/// <summary>
/// Assembles the stiffness matrix of defined model and return it back.
/// </summary>
/// <returns>Assembled stiffness matrix</returns>
public static CCS AssembleFullStiffnessMatrix(Model model)
{
model.ReIndexNodes();
var elements = model.Elements;
var maxNodePerElement = model.Elements.Any() ? model.Elements.Select(i => i.Nodes.Length).Max() : 1;
var rElmMap = new int[maxNodePerElement * 6];
var c = model.Nodes.Count * 6;
var kt = new CoordinateStorage <double>(c, c, c);
foreach (var elm in elements)
{
var c2 = elm.Nodes.Length;
for (var i = 0; i < c2; i++)
{
rElmMap[6 * i + 0] = elm.Nodes[i].Index * 6 + 0;
rElmMap[6 * i + 1] = elm.Nodes[i].Index * 6 + 1;
rElmMap[6 * i + 2] = elm.Nodes[i].Index * 6 + 2;
rElmMap[6 * i + 3] = elm.Nodes[i].Index * 6 + 3;
rElmMap[6 * i + 4] = elm.Nodes[i].Index * 6 + 4;
rElmMap[6 * i + 5] = elm.Nodes[i].Index * 6 + 5;
}
var mtx = elm.GetGlobalStifnessMatrix();
var d = c2 * 6;
for (var i = 0; i < d; i++)
{
for (var j = 0; j < d; j++)
{
kt.At(rElmMap[i], rElmMap[j], mtx[i, j]);
}
}
mtx.ReturnToPool();
}
var stiffness = (CCS)Converter.ToCompressedColumnStorage(kt, true);
return(stiffness);
}
/// <summary>
/// Generates the permutation for delta for specified model in specified loadCase.
/// Note that delta permutation = P_delta in reduction process
/// </summary>
/// <param name="target">The target.</param>
/// <param name="loadCase">The load case.</param>
/// <returns>delta permutation</returns>
public static CCS GenerateP_Delta(Model target, LoadCase loadCase)
{
throw new NotImplementedException();
target.ReIndexNodes();
var buf = new CoordinateStorage <double>(target.Nodes.Count * 6, target.Nodes.Count * 6, 1);
#region rigid elements
foreach (var elm in target.RigidElements)
{
var centralNode = elm.Nodes[0];
var masterIdx = centralNode.Index;
for (var i = 1; i < elm.Nodes.Count; i++)
{
var slaveIdx = elm.Nodes[i].Index;
var d = centralNode.Location - elm.Nodes[i].Location;
//buf[0, 4] = -(buf[1, 3] = d.Z);
//buf[2, 3] = -(buf[0, 5] = d.Y);
//buf[1, 5] = -(buf[2, 4] = d.X);
buf.At(6 * slaveIdx + 0, 6 * masterIdx + 0, 1);
buf.At(6 * slaveIdx + 1, 6 * masterIdx + 1, 1);
buf.At(6 * slaveIdx + 2, 6 * masterIdx + 2, 1);
buf.At(6 * slaveIdx + 1, 6 * masterIdx + 3, d.Z);
buf.At(6 * slaveIdx + 0, 6 * masterIdx + 4, -d.Z);
buf.At(6 * slaveIdx + 0, 6 * masterIdx + 5, d.Y);
buf.At(6 * slaveIdx + 2, 6 * masterIdx + 3, -d.Y); //
buf.At(6 * slaveIdx + 2, 6 * masterIdx + 4, d.X); //
buf.At(6 * slaveIdx + 1, 6 * masterIdx + 5, -d.X);
}
//add to buf
}
#endregion
throw new NotImplementedException();
return(buf.ToCCs());
}
public static CCS GenerateP_Delta_Mpc(Model target, LoadCase loadCase, IRrefFinder rrefFinder)
{
target.ReIndexNodes();
var n = target.Nodes.Count;
var boundaryConditions = GetModelBoundaryConditions(target, loadCase);
var lastRow = 0;
#region step 1
//step 1: combine all eqs to one system
//var filledCols = new bool[6 * n];
var extraEqCount = 0;
foreach (var mpcElm in target.MpcElements)
{
if (mpcElm.AppliesForLoadCase(loadCase))
{
extraEqCount += mpcElm.GetExtraEquationsCount();
}
}
extraEqCount += boundaryConditions.RowCount;
var allEqsCrd = new CoordinateStorage <double>(extraEqCount, n * 6 + 1, 1);//rows: extra eqs, cols: 6*n+1 (+1 is for right hand side)
foreach (var mpcElm in target.MpcElements)
{
if (mpcElm.AppliesForLoadCase(loadCase))
{
var extras = mpcElm.GetExtraEquations();
extras.EnumerateMembers((row, col, val) =>
{
allEqsCrd.At(row + lastRow, col, val);
});
lastRow += extras.RowCount;
}
}
{
boundaryConditions.EnumerateMembers((row, col, val) =>
{
allEqsCrd.At(row + lastRow, col, val);
});
lastRow += boundaryConditions.RowCount;
}
var allEqs = allEqsCrd.ToCCs();
#endregion
#region comment
/*
#region step 2
* //step 2: create adjacency matrix of variables
*
* //step 2-1: find nonzero pattern
* var allEqsNonzeroPattern = allEqs.Clone();
*
* for (var i = 0; i < allEqsNonzeroPattern.Values.Length; i++)
* allEqsNonzeroPattern.Values[i] = 1;
*
* //https://math.stackexchange.com/questions/2340450/extract-independent-sub-systems-from-a-bigger-linear-eq-system
* var tmp = allEqsNonzeroPattern.Transpose();
*
* var variableAdj = tmp.Multiply(allEqsNonzeroPattern);
#endregion
*
#region step 3
* //extract parts
* var parts = EnumerateGraphParts(variableAdj);
*
#endregion
*
#region step 4
* {
*
* allEqs.EnumerateColumns((colNum, vals) =>
* {
* if (vals.Count == 0)
* Console.WriteLine("Col {0} have {1} nonzeros", colNum, vals.Count);
* });
*
* var order = ColumnOrdering.MinimumDegreeAtPlusA;
*
* // Partial pivoting tolerance (0.0 to 1.0)
* double tolerance = 1.0;
*
* var lu = CSparse.Double.Factorization.SparseLU.Create(allEqs, order, tolerance);
*
* }
*
#endregion
*/
#endregion
rrefFinder.CalculateRref(allEqs);
var q = AMD.Generate(allEqs, ColumnOrdering.MinimumDegreeAtA);
var s = new SymbolicFactorization()
{
q = q
};
var qr = CSparse.Double.Factorization.SparseQR.Create(allEqs, ColumnOrdering.MinimumDegreeAtA);
var r = ((CCS)ReflectionUtils.GetFactorR(qr, "R"));
//var q = ((CCS)ReflectionUtils.GetFactorR(qr, "Q"));
//var s = ((SymbolicFactorization)ReflectionUtils.GetFactorR(qr, "S"));
var idependents = new bool[allEqs.RowCount];
var rd = allEqs.ToDenseMatrix();
r.EnumerateMembers((row, col, val) =>
{
if (row == col)
{
if (Math.Abs(val) < 1e-6)
{
return;
}
}
idependents[row] = true;
}
);
//var t=qr.
throw new NotImplementedException();
//return buf.ToCCs();
}
