// DPOSV uses Cholesky factorization A=U^T*U, A=L*L^T
// to compute the solution to a real system of linear
// equations A*X=B, where A is a square, (N,N) symmetric
// positive definite matrix and X and B are (N,NRHS).
//---------------------------------------------------------
void umSOLVE_CH(const DMat& mat, const DVec& b, DVec& x)
//---------------------------------------------------------
{
// check args
assert(mat.is_square()); // symmetric
assert(b.size() >= mat.num_rows()); // is b consistent?
assert(b.size() <= x.size()); // can x store solution?
DMat A(mat); // work with copy of input
x = b; // allocate solution vector
int rows=A.num_rows(), LDA=A.num_rows(), cols=A.num_cols();
int LDB=b.size(), NRHS=1, info=0;
if (rows<1) {umWARNING("umSOLVE_CH()", "system is empty"); return;}
// Solve the system.
POSV('U', rows, NRHS, A.data(), LDA, x.data(), LDB, info);
if (info < 0) {
x = 0.0;
umERROR("umSOLVE_CH(A,b, x)",
"Error in input argument (%d)\nNo solution computed.", -info);
} else if (info > 0) {
x = 0.0;
umERROR("umSOLVE_CH(A,b, x)",
"\nINFO = %d. The leading minor of order %d of A"
"\nis not positive definite, so the factorization"
"\ncould not be completed. No solution computed.",
info, info);
}
}
// access //////////////////////////////////////////////////////////////////////
void TabFunction::setData(const DVec &x, const DVec &y)
{
if (x.size() != y.size())
{
LATAN_ERROR(Size, "tabulated function x/y data size mismatch");
}
FOR_VEC(x, i)
{
value_[x(i)] = y(i);
}
//---------------------------------------------------------
void xyztorst
(
const DVec& X, // [in]
const DVec& Y, // [in]
const DVec& Z, // [in]
DVec& r, // [out]
DVec& s, // [out]
DVec& t // [out]
)
//---------------------------------------------------------
{
// function [r,s,t] = xyztorst(x, y, z)
// Purpose : Transfer from (x,y,z) in equilateral tetrahedron
// to (r,s,t) coordinates in standard tetrahedron
double sqrt3=sqrt(3.0), sqrt6=sqrt(6.0); int Nc=X.size();
DVec v1(3),v2(3),v3(3),v4(3);
DMat tmat1(3,Nc), A(3,3), rhs;
v1(1)=(-1.0); v1(2)=(-1.0/sqrt3); v1(3)=(-1.0/sqrt6);
v2(1)=( 1.0); v2(2)=(-1.0/sqrt3); v2(3)=(-1.0/sqrt6);
v3(1)=( 0.0); v3(2)=( 2.0/sqrt3); v3(3)=(-1.0/sqrt6);
v4(1)=( 0.0); v4(2)=( 0.0 ); v4(3)=( 3.0/sqrt6);
// back out right tet nodes
tmat1.set_row(1,X); tmat1.set_row(2,Y); tmat1.set_row(3,Z);
rhs = tmat1 - 0.5*outer(v2+v3+v4-v1, ones(Nc));
A.set_col(1,0.5*(v2-v1)); A.set_col(2,0.5*(v3-v1)); A.set_col(3,0.5*(v4-v1));
DMat RST = A|rhs;
r=RST.get_row(1); s=RST.get_row(2); t=RST.get_row(3);
}
//==================================================================
void MemFile::InitExclusiveOwenership( DVec<U8> &fromData )
{
mDataSize = fromData.size();
mOwnData.get_ownership( fromData );
mpData = &mOwnData[0];
mReadPos = 0;
mIsReadOnly = true;
}
BasicStats::BasicStats(DVec &raw) {
this->n = raw.size();
double fcount = raw.size();
DVec data(raw.begin(), raw.end());
std::sort(data.begin(), data.end());
this->min = data.front();
this->max = data.back();
this->median = data.at(data.size() / 2);
double s = 0;
for (decimal_t v : data)
s += v;
this->mean = s / fcount;
s = 0;
for (decimal_t v : data)
s += ::pow(v - this->mean, 2);
this->stdev = ::sqrt(s / fcount);
}
//---------------------------------------------------------
void CurvedINS2D::INScylinderBC2D
(
const DVec& xin, // [in]
const DVec& yin, // [in]
const DVec& nxi, // [in]
const DVec& nyi, // [in]
const IVec& MAPI, // [in]
const IVec& MAPO, // [in]
const IVec& MAPW, // [in]
const IVec& MAPC, // [in]
double ti, // [in]
double nu, // [in]
DVec& BCUX, // [out]
DVec& BCUY, // [out]
DVec& BCPR, // [out]
DVec& BCDUNDT // [out]
)
//---------------------------------------------------------
{
// function [bcUx, bcUy, bcPR, bcdUndt] = INScylinderBC2D(x, y, nx, ny, mapI, mapO, mapW, mapC, time, nu)
// Purpose: evaluate boundary conditions for channel bounded cylinder flow with walls at y=+/- .15
// TEST CASE: from
// V. John "Reference values for drag and lift of a two-dimensional time dependent flow around a cylinder",
// Int. J. Numer. Meth. Fluids 44, 777 - 788, 2004
DVec yI("yI"); int len = xin.size();
BCUX.resize(len); BCUY.resize(len); // resize result arrays
BCPR.resize(len); BCDUNDT.resize(len); // and set to zero
// inflow
#ifdef _MSC_VER
yI = yin(MAPI); yI += 0.20;
#else
int Ni=MAPI.size(); yI.resize(Ni);
for(int n=1;n<=Ni;++n) {yI(n)=yin(MAPI(n))+0.2;}
#endif
BCUX(MAPI) = SQ(1.0/0.41)*6.0 * yI.dm(0.41 - yI);
BCUY(MAPI) = 0.0;
BCDUNDT(MAPI) = -SQ(1.0/0.41)*6.0 * yI.dm(0.41 - yI);
// wall
BCUX(MAPW) = 0.0;
BCUY(MAPW) = 0.0;
// cylinder
BCUX(MAPC) = 0.0;
BCUY(MAPC) = 0.0;
// outflow
BCUX(MAPO) = 0.0;
BCUY(MAPO) = 0.0;
BCDUNDT(MAPO) = 0.0;
}
//---------------------------------------------------------
bool isInf(const DVec& V)
//---------------------------------------------------------
{
for (int i=1; i<=V.size(); ++i) {
double Vi = V(i);
if (isinf(Vi)) {
return true; // v has a non-finite element
}
}
return false; // all elements are finite
}
//---------------------------------------------------------
void VertexAngles
(
const DVec& x1, const DVec& x2, const DVec& x3,
const DVec& y1, const DVec& y2, const DVec& y3,
DVec& a1, DVec& a2, DVec& a3
)
//---------------------------------------------------------
{
//------------------------------------------
// Expand definitions from ElmTools
//------------------------------------------
// a1 = acos ( -a23() / sqrt(a22()*a33()) );
// a2 = acos ( -a13() / sqrt(a11()*a33()) );
// a3 = acos ( -a12() / sqrt(a11()*a22()) );
DVec g2x=(y3-y1), g2y=(x1-x3), g3x=(y1-y2), g3y=(x2-x1);
DVec det = g3y*g2x - g3x*g2y;
DVec d = 1.0/det;
g2x *= d; g2y *= d; g3x *= d; g3y *= d;
DVec g1x = - g2x - g3x;
DVec g1y = - g2y - g3y;
a1 = acos( -(g2x*g3x + g2y*g3y) / sqrt((sqr(g2x)+sqr(g2y)) * (sqr(g3x)+sqr(g3y)) ));
a2 = acos( -(g1x*g3x + g1y*g3y) / sqrt((sqr(g1x)+sqr(g1y)) * (sqr(g3x)+sqr(g3y)) ));
a3 = acos( -(g1x*g2x + g1y*g2y) / sqrt((sqr(g1x)+sqr(g1y)) * (sqr(g2x)+sqr(g2y)) ));
#if (0)
// check that the angles in each element sum to 180
int Ni = x1.size(); double sum=0.0;
umMSG(1, "\nChecking sum of angles in %d element\n", Ni);
for (int i=1; i<=Ni; ++i) {
sum = fabs(a1(i)) + fabs(a2(i)) + fabs(a3(i));
if ( fabs(sum-M_PI) > 1e-15) {
umMSG(1, "element %4d: %12.5e\n", i, fabs(sum-M_PI));
}
}
#endif
}
//---------------------------------------------------------
void umPOLISH(DVec& V, double eps)
//---------------------------------------------------------
{
// round elements close to certain values
int N = V.size();
double *p = V.data();
for (int i=0; i<N; ++i)
{
if (fabs(p[i]) < eps)
{
p[i] = 0.0;
}
else
{
if (p[i] > 0.0)
{
// check for proximity to certain positive values
if (fabs (p[i] - 0.10) < eps) { p[i] = 0.10; }
else if (fabs (p[i] - 0.20) < eps) { p[i] = 0.20; }
else if (fabs (p[i] - 0.25) < eps) { p[i] = 0.25; }
else if (fabs (p[i] - 0.50) < eps) { p[i] = 0.50; }
else if (fabs (p[i] - 0.75) < eps) { p[i] = 0.75; }
else if (fabs (p[i] - 0.80) < eps) { p[i] = 0.80; }
else if (fabs (p[i] - 0.90) < eps) { p[i] = 0.90; }
else if (fabs (p[i] - 1.00) < eps) { p[i] = 1.00; }
else if (fabs (p[i] - 2.00) < eps) { p[i] = 2.00; }
else if (fabs (p[i] - 4.00) < eps) { p[i] = 4.00; }
else if (fabs (p[i] - 4.50) < eps) { p[i] = 4.50; }
else if (fabs (p[i] - 5.00) < eps) { p[i] = 5.00; }
else if (fabs (p[i] - M_PI ) < eps) { p[i] = M_PI ; }
else if (fabs (p[i] - M_PI_2) < eps) { p[i] = M_PI_2; }
else if (fabs (p[i] - M_PI_4) < eps) { p[i] = M_PI_4; }
else if (fabs (p[i] - M_E ) < eps) { p[i] = M_E ; }
}
else
{
// check for proximity to certain negative values
if (fabs (p[i] + 0.10) < eps) { p[i] = -0.10; }
else if (fabs (p[i] + 0.20) < eps) { p[i] = -0.20; }
else if (fabs (p[i] + 0.25) < eps) { p[i] = -0.25; }
else if (fabs (p[i] + 0.50) < eps) { p[i] = -0.50; }
else if (fabs (p[i] + 0.75) < eps) { p[i] = -0.75; }
else if (fabs (p[i] + 0.80) < eps) { p[i] = -0.80; }
else if (fabs (p[i] + 0.90) < eps) { p[i] = -0.90; }
else if (fabs (p[i] + 1.00) < eps) { p[i] = -1.00; }
else if (fabs (p[i] + 2.00) < eps) { p[i] = -2.00; }
else if (fabs (p[i] + 4.00) < eps) { p[i] = -4.00; }
else if (fabs (p[i] + 4.50) < eps) { p[i] = -4.50; }
else if (fabs (p[i] + 5.00) < eps) { p[i] = -5.00; }
else if (fabs (p[i] + M_PI ) < eps) { p[i] = -M_PI ; }
else if (fabs (p[i] + M_PI_2) < eps) { p[i] = -M_PI_2; }
else if (fabs (p[i] + M_PI_4) < eps) { p[i] = -M_PI_4; }
else if (fabs (p[i] + M_E ) < eps) { p[i] = -M_E ; }
}
}
}
}
int OCCEdge::createNURBS(OCCVertex *start, OCCVertex *end, std::vector<OCCStruct3d> points,
DVec knots, DVec weights, IVec mult)
{
try {
Standard_Boolean periodic = false;
int vertices = 0;
if (start != NULL && end != NULL) {
vertices = 2;
periodic = true;
}
int nbControlPoints = points.size() + vertices;
TColgp_Array1OfPnt ctrlPoints(1, nbControlPoints);
TColStd_Array1OfReal _knots(1, knots.size());
TColStd_Array1OfReal _weights(1, weights.size());
TColStd_Array1OfInteger _mult(1, mult.size());
for (unsigned i = 0; i < knots.size(); i++) {
_knots.SetValue(i+1, knots[i]);
}
for (unsigned i = 0; i < weights.size(); i++) {
_weights.SetValue(i+1, weights[i]);
}
int totKnots = 0;
for (unsigned i = 0; i < mult.size(); i++) {
_mult.SetValue(i+1, mult[i]);
totKnots += mult[i];
}
const int degree = totKnots - nbControlPoints - 1;
int index = 1;
if (!periodic) {
ctrlPoints.SetValue(index++, gp_Pnt(start->X(), start->Y(), start->Z()));
}
for (unsigned i = 0; i < points.size(); i++) {
gp_Pnt aP(points[i].x,points[i].y,points[i].z);
ctrlPoints.SetValue(index++, aP);
}
if (!periodic) {
ctrlPoints.SetValue(index++, gp_Pnt(end->X(), end->Y(), end->Z()));
}
Handle(Geom_BSplineCurve) NURBS = new Geom_BSplineCurve
(ctrlPoints, _weights, _knots, _mult, degree, periodic);
if (!periodic) {
this->setShape(BRepBuilderAPI_MakeEdge(NURBS, start->vertex, end->vertex));
} else {
this->setShape(BRepBuilderAPI_MakeEdge(NURBS));
}
} catch(Standard_Failure &err) {
Handle_Standard_Failure e = Standard_Failure::Caught();
const Standard_CString msg = e->GetMessageString();
if (msg != NULL && strlen(msg) > 1) {
setErrorMessage(msg);
} else {
setErrorMessage("Failed to create nurbs");
}
return 1;
}
return 0;
}
// function call ///////////////////////////////////////////////////////////////
double DoubleModel::operator()(const DVec &arg, const DVec &par) const
{
checkSize(arg.size(), par.size());
return (*this)(arg.data(), par.data());
}
//---------------------------------------------------------
void CurvedINS2D::KovasznayBC2D
(
const DVec& xin, // [in]
const DVec& yin, // [in]
const DVec& nxi, // [in]
const DVec& nyi, // [in]
const IVec& MAPI, // [in]
const IVec& MAPO, // [in]
const IVec& MAPW, // [in]
const IVec& MAPC, // [in]
double ti, // [in]
double nu, // [in]
DVec& BCUX, // [out]
DVec& BCUY, // [out]
DVec& BCPR, // [out]
DVec& BCDUNDT // [out]
)
//---------------------------------------------------------
{
// function [bcUx, bcUy, bcPR, bcdUndt] = KovasznayBC2D(x, y, nx, ny, MAPI, MAPO, MAPW, MAPC, time, nu)
// Purpose: evaluate boundary conditions for Kovasznay flow
static DVec xI("xI"), yI("yI"), xO("xO"), yO("yO");
int len = xin.size();
BCUX.resize(len); BCUY.resize(len); // resize result arrays
BCPR.resize(len); BCDUNDT.resize(len); // and set to zero
double lam = (0.5/nu) - sqrt( (0.25/SQ(nu)) + 4.0*SQ(pi));
// inflow
#ifdef _MSC_VER
xI = xin(MAPI); yI = yin(MAPI);
#else
int Ni=MAPI.size(), n=0; xI.resize(Ni); yI.resize(Ni);
for (n=1;n<=Ni;++n) {xI(n)=xin(MAPI(n));}
for (n=1;n<=Ni;++n) {yI(n)=yin(MAPI(n));}
#endif
DVec elamXI = exp(lam*xI), twopiyI = 2.0*pi*yI;
BCUX(MAPI) = 1.0 - elamXI.dm(cos(twopiyI));
BCUY(MAPI) = (0.5*lam/pi) * elamXI.dm(sin(twopiyI));
// outflow
#ifdef _MSC_VER
xO = xin(MAPO); yO = yin(MAPO);
#else
int No=MAPO.size(); xO.resize(No); yO.resize(No);
for (n=1;n<=No;++n) {xO(n)=xin(MAPO(n));}
for (n=1;n<=No;++n) {yO(n)=yin(MAPO(n));}
#endif
DVec elamXO = exp(lam*xO), twopiyO = 2.0*pi*yO;
BCPR (MAPO) = 0.5*(1.0-exp(2.0*lam*xO));
//BCDUNDT(MAPO) = -lam*elamXO.dm(cos(twopiyO));
if (0) {
// THIS WORKED
BCUX(MAPO) = 1.0 - elamXO.dm(cos(twopiyO));
BCUY(MAPO) = (0.5*lam/pi) * elamXO.dm(sin(twopiyO));
} else {
// Neumann data for each velocity
BCUX(MAPO) = -lam* elamXO.dm(cos(twopiyO));
BCUY(MAPO) = lam*(0.5*lam/pi) * elamXO.dm(sin(twopiyO));
}
}
//==================================================================
void MakeTree( TokNode *pRoot, DVec<Token> &tokens, u_int &out_blockCnt )
{
//TokNode *pParent = pRoot;
//DVec<TokNode*> pParentsMemory;
//pParentsMemory.push_back( pParent );
//pPrev = pParent = pParent->AddNewChild( &tokens[i] );
//pParentsMemory.pop_back();
out_blockCnt = 0;
TokNode *pNode = pRoot;
DVec<TokenID> bracketsMemory;
for (size_t i=0; i < tokens.size(); ++i)
{
switch ( tokens[i].id )
{
case RSLC::T_OP_LFT_BRACKET :
case RSLC::T_OP_LFT_CRL_BRACKET :
case RSLC::T_OP_LFT_SQ_BRACKET :
bracketsMemory.push_back( tokens[i].id );
if ( tokens[i].id == RSLC::T_OP_LFT_SQ_BRACKET )
{
pNode->AddNewChild( &tokens[i] );
Token *pNewBrkTok =
DNEW Token(
"(",
RSLC::T_OP_LFT_BRACKET,
RSLC::T_TYPE_OPERATOR,
&tokens[i] );
pNode = pNode->AddNewChild( pNewBrkTok );
//pNode = pNewParent;
}
else
// square bracket is indents itself
//if ( tokens[i].id == RSLC::T_OP_LFT_SQ_BRACKET )
//{
// if NOT( pNode->mpChilds.size() )
// throw Exception( "Misplaced square bracket ?", &tokens[i] );
// pNode = pNode->mpChilds[pNode->mpChilds.size()-1]->AddNewChild( &tokens[i] );
//}
//else
{
pNode = pNode->AddNewChild( &tokens[i] );
}
break;
case RSLC::T_OP_RGT_BRACKET :
case RSLC::T_OP_RGT_CRL_BRACKET :
case RSLC::T_OP_RGT_SQ_BRACKET :
if (!pNode->mpParent ||
!bracketsMemory.size() ||
!doBracketsMatch( bracketsMemory.back(), tokens[i].id ) )
{
throw Exception( "Mismatched brackets ?", &tokens[i] );
}
pNode = pNode->mpParent;
// square bracket is indented itself
//if ( tokens[i].id == RSLC::T_OP_RGT_SQ_BRACKET )
// pNode = pNode->mpParent;
bracketsMemory.pop_back();
break;
default:
pNode->AddNewChild( &tokens[i] );
break;
}
}
defineBlockTypeAndID( pRoot, out_blockCnt );
}
