Language Reference: SHAPECOL Function

SHAPECOL Function

SHAPECOL( matrix, nrow <, ncol> <, pad-value> ) ;

The SHAPECOL function reshapes and repeats values in a matrix. It is similar to the SHAPE function except that the SHAPECOL function produces the result matrix by traversing the argument matrix in column-major order.

A = {1 2 3, 4 5 6};
c = shapecol(A, 3);
v = shapecol(A, 0, 1);
print c v;

Figure 23.272 Reshaped Matrices

c		v
1	5	1
4	3	4
2	6	2
		5
		3
		6

The vector v in the example is called the "vec of $\text{[math]}$ " and is written $\text{[math]}$ . Uses of the $\text{[math]}$ operator in matrix algebra are described in Harville (1997). One important property is the relationship between the $\text{[math]}$ operator and the Kronecker product. If $\text{[math]}$ , $\text{[math]}$ , and $\text{[math]}$ have the appropriate dimensions, then

$\text{[math]}$

There is also a relationship between the SHAPECOL function and the SHAPE function. If $\text{[math]}$ is a matrix, then the following two computations are equivalent:

b = shapecol(A, m, n, padVal);
c = T(shape(A`, n, m, padVal));

See the VECH function for a similar function that is useful for computing with symmetric matrices.