``````
// This program is free software; you can redistribute it and/or
// modify it under the terms of the GNU General Public License

// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.

// You should have received a copy of the GNU General Public License
// along with this program; if not, write to the Free Software
// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.

// Copyright 2007, Daniel Fontijne, University of Amsterdam -- fontijne@science.uva.nl

#include <libgasandbox/e3ga.h>
#include <libgasandbox/e3ga_util.h>
#include <libgasandbox/timing.h>

using namespace e3ga;

// SPOILER WARNING: solution to Chapter 6, Exercise 1 directly below

// exercise 1a: complete in this function
mv outerProduct_1a(const e3ga::vector &a, const mv &B) {
return 0.5f * (gp(a, B) + gp(gradeInvolution(B), a));
}

// exercise 1a: complete in this function
mv leftContraction_1a(const e3ga::vector &a, const mv &B) {
return 0.5f * (gp(a, B) - gp(gradeInvolution(B), a));
}

// exercise 1b: complete in this function
mv outerProduct_1b(const mv &A, const mv &B) {
mv result;
for (int i = 0; i <= 3; i++) {
if ((A.gu() & (1 << i)) == 0) continue; // skip if not in use
for (int j = 0; j <= 3-i; j++) {
if ((B.gu() & (1 << j)) == 0) continue; // skip if not in use
if (i + j <= 3) {
}
}
}
return result;
}

// exercise 1b: complete in this function
mv leftContraction_1b(const mv &A, const mv &B) {
mv result;
for (int i = 0; i <= 3; i++) {
if ((A.gu() & (1 << i)) == 0) continue; // skip if not in use
for (int j = i; j <= 3; j++) { // not j starts at i'
if ((B.gu() & (1 << j)) == 0) continue; // skip if not in use
}
}
return result;
}

int main(int argc, char*argv[]) {
// profiling for Gaigen 2:
e3ga::g2Profiling::init();

const int NB_TESTS = 100000;

// A test for Exercise 1a
// We generate random vectors and random multivectors, and use
// the regular outer product/left contraction functions to verify the results:
bool OK1a = true;
for (int i = 0; i < NB_TESTS; i++) {

// test outer product
{
mv X = op(a, B);
mv Y = outerProduct_1a(a, B);

if (_Float(norm_e2(X - Y)) > 1e-7f) {
// Not equal: complain
printf("\n\nouterProduct_1a() failed for\n%s\nand\n%s\n", a.toString_f().c_str(), B.toString_f().c_str());
OK1a = false;
}
}

// test left contraction
{
mv X = lcont(a, B);
mv Y = leftContraction_1a(a, B);
/*intf("a  = %s\n", a.toString_e().c_str());
printf("B  = %s\n", B.toString_e().c_str());
printf("X  = %s\n", X.toString_e().c_str());
printf("Y  = %s\n", Y.toString_e().c_str());*/

if (_Float(norm_e2(X - Y)) > 1e-7f) {
// Not equal: complain
printf("\n\nleftContraction_1a() failed for\n%s\nand\n%s\n", a.toString_f().c_str(), B.toString_f().c_str());
}
}
}
if (OK1a)
printf("outerProduct_1a() and leftContraction_1a() seem to be OK.\n");

// A test for Exercise 1b
// We generate pairs of random multivector, and use
// the regular outer product/left contraction functions to verify the results:
bool OK1b = true;
for (int i = 0; i < NB_TESTS; i++) {
mv A = randomMultivector();
mv B = randomMultivector();

// test outer product
{
mv X = op(A, B);
mv Y = outerProduct_1b(A, B);
if (_Float(norm_e2(X - Y)) > 1e-7f) {
// Not equal: complain
printf("\n\nouterProduct_1b() failed for\n%s\nand\n%s\n", A.toString().c_str(), B.toString().c_str());
OK1b = false;
}
}

// test left contraction
{
mv X = lcont(A, B);
mv Y = leftContraction_1b(A, B);
if (_Float(norm_e2(X - Y)) > 1e-7f) {
// Not equal: complain
printf("\n\nleftContraction_1b() failed for\n%s\nand\n%s\n", A.toString().c_str(), B.toString().c_str());
OK1b = false;
}
}
}

if (OK1b)
printf("outerProduct_1b() and leftContraction_1b() seem to be OK.\n");

return 0;
}

``````