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authorEric Andersen <andersen@codepoet.org>2001-05-10 00:40:28 +0000
committerEric Andersen <andersen@codepoet.org>2001-05-10 00:40:28 +0000
commit1077fa4d772832f77a677ce7fb7c2d513b959e3f (patch)
tree579bee13fb0b58d2800206366ec2caecbb15f3fc /libm/float/fdtrf.c
parent22358dd7ce7bb49792204b698f01a6f69b9c8e08 (diff)
uClibc now has a math library. muahahahaha!
-Erik
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+/* fdtrf.c
+ *
+ * F distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int df1, df2;
+ * float x, y, fdtrf();
+ *
+ * y = fdtrf( df1, df2, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the area from zero to x under the F density
+ * function (also known as Snedcor's density or the
+ * variance ratio density). This is the density
+ * of x = (u1/df1)/(u2/df2), where u1 and u2 are random
+ * variables having Chi square distributions with df1
+ * and df2 degrees of freedom, respectively.
+ *
+ * The incomplete beta integral is used, according to the
+ * formula
+ *
+ * P(x) = incbet( df1/2, df2/2, (df1*x/(df2 + df1*x) ).
+ *
+ *
+ * The arguments a and b are greater than zero, and x
+ * x is nonnegative.
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,100 5000 2.2e-5 1.1e-6
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * fdtrf domain a<0, b<0, x<0 0.0
+ *
+ */
+ /* fdtrcf()
+ *
+ * Complemented F distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int df1, df2;
+ * float x, y, fdtrcf();
+ *
+ * y = fdtrcf( df1, df2, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the area from x to infinity under the F density
+ * function (also known as Snedcor's density or the
+ * variance ratio density).
+ *
+ *
+ * inf.
+ * -
+ * 1 | | a-1 b-1
+ * 1-P(x) = ------ | t (1-t) dt
+ * B(a,b) | |
+ * -
+ * x
+ *
+ * (See fdtr.c.)
+ *
+ * The incomplete beta integral is used, according to the
+ * formula
+ *
+ * P(x) = incbet( df2/2, df1/2, (df2/(df2 + df1*x) ).
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,100 5000 7.3e-5 1.2e-5
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * fdtrcf domain a<0, b<0, x<0 0.0
+ *
+ */
+ /* fdtrif()
+ *
+ * Inverse of complemented F distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float df1, df2, x, y, fdtrif();
+ *
+ * x = fdtrif( df1, df2, y );
+ *
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Finds the F density argument x such that the integral
+ * from x to infinity of the F density is equal to the
+ * given probability y.
+ *
+ * This is accomplished using the inverse beta integral
+ * function and the relations
+ *
+ * z = incbi( df2/2, df1/2, y )
+ * x = df2 (1-z) / (df1 z).
+ *
+ * Note: the following relations hold for the inverse of
+ * the uncomplemented F distribution:
+ *
+ * z = incbi( df1/2, df2/2, y )
+ * x = df2 z / (df1 (1-z)).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * arithmetic domain # trials peak rms
+ * Absolute error:
+ * IEEE 0,100 5000 4.0e-5 3.2e-6
+ * Relative error:
+ * IEEE 0,100 5000 1.2e-3 1.8e-5
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * fdtrif domain y <= 0 or y > 1 0.0
+ * v < 1
+ *
+ */
+
+
+/*
+Cephes Math Library Release 2.2: July, 1992
+Copyright 1984, 1987, 1992 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+
+#include <math.h>
+
+#ifdef ANSIC
+float incbetf(float, float, float);
+float incbif(float, float, float);
+#else
+float incbetf(), incbif();
+#endif
+
+float fdtrcf( int ia, int ib, float xx )
+{
+float x, a, b, w;
+
+x = xx;
+if( (ia < 1) || (ib < 1) || (x < 0.0) )
+ {
+ mtherr( "fdtrcf", DOMAIN );
+ return( 0.0 );
+ }
+a = ia;
+b = ib;
+w = b / (b + a * x);
+return( incbetf( 0.5*b, 0.5*a, w ) );
+}
+
+
+
+float fdtrf( int ia, int ib, int xx )
+{
+float x, a, b, w;
+
+x = xx;
+if( (ia < 1) || (ib < 1) || (x < 0.0) )
+ {
+ mtherr( "fdtrf", DOMAIN );
+ return( 0.0 );
+ }
+a = ia;
+b = ib;
+w = a * x;
+w = w / (b + w);
+return( incbetf( 0.5*a, 0.5*b, w) );
+}
+
+
+float fdtrif( int ia, int ib, float yy )
+{
+float y, a, b, w, x;
+
+y = yy;
+if( (ia < 1) || (ib < 1) || (y <= 0.0) || (y > 1.0) )
+ {
+ mtherr( "fdtrif", DOMAIN );
+ return( 0.0 );
+ }
+a = ia;
+b = ib;
+w = incbif( 0.5*b, 0.5*a, y );
+x = (b - b*w)/(a*w);
+return(x);
+}