Language Reference

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.

The following statements demonstrate the SHAPECOL function: 

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

Figure 24.373: 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 $\mb{A}$" and is written $\mbox{vec}(\mb{A})$. Uses of the $\mbox{vec}$ operator in matrix algebra are described in Harville (1997). One important property is the relationship between the $\mbox{vec}$ operator and the Kronecker product operator
               . If $\mb{A}$, $\mb{B}$, and $\mb{X}$ have the appropriate dimensions, then 
            

            

               
\[  \mbox{vec}(\mb{A}\mb{X}\mb{B}) = (\mb{B}^\prime \otimes \mb{A})\mbox{vec}(\mb{X})  \]

            

            
  
            

            
There is also a relationship between the SHAPECOL function and the SHAPE function
               . If $\mb{A}$ 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.