void restrictedOptimizationHandler::simplex<Type>::simplexOptimization(const LinAlg::Matrix<Type> &c,
const LinAlg::Matrix<Type> &A,
const LinAlg::Matrix<Type> &b,
LinAlg::Matrix<Type> &B,
LinAlg::Matrix<Type> &N)
{
// %% selecione uma base B e calcule B^-1
LinAlg::Matrix<Type> An = A(from(1)-->A.getNumberOfRows(),N);
LinAlg::Matrix<Type> Ab = A(from(1)-->A.getNumberOfRows(),B);
// std::cout << N << "\n";
LinAlg::Matrix<Type> Abinv = LinAlg::inv_numeric(Ab);
// LinAlg::Matrix<Type> Abinv = (Ab^-1);
LinAlg::Matrix<Type> xb;
// %% Verifique o vetor dos custos reduzidos
for(unsigned terminate = 1; terminate <= 100; ++terminate)
{
LinAlg::Matrix<Type> cn = c(N,1);
LinAlg::Matrix<Type> cb = c(B,1);
LinAlg::Matrix<Type>An = A(from(1)-->A.getNumberOfRows(),N);
Ab = A(from(1)-->A.getNumberOfRows(),B);
LinAlg::Matrix<Type> r = (~cn) - (~cb)*Abinv*An;
this->cost = ((~cb)*Abinv*b)(1,1);
xb = Abinv*b;
unsigned contFlag = 0;
for (unsigned i=1; i <= r.getNumberOfColumns(); ++i)
if(r(1,i) >= 0)
{
contFlag = contFlag + 1;
//% break;
}
if(contFlag == r.getNumberOfColumns())
break;
//%determine o vetor de chegada
unsigned indMinD = LinAlg::lineOfMinValue(~r);
this->x = Abinv*An(from(1)-->An.getNumberOfRows(),indMinD);
LinAlg::Matrix<Type> d = LinAlg::divPoint(xb,this->x);
Type dMin = INFINITY;
unsigned indMinB = 1;
for (unsigned i = 1; i <= d.getNumberOfRows(); ++i)
if(this->x(i,1) > 0 && d(i,1) < dMin)
{
dMin = d(i,1);
indMinB = i;
}
Abinv = EscalSimplex((Abinv | xb | this->x),indMinB);
Type Bout = B(1,indMinB);
Type Nout = N(1,indMinD);
N = N(1,from(1)-->(indMinD-1)) | Bout | N(1, from(indMinD+1)-->(N.getNumberOfColumns()));
B = B(1,from(1)-->(indMinB-1)) | Nout | B(1,from(indMinB+1)-->(B.getNumberOfColumns()));
}
this->x = xb || LinAlg::Zeros<Type>(An.getNumberOfColumns(),1);
LinAlg::Matrix<Type> ind = LinAlg::sortColumnVectorIndices<Type>(B|N);
this->x = this->x(ind,1);
// std::cout << "\n\n" << ind << "\n\n";
N = LinAlg::sortColumnVector<Type>(N);
B = LinAlg::sortColumnVector<Type>(B);
}
LinAlg::Matrix<float> SistemasLineares::Gauss(LinAlg::Matrix<float> MatrizUni)
{
LinAlg::Matrix<float> MatrizGauss;
//Laço para contagem das colunas de MatrizUni.
for(unsigned i = 1; i < MatrizUni.getNumberOfColumns(); i++)
{ //Laço para contagem das linhas de MatrizUni.
for(unsigned j = i + 1; j <= MatrizUni.getNumberOfRows(); j++)
{
float m = MatrizUni(j,i)/MatrizUni(i,i);
//Laço para contagem das colunas da equação.
for(unsigned z = i ; z <= MatrizUni.getNumberOfColumns(); z++)
MatrizUni(j,z) = MatrizUni(j,z) - m*MatrizUni(i,z);
}
}
MatrizGauss = LinAlg::Zeros<float>(1, MatrizUni.getNumberOfRows());
float R;
for(unsigned i = 1; i <= MatrizUni.getNumberOfRows(); ++i)
{
unsigned k = MatrizUni.getNumberOfRows() - i + 1;
R = 0;
for(unsigned j = k + 1; j <= MatrizUni.getNumberOfColumns() - 1; ++j)
R = R + MatrizUni(k, j) * MatrizGauss(1, j);
MatrizGauss(1, k) = (MatrizUni(k, MatrizUni.getNumberOfColumns()) - R) / MatrizUni(k, k);
}
return MatrizGauss;
}
LinAlg::Matrix<float> SistemasLineares::GaussJacobi(LinAlg::Matrix<float> MatrizUni, unsigned MaxIterations)
{
//Matriz Resposta
LinAlg::Matrix<float> MatrizRes(MaxIterations, MatrizUni.getNumberOfColumns());
LinAlg::Matrix<float> C (MatrizUni.getNumberOfRows(), MatrizUni.getNumberOfColumns() - 1);
LinAlg::Matrix<float> g (MatrizUni.getNumberOfRows(), 1);
LinAlg::Matrix<float> x0(C.getNumberOfColumns(), 1);
// //Deixa o vetor de chute inicial padronizado como vetor linha
if(this->X0.getNumberOfColumns() < this->X0.getNumberOfRows())
~this->X0;
// //Insere o chute inicial na Matriz resposta
for(unsigned i = 1; i < MatrizRes.getNumberOfColumns() - 1; ++i)
x0(1,i) = this->X0(1,i);
//Laço para contar as linhas da MatrizUni e Matriz C.
for(unsigned i = 1; i <= MatrizUni.getNumberOfRows(); ++i)
{ //Laço para contar as colunas da MAtrizUni e Matriz C.
for(unsigned j = 1; j < MatrizUni.getNumberOfColumns(); ++j)
{
if(i != j)
C(i,j) = - MatrizUni(i,j)/MatrizUni(i,i);//Matriz com a diagonal zerada.
}
g(i,1) = MatrizUni(i,MatrizUni.getNumberOfColumns()) / MatrizUni(i,i);//Matriz dos termos independentes.
}
MatrizRes = ~x0;
for(unsigned k = 1; k < MaxIterations; ++k)
{
x0 = (C * x0) + g;
MatrizRes = MatrizRes || ~x0;
}
return MatrizRes;
}
LinAlg::Matrix<Type> LinAlg::Matrix<Type>::operator|| (LinAlg::Matrix<RightType> rhs)
{
LinAlg::Matrix<Type>ret;
if(this->mat == NULL)
ret = rhs;
else
{
unsigned aux = this->rows;
if(this->columns < rhs.getNumberOfColumns())
ret.Init(this->rows + rhs.getNumberOfRows(), rhs.getNumberOfColumns());
else
ret.Init(this->rows + rhs.getNumberOfRows(), this->columns);
for(unsigned i = 0; i < this->rows; i++)
for(unsigned j = 0; j < this->columns; j++)
ret.mat[i][j] = this->mat[i][j];
for(unsigned i = 1; i <= rhs.getNumberOfRows(); i++)
for(unsigned j = 1; j <= rhs.getNumberOfColumns(); j++)
ret(i + aux, j) = rhs(i, j);
}
return ret;
}
void PolynomHandler::Polynom<Type>::setDen(LinAlg::Matrix<Type> Den)
{
this->den = initPointer<Type>(Den.getNumberOfColumns());
this->sizeDen = Den.getNumberOfColumns();
for (unsigned i = 0; i < Den.getNumberOfColumns(); ++i)
this->den[i] = Den(1,i+1);
}
void PolynomHandler::Polynom<Type>::setNum(LinAlg::Matrix<Type> Num)
{
this->num = initPointer<Type>(Num.getNumberOfColumns());
this->sizeNum = Num.getNumberOfColumns();
for (unsigned i = 0; i < Num.getNumberOfColumns(); ++i)
this->num[i] = Num(1,i+1);
}
LinAlg::Matrix<Type> LinAlg::operator~ (LinAlg::Matrix<Type> mat)
{
LinAlg::Matrix<Type> temp(mat.getNumberOfColumns(), mat.getNumberOfRows());
for(unsigned i = 1; i <= mat.getNumberOfRows(); i++)
for(unsigned j = 1; j <= mat.getNumberOfColumns(); j++)
temp(j, i) = mat(i, j);
return temp;
}
void PolynomHandler::Polynom<Type>::init(LinAlg::Matrix<Type> Num)
{
this->sizeNum = Num.getNumberOfColumns();
this->num = initPointer(Num.getNumberOfColumns());
for (unsigned i = 0; i < Num.getNumberOfColumns(); ++i)
this->num[i] = (Type) Num(1, i+1);
this->sizeDen = 1;
this->den = initPointer<Type>(1);
this->den[0] = 1;
this->x = 'x';
}
void PlotHandler::plot<Type>::generalPlot(LinAlg::Matrix<Type> X, LinAlg::Matrix<Type> Y)
{
// centralWidget = new QWidget(this->properties.MainWindow);
// centralWidget->setGeometry(QRect(this->properties.windowPosX, this->properties.windowPosY, this->properties.windowSizeX, this->properties.windowSizeY));
customPlot = new QCustomPlot(this->properties.PlotFrame);
customPlot->setGeometry(QRect(0, 0,this->properties.PlotFrame->geometry().width(), this->properties.PlotFrame->geometry().height()));
// add title layout element:
if(this->properties.titleFlag)
{
customPlot->plotLayout()->insertRow(0);
customPlot->plotLayout()->addElement(0, 0, new QCPPlotTitle(this->customPlot, this->properties.title.c_str()));
}
if(X.getNumberOfColumns() == Y.getNumberOfColumns() && X.getNumberOfRows() == Y.getNumberOfRows())
{
this->properties.rows = X.getNumberOfRows();
this->properties.columns = X.getNumberOfColumns();
// this->setLegend();
QPen pen;
// add graphs with different scatter styles:
for (unsigned i = 0; i < this->properties.rows; ++i)
{
customPlot->addGraph();
pen.setColor(QColor(qSin(i*0.3)*100+100, qSin(i*0.6+0.7)*100+100, qSin(i*0.4+0.6)*100+100));
// generate data:
QVector<double> x(this->properties.columns), y(this->properties.columns);
for (unsigned k = 0; k < this->properties.columns; ++k)
{
x[k] = X(i+1,k+1);
y[k] = Y(i+1,k+1);
}
customPlot->graph()->setData(x, y);
customPlot->graph()->rescaleAxes(true);
customPlot->graph()->setPen(pen);
if(this->properties.variablesNameFlag)
customPlot->graph()->setName("Grafico" + QString::number(i+1));
customPlot->graph()->setLineStyle(QCPGraph::lsLine);
if(this->properties.xLabelFlag)
customPlot->xAxis->setLabel(this->properties.xLabel.c_str());
if(this->properties.yLabelFlag)
customPlot->yAxis->setLabel(this->properties.yLabel.c_str());
// set scatter style:
}
}
customPlot->rescaleAxes();
}
LinAlg::Matrix<Type> PolynomHandler::MultPoly(const LinAlg::Matrix<Type> &lhs, const LinAlg::Matrix<Type> &rhs)
{
unsigned lhsSize = lhs.getNumberOfColumns();
unsigned rhsSize = rhs.getNumberOfColumns();
LinAlg::Matrix<Type>ret(1,lhsSize+rhsSize+1);
for(unsigned i = 0; i < lhsSize; ++i)
for(unsigned j = 0; j < rhsSize; ++j)
{
ret(1,i+j+1) = ret(1,i+j+1) + lhs(1,i+1)*rhs(1,j+1);
}
return ret;
}
void LinAlg::Balance (LinAlg::Matrix<Type> &matrix_to_balance)
{
unsigned aux = 0;
Type radix = FLT_RADIX, sqrdx = radix*radix, s, r, g, f, c;
while(aux == 0)
{
aux = 1;
for(unsigned i = 1; i <= matrix_to_balance.getNumberOfRows(); i++)
{
r = c = 0.0;
for(unsigned j = 1; j <= matrix_to_balance.getNumberOfColumns(); j++)
if( j != i)
{
c += std::fabs(matrix_to_balance(j, i));
r += std::fabs(matrix_to_balance(i, j));
}
if(c && r)
{
g = r/radix;
f = 1.0;
s = c + r;
while(c < g)
{
f *= radix;
c *= sqrdx;
}
g = r*radix;
while(c > g)
{
f /= radix;
c /= sqrdx;
}
if((c + r)/f < 0.95*s)
{
aux = 0;
g = 1.0/f;
for(unsigned j = 1; j <= matrix_to_balance.getNumberOfColumns(); j++)
{
matrix_to_balance(i, j) *= g;
matrix_to_balance(j, i) *= f;
}
}
}
}
}
}
Type LinAlg::Trace (const LinAlg::Matrix<Type>& mat)
{
Type ret = 0;
if(mat.getNumberOfRows() != mat.getNumberOfColumns())
std::cout << "O traco so e calculado para matrizes quadradas.";
else
{
for(unsigned i = 1; i <= mat.getNumberOfRows(); i++)
for(unsigned j = 1; j <= mat.getNumberOfColumns(); j++)
if(i == j)
ret += mat(i, j);
}
return ret;
}
void SistemasLineares::LU_Factorization(LinAlg::Matrix<float> Matriz, LinAlg::Matrix<float> &L, LinAlg::Matrix<float> &U)//Para Matriz Quadrada.
{
L = LinAlg::Eye<float>(Matriz.getNumberOfRows());
for(unsigned i = 1; i < Matriz.getNumberOfColumns(); ++i)
{ //Laço para contagem das linhas de MatrizUni.
for(unsigned j = i + 1; j <= Matriz.getNumberOfRows(); ++j)
{
L(j, i) = Matriz(j, i)/Matriz(i, i);
//Laço para contagem das colunas da equação.
for(unsigned z = i ; z <= Matriz.getNumberOfColumns(); ++z)
Matriz(j, z) = Matriz(j, z) - L(j, i)*Matriz(i, z);
}
}
U = Matriz;
}
LinAlg::Matrix<Type> LinAlg::CaracteristicPolynom (const LinAlg::Matrix<Type>& mat)
{
unsigned n = mat.getNumberOfColumns();
Matrix<Type> z = EigenValues(mat);
Matrix<Type> zi = EigenValues(mat);
Matrix<Type> ret(1,n+1);
std::complex<Type> *tempPoly = new std::complex<Type> [2];
tempPoly[0] = 1;
tempPoly[1] = std::complex<Type>(-z(1,1),-z(1,2));
std::complex<Type> * tempPolyEigenvalue = new std::complex<Type>[2];
unsigned sizeTempPoly = 2;
tempPolyEigenvalue[0] = 1;
for(unsigned i = 2; i <= n ; ++i)
{
tempPolyEigenvalue[1] = std::complex<Type>(-z(i,1),-z(i,2));//apos o templade entre (real,imaginario) atribuição
tempPoly = LinAlg::MultPoly(tempPoly,tempPolyEigenvalue,sizeTempPoly,2);
sizeTempPoly++;
}
for(unsigned i = 0; i < sizeTempPoly ; ++i)
{
ret(1,i+1) = tempPoly[i].real();
}
return ret;
}
void PlotHandler::plot<Type>::realTimeDataUpdate(LinAlg::Matrix<Type> X, LinAlg::Matrix<Type> Y)
{
for(unsigned i = 1; i <= X.getNumberOfColumns(); i++)
{
this->realTimeDataUpdate(X(1,i),Y(1,i));
}
}
PlotHandler::plot<Type>::plot(LinAlg::Matrix<Type> Y, plotProperties properties)
{
LinAlg::Matrix<Type> X = LinAlg::LineVector<Type>(0,Y.getNumberOfColumns());
this->properties = properties;
this->properties.PlotFrame->hide();
this->generalPlot(X,Y);
this->properties.PlotFrame->show();
}
PlotHandler::plot<Type>::plot(LinAlg::Matrix<Type> Y, QWidget *PlotFrame)
{
LinAlg::Matrix<Type> X = LinAlg::LineVector<Type>(0,Y.getNumberOfColumns()-1);
this->properties.setPlotFrame(PlotFrame);
this->properties.PlotFrame->hide();
this->generalPlot(X,Y);
this->properties.PlotFrame->show();
}
LinAlg::Matrix<float> SistemasLineares::GaussSeidel(LinAlg::Matrix<float> MatrizUni, unsigned MaxIterations)
{
LinAlg::Matrix<float> MatrizRes(MaxIterations, MatrizUni.getNumberOfColumns());
//Deixa o vetor de chute inicial padronizado como vetor linha
if(this->X0.getNumberOfColumns() < this->X0.getNumberOfRows())
{
~this->X0;
}
//Insere o chute inicial na Matriz resposta
for(unsigned i = 1; i < MatrizRes.getNumberOfColumns(); i++){
MatrizRes(1,i) = this->X0(1,i);
}
//Laço para contar as linhas da Matriz Resposta
for(unsigned k = 2; k <= MaxIterations; k++)
{
//Laço para contar as colunas da MatrizRes e linhas da MatrizUni.
for(unsigned i = 1; i < MatrizUni.getNumberOfColumns(); i++)
{
float aux = 0;
//Verificação das variáveis atualizadas (mesma linha)
for(unsigned j = 1; j < i; j++)
{
aux += (MatrizUni(i,j)*MatrizRes(k, j));
}
//Verificação das variaveis não atualizadas (linha anterior)
for(unsigned j = i+1; j < MatrizUni.getNumberOfColumns(); j++)
{
aux += (MatrizUni(i,j)*MatrizRes(k-1, j));
}
//Aplicação da formula geral (Bi-x1-x2)/Aii
MatrizRes(k,i) = (MatrizUni(i, MatrizUni.getNumberOfColumns()) - aux)/MatrizUni(i,i);
//Verifica se o valor de erro d(k) é o maior encontrado
if(abs(MatrizRes(k,i) - MatrizRes(k-1,i)) > MatrizRes(k-1, MatrizRes.getNumberOfColumns()))
MatrizRes(k-1, MatrizRes.getNumberOfColumns()) = abs(MatrizRes(k,i) - MatrizRes(k-1,i));
}
}
return MatrizRes;
}
LinAlg::Matrix<Type> ModelHandler::NFIR<Type>::sim(LinAlg::Matrix<Type> Input)
{
this->Input = Input;
LinAlg::Matrix<Type> TempOutput;
for(unsigned i = 1; i <= Input.getNumberOfColumns(); ++i){
this->setLinearVector(Input.GetColumn(i),TempOutput);
TempOutput = TempOutput|~(this->LinearVectorA*this->ModelCoef);
}
this->Output = TempOutput;
return this->Output;
}
void restrictedOptimizationHandler::activeSet<Type>::KKT(LinAlg::Matrix<Type> A,
LinAlg::Matrix<Type> b,
LinAlg::Matrix<Type> &x,
LinAlg::Matrix<Type> &v)
{
LinAlg::Matrix<Type> K = (this->QuadMat | (~A)) ||
(A | LinAlg::Zeros<Type>(A.getNumberOfRows(),A.getNumberOfRows()));
LinAlg::Matrix<Type> L = -this->LinMat || b;
LinAlg::Matrix<Type> S = (((~K)*K)^-1)*(~K)*L;
x = S(from(1)-->this->LinMat.getNumberOfRows(),1);
if(A.getNumberOfRows() > 0)
v = S(from(this->LinMat.getNumberOfRows()+1)-->(this->LinMat.getNumberOfRows() + b.getNumberOfRows()),
from(1)-->S.getNumberOfColumns());
}
void LinAlg::Matrix<Type>::swap (const LinAlg::Matrix<OtherMatrixType>& otherMatrix)
{
using std::swap;
LinAlg::Matrix<Type> temp(otherMatrix.getNumberOfRows(), otherMatrix.getNumberOfColumns());
for(unsigned i = 0; i < temp.rows; i++)
for(unsigned j = 0; j < temp.columns; j++)
temp.mat[i][j] = otherMatrix(i, j);
swap (rows, temp.rows);
swap (columns, temp.columns);
swap (mat, temp.mat);
}
void LinAlg::QR_Factorization (const LinAlg::Matrix<Type>& input_matrix,
LinAlg::Matrix<Type>& output_Q_matrix,
LinAlg::Matrix<Type>& output_R_matrix)
{
//Constants calculated and needed for the QR algorithm.
unsigned R_rows = input_matrix.getNumberOfRows(), R_columns = input_matrix.getNumberOfColumns();
Type tal, gama, sigma;
output_Q_matrix = LinAlg::Eye<Type>(R_rows);
output_R_matrix = input_matrix;
for(unsigned j = 1; j <= R_columns; j++)
for(unsigned i = R_rows; i >= j + 1; i--)
{
if(output_R_matrix(i, j) != 0)
{
LinAlg::Matrix<Type> temp;
temp = LinAlg::Eye<Type>(R_rows);
if(std::abs(output_R_matrix(i - 1, j)) > std::abs(output_R_matrix(i, j)))
{
tal = output_R_matrix(i, j)/output_R_matrix(i - 1, j);
gama = 1/(std::sqrt(1 + std::pow(tal, 2)));
sigma = tal*gama;
}
else
{
tal = output_R_matrix(i - 1, j)/output_R_matrix(i, j);
sigma = 1/(std::sqrt(1 + std::pow(tal, 2)));
gama = sigma*tal;
}
temp(i, i) = gama;
temp(i, i - 1) = sigma;
temp(i - 1, i) = -sigma;
temp(i - 1, i - 1) = gama;
output_R_matrix = (~temp)*output_R_matrix;
output_Q_matrix *= temp;
}
}
}
Type NeuralNetworkHandler::Neuron<Type>::sim(LinAlg::Matrix<Type> Input, LinAlg::Matrix<Type> Weight, Type Bias){
Type tempOutput = 0;
if(Input.getNumberOfRows() < Input.getNumberOfColumns() || Weight.getNumberOfRows() < Weight.getNumberOfColumns())
std::cout<<"As dimensoes nao batem. Impossivel realizar operacao."<<std::endl;
else{
this->Input = Input;
this->Weight = Weight;
this->Bias = Bias;
tempOutput = ((~this->Input * this->Weight) - this->Bias)(1,1);
//std::cout<<tempOutput<<std::endl;
if(this->ActiveFunctionType == "Signal")
this->Output = this->Signal(tempOutput);
else if(this->ActiveFunctionType == "HardLimit")
this->Output = this->HardLimit(tempOutput);
else if(this->ActiveFunctionType == "Linear")
this->Output = this->Linear(tempOutput);
else if(this->ActiveFunctionType == "PositiveLinear")
this->Output = this->PositiveLinear(tempOutput);
else if(this->ActiveFunctionType == "SymmetricLinear")
this->Output = this->SymmetricLinear(tempOutput);
else if(this->ActiveFunctionType == "SaturatingLinear")
this->Output = this->SaturatingLinear(tempOutput);
else if(this->ActiveFunctionType == "Gaussian")
this->Output = this->Gaussian(tempOutput);
else if(this->ActiveFunctionType == "Multiquadrics")
this->Output = this->Multiquadrics(tempOutput);
else if(this->ActiveFunctionType == "InverseMultiquadrics")
this->Output = this->InverseMultiquadrics(tempOutput);
else if(this->ActiveFunctionType == "Sigmoid")
this->Output = this->Sigmoid(tempOutput);
else if(this->ActiveFunctionType == "HyperbolicTangentSigmoid")
this->Output = this->HyperbolicTangentSigmoid(tempOutput);
else{
std::cout<<"Metodo nao encontrado"<<std::endl;
this->Output = tempOutput;
}
return Output;
}
return 0;
}
void SistemasLineares::CritLinhas(LinAlg::Matrix<float> MatrizUni)
{
LinAlg::Matrix<float> MatrizRes(1,MatrizUni.getNumberOfRows());
for(unsigned i = 1; i <= MatrizUni.getNumberOfRows(); i++)
{
for(unsigned j =1; j <= MatrizUni.getNumberOfColumns(); j++)
{
if(i != j)
{
MatrizRes(1, i) += MatrizUni(i,j)/MatrizUni(i,i);
}
}
if(MatrizRes(1, i) > 1)
{
cout<<"O sistema não possui solução para qualquer valor inicial de X0";
break;
}
}
}
bool LinAlg::Matrix<Type>::CheckDimensions (const LinAlg::Matrix<OtherMatrixType>& rhs, unsigned operation)
{
bool checked;
switch(operation)
{
case 0:
try
{
if((this->rows == rhs.getNumberOfRows()) && (this->columns == rhs.getNumberOfColumns()))
checked = true;
else
{
throw "As dimensoes nao batem. Impossivel realizar operacao";
checked = false;
}
}
catch(const char* msg)
{
std::cerr << msg;
}
break;
case 1:
try
{
if(this->columns == rhs.getNumberOfRows())
checked = true;
else
{
throw "As dimensoes nao batem. Impossivel realizar operacao";
checked = false;
}
}
catch(const char* msg)
{
std::cerr << msg;
}
break;
}
return checked;
}
std::string PolynomHandler::printSmallPolynom(const LinAlg::Matrix<Type> &rhs, const char &variable)
{
std::ostringstream ret;
const char plusSignal = '+';
const char minusSignal = '-';
unsigned Size = rhs.getNumberOfColumns();
if(Size == 0)
return ret.str();
for(unsigned i = 1; i <= Size; ++i)
{
if(i != 1 && rhs(1,i) > 0)
{
ret << plusSignal << ' ';
}
else if(rhs(1,i) < 0)
{
ret << minusSignal << ' ';
}
if(((rhs(1,i) != 1) && (rhs(1,i) > 0)) || ((i == Size) && (rhs(1,i) > 0)))
ret << rhs(1,i);
else if((rhs(1,i) != -1 && rhs(1,i) < 0)|| ((i == Size) && (rhs(1,i) < 0)))
ret << -rhs(1,i);
if(Size-i > 0 && rhs(1,i) != 0)
{
ret << variable;
if(i != Size-1)
{
ret << '^';
ret << Size-i;
}
}
ret << ' ';
}
return ret.str();
}
void restrictedOptimizationHandler::simplex<Type>::optimize()
{
if(this->N.A.getNumberOfColumns() != 0 && this->N.A.getNumberOfRows() != 0)
{
this->P.A = (this->P.A | LinAlg::Eye<Type>(this->P.A.getNumberOfRows()) | LinAlg::Zeros<Type>(this->N.A.getNumberOfRows(),this->N.A.getNumberOfRows())) ||
(this->N.A | LinAlg::Zeros<Type>(this->P.A.getNumberOfRows(),this->P.A.getNumberOfRows()) | -LinAlg::Eye<Type>(this->N.A.getNumberOfRows()));
// std::cout << this->A << "\n";
this->P.b = this->P.b || this->N.b;
this->A = this->P.A | LinAlg::Eye<Type>(this->P.A.getNumberOfRows())||
this->E.A | LinAlg::Zeros<Type>(this->E.A.getNumberOfRows(),this->P.A.getNumberOfRows());
this->b = this->P.b || this->E.b;
// LinAlg::Matrix<Type> c = this->function2Optimize || LinAlg::Zeros<Type>(1,this->P.b.getNumberOfRows() - this->E.b.getNumberOfRows() + this->N.b.getNumberOfRows());
LinAlg::Matrix<Type> w = LinAlg::Zeros<Type>(this->A.getNumberOfColumns() - this->P.A.getNumberOfRows(),1)||
LinAlg::Ones<Type>(this->P.A.getNumberOfRows(),1);
LinAlg::Matrix<Type> B = LinAlg::LineVector<Type>(this->A.getNumberOfColumns() - this->P.A.getNumberOfRows() +1, this->A.getNumberOfColumns());
LinAlg::Matrix<Type> n = LinAlg::LineVector<Type>(1,this->A.getNumberOfColumns() - this->P.A.getNumberOfRows());
simplexOptimization(w,this->A,this->b,B,n);
this->x = this->x(1,from(1)-->this->x.getNumberOfRows()-this->P.A.getNumberOfRows());
this->A = this->A(from(1)-->this->A.getNumberOfRows(),from(1)-->this->A.getNumberOfColumns()-this->P.A.getNumberOfRows());
LinAlg::Matrix<Type> c = this->function2Optimize ||
LinAlg::Zeros<Type>(this->b.getNumberOfRows(),1);
n = n(1,from(1)-->n.getNumberOfColumns()-this->P.A.getNumberOfRows());
simplexOptimization(c,this->A,this->b,B,n);
this->set = B;
}
else
{
this->A = (this->P.A | LinAlg::Eye<Type>(this->P.A.getNumberOfRows()))||
(this->E.A | LinAlg::Zeros<Type>(this->E.A.getNumberOfRows(),this->P.A.getNumberOfRows()));
this->b = this->P.b || this->E.b;
LinAlg::Matrix<Type> c = this->function2Optimize ||
LinAlg::Zeros<Type>(this->b.getNumberOfColumns(), 1);
LinAlg::Matrix<Type> B = LinAlg::LineVector<Type>(this->A.getNumberOfColumns() - this->P.A.getNumberOfRows() +1, this->A.getNumberOfColumns(),1);
LinAlg::Matrix<Type> n = LinAlg::LineVector<Type>(1,this->A.getNumberOfColumns() - this->P.A.getNumberOfRows());
simplexOptimization(c,this->A,this->b,B,n);
this->set = B;
}
// std::cout << this->x << "\n\n";
}
void PolynomHandler::Polynom<Type>::init(LinAlg::Matrix<Type> Num, LinAlg::Matrix<Type> Den)
{
using namespace std;
this->sizeNum = Num.getNumberOfColumns();
this->num = initPointer<Type>(Num.getNumberOfColumns());
for (unsigned i = 0; i < Num.getNumberOfColumns(); ++i)
this->num[i] = (Type) Num(1, i+1);
this->sizeDen = Den.getNumberOfColumns();
this->den = initPointer<Type>(Den.getNumberOfColumns());
for (unsigned i = 0; i < Den.getNumberOfColumns(); ++i)
this->den[i] = (Type) Den(1 , i+1);
this->x = 'x';
}
bool LinAlg::Matrix<Type>::CheckDimensions (const LinAlg::Matrix<OtherMatrixType>& rhs, unsigned operation)
{
bool checked = false;
switch(operation)
{
case 0:
if((this->rows == rhs.getNumberOfRows()) && (this->columns == rhs.getNumberOfColumns()))
checked = true;
else
std::cout << "As dimensoes nao batem. Impossivel realizar operacao." << std::endl;
break;
case 1:
if(this->columns == rhs.getNumberOfRows())
checked = true;
else
std::cout << "As dimensoes nao batem. Impossivel realizar operacao." << std::endl;
break;
}
return checked;
}
LinAlg::Matrix<Type> restrictedOptimizationHandler::simplex<Type>::EscalSimplex(LinAlg::Matrix<Type> A,
unsigned index)
{
for(unsigned i = 1; i <= A.getNumberOfColumns(); ++i)
A(index,i) = A(index,i)/A(index,A.getNumberOfColumns());
for (unsigned i = 1; i <= A.getNumberOfRows(); ++i)
if(i != index)
{
Type m = A(i,A.getNumberOfColumns())/A(index,A.getNumberOfColumns());
for(unsigned j = 1; j <= A.getNumberOfColumns(); ++j)
A(i,j)=A(i,j)-m*A(index,j);
}
// Xb = A(from(1)-->A.getNumberOfRows(),A.getNumberOfColumns()-1);
LinAlg::Matrix<Type> Binv = A(from(1)-->A.getNumberOfRows(),from(1)-->A.getNumberOfColumns()-2);
// X = A(from(1)--> A.getNumberOfRows(),A.getNumberOfColumns());
return Binv;
}
