void GEPPGrowth( Matrix<T>& A, Int n )
{
DEBUG_ONLY(CSE cse("GEPPGrowth"))
Identity( A, n, n );
if( n <= 1 )
return;
// Set the last column to all ones
auto aLast = A( IR(0,n), IR(n-1,n) );
Fill( aLast, T(1) );
// Set the subdiagonals to -1
for( Int j=1; j<n; ++j )
FillDiagonal( A, T(-1), -j );
}
/**
* @brief SetScaleMatrix set the matrix as a scaling matrix.
* @param x_scale
* @param y_scale
*/
void SetScaleMatrix(float x_scale, float y_scale)
{
if(x_scale <= 0.0f) {
x_scale = 1.0f;
}
if(y_scale <= 0.0f) {
y_scale = 1.0f;
}
Identity();
data[0] = x_scale;
data[4] = y_scale;
}
inline void
ExplicitLQHelper( Matrix<Complex<Real> >& L, Matrix<Complex<Real> >& A )
{
Matrix<Complex<Real> > t;
LQ( A, t );
L = A;
MakeTrapezoidal( LEFT, LOWER, 0, L );
// TODO: Replace this with an in-place expansion of Q
Matrix<Complex<Real> > Q;
Identity( A.Height(), A.Width(), Q );
ApplyPackedReflectors
( RIGHT, UPPER, HORIZONTAL, BACKWARD, UNCONJUGATED, 0, A, t, Q );
A = Q;
}
inline void
NewtonSchulzStep( const Matrix<F>& X, Matrix<F>& XTmp, Matrix<F>& XNew )
{
#ifndef RELEASE
CallStackEntry entry("sign::NewtonSchulzStep");
#endif
typedef BASE(F) Real;
const Int n = X.Height();
// XTmp := 3I - X^2
Identity( XTmp, n, n );
Gemm( NORMAL, NORMAL, Real(-1), X, X, Real(3), XTmp );
// XNew := 1/2 X XTmp
Gemm( NORMAL, NORMAL, Real(1)/Real(2), X, XTmp, XNew );
}
Expression *IdentityExp::optimize(int result)
{
//printf("IdentityExp::optimize(result = %d) %s\n", result, toChars());
e1 = e1->optimize(WANTvalue | (result & WANTinterpret));
e2 = e2->optimize(WANTvalue | (result & WANTinterpret));
Expression *e = this;
if ((this->e1->isConst() && this->e2->isConst()) ||
(this->e1->op == TOKnull && this->e2->op == TOKnull))
{
e = Identity(op, type, this->e1, this->e2);
if (e == EXP_CANT_INTERPRET)
e = this;
}
return e;
}
static Matrix4<T> Rotate(T radians, const vec3& axis) {
T s = std::sin(radians);
T c = std::cos(radians);
Matrix4 m = Identity();
m.x.x = c + (1 - c) * axis.x * axis.x;
m.x.y = (1 - c) * axis.x * axis.y - axis.z * s;
m.x.z = (1 - c) * axis.x * axis.z + axis.y * s;
m.y.x = (1 - c) * axis.x * axis.y + axis.z * s;
m.y.y = c + (1 - c) * axis.y * axis.y;
m.y.z = (1 - c) * axis.y * axis.z - axis.x * s;
m.z.x = (1 - c) * axis.x * axis.z - axis.y * s;
m.z.y = (1 - c) * axis.y * axis.z + axis.x * s;
m.z.z = c + (1 - c) * axis.z * axis.z;
return m;
}
// Assumes that there is either no exogenous variables or there is a single
// exogenous variable that is constant and equal to one. The unconditional
// mean is obtained from the reduced form companion matrix.
TDenseMatrix UnconditionalVariance(const TDenseMatrix &A0, const TDenseMatrix &Aplus, bool IsConstant)
{
int n_lags=NumberLags(A0,Aplus,IsConstant), n_vars=A0.cols;
TDenseMatrix B=ReducedForm(A0,Aplus);
if (n_lags == 0) return ConditionalVariance(A0);
TDenseMatrix C=CompanionMatrix(B,n_lags), V=BlockDiagonalMatrix(A0,n_lags),
X=V*(Identity(n_vars*n_lags) - C);
try
{
return SubMatrix(Inverse(TransposeMultiply(X,X)),0,n_vars-1,0,n_vars-1);
}
catch (dw_exception &e)
{
throw dw_exception("UnconditionalMean(): Unconditional mean does not exist");
}
}
LRESULT ChatCtrl::onReport(WORD /*wNotifyCode*/, WORD /*wID*/, HWND /*hWndCtl*/, BOOL& /*bHandled*/) {
const OnlineUserPtr ou = client->findUser(Text::fromT(selectedUser));
if(ou) {
CHARFORMAT2 cf;
memzero(&cf, sizeof(CHARFORMAT2));
cf.cbSize = sizeof(cf);
cf.dwMask = CFM_BACKCOLOR | CFM_COLOR | CFM_BOLD;
cf.crBackColor = SETTING(BACKGROUND_COLOR);
cf.crTextColor = SETTING(ERROR_COLOR);
AppendText(Identity(NULL, 0), Text::toT(client->getCurrentNick()), Text::toT("[" + Util::getShortTimeString() + "] "), Text::toT(WinUtil::getReport(ou->getIdentity(), m_hWnd)) + _T('\n'), cf, false);
}
return 0;
}
const ECP::Point& ECP::Add(const Point &P, const Point &Q) const
{
if (P.identity) return Q;
if (Q.identity) return P;
if (GetField().Equal(P.x, Q.x))
return GetField().Equal(P.y, Q.y) ? Double(P) : Identity();
FieldElement t = GetField().Subtract(Q.y, P.y);
t = GetField().Divide(t, GetField().Subtract(Q.x, P.x));
FieldElement x = GetField().Subtract(GetField().Subtract(GetField().Square(t), P.x), Q.x);
m_R.y = GetField().Subtract(GetField().Multiply(t, GetField().Subtract(P.x, x)), P.y);
m_R.x.swap(x);
m_R.identity = false;
return m_R;
}
void GEPPGrowth( ElementalMatrix<T>& A, Int n )
{
DEBUG_ONLY(CSE cse("GEPPGrowth"))
Identity( A, n, n );
if( n <= 1 )
return;
// Set the last column to all ones
unique_ptr<ElementalMatrix<T>> aLast( A.Construct(A.Grid(),A.Root()) );
View( *aLast, A, IR(0,n), IR(n-1,n) );
Fill( *aLast, T(1) );
// Set the subdiagonals to -1
for( Int j=1; j<n; ++j )
FillDiagonal( A, T(-1), -j );
}
Matrix4x4 Matrix4x4::Perspective(float fov, float aspect, float zNear, float zFar)
{
Matrix4x4 m = Identity();
float yScale = 1/tan(Mathf::Deg2Rad * fov / 2);
float xScale = yScale/aspect;
m.m00 = xScale;
m.m11 = yScale;
m.m22 = (zNear + zFar) / (zNear - zFar);
m.m23 = 2 * zNear * zFar / (zNear - zFar);
m.m32 = -1.0f;
m.m33 = 0;
return m;
}
const EC2N::Point& EC2N::Double(const Point &P) const
{
if (P.identity) return P;
if (!m_field->IsUnit(P.x)) return Identity();
FieldElement t = m_field->Divide(P.y, P.x);
m_field->Accumulate(t, P.x);
m_R.y = m_field->Square(P.x);
m_R.x = m_field->Square(t);
m_field->Accumulate(m_R.x, t);
m_field->Accumulate(m_R.x, m_a);
m_field->Accumulate(m_R.y, m_field->Multiply(t, m_R.x));
m_field->Accumulate(m_R.y, m_R.x);
m_R.identity = false;
return m_R;
}
inline void
Explicit( Matrix<F>& L, Matrix<F>& A )
{
#ifndef RELEASE
CallStackEntry cse("lq::Explicit");
#endif
Matrix<F> t;
LQ( A, t );
L = A;
MakeTriangular( LOWER, L );
// TODO: Replace this with an in-place expansion of Q
Matrix<F> Q;
Identity( Q, A.Height(), A.Width() );
lq::ApplyQ( RIGHT, NORMAL, A, t, Q );
A = Q;
}
inline void
Explicit( DistMatrix<F>& A )
{
#ifndef RELEASE
CallStackEntry cse("lq::Explicit");
#endif
const Grid& g = A.Grid();
DistMatrix<F,MD,STAR> t( g );
LQ( A, t );
// TODO: Replace this with an in-place expansion of Q
DistMatrix<F> Q( g );
Q.AlignWith( A );
Identity( Q, A.Height(), A.Width() );
lq::ApplyQ( RIGHT, NORMAL, A, t, Q );
A = Q;
}
void Midpoint_SingleStep(Vector& x,
double t,
double& tau,
Vector& a,
double a0,
const Matrix& nu,
PropensityFunc propFunc,
PropensityJacobianFunc propJacFunc,
double abs_tol,
double rel_tol,
int& RXN,
Vector& p)
{
p = a;
// static Vector x1 = x;
static Vector a1 = a;
// static Vector delx = x;
/*
p = PoissonRandom(0.5* a * tau); // better midpoint method
p = 0.5* a * tau; // original midpoint method
x1 = x + nu*p;
*/
const Vector A = nu * a;
const Vector E = 0.5* tau * A;
Vector delx(x.Size(), 0);
bool converged = false;
int iterations = 0;
const Matrix I = Identity(x.Size());
Vector xPlusDelx(x.Size());
static Matrix AA = I;
static Vector BB = E;
static Vector deldelx = x;
while (!converged && iterations < 10) {
xPlusDelx = x+ delx;
AA = I - 0.5*tau * nu * propJacFunc(xPlusDelx);
BB = E + 0.5*tau * nu * propFunc(xPlusDelx) - delx;
SolveGE(AA, deldelx, BB);
converged = (Norm(deldelx, 2) <= rel_tol * Norm(delx, 2) + abs_tol);
delx += deldelx;
++iterations;
}
a1 = propFunc(x + delx);
a1 = 0.5*(a + a1)*tau;
p = PoissonRandom(a1);
}
void renderScene(void) {
int sx = glutGet(GLUT_WINDOW_WIDTH);
int sy = glutGet(GLUT_WINDOW_HEIGHT);
//SAspect = Scaling(1, (float)sx / sy, 1);
VECTOR4D worldRayOrigin, worldRayDir;
VECTOR4D modelRayOrigin, modelRayDir;
MATRIX4D InvW;
multimap<float, CMesh::INTERSECTIONINFO> faces;
bool fill = false;
SAspect = Scaling((float)sy / sx, 1, 1);
W = Identity();
P = PerspectiveWidthHeightRH(0.5f, 0.5f, 1.0f, 10.0f);
EC = SAspect * T * Translation(0.0f, 0.0f, -1.0f);
glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
BuildRayFromPerspective(EC, mx, my, worldRayOrigin, worldRayDir);
Inverse(W, InvW);
modelRayOrigin = InvW * worldRayOrigin;
modelRayDir = InvW * worldRayDir;
fill = g_EggCarton.RayCast(modelRayOrigin, modelRayDir, faces);
glPolygonMode(GL_FRONT_AND_BACK, GL_LINE);
glBegin(GL_TRIANGLES);
g_EggCarton.Draw(EC);
glEnd();
glPolygonMode(GL_FRONT_AND_BACK, GL_FILL);
glBegin(GL_TRIANGLES);
if (fill)
g_EggCarton.Draw(EC, faces.begin()->second.Face, 1);
glEnd();
if (bWireframe)
glPolygonMode(GL_FRONT_AND_BACK, GL_LINE);
else
glPolygonMode(GL_FRONT_AND_BACK, GL_FILL);
glBegin(GL_TRIANGLES);
g_Plate.Draw(SAspect * T * Translation(0.0f, 0.0f, -0.1f));
g_Sphere.Draw(SAspect * T * Translation(0.4f, 0.4f, 0.32f));
g_Bananas.Draw(SAspect * T * Translation(0.45f, 0.45f, 0.48f));
g_Flower.Draw(SAspect * T * Translation(-0.5f, 0.5f, 0.8f));
glEnd();
glutSwapBuffers();
}
Matrix4 Matrix4::Face(const Vec3f &V0, const Vec3f &V1)
{
//
// Rotate about the cross product of the two vectors by the angle between the two vectors
//
Vec3f Axis = Vec3f::Cross(V0, V1);
float Angle = Vec3f::AngleBetween(V0, V1);
if(Angle == 0.0f || Axis.Length() < 0.0f)
{
return Identity();
}
else
{
return Rotation(Axis, Angle);
}
}
Matrix3& Matrix3::Orthographic( const Real l, const Real r, const Real b, const Real t, const Real zn, const Real zf )
{
#ifdef __USE_D3DX__
D3DXMatrixOrthoOffCenterLH( (D3DXMATRIX*)this, l, r, b, t, zn, zf );
#else
Identity();
Real d = zf - zn;
e[0] = 2.0f / ( r - l );
e[5] = 2.0f / ( t - b );
e[10] = 1.0f / d;
e[14] = -zn / d;
#endif
return *this;
}
void
NewtonSchulzStep
( const Matrix<Field>& X,
Matrix<Field>& XTmp,
Matrix<Field>& XNew )
{
EL_DEBUG_CSE
typedef Base<Field> Real;
const Int n = X.Height();
// XTmp := 3I - X^2
Identity( XTmp, n, n );
Gemm( NORMAL, NORMAL, Real(-1), X, X, Real(3), XTmp );
// XNew := 1/2 X XTmp
Gemm( NORMAL, NORMAL, Real(1)/Real(2), X, XTmp, XNew );
}
inline void
ExplicitLQHelper
( DistMatrix<Complex<Real> >& L, DistMatrix<Complex<Real> >& A )
{
const Grid& g = A.Grid();
DistMatrix<Complex<Real>,MD,STAR> t( g );
LQ( A, t );
L = A;
MakeTrapezoidal( LEFT, LOWER, 0, L );
// TODO: Replace this with an in-place expansion of Q
DistMatrix<Complex<Real> > Q( g );
Identity( A.Height(), A.Width(), Q );
ApplyPackedReflectors
( RIGHT, UPPER, HORIZONTAL, BACKWARD, UNCONJUGATED, 0, A, t, Q );
A = Q;
}
// Takes care that there may be multiple values of attribute in valueMap
Identity RecognitionDatabase::Private::findByAttributes(const QString& attribute, const QMap<QString, QString>& valueMap) const
{
QMap<QString, QString>::const_iterator it = valueMap.find(attribute);
for (; it != valueMap.end() && it.key() == attribute; ++it)
{
foreach (const Identity& identity, identityCache)
{
if (identityContains(identity, attribute, it.value()))
{
return identity;
}
}
}
return Identity();
}
void handleMe(boost::system::error_code err, const Http::Message& response)
{
#ifndef WT_TARGET_JAVA
WApplication::instance()->resumeRendering();
#endif
if (!err && response.status() == 200) {
#ifndef WT_TARGET_JAVA
Json::ParseError e;
Json::Object me;
bool ok = Json::parse(response.body(), me, e);
#else
Json::Object me;
try {
me = (Json::Object)Json::Parser().parse(response.body());
} catch (Json::ParseError pe) {
}
bool ok = me.isNull();
#endif
if (!ok) {
LOG_ERROR("could not parse Json: '" << response.body() << "'");
setError(ERROR_MSG("badjson"));
authenticated().emit(Identity::Invalid);
} else {
std::string id = me.get("id");
WT_USTRING userName = me.get("name");
std::string email = me.get("email").orIfNull("");
bool emailVerified = !me.get("email").isNull();
authenticated().emit(Identity(service().name(), id, userName,
email, emailVerified));
}
} else {
if (!err) {
LOG_ERROR("user info request returned: " << response.status());
LOG_ERROR("with: " << response.body());
} else
LOG_ERROR("handleMe(): " << err.message());
setError(ERROR_MSG("badresponse"));
authenticated().emit(Identity::Invalid);
}
}
void Explicit
( ElementalMatrix<F>& APre,
ElementalMatrix<F>& R,
bool thinQR,
const QRCtrl<Base<F>>& ctrl )
{
DEBUG_CSE
DistMatrixReadWriteProxy<F,F,MC,MR> AProx( APre );
auto& A = AProx.Get();
const Grid& g = A.Grid();
DistMatrix<F,MD,STAR> householderScalars(g);
DistMatrix<Base<F>,MD,STAR> signature(g);
if( ctrl.colPiv )
{
DistPermutation Omega(g);
QR( A, householderScalars, signature, Omega, ctrl );
}
else
QR( A, householderScalars, signature );
const Int m = A.Height();
const Int n = A.Width();
const Int numIts = householderScalars.Height();
auto AT = A( IR(0,numIts), IR(0,n) );
Copy( AT, R );
MakeTrapezoidal( UPPER, R );
if( thinQR )
{
A.Resize( m, numIts );
ExpandPackedReflectors
( LOWER, VERTICAL, CONJUGATED, 0, A, householderScalars );
DiagonalScale( RIGHT, NORMAL, signature, A );
}
else
{
auto ACopy = A;
// TODO: Use an extension of ExpandPackedReflectors to make this faster
Identity( A, A.Height(), A.Height() );
qr::ApplyQ( LEFT, NORMAL, ACopy, householderScalars, signature, A );
}
}
// Assumes that there is either no exogenous variables or there is a single
// exogenous variable that is constant and equal to one. The unconditional
// mean is obtained from the reduced form companion matrix.
TDenseVector UnconditionalMean(const TDenseMatrix &A0, const TDenseMatrix &Aplus, bool IsConstant)
{
int n_lags=NumberLags(A0,Aplus,IsConstant), n_vars=A0.cols;
if (!IsConstant) return TDenseVector(n_vars,0.0);
TDenseMatrix B=ReducedForm(A0,Aplus);
if (n_lags == 0) return ColumnVector(B,0);
TDenseMatrix C=CompanionMatrix(B,n_lags);
TDenseVector b(n_vars*n_lags,0.0);
b.InsertColumnVector(0,B,n_vars*n_lags,0,n_vars-1);
try
{
return SubVector(InverseMultiply(Identity(n_vars*n_lags) - C,b),0,n_vars-1);
}
catch (dw_exception &e)
{
throw dw_exception("UnconditionalMean(): Unconditional mean does not exist");
}
}
void Topology::setRootServers(const Dictionary &sn)
{
std::map< Identity,std::vector<InetAddress> > m;
for(Dictionary::const_iterator d(sn.begin());d!=sn.end();++d) {
if ((d->first.length() == ZT_ADDRESS_LENGTH_HEX)&&(d->second.length() > 0)) {
try {
Dictionary snspec(d->second);
std::vector<InetAddress> &a = m[Identity(snspec.get("id"))];
std::string udp(snspec.get("udp",std::string()));
if (udp.length() > 0)
a.push_back(InetAddress(udp));
} catch ( ... ) {
TRACE("root server list contained invalid entry for: %s",d->first.c_str());
}
}
}
this->setRootServers(m);
}
Matrix4x4 Matrix4x4::Rotation(const Quaternion &r)
{
Matrix4x4 m = Identity();
m.m00 = 1 - 2*r.y*r.y - 2*r.z*r.z;
m.m10 = 2*r.x*r.y + 2*r.w*r.z;
m.m20 = 2*r.x*r.z - 2*r.w*r.y;
m.m01 = 2*r.x*r.y - 2*r.w*r.z;
m.m11 = 1 - 2*r.x*r.x - 2*r.z*r.z;
m.m21 = 2*r.y*r.z + 2*r.w*r.x;
m.m02 = 2*r.x*r.z + 2*r.w*r.y;
m.m12 = 2*r.y*r.z - 2*r.w*r.x;
m.m22 = 1 - 2*r.x*r.x - 2*r.y*r.y;
return m;
}
void ExplicitUnitary( AbstractDistMatrix<F>& APre )
{
EL_DEBUG_CSE
const Grid& g = APre.Grid();
DistMatrixReadWriteProxy<F,F,MC,MR> AProx( APre );
auto& A = AProx.Get();
DistMatrix<F,MD,STAR> householderScalars(g);
DistMatrix<Base<F>,MD,STAR> signature(g);
LQ( A, householderScalars, signature );
// TODO: Replace this with an in-place expansion of Q
DistMatrix<F> Q(g);
Q.AlignWith( A );
Identity( Q, A.Height(), A.Width() );
lq::ApplyQ( RIGHT, NORMAL, A, householderScalars, signature, Q );
Copy( Q, APre );
}
void Explicit
( ElementalMatrix<F>& APre,
ElementalMatrix<F>& R,
ElementalMatrix<Int>& OmegaFull,
bool thinQR,
const QRCtrl<Base<F>>& ctrl )
{
DEBUG_ONLY(CSE cse("qr::Explicit"))
DistMatrixReadWriteProxy<F,F,MC,MR> AProx( APre );
auto& A = AProx.Get();
const Grid& g = A.Grid();
DistMatrix<F,MD,STAR> t(g);
DistMatrix<Base<F>,MD,STAR> d(g);
DistPermutation Omega(g);
QR( A, t, d, Omega, ctrl );
const Int m = A.Height();
const Int n = A.Width();
const Int numIts = t.Height();
auto AT = A( IR(0,numIts), IR(0,n) );
Copy( AT, R );
MakeTrapezoidal( UPPER, R );
if( thinQR )
{
A.Resize( m, numIts );
ExpandPackedReflectors( LOWER, VERTICAL, CONJUGATED, 0, A, t );
DiagonalScale( RIGHT, NORMAL, d, A );
}
else
{
auto ACopy = A;
// TODO: Use an extension of ExpandPackedReflectors to make this faster
Identity( A, A.Height(), A.Height() );
qr::ApplyQ( LEFT, NORMAL, ACopy, t, d, A );
}
Omega.ExplicitMatrix( OmegaFull );
}
void Explicit( Matrix<F>& L, Matrix<F>& A )
{
EL_DEBUG_CSE
Matrix<F> householderScalars;
Matrix<Base<F>> signature;
LQ( A, householderScalars, signature );
const Int m = A.Height();
const Int n = A.Width();
const Int minDim = Min(m,n);
auto AL = A( IR(0,m), IR(0,minDim) );
L = AL;
MakeTrapezoidal( LOWER, L );
// TODO: Replace this with an in-place expansion of Q
Matrix<F> Q;
Identity( Q, A.Height(), A.Width() );
lq::ApplyQ( RIGHT, NORMAL, A, householderScalars, signature, Q );
A = Q;
}
MATRIX4D RotationAxis(float theta, VECTOR4D &Axis) {
MATRIX4D R = Identity();
float c = cosf(theta);
float s = sinf(theta);
float _1c = 1.0f - c;
R.m00 = c + _1c * Axis.x * Axis.x;
R.m01 = _1c * (Axis.x * Axis.y) - s * Axis.z;
R.m02 = _1c * (Axis.z * Axis.x) + s * Axis.y;
R.m10 = _1c * (Axis.x * Axis.y) + s * Axis.z;
R.m11 = c + _1c * Axis.y * Axis.y;
R.m12 = _1c * (Axis.z * Axis.y) - s * Axis.x;
R.m20 = _1c * (Axis.z * Axis.x) - s * Axis.y;
R.m21 = _1c * (Axis.z * Axis.y) + s * Axis.x;
R.m22 = c + _1c * Axis.z * Axis.z;
return R;
}