[clang-tools-extra] [MLIR][Presburger] Define matrix inverse for rational matrices (PR #67382)

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Mon Sep 25 16:32:33 PDT 2023


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``````````bash
git-clang-format --diff c74398649f28ab78c74bacfe82e69224377008e7 69cce307842ab6bfbca10f44d3826623379a0385 -- mlir/include/mlir/Analysis/Presburger/Fraction.h mlir/include/mlir/Analysis/Presburger/Matrix.h mlir/lib/Analysis/Presburger/Matrix.cpp mlir/unittests/Analysis/Presburger/MatrixTest.cpp mlir/unittests/Analysis/Presburger/Utils.h
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View the diff from clang-format here.
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``````````diff
diff --git a/mlir/include/mlir/Analysis/Presburger/Matrix.h b/mlir/include/mlir/Analysis/Presburger/Matrix.h
index b9048334c39f..74edddd6cb7d 100644
--- a/mlir/include/mlir/Analysis/Presburger/Matrix.h
+++ b/mlir/include/mlir/Analysis/Presburger/Matrix.h
@@ -247,27 +247,25 @@ public:
 // An inherited class for rational matrices, with no new data attributes.
 // This is only used for the matrix-related method which apply only
 // to fractions (inverse).
-class FracMatrix : public Matrix<Fraction>
-{
+class FracMatrix : public Matrix<Fraction> {
 public:
   FracMatrix(unsigned rows, unsigned columns, unsigned reservedRows = 0,
-            unsigned reservedColumns = 0) :
-    Matrix<Fraction>(rows, columns, reservedRows, reservedColumns) {};
+             unsigned reservedColumns = 0)
+      : Matrix<Fraction>(rows, columns, reservedRows, reservedColumns){};
 
-  FracMatrix(Matrix<Fraction> m) :
-    Matrix<Fraction>(m.getNumRows(), m.getNumColumns(), m.getNumReservedRows(), m.getNumReservedColumns())
-  {
+  FracMatrix(Matrix<Fraction> m)
+      : Matrix<Fraction>(m.getNumRows(), m.getNumColumns(),
+                         m.getNumReservedRows(), m.getNumReservedColumns()) {
     for (unsigned i = 0; i < m.getNumRows(); i++)
       for (unsigned j = 0; j < m.getNumColumns(); j++)
         at(i, j) = m(i, j);
   };
-  
+
   /// Return the identity matrix of the specified dimension.
   static FracMatrix identity(unsigned dimension);
 
   // Return the inverse of the matrix, leaving the calling object unmodified.
   FracMatrix inverse();
-
 };
 
 } // namespace presburger
diff --git a/mlir/lib/Analysis/Presburger/Matrix.cpp b/mlir/lib/Analysis/Presburger/Matrix.cpp
index c0fbc688be2e..de5e2bbe285a 100644
--- a/mlir/lib/Analysis/Presburger/Matrix.cpp
+++ b/mlir/lib/Analysis/Presburger/Matrix.cpp
@@ -392,7 +392,6 @@ MPInt IntMatrix::normalizeRow(unsigned row) {
   return normalizeRow(row, getNumColumns());
 }
 
-
 FracMatrix FracMatrix::identity(unsigned dimension) {
   FracMatrix matrix(dimension, dimension);
   for (unsigned i = 0; i < dimension; ++i)
@@ -400,60 +399,55 @@ FracMatrix FracMatrix::identity(unsigned dimension) {
   return matrix;
 }
 
-FracMatrix FracMatrix::inverse()
-{
-    // We use Gaussian elimination on the rows of [M | I]
-    // to find the integer inverse. We proceed left-to-right,
-    // top-to-bottom. M is assumed to be a dim x dim matrix.
+FracMatrix FracMatrix::inverse() {
+  // We use Gaussian elimination on the rows of [M | I]
+  // to find the integer inverse. We proceed left-to-right,
+  // top-to-bottom. M is assumed to be a dim x dim matrix.
 
-    unsigned dim = getNumRows();
+  unsigned dim = getNumRows();
 
-    // Construct the augmented matrix [M | I]
-    FracMatrix augmented(dim, dim + dim);
-    for (unsigned i = 0; i < dim; i++)
-    {
-        augmented.fillRow(i, 0);
-        for (unsigned j = 0; j < dim; j++)
-            augmented(i, j) = at(i, j);
-        augmented(i, dim+i).num = 1;
-        augmented(i, dim+i).den = 1;
-    }
-    Fraction a, b;
-    for (unsigned i = 0; i < dim; i++)
-    {
-        if (augmented(i, i) == Fraction(0, 1))
-            for (unsigned j = i+1; j < dim; j++)
-                if (augmented(j, i) != Fraction(0, 1))
-                {
-                    augmented.addToRow(i, augmented.getRow(j), Fraction(1, 1));
-                    break;
-                }
-
-        b = augmented(i, i);
-        for (unsigned j = 0; j < dim; j++)
-        {
-            if (i == j || augmented(j, i) == 0) continue;
-            a = augmented(j, i);
-            // Rj -> Rj - (b/a)Ri
-            augmented.addToRow(j, augmented.getRow(i), - a / b);
-            // Now (Rj)i = 0
+  // Construct the augmented matrix [M | I]
+  FracMatrix augmented(dim, dim + dim);
+  for (unsigned i = 0; i < dim; i++) {
+    augmented.fillRow(i, 0);
+    for (unsigned j = 0; j < dim; j++)
+      augmented(i, j) = at(i, j);
+    augmented(i, dim + i).num = 1;
+    augmented(i, dim + i).den = 1;
+  }
+  Fraction a, b;
+  for (unsigned i = 0; i < dim; i++) {
+    if (augmented(i, i) == Fraction(0, 1))
+      for (unsigned j = i + 1; j < dim; j++)
+        if (augmented(j, i) != Fraction(0, 1)) {
+          augmented.addToRow(i, augmented.getRow(j), Fraction(1, 1));
+          break;
         }
+
+    b = augmented(i, i);
+    for (unsigned j = 0; j < dim; j++) {
+      if (i == j || augmented(j, i) == 0)
+        continue;
+      a = augmented(j, i);
+      // Rj -> Rj - (b/a)Ri
+      augmented.addToRow(j, augmented.getRow(i), -a / b);
+      // Now (Rj)i = 0
     }
-    
-    // Now only diagonal elements are nonzero, but they are
-    // not necessarily 1.
-    for (unsigned i = 0; i < dim; i++)
-    {
-        a = augmented(i, i);
-        for (unsigned j = dim; j < dim + dim; j++)
-            augmented(i, j) = augmented(i, j) / a;
-    }
+  }
+
+  // Now only diagonal elements are nonzero, but they are
+  // not necessarily 1.
+  for (unsigned i = 0; i < dim; i++) {
+    a = augmented(i, i);
+    for (unsigned j = dim; j < dim + dim; j++)
+      augmented(i, j) = augmented(i, j) / a;
+  }
 
-    // Copy the right half of the augmented matrix.
-    FracMatrix inverse(dim, dim);
-    for (unsigned i = 0; i < dim; i++)
-        for (unsigned j = 0; j < dim; j++)
-            inverse(i, j) = augmented(i, j+dim);
+  // Copy the right half of the augmented matrix.
+  FracMatrix inverse(dim, dim);
+  for (unsigned i = 0; i < dim; i++)
+    for (unsigned j = 0; j < dim; j++)
+      inverse(i, j) = augmented(i, j + dim);
 
-    return inverse;
+  return inverse;
 }
\ No newline at end of file
diff --git a/mlir/unittests/Analysis/Presburger/MatrixTest.cpp b/mlir/unittests/Analysis/Presburger/MatrixTest.cpp
index d07318617e1a..efa6d4507d16 100644
--- a/mlir/unittests/Analysis/Presburger/MatrixTest.cpp
+++ b/mlir/unittests/Analysis/Presburger/MatrixTest.cpp
@@ -250,12 +250,16 @@ TEST(MatrixTest, computeHermiteNormalForm) {
 }
 
 TEST(MatrixTest, inverse) {
-    FracMatrix mat = makeFracMatrix(2, 2, {{Fraction(2, 1), Fraction(1, 1)}, {Fraction(7, 1), Fraction(0, 1)}});
-    FracMatrix inverse = makeFracMatrix(2, 2, {{Fraction(0, 1), Fraction(1, 7)}, {Fraction(1, 1), Fraction(-2, 7)}});
-
-    FracMatrix inv = mat.inverse();
-
-    for (unsigned row = 0; row < 2; row++)
-      for (unsigned col = 0; col < 2; col++)
-        EXPECT_EQ(inv(row, col), inverse(row, col));
+  FracMatrix mat = makeFracMatrix(
+      2, 2,
+      {{Fraction(2, 1), Fraction(1, 1)}, {Fraction(7, 1), Fraction(0, 1)}});
+  FracMatrix inverse = makeFracMatrix(
+      2, 2,
+      {{Fraction(0, 1), Fraction(1, 7)}, {Fraction(1, 1), Fraction(-2, 7)}});
+
+  FracMatrix inv = mat.inverse();
+
+  for (unsigned row = 0; row < 2; row++)
+    for (unsigned col = 0; col < 2; col++)
+      EXPECT_EQ(inv(row, col), inverse(row, col));
 }
diff --git a/mlir/unittests/Analysis/Presburger/Utils.h b/mlir/unittests/Analysis/Presburger/Utils.h
index c652daa583a8..ce149c32ffa3 100644
--- a/mlir/unittests/Analysis/Presburger/Utils.h
+++ b/mlir/unittests/Analysis/Presburger/Utils.h
@@ -41,7 +41,7 @@ inline IntMatrix makeIntMatrix(unsigned numRow, unsigned numColumns,
 }
 
 inline FracMatrix makeFracMatrix(unsigned numRow, unsigned numColumns,
-                         ArrayRef<SmallVector<Fraction, 8>> matrix) {
+                                 ArrayRef<SmallVector<Fraction, 8>> matrix) {
   FracMatrix results(numRow, numColumns);
   assert(matrix.size() == numRow);
   for (unsigned i = 0; i < numRow; ++i) {

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https://github.com/llvm/llvm-project/pull/67382


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