/**
* Get the Wilson's B-matrix
*/
void getBMatrix(Real** cartCoords, int numCartesians,
bondCoord** bonds, int numBonds,
angleCoord** angles, int numAngles,
dihedralCoord** dihedrals, int numDihedrals,
improperCoord** impropers, int numImpropers,
Matrix& B) {
#ifdef DEBUG
cout << "\n\ngetBMatrix - Constructing B Matrix\n";
#endif
// Constructing B Matrix
// follows method in chapter 4 of Molecular Vibrations by Wilson, Decius, and Cross
#ifdef DEBUG
int numInternals = numBonds + numAngles + numDihedrals + numImpropers;
cout << "numBonds: " << numBonds << "\n";
cout << "numAngles: " << numAngles << "\n";
cout << "numDihedrals: " << numDihedrals << "\n";
cout << "numImpropers: " << numImpropers << "\n";
cout << "numInternals: " << numInternals << "\n";
#endif
// Load Data
B = 0.0;
int i = 0;
int j = 0;
int index1 = 0;
int index2 = 0;
RowVector tempCoord1(3);
RowVector tempCoord2(3);
Real norm = 0.0;
// Bonds
for (i=0; i<numBonds; i++) {
index1 = bonds[i]->x1;
index2 = bonds[i]->x2;
//norm = bonds[i].val; // Could calculate this, like below.
#ifdef DEBUG
cout << "index1=" << index1 << "index2=" << index2 << "\n";
#endif
for (j=0; j<3; j++) {
tempCoord1(j+1) = cartCoords[index1][j];
tempCoord2(j+1) = cartCoords[index2][j];
}
tempCoord1 << tempCoord1 - tempCoord2;
norm = tempCoord1.NormFrobenius(); // XXX - don't delete
if (norm > 0.0) {
tempCoord1 << tempCoord1 / norm;
}
for (j=1; j<=3; j++) {
B(i+1,((index1)*3)+j) = tempCoord1(j);
B(i+1,((index2)*3)+j) = -tempCoord1(j);
}
}
#ifdef DEBUG
cout << "after bonds\n";
cout << "B:\n";
cout << setw(9) << setprecision(3) << (B);
cout << "\n\n";
#endif
// Angles
int index3 = 0;
RowVector tempCoord3(3);
RowVector tempCoord4(3);
RowVector tempCoord5(3);
RowVector r21(3); // Vector from 2nd to 1st point
RowVector r23(3); // Vector from 2nd to 3rd point
RowVector e21(3); // Unit vector from 2nd to 1st point
RowVector e23(3); // Unit vector from 2nd to 3rd point
Real norm21; // Norm of r21
Real norm23; // Norm of r23
Real angle = 0.0; // Angle in radians
Real cosAngle123 = 0.0;
Real sinAngle123 = 0.0;
//Real pi = 3.14159265;
Real scaleFactor = 0.529178; // Scaling factor (0.529178)
for (i=0; i<numAngles; i++) {
index1 = angles[i]->x1;
index2 = angles[i]->x2;
index3 = angles[i]->x3;
//angle = angles[i].val * (pi/180.0); // Convert to radians.
for (j=0; j<3; j++) {
tempCoord1(j+1) = cartCoords[index1][j];
tempCoord2(j+1) = cartCoords[index2][j];
tempCoord3(j+1) = cartCoords[index3][j];
}
r21 << tempCoord1 - tempCoord2;
r23 << tempCoord3 - tempCoord2;
norm21 = r21.NormFrobenius();
norm23 = r23.NormFrobenius();
e21 << r21;
if (norm21 > 0.0) {
e21 << e21 / norm21;
}
e23 << r23;
if (norm23 > 0.0) {
e23 << e23 / norm23;
}
angle = acos(DotProduct(r21,r23) / (norm21 * norm23));
cosAngle123 = DotProduct(r21,r23) / (norm21 * norm23);
sinAngle123 = sqrt(1 - (cosAngle123 * cosAngle123));
#ifdef DEBUG
cout << "r21: " << (r21) << "\n";
cout << "r23: " << (r23) << "\n";
cout << "norm21: " << norm21 << ", norm23: " << norm23 << "\n\n";
cout << "e21: " << (e21) << "\n";
cout << "e23: " << (e23) << "\n";
cout << "cos(" << angle << "): " << cos(angle) << "\n";
cout << "sin(" << angle << "): " << sin(angle) << "\n";
cout << "angle: " << acos(DotProduct(r21,r23) / (norm21 * norm23)) << "\n";
cout << "cosAngle123: " << cosAngle123 << "\n";
cout << "sinAngle123: " << sinAngle123 << "\n";
#endif
// First elements of coordinate triples
tempCoord4 << ((cosAngle123 * e21) - e23);
tempCoord4 << (tempCoord4 * scaleFactor) / (norm21 * sinAngle123);
for (j=1; j<=3; j++) {
B(i+numBonds+1,((index1)*3)+j) = tempCoord4(j);
}
// Third elements of coordinate triples
tempCoord5 << ((cosAngle123 * e23) - e21);
tempCoord5 << (tempCoord5 * scaleFactor) / (norm23 * sinAngle123);
for (j=1; j<=3; j++) {
B(i+numBonds+1,((index3)*3)+j) = tempCoord5(j);
}
// Second (middle) elements of coordinate triples (depends on 1st and 3rd)
tempCoord4 << -tempCoord4 - tempCoord5;
for (j=1; j<=3; j++) {
B(i+numBonds+1,((index2)*3)+j) = tempCoord4(j);
}
}
#ifdef DEBUG
cout << "after angles\n";
cout << "B:\n";
cout << setw(9) << setprecision(3) << (B);
cout << "\n\n";
#endif
// Dihedrals
RowVector r12(3); // Vector from 1st to 2nd point
RowVector r32(3); // Vector from 3rd to 2nd point
RowVector r34(3); // Vector from 3rd to 2nd point
RowVector r43(3); // Vector from 4th to 3rd point
RowVector e12(3); // Unit vector from 1st to 2nd point
RowVector e32(3); // Unit vector from 3rd to 2nd point
RowVector e34(3); // Unit vector from 3rd to 2nd point
RowVector e43(3); // Unit vector from 4th to 3rd point
Real norm12; // Norm of r12
Real norm32; // Norm of r32
Real norm34; // Norm of r34
Real norm43; // Norm of r43
RowVector cross1223(3); // Cross product of e12 and e23
RowVector cross4332(3); // Cross product of e43 and e32
Real angle123 = 0.0; // Angle in radians
Real angle234 = 0.0; // Angle in radians
Real cosAngle234 = 0.0;
Real sinAngle234 = 0.0;
scaleFactor = 0.529178; // Scaling factor (0.529178)
int index4 = 0;
RowVector tempCoord6(3);
for (i=0; i<numDihedrals; i++) {
index1 = dihedrals[i]->x1;
index2 = dihedrals[i]->x2;
index3 = dihedrals[i]->x3;
index4 = dihedrals[i]->x4;
for (j=0; j<3; j++) {
tempCoord1(j+1) = cartCoords[index1][j];
tempCoord2(j+1) = cartCoords[index2][j];
tempCoord3(j+1) = cartCoords[index3][j];
tempCoord4(j+1) = cartCoords[index4][j];
}
r12 << tempCoord2 - tempCoord1;
r21 << tempCoord1 - tempCoord2;
r23 << tempCoord3 - tempCoord2;
r32 << tempCoord2 - tempCoord3;
r34 << tempCoord4 - tempCoord3;
r43 << tempCoord3 - tempCoord4;
norm12 = r12.NormFrobenius();
norm21 = r21.NormFrobenius();
norm23 = r23.NormFrobenius();
norm32 = r32.NormFrobenius();
norm34 = r34.NormFrobenius();
norm43 = r43.NormFrobenius();
#ifdef DEBUG
cout << "norm12: " << norm12 << "\n";
cout << "norm21: " << norm21 << "\n";
cout << "norm23: " << norm23 << "\n";
cout << "norm32: " << norm32 << "\n";
cout << "norm34: " << norm34 << "\n";
cout << "norm43: " << norm43 << "\n";
#endif
e12 << r12 / norm12;
e21 << r21 / norm21;
e23 << r23 / norm23;
e32 << r32 / norm32;
e34 << r34 / norm34;
e43 << r43 / norm43;
angle123 = acos(DotProduct(r21,r23) / (norm21 * norm23)); // Wilson's angle 2
angle234 = acos(DotProduct(r32,r34) / (norm32 * norm34)); // Wilson's angle 3
cosAngle123 = DotProduct(r21,r23) / (norm21 * norm23);
cosAngle234 = DotProduct(r32,r34) / (norm32 * norm34);
sinAngle123 = sqrt(1 - (cosAngle123 * cosAngle123));
sinAngle234 = sqrt(1 - (cosAngle234 * cosAngle234));
#ifdef DEBUG
cout << "angle123: " << angle123 << ", cos(angle123): " << cos(angle123) << ", sin(angle123): " << sin(angle123) << "\n";
cout << "angle234: " << angle234 << ", cos(angle234): " << cos(angle234) << ", sin(angle234): " << sin(angle234) << "\n";
cout << "cosAngle123: " << cosAngle123 << ", sinAngle123: " << sinAngle123 << "\n";
cout << "cosAngle234: " << cosAngle234 << ", sinAngle234: " << sinAngle234 << "\n";
#endif
cross1223(1) = (e12(2)*e23(3)) - (e12(3)*e23(2));
cross1223(2) = (e12(3)*e23(1)) - (e12(1)*e23(3));
cross1223(3) = (e12(1)*e23(2)) - (e12(2)*e23(1));
cross4332(1) = (e43(2)*e32(3)) - (e43(3)*e32(2));
cross4332(2) = (e43(3)*e32(1)) - (e43(1)*e32(3));
cross4332(3) = (e43(1)*e32(2)) - (e43(2)*e32(1));
#ifdef DEBUG
cout << "cross1223 (norm " << cross1223.NormFrobenius() << "):\n";
cout << setw(9) << setprecision(6) << (cross1223);
cout << "\n\n";
cout << "cross4332 (norm " << cross4332.NormFrobenius() << "):\n";
cout << setw(9) << setprecision(6) << (cross4332);
cout << "\n\n";
#endif
// First elements of coordinate triples
tempCoord5 << -((cross1223 * scaleFactor) / (norm12 * sinAngle123 * sinAngle123));
for (j=1; j<=3; j++) {
B(i+numBonds+numAngles+1,((index1)*3)+j) = tempCoord5(j);
}
// Second elements of coordinate triples
tempCoord5 << ((norm23 - (norm12 * cosAngle123)) / (norm23 * norm12 * sinAngle123 * sinAngle123)) * (cross1223);
tempCoord6 << (cosAngle234 / (norm23 * sinAngle234 * sinAngle234)) * (cross4332);
#ifdef DEBUG
cout << "tempCoord5:\n";
cout << setw(9) << setprecision(6) << (tempCoord5);
cout << "tempCoord6:\n";
cout << setw(9) << setprecision(6) << (tempCoord6);
#endif
tempCoord5 << (tempCoord5 + tempCoord6) * scaleFactor;
#ifdef DEBUG
cout << "tempCoord5:\n";
cout << setw(9) << setprecision(6) << (tempCoord5);
#endif
for (j=1; j<=3; j++) {
B(i+numBonds+numAngles+1,((index2)*3)+j) = tempCoord5(j);
}
// Third elements of coordinate triples
tempCoord5 << ((norm32 - (norm43 * cosAngle234)) / (norm32 * norm43 * sinAngle234 * sinAngle234)) * (cross4332);
tempCoord6 << (cosAngle123 / (norm32 * sinAngle123 * sinAngle123)) * (cross1223);
tempCoord5 << (tempCoord5 + tempCoord6) * scaleFactor;
for (j=1; j<=3; j++) {
B(i+numBonds+numAngles+1,((index3)*3)+j) = tempCoord5(j);
}
// Fourth elements of coordinate triples
tempCoord5 << -((cross4332 * scaleFactor) / (norm43 * sinAngle234 * sinAngle234));
for (j=1; j<=3; j++) {
B(i+numBonds+numAngles+1,((index4)*3)+j) = tempCoord5(j);
}
}
#ifdef DEBUG
cout << "B:\n";
cout << setw(9) << setprecision(3) << (B);
cout << "\n\n";
#endif
// Impropers
RowVector r41(3); // Vector from 4th to 1st point
RowVector r42(3); // Vector from 4th to 2nd point
RowVector e41(3); // Unit vector from 4th to 1st point
RowVector e42(3); // Unit vector from 4th to 2nd point
RowVector normVector(3); // Normal to the plane
Real norm41; // Norm of r41
Real norm42; // Norm of r42
Real angle142 = 0.0; // Angle in radians
Real angle143 = 0.0; // Angle in radians
Real angle243 = 0.0; // Angle in radians
Real cosAngle142 = 0.0;
Real cosAngle143 = 0.0;
Real cosAngle243 = 0.0;
Real sinAngle142 = 0.0;
Real sinAngle143 = 0.0;
Real sinAngle243 = 0.0;
Real apexCoeff = 0.0; // Magnitude of central atom displacement
scaleFactor = -0.352313; // Scale factor (-0.352313)
for (i=0; i<numImpropers; i++) {
index1 = impropers[i]->x1;
index2 = impropers[i]->x2;
index3 = impropers[i]->x3;
index4 = impropers[i]->x4;
for (j=0; j<3; j++) {
tempCoord1(j+1) = cartCoords[index1][j];
tempCoord2(j+1) = cartCoords[index2][j];
tempCoord3(j+1) = cartCoords[index3][j];
tempCoord4(j+1) = cartCoords[index4][j];
}
r41 << tempCoord1 - tempCoord4;
r42 << tempCoord2 - tempCoord4;
r43 << tempCoord3 - tempCoord4;
norm41 = r41.NormFrobenius();
norm42 = r42.NormFrobenius();
norm43 = r43.NormFrobenius();
e41 << r41 / norm41;
e42 << r42 / norm42;
e43 << r43 / norm43;
angle142 = acos(DotProduct(r41,r42) / (norm41 * norm42));
angle143 = acos(DotProduct(r41,r43) / (norm41 * norm43));
angle243 = acos(DotProduct(r42,r43) / (norm42 * norm43));
cosAngle142 = DotProduct(r41,r42) / (norm41 * norm42);
cosAngle143 = DotProduct(r41,r43) / (norm41 * norm43);
cosAngle243 = DotProduct(r42,r43) / (norm42 * norm43);
sinAngle142 = sqrt(1 - (cosAngle142 * cosAngle142));
sinAngle143 = sqrt(1 - (cosAngle143 * cosAngle143));
sinAngle243 = sqrt(1 - (cosAngle243 * cosAngle243));
normVector(1) = (r41(2)*r42(3)) - (r41(3)*r42(2));
normVector(2) = (r41(3)*r42(1)) - (r41(1)*r42(3));
normVector(3) = (r41(1)*r42(2)) - (r41(2)*r42(1));
normVector << normVector / normVector.NormFrobenius();
// First elements of coordinate triples
tempCoord5 << normVector * (scaleFactor / norm41);
for (j=1; j<=3; j++) {
B(i+numBonds+numAngles+numDihedrals+1,((index1)*3)+j) = tempCoord5(j);
}
// Second elements of coordinate triples
tempCoord5 << normVector * sinAngle143 * scaleFactor;
tempCoord5 << tempCoord5 / (norm42 * sinAngle243);
for (j=1; j<=3; j++) {
B(i+numBonds+numAngles+numDihedrals+1,((index2)*3)+j) = tempCoord5(j);
}
// Third elements of coordinate triples
tempCoord5 << normVector * sinAngle142 * scaleFactor;
tempCoord5 << tempCoord5 / (norm43 * sinAngle243);
for (j=1; j<=3; j++) {
B(i+numBonds+numAngles+numDihedrals+1,((index3)*3)+j) = tempCoord5(j);
}
// Fourth elements of coordinate triples
apexCoeff = -1.0 / norm42;
apexCoeff -= sinAngle143 / (norm42 * sinAngle243);
apexCoeff -= sinAngle142 / (norm43 * sinAngle243);
tempCoord5 << normVector * apexCoeff * scaleFactor;
for (j=1; j<=3; j++) {
B(i+numBonds+numAngles+numDihedrals+1,((index4)*3)+j) = tempCoord5(j);
}
}
return;
}
int json_cpp_tests() {
json::Value e1(json::load_file("test.json"));
json::Value e2(e1);
json::Value e3;
json::Value e4(json::load_string("{\"foo\": true, \"bar\": \"test\"}"));
ASSERT_TRUE(e1.is_object(), "e1 is not an object");
ASSERT_TRUE(e2.is_object(), "e2 is not an object");
ASSERT_TRUE(e3.is_undefined(), "e3 has a defined value");
ASSERT_TRUE(e4.is_object(), "e4 is not an object");
ASSERT_EQ(e1.size(), 1, "e1 has too many properties");
ASSERT_EQ(e2.size(), 1, "e2 has too many properties");
ASSERT_EQ(e4.size(), 2, "e4 does not have 2 elements");
ASSERT_TRUE(e1.get("web-app").is_object(), "e1[0].web-app is not an object");
ASSERT_EQ(e1.get("web-app").get("servlet").at(0).get("servlet-class").as_string(), "org.cofax.cds.CDSServlet", "property has incorrect value");
ASSERT_EQ(e1["web-app"]["servlet"][0]["servlet-class"].as_string(), "org.cofax.cds.CDSServlet", "property has incorrect value");
ASSERT_EQ(e4["foo"].as_boolean(), true, "property has incorrect value");
// verify iterator results (note that they can be returned in any order)
json::Iterator i(e1.get("web-app"));
std::set<std::string> iteratorResults;
for ( int ii = 0; ii < 3; ++ii ) {
ASSERT_FALSE(i.key().empty(), "iterator returned a null value");
iteratorResults.insert(i.key());
i.next();
}
ASSERT_FALSE(i.valid(), "iterator has more values than expected");
ASSERT_EQ(iteratorResults.size(), 3, "iterator did not return enough values");
json::Value e5(json::Value(12.34));
ASSERT_TRUE(e5.is_number(), "e5 is not a number after assignment");
ASSERT_EQ(e5.as_real(), 12.34, "e5 has incorrect value after assignment");
json::Value e6(json::Value(true));
ASSERT_TRUE(e6.is_boolean(), "e6 is not a boolean after assignment");
ASSERT_EQ(e6.as_boolean(), true, "e6 has incorrect value after assignment");
json::Value e7(json::Value("foobar"));
ASSERT_TRUE(e7.is_string(), "e7 is not a string after assignment");
ASSERT_EQ(e7.as_string(), "foobar", "e7 has incorrect value after assignment");
json::Value e8(json::object());
ASSERT_TRUE(e8.is_object(), "e8 is not an object after assignment");
json::Value e9(json::null());
ASSERT_TRUE(e9.is_null(), "e9 is not null after assignment");
json::Value e10(json::array());
ASSERT_TRUE(e10.is_array(), "e10 is not an array after index assignment");
e10.set_at(0, json::Value("foobar"));
ASSERT_EQ(e10.size(), 1, "e10 has incorrect number of elements after assignment");
ASSERT_EQ(e10[0].as_string(), "foobar", "e10[0] has incorrect value after assignment");
e10.set_at(1, json::Value("foobar"));
ASSERT_TRUE(e10.is_array(), "e10 is not an array after index assignment");
ASSERT_EQ(e10.size(), 2, "e10 has incorrect number of elements after assignment");
ASSERT_EQ(e10[1].as_string(), "foobar", "e10[0] has incorrect value after assignment");
e10.set_at(0, json::Value("barfoo"));
ASSERT_TRUE(e10.is_array(), "e10 is not an array after index assignment");
ASSERT_EQ(e10.size(), 2, "e10 has incorrect number of elements after assignment");
ASSERT_EQ(e10[0].as_string(), "barfoo", "e10[0] has incorrect value after assignment");
e10.set_at(100, json::null());
ASSERT_TRUE(e10.is_array(), "e10 is not an array after index assignment");
ASSERT_EQ(e10.size(), 2, "e10 has incorrect number of elements after assignment");
e10.insert_at(1, json::Value("new"));
ASSERT_EQ(e10.size(), 3, "e10 has incorrect size after insert");
ASSERT_EQ(e10[1].as_string(), "new", "e10[1] has incorrect value after insert");
ASSERT_EQ(e10[2].as_string(), "foobar", "e10[2] has incorrect value after insert");
e10.del_at(0);
ASSERT_EQ(e10.size(), 2, "e10 has incorrect size after delete");
ASSERT_EQ(e10[1].as_string(), "foobar", "e10[1] has incorrect value after delete");
e10.clear();
ASSERT_EQ(e10.size(), 0, "e10 has incorrect number of elements after clear");
json::Value e11(json::object());
ASSERT_TRUE(e11.is_object(), "e11 is not an object after property assignment");
e11.set_key("foo", json::Value("test"));
ASSERT_EQ(e11.size(), 1, "e11 has incorrect number of properties after assignment");
ASSERT_EQ(e11["foo"].as_string(), "test", "e11.foo has incorrect value after assignment");
e11.set_key("foo", json::Value("again"));
ASSERT_TRUE(e11.is_object(), "e11 is not an object after property assignment");
ASSERT_EQ(e11.size(), 1, "e11 has incorrect number of properties after assignment");
ASSERT_EQ(e11["foo"].as_string(), "again", "e11.foo has incorrect value after assignment");
e11.set_key("bar", json::Value("test"));
ASSERT_TRUE(e11.is_object(), "e11 is not an object after property assignment");
ASSERT_EQ(e11.size(), 2, "e11 has incorrect number of properties after assignment");
ASSERT_EQ(e11["bar"].as_string(), "test", "e11.foo has incorrect value after assignment");
e11.clear();
ASSERT_EQ(e11.size(), 0, "e11 has incorrect number of properties after clear");
json::Value e12(json::object());
e12.set_key("foo", json::Value("test"));
e12.set_key("bar", json::Value(3));
char* out_cstr = e12.save_string(JSON_COMPACT);
std::string out(out_cstr);
free(out_cstr);
ASSERT_EQ(out, "{\"bar\":3,\"foo\":\"test\"}", "object did not serialize as expected");
std::istringstream instr(out);
instr >> e12;
ASSERT_TRUE(e12.is_object(), "e12 is not an object after stream read");
ASSERT_EQ(e12.size(), 2, "e12 has wrong size after stream read");
ASSERT_EQ(e12.get("bar").as_integer(), 3, "e12.bar has incorrect value after stream read");
ASSERT_EQ(e12.get("foo").as_string(), "test", "ee12.test has incorrect value after stream read");
std::ostringstream outstr;
outstr << e12;
ASSERT_EQ(instr.str(), "{\"bar\":3,\"foo\":\"test\"}", "object did not serialize as expected");
const json::Value e13(e12);
ASSERT_EQ(e13["bar"].as_integer(), 3, "e13.bar has incorrect value after copy");
json::Value e14(json::object());
ASSERT_TRUE(e14.is_object(), "e14 is not an object after construction");
e14.set_key("foo", json::object());
ASSERT_TRUE(e14["foo"].is_object(), "e14.foo is not an object after assignment");
e14["foo"]["bar"] = json::Value(42);
ASSERT_EQ(e14["foo"]["bar"].as_integer(), 42, "e14.foo.bar has incorrect value after assignment");
json::Value e15(json::array());
ASSERT_TRUE(e15.is_array(), "e15 is not an array after construction");
e15.set_at(0, json::Value(42));
ASSERT_EQ(e15[0].as_integer(), 42, "e15[0] has incorrect value after assignment");
e15[0] = json::Value("foo");
ASSERT_EQ(e15[0].as_string(), "foo", "e15[0] has incorrecy value after assignment");
return 0;
}
