function [ a, ierror ] = basis_map_3d ( u, v )
%*****************************************************************************80
%
%% basis_map_3d() computes the matrix which maps one basis to another.
%
% Discussion:
%
% As long as the column vectors U1, U2 and U3 are linearly independent,
% a matrix A will be computed that maps U1 to V1, U2 to V2, and
% U3 to V3, where V1, V2 and V3 are the columns of V.
%
% Depending on the values of the vectors, A may represent a
% rotation, reflection, dilation, project, or a combination of these
% basic linear transformations.
%
% Licensing:
%
% This code is distributed under the MIT license.
%
% Modified:
%
% 16 February 2005
%
% Author:
%
% John Burkardt
%
% Input:
%
% real U(3,3), the columns of U are the three
% "domain" or "preimage" vectors, which should be linearly independent.
%
% real V(3,3), the columns of V are the three
% "range" or "image" vectors.
%
% Output:
%
% real A(3,3), a matrix with the property that
% A * U1 = V1, A * U2 = V2 and A * U3 = V3.
%
% integer IERROR, error flag.
% 0, no error occurred.
% nonzero, the matrix [ U1 | U2 | U3 ] is exactly singular.
%
ierror = 0;
%
% Compute C = the inverse of [ U1 | U2 | U3 ].
%
b(1:3,1:3) = u(1:3,1:3);
[ c, det ] = r8mat_inverse_3d ( b );
if ( det == 0.0 )
ierror = 1;
a = [];
return
end
%
% A = [ V1 | V2 | V3 ] * inverse [ U1 | U2 | U3 ].
%
a(1:3,1:3) = v(1:3,1:3) * c(1:3,1:3);
return
end