Merge pull request #50 from PESchoenberg/develop

Added functions.

grsp2.scm

@@ -56,7 +56,8 @@
 	    grsp-method-newton
 	    grsp-method-euler
 	    grsp-lerp
-	    grsp-givens-rotation))
+	    grsp-givens-rotation
+	    grsp-fitin))
 
 
 ; grsp-gtels - Finds if p_n1 is greater, equal or smaller than p_n2.
@@ -545,7 +546,7 @@
     res))
 
 
-; grsp-fermat-number - Produces a Fermat numbernumber.
+; grsp-fermat-number - Produces a Fermat number.
 ;
 ; Arguments:
 ; - p_n: non-negative integer.
@@ -758,3 +759,26 @@
 
     res1))
 
+
+; grsp-fitin - truncates p_n1 if it does not fit in the interval [p_nmin, p_nmax].
+;
+; Arguments:
+; - p_n1: real.
+; - p_nmin: lower bounday of interval.
+; - p_nmax: higher boundary of th interval.
+;
+; Output:
+; - p_n1 if it is in [p_nmin,p:nmax]
+; - p_nmin if p_n1 < p_nmin.
+; - p_nmax if p_n1 > p_nmax.
+;
+(define (grsp-fitin p_n1 p_nmin p_nmax)
+  (let ((res1 p_n1))
+
+    (cond ((> p_n1 p_nmax)
+	   (set! res1 p_nmax))
+	  ((< p_n1 p_nmin)
+	   (set! res1 p_nmin)))
+
+  res1))
+

grsp3.scm

@@ -141,6 +141,10 @@
 ;   - "#CH": 0-1 checkerboard pattern matrix.
 ;   - "#+IJ": matrix containing the sum of i and j values.
 ;   - "#-IJ": matrix containing the substraction of i and j values.
+;   - "#+IJ": matrix containing the product of i and j values.
+;   - "#-IJ": matrix containing the quotient of i and j values.
+;   - "#US": upper shift matrix.
+;   - "#LS": lower shift matrix.
 
 ; - p_m: rows, positive integer.
 ; - p_n: cols, positive integer.
@@ -206,6 +210,12 @@
 			((equal? p_s "#/IJ")
 			 (set! s 1)
 			 (set! n m))
+			((equal? p_s "#US")
+			 (set! s 0)
+			 (set! n m))
+			((equal? p_s "#LS")
+			 (set! s 0)
+			 (set! n m))			
 
 			(else (set! s p_s)))
 
@@ -330,6 +340,17 @@
 					      (array-set! res (/ i j) i j)))
 				       (set! j (+ j 1)))
 				(set! i (+ i 1))))
+			((equal? p_s "#US")
+			 (while (< i m)
+				(set! j 0)
+				(while (< j (- n 1))
+				       (cond ((eq? i j)
+					      (array-set! res 1 i (+ j 1))))
+				       (set! j (+ j 1)))
+				(set! i (+ i 1))))
+			((equal? p_s "#LS")
+			 (set! res (grsp-matrix-create "#US" m n))
+			 (set! res (grsp-matrix-transpose res)))
 
 			((equal? p_s "#Q")
 			 (array-set! res -1 (- m 2) (- n 1))))))))
@@ -2066,4 +2087,4 @@
 
     res1))
 
-
+    

grsp5.scm

@@ -0,0 +1,209 @@
+; ==============================================================================
+;
+; grsp5.scm
+;
+; Statisitical and probabilistic functions.
+;
+; ==============================================================================
+;
+; Copyright (C) 2018  Pablo Edronkin (pablo.edronkin at yahoo.com)
+;
+;   This program is free software: you can redistribute it and/or modify
+;   it under the terms of the GNU Lesser General Public License as published by
+;   the Free Software Foundation, either version 3 of the License, or
+;   (at your option) any later version.
+;
+;   This program is distributed in the hope that it will be useful,
+;   but WITHOUT ANY WARRANTY; without even the implied warranty of
+;   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+;   GNU Lesser General Public License for more details.
+;
+;   You should have received a copy of the GNU Lesser General Public License
+;   along with this program. If not, see <https://www.gnu.org/licenses/>.
+;
+; ==============================================================================
+
+; https://en.wikipedia.org/wiki/Probability
+
+(define-module (grsp grsp5)
+  #:use-module (grsp grsp0)
+  #:use-module (grsp grsp1)
+  #:use-module (grsp grsp2)
+  #:use-module (grsp grsp3)
+  #:use-module (grsp grsp4)  
+  #:export (grsp-feature-scaling
+	    grsp-z-score
+	    grsp-binop
+	    grsp-pnot
+	    grsp-pand
+	    grsp-pnand
+	    grsp-por
+	    grsp-pxor
+	    grsp-pcond))
+
+
+; grsp-feature-scaling - scales (normalizes) p_n between [0,1].
+;
+; Arguments:
+; - p_n: scalar.
+; - p_nmin: min value for p_n.
+; - p_max: max value for p_x.
+;
+; Sources:
+; - https://www.statisticshowto.datasciencecentral.com/normalized/
+;
+(define (grsp-feature-scaling p_n p_nmin p_nmax)
+  (let ((res1 0))
+
+    (set! res1 (* 1.0 (/ (- p_n p_nmin) (- p_nmax p_nmin))))
+    res1))
+
+
+; grsp-z-score - calculates the z score for a sample data point.
+;
+; Arguments:
+; - p_n1: data point.
+; - p_m1: sample mean.
+; - p_s1: sample standard deviation.
+;
+; Sources:
+; - https://www.statisticshowto.datasciencecentral.com/normalized/
+;
+(define (grsp-z-score p_n1 p_m1 p_s1)
+  (let ((res1 0))
+
+    (set! res1 (* 1.0 (/ (- p_n1 p_m1) p_s1)))
+    res1))
+
+
+; grsp-binop - performs operation p_s1 on p_n1 and p_n2 and calculates the p_n3
+; power of that binomial operation.
+;
+; Arguments:
+; - p_s1: string determining the operation.
+;   - "#+": sum.
+;   - "#-": substraction.
+;   - "#*": multiplication.
+;   - "#/": division.
+; - p_n1: real.
+; - p_n2: real.
+; - p_n3: real.
+;
+(define (grsp-binop p_s1 p_n1 p_n2 p_n3)
+  (let ((res1 0))
+
+    (cond  ((equal? p_s1 "#+")
+	    (set! res1 (expt (+ p_n1 p_n2) p_n3)))
+	   ((equal? p_s1 "#-")
+	    (set! res1 (expt (- p_n1 p_n2) p_n3)))
+	   ((equal? p_s1 "#*")
+	    (set! res1 (expt (- p_n1 p_n2) p_n3)))
+	   ((equal? p_s1 "#/")
+	    (set! res1 (expt (- p_n1 p_n2) p_n3))))
+
+    res1))
+
+
+; grsp-pnot - calculates the complementary probability of p_n1.
+;
+; Arguments:
+;- p_n1: real representing a probability in [0,1]
+;
+(define (grsp-pnot p_n1)
+  (let ((res1 1))
+
+    (set! res1 (- res1 (grsp-fitin p_n1 0.0 1.0)))
+
+    res1))
+
+
+; grsp-pand - calculates the probability of p_n1 and p_n2 happening, 
+; being independent.
+;
+; Arguments:
+;- p_n1: real repesenting a probability in [0,1]
+;- p_n2: real repesenting a probability in [0,1]
+;
+(define (grsp-pand p_n1 p_n2)
+  (let ((res1 1))
+
+    (set! res1 (* (grsp-fitin p_n1 0.0 1.0) (grsp-fitin p_n2 0.0 1.0)))
+
+    res1))
+
+
+; grsp-pnand - calculates the probability of p_n1 and p_n2 happening, 
+; being not independent.
+;
+; Arguments:
+;- p_n1: real repesenting a probability in [0,1]
+;- p_n2: real repesenting a probability in [0,1]
+;
+(define (grsp-pnand p_n1 p_n2)
+  (let ((res1 1)
+	(n1 0)
+	(n2 0))
+
+    (set! n1 (grsp-fitin p_n1 0.0 1.0))
+    (set! n2 (grsp-fitin p_n2 0.0 1.0)) 
+    (set! res1 (* (grsp-pcond n1 n2) n2))
+
+    res1))
+
+
+; grsp-por - calculates the probability of p_n1 or p_n2 happening.
+;
+; Arguments:
+;- p_n1: real repesenting a probability in [0,1]
+;- p_n2: real repesenting a probability in [0,1]
+;
+(define (grsp-por p_n1 p_n2)
+  (let ((res1 1)
+	(n1 0)
+	(n2 0))
+
+    (set! n1 (grsp-fitin p_n1 0.0 1.0))
+    (set! n2 (grsp-fitin p_n2 0.0 1.0))    
+    (set! res1 (- (+ n1 n2) (grsp-pand n1 n2)))
+
+    res1))
+
+
+; grsp-pxor - calculates the probability of p_n1 or p_n2 happening, 
+; beign mutually exclusive.
+;
+; Arguments:
+;- p_n1: real repesenting a probability in [0,1]
+;- p_n2: real repesenting a probability in [0,1]
+;
+(define (grsp-pxor p_n1 p_n2)
+  (let ((res1 0)
+	(n1 0)
+	(n2 0))
+
+    (set! n1 (grsp-fitin p_n1 0.0 1.0))
+    (set! n2 (grsp-fitin p_n2 0.0 1.0))    
+    (cond ((<= (+ n1 n2) 1)
+	   (set! res1 (+ n1 n2))))
+
+    res1))
+
+
+; grsp-pcond - calculates the probability of p_n1 given p_n2 happening.
+;
+; Arguments:
+;- p_n1: real repesenting a probability in [0,1]
+;- p_n2: real repesenting a probability in [0,1]
+;
+(define (grsp-pcond p_n1 p_n2)
+  (let ((res1 0)
+	(n1 0)
+	(n2 0))
+
+    (set! n1 (grsp-fitin p_n1 0.0 1.0))
+    (set! n2 (grsp-fitin p_n2 0.0 1.0))
+    (cond ((> n2 0)
+	   (set! res1 (/ (grsp-pand n1 n2) n2))))
+
+    res1))
+