public static Boolean EvaluateDoubleDoubleFunctionEquality(DoubleDoubleFunction a, DoubleDoubleFunction b)
{
String FullNameA = a.Method.DeclaringType.FullName;
String FullNameB = b.Method.DeclaringType.FullName;
return(FullNameA.Equals(FullNameB));
}
/// <summary>
/// Constructs the function <i>g( h(a,b) )</i>.
/// </summary>
/// <param name="g">a unary function.</param>
/// <param name="h">a binary function.</param>
/// <returns>the unary function <i>g( h(a,b) )</i>.</returns>
public static DoubleDoubleFunction Chain(DoubleFunction g, DoubleDoubleFunction h)
{
return(new DoubleDoubleFunction((a, b) =>
{
return g(h(a, b));
}));
}
/// <summary>
/// Assigns the result of a function to each cell; <tt>x[i] = function(x[i],y[i])</tt>.
/// (Iterates downwards from <tt>[size()-1]</tt> to <tt>[0]</tt>).
/// </summary>
/// <param name="y">
/// The secondary matrix to operate on.
/// </param>
/// <param name="function">
/// The function taking as first argument the current cell's value of <tt>this</tt>,
/// and as second argument the current cell's value of <tt>y</tt>.
/// </param>
/// <returns>
/// <tt>this</tt> (for convenience only).
/// </returns>
/// <exception cref="ArgumentOutOfRangeException">
/// If <tt>size() != y.size()</tt>.
/// </exception>
public override DoubleMatrix1D Assign(DoubleMatrix1D y, DoubleDoubleFunction function)
{
// overriden for performance only
if (!(y is DenseDoubleMatrix1D))
{
return(base.Assign(y, function));
}
var other = (DenseDoubleMatrix1D)y;
CheckSize(y);
double[] elems = Elements;
double[] otherElems = other.Elements;
if (elems == null || otherElems == null)
{
throw new ApplicationException();
}
int s = Stride;
int ys = other.Stride;
int index = this.Index(0);
int otherIndex = other.Index(0);
// specialized for speed
for (int k = Size; --k >= 0;)
{
elems[index] = function(elems[index], otherElems[otherIndex]);
index += s;
otherIndex += ys;
}
return(this);
}
public void Assign(DoubleMatrix2D x, DoubleMatrix2D y, DoubleDoubleFunction function)
{
run(x, y, false, new Matrix2DMatrix2DFunction((AA, BB) =>
{
seqBlas.Assign(AA, BB, function);
return(0);
}));
}
/// <summary>
/// Assigns the result of a function to each cell; <tt>x[row,col] = function(x[row,col],y[row,col])</tt>.
/// </summary>
/// <param name="y">
/// The secondary matrix to operate on.
/// </param>
/// <param name="function">
/// The function taking as first argument the current cell's value of <tt>this</tt>,
/// and as second argument the current cell's value of <tt>y</tt>.
/// </param>
/// <returns>
/// <tt>this</tt> (for convenience only).
/// </returns>
/// <exception cref="ArgumentException">
/// If <tt>columns() != other.columns() || rows() != other.rows()</tt>
/// </exception>
public override DoubleMatrix2D Assign(DoubleMatrix2D y, DoubleDoubleFunction function)
{
if (!IsView)
{
CheckShape(y);
}
return(base.Assign(y, function));
}
/// <summary>
/// Assigns the result of a function to each cell; <tt>x[i] = function(x[i],y[i])</tt>.
/// </summary>
/// <param name="y">
/// The secondary matrix to operate on.
/// </param>
/// <param name="function">
/// A function taking as first argument the current cell's value of <tt>this</tt>,
/// and as second argument the current cell's value of <tt>y</tt>.
/// </param>
/// <returns>
/// <tt>this</tt> (for convenience only).
/// </returns>
/// <exception cref="ArgumentOutOfRangeException">
/// If <tt>size() != y.size()</tt>.
/// </exception>
public virtual DoubleMatrix1D Assign(DoubleMatrix1D y, DoubleDoubleFunction function)
{
CheckSize(y);
for (int i = Size; --i >= 0;)
{
this[i] = function(this[i], y[i]);
}
return(this);
}
/// <summary>
/// Assigns the result of a function to each cell; <tt>x[row,col] = function(x[row,col],y[row,col])</tt>.
/// </summary>
/// <param name="y">
/// The secondary matrix to operate on.
/// </param>
/// <param name="function">
/// The function taking as first argument the current cell's value of <tt>this</tt>,
/// and as second argument the current cell's value of <tt>y</tt>.
/// </param>
/// <returns>
/// <tt>this</tt> (for convenience only).
/// </returns>
/// <exception cref="ArgumentException">
/// If <tt>columns() != other.columns() || rows() != other.rows()</tt>
/// </exception>
public virtual DoubleMatrix2D Assign(DoubleMatrix2D y, DoubleDoubleFunction function)
{
CheckShape(y);
for (int row = Rows; --row >= 0;)
{
for (int column = Columns; --column >= 0;)
{
this[row, column] = function(this[row, column], y[row, column]);
}
}
return(this);
}
/// <summary>
/// Applies a function to each cell and aggregates the results.
/// </summary>
/// <param name="aggr">
/// An aggregation function taking as first argument the current aggregation and as second argument the transformed current cell value.
/// </param>
/// <param name="f">
/// A function transforming the current cell value.
/// </param>
/// <returns>
/// The aggregated measure.
/// </returns>
public virtual double Aggregate(DoubleDoubleFunction aggr, DoubleFunction f)
{
if (Size == 0)
{
return(double.NaN);
}
double a = f(this[Size - 1]);
for (int i = Size - 1; --i >= 0;)
{
a = aggr(a, f(this[i]));
}
return(a);
}
/// <summary>
/// Applies a function to each corresponding cell of two matrices and aggregates the results.
/// </summary>
/// <param name="other">
/// The other matrix.
/// </param>
/// <param name="aggr">
/// An aggregation function taking as first argument the current aggregation and as second argument the transformed current cell values.
/// </param>
/// <param name="f">
/// A function transforming the current cell values.
/// </param>
/// <returns>
/// The aggregated measure.
/// </returns>
/// <exception cref="ArgumentOutOfRangeException">
/// If <tt>size() != other.size()</tt>.
/// </exception>
public double Aggregate(DoubleMatrix1D other, DoubleDoubleFunction aggr, DoubleDoubleFunction f)
{
CheckSize(other);
if (Size == 0)
{
return(double.NaN);
}
double a = f(this[Size - 1], other[Size - 1]);
for (int i = Size - 1; --i >= 0;)
{
a = aggr(a, f(this[i], other[i]));
}
return(a);
}
/// <summary>
/// Assigns the result of a function to each cell; <tt>x[row,col] = function(x[row,col],y[row,col])</tt>.
/// </summary>
/// <param name="y">
/// The secondary matrix to operate on.
/// </param>
/// <param name="function">
/// A function taking as first argument the current cell's value of <tt>this</tt>, and as second argument the current cell's value of <tt>y</tt>.
/// </param>
/// <returns>
/// <tt>this</tt> (for convenience only).
/// </returns>
/// <exception cref="ArgumentOutOfRangeException">
/// If <tt>columns() != other.columns() || rows() != other.rows()</tt>
/// </exception>
public override DoubleMatrix2D Assign(DoubleMatrix2D y, DoubleDoubleFunction function)
{
// overriden for performance only
if (!(y is DenseDoubleMatrix2D))
{
return(base.Assign(y, function));
}
var other = (DenseDoubleMatrix2D)y;
CheckShape(y);
double[] elems = Elements;
double[] otherElems = other.Elements;
if (elems == null || otherElems == null)
{
throw new ApplicationException();
}
int cs = ColumnStride;
int ocs = ColumnStride;
int rs = RowStride;
int ors = other.RowStride;
int otherIndex = other.Index(0, 0);
int index = this.Index(0, 0);
// specialized for speed
for (int row = Rows; --row >= 0;)
{
for (int i = index, j = otherIndex, column = Columns; --column >= 0;)
{
elems[i] = function(elems[i], otherElems[j]);
i += cs;
j += ocs;
}
index += rs;
otherIndex += ors;
}
return(this);
}
/// <summary>
/// Applies a function to each cell and aggregates the results.
/// </summary>
/// <param name="aggr">
/// An aggregation function taking as first argument the current aggregation and as second argument the transformed current cell value.
/// </param>
/// <param name="f">
/// A function transforming the current cell value.
/// </param>
/// <returns>
/// The aggregated measure.
/// </returns>
public override double Aggregate(DoubleDoubleFunction aggr, DoubleFunction f)
{
double result = double.NaN;
bool first = true;
foreach (var e in Elements.Values)
{
if (first)
{
first = false;
result = f(e);
}
else
{
result = aggr(result, f(e));
}
}
return(result);
}
/// <summary>
/// Applies a function to each cell and aggregates the results.
/// </summary>
/// <param name="aggr">
/// An aggregation function taking as first argument the current aggregation and as second argument the transformed current cell value.
/// </param>
/// <param name="f">
/// A function transforming the current cell value.
/// </param>
/// <returns>
/// The aggregated measure.
/// </returns>
public double Aggregate(DoubleDoubleFunction aggr, DoubleFunction f)
{
if (Size == 0)
{
return(double.NaN);
}
double a = f(this[Rows - 1, Columns - 1]);
int d = 1; // last cell already done
for (int row = Rows; --row >= 0;)
{
for (int column = Columns - d; --column >= 0;)
{
a = aggr(a, f(this[row, column]));
}
d = 0;
}
return(a);
}
/// <summary>
/// Applies a function to each cell and aggregates the results.
/// </summary>
/// <param name="aggr">
/// An aggregation function taking as first argument the current aggregation and as second argument the transformed current cell value.
/// </param>
/// <param name="f">
/// A function transforming the current cell value.
/// </param>
/// <returns>
/// The aggregated measure.
/// </returns>
public override double Aggregate(DoubleDoubleFunction aggr, DoubleFunction f)
{
double result = double.NaN;
bool first = true;
AutoParallel.AutoParallelForEach(Elements.Values, (e) =>
{
if (first)
{
first = false;
result = f(e);
}
else
{
result = aggr(result, f(e));
}
});
return(result);
}
/// <summary>
/// Constructs the function <i>f( g(a), h(b) )</i>.
/// </summary>
/// <param name="f">a binary function.</param>
/// <param name="g">a binary function.</param>
/// <param name="h">a binary function.</param>
/// <returns>the binary function <i>f( g(a), h(b) )</i>.</returns>
public static DoubleDoubleFunction Chain(DoubleDoubleFunction f, DoubleFunction g, DoubleFunction h)
{
return(new DoubleDoubleFunction((a, b) => { return f(g(a), h(b)); }));
}
/// <summary>
/// Constructs and returns a new QR decomposition object; computed by Householder reflections;
/// The decomposed matrices can be retrieved via instance methods of the returned decomposition object.
/// Return a decomposition object to access <i>R</i> and the Householder vectors <i>H</i>, and to compute <i>Q</i>.
/// </summary>
/// <param name="A">A rectangular matrix.</param>
/// <exception cref="ArgumentException">if <i>A.Rows < A.Columns</i>.</exception>
public QRDecomposition(DoubleMatrix2D A)
{
Property.DEFAULT.CheckRectangular(A);
Functions F = Functions.functions;
// Initialize.
QR = A.Copy();
m = A.Rows;
n = A.Columns;
Rdiag = A.Like1D(n);
//Rdiag = new double[n];
DoubleDoubleFunction hypot = Algebra.HypotFunction();
// precompute and cache some views to avoid regenerating them time and again
DoubleMatrix1D[] QRcolumns = new DoubleMatrix1D[n];
DoubleMatrix1D[] QRcolumnsPart = new DoubleMatrix1D[n];
for (int k = 0; k < n; k++)
{
QRcolumns[k] = QR.ViewColumn(k);
QRcolumnsPart[k] = QR.ViewColumn(k).ViewPart(k, m - k);
}
// Main loop.
for (int k = 0; k < n; k++)
{
//DoubleMatrix1D QRcolk = QR.ViewColumn(k).ViewPart(k,m-k);
// Compute 2-norm of k-th column without under/overflow.
double nrm = 0;
//if (k<m) nrm = QRcolumnsPart[k].aggregate(hypot,F.identity);
for (int i = k; i < m; i++)
{ // fixes bug reported by [email protected]
nrm = Algebra.Hypot(nrm, QR[i, k]);
}
if (nrm != 0.0)
{
// Form k-th Householder vector.
if (QR[k, k] < 0)
{
nrm = -nrm;
}
QRcolumnsPart[k].Assign(F2.Div(nrm));
/*
* for (int i = k; i < m; i++) {
* QR[i][k] /= nrm;
* }
*/
QR[k, k] = QR[k, k] + 1;
// Apply transformation to remaining columns.
for (int j = k + 1; j < n; j++)
{
DoubleMatrix1D QRcolj = QR.ViewColumn(j).ViewPart(k, m - k);
double s = QRcolumnsPart[k].ZDotProduct(QRcolj);
/*
* // fixes bug reported by John Chambers
* DoubleMatrix1D QRcolj = QR.ViewColumn(j).ViewPart(k,m-k);
* double s = QRcolumnsPart[k].ZDotProduct(QRcolumns[j]);
* double s = 0.0;
* for (int i = k; i < m; i++) {
* s += QR[i][k]*QR[i][j];
* }
*/
s = -s / QR[k, k];
//QRcolumnsPart[j].Assign(QRcolumns[k], F.PlusMult(s));
for (int i = k; i < m; i++)
{
QR[i, j] = QR[i, j] + s * QR[i, k];
}
}
}
Rdiag[k] = -nrm;
}
}
/// <summary>
/// Constructs a unary function from a binary function with the second operand (argument) fixed to the given constant <i>c</i>.
/// The first operand is variable (free).
/// </summary>
/// <param name="function">a binary function taking operands in the form <i>function.apply(var,c)</i>.</param>
/// <param name="c"></param>
/// <returns>the unary function <i>function(var,c)</i>.</returns>
public static DoubleFunction BindArg2(DoubleDoubleFunction function, double c)
{
return(new DoubleFunction((var) => { return function(var, c); }));
}
/// <summary>
/// Constructs a function that returns <i>function.apply(b,a)</i>, i.ed applies the function with the first operand as second operand and the second operand as first operand.
/// </summary>
/// <param name="function">a function taking operands in the form <i>function.apply(a,b)</i>.</param>
/// <returns>the binary function <i>function(b, a)</i>.</returns>
public static DoubleDoubleFunction SwapArgs(DoubleDoubleFunction function)
{
return(new DoubleDoubleFunction((a, b) => { return function(b, a); }));
}
public PlusMult(double multiplicator)
{
this.Multiplicator = multiplicator;
Apply = new DoubleDoubleFunction((a, b) => { return(a + b * Multiplicator); });
}