Data update

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

@@ -0,0 +1 @@
+select j as i, i as j, value from A;

Task/Matrix-transposition/DuckDB/matrix-transposition-2.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);
+
+# transposition
+create or replace table AT as
+  (select j as i, i as j, value from A);
+
+.print The matrix-like representation of A:
+create or replace table AMatrix as (pivot A on j using max(value) order by i);
+from AMatrix;
+
+.print Convert the matrix-like representation back to the (i,j,value) representation:
+unpivot AMatrix on columns('^[1-9]') into name j VALUE value;
+
+.print The matrix-like representation of "A transpose":
+pivot AT on j using max(value) order by i;

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

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+# Note that if the input is not rectangular, the output might be lossy.
+create or replace function transpose(lst) as (
+  select list_transform( range(1, 1+length(lst[1])),
+                         j -> list_transform(range(1, length(lst)+1),
+                                              i -> lst[i][j]) ));