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+//===------ Math.h - PBQP Vector and Matrix classes -------------*- C++ -*-===//
+//
+//                     The LLVM Compiler Infrastructure
+//
+// This file is distributed under the University of Illinois Open Source
+// License. See LICENSE.TXT for details.
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef LLVM_CODEGEN_PBQP_MATH_H 
+#define LLVM_CODEGEN_PBQP_MATH_H
+
+#include <cassert>
+#include <algorithm>
+#include <functional>
+
+namespace PBQP {
+
+typedef float PBQPNum;
+
+/// \brief PBQP Vector class.
+class Vector {
+  public:
+
+    /// \brief Construct a PBQP vector of the given size.
+    explicit Vector(unsigned length) :
+      length(length), data(new PBQPNum[length]) {
+      }
+
+    /// \brief Construct a PBQP vector with initializer.
+    Vector(unsigned length, PBQPNum initVal) :
+      length(length), data(new PBQPNum[length]) {
+        std::fill(data, data + length, initVal);
+      }
+
+    /// \brief Copy construct a PBQP vector.
+    Vector(const Vector &v) :
+      length(v.length), data(new PBQPNum[length]) {
+        std::copy(v.data, v.data + length, data);
+      }
+
+    /// \brief Destroy this vector, return its memory.
+    ~Vector() { delete[] data; }
+
+    /// \brief Assignment operator.
+    Vector& operator=(const Vector &v) {
+      delete[] data;
+      length = v.length;
+      data = new PBQPNum[length];
+      std::copy(v.data, v.data + length, data);
+      return *this;
+    }
+
+    /// \brief Return the length of the vector
+    unsigned getLength() const {
+      return length;
+    }
+
+    /// \brief Element access.
+    PBQPNum& operator[](unsigned index) {
+      assert(index < length && "Vector element access out of bounds.");
+      return data[index];
+    }
+
+    /// \brief Const element access.
+    const PBQPNum& operator[](unsigned index) const {
+      assert(index < length && "Vector element access out of bounds.");
+      return data[index];
+    }
+
+    /// \brief Add another vector to this one.
+    Vector& operator+=(const Vector &v) {
+      assert(length == v.length && "Vector length mismatch.");
+      std::transform(data, data + length, v.data, data, std::plus<PBQPNum>()); 
+      return *this;
+    }
+
+    /// \brief Subtract another vector from this one.
+    Vector& operator-=(const Vector &v) {
+      assert(length == v.length && "Vector length mismatch.");
+      std::transform(data, data + length, v.data, data, std::minus<PBQPNum>()); 
+      return *this;
+    }
+
+    /// \brief Returns the index of the minimum value in this vector
+    unsigned minIndex() const {
+      return std::min_element(data, data + length) - data;
+    }
+
+  private:
+    unsigned length;
+    PBQPNum *data;
+};
+
+/// \brief Output a textual representation of the given vector on the given
+///        output stream.
+template <typename OStream>
+OStream& operator<<(OStream &os, const Vector &v) {
+  assert((v.getLength() != 0) && "Zero-length vector badness.");
+
+  os << "[ " << v[0];
+  for (unsigned i = 1; i < v.getLength(); ++i) {
+    os << ", " << v[i];
+  }
+  os << " ]";
+
+  return os;
+} 
+
+
+/// \brief PBQP Matrix class
+class Matrix {
+  public:
+
+    /// \brief Construct a PBQP Matrix with the given dimensions.
+    Matrix(unsigned rows, unsigned cols) :
+      rows(rows), cols(cols), data(new PBQPNum[rows * cols]) {
+    }
+
+    /// \brief Construct a PBQP Matrix with the given dimensions and initial
+    /// value.
+    Matrix(unsigned rows, unsigned cols, PBQPNum initVal) :
+      rows(rows), cols(cols), data(new PBQPNum[rows * cols]) {
+        std::fill(data, data + (rows * cols), initVal);
+    }
+
+    /// \brief Copy construct a PBQP matrix.
+    Matrix(const Matrix &m) :
+      rows(m.rows), cols(m.cols), data(new PBQPNum[rows * cols]) {
+        std::copy(m.data, m.data + (rows * cols), data);  
+    }
+
+    /// \brief Destroy this matrix, return its memory.
+    ~Matrix() { delete[] data; }
+
+    /// \brief Assignment operator.
+    Matrix& operator=(const Matrix &m) {
+      delete[] data;
+      rows = m.rows; cols = m.cols;
+      data = new PBQPNum[rows * cols];
+      std::copy(m.data, m.data + (rows * cols), data);
+      return *this;
+    }
+
+    /// \brief Return the number of rows in this matrix.
+    unsigned getRows() const { return rows; }
+
+    /// \brief Return the number of cols in this matrix.
+    unsigned getCols() const { return cols; }
+
+    /// \brief Matrix element access.
+    PBQPNum* operator[](unsigned r) {
+      assert(r < rows && "Row out of bounds.");
+      return data + (r * cols);
+    }
+
+    /// \brief Matrix element access.
+    const PBQPNum* operator[](unsigned r) const {
+      assert(r < rows && "Row out of bounds.");
+      return data + (r * cols);
+    }
+
+    /// \brief Returns the given row as a vector.
+    Vector getRowAsVector(unsigned r) const {
+      Vector v(cols);
+      for (unsigned c = 0; c < cols; ++c)
+        v[c] = (*this)[r][c];
+      return v; 
+    }
+
+    /// \brief Returns the given column as a vector.
+    Vector getColAsVector(unsigned c) const {
+      Vector v(rows);
+      for (unsigned r = 0; r < rows; ++r)
+        v[r] = (*this)[r][c];
+      return v;
+    }
+
+    /// \brief Reset the matrix to the given value.
+    Matrix& reset(PBQPNum val = 0) {
+      std::fill(data, data + (rows * cols), val);
+      return *this;
+    }
+
+    /// \brief Set a single row of this matrix to the given value.
+    Matrix& setRow(unsigned r, PBQPNum val) {
+      assert(r < rows && "Row out of bounds.");
+      std::fill(data + (r * cols), data + ((r + 1) * cols), val);
+      return *this;
+    }
+
+    /// \brief Set a single column of this matrix to the given value.
+    Matrix& setCol(unsigned c, PBQPNum val) {
+      assert(c < cols && "Column out of bounds.");
+      for (unsigned r = 0; r < rows; ++r)
+        (*this)[r][c] = val;
+      return *this;
+    }
+
+    /// \brief Matrix transpose.
+    Matrix transpose() const {
+      Matrix m(cols, rows);
+      for (unsigned r = 0; r < rows; ++r)
+        for (unsigned c = 0; c < cols; ++c)
+          m[c][r] = (*this)[r][c];
+      return m;
+    }
+
+    /// \brief Returns the diagonal of the matrix as a vector.
+    ///
+    /// Matrix must be square.
+    Vector diagonalize() const {
+      assert(rows == cols && "Attempt to diagonalize non-square matrix.");
+
+      Vector v(rows);
+      for (unsigned r = 0; r < rows; ++r)
+        v[r] = (*this)[r][r];
+      return v;
+    } 
+
+    /// \brief Add the given matrix to this one.
+    Matrix& operator+=(const Matrix &m) {
+      assert(rows == m.rows && cols == m.cols &&
+          "Matrix dimensions mismatch.");
+      std::transform(data, data + (rows * cols), m.data, data,
+          std::plus<PBQPNum>());
+      return *this;
+    }
+
+    /// \brief Returns the minimum of the given row
+    PBQPNum getRowMin(unsigned r) const {
+      assert(r < rows && "Row out of bounds");
+      return *std::min_element(data + (r * cols), data + ((r + 1) * cols));
+    }
+
+    /// \brief Returns the minimum of the given column
+    PBQPNum getColMin(unsigned c) const {
+      PBQPNum minElem = (*this)[0][c];
+      for (unsigned r = 1; r < rows; ++r)
+        if ((*this)[r][c] < minElem) minElem = (*this)[r][c];
+      return minElem;
+    }
+
+    /// \brief Subtracts the given scalar from the elements of the given row.
+    Matrix& subFromRow(unsigned r, PBQPNum val) {
+      assert(r < rows && "Row out of bounds");
+      std::transform(data + (r * cols), data + ((r + 1) * cols),
+          data + (r * cols),
+          std::bind2nd(std::minus<PBQPNum>(), val));
+      return *this;
+    }
+
+    /// \brief Subtracts the given scalar from the elements of the given column.
+    Matrix& subFromCol(unsigned c, PBQPNum val) {
+      for (unsigned r = 0; r < rows; ++r)
+        (*this)[r][c] -= val;
+      return *this;
+    }
+
+    /// \brief Returns true if this is a zero matrix.
+    bool isZero() const {
+      return find_if(data, data + (rows * cols),
+          std::bind2nd(std::not_equal_to<PBQPNum>(), 0)) ==
+        data + (rows * cols);
+    }
+
+  private:
+    unsigned rows, cols;
+    PBQPNum *data;
+};
+
+/// \brief Output a textual representation of the given matrix on the given
+///        output stream.
+template <typename OStream>
+OStream& operator<<(OStream &os, const Matrix &m) {
+
+  assert((m.getRows() != 0) && "Zero-row matrix badness.");
+
+  for (unsigned i = 0; i < m.getRows(); ++i) {
+    os << m.getRowAsVector(i);
+  }
+
+  return os;
+}
+
+}
+
+#endif // LLVM_CODEGEN_PBQP_MATH_H