int main(void)
{
x1();
x2();
x3();
x4();
printf("%d, %d, %d, %u\n", x1(), x2(), x3(), x4());
}
int main(void)
{
x1(0);
x2(0);
x3(0);
x4(0);
printf("%d, %d, %d, %u\n", x1(0), x2(0), x3(0), x4(0));
}
void plop (){
gca :: GCA_vector a (1.0 ,2.0 ,3.0 ,1.0);
gca :: GCA_vector b ;
b << 3.0 , 2.0 , 1.0 , 1.0;
gca :: GCA_bivector l = a ^ b ; // l is a Plucker line
std :: cout << "\n--------------- Plucker line ---------------" << std :: endl ;
std :: cout << "point ^ point l : " << l << std :: endl ;
gca :: GCA_vector x1 (2.0 , -1.0 , -1.0 ,1.0);
gca :: GCA_vector x2 (1.0 , -1.0 ,1.0 ,1.0);
gca :: GCA_vector x3 ( -1.0 , -1.0 , -2.0 ,1.0);
gca :: GCA_trivector d = x1 ^ x2 ^ x3 ; // d is a plane
gca :: GCA_trivector p = x1 ^ l ;
gca :: GCA_trivector r = x3 ^ l ;
std :: cout << "\n--------------- Plans ---------------" << std :: endl ;
std :: cout << "point ^ point ^ point d: " << d << std :: endl ;
std :: cout << "point ^ droite p: " << p << std :: endl ;
std :: cout << "Plan r: " << r << std :: endl ;
std :: cout << "\n--------------- Intersections ---------------" << std :: endl ;
std :: cout << "plan v plan v plan : " << (~d ^ ~p ^ ~r) << std :: endl ;
std :: cout << "plan v droite : " << (~d ^ ~l) << std :: endl ;
std :: cout << "plan v plan : " << (~d ^ ~p) << std :: endl ;
std :: cout << "\n--------------- Appartenances ---------------" << std :: endl ;
std :: cout << "point ^ droite : " << (l ^ a) << std :: endl;
std :: cout << "point ^ plan : " << (x1 ^ p) << std :: endl;
}
void test()
{
CXCode x1(CXCode::CHARSET_UTF8);
std::string sUTF8 = "abc\xe4\xb8\xad\xe5\x9b\xbd\xe4\xba\xba";
EXPECT_EQ(std::string("abc%u4E2D%u56FD%u4EBA"), CXCode::escape(sUTF8));
EXPECT_EQ(sUTF8, CXCode::unescape(CXCode::escape(sUTF8)));
EXPECT_EQ(std::string("abc%u4E2D%u56FD%u4EBA"), CXCode::escape(CXCode::unescape(CXCode::escape(sUTF8))));
EXPECT_EQ(sUTF8, CXCode::unescape((sUTF8)));
EXPECT_EQ(std::string("abc%E4%B8%AD%E5%9B%BD%E4%BA%BA"), CXCode::encodeURIComponent(sUTF8));
EXPECT_EQ(std::string("abc\\u4E2D\\u56FD\\u4EBA"), CXCode::encodeJSONComponent(sUTF8));
EXPECT_EQ(std::string("abc中国人"), CXCode::encodeXMLComponent(sUTF8));
std::string sUCS2 = CXCode::UCS2(CXCode::escape(sUTF8));
CXCode x2(CXCode::CHARSET_GBS);
std::string sGB="abc\xd6\xd0\xb9\xfa\xc8\xcb";
EXPECT_EQ(std::string("abc%u4E2D%u56FD%u4EBA"), CXCode::escape(sGB));
EXPECT_EQ(sGB, CXCode::unescape(CXCode::escape(sGB)));
EXPECT_EQ(std::string("abc%u4E2D%u56FD%u4EBA"), CXCode::escape(CXCode::unescape(CXCode::escape(sGB))));
EXPECT_EQ(sGB, CXCode::unescape((sGB)));
EXPECT_EQ(std::string("abc%E4%B8%AD%E5%9B%BD%E4%BA%BA"), CXCode::encodeURIComponent(sGB));
EXPECT_EQ(std::string("abc\\u4E2D\\u56FD\\u4EBA"), CXCode::encodeJSONComponent(sGB));
EXPECT_EQ(std::string("abc中国人"), CXCode::encodeXMLComponent(sGB));
CXCode x3(CXCode::CHARSET_UCS2);
T_UC tUC[6] = {'a','b','c',20013,22269,20154};
std::string sUC((char *)tUC, 12);
EXPECT_EQ(sUC, CXCode::UCS2(sUC));
EXPECT_EQ(sUCS2, CXCode::escape(sUC));
EXPECT_EQ(CXCode::UCS2(sUCS2), CXCode::escape(sUC));
EXPECT_EQ(CXCode::escape(sUC), CXCode::UCS2(CXCode::escape(sUC)));
EXPECT_EQ(sUC, CXCode::unescape(CXCode::escape(sUC)));
EXPECT_EQ(sUCS2, CXCode::escape(CXCode::unescape(CXCode::escape(sUC))));
EXPECT_EQ(sUC, CXCode::unescape((sUC)));
EXPECT_EQ(std::string("abc%E4%B8%AD%E5%9B%BD%E4%BA%BA"), CXCode::encodeURIComponent(sUC));
EXPECT_EQ(std::string("abc\\u4E2D\\u56FD\\u4EBA"), CXCode::encodeJSONComponent(sUC));
EXPECT_EQ(std::string("abc中国人"), CXCode::encodeXMLComponent(sUC));
EXPECT_EQ(sUC, CXCode::GBS2UCS((sGB)));
EXPECT_EQ(sUTF8, CXCode::GBS2UTF8((sGB)));
EXPECT_EQ(sUC, CXCode::UTF82UCS((sUTF8)));
EXPECT_EQ(sGB, CXCode::UTF82GBS((sUTF8)));
EXPECT_EQ(sGB, CXCode::UCS2GBS((sUC)));
EXPECT_EQ(sUTF8, CXCode::UCS2UTF8((sUC)));
//std::cout << sUC << std::endl;
//std::cout << CXCode::UCS2(CXCode::escape(sUC))<<std::endl;
//std::cout << CXCode::escape(sUC) <<std::endl;
//std::cout << CXCode::unescape(CXCode::escape(sUC)) <<std::endl;
//std::cout << std::string("abc%u4E2D%u56FD%u4EBA") <<std::endl;
//std::cout << CXCode::UCS2("abc%u4E2D%u56FD%u4EBA") <<std::endl;
//std::cout << CXCode::encodeJSONComponent(CXCode::GBS2UCS((sGB)))<<std::endl;
// return 0;
}
void plop(){
std::cout<<"Début de l'exemple de Nozick sensei"<<std::endl;
gca::GCA_vector a(1.0, 2.0, 3.0, 1.0);
gca::GCA_vector b;
b << -1.0, -3.0, 2.0, 1.0;
gca::GCA_bivector l = a ^ b; // l is a PLucker line
l.show();
gca::GCA_vector x1(2.0, -1.0, -1.0, 1.0);
gca::GCA_vector x2(1.0, -1.0, 1.0, 1.0);
gca::GCA_vector x3(-1.0, -1.0, -2.0, 1.0);
gca::GCA_trivector d = x1^x2^x3; //d is a plane
std::cout << d<<std::endl;
std::cout << "(~d^~l) n'est pas l'intersection : "<< (~d^~l) <<std::endl;
gca::GCA_antivector croisement = (~d^~l);
std::cout << "~(~d^~l) est l'intersection : "<< ~croisement <<std::endl;
//std::cout << "intersection : "<< ~d^~l <<std::endl;// ne peux pas pas compiler selon les normes du c++
std::cout<<"Fin de l'exemple de Nozick sensei"<<std::endl;
}
void fn ()
{
X x1(3.5); // WARNING - double to int
X x2(3.5f); // WARNING - float to int
X x3(1, 3.5); // WARNING - double to int
X x4(1, 3.5f); // WARNING - float to int
X x5(3.5, 1); // WARNING - double to int
X x6(3.5f, 1); // WARNING - float to int
X y1 = 3.5; // WARNING - double to int
X y2 = 3.5f; // WARNING - float to int
int j1 (3.5); // WARNING - double to int
int j2 (3.5f); // WARNING - float to int
int k1 = 3.5; // WARNING - double to int
int k2 = 3.5f; // WARNING - float to int
j1 = 3.5; // WARNING - double to int
j2 = 3.5f; // WARNING - float to int
foo (3.5); // WARNING - double to int
foo (3.5f); // WARNING - float to int
wibble (3.5); // WARNING - double to int
wibble (3.5f); // WARNING - float to int
wibble (1, 3.5); // WARNING - double to int
wibble (1, 3.5f); // WARNING - float to int
wibble (3.5, 1); // WARNING - double to int
wibble (3.5f, 1); // WARNING - float to int
punk (); // WARNING - double to int
rock (1); // WARNING - double to int
}
int main( void )
{
unsigned long ul = 0xCCCCCCCC;
void *pv = NULL;
x1 = test1;
x1( 1, 2, 3, 4, 5 );
if( res[0] != 1 ) fail( __LINE__ );
if( res[1] != 2 ) fail( __LINE__ );
if( res[2] != 3 ) fail( __LINE__ );
if( res[3] != 4 ) fail( __LINE__ );
if( res[4] != 5 ) fail( __LINE__ );
x2 = test1;
x2( 1, 2, 3, 4, 5 );
if( res[0] != 1 ) fail( __LINE__ );
if( res[1] != 2 ) fail( __LINE__ );
if( res[2] != 3 ) fail( __LINE__ );
if( res[3] != 4 ) fail( __LINE__ );
if( res[4] != 5 ) fail( __LINE__ );
x3 = test2;
x3( 1, 2, 3, 4, 5 );
if( res[0] != 1 ) fail( __LINE__ );
if( res[1] != 2 ) fail( __LINE__ );
if( res[2] != 3 ) fail( __LINE__ );
if( res[3] != 4 ) fail( __LINE__ );
if( res[4] != 5 ) fail( __LINE__ );
if( !fn1( ul, 0x55AA ) ) fail( __LINE__ );
if( !fn2( pv, 0x55AA ) ) fail( __LINE__ );
_PASS;
}
void g() {
X x1(5);
X x2(1.0, 3, 4.2);
X x3(1.0, 1.0); // expected-error{{no matching constructor for initialization of 'x3'; candidates are:}}
Y y(1.0);
X x4(3.14, y);
Z z; // expected-error{{no matching constructor for initialization of 'z'}}
}
void g() {
X x1(5);
X x2(1.0, 3, 4.2);
X x3(1.0, 1.0); // expected-error{{no matching constructor for initialization of 'X'}}
Y y(1.0);
X x4(3.14, y);
Z z; // expected-error{{no matching constructor for initialization of 'Z'}}
}
bool PolygonLine :: intersects(Element *element)
{
printf("Warning: entering PolygonLine :: intersects(Element *element).\n");
#ifdef __BOOST_MODULE
if ( !boundingBoxIntersects(element) ) {
return false;
}
double distTol = 1.0e-9;
int numSeg = this->giveNrVertices() - 1;
// Loop over the crack segments and test each segment for
// overlap with the element
for ( int segId = 1; segId <= numSeg; segId++ ) {
if ( element->giveGeometryType() == EGT_triangle_1 ) {
// Crack segment
bPoint2 crackP1( this->giveVertex ( segId )->at(1), this->giveVertex ( segId )->at(2) );
bPoint2 crackP2( this->giveVertex ( segId + 1 )->at(1), this->giveVertex ( segId + 1 )->at(2) );
bSeg2 crackSeg(crackP1, crackP2);
// Triangle vertices
bPoint2 x1( element->giveNode ( 1 )->giveCoordinate(1), element->giveNode ( 1 )->giveCoordinate(2) );
bPoint2 x2( element->giveNode ( 2 )->giveCoordinate(1), element->giveNode ( 2 )->giveCoordinate(2) );
bPoint2 x3( element->giveNode ( 3 )->giveCoordinate(1), element->giveNode ( 3 )->giveCoordinate(2) );
bSeg2 edge1(x1, x2);
bSeg2 edge2(x2, x3);
bSeg2 edge3(x3, x1);
double d1 = bDist(crackSeg, edge1);
if ( d1 < distTol ) {
return true;
}
double d2 = bDist(crackSeg, edge2);
if ( d2 < distTol ) {
return true;
}
double d3 = bDist(crackSeg, edge3);
if ( d3 < distTol ) {
return true;
}
}
}
#endif
return false;
}
int main() {
char user[3];
read(0, user, 3);
if (x0(user) || x1(user) || x2(user) || x3(user) || x4(user)) {
failure();
}
else {
success();
}
}
NT2_TEST_CASE_TPL( cols_nd_typed, NT2_TYPES )
{
nt2::table<T> x2 = nt2::cols(8,4, T(22.5) );
for(int i=1;i<=8;++i) for(int j=1;j<=4;++j) NT2_TEST_EQUAL( T(22.5+j-1), T(x2(i, j)) );
nt2::table<T> x3 = nt2::cols(2,4, T(22.5) );
for(int i=1;i<=2;++i) for(int j=1;j<=4;++j) NT2_TEST_EQUAL( T(22.5+j-1), T(x3(i, j)) );
nt2::table<T> x4 = nt2::cols(nt2::of_size(8, 6), T(22.5) );
for(int i=1;i<=8;++i) for(int j=1;j<=6;++j) NT2_TEST_EQUAL( T(22.5+j-1), T(x4(i, j)) );
}
Cube::Cube(float scale){
if(!ModelBase::GetInstance().HasModel("cube")){
ModelBase::GetInstance().AddModelTriangles("cube",12,
{ -1.0f,-1.0f,-1.0f, -1.0f,-1.0f, 1.0f, -1.0f, 1.0f, 1.0f, //
1.0f, 1.0f,-1.0f, -1.0f,-1.0f,-1.0f, -1.0f, 1.0f,-1.0f, //
1.0f,-1.0f, 1.0f, -1.0f,-1.0f,-1.0f, 1.0f,-1.0f,-1.0f, //
1.0f, 1.0f,-1.0f, 1.0f,-1.0f,-1.0f, -1.0f,-1.0f,-1.0f, //
-1.0f,-1.0f,-1.0f, -1.0f, 1.0f, 1.0f, -1.0f, 1.0f,-1.0f,
1.0f,-1.0f, 1.0f, -1.0f,-1.0f, 1.0f, -1.0f,-1.0f,-1.0f,
-1.0f, 1.0f, 1.0f, -1.0f,-1.0f, 1.0f, 1.0f,-1.0f, 1.0f,
1.0f, 1.0f, 1.0f, 1.0f,-1.0f,-1.0f, 1.0f, 1.0f,-1.0f,
1.0f,-1.0f,-1.0f, 1.0f, 1.0f, 1.0f, 1.0f,-1.0f, 1.0f,
1.0f, 1.0f, 1.0f, 1.0f, 1.0f,-1.0f, -1.0f, 1.0f,-1.0f,
1.0f, 1.0f, 1.0f, -1.0f, 1.0f,-1.0f, -1.0f, 1.0f, 1.0f,
1.0f, 1.0f, 1.0f, -1.0f, 1.0f, 1.0f, 1.0f,-1.0f, 1.0f},
// { x3b(-1.0f, 0.0f, 0.0f), x3b(0.0f, 0.0f, -1.0f), x3b(0.0f, -1.0f, 0.0f),
// x3b(0.0f, 0.0f, -1.0f),},
{ { CL,CD,CD,CL,CL,CL,CG,CG,CG,
CL,CL,CL,CL,CD,CL,CG,CG,CG,
CD,CD,CD,CD,CL,CL,CL,CD,CD,
CD,CL,CL,CD,CL,CD,CD,CD,CD,},
{ x4(x3(C_GREEN),x3(C_RED),x3(C_BLUE)),},
{ x4(x3(C_RED),x3(C_RED),x3(C_RED)),},
}
);
}
model_id = "cube";
SetScale(scale);
}
///////////////////////////////////////////////////////////////////////////////////////////////////
//int __stdcall WinMain(HINSTANCE, HINSTANCE, LPSTR, int)
int main()
{
{
X x1(4.5, 6);
X x2(x1);
x2 = x1;
X x3(std::move(x1));
x3 = std::move(x2);
X x4(4.5, 6);
}
return 0;
}
TEST(XmlEquality, SimpleValues) {
AmfXml x1;
AmfXml x2("");
EXPECT_EQ(x1, x2);
AmfXml x3("foo");
AmfXml x4("foo");
EXPECT_EQ(x3, x4);
EXPECT_NE(x1, x3);
AmfXml x5("foobar");
EXPECT_NE(x3, x5);
}
NT2_TEST_CASE_TPL( ric_nd_typed, NT2_TYPES )
{
nt2::table<T> x1 = nt2::ric(8, nt2::meta::as_<T>() );
for(int i=1;i<=8;++i) for(int j=1;j<=8;++j) NT2_TEST_EQUAL( T(i-1), T(x1(i, j)) );
nt2::table<T> x2 = nt2::ric(8,4, nt2::meta::as_<T>() );
for(int i=1;i<=8;++i) for(int j=1;j<=4;++j) NT2_TEST_EQUAL( T(i-1), T(x2(i, j)) );
nt2::table<T> x3 = nt2::ric(2,4, nt2::meta::as_<T>() );
for(int i=1;i<=2;++i) for(int j=1;j<=4;++j) NT2_TEST_EQUAL( T(i-1), T(x3(i, j)) );
nt2::table<T> x4 = nt2::ric(nt2::of_size(8, 6), nt2::meta::as_<T>() );
for(int i=1;i<=8;++i) for(int j=1;j<=6;++j) NT2_TEST_EQUAL( T(i-1), T(x4(i, j)) );
}
void tst_match(ast_manager & m, app * t, app * i) {
substitution s(m);
s.reserve(2, 10); // reserving a big number of variables to be safe.
matcher match;
std::cout << "Is " << mk_pp(i, m) << " an instance of " << mk_pp(t, m) << "\n";
if (match(t, i, s)) {
std::cout << "yes\n";
s.display(std::cout);
}
else {
std::cout << "no\n";
}
s.reset();
if (t->get_decl() == i->get_decl()) {
// trying to match the arguments of t and i
std::cout << "Are the arguments of " << mk_pp(i, m) << " an instance of the arguments of " << mk_pp(t, m) << "\n";
unsigned num_args = t->get_num_args();
unsigned j;
for (j = 0; j < num_args; j++) {
if (!match(t->get_arg(j), i->get_arg(j), s))
break;
}
if (j == num_args) {
std::cout << "yes\n";
s.display(std::cout);
// create some dummy term to test for applying the substitution.
sort_ref S( m.mk_uninterpreted_sort(symbol("S")), m);
sort * domain[3] = {S, S, S};
func_decl_ref r( m.mk_func_decl(symbol("r"), 3, domain, S), m);
expr_ref x1( m.mk_var(0, S), m);
expr_ref x2( m.mk_var(1, S), m);
expr_ref x3( m.mk_var(2, S), m);
app_ref rxyzw( m.mk_app(r, x1.get(), x2.get(), x3.get()), m);
expr_ref result(m);
unsigned deltas[2] = {0,0};
s.apply(2, deltas, expr_offset(rxyzw, 0), result);
std::cout << "applying substitution to\n" << mk_pp(rxyzw,m) << "\nresult:\n" << mk_pp(result,m) << "\n";
}
else {
std::cout << "no\n";
}
}
std::cout << "\n";
}
void string0_tests()
{
std::string x1(1, '\0');
std::string x2(2, '\0');
std::string x3(3, '\0');
std::string x4(10, '\0');
BOOST_HASH_TEST_NAMESPACE::hash<std::string> hasher;
BOOST_TEST(hasher(x1) != hasher(x2));
BOOST_TEST(hasher(x1) != hasher(x3));
BOOST_TEST(hasher(x1) != hasher(x4));
BOOST_TEST(hasher(x2) != hasher(x3));
BOOST_TEST(hasher(x2) != hasher(x4));
BOOST_TEST(hasher(x3) != hasher(x4));
}
void fwd_test()
{
test::test_type1<int> x1(3);
test::test_type1<std::string> y1("Black");
test::test_type2<int> x2(25, 16);
test::test_type2<std::string> y2("White", "Green");
std::vector<int> empty;
std::vector<std::string> empty2;
test::test_type3<int> x3(empty.begin(), empty.end());
test::test_type3<std::string> y3(empty2.begin(), empty2.end());
// Prevent gcc warnings:
unused(x1); unused(x2); unused(x3);
unused(y1); unused(y2); unused(y3);
}
void IntegrationRule::DefineIntegrationRuleTetrahedron(IntegrationRule & integrationRule, int ruleOrder)
{
// we use a ready function, which provides a tetrahedral integration rule
Vector x1, x2, x3, w;
GetIntegrationRuleTet(x1, x2, x3, w, ruleOrder);
// and now we create a 3D integration rule
integrationRule.integrationPoints.SetLen(x1.Length());
assert(x1.Length() == x2.Length());
assert(x1.Length() == x3.Length());
assert(x1.Length() == w.Length());
for (int i1 = 1; i1 <= x1.GetLen(); i1++)
{
integrationRule.integrationPoints(i1).x = x1(i1);
integrationRule.integrationPoints(i1).y = x2(i1);
integrationRule.integrationPoints(i1).z = x3(i1);
integrationRule.integrationPoints(i1).weight = w(i1);
}
}
void RSA_TestInstantiations()
{
RSASS<PKCS1v15, SHA>::Verifier x1(1, 1);
RSASS<PKCS1v15, SHA>::Signer x2(NullRNG(), 1);
RSASS<PKCS1v15, SHA>::Verifier x3(x2);
RSASS<PKCS1v15, SHA>::Verifier x4(x2.GetKey());
RSASS<PSS, SHA>::Verifier x5(x3);
#ifndef __MWERKS__
RSASS<PSSR, SHA>::Signer x6 = x2;
x3 = x2;
x6 = x2;
#endif
RSAES<PKCS1v15>::Encryptor x7(x2);
#ifndef __GNUC__
RSAES<PKCS1v15>::Encryptor x8(x3);
#endif
RSAES<OAEP<SHA> >::Encryptor x9(x2);
x4 = x2.GetKey();
}
void IntegrationRulesCreator::CreateTetrahedralRule(int order)
{
// we use a ready function, which provides a one-dimensional integration rule
Vector x1, x2, x3, w;
GetIntegrationRuleTet(x1, x2, x3, w, order);
// and now we create a 3D integration rule
currentIntegrationRuleInfo = new IntegrationRule::IntegrationRuleInfo();
currentIntegrationRuleInfo->integrationRule.SetLen(x1.Length());
assert(x1.Length() == x2.Length());
assert(x1.Length() == x3.Length());
assert(x1.Length() == w.Length());
for (int i1 = 1; i1 <= x1.GetLen(); i1++)
{
currentIntegrationRuleInfo->integrationRule(i1).x = x1(i1);
currentIntegrationRuleInfo->integrationRule(i1).y = x2(i1);
currentIntegrationRuleInfo->integrationRule(i1).z = x3(i1);
currentIntegrationRuleInfo->integrationRule(i1).weight = w(i1);
}
}
boost::shared_ptr<Mesh<Simplex<2> > >
createMeshLaplacianLM()
{
typedef Mesh<Simplex<2> > mesh_type;
double meshSize = option("gmsh.hsize").as<double>();
GeoTool::Node x1(-2,-1);
GeoTool::Node x2(2,1);
GeoTool::Rectangle R( meshSize ,"OMEGA",x1,x2);
//R.setMarker(_type="line",_name="Paroi",_marker3=true);
R.setMarker(_type="line",_name="gamma",_markerAll=true);
R.setMarker(_type="surface",_name="Omega",_markerAll=true);
GeoTool::Node x3(0,0); //center
GeoTool::Node x4(1);//majorRadiusParam
GeoTool::Node x5(0.7);//minorRadiusParam
GeoTool::Node x6(0.1);//penautRadiusParam
GeoTool::Peanut P( meshSize ,"OMEGA2",x3,x4,x5,x6);
P.setMarker(_type="line",_name="peanut",_markerAll=true);
P.setMarker(_type="surface",_name="Omega2",_markerAll=true);
auto mesh = (R-P).createMesh(_mesh=new mesh_type,_name="mymesh.msh");
return mesh;
}
void MathPlot::setupMultiAxisDemo(QCustomPlot *customPlot)
{
customPlot->setInteractions(QCP::iRangeDrag | QCP::iRangeZoom);
customPlot->setLocale(QLocale(QLocale::English, QLocale::UnitedKingdom)); // period as decimal separator and comma as thousand separator
customPlot->legend->setVisible(true);
QFont legendFont = font(); // start out with MainWindow's font..
legendFont.setPointSize(9); // and make a bit smaller for legend
customPlot->legend->setFont(legendFont);
customPlot->legend->setBrush(QBrush(QColor(255,255,255,230)));
// by default, the legend is in the inset layout of the main axis rect. So this is how we access it to change legend placement:
customPlot->axisRect()->insetLayout()->setInsetAlignment(0, Qt::AlignBottom|Qt::AlignRight);
// setup for graph 0: key axis left, value axis bottom
// will contain left maxwell-like function
customPlot->addGraph(customPlot->yAxis, customPlot->xAxis);
customPlot->graph(0)->setPen(QPen(QColor(255, 100, 0)));
customPlot->graph(0)->setBrush(QBrush(QPixmap("://skin/images/balboa.jpg"))); // fill with texture of specified image
customPlot->graph(0)->setLineStyle(QCPGraph::lsLine);
customPlot->graph(0)->setScatterStyle(QCPScatterStyle(QCPScatterStyle::ssDisc, 5));
customPlot->graph(0)->setName("Left maxwell function");
// setup for graph 1: key axis bottom, value axis left (those are the default axes)
// will contain bottom maxwell-like function
customPlot->addGraph();
customPlot->graph(1)->setPen(QPen(Qt::red));
customPlot->graph(1)->setBrush(QBrush(QPixmap("://skin/images/balboa.jpg"))); // same fill as we used for graph 0
customPlot->graph(1)->setLineStyle(QCPGraph::lsStepCenter);
customPlot->graph(1)->setScatterStyle(QCPScatterStyle(QCPScatterStyle::ssCircle, Qt::red, Qt::white, 7));
customPlot->graph(1)->setErrorType(QCPGraph::etValue);
customPlot->graph(1)->setName("Bottom maxwell function");
// setup for graph 2: key axis top, value axis right
// will contain high frequency sine with low frequency beating:
customPlot->addGraph(customPlot->xAxis2, customPlot->yAxis2);
customPlot->graph(2)->setPen(QPen(Qt::blue));
customPlot->graph(2)->setName("High frequency sine");
// setup for graph 3: same axes as graph 2
// will contain low frequency beating envelope of graph 2
customPlot->addGraph(customPlot->xAxis2, customPlot->yAxis2);
QPen blueDotPen;
blueDotPen.setColor(QColor(30, 40, 255, 150));
blueDotPen.setStyle(Qt::DotLine);
blueDotPen.setWidthF(4);
customPlot->graph(3)->setPen(blueDotPen);
customPlot->graph(3)->setName("Sine envelope");
// setup for graph 4: key axis right, value axis top
// will contain parabolically distributed data points with some random perturbance
customPlot->addGraph(customPlot->yAxis2, customPlot->xAxis2);
customPlot->graph(4)->setPen(QColor(50, 50, 50, 255));
customPlot->graph(4)->setLineStyle(QCPGraph::lsNone);
customPlot->graph(4)->setScatterStyle(QCPScatterStyle(QCPScatterStyle::ssCircle, 4));
customPlot->graph(4)->setName("Some random data around\na quadratic function");
// generate data, just playing with numbers, not much to learn here:
QVector<double> x0(25), y0(25);
QVector<double> x1(15), y1(15), y1err(15);
QVector<double> x2(250), y2(250);
QVector<double> x3(250), y3(250);
QVector<double> x4(250), y4(250);
for (int i=0; i<25; ++i) // data for graph 0
{
x0[i] = 3*i/25.0;
y0[i] = exp(-x0[i]*x0[i]*0.8)*(x0[i]*x0[i]+x0[i]);
}
for (int i=0; i<15; ++i) // data for graph 1
{
x1[i] = 3*i/15.0;;
y1[i] = exp(-x1[i]*x1[i])*(x1[i]*x1[i])*2.6;
y1err[i] = y1[i]*0.25;
}
for (int i=0; i<250; ++i) // data for graphs 2, 3 and 4
{
x2[i] = i/250.0*3*M_PI;
x3[i] = x2[i];
x4[i] = i/250.0*100-50;
y2[i] = sin(x2[i]*12)*cos(x2[i])*10;
y3[i] = cos(x3[i])*10;
y4[i] = 0.01*x4[i]*x4[i] + 1.5*(rand()/(double)RAND_MAX-0.5) + 1.5*M_PI;
}
// pass data points to graphs:
customPlot->graph(0)->setData(x0, y0);
customPlot->graph(1)->setDataValueError(x1, y1, y1err);
customPlot->graph(2)->setData(x2, y2);
customPlot->graph(3)->setData(x3, y3);
customPlot->graph(4)->setData(x4, y4);
// activate top and right axes, which are invisible by default:
customPlot->xAxis2->setVisible(true);
customPlot->yAxis2->setVisible(true);
// set ranges appropriate to show data:
customPlot->xAxis->setRange(0, 2.7);
customPlot->yAxis->setRange(0, 2.6);
customPlot->xAxis2->setRange(0, 3.0*M_PI);
customPlot->yAxis2->setRange(-70, 35);
// set pi ticks on top axis:
QVector<double> piTicks;
QVector<QString> piLabels;
piTicks << 0 << 0.5*M_PI << M_PI << 1.5*M_PI << 2*M_PI << 2.5*M_PI << 3*M_PI;
piLabels << "0" << QString::fromUtf8("½π") << QString::fromUtf8("π") << QString::fromUtf8("1½π") << QString::fromUtf8("2π") << QString::fromUtf8("2½π") << QString::fromUtf8("3π");
customPlot->xAxis2->setAutoTicks(false);
customPlot->xAxis2->setAutoTickLabels(false);
customPlot->xAxis2->setTickVector(piTicks);
customPlot->xAxis2->setTickVectorLabels(piLabels);
// add title layout element:
customPlot->plotLayout()->insertRow(0);
customPlot->plotLayout()->addElement(0, 0, new QCPPlotTitle(customPlot, "Way too many graphs in one plot"));
// set labels:
customPlot->xAxis->setLabel("Bottom axis with outward ticks");
customPlot->yAxis->setLabel("Left axis label");
customPlot->xAxis2->setLabel("Top axis label");
customPlot->yAxis2->setLabel("Right axis label");
// make ticks on bottom axis go outward:
customPlot->xAxis->setTickLength(0, 5);
customPlot->xAxis->setSubTickLength(0, 3);
// make ticks on right axis go inward and outward:
customPlot->yAxis2->setTickLength(3, 3);
customPlot->yAxis2->setSubTickLength(1, 1);
}
// This function creates the following model:
// Minimize
// obj: x1 + x2 + x3 + x4 + x5 + x6
// Subject To
// c1: x1 + x2 + x5 = 8
// c2: x3 + x5 + x6 = 10
// q1: [ -x1^2 + x2^2 + x3^2 ] <= 0
// q2: [ -x4^2 + x5^2 ] <= 0
// Bounds
// x2 Free
// x3 Free
// x5 Free
// End
// which is a second order cone program in standard form.
// The function returns objective, variables and constraints in the
// values obj, vars and rngs.
// The function also sets up cone so that for a column j we have
// cone[j] >= 0 Column j is in a cone constraint and is the
// cone's head variable.
// cone[j] == NOT_CONE_HEAD Column j is in a cone constraint but is
// not the cone's head variable..
// cone[j] == NOT_IN_CONE Column j is not contained in any cone constraint.
static void
createmodel (IloModel& model, IloObjective &obj, IloNumVarArray &vars,
IloRangeArray &rngs, IloIntArray& cone)
{
// The indices we assign as user objects to the modeling objects.
// We define them as static data so that we don't have to worry about
// dynamic memory allocation/leakage.
static int indices[] = { 0, 1, 2, 3, 4, 5, 6 };
IloEnv env = model.getEnv();
// Create variables.
IloNumVar x1(env, 0, IloInfinity, "x1");
IloNumVar x2(env, -IloInfinity, IloInfinity, "x2");
IloNumVar x3(env, -IloInfinity, IloInfinity, "x3");
IloNumVar x4(env, 0, IloInfinity, "x4");
IloNumVar x5(env, -IloInfinity, IloInfinity, "x5");
IloNumVar x6(env, 0, IloInfinity, "x6");
// Create objective function and immediately store it in return value.
obj = IloMinimize(env, x1 + x2 + x3 + x4 + x5 + x6);
// Create constraints.
IloRange c1(env, 8, x1 + x2 + x5, 8, "c1");
IloRange c2(env, 10, x3 + x5 + x6, 10, "c2");
IloRange q1(env, -IloInfinity, -x1*x1 + x2*x2 + x3*x3, 0, "q1");
cone.add(2); // x1, cone head of constraint at index 2
cone.add(NOT_CONE_HEAD); // x2
cone.add(NOT_CONE_HEAD); // x3
IloRange q2(env, -IloInfinity, -x4*x4 + x5*x5, 0, "q2");
cone.add(3); // x4, cone head of constraint at index 3
cone.add(NOT_CONE_HEAD); // x5
cone.add(NOT_IN_CONE); // x6
// Setup model.
model.add(obj);
model.add(obj);
model.add(c1);
model.add(c2);
model.add(q1);
model.add(q2);
// Setup return values.
vars.add(x1);
vars.add(x2);
vars.add(x3);
vars.add(x4);
vars.add(x5);
vars.add(x6);
rngs.add(c1);
rngs.add(c2);
rngs.add(q1);
rngs.add(q2);
// We set the user object for each modeling object to its index in the
// respective array. This makes the code in checkkkt a little simpler.
for (IloInt i = 0; i < vars.getSize(); ++i)
vars[i].setObject(&indices[i]);
for (IloInt i = 0; i < rngs.getSize(); ++i)
rngs[i].setObject(&indices[i]);
}
int main()
{
X x1( 1 );
X x2( 2 );
X x3( 3 );
static_assert( noexcept( x1 + x2 ), "oops" );
static_assert( !noexcept( x1 * x2 ), "oops" );
assert( x1 == x1 );
assert( x1 != x2 );
assert( x1 == 1 );
assert( 2 == x2 );
assert( x3 != 1 );
assert( 2 != x3 );
assert( x1 < x2 );
assert( x1 <= x2 );
assert( x2 <= x2 );
assert( x3 > x2 );
assert( x3 >= x2 );
assert( x2 >= x2 );
assert( x1 < 2 );
assert( x1 <= 2 );
assert( x2 <= 2 );
assert( x3 > 2 );
assert( x3 >= 2 );
assert( x2 >= 2 );
assert( 1 < x2 );
assert( 1 <= x2 );
assert( 2 <= x2 );
assert( 3 > x2 );
assert( 3 >= x2 );
assert( 2 >= x2 );
assert( x1 + x2 == x3 );
assert( 1 + x2 == x3 );
assert( x1 + 2 == x3 );
assert( x2 + x1 == 3 );
assert( x3 - x1 == x2 );
assert( 3 - x1 == x2 );
assert( x3 - 1 == x2 );
assert( x1 - x3 == -2 );
assert( x2 * x2 == 4 );
assert( x2 * 3 == 6 );
assert( 4 * x2 == 8 );
assert( ( x3 + x1 ) / x2 == 2 );
assert( ( x1 + x3 ) / 2 == x2 );
assert( x3 % x2 == 1 );
assert( x3 % 2 == 1 );
static_assert( std::is_empty< E >::value, "oops" );
adl_test( E{} );
S s;
S s2( s, s );
#if !defined( _MSC_VER ) || defined( __clang__ )
constexpr C c1( 1 );
constexpr C c2( 2 );
constexpr C c3( 3 );
static_assert( c1 < c2, "oops" );
static_assert( c2 < c3, "oops" );
static_assert( c1 < c3, "oops" );
static_assert( c1 < 2, "oops" );
static_assert( c2 < 3, "oops" );
static_assert( c1 < 3, "oops" );
static_assert( c1 <= c2, "oops" );
static_assert( c2 <= c3, "oops" );
static_assert( c1 <= c3, "oops" );
static_assert( c1 <= 2, "oops" );
static_assert( c2 <= 3, "oops" );
static_assert( c1 <= 3, "oops" );
static_assert( 1 <= c2, "oops" );
static_assert( 2 <= c3, "oops" );
static_assert( 1 <= c3, "oops" );
static_assert( c2 > c1, "oops" );
static_assert( c3 > c2, "oops" );
static_assert( c3 > c1, "oops" );
static_assert( c2 > 1, "oops" );
static_assert( c3 > 2, "oops" );
static_assert( c3 > 1, "oops" );
static_assert( 2 > c1, "oops" );
static_assert( 3 > c2, "oops" );
static_assert( 3 > c1, "oops" );
static_assert( c2 >= c1, "oops" );
static_assert( c3 >= c2, "oops" );
static_assert( c3 >= c1, "oops" );
static_assert( c2 >= 1, "oops" );
static_assert( c3 >= 2, "oops" );
static_assert( c3 >= 1, "oops" );
static_assert( 2 >= c1, "oops" );
static_assert( 3 >= c2, "oops" );
static_assert( 3 >= c1, "oops" );
static_assert( !( c1 < c1 ), "oops" ); // NOLINT
static_assert( !( c1 > c1 ), "oops" ); // NOLINT
static_assert( c1 <= c1, "oops" ); // NOLINT
static_assert( c1 >= c1, "oops" ); // NOLINT
#endif
}
//---------------------------------------------------------
DMat& NDG2D::ConformingHrefine2D(IMat& edgerefineflag, const DMat& Qin)
//---------------------------------------------------------
{
#if (0)
OutputNodes(false); // volume nodes
//OutputNodes(true); // face nodes
#endif
// function newQ = ConformingHrefine2D(edgerefineflag, Q)
// Purpose: apply edge splits as requested by edgerefineflag
IVec v1("v1"), v2("v2"), v3("v3"), tvi;
DVec x1("x1"), x2("x2"), x3("x3"), y1("y1"), y2("y2"), y3("y3");
DVec a1("a1"), a2("a2"), a3("a3");
// count vertices
assert (VX.size() == Nv);
// find vertex triplets for elements to be refined
v1 = EToV(All,1); v2 = EToV(All,2); v3 = EToV(All,3);
x1 = VX(v1); x2 = VX(v2); x3 = VX(v3);
y1 = VY(v1); y2 = VY(v2); y3 = VY(v3);
// find angles at each element vertex (in radians)
VertexAngles(x1,x2,x3,y1,y2,y3, a1,a2,a3);
// absolute value of angle size
a1.set_abs(); a2.set_abs(); a3.set_abs();
int k=0,k1=0,f1=0,k2=0,f2=0, e1=0,e2=0,e3=0, b1=0,b2=0,b3=0, ref=0;
IVec m1,m2,m3; DVec mx1, my1, mx2, my2, mx3, my3;
// create new vertices at edge centers of marked elements
// (use unique numbering derived from unique edge number))
m1 = max(IVec(Nv*(v1-1)+v2+1), IVec(Nv*(v2-1)+v1+1)); mx1=0.5*(x1+x2); my1=0.5*(y1+y2);
m2 = max(IVec(Nv*(v2-1)+v3+1), IVec(Nv*(v3-1)+v2+1)); mx2=0.5*(x2+x3); my2=0.5*(y2+y3);
m3 = max(IVec(Nv*(v1-1)+v3+1), IVec(Nv*(v3-1)+v1+1)); mx3=0.5*(x3+x1); my3=0.5*(y3+y1);
// ensure that both elements sharing an edge are split
for (k1=1; k1<=K; ++k1) {
for (f1=1; f1<=Nfaces; ++f1) {
if (edgerefineflag(k1,f1)) {
k2 = EToE(k1,f1);
f2 = EToF(k1,f1);
edgerefineflag(k2,f2) = 1;
}
}
}
// store old data
IMat oldEToV = EToV; DVec oldVX = VX, oldVY = VY;
// count the number of elements in the refined mesh
int newK = countrefinefaces(edgerefineflag);
EToV.resize(newK, Nfaces, true, 0);
IMat newBCType(newK,3, "newBCType");
// kold = [];
IVec kold(newK, "kold"); Index1D KI,KIo;
int sk=1, skstart=0, skend=0;
for (k=1; k<=K; ++k)
{
skstart = sk;
e1 = edgerefineflag(k,1); b1 = BCType(k,1);
e2 = edgerefineflag(k,2); b2 = BCType(k,2);
e3 = edgerefineflag(k,3); b3 = BCType(k,3);
ref = e1 + 2*e2 + 4*e3;
switch (ref) {
case 0:
EToV(sk, All) = IVec(v1(k),v2(k),v3(k)); newBCType(sk,All) = IVec(b1, b2, b3); ++sk;
break;
case 1:
EToV(sk, All) = IVec(v1(k),m1(k),v3(k)); newBCType(sk,All) = IVec(b1, 0, b3); ++sk;
EToV(sk, All) = IVec(m1(k),v2(k),v3(k)); newBCType(sk,All) = IVec(b1, b2, 0); ++sk;
break;
case 2:
EToV(sk, All) = IVec(v2(k),m2(k),v1(k)); newBCType(sk,All) = IVec(b2, 0, b1); ++sk;
EToV(sk, All) = IVec(m2(k),v3(k),v1(k)); newBCType(sk,All) = IVec(b2, b3, 0); ++sk;
break;
case 4:
EToV(sk, All) = IVec(v3(k),m3(k),v2(k)); newBCType(sk,All) = IVec(b3, 0, b2); ++sk;
EToV(sk, All) = IVec(m3(k),v1(k),v2(k)); newBCType(sk,All) = IVec(b3, b1, 0); ++sk;
break;
case 3:
EToV(sk, All) = IVec(m1(k),v2(k),m2(k)); newBCType(sk,All) = IVec(b1, b2, 0); ++sk;
if (a1(k) > a3(k)) { // split largest angle
EToV(sk, All) = IVec(v1(k),m1(k),m2(k)); newBCType(sk,All) = IVec(b1, 0, 0); ++sk;
EToV(sk, All) = IVec(v1(k),m2(k),v3(k)); newBCType(sk,All) = IVec( 0, b2, b3); ++sk;
} else {
EToV(sk, All) = IVec(v3(k),m1(k),m2(k)); newBCType(sk,All) = IVec( 0, 0, b2); ++sk;
EToV(sk, All) = IVec(v3(k),v1(k),m1(k)); newBCType(sk,All) = IVec(b3, b1, 0); ++sk;
}
break;
case 5:
EToV(sk, All) = IVec(v1(k),m1(k),m3(k)); newBCType(sk,All) = IVec(b1, 0, b3); ++sk;
if (a2(k) > a3(k)) {
// split largest angle
EToV(sk, All) = IVec(v2(k),m3(k),m1(k)); newBCType(sk,All) = IVec( 0, 0, b1); ++sk;
EToV(sk, All) = IVec(v2(k),v3(k),m3(k)); newBCType(sk,All) = IVec(b2, b3, 0); ++sk;
} else {
EToV(sk, All) = IVec(v3(k),m3(k),m1(k)); newBCType(sk,All) = IVec(b3, 0, 0); ++sk;
EToV(sk, All) = IVec(v3(k),m1(k),v2(k)); newBCType(sk,All) = IVec( 0, b1, b2); ++sk;
}
break;
case 6:
EToV(sk, All) = IVec(v3(k),m3(k),m2(k)); newBCType(sk,All) = IVec(b3, 0, b2); ++sk;
if (a1(k) > a2(k)) {
// split largest angle
EToV(sk, All) = IVec(v1(k),m2(k),m3(k)); newBCType(sk,All) = IVec( 0, 0, b3); ++sk;
EToV(sk, All) = IVec(v1(k),v2(k),m2(k)); newBCType(sk,All) = IVec(b1, b2, 0); ++sk;
} else {
EToV(sk, All) = IVec(v2(k),m2(k),m3(k)); newBCType(sk,All) = IVec(b2, 0, 0); ++sk;
EToV(sk, All) = IVec(v2(k),m3(k),v1(k)); newBCType(sk,All) = IVec( 0 , b3, b1); ++sk;
}
break;
default:
// split all
EToV(sk, All) = IVec(m1(k),m2(k),m3(k)); newBCType(sk, All) = IVec( 0, 0, 0); ++sk;
EToV(sk, All) = IVec(v1(k),m1(k),m3(k)); newBCType(sk, All) = IVec(b1, 0, b3); ++sk;
EToV(sk, All) = IVec(v2(k),m2(k),m1(k)); newBCType(sk, All) = IVec(b2, 0, b1); ++sk;
EToV(sk, All) = IVec(v3(k),m3(k),m2(k)); newBCType(sk, All) = IVec(b3, 0, b2); ++sk;
break;
}
skend = sk;
// kold = [kold; k*ones(skend-skstart, 1)];
// element k is to be refined into (1:4) child elements.
// store parent element numbers in array "kold" to help
// with accessing parent vertex data during refinement.
KI.reset(skstart, skend-1); // ids of child elements
kold(KI) = k; // mark as children of element k
}
// Finished with edgerefineflag. Delete if OBJ_temp
if (edgerefineflag.get_mode() == OBJ_temp) {
delete (&edgerefineflag);
}
// renumber new nodes contiguously
// ids = unique([v1;v2;v3;m1;m2;m3]);
bool unique=true; IVec IDS, ids;
IDS = concat( concat(v1,v2,v3), concat(m1,m2,m3) );
ids = sort(IDS, unique);
Nv = ids.size();
int max_id = EToV.max_val();
umMSG(1, "max id in EToV is %d\n", max_id);
// M N nnz vals triplet
CSi newids(max_id,1, Nv, 1, 1 );
// newids = sparse(max(max(EToV)),1);
int i=0, j=1;
for (i=1; i<=Nv; ++i) {
// newids(ids)= (1:Nv);
newids.set1(ids(i),j, i); // load 1-based triplets
} // row col x
newids.compress(); // convert to csc form
// Matlab -----------------------------------------------
// v1 = newids(v1); v2 = newids(v2); v3 = newids(v3);
// m1 = newids(m1); m2 = newids(m2); m3 = newids(m3);
//-------------------------------------------------------
int KVi=v1.size(), KMi=m1.size();
// read from copies, overwrite originals
// 1. reload ids for new vertices
tvi = v1; for (i=1;i<=KVi;++i) {v1(i) = newids(tvi(i), 1);}
tvi = v2; for (i=1;i<=KVi;++i) {v2(i) = newids(tvi(i), 1);}
tvi = v3; for (i=1;i<=KVi;++i) {v3(i) = newids(tvi(i), 1);}
// 2. load ids for new (midpoint) vertices
tvi = m1; for (i=1;i<=KMi;++i) {m1(i) = newids(tvi(i), 1);}
tvi = m2; for (i=1;i<=KMi;++i) {m2(i) = newids(tvi(i), 1);}
tvi = m3; for (i=1;i<=KMi;++i) {m3(i) = newids(tvi(i), 1);}
VX.resize(Nv); VY.resize(Nv);
VX(v1) = x1; VX(v2) = x2; VX(v3) = x3;
VY(v1) = y1; VY(v2) = y2; VY(v3) = y3;
VX(m1) = mx1; VX(m2) = mx2; VX(m3) = mx3;
VY(m1) = my1; VY(m2) = my2; VY(m3) = my3;
if (newK != (sk-1)) {
umERROR("NDG2D::ConformingHrefine2D", "Inconsistent element count: expect %d, but sk = %d", newK, (sk-1));
} else {
K = newK; // sk-1;
}
// dumpIMat(EToV, "EToV (before)");
// EToV = newids(EToV);
for (j=1; j<=3; ++j) {
for (k=1; k<=K; ++k) {
EToV(k,j) = newids(EToV(k,j), 1);
}
}
#if (0)
dumpIMat(EToV, "EToV (after)");
// umERROR("Checking ids", "Nigel, check EToV");
#endif
BCType = newBCType;
Nv = VX.size();
// xold = x; yold = y;
StartUp2D();
#if (1)
OutputNodes(false); // volume nodes
//OutputNodes(true); // face nodes
//umERROR("Exiting early", "Check adapted {volume,face} nodes");
#endif
// allocate return object
int Nfields = Qin.num_cols();
DMat* tmpQ = new DMat(Np*K, Nfields, "newQ", OBJ_temp);
DMat& newQ = *tmpQ; // use a reference for syntax
// quick return, if no interpolation is required
if (Qin.size()<1) {
return newQ;
}
DVec rOUT(Np),sOUT(Np),xout,yout,xy1(2),xy2(2),xy3(2),tmp(2),rhs;
int ko=0,kv1=0,kv2=0,kv3=0,n=0; DMat A(2,2), interp;
DMat oldQ = const_cast<DMat&>(Qin);
for (k=1; k<=K; ++k)
{
ko = kold(k); xout = x(All,k); yout = y(All,k);
kv1=oldEToV(ko,1); kv2=oldEToV(ko,2); kv3=oldEToV(ko,3);
xy1.set(oldVX(kv1), oldVY(kv1));
xy2.set(oldVX(kv2), oldVY(kv2));
xy3.set(oldVX(kv3), oldVY(kv3));
A.set_col(1, xy2-xy1); A.set_col(2, xy3-xy1);
for (i=1; i<=Np; ++i) {
tmp.set(xout(i), yout(i));
rhs = 2.0*tmp - xy2 - xy3;
tmp = A|rhs;
rOUT(i) = tmp(1);
sOUT(i) = tmp(2);
}
KI.reset (Np*(k -1)+1, Np*k ); // nodes in new element k
KIo.reset(Np*(ko-1)+1, Np*ko); // nodes in old element ko
interp = Vandermonde2D(N, rOUT, sOUT)*invV;
for (n=1; n<=Nfields; ++n)
{
//newQ(:,k,n)= interp* Q(:,ko,n);
//DVec tm1 = interp*oldQ(KIo,n);
//dumpDVec(tm1, "tm1");
newQ(KI,n) = interp*oldQ(KIo,n);
}
}
return newQ;
}
int main(int argc, char *argv[]) {
int i;
char *passPhrase;
int outputLen = 0;
FILE *inputFile;
if (argc <= 1) {
usage();
return 0;
}
// Variable parsing for tablecheck
if (strncmp(argv[1], "rc4", 3) == 0) {
if (argc < 3) {
usage();
return 0;
}
for (i = 1; i < argc; i++) {
if (argc == 4) {
if (strncmp(argv[i], "-p=", 3) == 0) {
passPhrase = argv[i] + 3;
}
if (strncmp(argv[i], "-l=", 3) == 0) {
outputLen = atoi(argv[i] + 3);
}
if (!argv[i]) {
usage();
return 0;
}
}
else if (argc == 3) {
if (strncmp(argv[i], "-p=", 3) == 0) {
passPhrase = argv[i] + 3;
}
outputLen = 256;
}
else {
usage();
return 0;
}
}
if (passPhrase == NULL || outputLen < 1) {
usage();
return 0;
}
else {
// Call tablecheck function
rc4(passPhrase, outputLen);
}
}
else if (strncmp(argv[1], "x1", 2) == 0) {
if (argc < 2) {
usage();
return 0;
}
//for (i = 1; i < argc; i++) {
if (argc == 3) {
inputFile = fopen(argv[2], "rb");
}
else if (argc == 2) {
inputFile = stdin;
if(isatty(fileno(inputFile))) {
fprintf(stderr, "Invalid use of arguments. Please specify a file name or pipe input.\n");
return -1;
}
}
else {
usage();
return 0;
}
//}
if (inputFile == NULL) {
usage();
return 0;
}
else {
// Call keyExpand function
x1(inputFile);
}
}
else if (strncmp(argv[1], "x2", 2) == 0) {
if (argc < 2) {
usage();
return 0;
}
//for (i = 1; i < argc; i++) {
if (argc == 3) {
inputFile = fopen(argv[2], "rb");
}
else if (argc == 2) {
inputFile = stdin;
if(isatty(fileno(inputFile))) {
fprintf(stderr, "Invalid use of arguments. Please specify a file name or pipe input.\n");
return -1;
}
}
else {
usage();
return 0;
}
//}
if (inputFile == NULL) {
usage();
return 0;
}
else {
// Call keyExpand function
x2(inputFile);
}
}
else if (strncmp(argv[1], "x3", 2) == 0) {
if (argc < 2) {
usage();
return 0;
}
//for (i = 1; i < argc; i++) {
if (argc == 3) {
inputFile = fopen(argv[2], "rb");
}
else if (argc == 2) {
inputFile = stdin;
if(isatty(fileno(inputFile))) {
fprintf(stderr, "Invalid use of arguments. Please specify a file name or pipe input.\n");
return -1;
}
}
else {
usage();
return 0;
}
//}
if (inputFile == NULL) {
usage();
return 0;
}
else {
// Call keyExpand function
x3(inputFile);
}
}
// If these conditions are not met, then print usage and quit.
else {
usage();
return 0;
}
return 0;
}
Vector Rosen34(
Fun &F ,
size_t M ,
const Scalar &ti ,
const Scalar &tf ,
const Vector &xi ,
Vector &e )
{
CPPAD_ASSERT_FIRST_CALL_NOT_PARALLEL;
// check numeric type specifications
CheckNumericType<Scalar>();
// check simple vector class specifications
CheckSimpleVector<Scalar, Vector>();
// Parameters for Shampine's Rosenbrock method
// are static to avoid recalculation on each call and
// do not use Vector to avoid possible memory leak
static Scalar a[3] = {
Scalar(0),
Scalar(1),
Scalar(3) / Scalar(5)
};
static Scalar b[2 * 2] = {
Scalar(1),
Scalar(0),
Scalar(24) / Scalar(25),
Scalar(3) / Scalar(25)
};
static Scalar ct[4] = {
Scalar(1) / Scalar(2),
- Scalar(3) / Scalar(2),
Scalar(121) / Scalar(50),
Scalar(29) / Scalar(250)
};
static Scalar cg[3 * 3] = {
- Scalar(4),
Scalar(0),
Scalar(0),
Scalar(186) / Scalar(25),
Scalar(6) / Scalar(5),
Scalar(0),
- Scalar(56) / Scalar(125),
- Scalar(27) / Scalar(125),
- Scalar(1) / Scalar(5)
};
static Scalar d3[3] = {
Scalar(97) / Scalar(108),
Scalar(11) / Scalar(72),
Scalar(25) / Scalar(216)
};
static Scalar d4[4] = {
Scalar(19) / Scalar(18),
Scalar(1) / Scalar(4),
Scalar(25) / Scalar(216),
Scalar(125) / Scalar(216)
};
CPPAD_ASSERT_KNOWN(
M >= 1,
"Error in Rosen34: the number of steps is less than one"
);
CPPAD_ASSERT_KNOWN(
e.size() == xi.size(),
"Error in Rosen34: size of e not equal to size of xi"
);
size_t i, j, k, l, m; // indices
size_t n = xi.size(); // number of components in X(t)
Scalar ns = Scalar(double(M)); // number of steps as Scalar object
Scalar h = (tf - ti) / ns; // step size
Scalar zero = Scalar(0); // some constants
Scalar one = Scalar(1);
Scalar two = Scalar(2);
// permutation vectors needed for LU factorization routine
CppAD::vector<size_t> ip(n), jp(n);
// vectors used to store values returned by F
Vector E(n * n), Eg(n), f_t(n);
Vector g(n * 3), x3(n), x4(n), xf(n), ftmp(n), xtmp(n), nan_vec(n);
// initialize e = 0, nan_vec = nan
for(i = 0; i < n; i++)
{ e[i] = zero;
nan_vec[i] = nan(zero);
}
xf = xi; // initialize solution
for(m = 0; m < M; m++)
{ // time at beginning of this interval
Scalar t = ti * (Scalar(int(M - m)) / ns)
+ tf * (Scalar(int(m)) / ns);
// value of x at beginning of this interval
x3 = x4 = xf;
// evaluate partial derivatives at beginning of this interval
F.Ode_ind(t, xf, f_t);
F.Ode_dep(t, xf, E); // E = f_x
if( hasnan(f_t) || hasnan(E) )
{ e = nan_vec;
return nan_vec;
}
// E = I - f_x * h / 2
for(i = 0; i < n; i++)
{ for(j = 0; j < n; j++)
E[i * n + j] = - E[i * n + j] * h / two;
E[i * n + i] += one;
}
// LU factor the matrix E
# ifndef NDEBUG
int sign = LuFactor(ip, jp, E);
# else
LuFactor(ip, jp, E);
# endif
CPPAD_ASSERT_KNOWN(
sign != 0,
"Error in Rosen34: I - f_x * h / 2 not invertible"
);
// loop over integration steps
for(k = 0; k < 3; k++)
{ // set location for next function evaluation
xtmp = xf;
for(l = 0; l < k; l++)
{ // loop over previous function evaluations
Scalar bkl = b[(k-1)*2 + l];
for(i = 0; i < n; i++)
{ // loop over elements of x
xtmp[i] += bkl * g[i*3 + l] * h;
}
}
// ftmp = F(t + a[k] * h, xtmp)
F.Ode(t + a[k] * h, xtmp, ftmp);
if( hasnan(ftmp) )
{ e = nan_vec;
return nan_vec;
}
// Form Eg for this integration step
for(i = 0; i < n; i++)
Eg[i] = ftmp[i] + ct[k] * f_t[i] * h;
for(l = 0; l < k; l++)
{ for(i = 0; i < n; i++)
Eg[i] += cg[(k-1)*3 + l] * g[i*3 + l];
}
// Solve the equation E * g = Eg
LuInvert(ip, jp, E, Eg);
// save solution and advance x3, x4
for(i = 0; i < n; i++)
{ g[i*3 + k] = Eg[i];
x3[i] += h * d3[k] * Eg[i];
x4[i] += h * d4[k] * Eg[i];
}
}
// Form Eg for last update to x4 only
for(i = 0; i < n; i++)
Eg[i] = ftmp[i] + ct[3] * f_t[i] * h;
for(l = 0; l < 3; l++)
{ for(i = 0; i < n; i++)
Eg[i] += cg[2*3 + l] * g[i*3 + l];
}
// Solve the equation E * g = Eg
LuInvert(ip, jp, E, Eg);
// advance x4 and accumulate error bound
for(i = 0; i < n; i++)
{ x4[i] += h * d4[3] * Eg[i];
// cant use abs because cppad.hpp may not be included
Scalar diff = x4[i] - x3[i];
if( diff < zero )
e[i] -= diff;
else e[i] += diff;
}
// advance xf for this step using x4
xf = x4;
}
return xf;
}
TEST(MathLib, DenseGaussAlgorithmDenseVector)
{
std::size_t n_rows(50);
std::size_t n_cols(n_rows);
MathLib::DenseMatrix<double,std::size_t> mat(n_rows, n_cols);
// *** fill matrix with arbitrary values
// ** initialize random seed
srand ( static_cast<unsigned>(time(nullptr)) );
// ** loop over rows and columns
for (std::size_t i(0); i<n_rows; i++) {
for (std::size_t j(0); j<n_cols; j++) {
mat(i,j) = rand()/static_cast<double>(RAND_MAX);
}
}
// *** create solution vector, set all entries to 0.0
MathLib::DenseVector<double> x(n_cols);
std::fill(std::begin(x), std::end(x), 0.0);
MathLib::DenseVector<double> b0(mat * x);
// *** create other right hand sides,
// set all entries of the solution vector to 1.0
std::fill(std::begin(x), std::end(x), 1.0);
MathLib::DenseVector<double> b1(mat * x);
std::generate(std::begin(x), std::end(x), std::rand);
MathLib::DenseVector<double> b2(mat * x);
// right hand side and solution vector with random entries
MathLib::DenseVector<double> b3(mat * x);
MathLib::DenseVector<double> b3_copy(mat * x);
MathLib::DenseVector<double> x3 (n_cols);
std::generate(std::begin(x3),std::end(x3), std::rand);
MathLib::GaussAlgorithm<MathLib::DenseMatrix<double, std::size_t>, MathLib::DenseVector<double>> gauss(mat);
// solve with b0 as right hand side
gauss.solve(b0, true);
for (std::size_t i(0); i<n_rows; i++) {
ASSERT_NEAR(b0[i], 0.0, 1e5 * std::numeric_limits<float>::epsilon());
}
// solve with b1 as right hand side
gauss.solve(b1, false);
for (std::size_t i(0); i<n_rows; i++) {
ASSERT_NEAR(b1[i], 1.0, std::numeric_limits<float>::epsilon());
}
// solve with b2 as right hand side
gauss.solve(b2, false);
for (std::size_t i(0); i<n_rows; i++) {
ASSERT_NEAR(fabs(b2[i]-x[i])/fabs(x[i]), 0.0, std::numeric_limits<float>::epsilon());
}
gauss.solve(b3, x3, false);
for (std::size_t i(0); i<n_rows; i++) {
ASSERT_NEAR(fabs(x3[i]-x[i])/fabs(x[i]), 0.0, std::numeric_limits<float>::epsilon());
}
// assure entries of vector b3 are not changed
for (std::size_t i(0); i<n_rows; i++) {
ASSERT_NEAR(fabs(b3[i]-b3_copy[i])/fabs(b3[i]), 0.0, std::numeric_limits<float>::epsilon());
}
}