#
# Numerical Mathematics and Computing, Fifth Edition
# Ward Cheney & David Kincaid
# Brooks/Cole Publ. Co.
# (c) 2003
#
# file:  Svd
#
# Using Maple linalg package to determine
# the singular-value decomposition of the matrix A:


 with(linalg):
 A := matrix([[1, 3, -2], [2, 7, 5], [-2, -3, 4], [5, -3, -2]]);
 S := evalf(Svd(A, U, V));
 U := evalm(U);
 V := evalm(V);
 UAV :=  evalm(transpose(U) &* A &* V);

# Creating the diagonal matrix D, and checking the work
# done by Maple:

 evalm(transpose(U) &* U);
 evalm(V &* transpose(V));
 DD := diag(S[1], S[2], S[3]);
# DD2:= stack(DD, [0,0,0]);
 DD2 := matrix(4,3,DD);
DD2[4,1]:=0;DD2[4,2]:=0;DD2[4,3]:=0;
 evalm(U &* DD2 &* transpose(V));    # This product gives the matrix A