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diff --git a/spec/rubyspec/library/matrix/lup_decomposition/solve_spec.rb b/spec/rubyspec/library/matrix/lup_decomposition/solve_spec.rb
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+++ b/spec/rubyspec/library/matrix/lup_decomposition/solve_spec.rb
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+require File.expand_path('../../../../spec_helper', __FILE__)
+require 'matrix'
+
+describe "Matrix::LUPDecomposition#solve" do
+  describe "for rectangular matrices" do
+    it "raises an error for singular matrices" do
+      a = Matrix[[1, 2, 3], [1, 3, 5], [2, 5, 8]]
+      lu = Matrix::LUPDecomposition.new(a)
+      lambda {
+        lu.solve(a)
+      }.should raise_error(Matrix::ErrNotRegular)
+    end
+
+    describe "for non singular matrices" do
+      before :each do
+        @a = Matrix[[7, 8, 9], [14, 46, 51], [28, 82, 163]]
+        @lu = Matrix::LUPDecomposition.new(@a)
+      end
+
+      it "returns the appropriate empty matrix when given an empty matrix" do
+        @lu.solve(Matrix.empty(3,0)).should == Matrix.empty(3,0)
+        empty = Matrix::LUPDecomposition.new(Matrix.empty(0, 0))
+        empty.solve(Matrix.empty(0,3)).should == Matrix.empty(0,3)
+      end
+
+      it "returns the right matrix when given a matrix of the appropriate size" do
+        solution = Matrix[[1, 2, 3, 4], [0, 1, 2, 3], [-1, -2, -3, -4]]
+        values = Matrix[[-2, 4, 10, 16], [-37, -28, -19, -10], [-135, -188, -241, -294]] # == @a * solution
+        @lu.solve(values).should == solution
+      end
+
+      it "raises an error when given a matrix of the wrong size" do
+        values = Matrix[[1, 2, 3, 4], [0, 1, 2, 3]]
+        lambda {
+          @lu.solve(values)
+        }.should raise_error(Matrix::ErrDimensionMismatch)
+      end
+
+      it "returns the right vector when given a vector of the appropriate size" do
+        solution = Vector[1, 2, -1]
+        values = Vector[14, 55, 29] # == @a * solution
+        @lu.solve(values).should == solution
+      end
+
+      it "raises an error when given a vector of the wrong size" do
+        values = Vector[14, 55]
+        lambda {
+          @lu.solve(values)
+        }.should raise_error(Matrix::ErrDimensionMismatch)
+      end
+    end
+  end
+end