/// <summary>
/// 3x3 Rotation Matrix From normalized quaternion
/// </summary>
/// <returns></returns>
public QsMatrix To_3x3_RotationMatrix()
{
var w = a;
var x = i;
var y = j;
var z = k;
var v0 = new QsVector();
var v1 = new QsVector();
var v2 = new QsVector();
v0.AddComponent(1 - 2 * y * y - 2 * z * z);
v0.AddComponent(2 * x * y - 2 * w * z);
v0.AddComponent(2 * x * z + 2 * w * y);
v1.AddComponent(2 * x * y + 2 * w * z);
v1.AddComponent(1 - 2 * x * x - 2 * z * z);
v1.AddComponent(2 * y * z - 2 * w * x);
v2.AddComponent(2 * x * z - 2 * w * y);
v2.AddComponent(2 * y * z + 2 * w * x);
v2.AddComponent(1 - 2 * x * x - 2 * y * y);
var rm = new QsMatrix(v0, v1, v2);
return(rm);
}
public QsValue QsValueElements(int fromIndex, int toIndex, QsValue arg0, QsValue arg1, QsValue arg2, QsValue arg3, QsValue arg4, QsValue arg5)
{
QsValue firstElement = GetElementValue(fromIndex, arg0, arg1, arg2, arg3, arg4, arg5);
if (firstElement is QsScalar)
{
//return vector
QsVector Total = new QsVector(System.Math.Abs(toIndex - fromIndex) + 1);
Total.AddComponent((QsScalar)firstElement);
if (toIndex >= fromIndex)
{
for (int i = fromIndex + 1; i <= toIndex; i++)
{
Total.AddComponent((QsScalar)GetElementValue(i, arg0, arg1, arg2, arg3, arg4, arg5));
}
}
else
{
for (int i = fromIndex - 1; i >= toIndex; i--)
{
Total.AddComponent((QsScalar)GetElementValue(i, arg0, arg1, arg2, arg3, arg4, arg5));
}
}
return(Total);
}
else if (firstElement is QsVector)
{
//return vector
QsMatrix Total = new QsMatrix();
Total.AddVector((QsVector)firstElement);
if (toIndex >= fromIndex)
{
for (int i = fromIndex + 1; i <= toIndex; i++)
{
Total.AddVector((QsVector)GetElementValue(i, arg0, arg1, arg2, arg3, arg4, arg5));
}
}
else
{
for (int i = fromIndex - 1; i >= toIndex; i++)
{
Total.AddVector((QsVector)GetElementValue(i, arg0, arg1, arg2, arg3, arg4, arg5));
}
}
return(Total);
}
else if (firstElement is QsMatrix)
{
throw new NotImplementedException();
}
else
{
throw new NotSupportedException();
}
}
public static QsValue Determinant(QsParameter matrix)
{
if (matrix.QsNativeValue is QsMatrix)
{
return(QsMatrix.Determinant(((QsMatrix)matrix.QsNativeValue)));
}
else
{
throw new QsInvalidInputException("Expected matrix input");
}
}
public static QsValue Log(QsParameter val, QsParameter newBase)
{
if (val.IsQsValue)
{
if (val.ParameterValue is QsScalar)
{
AnyQuantity <double> q = ((QsScalar)val.ParameterValue).NumericalQuantity;
if (q.Dimension.IsDimensionless)
{
double r = System.Math.Log(q.Value, ((QsScalar)newBase.ParameterValue).NumericalQuantity.Value);
return(r.ToQuantity().ToScalarValue());
}
else
{
throw new QsInvalidInputException("Non dimensionless number");
}
}
else if (val.ParameterValue is QsVector)
{
QsVector vec = (QsVector)val.ParameterValue;
QsVector rv = new QsVector(vec.Count);
foreach (QsScalar var in vec)
{
if (var.NumericalQuantity.Dimension.IsDimensionless)
{
double r = System.Math.Log(var.NumericalQuantity.Value, ((QsScalar)newBase.ParameterValue).NumericalQuantity.Value);
rv.AddComponent(r.ToQuantity().ToScalar());
}
else
{
throw new QsInvalidInputException("Non dimensionless component");
}
}
return(rv);
}
else if (val.ParameterValue is QsMatrix)
{
QsMatrix mat = (QsMatrix)val.ParameterValue;
QsMatrix rm = new QsMatrix();
foreach (var vec in mat.Rows)
{
rm.AddVector((QsVector)Log(QsParameter.MakeParameter(vec, string.Empty)));
}
return(rm);
}
else
{
return(null);
}
}
else
{
//not known may be ordinary string
return(null);
}
}
/// <summary>
/// Get factorial for the <see>QsValue</see> whether it is Scalar, Vector, Matrix, and later Tensor.
/// </summary>
/// <param name="value"></param>
/// <returns></returns>
public static QsValue Factorial(QsValue value)
{
if (value is QsBoolean)
{
var b = (QsBoolean)value;
return(new QsBoolean {
Value = !b.Value
});
}
if (value is QsScalar)
{
QsScalar sv = (QsScalar)value;
if (sv.ScalarType == ScalarTypes.NumericalQuantity)
{
AnyQuantity <double> number = sv.NumericalQuantity;
return(new QsScalar {
NumericalQuantity = QuantityFactorial(number)
});
}
else
{
throw new QsException("Unsupported scalar object");
}
}
else if (value is QsVector)
{
var vec = value as QsVector;
QsVector rvec = new QsVector(vec.Count);
foreach (var v in vec)
{
rvec.AddComponent((QsScalar)Factorial(v));
}
return(rvec);
}
else if (value is QsMatrix)
{
var mat = value as QsMatrix;
QsMatrix Total = new QsMatrix();
for (int IY = 0; IY < mat.RowsCount; IY++)
{
List <QsScalar> row = new List <QsScalar>(mat.ColumnsCount);
for (int IX = 0; IX < mat.ColumnsCount; IX++)
{
row.Add((QsScalar)Factorial(mat[IY, IX]));
}
Total.AddRow(row.ToArray());
}
return(Total);
}
else
{
throw new NotSupportedException();
}
}
/// <summary>
/// This is a tricky functions
/// it returns Vector if components are Scalars.
/// Matrix if components are Vectors
/// </summary>
/// <param name="fromIndex"></param>
/// <param name="toIndex"></param>
/// <returns></returns>
public QsValue QsValueElements(int fromIndex, int toIndex)
{
if (this.Parameters.Length > 0)
{
List <string> ProcessedElements = new List <string>();
#region symbolic representation
if (fromIndex > toIndex)
{
for (int e_ix = fromIndex; e_ix >= toIndex; e_ix--)
{
var se = GetElement(e_ix);
// s[n](x) ..> $x*x^n+$n # symbolic variables shouldn't be changed ($x, $n) we should take care.
// first preserve the symbolic variable with the same index name that we are going to change.
string se_text = se.ElementDeclaration.Replace("$" + this.SequenceIndexName, "`");
// replace the index name with the
se_text = se_text.Replace(this.SequenceIndexName, e_ix.ToString(CultureInfo.InvariantCulture));
// get back the symbolic
se_text = se_text.Replace("`", "$" + this.SequenceIndexName);
if (!string.IsNullOrEmpty(SequenceRangeStartName))
{
se_text = se_text.Replace("$" + SequenceRangeStartName, "`");
se_text = se_text.Replace(SequenceRangeStartName, StartIndex.ToString(CultureInfo.InvariantCulture));
se_text = se_text.Replace("`", "$" + SequenceRangeStartName);
}
if (!string.IsNullOrEmpty(SequenceRangeEndName))
{
se_text = se_text.Replace("$" + SequenceRangeEndName, "`");
se_text = se_text.Replace(SequenceRangeEndName, EndIndex.ToString(CultureInfo.InvariantCulture));
se_text = se_text.Replace("`", "$" + SequenceRangeEndName);
}
// replace the parameters in declaration with the same
foreach (var param in this.Parameters)
{
se_text = se_text.Replace("$" + param.Name, "`");
se_text = se_text.Replace(param.Name, "$" + param.Name);
se_text = se_text.Replace("`", "$" + param.Name);
}
ProcessedElements.Add(se_text);
}
}
else
{
for (int e_ix = fromIndex; e_ix <= toIndex; e_ix++)
{
var se = GetElement(e_ix);
string se_text = se.ElementDeclaration.Replace("$" + this.SequenceIndexName, "`");
se_text = se_text.Replace(this.SequenceIndexName, e_ix.ToString(CultureInfo.InvariantCulture));
se_text = se_text.Replace("`", "$" + this.SequenceIndexName);
if (!string.IsNullOrEmpty(SequenceRangeStartName))
{
se_text = se_text.Replace("$" + SequenceRangeStartName, "`");
se_text = se_text.Replace(SequenceRangeStartName, StartIndex.ToString(CultureInfo.InvariantCulture));
se_text = se_text.Replace("`", "$" + SequenceRangeStartName);
}
if (!string.IsNullOrEmpty(SequenceRangeEndName))
{
se_text = se_text.Replace("$" + SequenceRangeEndName, "`");
se_text = se_text.Replace(SequenceRangeEndName, EndIndex.ToString(CultureInfo.InvariantCulture));
se_text = se_text.Replace("`", "$" + SequenceRangeEndName);
}
// replace the parameters with names
foreach (var param in this.Parameters)
{
se_text = se_text.Replace("$" + param.Name, "`");
se_text = se_text.Replace(param.Name, "$" + param.Name);
se_text = se_text.Replace("`", "$" + param.Name);
}
ProcessedElements.Add(se_text);
}
}
var ee = QsEvaluator.CurrentEvaluator.SilentEvaluate(ProcessedElements[0]);
QsValue Total;
if (ee is QsScalar)
{
Total = new QsVector(System.Math.Abs(toIndex - fromIndex) + 1);
foreach (string pel in ProcessedElements)
{
((QsVector)Total).AddComponent((QsScalar)QsEvaluator.CurrentEvaluator.SilentEvaluate(pel));
}
}
else if (ee is QsVector)
{
Total = new QsMatrix();
foreach (string pel in ProcessedElements)
{
((QsMatrix)Total).AddVector((QsVector)QsEvaluator.CurrentEvaluator.SilentEvaluate(pel));
}
}
else if (ee is QsMatrix)
{
Total = new QsTensor();
foreach (string pel in ProcessedElements)
{
((QsTensor)Total).AddMatrix((QsMatrix)QsEvaluator.CurrentEvaluator.SilentEvaluate(pel));
}
}
else
{
throw new QsException("This is enough, no more than matrix values please.");
}
#endregion
return(Total);
}
QsValue firstElement = (QsValue)GetElementValue(fromIndex);
if (firstElement is QsScalar)
{
//return vector
QsVector Total = new QsVector(System.Math.Abs(toIndex - fromIndex) + 1);
#region Numerical Representation
Total.AddComponent((QsScalar)firstElement);
if (toIndex >= fromIndex)
{
for (int i = fromIndex + 1; i <= toIndex; i++)
{
Total.AddComponent((QsScalar)GetElementValue(i));
}
}
else
{
for (int i = fromIndex - 1; i >= toIndex; i--)
{
Total.AddComponent((QsScalar)GetElementValue(i));
}
}
#endregion
return(Total);
}
else if (firstElement is QsVector)
{
//return vector
QsMatrix Total = new QsMatrix();
Total.AddVector((QsVector)firstElement);
if (toIndex >= fromIndex)
{
for (int i = fromIndex + 1; i <= toIndex; i++)
{
Total.AddVector((QsVector)GetElementValue(i));
}
}
else
{
for (int i = fromIndex - 1; i >= toIndex; i--)
{
Total.AddVector((QsVector)GetElementValue(i));
}
}
return(Total);
}
else if (firstElement is QsMatrix)
{
throw new NotImplementedException();
}
else
{
throw new NotSupportedException();
}
}
public static QsMatrix Identity(int diagonal)
{
return(QsMatrix.MakeIdentity(diagonal));
}
