public void TestSolveOverdetermined()
{
// Load matrix from a file.
var A = ResourceLoader.Get <double>("general-40x20.mat");
int m = A.RowCount;
int n = A.ColumnCount;
Assert.IsTrue(m > n);
// Create test data.
var x = Helper.CreateTestVector(n);
var b = Helper.Multiply(A, x);
var r = Vector.Clone(b);
var qr = SparseQR.Create(A, ColumnOrdering.MinimumDegreeAtA);
// Compute min norm(Ax - b).
qr.Solve(b, x);
// Compute residual r = b - Ax.
A.Multiply(-1.0, x, 1.0, r);
Assert.IsTrue(Vector.Norm(r) < EPS);
}
private static void QrTest()
{
var coord = new CoordinateStorage <double>(7, 7, 1);
coord.At(0, 2, 1);
coord.At(0, 3, 1);
coord.At(0, 4, 3);
coord.At(0, 6, 2);
coord.At(1, 2, 2);
coord.At(1, 3, 6);
coord.At(1, 4, 1);
coord.At(1, 6, 5);
coord.At(2, 2, 3);
coord.At(2, 3, 7);
coord.At(2, 4, 4);
coord.At(2, 6, 7);
var ccs = coord.ToCCs();
var qr = SparseQR.Create(ccs, ColumnOrdering.Natural);
//var r = GetFactorR(qr, "R").ToDenseMatrix();
//var q = GetFactorR(qr, "Q").ToDenseMatrix();
//var t = (q * r.Transpose());
}
public void TestSolveUnderdetermined()
{
// Load matrix from a file.
var A = ResourceLoader.Get <double>("general-20x40.mat");
int m = A.RowCount;
int n = A.ColumnCount;
Assert.IsTrue(m < n);
// Create test data.
var x = Helper.CreateTestVector(n);
var b = Helper.Multiply(A, x);
var r = Vector.Clone(b);
var qr = SparseQR.Create(A, ColumnOrdering.MinimumDegreeAtA);
// Assuming A has full rank m, we have N(A) = n - m degrees of freedom.
// Compute solution x with min norm(Ax - b).
qr.Solve(b, x);
// Compute residuals.
A.Multiply(-1.0, x, 1.0, r);
Assert.IsTrue(Vector.Norm(r) < EPS);
}
public static Vector SolveQR(CompressedColumnStorage <double> A, Vector x, Vector b, out bool status, out string algorithm)
{
var orderings = new[] { CSparse.ColumnOrdering.MinimumDegreeAtA, CSparse.ColumnOrdering.MinimumDegreeAtPlusA, CSparse.ColumnOrdering.MinimumDegreeStS, CSparse.ColumnOrdering.Natural };
status = false;
algorithm = "QR";
foreach (var ordering in orderings)
{
try
{
if (A.RowCount == A.ColumnCount)
{
var qr = new SparseQR(A, ordering);
var xc = x.Clone();
var bc = b.Clone();
qr.Solve(bc.ToDouble(), xc.ToDouble());
algorithm = "QR/" + ordering;
status = true;
return(xc);
}
}
catch (Exception e)
{
status = false;
}
}
return(x);
}
public void TestSolveTranspose()
{
// Load matrix from a file.
var A = ResourceLoader.Get <Complex>("general-40x40.mat");
Assert.AreEqual(A.RowCount, A.ColumnCount);
var AT = A.Transpose();
// Create test data.
var x = Helper.CreateTestVector(A.ColumnCount);
var b = Helper.Multiply(AT, x);
var r = Vector.Clone(b);
// Create LU factorization.
var qr = SparseQR.Create(A, ColumnOrdering.MinimumDegreeAtA);
// Solve A'x = b.
qr.SolveTranspose(b, x);
// Compute residual r = b - A'x.
AT.Multiply(-1.0, x, 1.0, r);
Assert.IsTrue(Vector.Norm(r.Length, r) < EPS);
}
public void TestEmptyFactorize(int rows, int columns)
{
var A = new SparseMatrix(rows, columns, 0);
var qr = SparseQR.Create(A, ColumnOrdering.MinimumDegreeAtA);
Assert.NotNull(qr);
Assert.IsTrue(qr.NonZerosCount == -rows);
}
public void TestSolve()
{
// Load matrix from a file.
var A = ResourceLoader.Get <double>("general-40x40.mat");
Assert.AreEqual(A.RowCount, A.ColumnCount);
// Create test data.
var x = Helper.CreateTestVector(A.ColumnCount);
var b = Helper.Multiply(A, x);
var r = Vector.Clone(b);
var qr = SparseQR.Create(A, ColumnOrdering.MinimumDegreeAtA);
// Solve Ax = b.
qr.Solve(b, x);
// Compute residual r = b - Ax.
A.Multiply(-1.0, x, 1.0, r);
Assert.IsTrue(Vector.Norm(r) < EPS);
}
/// <inheritdoc />
public void Initialize()
{
var matrix = A;
var sp = new Stopwatch();
sp.Start();
qr =
SparseQR.Create(matrix, ColumnOrdering.MinimumDegreeAtPlusA);
IsInitialized = true;
sp.Stop();
if (Target != null)
{
Target.Trace.Write(TraceRecord.Create(BriefFiniteElementNet.Common.TraceLevel.Info,
string.Format(CultureInfo.CurrentCulture, "QR decomposition of matrix took about {0:#,##0} ms",
sp.ElapsedMilliseconds)));
}
}
public void TestSolveTransposeUnderdetermined()
{
// Load matrix from a file.
var A = ResourceLoader.Get <double>("general-20x40.mat");
Assert.IsTrue(A.RowCount < A.ColumnCount);
var AT = A.Transpose();
// Create test data.
var x = Helper.CreateTestVector(A.RowCount);
var b = Helper.Multiply(AT, x);
var r = Vector.Clone(b);
var qr = SparseQR.Create(A, ColumnOrdering.MinimumDegreeAtA);
qr.SolveTranspose(b, x);
// Compute residuals.
AT.Multiply(-1.0, x, 1.0, r);
Assert.IsTrue(Vector.Norm(r.Length, r) < EPS);
}
SymbolicFactorization GetSymbolicFactorization(SparseQR qr)
{
var info = typeof(SparseQR).GetField("S", BindingFlags.Instance | BindingFlags.NonPublic);
return(info.GetValue(qr) as SymbolicFactorization);
}
CompressedColumnStorage <double> GetFactorQ(SparseQR qr)
{
var info = typeof(SparseQR).GetField("Q", BindingFlags.Instance | BindingFlags.NonPublic);
return(info.GetValue(qr) as CompressedColumnStorage <double>);
}
public Tuple <SparseMatrix, double[]> CalculateDisplacementPermutation(SparseMatrix a)
{
if (a.RowCount < a.ColumnCount)
{
// See https://github.com/wo80/CSparse.NET/issues/7#issuecomment-317268696
//
// For a matrix A with rows < columns, SparseQR does a factorization of the
// transpose A' so we add zero rows to A and make it square!
//
// Since the matrix entries are in column order, reshaping is just a matter of
// setting the correct row count and then reusing the existing storage arrays.
a = new SparseMatrix(a.ColumnCount, a.ColumnCount, a.Values, a.RowIndices, a.ColumnPointers);
}
SparseMatrix buf;
var n = a.RowCount;
var m = a.ColumnCount;
var order = ColumnOrdering.Natural;
var sp = System.Diagnostics.Stopwatch.StartNew();
var qr = SparseQR.Create(a, order);
var t2 = sp.ElapsedMilliseconds;
var r = GetFactorR(qr);
var q = GetFactorQ(qr);
var s = GetSymbolicFactorization(qr);
var leads = new int[a.RowCount];
leads.FillWith(-1);
//leads[i] = columnIndex of first nonzero in i'th row of r fasctor
//if leads[i] == -1, then there is no nonzero in row[i] then i'th equation in original a matrix in non usable
//this will be used for rdep and rindep
var epsilon = 1e-8;
foreach (var r_item in r.EnumerateIndexed())
{
var rowNum = r_item.Item1;
var colNum = r_item.Item2;
var val = r_item.Item3;
/*
* if (Math.Abs(val) <= epsilon)
* ;//then row at
*/
if (Math.Abs(val) > epsilon) //Then, if abs(R[i, i]) > tol, you found an independent row
//Make sure to take row permutations into account (again, you can get the SymbolicFactorization containing row and column permutations using reflection)
{
if (leads[rowNum] == -1)
{
leads[rowNum] = colNum;
}
else
{
leads[rowNum] = Math.Min(leads[rowNum], colNum);
}
}
}
//throw new NotImplementedException("above section not right");
var leadCount = leads.Count(i => i != -1);
{
var nnzApprox = leadCount;
var p1Crd = new CoordinateStorage <double>(leadCount, r.RowCount, nnzApprox);
var p2Crd = new CoordinateStorage <double>(r.ColumnCount, leadCount, nnzApprox);
var p2pCrd = new CoordinateStorage <double>(r.ColumnCount, r.ColumnCount - leadCount, nnzApprox);
var cnt1 = 0;
var cnt2 = 0;
for (var i = 0; i < leads.Length; i++)
{
if (leads[i] != -1)
{
var j = leads[i];
p1Crd.At(cnt1, i, 1);
p2Crd.At(j, cnt1, 1);
cnt1++;
}
if (leads[i] == -1)
{
var j = i;// leads[i];
p2pCrd.At(j, cnt2, 1);
cnt2++;
}
}
var p1 = p1Crd.ToCCs();
var p2 = p2Crd.ToCCs();
var p2p = p2pCrd.ToCCs();
//var rp = r.Transpose();
var rdep = p1.Multiply(r).Multiply(p2);
var rinDep = p1.Multiply(r).Multiply(p2p);
var qr2 = SparseQR.Create(rdep, order);
var t = sp.ElapsedMilliseconds;
var right = new double[rinDep.RowCount];
var sol = new double[rinDep.RowCount];
var bufCrd = new CoordinateStorage <double>(leadCount, a.ColumnCount - leadCount, leadCount);
for (var j = 0; j < rinDep.ColumnCount; j++)
{
//put the j'th column of r into the rightSide
right.FillWith(0);
{
var col = j;
var st = rinDep.ColumnPointers[j];
var end = rinDep.ColumnPointers[j + 1];
for (var ii = st; ii < end; ii++)
{
var row = rinDep.RowIndices[ii];
var val = rinDep.Values[ii];
right[row] = val;
}
}
qr2.Solve(right, sol);
for (var i = 0; i < rdep.RowCount; i++)
{
bufCrd.At(i, j, sol[i]);
}
}
buf = bufCrd.ToCCs();
}
//var top = buf.ToDenseMatrix();
var buft = buf.Transpose();
var masterCount = a.ColumnCount - 1 - leadCount;
//var p_d_dense = new Matrix(a.ColumnCount - 1, masterCount);
var p_d = new CoordinateStorage <double>(a.ColumnCount - 1, masterCount, 1);
var rightSideDense = new double[a.ColumnCount - 1];
var rightSide = new double[a.ColumnCount - 1];
var cnt = 0;
var cnt3 = 0;
for (var i = 0; i < a.ColumnCount - 1; i++)
{
if (leads[i] != -1)
{
/*{//dense
* var rw = top.ExtractRow(cnt).CoreArray;
*
* var right = rw.Last();
* Array.Resize(ref rw, rw.Length - 1);
*
* for (var j = 0; j < rw.Length; j++)
* {
* p_d_dense[i, j] = -rw[j];
* }
*
* rightSideDense[i] = -right;
* }*/
{//sparse
var right = 0.0;
//var rowNum = s.pinv[i];
foreach (var t in buft.EnumerateColumnMembers(cnt))//enumerate column members of transposed matrix
{
var rowNum = i;
var colNum = t.Item1;
//var colNum = s.q[t.Item1];
var value = t.Item2;
if (t.Item1 != p_d.ColumnCount)
{
p_d.At(rowNum, colNum, -value);
}
else
{
right = value;
}
}
//rightSide[s.cp[i]] = -right;
rightSide[i] = -right;
}
cnt++;
}
else
{
var t = cnt3++;
var rowNum = i; // s.pinv[ i];
var colNum = t; // s.q[ t];
p_d.At(rowNum, colNum, 1);
}
}
//var top2 = p_d_dense;//.ToDenseMatrix();
//var top3 = p_d.ToCCs().ToDenseMatrix();
//var d = (top2 - top3);
//var d2 = rightSide.Plus(rightSideDense, -1);
var pdd = p_d.ToCCs();
return(Tuple.Create(pdd, rightSide));
var tol = 1e-6;
throw new NotImplementedException();
}
public Tuple <CCS, double[]> CalculateDisplacementPermutation(CCS a)
{
//based on this solution : https://github.com/wo80/CSparse.NET/issues/7#issuecomment-317268696
if (a.RowCount < a.ColumnCount)
{
//For a matrix A with rows < columns, SparseQR does a factorization of the transpose A'
//so we add zero rows to A and make it rectangular!
var a2 = new CoordinateStorage <double>(a.ColumnCount, a.ColumnCount, a.NonZerosCount);
foreach (var t in a.EnumerateIndexed())
{
a2.At(t.Item1, t.Item2, t.Item3);
}
a = a2.ToCCs();
}
SparseMatrix buf;
var n = a.RowCount;
var m = a.ColumnCount;
var order = ColumnOrdering.MinimumDegreeAtA;
var sp = System.Diagnostics.Stopwatch.StartNew();
var qr = SparseQR.Create(a, order);
var t2 = sp.ElapsedMilliseconds;
var r = GetFactorR(qr);
var q = GetFactorQ(qr);
var leads = new int[a.RowCount];
leads.FillWith(-1);
var epsilon = 1e-8;
foreach (var t in r.EnumerateIndexed())
{
if (Math.Abs(t.Item3) > epsilon)
{
if (leads[t.Item1] == -1)
{
leads[t.Item1] = t.Item2;
}
else
{
leads[t.Item1] = Math.Min(leads[t.Item1], t.Item2);
}
}
}
var leadCount = leads.Count(i => i != -1);
{
var nnzApprox = leadCount;
var p1Crd = new CoordinateStorage <double>(leadCount, r.RowCount, nnzApprox);
var p2Crd = new CoordinateStorage <double>(r.ColumnCount, leadCount, nnzApprox);
var p2pCrd = new CoordinateStorage <double>(r.ColumnCount, r.ColumnCount - leadCount, nnzApprox);
var cnt1 = 0;
var cnt2 = 0;
for (var i = 0; i < leads.Length; i++)
{
if (leads[i] != -1)
{
var j = leads[i];
p1Crd.At(cnt1, i, 1);
p2Crd.At(j, cnt1, 1);
cnt1++;
}
if (leads[i] == -1)
{
var j = i;// leads[i];
p2pCrd.At(j, cnt2, 1);
cnt2++;
}
}
var p1 = p1Crd.ToCCs();
var p2 = p2Crd.ToCCs();
var p2p = p2pCrd.ToCCs();
//var rp = r.Transpose();
var rdep = p1.Multiply(r).Multiply(p2);
var rinDep = p1.Multiply(r).Multiply(p2p);
var qr2 = SparseQR.Create(rdep, order);
var t = sp.ElapsedMilliseconds;
var right = new double[rinDep.RowCount];
var sol = new double[rinDep.RowCount];
var bufCrd = new CoordinateStorage <double>(leadCount, a.ColumnCount - leadCount, leadCount);
for (var j = 0; j < rinDep.ColumnCount; j++)
{
//put the j'th column of r into the rightSide
right.FillWith(0);
{
var col = j;
var st = rinDep.ColumnPointers[j];
var end = rinDep.ColumnPointers[j + 1];
for (var ii = st; ii < end; ii++)
{
var row = rinDep.RowIndices[ii];
var val = rinDep.Values[ii];
right[row] = val;
}
}
qr2.Solve(right, sol);
for (var i = 0; i < rdep.RowCount; i++)
{
bufCrd.At(i, j, sol[i]);
}
}
buf = bufCrd.ToCCs();
}
//var top = buf.ToDenseMatrix();
var buft = buf.Transpose();
var masterCount = a.ColumnCount - 1 - leadCount;
//var p_d_dense = new Matrix(a.ColumnCount - 1, masterCount);
var p_d = new CoordinateStorage <double>(a.ColumnCount - 1, masterCount, 1);
var rightSideDense = new double[a.ColumnCount - 1];
var rightSide = new double[a.ColumnCount - 1];
var cnt = 0;
var cnt3 = 0;
for (var i = 0; i < a.ColumnCount - 1; i++)
{
if (leads[i] != -1)
{
/*{//dense
* var rw = top.ExtractRow(cnt).CoreArray;
*
* var right = rw.Last();
* Array.Resize(ref rw, rw.Length - 1);
*
* for (var j = 0; j < rw.Length; j++)
* {
* p_d_dense[i, j] = -rw[j];
* }
*
* rightSideDense[i] = -right;
* }*/
{//sparse
var right = 0.0;
foreach (var t in buft.EnumerateColumnMembers(cnt))//enumerate column members of transposed matrix
{
if (t.Item1 != p_d.ColumnCount)
{
p_d.At(i, t.Item1, -t.Item2);
}
else
{
right = t.Item2;
}
}
rightSide[i] = -right;
}
cnt++;
}
else
{
{
var t = cnt3++;
//p_d_dense[i, t] = 1;
p_d.At(i, t, 1);
}
}
}
//var top2 = p_d_dense;//.ToDenseMatrix();
//var top3 = p_d.ToCCs().ToDenseMatrix();
//var d = (top2 - top3);
//var d2 = rightSide.Plus(rightSideDense, -1);
var pdd = (CCS)p_d.ToCCs();
return(Tuple.Create(pdd, rightSide));
var tol = 1e-6;
throw new NotImplementedException();
}
public DisposableSparseQR(SparseMatrix matrix)
{
qr = SparseQR.Create(matrix, ColumnOrdering.MinimumDegreeAtA);
}
public static object GetFactorR(SparseQR qr, string field)
{
var info = typeof(SparseQR).GetField(field, BindingFlags.Instance | BindingFlags.NonPublic);
return(info.GetValue(qr));// as CompressedColumnStorage<double>;
}
