public static CompressedColumnStorage <T> Get <T>(string resource)
where T : struct, IEquatable <T>, IFormattable
{
try
{
string type = (typeof(T) == typeof(double)) ? "Double" : "Complex";
string path = NS.Replace("{Type}", type) + "." + resource;
object obj;
if (cache.TryGetValue(path, out obj))
{
return((CompressedColumnStorage <T>)obj);
}
var stream = Assembly.GetExecutingAssembly().GetManifestResourceStream(path);
var matrix = MatrixMarketReader.ReadMatrix <T>(stream);
cache.Add(path, matrix);
return(matrix);
}
catch (Exception e)
{
throw e;
}
}
public void CanReadSparseHermitianComplexMatrix()
{
var sb = new StringBuilder();
sb.AppendLine("%%MatrixMarket matrix coordinate complex hermitian");
sb.AppendLine("5 5 7");
sb.AppendLine("1 1 1.0 0");
sb.AppendLine("2 2 10.5 0");
sb.AppendLine("4 2 250.5 22.22");
sb.AppendLine("3 3 1.5e-2 0");
sb.AppendLine("4 4 -2.8e2 0.0");
sb.AppendLine("5 5 12. 0.");
sb.AppendLine("5 4 0 33.32");
var m = MatrixMarketReader.ReadMatrix <Complex>(new StringReader(sb.ToString()));
Assert.IsInstanceOf <LinearAlgebra.Complex.SparseMatrix>(m);
Assert.AreEqual(5, m.RowCount);
Assert.AreEqual(5, m.ColumnCount);
Assert.AreEqual(9, ((LinearAlgebra.Complex.SparseMatrix)m).NonZerosCount);
Assert.AreEqual(1.0d, m[0, 0].Real);
Assert.AreEqual(10.5d, m[1, 1].Real);
Assert.AreEqual(250.5d, m[3, 1].Real);
Assert.AreEqual(22.22d, m[3, 1].Imaginary);
Assert.AreEqual(-22.22d, m[1, 3].Imaginary);
Assert.AreEqual(-280d, m[3, 3].Real);
Assert.AreEqual(0d, m[4, 3].Real);
Assert.AreEqual(33.32d, m[4, 3].Imaginary);
Assert.AreEqual(-33.32d, m[3, 4].Imaginary);
}
public void CanReadDenseSkewSymmetricMatrix()
{
/* 0 1 2 3
* 1 0 6 7
* 2 6 0 11
* 3 7 11 0 */
var sb = new StringBuilder();
sb.AppendLine("%%MatrixMarket matrix array integer skew-symmetric");
sb.AppendLine("4 4");
sb.Append("1\n2\n3\n6\n7\n11");
var m = MatrixMarketReader.ReadMatrix <double>(new StringReader(sb.ToString()));
Assert.IsInstanceOf <LinearAlgebra.Double.DenseMatrix>(m);
Assert.AreEqual(4, m.RowCount);
Assert.AreEqual(4, m.ColumnCount);
Assert.AreEqual(0.0, m.Diagonal().InfinityNorm());
Assert.AreEqual(0d, m[0, 0]);
Assert.AreEqual(1d, m[1, 0]);
Assert.AreEqual(1d, m[0, 1]);
Assert.AreEqual(7d, m[3, 1]);
Assert.AreEqual(7d, m[1, 3]);
}
public void MatrixMarketReaderReadSameVectorsAsMatrixMarketWriterWrited()
{
// arrange
const int rows = 100;
const int columns = 100;
const double density = 0.01;
var originalVectors = SparseVectorHelper.GenerateSparseVectors(rows, columns, density, () => SparseVectorHelper.RandomInInterval(-100, 100, 2)).ToArray();
// act
// write
byte[] memory;
int rowsWrited;
int columnsWrited;
long elementsWrited;
using (var stream = new MemoryStream())
using (var writer = new MatrixMarketWriter <double>(stream))
{
writer.Write(originalVectors);
stream.Flush();
memory = stream.ToArray();
rowsWrited = writer.RowsCount;
columnsWrited = writer.ColumnsCount;
elementsWrited = writer.ElementsCount;
}
// read
SparseVector <double>[] readedVectors;
int rowsToRead;
int columnsToRead;
long elementToRead;
using (var stream = new MemoryStream(memory, false))
using (var reader = new MatrixMarketReader <double>(stream))
{
rowsToRead = reader.RowsCount;
columnsToRead = reader.ColumnsCount;
elementToRead = reader.ElementsCount;
readedVectors = reader.ReadRows().ToArray();
}
string text;
using (var stream = new MemoryStream(memory, false))
using (var reader = new StreamReader(stream))
{
text = reader.ReadToEnd();
}
// assert
Assert.AreEqual(rowsWrited, rowsToRead, string.Format("Rows count does not equal:\r\n{0}", text));
Assert.AreEqual(columnsWrited, columnsToRead, string.Format("Columns count does not equal:\r\n{0}", text));
Assert.AreEqual(elementsWrited, elementToRead, string.Format("Elements count does not equal:\r\n{0}", text));
Assert.IsTrue(originalVectors.SequenceEqual(readedVectors), string.Format("Vectors do not equal:\r\n{0}", text));
}
public void MatrixMarketReaderReadSameVectorsAsMatrixMarketWriterWrited()
{
// arrange
const int rows = 100;
const int columns = 100;
const double density = 0.01;
var originalVectors = SparseVectorHelper.GenerateSparseVectors(rows, columns, density, () => SparseVectorHelper.RandomInInterval(-100, 100, 2)).ToArray();
// act
// write
byte[] memory;
int rowsWrited;
int columnsWrited;
long elementsWrited;
using (var stream = new MemoryStream())
using (var writer = new MatrixMarketWriter<double>(stream))
{
writer.Write(originalVectors);
stream.Flush();
memory = stream.ToArray();
rowsWrited = writer.RowsCount;
columnsWrited = writer.ColumnsCount;
elementsWrited = writer.ElementsCount;
}
// read
SparseVector<double>[] readedVectors;
int rowsToRead;
int columnsToRead;
long elementToRead;
using (var stream = new MemoryStream(memory, false))
using (var reader = new MatrixMarketReader<double>(stream))
{
rowsToRead = reader.RowsCount;
columnsToRead = reader.ColumnsCount;
elementToRead = reader.ElementsCount;
readedVectors = reader.ReadRows().ToArray();
}
string text;
using (var stream = new MemoryStream(memory, false))
using (var reader = new StreamReader(stream))
{
text = reader.ReadToEnd();
}
// assert
Assert.AreEqual(rowsWrited, rowsToRead, string.Format("Rows count does not equal:\r\n{0}", text));
Assert.AreEqual(columnsWrited, columnsToRead, string.Format("Columns count does not equal:\r\n{0}", text));
Assert.AreEqual(elementsWrited, elementToRead, string.Format("Elements count does not equal:\r\n{0}", text));
Assert.IsTrue(originalVectors.SequenceEqual(readedVectors), string.Format("Vectors do not equal:\r\n{0}", text));
}
public void CanReadFudao007AsSingle()
{
var m = MatrixMarketReader.ReadMatrix <float>("./data/MatrixMarket/fidap007.mtx");
Assert.IsInstanceOf <LinearAlgebra.Single.SparseMatrix>(m);
Assert.AreEqual(1633, m.RowCount);
Assert.AreEqual(1633, m.ColumnCount);
Assert.GreaterOrEqual(54487, ((LinearAlgebra.Single.SparseMatrix)m).NonZerosCount);
Assert.Less(46000, ((LinearAlgebra.Single.SparseMatrix)m).NonZerosCount);
Assert.AreEqual(-6.8596032449032e+06f, m[1604, 1631]);
Assert.AreEqual(-9.1914585107976e+06f, m[1616, 1628]);
Assert.AreEqual(7.9403870156486e+07f, m[905, 726]);
}
public void CanReadFudao007AsDouble()
{
using (Stream stream = TestData.Data.ReadStream("MatrixMarket.fidap007.mtx"))
{
var m = MatrixMarketReader.ReadMatrix <double>(stream);
Assert.IsInstanceOf <LinearAlgebra.Double.SparseMatrix>(m);
Assert.AreEqual(1633, m.RowCount);
Assert.AreEqual(1633, m.ColumnCount);
Assert.GreaterOrEqual(54487, ((LinearAlgebra.Double.SparseMatrix)m).NonZerosCount);
Assert.Less(46000, ((LinearAlgebra.Double.SparseMatrix)m).NonZerosCount);
Assert.AreEqual(-6.8596032449032e+06d, m[1604, 1631]);
Assert.AreEqual(-9.1914585107976e+06d, m[1616, 1628]);
Assert.AreEqual(7.9403870156486e+07d, m[905, 726]);
}
}
public void Should_solve_tridiagonal_matrix_system()
{
var a = MatrixMarketReader.ReadMatrix <double>("matrix1.mtx");
var b = MatrixMarketReader.ReadVector <double>("vector1.mtx");
var result = GmresSolver.Solve(a, b, 15, 1);
result.IsConverged.Should().BeTrue();
result.OuterIterations.Should().Be(0);
result.InnerIterations.Should().Be(11);
foreach (var xValue in result.X)
{
xValue.Should().BeApproximately(1.0, GmresSolver.DefaultEpsilon);
}
}
public void TestSymmetric()
{
var stream = ResourceLoader.GetStream("LFAT5.mtx", "Double");
using (var reader = new StreamReader(stream))
{
var A = MatrixMarketReader.ReadStorage <double>(reader);
Assert.AreEqual(A.RowCount, 14);
Assert.AreEqual(A.ColumnCount, 14);
// Symmetric mtx file has 30 entries -> auto expand = 2 * 30 - 14 = 46.
Assert.AreEqual(A.NonZerosCount, 46);
}
}
public void TestPatternSymmetric()
{
var stream = ResourceLoader.GetStream("bcspwr01.mtx", "Double");
using (var reader = new StreamReader(stream))
{
var A = MatrixMarketReader.ReadStorage <double>(reader, false);
Assert.AreEqual(A.RowCount, 39);
Assert.AreEqual(A.ColumnCount, 39);
// Symmetric mtx file has 85 entries, no auto expand.
Assert.AreEqual(A.NonZerosCount, 85);
}
}
public static void Main()
{
//create the MatrixMarketReader
SingleMatrixReader reader = new MatrixMarketReader();
//create a matrix from a Matrix Market text file by passing the
//reader the name/path of the file
Matrix matrix = reader.ReadMatrix("somefile.mtx", StorageType.Dense);
//create a matrix from a Matrix Market text file by passing the
//reader the file stream. the stream could have been any type
//of stream that contains the matrix data.
using (Stream stream = File.Open("somefile.mtx", FileMode.Open, FileAccess.Read, FileShare.Read))
{
matrix = reader.ReadMatrix(stream, StorageType.Dense);
}
}
public void Should_solve_dense_matrix_system()
{
var a = MatrixMarketReader.ReadMatrix <double>("matrix2.mtx");
var b = MatrixMarketReader.ReadVector <double>("vector2.mtx");
var result = GmresSolver.Solve(a, b);
result.IsConverged.Should().BeTrue();
result.OuterIterations.Should().Be(0);
result.InnerIterations.Should().Be(6);
var expectedX = new[] { -4.0306249, 3.3608880, 3.8133424, -1.0654047, 3.4175426, -2.0298796 };
for (var i = 0; i < expectedX.Length; i++)
{
result.X[i].Should().BeApproximately(expectedX[i], GmresSolver.DefaultEpsilon);
}
}
public int Preload <T>() where T : struct, IEquatable <T>, IFormattable
{
int count = 0;
foreach (var item in generalList)
{
item.Matrix = MatrixMarketReader.ReadMatrix <T>(item.Path);
count++;
}
foreach (var item in symmetricList)
{
item.Matrix = MatrixMarketReader.ReadMatrix <T>(item.Path);
count++;
}
return(count);
}
public void CanReadFudao007AsComplex32()
{
using (TextReader reader = TestData.Data.ReadText("MatrixMarket.fidap007.mtx"))
{
var m = MatrixMarketReader.ReadMatrix <Complex32>(reader);
Assert.IsInstanceOf <LinearAlgebra.Complex32.SparseMatrix>(m);
Assert.AreEqual(1633, m.RowCount);
Assert.AreEqual(1633, m.ColumnCount);
Assert.GreaterOrEqual(54487, ((LinearAlgebra.Complex32.SparseMatrix)m).NonZerosCount);
Assert.Less(46000, ((LinearAlgebra.Complex32.SparseMatrix)m).NonZerosCount);
Assert.AreEqual(-6.8596032449032e+06f, m[1604, 1631].Real);
Assert.AreEqual(0.0f, m[1604, 1631].Imaginary);
Assert.AreEqual(-9.1914585107976e+06f, m[1616, 1628].Real);
Assert.AreEqual(0.0f, m[1616, 1628].Imaginary);
Assert.AreEqual(7.9403870156486e+07f, m[905, 726].Real);
Assert.AreEqual(0.0f, m[905, 726].Imaginary);
}
}
private void Run(MatrixFile file, Stopwatch timer, List <BenchmarkResult> results)
{
string name = Path.GetFileName(file.Path);
if (!File.Exists(file.Path))
{
results.Add(new BenchmarkResult(file, "File not found."));
return;
}
try
{
var A = (CompressedColumnStorage <T>)file.Matrix;
if (A == null)
{
A = MatrixMarketReader.ReadMatrix <T>(file.Path);
}
int columns = A.ColumnCount;
var x = CreateTestVector(columns);
var s = CreateTestVector(columns);
var b = new T[A.RowCount];
A.Multiply(x, b);
Array.Clear(x, 0, columns);
var info = new BenchmarkResult(file, A.RowCount, columns, GetNonZerosCount(A));
info.Time = Solve(A, b, x, file.Symmetric, timer);
info.Residual = ComputeError(x, s);
results.Add(info);
}
catch (Exception e)
{
results.Add(new BenchmarkResult(file, e.Message));
}
}
static void Main(string[] args)
{
const string matrixFileName = @"c:\temp\matrix.txt";
const int rows = 10000;
const int columns = 1000;
const double density = 0.01;
const int featuresCount = 10;
const int iterationsCount = 30;
Console.WriteLine("Generating matrix {0}x{1} with avg. {2} non-zero elements ({3}%)...", rows, columns, (long)((double)rows * columns * density), density * 100.0);
using (var file = new FileStream(matrixFileName, FileMode.Create))
using (var mmwriter = new MatrixMarketWriter <double>(file))
{
var vectors = SparseVectorHelper.GenerateSparseVectors(rows, columns, density, () => SparseVectorHelper.RandomInInterval(0.01, 100, 2));
mmwriter.Write(vectors);
}
Console.WriteLine("Matrix factorization (features=" + featuresCount + ", iterations=" + iterationsCount + ")...");
using (var file = new FileStream(matrixFileName, FileMode.Open))
using (var mmreader = new MatrixMarketReader <double>(file))
using (var cachedReader = new CachedMatrixMarketReader <double>(mmreader))
{
var nmf = new NMF(cachedReader);
// act
var sw = Stopwatch.StartNew();
using (var factorization = nmf.Factorize(featuresCount, iterationsCount))
{
sw.Stop();
Console.WriteLine("Factorization time: " + sw.ElapsedMilliseconds + " ms.");
Console.WriteLine("Euclidean distance calculation...");
sw = Stopwatch.StartNew();
var euclideanDistance = nmf.GetEuclideanDistance(factorization);
sw.Stop();
Console.WriteLine("Euclidean distance calculation time: " + sw.ElapsedMilliseconds + " ms.");
Console.WriteLine("Factorization Euclidean distance: " + euclideanDistance);
}
}
}
private static void TestNormalEquationsSolution()
{
// Load a regtangular matrix from a file.
string filePath = null;
var A = MatrixMarketReader.ReadMatrix <double>(filePath);
int m = A.RowCount;
int n = A.ColumnCount;
// Create test data.
var x = CSparse.Double.Vector.Create(n, 1.0);
var b = new double[m];
// Compute right hand side vector b.
A.Multiply(1.0, x, 0.0, b);
// Apply column ordering to A to reduce fill-in.
var order = ColumnOrdering.MinimumDegreeAtPlusA;
if (m > n)
{
var At = A.Transpose();
var AtA = At.Multiply(A);
var c = CSparse.Double.Vector.Create(n, 0.0);
At.Multiply(b, c);
var chol = SparseCholesky.Create(AtA, order);
// Solve normal equation A'Ax = A'b (overwrite x).
chol.Solve(c, x);
}
else
{
Assert.True(false);
}
// Compute residual b - Ax (overwrite b).
A.Multiply(-1.0, x, 1.0, b);
}
static void Main(string[] args)
{
const string matrixFileName = @"c:\temp\matrix.txt";
const int rows = 10000;
const int columns = 1000;
const double density = 0.01;
const int featuresCount = 10;
const int iterationsCount = 30;
Console.WriteLine("Generating matrix {0}x{1} with avg. {2} non-zero elements ({3}%)...", rows, columns, (long)((double)rows * columns * density), density * 100.0);
using (var file = new FileStream(matrixFileName, FileMode.Create))
using (var mmwriter = new MatrixMarketWriter<double>(file))
{
var vectors = SparseVectorHelper.GenerateSparseVectors(rows, columns, density, () => SparseVectorHelper.RandomInInterval(0.01, 100, 2));
mmwriter.Write(vectors);
}
Console.WriteLine("Matrix factorization (features=" + featuresCount + ", iterations=" + iterationsCount + ")...");
using (var file = new FileStream(matrixFileName, FileMode.Open))
using (var mmreader = new MatrixMarketReader<double>(file))
using (var cachedReader = new CachedMatrixMarketReader<double>(mmreader))
{
var nmf = new NMF(cachedReader);
// act
var sw = Stopwatch.StartNew();
using (var factorization = nmf.Factorize(featuresCount, iterationsCount))
{
sw.Stop();
Console.WriteLine("Factorization time: " + sw.ElapsedMilliseconds + " ms.");
Console.WriteLine("Euclidean distance calculation...");
sw = Stopwatch.StartNew();
var euclideanDistance = nmf.GetEuclideanDistance(factorization);
sw.Stop();
Console.WriteLine("Euclidean distance calculation time: " + sw.ElapsedMilliseconds + " ms.");
Console.WriteLine("Factorization Euclidean distance: " + euclideanDistance);
}
}
}
public void TestWriteSparseSymmetric()
{
var A = SparseMatrix.OfColumnMajor(3, 3, new double[]
{
1.0, 0.0, 0.5,
0.0, 2.0, 0.1,
0.5, 0.1, 3.0,
});
using (var stream = new MemoryStream(256))
using (var writer = new StreamWriter(stream, leaveOpen: true))
{
MatrixMarketWriter.WriteMatrix(writer, A, true);
stream.Position = 0;
var B = MatrixMarketReader.ReadMatrix <double>(stream);
Assert.IsTrue(A.Equals(B));
}
}
public static void Execute(Options options)
{
var stopwatch = new Stopwatch();
stopwatch.Start();
Console.WriteLine($"Reading from {options.InputMatrixFileName}...");
var a = MatrixMarketReader.ReadMatrix <double>(options.InputMatrixFileName);
Console.WriteLine($"Reading from {options.InputVectorFileName}...");
var b = MatrixMarketReader.ReadVector <double>(options.InputVectorFileName);
Console.WriteLine("Start solving...");
var result = GmresSolver.Solve(a, b, options.MaxInnerIterations, options.MaxOuterIterations, options.Epsilon, degreeOfParallelism: options.DegreeOfParallelism);
Console.WriteLine($"Finished. IsConverged = {result.IsConverged}. Last error: {result.Errors.Last()}");
Console.WriteLine($"Performed {result.InnerIterations} inner iterations and {result.OuterIterations} outer iterations");
Console.WriteLine($"Writing solution to {options.OutputFileName}...");
MatrixMarketWriter.WriteVector(options.OutputFileName, result.X);
Console.WriteLine($"Total execution time, ms: {stopwatch.Elapsed.TotalMilliseconds}");
}
public static void TestLinearSystemSolution()
{
// Load matrix from a file.
var A = MatrixMarketReader.ReadMatrix <double>(PosDefMatrixPath);
int m = A.RowCount;
int n = A.ColumnCount;
Assert.True(m == n);
// Create test data.
var xExpected = CSparse.Double.Vector.Create(n, 1.0);
var b = new double[m];
// Compute right hand side vector b.
A.Multiply(1.0, xExpected, 0.0, b);
// Apply column ordering to A to reduce fill-in.
var order = ColumnOrdering.MinimumDegreeAtPlusA;
// Factorize
var xComputed = new double[n];
var chol = SparseCholesky.Create(A, order);
// Solve Ax = b (do not overwrite x).
chol.Solve(b, xComputed);
// Check the solution
comparer.AssertEqual(xExpected, xComputed);
// Compute residual b - Ax (do not overwrite b).
var r = new double[m];
Array.Copy(b, r, m);
A.Multiply(-1.0, xComputed, 1.0, r);
}
public static IStorageAdapter LoadMatrix(string file)
{
var A = (SparseMatrix)MatrixMarketReader.ReadMatrix <Complex>(file);
return(new SparseStorageAdapter(A));
}
public static Matrix <double> createMatrixFromMatrixMarketFile(string path)
{
Matrix <double> matrix = Matrix <double> .Build.SparseOfMatrix(MatrixMarketReader.ReadMatrix <double>(path));
return(matrix);
}
