Data update

Task/Matrix-multiplication/DuckDB/matrix-multiplication-1.duckdb

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+# Given two tables, A and B, representing two matrices in (i,j,value) format, the product
+# can be computed as follows, with the result being in the same format.
+SELECT A.i, B.j,
+    SUM(A.value * B.value) AS value
+  FROM A INNER JOIN B
+  ON A.j = B.i
+  GROUP BY A.i, B.j;

Task/Matrix-multiplication/DuckDB/matrix-multiplication-2.duckdb

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+# The following SQL statement will convert a table A representing an m by n matrix
+# in (i,j,value) format to a table with m rows and (n+1) columns, the first being the row id:
+pivot A on j using max(value) order by i;
+
+# To exclude the row id column:
+select columns(* exclude (i)) from (pivot A on j using max(value)) order by i;
+
+# To ensure the columns are presented in their natural order,
+# the above 'select' statement may need to be adjusted.
+# If n < 10, the following would suffice:
+select columns(* exclude (i)) from (pivot A on j using max(value)) order by i;
+
+# For 10 to 99 columns:
+select columns('^[1-9]$'), columns('^[1-9][0-9]') from (pivot A on j using max(value)) order by i;
+
+# If there are more than 99 columns, the above can be extended in the obvious way.

Task/Matrix-multiplication/DuckDB/matrix-multiplication-3.duckdb

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+create or replace table A (i integer, j integer, value float );
+insert into A values
+  (1, 1, 1),
+  (1, 2, 2),
+  (1, 3, 3),
+  (2, 1, 2),
+  (2, 2, 5),
+  (2, 3, 7);
+
+create or replace table B (i integer, j integer, value float );
+insert into B values
+  (1, 1, 2),
+  (1, 2, 4),
+  (1, 3, 8),
+  (2, 1, 1),
+  (2, 2, 5),
+  (2, 3, -10),
+  (3, 1, 3),
+  (3, 2, 6),
+  (3, 3, 9);
+
+.print Display A in a matrix format including the row id
+pivot A on j using max(value) order by i;
+
+.print Display B likewise
+pivot B on j using max(value) order by i;
+
+. print Compute C = A * B
+CREATE OR REPLACE table C as
+  SELECT A.i, B.j,
+       SUM(A.value * B.value) AS value
+  FROM A INNER JOIN B
+  ON A.j = B.i
+  GROUP BY A.i, B.j;
+
+.print Display C in matrix format excluding the row id
+select columns(* exclude (i))
+  from (pivot C on j using max(value))
+  order by i;