Fixes bug in coefficient_of_determination.

fit_goodness and cofficient_of_determination now output the same results. I
forgot to square the result of the norm in coefficient_of_determination. The
tests pass with high precision now.

Fixes issue #11.

dtk/process.py

@@ -247,8 +247,8 @@ def coefficient_of_determination(measured, predicted):
     Notes
     -----
 
-    The coefficient of determination (also referred to as R^2 and VAF
-    (variance accounted for) is computed either of these two ways::
+    The coefficient of determination [also referred to as R^2 and VAF
+    (variance accounted for)] is computed either of these two ways::
 
             sum( [predicted - mean(measured)] ** 2 )
       R^2 = ----------------------------------------
@@ -262,9 +262,10 @@ def coefficient_of_determination(measured, predicted):
 
 
     """
+    # 2-norm => np.sqrt(np.sum(measured - predicted)**2))
 
-    numerator = np.linalg.norm(measured - predicted)
-    denominator = np.linalg.norm(measured - measured.mean())
+    numerator = np.linalg.norm(measured - predicted) ** 2
+    denominator = np.linalg.norm(measured - measured.mean()) ** 2
 
     r_squared = 1.0 - numerator / denominator
 

dtk/test/test_process.py

@@ -91,15 +91,15 @@ def test_coefficient_of_determination():
     y_predicted = np.dot(A, xhat)
 
     # find R^2 the linear algebra way
-    expected_r_squared = 1.0 - sums_of_squares_of_residuals / \
-        np.linalg.norm(b - b.mean())
+    expected_r_squared = (1.0 - sums_of_squares_of_residuals /
+                          np.linalg.norm(b - b.mean()) ** 2)
 
     # find R^2 the statistics way
     residuals = np.dot(A, xhat) - b
     expected_error_sum_of_squares = np.sum(residuals ** 2)
     expected_total_sum_of_squares = np.sum((b - b.mean()) ** 2)
-    second_expected_r_squared = 1.0 - expected_error_sum_of_squares / \
-        expected_total_sum_of_squares
+    second_expected_r_squared = (1.0 - expected_error_sum_of_squares /
+                                 expected_total_sum_of_squares)
 
     # find R^2 another statistics way
     r_squared, error_sum_of_squares, total_sum_of_squares, regression_sum_of_squares = \
@@ -111,7 +111,7 @@ def test_coefficient_of_determination():
 
     testing.assert_allclose(xhat, [slope, intercept], rtol=0.0, atol=0.3)
 
-    # It seems that numpy.linalg.lstsq doesn't output a fery high precision
+    # It seems that numpy.linalg.lstsq doesn't output a very high precision
     # value for the residual sum of squares, so I set the tolerance here to
     # pass.
     testing.assert_allclose(error_sum_of_squares,
@@ -124,16 +124,10 @@ def test_coefficient_of_determination():
 
     testing.assert_allclose(total_sum_of_squares,
                             expected_total_sum_of_squares)
-
-    # This precision issue carryies through to these compuations.
-    testing.assert_allclose(r_squared, expected_r_squared, rtol=0.0,
-                            atol=5e-6)
-    # This passes with default tolerances
+    testing.assert_allclose(r_squared, expected_r_squared)
     testing.assert_allclose(r_squared, second_expected_r_squared)
-    testing.assert_allclose(second_r_squared, expected_r_squared, rtol=0.0,
-                            atol=2e-5)
-    testing.assert_allclose(second_r_squared, second_expected_r_squared,
-                            rtol=0.0, atol=2e-5)
+    testing.assert_allclose(second_r_squared, expected_r_squared)
+    testing.assert_allclose(second_r_squared, second_expected_r_squared)
 
 
 def test_least_squares_variance():