Created #positive_definite? (#561)

Author: shardulparab97

lib/nmatrix/math.rb

@@ -1387,6 +1387,33 @@ def scale(alpha, incx=1, n=nil)
   alias :permute_columns  :laswp
   alias :permute_columns! :laswp!
 
+
+  #
+  # call-seq:
+  #     positive_definite? -> boolean
+  #
+  # A matrix is positive definite if it’s symmetric and all its eigenvalues are positive
+  #
+  # * *Returns* :
+  #   - A boolean value telling if the NMatrix is positive definite or not.
+  # * *Raises* :
+  #   - +ShapeError+ -> Must be used on square matrices.
+  #
+  def positive_definite?
+    raise(ShapeError, "positive definite calculated only for square matrices") unless 
+      self.dim == 2 && self.shape[0] == self.shape[1]
+    ans = true
+    cond = 0
+    while cond != self.cols
+      if self[0..cond, 0..cond].det <= 0
+        ans = false
+        break
+      end
+      cond += 1
+    end
+    ans
+  end
+    
 protected
   # Define the element-wise operations for lists. Note that the __list_map_merged_stored__ iterator returns a Ruby Object
   # matrix, which we then cast back to the appropriate type. If you don't want that, you can redefine these functions in

spec/math_spec.rb

@@ -1267,4 +1267,13 @@
       end
     end
   end
+
+  context "#positive_definite?" do
+      it "should return true for positive_definite? matrix" do
+        n = NMatrix.new([3,3], [2, -1, -1,
+                                -1, 2, -1,
+                                -1, -1, 3])
+        expect(n.positive_definite?).to be_truthy
+      end
+  end
 end