Initial data commit

Task/Multiple-regression/PicoLisp/multiple-regression-1.l

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+(scl 20)
+
+# Matrix transposition
+(de matTrans (Mat)
+   (apply mapcar Mat list) )
+
+# Matrix multiplication
+(de matMul (Mat1 Mat2)
+   (mapcar
+      '((Row)
+         (apply mapcar Mat2
+            '(@ (sum */ Row (rest) (1.0 .))) ) )
+      Mat1 ) )
+
+# Matrix identity
+(de matIdent (N)
+   (let L (need N (1.0) 0)
+      (mapcar '(() (copy (rot L))) L) ) )
+
+# Reduced row echelon form
+(de reducedRowEchelonForm (Mat)
+   (let (Lead 1  Cols (length (car Mat)))
+      (for (X Mat X (cdr X))
+         (NIL
+            (loop
+               (T (seek '((R) (n0 (get R 1 Lead))) X)
+                  @ )
+               (T (> (inc 'Lead) Cols)) ) )
+         (xchg @ X)
+         (let D (get X 1 Lead)
+            (map
+               '((R) (set R (*/ (car R) 1.0 D)))
+               (car X) ) )
+         (for Y Mat
+            (unless (== Y (car X))
+               (let N (- (get Y Lead))
+                  (map
+                     '((Dst Src)
+                        (inc Dst (*/ N (car Src) 1.0)) )
+                     Y
+                     (car X) ) ) ) )
+         (T (> (inc 'Lead) Cols)) ) )
+   Mat )

Task/Multiple-regression/PicoLisp/multiple-regression-2.l

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+(de matInverse (Mat)
+   (let N (length Mat)
+      (unless (= N (length (car Mat)))
+         (quit "can't invert a non-square matrix") )
+      (mapc conc Mat (matIdent N))
+      (mapcar '((L) (tail N L)) (reducedRowEchelonForm Mat)) ) )
+
+(de columnVector (Ary)
+   (mapcar cons Ary) )
+
+(de regressionCoefficients (Mat X)
+   (let Xt (matTrans X)
+      (matMul (matMul (matInverse (matMul Xt X)) Xt) Mat) ) )
+
+(setq
+   Y (columnVector (1.0 2.0 3.0 4.0 5.0))
+   X (columnVector (2.0 1.0 3.0 4.0 5.0)) )
+
+(round (caar (regressionCoefficients Y X)) 17)