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Merge pull request #55 from hbadi/feature/numeric-refactorize
Add Refactorize() for numeric refactorization reusing the symbolic analysis
2 parents c736f87 + e08a79a commit 8898899

12 files changed

Lines changed: 344 additions & 0 deletions

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‎CSparse.Tests/Complex/Factorization/SparseCholeskyTest.cs‎

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@@ -54,5 +54,34 @@ public void TestEmptyFactorize()
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Assert.That(chol, Is.Not.Null);
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Assert.That(chol.NonZerosCount == 0, Is.True);
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}
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[Test]
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public void TestRefactorize()
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{
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var A = ResourceLoader.Get<Complex>("hermitian-40-spd.mat");
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var chol = SparseCholesky.Create(A, ColumnOrdering.MinimumDegreeAtPlusA);
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// Same sparsity pattern, different values (B = 2*A stays Hermitian SPD) :
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// the numeric refactorization must reuse the cached symbolic analysis.
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var B = A.Clone();
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var bv = B.Values;
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for (int i = 0; i < bv.Length; i++) bv[i] *= 2.0;
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chol.Refactorize(B);
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var x = Helper.CreateTestVector(B.ColumnCount);
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var b = Helper.Multiply(B, x);
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var r = Vector.Clone(b);
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chol.Solve(b, x);
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B.Multiply(-1.0, x, 1.0, r);
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Assert.That(Vector.Norm(r.Length, r) < EPS, Is.True);
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// Dimension guard.
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var small = new SparseMatrix(3, 3, 0);
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Assert.Throws<ArgumentException>(() => chol.Refactorize(small));
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}
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}
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}

‎CSparse.Tests/Complex/Factorization/SparseLDLTest.cs‎

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@@ -1,6 +1,7 @@
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namespace CSparse.Tests.Complex.Factorization
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{
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using System;
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using CSparse.Complex;
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using CSparse.Complex.Factorization;
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using NUnit.Framework;
@@ -54,5 +55,34 @@ public void TestSolveNonSpd()
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Assert.That(Vector.Norm(r.Length, r) < EPS, Is.True);
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}
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[Test]
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public void TestRefactorize()
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{
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var A = ResourceLoader.Get<Complex>("hermitian-40-spd.mat");
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var ldl = SparseLDL.Create(A, ColumnOrdering.MinimumDegreeAtPlusA);
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// Same sparsity pattern, different values (B = 2*A) : the numeric
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// refactorization must reuse the cached symbolic analysis.
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var B = A.Clone();
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var bv = B.Values;
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for (int i = 0; i < bv.Length; i++) bv[i] *= 2.0;
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ldl.Refactorize(B);
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var x = Helper.CreateTestVector(B.ColumnCount);
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var b = Helper.Multiply(B, x);
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var r = Vector.Clone(b);
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ldl.Solve(b, x);
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B.Multiply(-1.0, x, 1.0, r);
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Assert.That(Vector.Norm(r.Length, r) < EPS, Is.True);
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// Dimension guard.
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var small = new SparseMatrix(3, 3, 0);
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Assert.Throws<ArgumentException>(() => ldl.Refactorize(small));
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}
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}
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}

‎CSparse.Tests/Complex/Factorization/SparseLUTest.cs‎

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@@ -76,5 +76,34 @@ public void TestEmptyFactorize()
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Assert.That(lu, Is.Not.Null);
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Assert.That(lu.NonZerosCount == 0, Is.True);
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}
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[Test]
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public void TestRefactorize()
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{
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var A = ResourceLoader.Get<Complex>("general-40x40.mat");
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var lu = SparseLU.Create(A, ColumnOrdering.MinimumDegreeAtPlusA, 1.0);
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// Same sparsity pattern, different values (B = 2*A) : numeric refactorization
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// must reuse the cached symbolic ordering and still solve correctly.
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var B = A.Clone();
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var bv = B.Values;
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for (int i = 0; i < bv.Length; i++) bv[i] *= 2.0;
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lu.Refactorize(B, 1.0);
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var x = Helper.CreateTestVector(B.ColumnCount);
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var b = Helper.Multiply(B, x);
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var r = Vector.Clone(b);
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lu.Solve(b, x);
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B.Multiply(-1.0, x, 1.0, r);
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Assert.That(Vector.Norm(r.Length, r) < EPS, Is.True);
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// Dimension guard.
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var small = new SparseMatrix(3, 3, 0);
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Assert.Throws<ArgumentException>(() => lu.Refactorize(small, 1.0));
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}
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}
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}

‎CSparse.Tests/Double/Factorization/SparseCholeskyTest.cs‎

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Original file line numberDiff line numberDiff line change
@@ -53,5 +53,34 @@ public void TestEmptyFactorize()
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Assert.That(chol, Is.Not.Null);
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Assert.That(chol.NonZerosCount == 0, Is.True);
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}
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[Test]
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public void TestRefactorize()
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{
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var A = ResourceLoader.Get<double>("symmetric-40-spd.mat");
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var chol = SparseCholesky.Create(A, ColumnOrdering.MinimumDegreeAtPlusA);
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// Same sparsity pattern, different values (B = 2*A stays SPD) : the numeric
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// refactorization must reuse the cached symbolic analysis and still solve.
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var B = A.Clone();
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var bv = B.Values;
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for (int i = 0; i < bv.Length; i++) bv[i] *= 2.0;
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chol.Refactorize(B);
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var x = Helper.CreateTestVector(B.ColumnCount);
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var b = Helper.Multiply(B, x);
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var r = Vector.Clone(b);
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chol.Solve(b, x);
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B.Multiply(-1.0, x, 1.0, r);
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Assert.That(Vector.Norm(r.Length, r) < EPS, Is.True);
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// Dimension guard.
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var small = new SparseMatrix(3, 3, 0);
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Assert.Throws<ArgumentException>(() => chol.Refactorize(small));
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}
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}
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}

‎CSparse.Tests/Double/Factorization/SparseLDLTest.cs‎

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@@ -53,5 +53,34 @@ public void TestSolveNonSpd()
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Assert.That(Vector.Norm(r.Length, r) < EPS, Is.True);
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}
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[Test]
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public void TestRefactorize()
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{
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var A = ResourceLoader.Get<double>("symmetric-40-spd.mat");
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var ldl = SparseLDL.Create(A, ColumnOrdering.MinimumDegreeAtPlusA);
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// Same sparsity pattern, different values (B = 2*A) : the numeric
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// refactorization must reuse the cached symbolic analysis and still solve.
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var B = A.Clone();
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var bv = B.Values;
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for (int i = 0; i < bv.Length; i++) bv[i] *= 2.0;
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ldl.Refactorize(B);
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var x = Helper.CreateTestVector(B.ColumnCount);
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var b = Helper.Multiply(B, x);
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var r = Vector.Clone(b);
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ldl.Solve(b, x);
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B.Multiply(-1.0, x, 1.0, r);
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Assert.That(Vector.Norm(r.Length, r) < EPS, Is.True);
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// Dimension guard.
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var small = new SparseMatrix(3, 3, 0);
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Assert.Throws<ArgumentException>(() => ldl.Refactorize(small));
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}
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}
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}

‎CSparse.Tests/Double/Factorization/SparseLUTest.cs‎

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Original file line numberDiff line numberDiff line change
@@ -75,5 +75,39 @@ public void TestEmptyFactorize()
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Assert.That(lu, Is.Not.Null);
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Assert.That(lu.NonZerosCount == 0, Is.True);
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}
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[Test]
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public void TestRefactorize()
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{
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// Load matrix from a file.
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var A = ResourceLoader.Get<double>("general-40x40.mat");
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// Symbolic + numeric factorization of A.
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var lu = SparseLU.Create(A, ColumnOrdering.MinimumDegreeAtPlusA, 1.0);
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// Same sparsity pattern, different values (B = 2*A) : numeric refactorization
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// must reuse the cached symbolic ordering and still solve correctly.
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var B = A.Clone();
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var bv = B.Values;
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for (int i = 0; i < bv.Length; i++) bv[i] *= 2.0;
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lu.Refactorize(B, 1.0);
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var x = Helper.CreateTestVector(B.ColumnCount);
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var b = Helper.Multiply(B, x);
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var r = Vector.Clone(b);
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// Solve Bx = b with the refactorized decomposition.
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lu.Solve(b, x);
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// Residual r = b - Bx.
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B.Multiply(-1.0, x, 1.0, r);
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Assert.That(Vector.Norm(r.Length, r) < EPS, Is.True);
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// Dimension guard.
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var small = new SparseMatrix(3, 3, 0);
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Assert.Throws<ArgumentException>(() => lu.Refactorize(small, 1.0));
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}
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}
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}

‎CSparse/Complex/Factorization/SparseCholesky.cs‎

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@@ -106,6 +106,32 @@ public int NonZerosCount
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get { return L.NonZerosCount; }
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}
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/// <summary>
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/// Numerically re-factorizes a Hermitian positive definite matrix that has the
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/// <b>same sparsity pattern</b> as the one passed to <c>Create</c>, reusing the
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/// cached symbolic analysis (ordering, elimination tree and column counts).
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/// </summary>
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/// <param name="A">Column-compressed matrix, same size and pattern as in <c>Create</c>.</param>
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/// <remarks>
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/// Intended for Newton iterations and time-stepping loops where the matrix
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/// values change but its pattern does not: the fill-reducing ordering and the
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/// symbolic analysis are skipped, keeping only the numeric work. The matrix
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/// must keep the pattern used in <c>Create</c> (the symbolic structure is
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/// reused) and stay positive definite.
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/// </remarks>
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public void Refactorize(CompressedColumnStorage<Complex> A)
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{
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Check.NotNull(A, "A");
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Check.SquareMatrix(A, "A");
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if (A.ColumnCount != n)
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{
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throw new ArgumentException("Matrix dimensions don't match the factorization.", "A");
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}
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Factorize(A, null);
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}
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/// <summary>
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/// Solves a system of linear equations, <c>Ax = b</c>.
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/// </summary>

‎CSparse/Complex/Factorization/SparseLDL.cs‎

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@@ -112,6 +112,31 @@ public int NonZerosCount
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get { return L.NonZerosCount; }
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}
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/// <summary>
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/// Numerically re-factorizes a matrix that has the <b>same sparsity pattern</b>
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/// as the one passed to <c>Create</c>, reusing the cached symbolic analysis
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/// (ordering and elimination tree).
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/// </summary>
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/// <param name="A">Column-compressed matrix, same size and pattern as in <c>Create</c>.</param>
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/// <remarks>
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/// Intended for Newton iterations and time-stepping loops where the matrix
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/// values change but its pattern does not: the fill-reducing ordering and the
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/// symbolic analysis are skipped, keeping only the numeric work. The matrix
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/// must keep the pattern used in <c>Create</c> (the symbolic structure is reused).
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/// </remarks>
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public void Refactorize(CompressedColumnStorage<Complex> A)
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{
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Check.NotNull(A, "A");
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Check.SquareMatrix(A, "A");
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if (A.ColumnCount != n)
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{
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throw new ArgumentException("Matrix dimensions don't match the factorization.", "A");
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}
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Factorize(A, null);
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}
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/// <summary>
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/// Solves a linear system Ax=b, where A is symmetric positive definite.
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/// </summary>

‎CSparse/Complex/Factorization/SparseLU.cs‎

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@@ -110,6 +110,37 @@ public int NonZerosCount
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get { return (L.NonZerosCount + U.NonZerosCount - n); }
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}
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/// <summary>
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/// Numerically re-factorizes a matrix that has the <b>same sparsity pattern</b>
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/// as the one passed to <c>Create</c>, reusing the cached symbolic ordering.
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/// </summary>
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/// <param name="A">Column-compressed matrix, same size as the one used in <c>Create</c>.</param>
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/// <param name="tol">Partial pivoting tolerance (from 0.0 to 1.0).</param>
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/// <remarks>
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/// Intended for Newton iterations and time-stepping loops where the matrix
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/// values change but its pattern does not: the fill-reducing column ordering
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/// and symbolic analysis are skipped, keeping only the (dominant) numeric work.
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/// The column ordering is a permutation, so a different pattern still factorizes
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/// correctly, but the fill may then be sub-optimal.
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/// </remarks>
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public void Refactorize(CompressedColumnStorage<Complex> A, double tol = 1.0)
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{
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Check.NotNull(A, "A");
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Check.SquareMatrix(A, "A");
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Check.NotNaN(tol, "tol");
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if (A.ColumnCount != n)
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{
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throw new ArgumentException("Matrix dimensions don't match the factorization.", "A");
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}
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// Ensure tol is in range.
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tol = Math.Min(Math.Max(tol, 0.0), 1.0);
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// Reuse the cached symbolic ordering (S); recompute L, U and the pivoting.
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Factorize(A, tol, null);
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}
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/// <summary>
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/// Solves a system of linear equations, <c>Ax = b</c>.
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/// </summary>

‎CSparse/Double/Factorization/SparseCholesky.cs‎

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Original file line numberDiff line numberDiff line change
@@ -105,6 +105,32 @@ public int NonZerosCount
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get { return L.NonZerosCount; }
106106
}
107107

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/// <summary>
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/// Numerically re-factorizes a symmetric positive definite matrix that has the
110+
/// <b>same sparsity pattern</b> as the one passed to <c>Create</c>, reusing the
111+
/// cached symbolic analysis (ordering, elimination tree and column counts).
112+
/// </summary>
113+
/// <param name="A">Column-compressed matrix, same size and pattern as in <c>Create</c>.</param>
114+
/// <remarks>
115+
/// Intended for Newton iterations and time-stepping loops where the matrix
116+
/// values change but its pattern does not: the fill-reducing ordering and the
117+
/// symbolic analysis are skipped, keeping only the numeric work. The matrix
118+
/// must keep the pattern used in <c>Create</c> (the symbolic structure is
119+
/// reused) and stay positive definite.
120+
/// </remarks>
121+
public void Refactorize(CompressedColumnStorage<double> A)
122+
{
123+
Check.NotNull(A, "A");
124+
Check.SquareMatrix(A, "A");
125+
126+
if (A.ColumnCount != n)
127+
{
128+
throw new ArgumentException("Matrix dimensions don't match the factorization.", "A");
129+
}
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131+
Factorize(A, null);
132+
}
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108134
/// <summary>
109135
/// Solves a system of linear equations, <c>Ax = b</c>.
110136
/// </summary>

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