Exponentially scaled modified Bessel functions of order zero and one.

The functions are conventionally called i0e and i1e. The exponentially scaled version is more numerically stable. The standard Bessel functions can be obtained as i0(x) = exp(|x|) i0e(x)

The code is ported from Cephes and tested against SciPy.

1 files changed, 40 insertions, 0 deletions

diff --git a/unsupported/test/special_functions.cpp b/unsupported/test/special_functions.cpp
index 057fb3e92..48d0db95e 100644
--- a/unsupported/test/special_functions.cpp
+++ b/unsupported/test/special_functions.cpp
@@ -335,6 +335,46 @@ template<typename ArrayType> void array_special_functions()
         ArrayType test = betainc(a, b + one, x) + eps;
         verify_component_wise(test, expected););
   }
+
+  // Test Bessel function i0e. Reference results obtained with SciPy.
+  {
+    ArrayType x(21);
+    ArrayType expected(21);
+    ArrayType res(21);
+
+    x << -20.0, -18.0, -16.0, -14.0, -12.0, -10.0, -8.0, -6.0, -4.0, -2.0, 0.0,
+        2.0, 4.0, 6.0, 8.0, 10.0, 12.0, 14.0, 16.0, 18.0, 20.0;
+
+    expected << 0.0897803118848, 0.0947062952128, 0.100544127361,
+        0.107615251671, 0.116426221213, 0.127833337163, 0.143431781857,
+        0.16665743264, 0.207001921224, 0.308508322554, 1.0, 0.308508322554,
+        0.207001921224, 0.16665743264, 0.143431781857, 0.127833337163,
+        0.116426221213, 0.107615251671, 0.100544127361, 0.0947062952128,
+        0.0897803118848;
+
+    CALL_SUBTEST(res = i0e(x);
+                 verify_component_wise(res, expected););
+  }
+
+  // Test Bessel function i1e. Reference results obtained with SciPy.
+  {
+    ArrayType x(21);
+    ArrayType expected(21);
+    ArrayType res(21);
+
+    x << -20.0, -18.0, -16.0, -14.0, -12.0, -10.0, -8.0, -6.0, -4.0, -2.0, 0.0,
+        2.0, 4.0, 6.0, 8.0, 10.0, 12.0, 14.0, 16.0, 18.0, 20.0;
+
+    expected << -0.0875062221833, -0.092036796872, -0.0973496147565,
+        -0.103697667463, -0.11146429929, -0.121262681384, -0.134142493293,
+        -0.152051459309, -0.178750839502, -0.215269289249, 0.0, 0.215269289249,
+        0.178750839502, 0.152051459309, 0.134142493293, 0.121262681384,
+        0.11146429929, 0.103697667463, 0.0973496147565, 0.092036796872,
+        0.0875062221833;
+
+    CALL_SUBTEST(res = i1e(x);
+                 verify_component_wise(res, expected););
+  }
 #endif
 }