private Matrix SquareMatrixInverse(Matrix argument)
{
int size = argument.Rows;
Matrix original = argument.Clone();
Matrix inverse = new SimpleMatrix(size, size);
for (int i = 0; i < size; i++)
{
inverse[i, i] = 1;
}
for (int i = 0; i < size; i++)
{
double reciprocal = 1 / original[i, i];
for (int k = 0; k < size; k++)
{
original[i, k] *= reciprocal;
inverse[i, k] *= reciprocal;
}
for (int j = 0; j < size; j++)
{
if (i == j)
{
continue;
}
double quotient = original[j, i] / original[i, i];
for (int k = 0; k < size; k++)
{
original[j, k] = original[j, k] - quotient * original[i, k];
inverse[j, k] = inverse[j, k] - quotient * inverse[i, k];
}
}
}
for (int i = 0; i < size; i++)
{
for (int j = 0; j < size; j++)
{
if ((i == j && original[i, j] != 1) ||
(i != j && original[i, j] != 0))
{
// no inverse found report error
throw new Error.Domain(DomainErrorText);
}
}
}
return inverse;
}
internal static Matrix MatrixFromAType(AType argument)
{
Matrix result = new SimpleMatrix(new double[argument.Shape[0], argument.Shape[1]]);
for (int i = 0; i < argument.Shape[0]; i++)
{
for (int j = 0; j < argument.Shape[1]; j++)
{
result[i, j] = argument[i][j].asFloat;
}
}
return result;
}
public static Matrix operator *(Matrix matrix1, Matrix matrix2)
{
int rows = matrix1.Rows;
int columns = matrix2.Columns;
SimpleMatrix result = new SimpleMatrix(rows, columns);
for (int i = 0; i < rows; i++)
{
for (int j = 0; j < columns; j++)
{
for (int k = 0; k < matrix1.Columns; k++)
{
result[i, j] += matrix1[i, k] * matrix2[k, j];
}
}
}
return(result);
}
public static Matrix operator *(Matrix matrix1, Matrix matrix2)
{
int rows = matrix1.Rows;
int columns = matrix2.Columns;
SimpleMatrix result = new SimpleMatrix(rows, columns);
for (int i = 0; i < rows; i++)
{
for (int j = 0; j < columns; j++)
{
for (int k = 0; k < matrix1.Columns; k++)
{
result[i, j] += matrix1[i, k] * matrix2[k, j];
}
}
}
return result;
}
private AType SolveEquation(AType constants, AType equations)
{
AType lhs;
AType rhs;
if (constants.TryFirstScalar(out lhs, true) && equations.TryFirstScalar(out rhs, true))
{
// both left and right values are one element arrays.
return AFloat.Create(lhs.asFloat / rhs.asFloat);
}
Matrix constantsArray = new SimpleMatrix(ExtractConstants(constants));
Matrix originalEquations = new SimpleMatrix(FloatFromAType(equations));
int[] rowsSequence;
Matrix eliminatedConstants;
GaussianElimination(originalEquations, constantsArray, out rowsSequence, out eliminatedConstants);
AType result = AArray.Create(ATypes.AFloat);
if (equations.Shape[0] == equations.Shape[1])
{
// square equation
if (constants.Rank > 1)
{
foreach (int item in rowsSequence)
{
AType subArray = AArray.Create(ATypes.AFloat);
for (int i = 0; i < eliminatedConstants.Columns; i++)
{
subArray.Add(AFloat.Create(eliminatedConstants[item, i]));
}
result.Add(subArray);
}
}
else
{
foreach (int item in rowsSequence)
{
result.Add(AFloat.Create(eliminatedConstants[item, 0]));
}
}
}
else
{
double[][] independentConstants = BuildIndependentConstants(rowsSequence, eliminatedConstants);
double[] beta;
double[] actualconstants;
if (constants.Rank == 1)
{
beta = independentConstants.Select(item => item[0]).ToArray();
actualconstants = constants.Select(item => item.asFloat).ToArray();
double[] solution = OverDeterminedEquationSolve(beta, actualconstants, originalEquations);
foreach (double item in solution)
{
result.Add(AFloat.Create(item));
}
}
else
{
for (int objective = 0; objective < constants.Shape[1]; objective++)
{
beta = independentConstants.Select(item => item[objective]).ToArray();
actualconstants = constants.Select(item => item[objective].asFloat).ToArray();
double[] solution = OverDeterminedEquationSolve(beta, actualconstants, originalEquations);
AType solutionArray = AArray.Create(ATypes.AFloat);
foreach (double item in solution)
{
solutionArray.Add(AFloat.Create(item));
}
result.Add(solutionArray);
}
}
}
return result;
}