TEST(AgradRevMatrix, trace_gen_quad_form_mat_grad_vdd) {
using stan::math::trace_gen_quad_form;
using stan::math::sum;
using stan::agrad::matrix_v;
using stan::math::matrix_d;
matrix_v av(4,4);
matrix_d ad(4,4);
matrix_d bd(4,2);
matrix_v bv(4,2);
matrix_d cd(2,2);
matrix_v cv(2,2);
AVAR res;
AVEC vars;
VEC grad;
size_t i,j,pos;
bd << 100, 10,
0, 1,
-3, -3,
5, 2;
bv << 100, 10,
0, 1,
-3, -3,
5, 2;
ad << 2.0, 3.0, 4.0, 5.0,
6.0, 10.0, 2.0, 2.0,
7.0, 2.0, 7.0, 1.0,
8.0, 2.0, 1.0, 112.0;
av << 2.0, 3.0, 4.0, 5.0,
6.0, 10.0, 2.0, 2.0,
7.0, 2.0, 7.0, 1.0,
8.0, 2.0, 1.0, 112.0;
cd.setIdentity(2,2);
cv.setIdentity(2,2);
matrix_d dqdc(bd.transpose()*ad.transpose()*bd);
res = trace_gen_quad_form(cv,ad,bd);
vars.clear();
for (i = 0; i < 2; i++)
for (j = 0; j < 2; j++)
vars.push_back(cv(i,j));
grad = cgradvec(res,vars);
pos = 0;
for (i = 0; i < 2; i++)
for (j = 0; j < 2; j++, pos++)
EXPECT_FLOAT_EQ(grad[pos], dqdc(i,j));
}
TEST(AgradRevMatrix, trace_gen_inv_quad_form_ldlt_grad_ddv) {
using stan::math::sum;
using stan::agrad::matrix_v;
using stan::math::matrix_d;
matrix_d ad(4,4);
matrix_d bd(4,2);
matrix_v bv(4,2);
matrix_d cd(2,2);
AVAR res;
AVEC vars;
VEC grad;
size_t i,j,pos;
bd << 100, 10,
0, 1,
-3, -3,
5, 2;
bv << 100, 10,
0, 1,
-3, -3,
5, 2;
ad << 9.0, 3.0, 3.0, 3.0,
3.0, 10.0, 2.0, 2.0,
3.0, 2.0, 7.0, 1.0,
3.0, 2.0, 1.0, 112.0;
cd.setIdentity(2,2);
stan::math::LDLT_factor<double,-1,-1> ldlt_ad;
ldlt_ad.compute(ad);
ASSERT_TRUE(ldlt_ad.success());
matrix_d ainv(ad.inverse());
matrix_d dqdb(ainv*bd*cd.transpose() + ainv.transpose()*bd*cd);
// var-var
res = trace_gen_inv_quad_form_ldlt(cd,ldlt_ad,bv);
vars.clear();
for (i = 0; i < 4; i++)
for (j = 0; j < 2; j++)
vars.push_back(bv(i,j));
grad = cgradvec(res,vars);
pos = 0;
for (i = 0; i < 4; i++)
for (j = 0; j < 2; j++, pos++)
EXPECT_FLOAT_EQ(grad[pos], dqdb(i,j));
}
TEST(AgradRevMatrix, trace_quad_form_ldlt_mat_grad_vd) {
using stan::math::sum;
using stan::math::matrix_v;
using stan::math::matrix_d;
matrix_v av(4,4);
matrix_d ad(4,4);
matrix_d bd(4,2);
AVAR res;
AVEC vars;
VEC grad;
size_t i,j,pos;
bd << 100, 10,
0, 1,
-3, -3,
5, 2;
ad << 9.0, 3.0, 3.0, 3.0,
3.0, 10.0, 2.0, 2.0,
3.0, 2.0, 7.0, 1.0,
3.0, 2.0, 1.0, 112.0;
av << 9.0, 3.0, 3.0, 3.0,
3.0, 10.0, 2.0, 2.0,
3.0, 2.0, 7.0, 1.0,
3.0, 2.0, 1.0, 112.0;
stan::math::LDLT_factor<stan::math::var,-1,-1> ldlt_av;
ldlt_av.compute(av);
ASSERT_TRUE(ldlt_av.success());
matrix_d ainv(ad.inverse());
matrix_d dqda(-ainv*bd*bd.transpose()*ainv);
// var-var
res = trace_inv_quad_form_ldlt(ldlt_av,bd);
vars.clear();
for (i = 0; i < 4; i++)
for (j = 0; j < 4; j++)
vars.push_back(av(i,j));
grad = cgradvec(res,vars);
pos = 0;
for (i = 0; i < 4; i++)
for (j = 0; j < 4; j++, pos++)
EXPECT_FLOAT_EQ(grad[pos], dqda(i,j));
}
TEST(AgradRevMatrix, quad_form_sym_vec_grad_vv) {
using stan::math::quad_form_sym;
using stan::agrad::matrix_v;
using stan::agrad::vector_v;
using stan::math::matrix_d;
using stan::math::vector_d;
matrix_v av(4,4);
matrix_d ad(4,4);
vector_d bd(4);
vector_v bv(4);
stan::agrad::var res;
AVEC vars;
VEC grad;
size_t pos, i, j;
bd << 100, 0, -3, 5;
bv << 100, 0, -3, 5;
ad << 2.0, 3.0, 4.0, 5.0,
3.0, 10.0, 2.0, 2.0,
4.0, 2.0, 7.0, 1.0,
5.0, 2.0, 1.0, 112.0;
av << 2.0, 3.0, 4.0, 5.0,
3.0, 10.0, 2.0, 2.0,
4.0, 2.0, 7.0, 1.0,
5.0, 2.0, 1.0, 112.0;
matrix_d dqda(bd*bd.transpose());
vector_d dqdb(ad*bd + ad.transpose()*bd);
// var-var
res = quad_form_sym(av,bv);
vars.clear();
for (size_t i = 0; i < 4; i++)
vars.push_back(bv[i]);
for (i = 0; i < 4; i++)
for (j = 0; j < 4; j++)
vars.push_back(av(i,j));
grad = cgradvec(res,vars);
for (i = 0, pos = 0; i < 4; i++, pos++)
EXPECT_FLOAT_EQ(grad[pos], dqdb[i]);
for (i = 0; i < 4; i++)
for (j = 0; j < 4; j++, pos++)
EXPECT_FLOAT_EQ(grad[pos], dqda(i,j));
}
TEST(AgradRevMatrix, quad_form_mat_grad_vd) {
using stan::math::quad_form;
using stan::math::sum;
using stan::agrad::matrix_v;
using stan::math::matrix_d;
matrix_v av(4,4);
matrix_d ad(4,4);
matrix_d bd(4,2);
AVAR res;
AVEC vars;
VEC grad;
size_t i,j,pos;
bd << 100, 10,
0, 1,
-3, -3,
5, 2;
ad << 2.0, 3.0, 4.0, 5.0,
6.0, 10.0, 2.0, 2.0,
7.0, 2.0, 7.0, 1.0,
8.0, 2.0, 1.0, 112.0;
av << 2.0, 3.0, 4.0, 5.0,
6.0, 10.0, 2.0, 2.0,
7.0, 2.0, 7.0, 1.0,
8.0, 2.0, 1.0, 112.0;
matrix_d dqda(bd*matrix_d::Ones(2,2)*bd.transpose());
// var-var
res = sum(quad_form(av,bd));
vars.clear();
for (i = 0; i < 4; i++)
for (j = 0; j < 4; j++)
vars.push_back(av(i,j));
grad = cgradvec(res,vars);
pos = 0;
for (i = 0; i < 4; i++)
for (j = 0; j < 4; j++, pos++)
EXPECT_FLOAT_EQ(grad[pos], dqda(i,j));
}
TEST(AgradRevMatrix, trace_gen_inv_quad_form_ldlt_grad_vvv_basic) {
using stan::math::sum;
using stan::agrad::matrix_v;
using stan::math::matrix_d;
using stan::math::inverse;
using stan::math::multiply;
using stan::math::trace;
using stan::math::transpose;
matrix_v cv(2,2);
matrix_v av(4,4);
matrix_v bv(4,2);
AVAR result, result_basic;
double result_val, result_basic_val;
AVEC vars;
VEC grad, grad_basic;
size_t i,j;
stan::math::LDLT_factor<stan::agrad::var,-1,-1> ldlt_av;
// calculate gradient using trace_gen_inv_quad_form_ldlt
bv << 100, 10,
0, 1,
-3, -3,
5, 2;
av << 9.0, 3.0, 3.0, 3.0,
3.0, 10.0, 2.0, 2.0,
3.0, 2.0, 7.0, 1.0,
3.0, 2.0, 1.0, 112.0;
cv << 1, 2, 3, 4;
ldlt_av.compute(av);
ASSERT_TRUE(ldlt_av.success());
result = trace_gen_inv_quad_form_ldlt(cv,ldlt_av,bv);
vars.clear();
for (i = 0; i < 2; i++)
for (j = 0; j < 2; j++)
vars.push_back(cv(i,j));
for (i = 0; i < 4; i++)
for (j = 0; j < 2; j++)
vars.push_back(bv(i,j));
for (i = 0; i < 4; i++)
for (j = 0; j < 4; j++)
vars.push_back(av(i,j));
grad = cgradvec(result,vars);
result_val = result.val();
// calculate gradient using basic math
bv << 100, 10,
0, 1,
-3, -3,
5, 2;
av << 9.0, 3.0, 3.0, 3.0,
3.0, 10.0, 2.0, 2.0,
3.0, 2.0, 7.0, 1.0,
3.0, 2.0, 1.0, 112.0;
cv << 1, 2, 3, 4;
matrix_v tmp = bv.transpose() * inverse(av) * bv;
matrix_v gen_inv_quad_form = multiply(cv, tmp);
result_basic = trace(gen_inv_quad_form);
vars.clear();
for (i = 0; i < 2; i++)
for (j = 0; j < 2; j++)
vars.push_back(cv(i,j));
for (i = 0; i < 4; i++)
for (j = 0; j < 2; j++)
vars.push_back(bv(i,j));
for (i = 0; i < 4; i++)
for (j = 0; j < 4; j++)
vars.push_back(av(i,j));
grad_basic = cgradvec(result_basic,vars);
result_basic_val = result_basic.val();
// check values;
EXPECT_FLOAT_EQ(result_basic_val, result_val);
ASSERT_EQ(grad_basic.size(), grad.size());
for (size_t n = 0; n < grad_basic.size(); n++) {
EXPECT_FLOAT_EQ(grad_basic[n], grad[n]);
}
}
