind in i)
{
if (Math.Abs(Rjk[ind, 0]) > max)
{
max = Math.Abs(Rjk[ind, 0]);
row = ind;
}
}
//I[1] = i[row];
I[1] = row;
i.Remove(I[1]);
//Iteration
for (int k = 1; k < Math.Min(M, N); k++)
{
//Update (Ik)th row of the approximate error matrix:
List<int> t1 = new List<int>();
t1.Add(m[I[k]]);
Rik = (Matrix)(UserImpedance(t1, n) - U.SubMatrix(I[k], 1, 0, U.ColumnCount).Multiply(V));
//CHECKED OK all code before works fine
//Find kth column index Jk
max = -1.0;
col = 0;
foreach (int ind in j)
{
if (Math.Abs(Rik[0, ind]) > max)
{
max = Math.Abs(Rik[0, ind]);
col = ind;
}
}
J[k] = col;
j.Remove(J[k]);
//Terminate if R(I(k),J(k)) == 0
if (Rik[0, J[k]] == 0)
{
break;
}
//Set k-th row of V equal to normalized error
Matrix Vk = (Matrix)Rik.Divide(Rik[0, J[k]]);
//Update (Jk)th column of the approximate error matrix
List<int> n1 = new List<int>();
n1.Add(n[J[k]]);
Rjk = (Matrix)(UserImpedance(m, n1) - U.Multiply(V.SubMatrix(0, V.RowCount, J[k], 1)));
// Set k-th column of U equal to updated error
Matrix Uk = Rjk;
//Norm of approximate Z
//Matrix s = (Matrix)(U.Transpose().Multiply(Uk)).Multiply((Vk.Multiply(V.Transpose())).Transpose());
//Matrix s = (Matrix)((U.Transpose()).Multiply(Uk)).Multiply(((Vk.Multiply(V.Transpose())).Transpose()));
Matrix a = (Matrix)U.Transpose().Multiply(Uk);
Matrix b = (Matrix)Vk.Multiply(V.Transpose()).Transpose();
Matrix s = (Matrix)a.PointwiseMultiply(b);
double sum = 0;
for (int i1 = 0; i1 < s.RowCount; i1++)
{
for (int j1 = 0; j1 < s.ColumnCount; j1++)
{
sum += s[i1, j1];
}
}
d1 = Uk.L2Norm();
d2 = Vk.L2Norm();
normZ += 2 * sum + d1 * d1 * d2 * d2;
//Update U and V
//U.SetColumn(U.ColumnCount - 1, Uk.Column(0));
//V.SetRow(V.RowCount - 1, Vk.Row(0));
U = AddColumn(U, (Vector)Uk.Column(0));
//U.SetColumn(k, Uk.Column(0));
V = AddRow(V, (Vector)Vk.Row(0));
//V.SetRow(k, Vk.Row(0));
if (d1 * d2 <= acaThres * Math.Sqrt(normZ))
{
break;
}
if (k == Math.Min(N, M) - 1)
{
break;
}
max = -1;
row = 0;
foreach (int ind in i)
{
if (Math.Abs(Rjk[ind, 0]) > max)
{
max = Math.Abs(Rjk[ind, 0]);
row = ind;
}
}
I[k + 1] = row;
//i = removeIndex(i,I[k+1]);
i.Remove(I[k + 1]);
}
return new Tuple<Matrix, Matrix>(U, V);
}
static Tuple<int, double, double> RunValidation(double[][] trainingData, double[][] validationData, double[][] outSampleData, int k)
{
int N = trainingData.Length;
var ZZ = new DenseMatrix(N, 8);
var Y = new DenseVector(N);
for (int j = 0; j < N; j++)
{
double x1 = trainingData[j][0], x2 = trainingData[j][1];
ZZ[j, 0] = 1;
ZZ[j, 1] = x1;
ZZ[j, 2] = x2;
ZZ[j, 3] = x1 * x1;
ZZ[j, 4] = x2 * x2;
ZZ[j, 5] = x1 * x2;
ZZ[j, 6] = Math.Abs(x1 - x2);
ZZ[j, 7] = Math.Abs(x1 + x2);
Y[j] = trainingData[j][2];
}
var Z = ZZ.SubMatrix(0, N, 0, k + 1);
var WW = Z.TransposeThisAndMultiply(Z).Inverse().TransposeAndMultiply(Z).Multiply(Y);
var W = new DenseVector(8);
WW.CopySubVectorTo(W, 0, 0, k + 1);
Func<double, double, double> h = (x1, x2) =>
W[0] + W[1] * x1 + W[2] * x2 + W[3] * x1 * x1 + W[4] * x2 * x2 + W[5] * x1 * x2
+ W[6] * Math.Abs(x1 - x2) + W[7] * Math.Abs(x1 + x2) >= 0 ? 1.0 : -1.0;
return Tuple.Create(
k,
(validationData.Count(v => Math.Sign(h(v[0], v[1])) != Math.Sign(v[2])) + 0.0) / validationData.Length,
(outSampleData.Count(v => Math.Sign(h(v[0], v[1])) != Math.Sign(v[2])) + 0.0) / outSampleData.Length);
}
public static ResultFEM Solve(Matrix<double> K, Matrix<double> f, int[] bc)
{
// Create dof array:
int ndof = f.RowCount;
// Initialize displacement vector
Matrix u = new DenseMatrix(ndof, 1);
int[] dof = new int[ndof];
for (int i = 0; i < ndof; i++)
{
dof[i] = i;
}
// Create the free dofs:
int[] fdof = dof.Except(bc).ToArray();
int nfdof = fdof.Length; // Number of free dofs.
int nbdof = ndof - nfdof; //Constrained dofs
// Create the permutation array which puts the constrained dofs last:
int[] permute = bc.Union(fdof).ToArray();
Permutation perm = new Permutation(permute);
Permutation invPerm = perm.Inverse();
Matrix<double> KPermuted = DenseMatrix.OfMatrix(K);
KPermuted.PermuteRows(invPerm);
KPermuted.PermuteColumns(invPerm);
// Split K:::
Matrix<double> Kff = KPermuted.SubMatrix(nbdof, nfdof, nbdof, nfdof);
System.Console.WriteLine(Kff); //Down right corner of matrix
Matrix<double> Kfp = KPermuted.SubMatrix(nbdof, nfdof, 0, nbdof); //Down left corner of matrix
// Split F:::
Matrix<double> fPermuted = DenseMatrix.OfMatrix(f);
fPermuted.PermuteRows(invPerm);
Matrix<double> ff = fPermuted.SubMatrix(nbdof, nfdof, 0, 1);
Matrix<double> up = u.SubMatrix(0, nbdof, 0, 1); // Must set up to constrained values in bc.
// Solve for the unknown displacements:::
Matrix<double> s = Kff.Solve(ff.Subtract(Kfp.Multiply(up)));
u.SetSubMatrix(nbdof, 0, s); // Set displacements back.
System.Console.WriteLine(u);
// Permute back u
u.PermuteRows(perm);
System.Console.WriteLine("U after permut");
System.Console.WriteLine(K);
System.Console.WriteLine(u);
System.Console.WriteLine(f);
// Get reaction forces:
Matrix<double> Q = K.Multiply(u).Subtract(f);
ResultFEM result = new ResultFEM(u, Q);
return result;
}
