Merge branch 'master' into dev_poly

Author: tturocy

.gitignore

@@ -43,5 +43,8 @@ Gambit.app/*
 *.so
 doc/tutorials/games/*.nfg
 doc/tutorials/games/*.efg
+doc/tutorials/*.png
 *.dmg
 Gambit.app/*
+*.ipynb_checkpoints
+*.ef

.readthedocs.yml

@@ -12,6 +12,7 @@ build:
   apt_packages:
     - libgmp-dev
     - pandoc
+    - texlive-full
 
 python:
   install:

Makefile.am

@@ -251,14 +251,11 @@ core_SOURCES = \
 	src/core/recarray.h \
 	src/core/matrix.h \
 	src/core/matrix.imp \
-	src/core/sqmatrix.h \
-	src/core/sqmatrix.imp \
 	src/core/integer.cc \
 	src/core/integer.h \
 	src/core/rational.cc \
 	src/core/rational.h \
 	src/core/matrix.cc \
-	src/core/sqmatrix.cc \
 	src/core/function.cc \
 	src/core/function.h \
 	src/core/tinyxml.cc \

doc/requirements.txt

@@ -10,3 +10,4 @@ matplotlib
 pickleshare
 jupyter
 open_spiel; sys_platform != 'win32'
+draw-tree @ git+https://github.com/gambitproject/draw_tree.git@v0.2.0

doc/tutorials/02_extensive_form.ipynb

@@ -28,6 +28,12 @@
 
 namespace Gambit {
 
+class SingularMatrixException final : public std::runtime_error {
+public:
+  SingularMatrixException() : std::runtime_error("Attempted to invert a singular matrix") {}
+  ~SingularMatrixException() noexcept override = default;
+};
+
 template <class T> Vector<T> operator*(const Vector<T> &, const Matrix<T> &);
 
 template <class T> class Matrix : public RectArray<T> {
@@ -49,6 +55,10 @@ template <class T> class Matrix : public RectArray<T> {
 
   /// @name Extracting rows and columns
   //@{
+  bool IsSquare() const
+  {
+    return this->MinRow() == this->MinCol() && this->MaxRow() == this->MaxCol();
+  }
   Vector<T> Row(int) const;
   Vector<T> Column(int) const;
   //@}
@@ -93,6 +103,9 @@ template <class T> class Matrix : public RectArray<T> {
   void MakeIdent();
   void Pivot(int, int);
   //@}
+
+  Matrix Inverse() const;
+  T Determinant() const;
 };
 
 template <class T> Vector<T> operator*(const Vector<T> &, const Matrix<T> &);

doc/tutorials/03_stripped_down_poker.ipynb

@@ -384,6 +384,9 @@ template <class T> Vector<T> Matrix<T>::Column(int j) const
 
 template <class T> void Matrix<T>::MakeIdent()
 {
+  if (!IsSquare()) {
+    throw DimensionException();
+  }
   for (int i = this->minrow; i <= this->maxrow; i++) {
     for (int j = this->mincol; j <= this->maxcol; j++) {
       if (i == j) {
@@ -426,4 +429,139 @@ template <class T> void Matrix<T>::Pivot(int row, int col)
   }
 }
 
+template <class T> Matrix<T> Matrix<T>::Inverse() const
+{
+  if (!IsSquare()) {
+    throw DimensionException();
+  }
+
+  Matrix copy(*this);
+  Matrix inv(this->MaxRow(), this->MaxRow());
+
+  // initialize inverse matrix and prescale row vectors
+  for (int i = this->MinRow(); i <= this->MaxRow(); i++) {
+    T max = (T)0;
+    for (int j = this->MinCol(); j <= this->MaxCol(); j++) {
+      T abs = copy(i, j);
+      if (abs < (T)0) {
+        abs = -abs;
+      }
+      if (abs > max) {
+        max = abs;
+      }
+    }
+
+    if (max == (T)0) {
+      throw SingularMatrixException();
+    }
+
+    T scale = (T)1 / max;
+    for (int j = this->MinCol(); j <= this->MaxCol(); j++) {
+      copy(i, j) *= scale;
+      if (i == j) {
+        inv(i, j) = scale;
+      }
+      else {
+        inv(i, j) = (T)0;
+      }
+    }
+  }
+
+  for (int i = this->MinCol(); i <= this->MaxCol(); i++) {
+    // find pivot row
+    T max = copy(i, i);
+    if (max < (T)0) {
+      max = -max;
+    }
+    int row = i;
+    for (int j = i + 1; j <= this->MaxRow(); j++) {
+      T abs = copy(j, i);
+      if (abs < (T)0) {
+        abs = -abs;
+      }
+      if (abs > max) {
+        max = abs;
+        row = j;
+      }
+    }
+
+    if (max <= (T)0) {
+      throw SingularMatrixException();
+    }
+
+    copy.SwitchRows(i, row);
+    inv.SwitchRows(i, row);
+    // scale pivot row
+    T factor = (T)1 / copy(i, i);
+    for (int k = this->MinCol(); k <= this->MaxCol(); k++) {
+      copy(i, k) *= factor;
+      inv(i, k) *= factor;
+    }
+
+    // reduce other rows
+    for (int j = this->MinRow(); j <= this->MaxRow(); j++) {
+      if (j != i) {
+        T mult = copy(j, i);
+        for (int k = this->MinCol(); k <= this->MaxCol(); k++) {
+          copy(j, k) -= copy(i, k) * mult;
+          inv(j, k) -= inv(i, k) * mult;
+        }
+      }
+    }
+  }
+
+  return inv;
+}
+
+template <class T> T Matrix<T>::Determinant() const
+{
+  if (!IsSquare()) {
+    throw DimensionException();
+  }
+
+  T factor = (T)1;
+  Matrix M(*this);
+
+  for (int row = this->MinRow(); row <= this->MaxRow(); row++) {
+
+    // Experience (as of 3/22/99) suggests that, in the interest of
+    // numerical stability, it might be best to do Gaussian
+    // elimination with respect to the row (of those feasible)
+    // whose entry has the largest absolute value.
+    int swap_row = row;
+    for (int i = row + 1; i <= this->MaxRow(); i++) {
+      if (abs(M.data[i][row]) > abs(M.data[swap_row][row])) {
+        swap_row = i;
+      }
+    }
+
+    if (swap_row != row) {
+      M.SwitchRows(row, swap_row);
+      for (int j = this->MinCol(); j <= this->MaxCol(); j++) {
+        M.data[row][j] *= (T)-1;
+      }
+    }
+
+    if (M.data[row][row] == (T)0) {
+      return (T)0;
+    }
+
+    // now do row operations to clear the row'th column
+    // below the diagonal
+    for (int row1 = row + 1; row1 <= this->MaxRow(); row1++) {
+      factor = -M.data[row1][row] / M.data[row][row];
+      for (int i = this->MinCol(); i <= this->MaxCol(); i++) {
+        M.data[row1][i] += M.data[row][i] * factor;
+      }
+    }
+  }
+
+  // finally we multiply the diagonal elements
+  T det = (T)1;
+  for (int row = this->MinRow(); row <= this->MaxRow(); row++) {
+    det *= M.data[row][row];
+  }
+  return det;
+}
+
 } // end namespace Gambit