/**
* <p>
* Computes the inner product between a vector and the conjugate of another one.
* <br>
* <br>
* ∑<sub>k=1:n</sub> x<sub>k</sub> * conj(y<sub>k</sub>)<br>
* where x and y are vectors with n elements.
* </p>
*
* <p>
* These functions are often used inside of highly optimized code and therefor sanity checks are
* kept to a minimum. It is not recommended that any of these functions be used directly.
* </p>
*
* @param x A vector with n elements. Not modified.
* @param y A vector with n elements. Not modified.
* @return The inner product of the two vectors.
*/
public static Complex_F64 innerProdH(ZMatrixRMaj x, ZMatrixRMaj y, Complex_F64 output)
{
if (output == null)
{
output = new Complex_F64();
}
else
{
output.real = output.imaginary = 0;
}
int m = x.getDataLength();
for (int i = 0; i < m; i += 2)
{
double realX = x.data[i];
double imagX = x.data[i + 1];
double realY = y.data[i];
double imagY = -y.data[i + 1];
output.real += realX * realY - imagX * imagY;
output.imaginary += realX * imagY + imagX * realY;
}
return(output);
}
/**
* Sets all the diagonal elements equal to one and everything else equal to zero.
* If this is a square matrix then it will be an identity matrix.
*
* @param mat A square matrix.
*/
public static void setIdentity(ZMatrixRMaj mat)
{
int width = mat.numRows < mat.numCols ? mat.numRows : mat.numCols;
Array.Clear(mat.data, 0, mat.getDataLength());
int index = 0;
int stride = mat.getRowStride();
for (int i = 0; i < width; i++, index += stride + 2)
{
mat.data[index] = 1;
}
}
/**
* Q = I - gamma*u*u<sup>H</sup>
*/
public static ZMatrixRMaj householder(ZMatrixRMaj u, double gamma)
{
int N = u.getDataLength() / 2;
// u*u^H
ZMatrixRMaj uut = new ZMatrixRMaj(N, N);
VectorVectorMult_ZDRM.outerProdH(u, u, uut);
// foo = -gamma*u*u^H
CommonOps_ZDRM.elementMultiply(uut, -gamma, 0, uut);
// I + foo
for (int i = 0; i < N; i++)
{
int index = (i * uut.numCols + i) * 2;
uut.data[index] = 1 + uut.data[index];
}
return(uut);
}
/**
* <p>
* Returns the absolute value of the element in the matrix that has the largest absolute value.<br>
* <br>
* Max{ |a<sub>ij</sub>| } for all i and j<br>
* </p>
*
* @param a A matrix. Not modified.
* @return The max abs element value of the matrix.
*/
public static double elementMaxAbs(ZMatrixRMaj a)
{
int size = a.getDataLength();
double max = 0;
for (int i = 0; i < size; i += 2)
{
double real = a.data[i];
double imag = a.data[i + 1];
double val = real * real + imag * imag;
if (val > max)
{
max = val;
}
}
return(Math.Sqrt(max));
}
/**
* <p>
* Computes the Frobenius matrix norm:<br>
* <br>
* normF = Sqrt{ ∑<sub>i=1:m</sub> ∑<sub>j=1:n</sub> { a<sub>ij</sub><sup>2</sup>} }
* </p>
* <p>
* This is equivalent to the element wise p=2 norm.
* </p>
*
* @param a The matrix whose norm is computed. Not modified.
* @return The norm's value.
*/
public static double normF(ZMatrixRMaj a)
{
double total = 0;
double scale = CommonOps_ZDRM.elementMaxAbs(a);
if (scale == 0.0)
{
return(0.0);
}
int size = a.getDataLength();
for (int i = 0; i < size; i += 2)
{
double real = a.data[i] / scale;
double imag = a.data[i + 1] / scale;
total += real * real + imag * imag;
}
return(scale * Math.Sqrt(total));
}