public static Matrix InverseAlt(Matrix matrix, ref Double timeS, ref double timeP)
{
if (!matrix.isSquare)
{
Exception e = new Exception("Matrix must be square!");
throw e;
}
benchmark bm = new benchmark();
bm.start();
int n = matrix.dim1;
Matrix result = Matrix.zeroLike(matrix);
int[] perm;
int toggle;
Matrix lum = LUPDecompose(matrix, out perm, out toggle);
if (lum == null)
{
return(Matrix.zeroLike(matrix)); //throw new Exception("Unable to compute inverse");
}
Double det = Determinant(lum, perm, toggle);
if (det == 0) // not invertible
{
// still return for the sake of simplicity
// Zero matrix * any matrix = zero matrix
// so it's never a valid answer
return(Matrix.zeroLike(matrix));
}
bm.pause();
timeS += bm.getElapsedSeconds();
bm.start();
double[] b = new double[n];
for (int i = 0; i < n; ++i)
{
for (int j = 0; j < n; ++j)
{
if (i == perm[j])
{
b[j] = 1.0;
}
else
{
b[j] = 0.0;
}
}
double[] x = HelperSolve(lum, b);
for (int j = 0; j < n; ++j)
{
result[j, i] = x[j];
}
}
timeP += bm.getElapsedSeconds();
return(result);
}
static void Main(string[] _args)
{
string programName = "Gauss-Seidel Linear System of Equations Solver";
string programVer = "1.0 (sequential)";
string programAuthor = "Quy N.H.";
Console.WriteLine(programName + " v" + programVer + " by " + programAuthor + "\n");
bool testing = false;
string[] args = _args;
if (testing)
{
args = "-o output.txt -b 200 -t 10".Split(new char[] { ' ' });
}
// parse args
string inputFile = "", outputFile = "";
bool benchmarkMode = false, showEquation = false, generateInput = false, showBenchmark = false;
int benchmarkSize = 3;
int benchmarkTime = 1;
int i = 0;
while (i < args.Length)
{
string arg = args[i];
if (arg.StartsWith("--"))
{
arg = arg.Substring(2);
switch (arg)
{
case "input": if (i + 1 < args.Length)
{
inputFile = args[i + 1];
}
break;
case "output": if (i + 1 < args.Length)
{
outputFile = args[i + 1];
}
break;
case "show-equation": showEquation = true; break;
case "show-benchmark": showBenchmark = true; break;
case "generate-input": generateInput = true; break;
case "benchmark": if (i + 1 < args.Length && int.TryParse(args[i + 1], out benchmarkSize))
{
benchmarkMode = true; i++;
}
; break;
case "times": if (i + 1 < args.Length && int.TryParse(args[i + 1], out benchmarkTime))
{
benchmarkMode = true; i++;
}
; break;
}
}
else if (arg.StartsWith("-"))
{
arg = arg.Substring(1);
switch (arg)
{
case "i": if (i + 1 < args.Length)
{
inputFile = args[i + 1];
}
break;
case "o": if (i + 1 < args.Length)
{
outputFile = args[i + 1];
}
break;
case "e": showEquation = true; break;
case "m": showBenchmark = true; break;
case "g": generateInput = true; break;
case "b": if (i + 1 < args.Length && int.TryParse(args[i + 1], out benchmarkSize))
{
benchmarkMode = true; i++;
}
; break;
case "t": if (i + 1 < args.Length && int.TryParse(args[i + 1], out benchmarkTime))
{
benchmarkMode = true; i++;
}
; break;
}
}
i++;
}
// get input(s)
List <Matrix> As = new List <Matrix>(), bs = new List <Matrix>(), sols = new List <Matrix>(), xs = new List <Matrix>();
if (benchmarkMode)
{
// generate input
for (int j = 0; j < benchmarkTime; j++)
{
As.Add(Matrix.generateDiagonallyDominantMatrix(benchmarkSize, true, -100, 100));
bs.Add(Matrix.random(benchmarkSize, 1, -100, 100, true));
}
Console.WriteLine("Generated " + benchmarkTime.ToString() + " random system(s) to solve.");
}
else if (inputFile.Length > 0 && File.Exists(inputFile))
{
// parse input
string inputArray = File.ReadAllText(inputFile);
Utils.parseInput(inputArray, out As, out bs, out sols);
Console.WriteLine("Got " + As.Count.ToString() + " system(s) from input file.");
}
else
{
// yell at user
Console.WriteLine("Give me some inputs!");
Console.ReadKey();
Environment.Exit(1);
}
// do the calculation
List <bool> converges = new List <bool>();
List <int> loopses = new List <int>();
List <Matrix> errs = new List <Matrix>();
int equCounts = As.Count;
benchmark bm = new benchmark();
string bmResult = "";
Gauss_Seidel.showBenchmark = showBenchmark;
bm.start();
for (int j = 0; j < equCounts; j++)
{
Console.Write("Solving system #" + (j + 1).ToString() + "... ");
Matrix x, err;
int loops = 0;
bool converge = Gauss_Seidel.solve(As[j], bs[j], out x, out err, out loops);
xs.Add(x);
loopses.Add(loops);
converges.Add(converge);
errs.Add(err);
Console.WriteLine("Done.");
}
bmResult = bm.getResult();
// write output
if (!generateInput)
{
// show the result as usual
writeOutput(outputFile, "\n");
for (int j = 0; j < equCounts; j++)
{
Matrix x = xs[j], err = errs[j];
int loops = loopses[j];
bool converge = converges[j];
string strResult = "";
if (showEquation)
{
strResult += "\nEquation:\n" + Utils.writeEquation(As[j], bs[j]);
}
strResult += "\nNo. equations: " + x.Height.ToString();
strResult += "\nSolution: " + Matrix.Transpose(x).ToString(1e-14);
strResult += "\nErrors: " + Matrix.Transpose(err).ToString(1e-14);
strResult += "\nMean absolute error: " + string.Format("{0:0.##############}", Matrix.Abs(err).avgValue);
strResult += "\nConverged: " + converge.ToString();
strResult += "\nLoops: " + loops.ToString();
writeOutput(outputFile, strResult);
}
writeOutput(outputFile, "\nElapsed time: " + bmResult + " (" + string.Format("{0:0.###}", bm.getElapsedSeconds() / equCounts) + " sec / equation).");
writeOutput(outputFile, "");
}
else
{
// create a valid input file
for (int j = 0; j < equCounts; j++)
{
Matrix x = xs[j], err = errs[j];
int loops = loopses[j];
bool converge = converges[j];
string strResult = "\n-----------\n";
strResult += x.Height.ToString();
strResult += "\n";
strResult += As[j].ToString();
strResult += "\n";
strResult += Matrix.Transpose(bs[j]).ToString();
strResult += "\n";
strResult += Matrix.Transpose(x).ToString(1e-14);
strResult += "\n";
writeOutput(outputFile, strResult);
}
writeOutput("", "\nElapsed time: " + bmResult + " (" + string.Format("{0:0.###}", bm.getElapsedSeconds() / equCounts) + " sec / equation).");
writeOutput("", "");
}
Console.WriteLine("Done. Press a key to exit...");
Console.ReadKey();
}
// return true if it converges. Output: solution matrix, errors, loops it took
public static Boolean solve(Matrix A, Matrix b, out Matrix x, out Matrix err, out int loops)
{
// check sanity
if (!A.isSquare || !b.isColumn || (A.Height != b.Height))
{
Exception e = new Exception("Matrix A must be square! Matrix b must be a column matrix with the same height as matrix A!");
throw e;
}
// follow samples in Wikipedia step by step https://en.wikipedia.org/wiki/Gauss%E2%80%93Seidel_method
benchmark bm = new benchmark(), bm2 = new benchmark(), bm3 = new benchmark();
double sequential = 0, parallel = 0;
bm.start();
bm2.start();
// decompose A into the sum of a lower triangular component L* and a strict upper triangular component U
int size = A.Height;
Matrix L, U;
Matrix.Decompose(A, out L, out U);
sequential += bm2.getElapsedSeconds();
// Inverse matrix L*
Matrix L_1 = Matrix.InverseAlt(L, ref sequential, ref parallel);
// Main iteration: x (at step k+1) = T * x (at step k) + C
// where T = - (inverse of L*) * U, and C = (inverse of L*) * b
bm2.start();
// init necessary variables
x = Matrix.zeroLike(b); // at step k
Matrix new_x; // at step k + 1
sequential += bm2.getElapsedSeconds();
bm2.start();
Matrix T = -L_1 * U;
Matrix C = L_1 * b;
parallel += bm2.getElapsedSeconds();
// Console.WriteLine(T.ToString(0.00001));
// Console.WriteLine(C.ToString(0.00001));
// the actual iteration
// if it still doesn't converge after this many loops, assume it won't converge and give up
bm2.start();
loops = 0;
Boolean converge = false;
int loopLimit = 100;
sequential += bm2.getElapsedSeconds();
bm2.start();
for (; loops < loopLimit; loops++)
{
new_x = T * x + C; // yup, only one line
// Console.WriteLine("Loop #" + loops);
// Console.WriteLine(new_x.ToString(0.00001));
// consider it's converged if it changes less than threshold (1e-15)
if (converge = Matrix.AllClose(new_x, x, 1e-15))
{
x = new_x;
loops++;
break;
}
// save result
x = new_x;
}
parallel += bm2.getElapsedSeconds();
bm2.start();
// round the result slightly
x.Round(1e-14);
err = A * x - b;
err.Round(1e-14);
sequential += bm2.getElapsedSeconds();
bm.pause();
if (showBenchmark)
{
Console.WriteLine("Sequential part took " + sequential + " secs.");
Console.WriteLine("Parallel part took " + parallel + " secs.");
Console.WriteLine("Total: " + bm.getResult() + " (" + bm.getElapsedSeconds() + " secs). Seq + Parallel: " + (sequential + parallel));
}
return(converge);
}
