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new 0303969 NUMBERS-153: Iterative implementation of "trigamma" function.
new 361376e Merge branch 'master' of
https://gitbox.apache.org/repos/asf/commons-numbers
0303969 is described below
commit 03039699f5abe9f4342cd4a5f0bb0b6e4ceefb73
Author: Gilles Sadowski <gillese...@gmail.com>
AuthorDate: Fri Oct 30 01:31:20 2020 +0100
NUMBERS-153: Iterative implementation of "trigamma" function.
---
.../org/apache/commons/numbers/gamma/Trigamma.java | 20 ++++++++-----
.../apache/commons/numbers/gamma/TrigammaTest.java | 35 +++++++++++++++++-----
2 files changed, 40 insertions(+), 15 deletions(-)
diff --git
a/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/Trigamma.java
b/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/Trigamma.java
index 0eef4e3..b0e50a7 100644
---
a/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/Trigamma.java
+++
b/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/Trigamma.java
@@ -55,15 +55,19 @@ public final class Trigamma {
return 1 / (x * x);
}
- if (x >= C_LIMIT) {
- final double inv = 1 / (x * x);
- // 1 1 1 1 1
- // - + ---- + ---- - ----- + -----
- // x 2 3 5 7
- // 2 x 6 x 30 x 42 x
- return 1 / x + inv / 2 + inv / x * (F_1_6 - inv * (F_1_30 + F_1_42
* inv));
+ double trigamma = 0;
+ while (x < C_LIMIT) {
+ trigamma += 1 / (x * x);
+ x += 1;
}
- return value(x + 1) + 1 / (x * x);
+ final double inv = 1 / (x * x);
+ // 1 1 1 1 1
+ // - + ---- + ---- - ----- + -----
+ // x 2 3 5 7
+ // 2 x 6 x 30 x 42 x
+ trigamma += 1 / x + inv / 2 + inv / x * (F_1_6 - inv * (F_1_30 +
F_1_42 * inv));
+
+ return trigamma;
}
}
diff --git
a/commons-numbers-gamma/src/test/java/org/apache/commons/numbers/gamma/TrigammaTest.java
b/commons-numbers-gamma/src/test/java/org/apache/commons/numbers/gamma/TrigammaTest.java
index eb481a5..09b7c2d 100644
---
a/commons-numbers-gamma/src/test/java/org/apache/commons/numbers/gamma/TrigammaTest.java
+++
b/commons-numbers-gamma/src/test/java/org/apache/commons/numbers/gamma/TrigammaTest.java
@@ -25,12 +25,24 @@ import org.junit.jupiter.api.Test;
class TrigammaTest {
@Test
void testTrigamma() {
- double eps = 1e-8;
+ final double eps = 1e-9; // Allowed relative error.
// computed using webMathematica. For example, to compute
trigamma($i) = Polygamma(1, $i), use
//
//
http://functions.wolfram.com/webMathematica/Evaluated.jsp?name=PolyGamma2&plottype=0&vars={%221%22,%22$i%22}&digits=20
- double[] data = {
- 0.0, Double.POSITIVE_INFINITY,
+ final double[] data = {
+ -98765.4321, 10.332673372988805424,
+ -100.5, 9.8597034918700861520,
+ -50.5, 9.8499971860824842274,
+ -20.5, 9.8219943446498794821,
+ -10.5, 9.7787577398148123845,
+ -5.5, 9.7033198653394003812,
+ -2.5, 9.5392466449891237539,
+ -0.5, 8.9348022005446793094,
+ -1e-1, 101.92253995947720352,
+ -1e-2, 10001.669304101071825,
+ -1e-3, 1.0000016473414317771e6,
+ -1e-4, 1.0000000164517451070e8,
+ -1e-5, 1.0000000001644958108e10,
1e-11, 1e22,
1e-10, 1e20,
1e-9, 1.0000000000000000016e18,
@@ -43,25 +55,34 @@ class TrigammaTest {
1e-2, 10001.621213528313220,
1e-1, 101.43329915079275882,
1, 1.6449340668482264365,
+ 1.5, 0.93480220054467930942,
2, 0.64493406684822643647,
+ 2.5, 0.49035775610023486497,
3, 0.39493406684822643647,
+ 3.5, 0.33035775610023486497,
4, 0.28382295573711532536,
+ 4.5, 0.24872510303901037518,
5, 0.22132295573711532536,
+ 7.5, 0.14261589669670379977,
10, 0.10516633568168574612,
20, 0.051270822935203119832,
50, 0.020201333226697125806,
- 100, 0.010050166663333571395
+ 100, 0.010050166663333571395,
+ 12345.6789, 0.000081003281325733214110
};
for (int i = data.length - 2; i >= 0; i -= 2) {
final double value = data[i];
final double expected = data[i + 1];
- // Allowed error is 1e-8 relative or absolute error whichever is
larger.
- final double error = Math.max(expected * eps, eps);
- Assertions.assertEquals(expected, Trigamma.value(value), error, ()
-> "trigamma " + value);
+ Assertions.assertEquals(1, Trigamma.value(value) / expected, eps,
() -> "trigamma " + value);
}
}
@Test
+ void testTrigammaZero() {
+ Assertions.assertEquals(Double.POSITIVE_INFINITY, Trigamma.value(0),
0d);
+ }
+
+ @Test
void testTrigammaNonRealArgs() {
Assertions.assertTrue(Double.isNaN(Trigamma.value(Double.NaN)));
Assertions.assertTrue(Double.isInfinite(Trigamma.value(Double.POSITIVE_INFINITY)));
