protected override KeyedVector <NodalDegreeOfFreedom> Solve(StiffnessMatrix stiffnessMatrix, KeyedVector <NodalDegreeOfFreedom> forceVector)
{
KeyedSquareMatrix <NodalDegreeOfFreedom> inverse = stiffnessMatrix.Inverse();
KeyedVector <NodalDegreeOfFreedom> solution = inverse.Multiply(forceVector);
return(solution);
}
/// <summary>
///
/// </summary>
/// <returns></returns>
public KeyedSquareMatrix <DegreeOfFreedom> CalculateElementRotationMatrix()
{
KeyedSquareMatrix <DegreeOfFreedom> rotationMatrix = FiniteElement.CreateFromRows(this.LocalXAxis, this.LocalYAxis, this.LocalZAxis);
rotationMatrix = rotationMatrix.NormalizeRows(2);
return(rotationMatrix);
}
/// <summary>
/// Creates a new keyed matrix from keyed vectors representing the rows of the new matrix
/// </summary>
/// <param name="axis1">The vector representing the first row</param>
/// <param name="axis2">The vector representing the second row</param>
/// <param name="axis3">The vector representing the third row</param>
/// <returns>A matrix built from the vectors</returns>
protected static KeyedSquareMatrix <DegreeOfFreedom> CreateFromRows(KeyedVector <DegreeOfFreedom> axis1, KeyedVector <DegreeOfFreedom> axis2, KeyedVector <DegreeOfFreedom> axis3)
{
////TODO this should be devolved to the KeyedMatrix class
Guard.AgainstBadArgument(
"axis1",
() => { return(axis1.Count != 3); },
"All axes should be 3D, i.e. have 3 items");
Guard.AgainstBadArgument(
"axis2",
() => { return(axis2.Count != 3); },
"All axes should be 3D, i.e. have 3 items");
Guard.AgainstBadArgument(
"axis3",
() => { return(axis3.Count != 3); },
"All axes should be 3D, i.e. have 3 items");
Guard.AgainstBadArgument(
"axis1",
() => { return(axis1.SumMagnitudes().IsApproximatelyEqualTo(0.0)); },
string.Format(
System.Globalization.CultureInfo.InvariantCulture,
"Axis should not be zero: {0}",
axis1));
Guard.AgainstBadArgument(
"axis2",
() => { return(axis2.SumMagnitudes().IsApproximatelyEqualTo(0.0)); },
string.Format(
System.Globalization.CultureInfo.InvariantCulture,
"Axis should not be zero: {0}",
axis2));
Guard.AgainstBadArgument(
"axis3",
() => { return(axis3.SumMagnitudes().IsApproximatelyEqualTo(0.0)); },
string.Format(
System.Globalization.CultureInfo.InvariantCulture,
"Axis should not be zero: {0}",
axis3));
KeyedVector <DegreeOfFreedom> axis1Norm = axis1.Normalize(2);
KeyedVector <DegreeOfFreedom> axis2Norm = axis2.Normalize(2);
KeyedVector <DegreeOfFreedom> axis3Norm = axis3.Normalize(2);
IList <DegreeOfFreedom> dof = new List <DegreeOfFreedom>(3)
{
DegreeOfFreedom.X, DegreeOfFreedom.Y, DegreeOfFreedom.Z
};
KeyedSquareMatrix <DegreeOfFreedom> result = new KeyedSquareMatrix <DegreeOfFreedom>(dof);
result.At(DegreeOfFreedom.X, DegreeOfFreedom.X, axis1Norm[DegreeOfFreedom.X]);
result.At(DegreeOfFreedom.X, DegreeOfFreedom.Y, axis1Norm[DegreeOfFreedom.Y]);
result.At(DegreeOfFreedom.X, DegreeOfFreedom.Z, axis1Norm[DegreeOfFreedom.Z]);
result.At(DegreeOfFreedom.Y, DegreeOfFreedom.X, axis2Norm[DegreeOfFreedom.X]);
result.At(DegreeOfFreedom.Y, DegreeOfFreedom.Y, axis2Norm[DegreeOfFreedom.Y]);
result.At(DegreeOfFreedom.Y, DegreeOfFreedom.Z, axis2Norm[DegreeOfFreedom.Z]);
result.At(DegreeOfFreedom.Z, DegreeOfFreedom.X, axis3Norm[DegreeOfFreedom.X]);
result.At(DegreeOfFreedom.Z, DegreeOfFreedom.Y, axis3Norm[DegreeOfFreedom.Y]);
result.At(DegreeOfFreedom.Z, DegreeOfFreedom.Z, axis3Norm[DegreeOfFreedom.Z]);
return(result);
}
public CartesianPoint ConvertGlobalCoordinatesToLocalCoordinates(CartesianPoint globalPoint)
{
GeometricVector localCoordRelativeToLocalOrigin = globalPoint.Subtract(this.LocalOrigin);
KeyedSquareMatrix <DegreeOfFreedom> rotationMatrix = CalculateElementRotationMatrix();
CartesianPoint localCoord = new CartesianPoint(rotationMatrix.Multiply(localCoordRelativeToLocalOrigin));
return(new CartesianPoint(localCoord));
}
public CartesianPoint ConvertLocalCoordinatesToGlobalCoordinates(CartesianPoint localPoint)
{
KeyedSquareMatrix <DegreeOfFreedom> rotationMatrix = CalculateElementRotationMatrix().Transpose();
CartesianPoint globalCoordRelativeToLocalOrigin = new CartesianPoint(rotationMatrix.Multiply(localPoint));
GeometricVector globalCoord = globalCoordRelativeToLocalOrigin.Add(this.LocalOrigin);
return(new CartesianPoint(globalCoord));
}
/// <summary>
/// Creates a matrix which contains values from the requested sub-matrix
/// </summary>
/// <param name="rowsToInclude">A list of the keys of rows to include in the new matrix</param>
/// <param name="columnsToInclude">A list of the keys of columns to include in the new matrix</param>
/// <returns>A KeyedMatrix which contains values from the requested sub-matrix</returns>
public KeyedSquareMatrix <TKey> SubMatrix(IList <TKey> keysToInclude)
{
KeyedSquareMatrix <TKey> subMatrix = new KeyedSquareMatrix <TKey>(keysToInclude);
foreach (TKey rowKey in keysToInclude) //rows
{
foreach (TKey columnKey in keysToInclude) //columns
{
subMatrix.At(rowKey, columnKey, this.At(rowKey, columnKey));
}
}
return(subMatrix);
}
/// <summary>
/// Initializes a new instance of the <see cref="KeyedMatrix{TKey}" /> class.
/// </summary>
/// <param name="keysForRows">The keys which will be used to look up rows of this matrix. One unique key is expected per row.</param>
/// <param name="keysForColumns">The keys which will be used to look up columns of this matrix. One unique key is expected per column.</param>
/// <param name="matrix">The value to which we assign to each element of the matrix</param>
public KeyedSquareMatrix(IList <TKey> keysForRows, IList <TKey> keysForColumns, KeyedSquareMatrix <TKey> matrix)
: base(keysForRows, keysForColumns, matrix)
{
// empty
}
public KeyedSquareMatrix <TKey> TransposeThisAndMultiply(KeyedSquareMatrix <TKey> other)
{
KeyedRowColumnMatrix <TKey, TKey> result = base.TransposeThisAndMultiply(other);
return(new KeyedSquareMatrix <TKey>(result));
}
public KeyedSquareMatrix <TKey> Add(KeyedSquareMatrix <TKey> other)
{
KeyedRowColumnMatrix <TKey, TKey> result = base.Add(other);
return(new KeyedSquareMatrix <TKey>(result));
}
/// <summary>
/// Initializes a new instance of the <see cref="KeyedMatrix{TKey}" /> class.
/// </summary>
/// <param name="matrix">The matrix which holds the keys and data to copy into this new matrix</param>
public KeyedSquareMatrix(KeyedSquareMatrix <TKey> matrix)
: base(matrix)
{
// empty
}