Solution to task 1

1 files changed, 85 insertions, 0 deletions

diff --git a/challenge-211/jo-37/perl/ch-1.pl b/challenge-211/jo-37/perl/ch-1.pl
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+#!/usr/bin/perl -s
+
+use v5.16;
+use Test2::V0 '!float';
+use PDL;
+
+our ($tests, $examples);
+
+run_tests() if $tests || $examples;	# does not return
+
+die <<EOS unless @ARGV;
+usage: $0 [-examples] [-tests] [Matrix]
+
+-examples
+    run the examples from the challenge
+ 
+-tests
+    run some tests
+
+Matrix
+    a string representation of a matrix as accepted by the PDL constructor,
+    e.g. "[3 2 1] [4 3 2]"
+
+EOS
+
+
+### Input and Output
+
+say is_toeplitz("@ARGV") ? 'true' : 'false';
+
+
+### Implementation
+
+# A NxM matrix (N,M > 1) has N + M - 3 diagonals having more than one
+# element.  Creating a set of NxN matrices where each of them have one
+# of the orignal matrix' diagonals as its main diagonal.  Then take the
+# diagonal of these matrices and re-arrange them into a new matrix
+# having the main diagonals of the matrix series as rows. Taking minimum
+# and maximum over the rows.  If min and max equals for every row, the
+# matrix is Toeplitz.
+# Note: Utilizing BAD values in incomplete diagonals that do not account
+# for minimum or maximum.
+sub is_toeplitz {
+	(my $m = pdl @_)->badflag(1);
+    my ($min, $max) = (
+        cat map $_->diagonal(0, 1),
+        $m->range($m->dim(0) - 2 - sequence(indx, 1, $m->shape->sum - 3),
+            $m->dim(1), 't')
+        ->reorder(1,2,0)->dog
+    )->minmaximum;
+
+    all $min == $max;
+}
+
+
+### Examples and tests
+
+sub run_tests {
+    SKIP: {
+        skip "examples" unless $examples;
+        
+        ok is_toeplitz(
+            [4, 3, 2, 1],
+            [5, 4, 3, 2],
+            [6, 5, 4, 3]), 'example 1';
+
+        ok !is_toeplitz(
+            [1, 2, 3],
+            [3, 2, 1]), 'example 2';
+    }
+
+    SKIP: {
+        skip "tests" unless $tests;
+
+        ok is_toeplitz(sequence(4) + 5 - sequence(5)->dummy(0)), '4 x 5';
+        ok is_toeplitz(sequence(5) + 4 - sequence(4)->dummy(0)), '5 x 4';
+
+        my $nt = sequence(4) + 5 - sequence(5)->dummy(0);
+        $nt->set(1, 4, 0);
+        ok !is_toeplitz($nt), 'one element failing';
+	}
+
+    done_testing;
+    exit;
+}