/**
* <p>
* Sets every element in the matrix to the specified value.<br>
* <br>
* a<sub>ij</sub> = value
* <p>
*
* @param a A matrix whose elements are about to be set. Modified.
* @param real The real component
* @param imaginary The imaginary component
*/
public static void fill(CMatrixD1 a, float real, float imaginary)
{
int N = a.getDataLength();
for (int i = 0; i < N; i += 2)
{
a.data[i] = real;
a.data[i + 1] = imaginary;
}
}
/**
* <p>
* Sets each element in the matrix to a value drawn from an uniform distribution from 'min' to 'max' inclusive.
* </p>
*
* @param min The minimum value each element can be.
* @param max The maximum value each element can be.
* @param mat The matrix who is to be randomized. Modified.
* @param rand Random number generator used to fill the matrix.
*/
public static void fillUniform(CMatrixD1 mat, float min, float max, IMersenneTwister rand)
{
float[] d = mat.getData();
int size = mat.getDataLength();
float r = max - min;
for (int i = 0; i < size; i++)
{
d[i] = r * rand.NextFloat() + min;
}
}
/**
* Checks to see all the elements in the matrix are zeros
*
* @param m A matrix. Not modified.
* @return True if all elements are zeros or false if not
*/
public static bool isZeros(CMatrixD1 m, float tol)
{
int length = m.getNumElements() * 2;
for (int i = 0; i < length; i++)
{
if (Math.Abs(m.data[i]) > tol)
{
return(false);
}
}
return(true);
}
/**
* Checks to see if any element in the matrix is NaN.
*
* @param m A matrix. Not modified.
* @return True if any element in the matrix is NaN.
*/
public static bool hasNaN(CMatrixD1 m)
{
int length = m.getDataLength();
for (int i = 0; i < length; i++)
{
if (float.IsNaN(m.data[i]))
{
return(true);
}
}
return(false);
}
/**
* Checks to see if any element in the matrix is NaN of Infinite.
*
* @param m A matrix. Not modified.
* @return True if any element in the matrix is NaN of Infinite.
*/
public static bool hasUncountable(CMatrixD1 m)
{
int length = m.getDataLength();
for (int i = 0; i < length; i++)
{
float a = m.data[i];
if (float.IsNaN(a) || float.IsInfinity(a))
{
return(true);
}
}
return(false);
}
/**
* <p>
* Computes the complex conjugate of the input matrix.<br>
* <br>
* real<sub>i,j</sub> = real<sub>i,j</sub><br>
* imaginary<sub>i,j</sub> = -1*imaginary<sub>i,j</sub><br>
* </p>
*
* @param input Input matrix. Not modified.
* @param output The complex conjugate of the input matrix. Modified.
*/
public static void conjugate(CMatrixD1 input, CMatrixD1 output)
{
if (input.numCols != output.numCols || input.numRows != output.numRows)
{
throw new ArgumentException("The matrices are not all the same dimension.");
}
int length = input.getDataLength();
for (int i = 0; i < length; i += 2)
{
output.data[i] = input.data[i];
output.data[i + 1] = -input.data[i + 1];
}
}
/**
* <p>Performs the following operation:<br>
* <br>
* c = a - b <br>
* c<sub>ij</sub> = a<sub>ij</sub> - b<sub>ij</sub> <br>
* </p>
*
* <p>
* Matrix C can be the same instance as Matrix A and/or B.
* </p>
*
* @param a A Matrix. Not modified.
* @param b A Matrix. Not modified.
* @param c A Matrix where the results are stored. Modified.
*/
public static void subtract(CMatrixD1 a, CMatrixD1 b, CMatrixD1 c)
{
if (a.numCols != b.numCols || a.numRows != b.numRows ||
a.numCols != c.numCols || a.numRows != c.numRows)
{
throw new ArgumentException("The matrices are not all the same dimension.");
}
int length = a.getDataLength();
for (int i = 0; i < length; i++)
{
c.data[i] = a.data[i] - b.data[i];
}
}
/**
* <p>
* Performs an in-place element by element scalar multiplication.<br>
* <br>
* a<sub>ij</sub> = α*a<sub>ij</sub>
* </p>
*
* @param a The matrix that is to be scaled. Modified.
* @param alphaReal real component of scale factor
* @param alphaImag imaginary component of scale factor
*/
public static void scale(float alphaReal, float alphaImag, CMatrixD1 a)
{
// on very small matrices (2 by 2) the call to getNumElements() can slow it down
// slightly compared to other libraries since it involves an extra multiplication.
int size = a.getNumElements() * 2;
for (int i = 0; i < size; i += 2)
{
float real = a.data[i];
float imag = a.data[i + 1];
a.data[i] = real * alphaReal - imag * alphaImag;
a.data[i + 1] = real * alphaImag + imag * alphaReal;
}
}
/**
* Converts the real matrix into a complex matrix.
*
* @param input Real matrix. Not modified.
* @param output Complex matrix. Modified.
*/
public static void convert(FMatrixD1 input, CMatrixD1 output)
{
if (input.numCols != output.numCols || input.numRows != output.numRows)
{
throw new ArgumentException("The matrices are not all the same dimension.");
}
Array.Clear(output.data, 0, output.getDataLength());
int length = output.getDataLength();
for (int i = 0; i < length; i += 2)
{
output.data[i] = input.data[i / 2];
}
}
/**
* <p>
* Returns the value of the imaginary element in the matrix that has the minimum value.<br>
* <br>
* Min{ a<sub>ij</sub> } for all i and j<br>
* </p>
*
* @param a A matrix. Not modified.
* @return The the minimum value out of all the real values.
*/
public static float elementMinImaginary(CMatrixD1 a)
{
int size = a.getDataLength();
float min = a.data[1];
for (int i = 3; i < size; i += 2)
{
float val = a.data[i];
if (val < min)
{
min = val;
}
}
return(min);
}
/**
* <p>
* Returns the value of the imaginary element in the matrix that has the minimum value.<br>
* <br>
* Min{ a<sub>ij</sub> } for all i and j<br>
* </p>
*
* @param a A matrix. Not modified.
* @return The the minimum value out of all the real values.
*/
public static float elementMaxImaginary(CMatrixD1 a)
{
int size = a.getDataLength();
float max = a.data[1];
for (int i = 3; i < size; i += 2)
{
float val = a.data[i];
if (val > max)
{
max = val;
}
}
return(max);
}
/**
* <p>
* Computes the magnitude of the complex number in the input matrix and stores the results in the output
* matrix.
* </p>
*
* magnitude = sqrt(real^2 + imaginary^2)
*
* @param input Complex matrix. Not modified.
* @param output real matrix. Modified.
*/
public static void magnitude(CMatrixD1 input, FMatrixD1 output)
{
if (input.numCols != output.numCols || input.numRows != output.numRows)
{
throw new ArgumentException("The matrices are not all the same dimension.");
}
int length = input.getDataLength();
for (int i = 0; i < length; i += 2)
{
float real = input.data[i];
float imaginary = input.data[i + 1];
output.data[i / 2] = (float)Math.Sqrt(real * real + imaginary * imaginary);
}
}
/**
* <p>
* Checks to see if each corresponding element in the two matrices are
* within tolerance of each other or have the some symbolic meaning. This
* can handle NaN and Infinite numbers.
* <p>
*
* <p>
* If both elements are countable then the following equality test is used:<br>
* |a<sub>ij</sub> - b<sub>ij</sub>| ≤ tol.<br>
* Otherwise both numbers must both be Float.NaN, Float.POSITIVE_INFINITY, or
* Float.NEGATIVE_INFINITY to be identical.
* </p>
*
* @param a A matrix. Not modified.
* @param b A matrix. Not modified.
* @param tol Tolerance for equality.
* @return true if identical and false otherwise.
*/
public static bool isIdentical(CMatrixD1 a, CMatrixD1 b, float tol)
{
if (a.numRows != b.numRows || a.numCols != b.numCols)
{
return(false);
}
if (tol < 0)
{
throw new ArgumentException("Tolerance must be greater than or equal to zero.");
}
int length = a.getDataLength();
for (int i = 0; i < length; i++)
{
float valA = a.data[i];
float valB = b.data[i];
// if either is negative or positive infinity the result will be positive infinity
// if either is NaN the result will be NaN
float diff = Math.Abs(valA - valB);
// diff = NaN == false
// diff = infinity == false
if (tol >= diff)
{
continue;
}
if (float.IsNaN(valA))
{
return(float.IsNaN(valB));
}
else if (float.IsInfinity(valA))
{
return(valA == valB);
}
else
{
return(false);
}
}
return(true);
}
/**
* <p>Performs element by element multiplication operation with a complex numbert<br>
* <br>
* output<sub>ij</sub> = input<sub>ij</sub> * (real + imaginary*i) <br>
* </p>
* @param input The left matrix in the multiplication operation. Not modified.
* @param real Real component of the number it is multiplied by
* @param imaginary Imaginary component of the number it is multiplied by
* @param output Where the results of the operation are stored. Modified.
*/
public static void elementMultiply(CMatrixD1 input, float real, float imaginary, CMatrixD1 output)
{
if (input.numCols != output.numCols || input.numRows != output.numRows)
{
throw new ArgumentException("The 'input' and 'output' matrices do not have compatible dimensions");
}
int N = input.getDataLength();
for (int i = 0; i < N; i += 2)
{
float inReal = input.data[i];
float intImag = input.data[i + 1];
output.data[i] = inReal * real - intImag * imaginary;
output.data[i + 1] = inReal * imaginary + intImag * real;
}
}
/**
* <p>
* Checks to see if the two matrices are the negative of each other:<br>
* <br>
* a<sub>ij</sub> = -b<sub>ij</sub>
* </p>
*
* @param a First matrix. Not modified.
* @param b Second matrix. Not modified.
* @param tol Numerical tolerance.
* @return True if they are the negative of each other within tolerance.
*/
public static bool isNegative(CMatrixD1 a, CMatrixD1 b, float tol)
{
if (a.numRows != b.numRows || a.numCols != b.numCols)
{
throw new ArgumentException("Matrix dimensions must match");
}
int length = a.getNumElements() * 2;
for (int i = 0; i < length; i++)
{
if (!(Math.Abs(a.data[i] + b.data[i]) <= tol))
{
return(false);
}
}
return(true);
}
/**
* <p>
* Checks to see if each element in the two matrices are equal:
* a<sub>ij</sub> == b<sub>ij</sub>
* <p>
*
* <p>
* NOTE: If any of the elements are NaN then false is returned. If two corresponding
* elements are both positive or negative infinity then they are equal.
* </p>
*
* @param a A matrix. Not modified.
* @param b A matrix. Not modified.
* @return true if identical and false otherwise.
*/
public static bool isEquals(CMatrixD1 a, CMatrixD1 b)
{
if (a.numRows != b.numRows || a.numCols != b.numCols)
{
return(false);
}
int length = a.getDataLength();
for (int i = 0; i < length; i++)
{
if (!(a.data[i] == b.data[i]))
{
return(false);
}
}
return(true);
}
/**
* Places the imaginary component of the input matrix into the output matrix.
*
* @param input Complex matrix. Not modified.
* @param output real matrix. Modified.
*/
public static FMatrixRMaj stripImaginary(CMatrixD1 input, FMatrixRMaj output)
{
if (output == null)
{
output = new FMatrixRMaj(input.numRows, input.numCols);
}
else if (input.numCols != output.numCols || input.numRows != output.numRows)
{
throw new ArgumentException("The matrices are not all the same dimension.");
}
int length = input.getDataLength();
for (int i = 1; i < length; i += 2)
{
output.data[i / 2] = input.data[i];
}
return(output);
}
/**
* <p>Performs element by element division operation with a complex number on the right<br>
* <br>
* output<sub>ij</sub> = (real + imaginary*i) / input<sub>ij</sub> <br>
* </p>
* @param real Real component of the number it is multiplied by
* @param imaginary Imaginary component of the number it is multiplied by
* @param input The right matrix in the multiplication operation. Not modified.
* @param output Where the results of the operation are stored. Modified.
*/
public static void elementDivide(float real, float imaginary, CMatrixD1 input, CMatrixD1 output)
{
if (input.numCols != output.numCols || input.numRows != output.numRows)
{
throw new ArgumentException("The 'input' and 'output' matrices do not have compatible dimensions");
}
int N = input.getDataLength();
for (int i = 0; i < N; i += 2)
{
float inReal = input.data[i];
float inImag = input.data[i + 1];
float norm = inReal * inReal + inImag * inImag;
output.data[i] = (real * inReal + imaginary * inImag) / norm;
output.data[i + 1] = (imaginary * inReal - real * inImag) / norm;
}
}
/**
* <p>
* Returns the magnitude squared of the complex element with the largest magnitude<br>
* <br>
* Max{ |a<sub>ij</sub>|^2 } for all i and j<br>
* </p>
*
* @param a A matrix. Not modified.
* @return The max magnitude squared
*/
public static float elementMaxMagnitude2(CMatrixD1 a)
{
int size = a.getDataLength();
float max = 0;
for (int i = 0; i < size;)
{
float real = a.data[i++];
float imaginary = a.data[i++];
float m = real * real + imaginary * imaginary;
if (m > max)
{
max = m;
}
}
return(max);
}
/**
* <p>
* Checks to see if each element in the two matrices are within tolerance of
* each other: tol ≥ |a<sub>ij</sub> - b<sub>ij</sub>|.
* <p>
*
* <p>
* NOTE: If any of the elements are not countable then false is returned.<br>
* NOTE: If a tolerance of zero is passed in this is equivalent to calling
* {@link #isEquals(CMatrixD1, CMatrixD1)}
* </p>
*
* @param a A matrix. Not modified.
* @param b A matrix. Not modified.
* @param tol How close to being identical each element needs to be.
* @return true if equals and false otherwise.
*/
public static bool isEquals(CMatrixD1 a, CMatrixD1 b, float tol)
{
if (a.numRows != b.numRows || a.numCols != b.numCols)
{
return(false);
}
if (tol == 0.0f)
{
return(isEquals(a, b));
}
int length = a.getDataLength();
for (int i = 0; i < length; i++)
{
if (!(tol >= Math.Abs(a.data[i] - b.data[i])))
{
return(false);
}
}
return(true);
}