private void Test_conj()
{
// test for common matrix 4x3
ILArray <complex> A = new complex[, ] {
{ new complex(1, 2), new complex(3, 4), new complex(5, 6) },
{ new complex(7, 8), new complex(9, 10), new complex(11, 12) },
{ new complex(13, 14), new complex(15, 16), new complex(17, 18) },
{ new complex(19, 20), new complex(21, 22), new complex(23, 24) }
};
ILArray <fcomplex> Af = ILMath.tofcomplex(A);
Test_isConj(A, ILMath.conj(A));
Test_isfConj(Af, ILMath.conj(Af));
// test on reference matrix
Test_isConj(A, ILMath.conj(A.R));
Test_isfConj(Af, ILMath.conj(Af.R));
// test on 2x2x3 matrix (reference)
A = A.Reshape(new ILDimension(2, 2, 3)).R;
if (!A.IsReference)
{
throw new Exception("Unable to test conj() for reference 2x2x3!");
}
Af = Af.Reshape(new ILDimension(2, 2, 3)).R;
if (!Af.IsReference)
{
throw new Exception("Unable to test conj() for reference 2x2x3!");
}
Test_isConj(A, ILMath.conj(A));
Test_isfConj(Af, ILMath.conj(Af));
// test those on dense array
Test_isConj(A, ILMath.conj(A.C));
Test_isfConj(Af, ILMath.conj(Af.C));
// test for empty
A = ILArray <complex> .empty();
Af = ILArray <fcomplex> .empty();
Test_isConj(A, ILMath.conj(A));
Test_isfConj(Af, ILMath.conj(Af));
// test on vector
A = new complex[] { new complex(1, 2), new complex(3, 4), new complex(5, 6) };
Af = ILMath.tofcomplex(A);
Test_isConj(A, ILMath.conj(A));
Test_isfConj(Af, ILMath.conj(Af));
// transpose
Test_isConj(A.T, ILMath.conj(A.T));
Test_isfConj(Af.T, ILMath.conj(Af.T));
// test on scalar
A = A[2]; Af = Af[2];
Test_isConj(A, ILMath.conj(A));
Test_isfConj(Af, ILMath.conj(Af));
}
internal static ILArray <double> CreateVertices(ILBaseArray dataInput
, out ILArray <double> indices
, double beta, double scaling
, ILColormap colormap)
{
// each arrow needs 4 vertices (indexed rendering)
ILArray <double> data = todouble(dataInput);
int numRows = data.Dimensions[0];
int numCols = data.Dimensions[1];
ILArray <double> ret = new ILArray <double>(4, numCols * numRows, 2);
// prepare indices
indices = repmat(new ILArray <double>(new double[] { 0, 2, 1, 2, 3, 2 }, 6, 1), 1, numCols * numRows);
indices = indices + repmat(counter(0.0, 4.0, 1, numCols * numRows), 6, 1);
indices = indices.Reshape(2, numRows * numCols * 3);
// normalize incoming data to length 1.0
ILArray <double> l = sqrt(sum(data * data, 2));
double maxL = (double)max(maxall(l), MachineParameterDouble.eps);
l = (l / maxL)[":"].T * scaling;
ILArray <double> alpha = atan2(data[":;:;1"], data[":;:;0"]);
alpha = alpha[":"].T;
ILArray <double> x = data[":;:;0"][":"].T * scaling;
ILArray <double> y = data[":;:;1"][":"].T * scaling;
ILArray <double> xO = repmat(linspace(1, numCols, numCols), numRows, 1)[":"].T;
ILArray <double> yO = repmat(linspace(numRows, 1, numRows).T, 1, numCols)[":"].T;
ret["0;:;0"] = xO - x;
ret["1;:;0"] = xO + x - l / 2 * cos(alpha + beta);
ret["2;:;0"] = xO + x;
ret["3;:;0"] = xO + x - l / 2 * cos(alpha - beta);
ret["0;:;1"] = yO - y;
ret["1;:;1"] = yO + y - l / 2 * sin(alpha + beta);
ret["2;:;1"] = yO + y;
ret["3;:;1"] = yO + y - l / 2 * sin(alpha - beta);
ret["0;0;2"] = 0.0;
// prepare colors
ret[":;:;3:5"] = todouble(
repmat(colormap.Map
(tosingle(l) * colormap.Length).Reshape(1, l.Length, 3) * 255, 4, 1, 1));
return(ret.Reshape(4 * numRows * numCols, 6).T);
}
/// <summary>
/// Create three 3D arrays for the valuation and visualization of functions of three variables
/// </summary>
/// <param name="x">Vector of x values</param>
/// <param name="y">Vector of y values</param>
/// <param name="z">Vector of z values</param>
/// <returns>A List of three arrays, the rows of the first comprising the x vector values and the columns of the second comprising the y vector values</returns>
/// <remarks></remarks>
public static List <ILArray <double> > meshgrid(ILArray <double> x, ILArray <double> y, ILArray <double> z)
{
if (!x.IsVector || !y.IsVector || !z.IsVector)
{
throw new ILArgumentException("meshgrid: inputs must be vectors");
}
int xLength = x.Length;
int yLength = y.Length;
int zLength = z.Length;
//ILDimension dimRet = new ILDimension(xLength, yLength, zLength);
//double[] retArrX = ILMemoryPool.Pool.New<double>(dimRet.NumberOfElements);
//double[] retArrY = ILMemoryPool.Pool.New<double>(dimRet.NumberOfElements);
//double[] retArrZ = ILMemoryPool.Pool.New<double>(dimRet.NumberOfElements);
//unsafe
//{
// fixed (double* pRetArrX = retArrX)
// fixed (double* pRetArrY = retArrY)
// fixed (double* pRetArrZ = retArrZ)
// fixed (double* pX = x.m_data)
// fixed (double* pY = y.m_data)
// fixed (double* pZ = z.m_data)
// {
// double* pRetArrayX = pRetArrX;
// double* pRetArrayY = pRetArrY;
// double* pRetArrayZ = pRetArrZ;
// double* pArrayX;
// double* pArrayY;
// double* pArrayZ = pZ;
// double* pXEnd = pX + xLength;
// double* pYEnd = pY + yLength;
// double* pZEnd = pZ + zLength;
// while (pArrayZ < pZEnd)
// {
// pArrayY = pY;
// while (pArrayY < pYEnd)
// {
// pArrayX = pX;
// while (pArrayX < pXEnd)
// {
// *pRetArrayX = *pArrayX;
// *pRetArrayY = *pArrayY;
// *pRetArrayZ = *pArrayZ;
// pArrayX++;
// pRetArrayX++;
// pRetArrayY++;
// pRetArrayZ++;
// }
// pArrayY++;
// }
// pArrayZ++;
// }
// }
//}
List <ILArray <double> > retList = new List <ILArray <double> >();
if (!x.IsRowVector)
{
x.Reshape(1, x.Length);
}
if (!y.IsColumnVector)
{
y.Reshape(y.Length, 1);
}
z = z[":"].Reshape(1, 1, z.Dimensions.NumberOfElements);
retList.Add(repmat(x, yLength, 1, zLength));
retList.Add(repmat(y, 1, xLength, zLength));
retList.Add(repmat(z, yLength, xLength, 1));
return(retList);
}
/// <summary>
/// Create three 3D arrays for the valuation and visualization of functions of three variables
/// </summary>
/// <param name="x">Vector of x values</param>
/// <param name="y">Vector of y values</param>
/// <param name="z">Vector of z values</param>
/// <returns>A List of three arrays, the rows of the first comprising the x vector values and the columns of the second comprising the y vector values</returns>
/// <remarks></remarks>
public static List<ILArray<double>> meshgrid(ILArray<double> x, ILArray<double> y, ILArray<double> z)
{
if (!x.IsVector || !y.IsVector || !z.IsVector)
{
throw new ILArgumentException("meshgrid: inputs must be vectors");
}
int xLength = x.Length;
int yLength = y.Length;
int zLength = z.Length;
//ILDimension dimRet = new ILDimension(xLength, yLength, zLength);
//double[] retArrX = ILMemoryPool.Pool.New<double>(dimRet.NumberOfElements);
//double[] retArrY = ILMemoryPool.Pool.New<double>(dimRet.NumberOfElements);
//double[] retArrZ = ILMemoryPool.Pool.New<double>(dimRet.NumberOfElements);
//unsafe
//{
// fixed (double* pRetArrX = retArrX)
// fixed (double* pRetArrY = retArrY)
// fixed (double* pRetArrZ = retArrZ)
// fixed (double* pX = x.m_data)
// fixed (double* pY = y.m_data)
// fixed (double* pZ = z.m_data)
// {
// double* pRetArrayX = pRetArrX;
// double* pRetArrayY = pRetArrY;
// double* pRetArrayZ = pRetArrZ;
// double* pArrayX;
// double* pArrayY;
// double* pArrayZ = pZ;
// double* pXEnd = pX + xLength;
// double* pYEnd = pY + yLength;
// double* pZEnd = pZ + zLength;
// while (pArrayZ < pZEnd)
// {
// pArrayY = pY;
// while (pArrayY < pYEnd)
// {
// pArrayX = pX;
// while (pArrayX < pXEnd)
// {
// *pRetArrayX = *pArrayX;
// *pRetArrayY = *pArrayY;
// *pRetArrayZ = *pArrayZ;
// pArrayX++;
// pRetArrayX++;
// pRetArrayY++;
// pRetArrayZ++;
// }
// pArrayY++;
// }
// pArrayZ++;
// }
// }
//}
List<ILArray<double>> retList = new List<ILArray<double>>();
if (!x.IsRowVector) x.Reshape(1,x.Length);
if (!y.IsColumnVector) y.Reshape(y.Length,1);
z = z[":"].Reshape(1,1,z.Dimensions.NumberOfElements);
retList.Add(repmat(x,yLength,1,zLength));
retList.Add(repmat(y,1,xLength,zLength));
retList.Add(repmat(z,yLength,xLength,1));
return retList;
}
internal static ILArray<double> CreateVertices(ILBaseArray dataInput
,out ILArray<double> indices
,double beta, double scaling
, ILColormap colormap) {
// each arrow needs 4 vertices (indexed rendering)
ILArray<double> data = todouble(dataInput);
int numRows = data.Dimensions[0];
int numCols = data.Dimensions[1];
ILArray<double> ret = new ILArray<double>(4, numCols * numRows, 2);
// prepare indices
indices = repmat(new ILArray<double>(new double[] { 0, 2, 1, 2, 3, 2 }, 6, 1), 1, numCols * numRows);
indices = indices + repmat(counter(0.0, 4.0, 1, numCols * numRows), 6, 1);
indices = indices.Reshape(2, numRows * numCols * 3);
// normalize incoming data to length 1.0
ILArray<double> l = sqrt(sum(data * data, 2));
double maxL = (double)max(maxall(l),MachineParameterDouble.eps);
l = (l / maxL)[":"].T * scaling;
ILArray<double> alpha = atan2(data[":;:;1"], data[":;:;0"]);
alpha = alpha[":"].T;
ILArray<double> x = data[":;:;0"][":"].T * scaling;
ILArray<double> y = data[":;:;1"][":"].T * scaling;
ILArray<double> xO = repmat(linspace(1, numCols, numCols), numRows, 1)[":"].T;
ILArray<double> yO = repmat(linspace(numRows, 1, numRows).T, 1, numCols)[":"].T;
ret["0;:;0"] = xO - x;
ret["1;:;0"] = xO + x - l / 2 * cos(alpha + beta);
ret["2;:;0"] = xO + x;
ret["3;:;0"] = xO + x - l / 2 * cos(alpha - beta);
ret["0;:;1"] = yO - y;
ret["1;:;1"] = yO + y - l / 2 * sin(alpha + beta);
ret["2;:;1"] = yO + y;
ret["3;:;1"] = yO + y - l / 2 * sin(alpha - beta);
ret["0;0;2"] = 0.0;
// prepare colors
ret[":;:;3:5"] = todouble(
repmat(colormap.Map
(tosingle(l) * colormap.Length).Reshape(1, l.Length, 3) * 255, 4, 1, 1));
return ret.Reshape(4 * numRows * numCols, 6).T;
}