public void derivation_test()
{
var p = new SingleVariablePolynomial(9, 8, 7, 6, 5, 4, 3, 2, 1, 0);
var p1_1 = p.GetDerivative(2);
var p1_2 = p.GetDerivative(1).GetDerivative(1);
Assert.AreEqual(p1_2, p1_1, "");
}
/// <inheritdoc/>
public Matrix GetNMatrixAt(Element targetElement, params double[] isoCoords)
{
//note: this method gives the shape function on variable node count beam with variable constraint on each node
SingleVariablePolynomial[] nss = null;
SingleVariablePolynomial[] mss = null;
var bar = targetElement as BarElement;
if (!GetShapeFunctions(targetElement, out nss, out mss))
{
throw new Exception();
}
var n = bar.NodeCount;
var xi = isoCoords[0];
var buf =
targetElement.MatrixPool.Allocate(4, 2 * n);
for (var i = 0; i < n; i++)
{
if (nss[i] == null)
{
nss[i] = new SingleVariablePolynomial();
}
if (mss[i] == null)
{
mss[i] = new SingleVariablePolynomial();
}
}
for (var i = 0; i < n; i++)
{
var ni = nss[i];
var mi = mss[i];
for (var ii = 0; ii < 4; ii++)
{
buf[ii, 2 * i + 0] = ni.EvaluateDerivative(xi, ii);
buf[ii, 2 * i + 1] = mi.EvaluateDerivative(xi, ii);
}
}
return(buf);
}
public void interpolation_test()
{
var tpls = new Tuple <double, double>[] { Tuple.Create(-5.0, 3.0), Tuple.Create(-4.0, 4.0), Tuple.Create(-3.0, 7.0), Tuple.Create(1.0, 0.0), Tuple.Create(5.0, 0.0) };
var p = SingleVariablePolynomial.FromPoints(tpls);
var epsilon = 1e-10;
foreach (var tpl in tpls)
{
var diff = Math.Abs(p.Evaluate(tpl.Item1) - tpl.Item2);
Assert.IsTrue(diff < epsilon);
}
}
public Matrix GetNMatrixAt(Element targetElement, params double[] isoCoords)
{
var br = targetElement as BarElement;
var xi = isoCoords[0];
SingleVariablePolynomial[] ns = null;
{ //retrieve or generate shapefunctions
var nsKey = "011F9D96-6398-4126-BC4E-FFDA7F91D6E3"; //a random unified key for store truss shape functions for bar element
object obj;
targetElement.TryGetCache(nsKey, out ns);
if (ns == null)
{
ns = new SingleVariablePolynomial[targetElement.Nodes.Length];
for (var i = 0; i < ns.Length; i++)
{
ns[i] = GetN_i(targetElement, i);
}
targetElement.SetCache(nsKey, ns);
}
}
//var buf = new Matrix(2, br.Nodes.Length);
var buf =
//new Matrix(2, ns.Length);
targetElement.MatrixPool.Allocate(2, ns.Length);
{//fill buff
for (var i = 0; i < ns.Length; i++)
{
buf[0, i] = ns[i].EvaluateDerivative(xi, 0);
buf[1, i] = ns[i].EvaluateDerivative(xi, 1);
}
}
return(buf);
}
public SingleVariablePolynomial GetN_i(Element targetElement, int ith)
{
var bar = targetElement as BarElement;
if (bar == null)
{
return(null);
}
var n = bar.NodeCount;
var xis = new Func <int, double>(i =>
{
var delta = 2.0 / (n - 1);
return(-1 + delta * i);
});
var conditions = new List <Tuple <double, double> >();
for (var i = 0; i < n; i++)
{
if (bar._nodalReleaseConditions[i].DX == DofConstraint.Fixed)
{
conditions.Add(Tuple.Create(xis(i), ith == i ? 1.0 : 0.0));
}
}
var condCount = conditions.Count;
var condMtx = new Matrix(condCount, condCount);
var rMtx = new Matrix(condCount, 1);
for (var i = 0; i < condCount; i++)
{
var rw = new double[condCount];
var cond = conditions[i];
for (var j = 0; j < condCount; j++)
{
var origPow = condCount - 1 - j;
rw[j] = Math.Pow(cond.Item1, origPow);
}
condMtx.SetRow(i, rw);
rMtx.SetRow(i, cond.Item2);
}
var res = condMtx.Inverse() * rMtx;
var buf = new SingleVariablePolynomial(res.CoreArray);
{ //test
var epsilon = 0.0;
for (var i = 0; i < condCount; i++)
{
var cond = conditions[i];
var d = buf.Evaluate(cond.Item1) - cond.Item2;
epsilon = Math.Max(epsilon, Math.Abs(d));
}
if (epsilon > 1e-7)
{
throw new Exception();
}
}
return(buf);
}
//private readonly string mssKey = "82069A88-26BD-4902-9CA6-7AE324193FE3:X";
//private readonly string nssKey = "0EECCFF2-8CAE-4D65-935F-15E1AF31709B:X" ;
public bool GetShapeFunctions(Element targetElement, out SingleVariablePolynomial[] nss, out SingleVariablePolynomial[] mss)
{
nss = null;
mss = null;
var mssKey = "7AE324193FE3:X" + this.Direction;
var nssKey = "15E1AF31709B:X" + this.Direction;
var sb = new StringBuilder();
var bar = targetElement as BarElement;
var n = bar.NodeCount;
{
var xis = new Func <int, double>(i =>
{
var delta = 2.0 / (n - 1);
return(-1 + delta * i);
});
bar.TryGetCache(mssKey, out mss);
bar.TryGetCache(nssKey, out nss);
if (nss != null && mss != null)
{
return(true);
}
}
var cnds = GetShapeFunctionConditions(bar);
var grpd = cnds.GroupBy(i => Tuple.Create(i.NodeNumber, i.Type)).ToArray();
CondsListPool.Free(cnds);
mss = new SingleVariablePolynomial[n];
nss = new SingleVariablePolynomial[n];
foreach (var grp in grpd)
{
var nodeNum = grp.Key.Item1;
var tp = grp.Key.Item2;
var condCount = grp.Count();
var mtx =
bar.MatrixPool.Allocate(condCount, condCount);
//new Matrix(condCount, condCount);
var rightSide =
bar.MatrixPool.Allocate(condCount, 1);
//new Matrix(condCount, 1);
var arr = grp.ToArray();
for (var i = 0; i < arr.Length; i++)
{
var itm = arr[i];
mtx.SetRow(i, Diff(itm.Xi, condCount - 1, itm.DifferentialDegree));
rightSide.SetRow(i, itm.RightSide);
}
SingleVariablePolynomial pl;
if (arr.Length != 0)
{
//var cfs = mtx.Inverse2() * rightSide;
var cfs = mtx.Solve(rightSide.CoreArray);//.Inverse2() * rightSide;
pl = new SingleVariablePolynomial(cfs);
}
else
{
pl = new SingleVariablePolynomial();
}
//bar.ReturnMatrixToPool(rightSide, mtx);
if (tp == Condition.FunctionType.M)
{
mss[nodeNum] = pl;
}
if (tp == Condition.FunctionType.N)
{
nss[nodeNum] = pl;
}
mtx.ReturnToPool();
rightSide.ReturnToPool();
}
for (var i = 0; i < n; i++)
{
if (nss[i] == null)
{
nss[i] = new SingleVariablePolynomial();
}
if (mss[i] == null)
{
mss[i] = new SingleVariablePolynomial();
}
}
{
bar.SetCache(nssKey, nss);
bar.SetCache(mssKey, mss);
}
return(true);
}
