Add submatrix_set and block_matrix and tests

arrays.scad

@@ -1199,6 +1199,42 @@ function zip(vecs, v2, v3, fit=false, fill=undef) =
     :   [for(i=[0:1:minlen-1]) [for(v=vecs) for(x=v[i]) x] ];
 
 
+// Function: block_matrix()
+// Usage:
+//    block_matrix([[M11, M12,...],[M21, M22,...], ... ])
+// Description:
+//    Create a block matrix by supplying a matrix of matrices, which will
+//    be combined into one unified matrix.  Every matrix in one row
+//    must have the same height, and the combined width of the matrices
+//    in each row must be equal.  
+function block_matrix(M) =
+    let(
+        bigM = [for(bigrow = M) each zip(bigrow)],
+        len0=len(bigM[0]),
+        badrows = [for(row=bigM) if (len(row)!=len0) 1]
+    )
+    assert(badrows==[], "Inconsistent or invalid input")
+    bigM;
+
+
+// Function: submatrix_set()
+// Usage: submatrix_set(M,A,[m],[n])
+// Description:
+//    Sets a submatrix of M equal to the matrix A.  By default the top left corner of M is set to A, but
+//    you can specify offset coordinates m and n.  If A (as adjusted by m and n) extends beyond the bounds
+//    of M then the extra entries are ignored.  You can pass in A=[[]], a null matrix, and M will be
+//    returned unchanged.  Note that the input M need not be rectangular in shape.  
+function submatrix_set(M,A,m=0,n=0) =
+    assert(is_list(M))
+    assert(is_list(A))
+    let( badrows = [for(i=idx(A)) if (!is_list(A[i])) i])
+    assert(badrows==[], str("Input submatrix malformed rows: ",badrows))
+    [for(i=[0:1:len(M)-1])
+        assert(is_list(M[i]), str("Row ",i," of input matrix is not a list"))
+        [for(j=[0:1:len(M[i])-1]) 
+            i>=m && i <len(A)+m && j>=n && j<len(A[0])+n ? A[i-m][j-n] : M[i][j]]];
+
+
 // Function: array_group()
 // Description:
 //   Takes a flat array of values, and groups items in sets of `cnt` length.

tests/test_arrays.scad

@@ -470,6 +470,31 @@ module test_zip() {
 }
 test_zip();
 
+module test_block_matrix() {
+    A = [[1,2],[3,4]];
+    B = ident(2);
+    assert_equal(block_matrix([[A,B],[B,A],[A,B]]), [[1,2,1,0],[3,4,0,1],[1,0,1,2],[0,1,3,4],[1,2,1,0],[3,4,0,1]]);
+    assert_equal(block_matrix([[A,B],ident(4)]), [[1,2,1,0],[3,4,0,1],[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]);
+    text = [["a","b"],["c","d"]];
+    assert_equal(block_matrix([[text,B]]), [["a","b",1,0],["c","d",0,1]]);
+}
+test_block_matrix();
+
+
+module test_submatrix_set() {
+    test = [[1,2,3,4,5],[6,7,8,9,10],[11,12,13,14,15], [16,17,18,19,20]];
+    ragged = [[1,2,3,4,5],[6,7,8,9,10],[11,12], [16,17]];
+    assert_equal(submatrix_set(test,[[9,8],[7,6]]), [[9,8,3,4,5],[7,6,8,9,10],[11,12,13,14,15], [16,17,18,19,20]]);
+    assert_equal(submatrix_set(test,[[9,7],[8,6]],1),[[1,2,3,4,5],[9,7,8,9,10],[8,6,13,14,15], [16,17,18,19,20]]);
+    assert_equal(submatrix_set(test,[[9,8],[7,6]],n=1), [[1,9,8,4,5],[6,7,6,9,10],[11,12,13,14,15], [16,17,18,19,20]]);
+    assert_equal(submatrix_set(test,[[9,8],[7,6]],1,2), [[1,2,3,4,5],[6,7,9,8,10],[11,12,7,6,15], [16,17,18,19,20]]);
+    assert_equal(submatrix_set(test,[[9,8],[7,6]],-1,-1), [[6,2,3,4,5],[6,7,8,9,10],[11,12,13,14,15], [16,17,18,19,20]]);
+    assert_equal(submatrix_set(test,[[9,8],[7,6]],n=4), [[1,2,3,4,9],[6,7,8,9,7],[11,12,13,14,15], [16,17,18,19,20]]);
+    assert_equal(submatrix_set(test,[[9,8],[7,6]],7,7), [[1,2,3,4,5],[6,7,8,9,10],[11,12,13,14,15], [16,17,18,19,20]]);
+    assert_equal(submatrix_set(ragged, [["a","b"],["c","d"]], 1, 1), [[1,2,3,4,5],[6,"a","b",9,10],[11,"c"], [16,17]]);
+}
+test_submatrix_set();
+
 
 module test_array_group() {
     v = [1,2,3,4,5,6];