void SystemMatrix::ypAx(escript::Data& y, escript::Data& x) const
{
if (x.isComplex() || y.isComplex())
{
throw PasoException("SystemMatrix::ypAx: complex arguments not supported.");
}
if (x.getDataPointSize() != getColumnBlockSize()) {
throw PasoException("matrix vector product: column block size does not match the number of components in input.");
} else if (y.getDataPointSize() != getRowBlockSize()) {
throw PasoException("matrix vector product: row block size does not match the number of components in output.");
} else if (x.getFunctionSpace() != getColumnFunctionSpace()) {
throw PasoException("matrix vector product: column function space and function space of input don't match.");
} else if (y.getFunctionSpace() != getRowFunctionSpace()) {
throw PasoException("matrix vector product: row function space and function space of output don't match.");
}
x.expand();
y.expand();
x.requireWrite();
y.requireWrite();
double* x_dp = x.getExpandedVectorReference(static_cast<escript::DataTypes::real_t>(0)).data();
double* y_dp = y.getExpandedVectorReference(static_cast<escript::DataTypes::real_t>(0)).data();
MatrixVector(1., x_dp, 1., y_dp);
}
//Draw the line to the XPM file.
//This applies the 2D transformations specified in the command-line inputs
//and applies Cohen-Sutherland to clip the lines to the world window.
//This includes an implementation of Bresenham's line-drawing algorithm.
void Line::execute(XPMData *thefile)
{
//Create the composite transformation matrix
//from the command-line inputs.
CreateTransformationMatrix(thefile);
// With the matrix, we can transform both endpoints of the line
double VectorToTransform[3];
double TransformedVector1[3];
double TransformedVector2[3];
VectorToTransform[0] = x1;
VectorToTransform[1] = y1;
VectorToTransform[2] = 1;
MatrixVector(TransformedVector1, TransformationMatrix, VectorToTransform);
x1 = TransformedVector1[0];
y1 = TransformedVector1[1];
VectorToTransform[0] = x2;
VectorToTransform[1] = y2;
VectorToTransform[2] = 1;
MatrixVector(TransformedVector2, TransformationMatrix, VectorToTransform);
x2 = TransformedVector2[0];
y2 = TransformedVector2[1];
// Clip to world window, do not draw anything if length = 0
if (!Clip(thefile->getCmdLine()->getlowX(), thefile->getCmdLine()->getupperX(),
thefile->getCmdLine()->getlowY(), thefile->getCmdLine()->getupperY()))
return;
// Now everything is clipped and transformed. Let's draw the line.
// First, we need to handle vertical lines (they have an undefined slope)
if ((x2-x1) == 0)
{
if (y2 > y1)
{
for(int y = y1; y <= y2; y++)
{
thefile->plot(x1, y);
}
}
else
{
for(int y = y2; y <= y1; y++)
{
thefile->plot(x1, y);
}
}
return;
}
// Bresnehan's algorithm should handle everything else.
double slope = fabs(y2 - y1) / fabs(x2-x1);
if (slope > 1)
{
//for steep lines, we can reflect to get a lesser slope
int temp = x1;
x1 = y1;
y1 = temp;
temp = x2;
x2 = y2;
y2 = temp;
}
if (x1 > x2)
{
// we can swap the points and still get the same line
// this is done to help generalize the algorithm
int temp = x1;
x1 = x2;
x2 = temp;
temp = y1;
y1 = y2;
y2 = temp;
}
int dx = x2 - x1;
int dy = abs(y2 - y1);
int D = dx/2;
int y = y1;
for (int x = x1; x <= x2; x++)
{
if (slope > 1)
{
thefile->plot(y, x);
}
else thefile->plot(x, y);
D = D - dy;
if (D < 0)
{
if (y1 < y2) y++;
else y--;
D += dx;
}
}
}
