private void Test_isConj(ILArray <complex> A, ILArray <complex> conjA)
{
try {
if (A.IsEmpty)
{
if (!conjA.IsEmpty)
{
throw new Exception("conj of empty array must be empty!");
}
else
{
Success();
return;
}
}
if (!A.Dimensions.IsSameSize(conjA.Dimensions))
{
throw new Exception("dimensions must match!");
}
if (ILMath.sumall(ILMath.real(A) != ILMath.real(conjA)) > 0.0)
{
throw new Exception("real parts must match!");
}
if (ILMath.sumall(-ILMath.imag(A) != ILMath.imag(conjA)) > 0.0)
{
throw new Exception("imag parts must be the inverse of each other!");
}
Success();
} catch (Exception exc) {
Error(exc.Message);
}
}
/// <summary>
/// Multidimensional scaling/PCoA: transform distances to points in a coordinate system.
/// </summary>
/// <param name="input">A matrix of pairwise distances. Zero indicates identical objects.</param>
/// <returns>A matrix, the columns of which are coordinates in the nth dimension.
/// The rows are in the same order as the input.</returns>
public static ILArray <double> Scale(ILArray <double> input)
{
int n = input.Length;
ILArray <double> p = ILMath.eye <double>(n, n) - ILMath.repmat(1.0 / n, n, n);
ILArray <double> a = -.5 * ILMath.multiplyElem(input, input);
ILArray <double> b = ILMath.multiply(p, a, p);
ILArray <complex> V = ILMath.empty <complex>();
ILArray <complex> E = ILMath.eig((b + b.T) / 2, V);
ILArray <int> i = ILMath.empty <int>();
ILArray <double> e = ILMath.sort(ILMath.diag(ILMath.real(E)), i);
e = ILMath.flipud(e);
i = ILMath.toint32(ILMath.flipud(ILMath.todouble(i)));
ILArray <int> keep = ILMath.empty <int>();
for (int j = 0; j < e.Length; j++)
{
if (e[j] > 0.000000001)
{
keep.SetValue(j, keep.Length);
}
}
ILArray <double> Y;
if (ILMath.isempty(keep))
{
Y = ILMath.zeros(n, 1);
}
else
{
Y = ILMath.zeros <double>(V.S[0], keep.Length);
for (int j = 0; j < keep.Length; j++)
{
Y[ILMath.full, j] = ILMath.todouble(-V[ILMath.full, i[keep[j]]]);
}
Y = ILMath.multiply(Y, ILMath.diag(ILMath.sqrt(e[keep])));
}
ILArray <int> maxind = ILMath.empty <int>();
ILMath.max(ILMath.abs(Y), maxind, 0);
int d = Y.S[1];
ILArray <int> indices = maxind + ILMath.toint32(ILMath.array <int>(SteppedRange(0, n, (d - 1) * n)));
ILArray <double> colsign = ILMath.sign(Y[indices]);
for (int j = 0; j < Y.S[1]; j++)
{
Y[ILMath.full, j] = Y[ILMath.full, j] * colsign[j];
}
return(Y);
}
/*!HC:TYPELIST:
* <hycalper>
* <type>
* <source locate="after">
* HCretArr
* </source>
* </type>
* <type>
* <source locate="after">
* HCinArr
* </source>
* </type>
* <type>
* <source locate="after">
* mklPrec
* </source>
* </type>
* </hycalper>
*/
public ILArray </*!HC:HCretArr*/ double> FFTBackwSym(ILArray </*!HC:HCinArr*/ complex> A, int nDims)
{
return(ILMath.real(FFTBackward(A, nDims)));
}
/*!HC:TYPELIST:
* <hycalper>
* <type>
* <source locate="after">
* HCretArr
* </source>
* </type>
* <type>
* <source locate="after">
* inArr
* </source>
* </type>
* </hycalper>
*/
public ILArray </*!HC:HCretArr*/ double> FFTBackwSym1D(ILArray </*!HC:inArr*/ complex> A, int dim)
{
return(ILMath.real(FFTBackward1D(A, dim)));
}
public ILArray <double> FFTBackwSym(ILArray <complex> A, int nDims)
{
return(ILMath.real(FFTBackward(A, nDims)));
}
public ILArray <double> FFTBackwSym1D(ILArray <complex> A, int dim)
{
return(ILMath.real(FFTBackward1D(A, dim)));
}
/*!HC:TYPELIST:
* <hycalper>
* <type>
* <source locate="after">
* HCretArr
* </source>
* </type>
* <type>
* <source locate="after">
* HCinArr
* </source>
* </type>
* <type>
* <source locate="after">
* mklPrec
* </source>
* </type>
* </hycalper>
*/
public ILArray </*!HC:HCretArr*/ double> FFTBackwSym(ILArray </*!HC:HCinArr*/ complex> A, int nDims)
{
if (A == null || nDims <= 0)
{
throw new ILArgumentException("invalid argument!");
}
if (A.IsEmpty)
{
return(ILArray </*!HC:HCretArr*/ double> .empty(A.Dimensions));
}
if (A.IsScalar || (A.Dimensions[0] == 1 && nDims == 1))
{
return(ILMath.real(A));
}
if (nDims > A.Dimensions.NumberOfDimensions)
{
nDims = A.Dimensions.NumberOfDimensions;
}
// MKL currently does not handle more than 3 dimensions this way
if (nDims > 3)
{
return(ILMath.real(FFTBackward(A, nDims)));
}
// prepare output array, if we query the memory directly from
// memory pool, we prevent from clearing the elements since every
// single one will be overwritten by fft anyway
/*!HC:HCretArr*/ double [] retArr = ILMemoryPool.Pool.New </*!HC:HCretArr*/ double>(A.Dimensions.NumberOfElements);
ILArray </*!HC:HCretArr*/ double> ret = new ILArray </*!HC:HCretArr*/ double>(retArr, A.Dimensions);
IntPtr descriptor = IntPtr.Zero;
int error = -1;
int[] tmpDims = A.Dimensions.ToIntArray(nDims + 1);
string hash = hashPlan(/*!HC:mklPrec*/ MKLValues.DOUBLE, MKLValues.REAL, nDims, tmpDims);
// try to reuse existing descriptor
lock (_lockobject) {
if (!m_descriptors.TryGetValue(hash, out descriptor))
{
error = MKLImports.DftiCreateDescriptor(ref descriptor, /*!HC:mklPrec*/ MKLValues.DOUBLE, MKLValues.REAL, nDims, tmpDims);
if (isMKLError(error))
{
throw new ILInvalidOperationException("error creating descriptor: " + MKLImports.DftiErrorMessage(error));
}
m_descriptors[hash] = descriptor;
}
}
// how many transformations ?
int tmp = A.Dimensions.SequentialIndexDistance(nDims);
MKLImports.DftiSetValue(descriptor, MKLParameter.NUMBER_OF_TRANSFORMS, __arglist(A.Dimensions.NumberOfElements / tmp));
MKLImports.DftiSetValue(descriptor, MKLParameter.INPUT_DISTANCE, __arglist(tmp));
MKLImports.DftiSetValue(descriptor, MKLParameter.OUTPUT_DISTANCE, __arglist(tmp));
error = MKLImports.DftiSetValue(descriptor, MKLParameter.PLACEMENT, __arglist(MKLValues.NOT_INPLACE));
error = MKLImports.DftiSetValue(descriptor, MKLParameter.REAL_STORAGE, __arglist(MKLValues.REAL_REAL));
error = MKLImports.DftiSetValue(descriptor, MKLParameter.CONJUGATE_EVEN_STORAGE, __arglist(MKLValues.COMPLEX_COMPLEX));
error = MKLImports.DftiSetValue(descriptor, MKLParameter.BACKWARD_SCALE, __arglist(1.0 / tmp));
// spacing between elements
tmpDims[0] = 0;
for (int i = 0; i < nDims; i++)
{
tmpDims[i + 1] = A.Dimensions.SequentialIndexDistance(i);
}
MKLImports.DftiSetValue(descriptor, MKLParameter.INPUT_STRIDES, __arglist(tmpDims));
error = MKLImports.DftiSetValue(descriptor, MKLParameter.OUTPUT_STRIDES, __arglist(tmpDims));
if (isMKLError(error))
{
throw new ILInvalidOperationException("error: " + MKLImports.DftiErrorMessage(error));
}
error = MKLImports.DftiCommitDescriptor(descriptor);
if (isMKLError(error))
{
throw new ILInvalidOperationException("error: " + MKLImports.DftiErrorMessage(error));
}
// do the transform(s)
unsafe
{
fixed(/*!HC:HCretArr*/ double *retArrP = ret.m_data)
fixed(/*!HC:HCinArr*/ complex * inArr = A.m_data)
{
error = MKLImports.DftiComputeBackward(descriptor, __arglist(inArr, retArrP));
}
}
if (isMKLError(error))
{
throw new ILInvalidOperationException("error: " + MKLImports.DftiErrorMessage(error));
}
return(ret);
}
/*!HC:TYPELIST:
* <hycalper>
* <type>
* <source locate="after">
* HCretArr
* </source>
* </type>
* <type>
* <source locate="after">
* inArr
* </source>
* </type>
* <type>
* <source locate="after">
* mklPrec
* </source>
* </type>
* </hycalper>
*/
public ILArray </*!HC:HCretArr*/ double> FFTBackwSym1D(ILArray </*!HC:inArr*/ complex> A, int dim)
{
if (A == null || dim < 0)
{
throw new ILArgumentException("invalid parameter!");
}
if (A.IsEmpty)
{
return(ILArray </*!HC:HCretArr*/ double> .empty(A.Dimensions));
}
if (A.IsScalar || A.Dimensions[dim] == 1)
{
return(ILMath.real(A));
}
// prepare output array, if we query the memory directly from
// memory pool, we prevent from clearing the elements since every
// single one will be overwritten by fft anyway
int error = 0, inDim = A.Dimensions[dim];
/*!HC:HCretArr*/ double [] retArr = ILMemoryPool.Pool.New </*!HC:HCretArr*/ double>(A.Dimensions.NumberOfElements);
ILArray </*!HC:HCretArr*/ double> ret = new ILArray </*!HC:HCretArr*/ double>(retArr, A.Dimensions);
string hash = hashPlan(/*!HC:mklPrec*/ MKLValues.DOUBLE, MKLValues.REAL, 1, inDim);
IntPtr descriptor = IntPtr.Zero;
// try to reuse existing descriptor
lock (_lockobject) {
if (!m_descriptors.TryGetValue(hash, out descriptor))
{
error = MKLImports.DftiCreateDescriptor(ref descriptor, /*!HC:mklPrec*/ MKLValues.DOUBLE, MKLValues.REAL, 1, inDim);
if (isMKLError(error))
{
throw new ILInvalidOperationException("error creating descriptor: " + MKLImports.DftiErrorMessage(error));
}
m_descriptors[hash] = descriptor;
}
}
// spacing between elements
int tmp = A.Dimensions.SequentialIndexDistance(dim);
int[] stride = new int[] { 0, tmp };
MKLImports.DftiSetValue(descriptor, MKLParameter.INPUT_STRIDES, __arglist(stride));
error = MKLImports.DftiSetValue(descriptor, MKLParameter.OUTPUT_STRIDES, __arglist(stride));
if (isMKLError(error))
{
throw new ILInvalidOperationException("error: " + MKLImports.DftiErrorMessage(error));
}
// storage of subsequent transformations
tmp = inDim * tmp;
MKLImports.DftiSetValue(descriptor, MKLParameter.INPUT_DISTANCE, __arglist(tmp));
MKLImports.DftiSetValue(descriptor, MKLParameter.OUTPUT_DISTANCE, __arglist(tmp));
// how many transformations ?
tmp = A.Dimensions.NumberOfElements / tmp;
MKLImports.DftiSetValue(descriptor, MKLParameter.NUMBER_OF_TRANSFORMS, __arglist(tmp));
error = MKLImports.DftiSetValue(descriptor, MKLParameter.PLACEMENT, __arglist(MKLValues.NOT_INPLACE));
error = MKLImports.DftiSetValue(descriptor, MKLParameter.REAL_STORAGE, __arglist(MKLValues.REAL_REAL));
error = MKLImports.DftiSetValue(descriptor, MKLParameter.CONJUGATE_EVEN_STORAGE, __arglist(MKLValues.COMPLEX_COMPLEX));
error = MKLImports.DftiSetValue(descriptor, MKLParameter.BACKWARD_SCALE, __arglist(1.0 / inDim));
error = MKLImports.DftiCommitDescriptor(descriptor);
if (isMKLError(error))
{
throw new ILInvalidOperationException("error: " + MKLImports.DftiErrorMessage(error));
}
// do the transform(s)
tmp = A.Dimensions.SequentialIndexDistance(dim);
unsafe
{
fixed(/*!HC:HCretArr*/ double *retArrP = ret.m_data)
fixed(/*!HC:inArr*/ complex * pA = A.m_data)
{
for (int i = 0; i < tmp && error == 0; i++)
{
error = MKLImports.DftiComputeBackward(descriptor, __arglist(pA + i, retArrP + i));
}
}
}
if (isMKLError(error))
{
throw new ILInvalidOperationException("error: " + MKLImports.DftiErrorMessage(error));
}
return(ret);
}