June 2018 Update

Task/Matrix-arithmetic/00DESCRIPTION

@@ -8,6 +8,7 @@ In both cases the sum is over the permutations <math>\sigma</math> of the permut
 
 More efficient algorithms for the determinant are known: [[LU decomposition]], see for example [[wp:LU decomposition#Computing the determinant]]. Efficient methods for calculating the permanent are not known.
 
-;Cf.:
+
+;Related task:
 * [[Permutations by swapping]]
 <br><br>

Task/Matrix-arithmetic/Go/matrix-arithmetic-4.go

@@ -3,14 +3,14 @@ package main
 import (
     "fmt"
 
-    "github.com/gonum/matrix/mat64"
+    "gonum.org/v1/gonum/mat"
 )
 
 func main() {
-    fmt.Println(mat64.Det(mat64.NewDense(2, 2, []float64{
+    fmt.Println(mat.Det(mat.NewDense(2, 2, []float64{
         1, 2,
         3, 4})))
-    fmt.Println(mat64.Det(mat64.NewDense(3, 3, []float64{
+    fmt.Println(mat.Det(mat.NewDense(3, 3, []float64{
         2, 9, 4,
         7, 5, 3,
         6, 1, 8})))

Task/Matrix-arithmetic/Perl/matrix-arithmetic.pl

@@ -0,0 +1,27 @@
+#!/usr/bin/perl
+use strict;
+use warnings;
+use PDL;
+use PDL::NiceSlice;
+
+sub permanent{
+	my $mat = shift;
+	my $n = shift // $mat->dim(0);
+	return undef if $mat->dim(0) != $mat->dim(1);
+	return $mat(0,0) if $n == 1;
+	my $sum = 0;
+	--$n;
+	my $m = $mat(1:,1:)->copy;
+	for(my $i = 0; $i <= $n; ++$i){
+		$sum += $mat($i,0) * permanent($m, $n);
+		last if $i == $n;
+		$m($i,:) .= $mat($i,1:);
+	}
+	return sclr($sum);
+}
+
+my $M = pdl([[2,9,4], [7,5,3], [6,1,8]]);
+print "M = $M\n";
+print "det(M) = " . $M->determinant . ".\n";
+print "det(M) = " . $M->det . ".\n";
+print "perm(M) = " . permanent($M) . ".\n";

Task/Matrix-arithmetic/Sidef/matrix-arithmetic.sidef

@@ -0,0 +1,31 @@
+class Array {
+    method permanent {
+        var r = @^self.len
+
+        var sum = 0
+        r.permutations { |*a|
+            var prod = 1
+            [a,r].zip {|row,col| prod *= self[row][col] }
+            sum += prod
+        }
+
+        return sum
+    }
+}
+
+var m1 = [[1,2],[3,4]]
+
+var m2 = [[1, 2, 3, 4],
+          [4, 5, 6, 7],
+          [7, 8, 9, 10],
+          [10, 11, 12, 13]]
+
+var m3 = [[0, 1, 2, 3, 4],
+          [5, 6, 7, 8, 9],
+          [10, 11, 12, 13, 14],
+          [15, 16, 17, 18, 19],
+          [20, 21, 22, 23, 24]]
+
+[m1, m2, m3].each { |m|
+  say "determinant:\t #{m.determinant}\npermanent:\t #{m.permanent}\n"
+}

Task/Matrix-arithmetic/Simula/matrix-arithmetic.simula

@@ -1,24 +1,18 @@
 ! MATRIX ARITHMETIC ;
 BEGIN
 
-    INTEGER PROCEDURE LENGTH(A); REAL ARRAY A;
+    INTEGER PROCEDURE LENGTH(A); ARRAY A;
         LENGTH := UPPERBOUND(A, 1) - LOWERBOUND(A, 1) + 1;
 
-    PROCEDURE MINOR(A, X, Y, MAT); REAL ARRAY A, MAT; INTEGER X, Y;
+    ! Set MAT to the first minor of A dropping row X and column Y ;
+    PROCEDURE MINOR(A, X, Y, MAT); ARRAY A, MAT; INTEGER X, Y;
     BEGIN
-        INTEGER I, J, M; M := LENGTH(A) - 1;
-        FOR I := 1 STEP 1 UNTIL M DO
+        INTEGER I, J, rowA, M; M := LENGTH(A) - 1; ! not a constant;
+        FOR I := 1 STEP 1 UNTIL M DO BEGIN
+            rowA := IF I < X THEN I ELSE I + 1;
             FOR J := 1 STEP 1 UNTIL M DO
-            BEGIN
-                IF I < X AND J < Y THEN
-                    MAT(I, J) := A(I, J)
-                ELSE IF I >= X AND J < Y THEN
-                    MAT(I, J) := A(I + 1, J)
-                ELSE IF I < X AND J >= Y THEN
-                    MAT(I, J) := A(I, J + 1)
-                ELSE ! I > X AND J > Y ;
-                    MAT(I, J) := A(I + 1, J + 1)
-            END
+                MAT(I, J) := A(rowA, IF J < Y THEN J else J + 1);
+        END
     END MINOR;
 
     REAL PROCEDURE DET(A); REAL ARRAY A;
@@ -68,18 +62,17 @@ BEGIN
         REAL ARRAY A(1:SIZE, 1:SIZE);
         INTEGER I, J;
 
-        FOR I := 1 STEP 1 UNTIL SIZE DO
+        FOR I := 1 STEP 1 UNTIL SIZE DO BEGIN
+            ! may be need here: INIMAGE;
             FOR J := 1 STEP 1 UNTIL SIZE DO
-                A(I, J) := INREAL;
-
+                A(I, J) := INREAL
+        END;
         OUTTEXT("DETERMINANT ... : "); OUTREAL(DET (A), 10, 20); OUTIMAGE;
         OUTTEXT("PERMANENT ..... : "); OUTREAL(PERM(A), 10, 20); OUTIMAGE;
     END
 
-    ! NOTE THAT THE FIRST INPUT IS THE SIZE OF THE MATRIX.
-    ! FOR EXAMPLE:
+    COMMENT  THE FIRST INPUT IS THE SIZE OF THE MATRIX, FOR EXAMPLE:
 
-    COMMENT
     ! 2
     ! 1 2
     ! 3 4

Task/Matrix-arithmetic/Stata/matrix-arithmetic-1.stata

@@ -0,0 +1,28 @@
+real vector range1(real scalar n, real scalar i) {
+	if (i < 1 | i > n) {
+		return(1::n)
+	} else if (i == 1) {
+		return(2::n)
+	} else if (i == n) {
+		return(1::n-1)
+	} else {
+		return(1::i-1\i+1::n)
+	}
+}
+
+real matrix submat(real matrix a, real scalar i, real scalar j) {
+	return(a[range1(rows(a), i), range1(cols(a), j)])
+}
+
+real scalar sumrec(real matrix a, real scalar x) {
+	real scalar n, s, p
+	n = rows(a)
+	if (n==1) return(a[1,1])
+	s = 0
+	p = 1
+	for (i=1; i<=n; i++) {
+		s = s+p*a[i,1]*sumrec(submat(a, i, 1), x)
+		p = p*x
+	}
+	return(s)
+}

Task/Matrix-arithmetic/Stata/matrix-arithmetic-2.stata

@@ -0,0 +1,19 @@
+: a=1,1,1,0\1,1,0,1\1,0,1,1\0,1,1,1
+: a
+[symmetric]
+       1   2   3   4
+    +-----------------+
+  1 |  1              |
+  2 |  1   1          |
+  3 |  1   0   1      |
+  4 |  0   1   1   1  |
+    +-----------------+
+
+: det(a)
+  -3
+
+: sumrec(a,-1)
+  -3
+
+: sumrec(a,1)
+  9