public static void ConstructionTest()
{
TestUtils.AddTestStartingMessage("MathematicaScalar Creation Test Started.");
var s = MathematicaScalar.CreateRational(Cas, 3, 5);
TestUtils.AddTest("Try create scalar from rational 3/5 ... ", s);
s = MathematicaScalar.CreateSymbol(Cas, "x3");
TestUtils.AddTest("Try create scalar from symbol name ... ", s);
s = MathematicaScalar.Create(Cas, 5);
TestUtils.AddTest("Try create scalar from integer 5 ... ", s);
s = MathematicaScalar.Create(Cas, 5.0f);
TestUtils.AddTest("Try create scalar from float 5.0f ... ", s);
s = MathematicaScalar.Create(Cas, 5.0d);
TestUtils.AddTest("Try create scalar from double 5.0d ... ", s);
var e = Mfs.Plus["v1".ToSymbolExpr(), Mfs.Power[5.ToExpr(), "n".ToSymbolExpr()]];
s = MathematicaScalar.Create(Cas, e);
TestUtils.AddTest("Try create scalar from expression object ... ", s);
s = MathematicaScalar.Create(Cas, @"Pi + 5 / 3");
TestUtils.AddTest("Try create scalar from expression text \"Pi + 5 / 3\" ... ", s);
TestUtils.AddTestCompletionMessage("MathematicaScalar Creation Test Completed.");
}
/// <summary>
/// Create a symbolic scalar from this pattern. If the pattern is a constant its internal
/// expression is returned, else a symbolic expression with a single variable is created and returned
/// </summary>
/// <param name="varNameTemplate"></param>
/// <returns></returns>
internal MathematicaScalar ToMathematicaScalar(StringSequenceTemplate varNameTemplate)
{
return
(IsConstant
? ConstantSymbolicScalar
: MathematicaScalar.Create(SymbolicUtils.Cas, varNameTemplate.GenerateNextString()));
}
/// <summary>
/// Convert this binding pattern into a multivector value
/// </summary>
/// <param name="basisBladeToVarName"></param>
/// <returns></returns>
public AstValueMultivector ToValue(Func <AstFrameBasisBlade, string> basisBladeToVarName)
{
var frameInfo = new AstFrame(BaseFrameMultivector.AssociatedFrameMultivector.ParentFrame);
var mv = GaSymMultivector.CreateZero(
BaseFrameMultivector.AssociatedFrameMultivector.ParentFrame.GaSpaceDimension
);
foreach (var pair in _patternDictionary)
{
mv.AddFactor(
pair.Key,
pair.Value.IsConstant
? pair.Value.ConstantSymbolicScalar
: MathematicaScalar.Create(SymbolicUtils.Cas, basisBladeToVarName(frameInfo.BasisBlade(pair.Key)))
);
}
return
(new AstValueMultivector(
GMacValueMultivector.Create(
BaseFrameMultivector.AssociatedFrameMultivector,
mv
)
));
}
private ValuePrimitive <MathematicaScalar> GetRandomValue(ILanguageType valueType)
{
Expr valueExpr;
if (valueType.IsInteger())
{
valueExpr = new Expr(_randomSource.Next(1, 10));
}
else if (valueType.IsBoolean())
{
valueExpr = new Expr(_randomSource.Next(0, 1) != 0);
}
else if (valueType.IsScalar())
{
valueExpr = new Expr(_randomSource.NextDouble() * 10.0 - 5.0);
}
//value_expr = new Expr(new Expr(ExpressionType.Symbol, "Rational"), _RandomSource.Next(1, 10), _RandomSource.Next(1, 10));
else
{
throw new InvalidOperationException();
}
return
(ValuePrimitive <MathematicaScalar> .Create(
(TypePrimitive)valueType,
MathematicaScalar.Create(SymbolicUtils.Cas, valueExpr)
));
}
private void translate_Dependency_List(string expressionText, out MathematicaScalar scalar, out OperandsByName operands)
{
var finalScalarText = new StringBuilder(expressionText);
operands = OperandsByName.Create();
var varIdx = 1;
var allMatches = GenUtils.ExtractDistinctInternalExpressions(expressionText);
foreach (var rgexMatch in allMatches)
{
var rhsExprText = rgexMatch.Value.Substring(1, rgexMatch.Value.Length - 2);
var rhsExpr =
BasicExpressionGenerator.Generate_PolyadicOperand(
GMacRootAst.ScalarType,
translate_LanguageExpression(rhsExprText)
);
var lhsVarName = "var" + (varIdx++).ToString("0000");
finalScalarText = finalScalarText.Replace(rgexMatch.Value, lhsVarName);
operands.AddOperand(lhsVarName, rhsExpr);
}
scalar = MathematicaScalar.Create(Cas, finalScalarText.ToString());
}
private bool InitSymbolicEngine()
{
try
{
_log.Append("Initializing Symbolic Engine...");
labelStatus.Text = _log.ToString();
Application.DoEvents();
MathematicaScalar.Create(SymbolicUtils.Cas, "0");
_log.AppendLine("Done").AppendLine();
labelStatus.Text = _log.ToString();
Application.DoEvents();
return(true);
}
catch (Exception e)
{
_log.AppendLine("Failed").AppendLine(e.Message).AppendLine();
labelStatus.Text = _log.ToString();
Application.DoEvents();
return(false);
}
}
/// <summary>
/// Finds the value of a primitive value access if exists; else returns the default primitive value
/// </summary>
/// <param name="valueAccess"></param>
/// <returns></returns>
public ValuePrimitive <MathematicaScalar> ReadRhsPrimitiveValue(LanguageValueAccess valueAccess)
{
//Try to read the value from the existing table low-level entries
var result = ReadRHSPrimitiveValue_ExistingOnly(valueAccess);
//If an entry is found just return the value
if (ReferenceEquals(result, null) == false)
{
return(result);
}
//If an entry is not found create and return a default value
if (valueAccess.ExpressionType.IsBoolean())
{
ValuePrimitive <MathematicaScalar> .Create(
(TypePrimitive)valueAccess.ExpressionType,
MathematicaScalar.Create(SymbolicUtils.Cas, "False")
);
}
return
(ValuePrimitive <MathematicaScalar> .Create(
(TypePrimitive)valueAccess.ExpressionType,
SymbolicUtils.Constants.Zero
));
}
internal MathematicaConstants(MathematicaInterface parentCas)
{
Cas = parentCas;
True = MathematicaCondition.Create(parentCas, true);
_constantsDictionary.Add("true", True);
False = MathematicaCondition.Create(parentCas, false);
_constantsDictionary.Add("false", False);
Zero = MathematicaScalar.Create(parentCas, 0);
_constantsDictionary.Add("zero", Zero);
One = MathematicaScalar.Create(parentCas, 1);
_constantsDictionary.Add("one", One);
MinusOne = MathematicaScalar.Create(parentCas, -1);
_constantsDictionary.Add("minusone", MinusOne);
Pi = MathematicaScalar.Create(parentCas, CasConnection.EvaluateToExpr("Pi"));
_constantsDictionary.Add("pi", Pi);
TwoPi = MathematicaScalar.Create(parentCas, CasConnection.EvaluateToExpr("Times[2, Pi]"));
_constantsDictionary.Add("twopi", TwoPi);
}
///Translate a constant number (Int32 or Double)
private ILanguageExpression translate_Constant_Number(ParseTreeNode node)
{
var numberText = node.FindTokenAndGetText();
Int32 intNumber;
if (Int32.TryParse(numberText, out intNumber))
{
return(ValuePrimitive <MathematicaScalar> .Create(
GMacRootAst.ScalarType,
MathematicaScalar.Create(SymbolicUtils.Cas, intNumber)
));
}
Double doubleNumber;
if (Double.TryParse(numberText, out doubleNumber))
{
return(ValuePrimitive <MathematicaScalar> .Create(
GMacRootAst.ScalarType,
MathematicaScalar.Create(SymbolicUtils.Cas, doubleNumber)
));
}
return(CompilationLog.RaiseGeneratorError <ILanguageExpression>("Constant number not recognized", node));
}
protected override void ComputeIpm()
{
var bvSig = _basisVectorsSignatures.Select(i => MathematicaScalar.Create(CasInterface, i));
var v = MathematicaVector.CreateFullVector(CasInterface, bvSig);
InnerProductMatrix = MathematicaMatrix.CreateDiagonal(v);
}
/// <summary>
/// Create a symbolic value from this pattern. If the pattern is a constant its internal
/// expression is returned, else a symbolic expression with a single variable is created and returned
/// </summary>
/// <param name="varNameTemplate"></param>
/// <returns></returns>
public AstValueScalar ToValue(StringSequenceTemplate varNameTemplate)
{
return
(IsConstant
? ConstantValue
: new AstValueScalar(
ValuePrimitive <MathematicaScalar> .Create(
GMacType.AssociatedPrimitiveType,
MathematicaScalar.Create(SymbolicUtils.Cas, varNameTemplate.GenerateNextString())
)
));
}
public static string InitializeGMac()
{
var log = new LinearComposer();
try
{
log.Append("Initializing GA Data...");
GMacLookupTables.Choose(1, 1);
log.AppendLine("Done").AppendLine();
log.Append("Initializing GMac Resources...");
if (Directory.Exists(IconsPath) == false)
{
Directory.CreateDirectory(IconsPath);
}
SaveIcon(Resources.BasisVector64, "BasisVector64");
SaveIcon(Resources.Compile64, "Compile64");
SaveIcon(Resources.Constant64, "Constant64");
SaveIcon(Resources.Filter64, "Filter64");
SaveIcon(Resources.Frame64, "Frame64");
SaveIcon(Resources.GMacAST64, "GMacAST64");
SaveIcon(Resources.GMac_Icon64, "GMac_Icon64");
SaveIcon(Resources.Idea64, "Idea64");
SaveIcon(Resources.Input64, "Input64");
SaveIcon(Resources.Macro64, "Macro64");
SaveIcon(Resources.Namespace64, "Namespace64");
SaveIcon(Resources.Output64, "Output64");
SaveIcon(Resources.Scalar64, "Scalar64");
SaveIcon(Resources.Structure64, "Structure64");
SaveIcon(Resources.Subspace64, "Subspace64");
SaveIcon(Resources.Transform64, "Transform64");
log.AppendLine("Done").AppendLine();
log.Append("Initializing Symbolic Engine...");
MathematicaScalar.Create(SymbolicUtils.Cas, "0");
log.AppendLine("Done").AppendLine();
}
catch (Exception e)
{
log.AppendLine("Failed").AppendLine(e.Message).AppendLine();
}
return(log.ToString());
}
private ILanguageValue EvaluateBasicUnaryCastToScalar(BasicUnary expr)
{
var value1 = expr.Operand.AcceptVisitor(this);
if (value1.ExpressionType.IsInteger())
{
return(ValuePrimitive <MathematicaScalar> .Create(
(TypePrimitive)expr.ExpressionType,
MathematicaScalar.Create(SymbolicUtils.Cas, ((ValuePrimitive <int>)value1).Value)
));
}
throw new InvalidOperationException("Invalid cast operation");
}
/// <summary>
/// Low level processing requires the use of MathematicaScalar primitive values only. This method preforms
/// the required conversion of primitive values of other forms.
/// </summary>
/// <param name="value"></param>
/// <returns></returns>
public static ValuePrimitive <MathematicaScalar> ToScalarValue(this ILanguageValuePrimitive value)
{
var primitive1 = value as ValuePrimitive <MathematicaScalar>;
if (primitive1 != null)
{
return(primitive1);
}
//Convert into equivalent Mathematica scalar value
var primitive2 = value as ValuePrimitive <int>;
if (primitive2 != null)
{
return(ValuePrimitive <MathematicaScalar> .Create(
(TypePrimitive)value.ExpressionType,
MathematicaScalar.Create(SymbolicUtils.Cas, primitive2.Value)
));
}
//Convert into equivalent Mathematica scalar value
var primitive3 = value as ValuePrimitive <bool>;
if (primitive3 != null)
{
return(ValuePrimitive <MathematicaScalar> .Create(
(TypePrimitive)value.ExpressionType,
MathematicaScalar.Create(SymbolicUtils.Cas, primitive3.Value ? "True" : "False")
));
}
//if (value is ValuePrimitive<double>)
//{
//return ValuePrimitive<MathematicaScalar>.Create(
// (TypePrimitive)value.ExpressionType,
// MathematicaScalar.Create(SymbolicUtils.CAS, ((ValuePrimitive<double>)value).Value)
// );
//}
//if (value is ValuePrimitive<float>)
//{
//return ValuePrimitive<MathematicaScalar>.Create(
// (TypePrimitive)value.ExpressionType,
// MathematicaScalar.Create(SymbolicUtils.CAS, ((ValuePrimitive<float>)value).Value)
// );
//}
//This should never happen
throw new InvalidOperationException();
}
public static void ConstructionTest()
{
TestUtils.AddTestStartingMessage("MathematicaMatrix Creation Test Started.");
var scalarsArray = new MathematicaScalar[2, 2];
scalarsArray[0, 0] = MathematicaScalar.Create(Cas, 2);
scalarsArray[0, 1] = MathematicaScalar.Create(Cas, -2);
scalarsArray[1, 0] = MathematicaScalar.Create(Cas, 3);
scalarsArray[1, 1] = MathematicaScalar.Create(Cas, 1);
var s = MathematicaMatrix.CreateFullMatrix(Cas, scalarsArray);
TestUtils.AddTest("Try create full matrix from array of scalars ... ", s);
s = MathematicaMatrix.CreateIdentity(Cas, 3);
TestUtils.AddTest("Try create full 3x3 identity matrix ... ", s);
s = MathematicaMatrix.CreateIdentity(Cas, 3, false);
TestUtils.AddTest("Try create sparse 3x3 identity matrix ... ", s);
var v = MathematicaVector.CreateFullVector(Cas, Cas.Constants.Zero, Cas.Constants.TwoPi, Cas.Constants.One);
s = MathematicaMatrix.CreateDiagonal(v);
TestUtils.AddTest("Try create full 3x3 diagonal matrix from vector {0, 2 Pi, 1} ... ", s);
s = MathematicaMatrix.CreateDiagonal(v, false);
TestUtils.AddTest("Try create sparse 3x3 diagonal matrix from vector {0, 2 Pi, 1} ... ", s);
s = MathematicaMatrix.CreateRowVector(v);
TestUtils.AddTest("Try create full row vector matrix from vector {0, 2 Pi, 1} ... ", s);
s = MathematicaMatrix.CreateRowVector(v, false);
TestUtils.AddTest("Try create sparse row vector matrix from vector {0, 2 Pi, 1} ... ", s);
s = MathematicaMatrix.CreateColumnVector(v);
TestUtils.AddTest("Try create full row vector matrix from vector {0, 2 Pi, 1} ... ", s);
s = MathematicaMatrix.CreateColumnVector(v, false);
TestUtils.AddTest("Try create sparse row vector matrix from vector {0, 2 Pi, 1} ... ", s);
s = MathematicaMatrix.CreateConstant(Cas.Constants.Pi, 2, 3);
TestUtils.AddTest("Try create 2x3 matrix with constant elements of Pi ... ", s);
s = MathematicaMatrix.Create(Cas, @"{{1, x}, {2, y}, {3, z}}");
TestUtils.AddTest("Try create matrix from expression text \"{{1, x}, {2, y}, {3, z}}\" ... ", s);
TestUtils.AddTestCompletionMessage("MathematicaMatrix Creation Test Completed.");
}
private static ILanguageExpressionAtomic AtomicExpressionToMultivectorAtomicExpression(this CommandBlock commandBlock, GMacFrameMultivector mvType, ILanguageExpressionAtomic oldExpr)
{
if (oldExpr.ExpressionType.IsSameType(mvType))
{
return(oldExpr);
}
if (!oldExpr.ExpressionType.IsNumber())
{
throw new InvalidCastException("Cannot convert atomic expression of type " + oldExpr.ExpressionType.TypeSignature + " to a expression of type " + mvType.TypeSignature);
}
var valuePrimitive = oldExpr as ValuePrimitive <int>;
if (valuePrimitive != null)
{
return(GMacValueMultivector.CreateScalar(
mvType,
MathematicaScalar.Create(SymbolicUtils.Cas, valuePrimitive.Value)
));
}
var primitive = oldExpr as ValuePrimitive <MathematicaScalar>;
if (primitive != null)
{
return(GMacValueMultivector.CreateScalar(
mvType,
primitive.Value
));
}
//This should be a value access of type integer or scalar
if (!(oldExpr is LanguageValueAccess))
{
throw new InvalidCastException(
"Cannot convert atomic expression " + oldExpr + " of type " +
oldExpr.ExpressionType.TypeSignature + " to a atomic expression of type" +
mvType.TypeSignature
);
}
//Create a cast operation
var newRhsExpr = BasicUnary.Create(mvType, mvType, oldExpr);
//The new expresssion is not atomic. Create a local variable to hold value and return the local variable
//as a direct value access object
return(NonAtomicExpressionToValueAccess(commandBlock, newRhsExpr));
}
public static GaSymFrameOrthogonal CreateProjective(int vSpaceDim)
{
VerifyVSpaceDim(vSpaceDim, 2);
var sigArray = Enumerable.Repeat(1, vSpaceDim).ToArray();
sigArray[vSpaceDim - 1] = 0;
var frameSigList =
sigArray.Select(
i => MathematicaScalar.Create(SymbolicUtils.Cas, i)
);
return(new GaSymFrameOrthogonal(frameSigList));
}
internal static GaMultivector ToMultivector(this Dictionary <int, ListComposer> accumExprDict, int gaSpaceDim)
{
var resultMv = GaMultivector.CreateZero(gaSpaceDim);
foreach (var pair in accumExprDict)
{
var resultCoef = SymbolicUtils.Cas[pair.Value.ToString()];
if (!(resultCoef.Args.Length == 0 && resultCoef.ToString() == "0"))
{
resultMv.Add(pair.Key, MathematicaScalar.Create(SymbolicUtils.Cas, resultCoef));
}
}
return(resultMv);
}
private ILanguageValue EvaluateBasicUnaryCastToMultivector(BasicUnary expr)
{
var value1 = expr.Operand.AcceptVisitor(this);
var mvType = (GMacFrameMultivector)expr.Operator;
if (value1.ExpressionType.IsInteger())
{
var intValue = ((ValuePrimitive <int>)value1).Value;
return(GMacValueMultivector.Create(
mvType,
GaMultivector.CreateScalar(
mvType.ParentFrame.GaSpaceDimension,
MathematicaScalar.Create(SymbolicUtils.Cas, intValue)
)
));
}
if (value1.ExpressionType.IsScalar())
{
var scalarValue = ((ValuePrimitive <MathematicaScalar>)value1).Value;
return(GMacValueMultivector.Create(
mvType,
GaMultivector.CreateScalar(
mvType.ParentFrame.GaSpaceDimension,
scalarValue
)
));
}
if (value1.ExpressionType.IsFrameMultivector() &&
value1.ExpressionType.GetFrame().VSpaceDimension == mvType.ParentFrame.VSpaceDimension)
{
var mvValue = ((GMacValueMultivector)value1);
return(GMacValueMultivector.Create(
mvType,
GaMultivector.CreateCopy(mvValue.MultivectorCoefficients)
));
}
throw new InvalidOperationException("Invalid cast operation");
}
/// <summary>
/// Replace the given value by a processed version depending on some GMac compiler options
/// </summary>
/// <param name="value"></param>
/// <returns></returns>
private static ValuePrimitive <MathematicaScalar> ProcessRhsValue(ValuePrimitive <MathematicaScalar> value)
{
//No simplification or sub-expression refactoring required; just return the value without any processing
if (GMacCompilerOptions.SimplifyLowLevelRhsValues == false)
{
return(value);
}
//Symbolically simplify the value if indicated. This takes a lot of Mathematica processing and slows
//compilation but produces target code with better processing performance in some cases
var finalExpr = SymbolicUtils.Evaluator.Simplify(value.Value.Expression);
return
(ValuePrimitive <MathematicaScalar> .Create(
(TypePrimitive)value.ExpressionType,
MathematicaScalar.Create(SymbolicUtils.Cas, finalExpr)
));
}
//private static readonly Regex LlVarOnlyRegex = new Regex(@"^\b" + LlVarNamePrefix + @"[0-9A-F][0-9A-F][0-9A-F][0-9A-F]\b$", RegexOptions.ECMAScript);
/// <summary>
/// Low level processing requires the use of MathematicaScalar primitive values only. This method extracts
/// the a primitive value of the given type as a MathematicaScalar primitive value.
/// </summary>
/// <param name="langType"></param>
/// <returns></returns>
public static ValuePrimitive <MathematicaScalar> GetDefaultScalarValue(this TypePrimitive langType)
{
MathematicaScalar scalar;
if (langType.IsNumber())
{
scalar = MathematicaScalar.Create(SymbolicUtils.Cas, 0);
}
else if (langType.IsBoolean())
{
scalar = MathematicaScalar.Create(SymbolicUtils.Cas, "False");
}
else
{
throw new InvalidOperationException();
}
return(ValuePrimitive <MathematicaScalar> .Create(langType, scalar));
}
private static ILanguageExpressionAtomic AtomicExpressionToScalarAtomicExpression(this CommandBlock commandBlock, ILanguageExpressionAtomic oldExpr)
{
var scalarType = ((GMacAst)commandBlock.RootAst).ScalarType;
if (oldExpr.ExpressionType.IsSameType(scalarType))
{
return(oldExpr);
}
if (!oldExpr.ExpressionType.IsInteger())
{
throw new InvalidCastException("Cannot convert atomic expression of type " + oldExpr.ExpressionType.TypeSignature + " to a scalar atomic expression");
}
var valuePrimitive = oldExpr as ValuePrimitive <int>;
if (valuePrimitive != null)
{
return(ValuePrimitive <MathematicaScalar> .Create(
scalarType,
MathematicaScalar.Create(SymbolicUtils.Cas, valuePrimitive.Value)
));
}
//This should be a value access of type integer
if (!(oldExpr is LanguageValueAccess))
{
throw new InvalidCastException("Cannot convert atomic expression " + oldExpr + " of type " +
oldExpr.ExpressionType.TypeSignature + " to a scalar atomic expression");
}
//Create a cast operation
var newRhsExpr = BasicUnary.Create(scalarType, scalarType, oldExpr);
//The new expresssion is not atomic. Create a local variable to hold value and return the local variable
//as a direct value access object
return(NonAtomicExpressionToValueAccess(commandBlock, newRhsExpr));
}
private ValuePrimitive <MathematicaScalar> EvaluateBasicPolyadicSymbolicExpressionCall(GMacParametricSymbolicExpression symbolicExpr, OperandsByName operands)
{
var exprText = symbolicExpr.AssociatedMathematicaScalar.ExpressionText;
foreach (var pair in operands.OperandsDictionary)
{
var rhsValue = pair.Value.AcceptVisitor(this);
exprText = exprText.Replace(pair.Key, ((ValuePrimitive <MathematicaScalar>)rhsValue).Value.ExpressionText);
}
var scalar =
MathematicaScalar.Create(symbolicExpr.AssociatedMathematicaScalar.CasInterface, exprText);
//May be required
//scalar = MathematicaScalar.Create(scalar.CAS, scalar.CASEvaluator.FullySimplify(scalar.MathExpr));
return
(ValuePrimitive <MathematicaScalar> .Create(
GMacRootAst.ScalarType,
scalar
));
}
public static void BasicOpsTest()
{
//Expr e;
var s1 = MathematicaScalar.CreateRational(Cas, -3, 5);
var s2 = MathematicaScalar.CreateRational(Cas, 9, 5);
var s3 = MathematicaScalar.Create(Cas, "Pi");
TestUtils.AddTestStartingMessage("MathematicaScalar Basic Operations Test Started.");
TestUtils.AddTest("Try negate rational -3/5 ... ", -s1);
TestUtils.AddTest("Try add rationals -3/5 and 9/5 ... ", s1 + s2);
TestUtils.AddTest("Try subtract rationals -3/5 and 9/5 ... ", s1 - s2);
TestUtils.AddTest("Try multiply rationals -3/5 and 9/5 ... ", s1 * s2);
TestUtils.AddTest("Try divide rationals -3/5 and 9/5 ... ", s1 / s2);
TestUtils.AddTest("Try rise rational 9/5 to the power of Pi ... ", s2 ^ s3);
TestUtils.AddTest("Try apply Abs to rational -3/5 ... ", s1.Abs());
TestUtils.AddTest("Try apply Sqrt to rational -3/5 ... ", s1.Sqrt());
TestUtils.AddTest("Try apply Sin to rational 9/5 ... ", s2.Sin());
TestUtils.AddTest("Try apply Cos to rational 9/5 ... ", s2.Cos());
TestUtils.AddTest("Try apply Tan to rational 9/5 ... ", s2.Tan());
TestUtils.AddTest("Try apply Sinh to rational 9/5 ... ", s2.Sinh());
TestUtils.AddTest("Try apply Cosh to rational 9/5 ... ", s2.Cosh());
TestUtils.AddTest("Try apply Tanh to rational 9/5 ... ", s2.Tanh());
TestUtils.AddTest("Try apply Log to rational 9/5 ... ", s2.Log());
TestUtils.AddTest("Try apply Log10 to rational 9/5 ... ", s2.Log10());
TestUtils.AddTest("Try apply Log2 to rational 9/5 ... ", s2.Log2());
TestUtils.AddTest("Try apply Exp to rational 9/5 ... ", s2.Exp());
var s = MathematicaScalar.Create(Cas, @"3 x ^ 2 + 2 Pi ^ x - Sin[x]");
var d = MathematicaScalar.CreateSymbol(Cas, "x");
TestUtils.AddTest("Try differentiate 3 x ^ 2 + 2 Pi ^ x - Sin[x] w.r.t. x ... ", s.DiffBy(d));
TestUtils.AddTestCompletionMessage("MathematicaScalar Basic Operations Test Completed.");
}
/// <summary>
/// frameSigList must have all items equal to 1 (false) or -1 (true) with at least one negative item
/// </summary>
/// <param name="frameSigList"></param>
internal GaSymFrameOrthonormal(IEnumerable <bool> frameSigList)
{
BasisVectorsSignatures = frameSigList.Select(b => b ? -1 : 1).ToArray();
OrthonormalMetric = GaSymMetricOrthonormal.Create(BasisVectorsSignatures);
Op = ComputedOp = new GaSymOp(VSpaceDimension);
Gp = ComputedGp = new GaSymOrthonormalGp(OrthonormalMetric);
Sp = ComputedSp = new GaSymOrthonormalSp(OrthonormalMetric);
Lcp = ComputedLcp = new GaSymOrthonormalLcp(OrthonormalMetric);
Rcp = ComputedRcp = new GaSymOrthonormalRcp(OrthonormalMetric);
Fdp = ComputedFdp = new GaSymOrthonormalFdp(OrthonormalMetric);
Hip = ComputedHip = new GaSymOrthonormalHip(OrthonormalMetric);
Acp = ComputedAcp = new GaSymOrthonormalAcp(OrthonormalMetric);
Cp = ComputedCp = new GaSymOrthonormalCp(OrthonormalMetric);
UnitPseudoScalarCoef =
MathematicaScalar.Create(
SymbolicUtils.Cas,
MaxBasisBladeId.BasisBladeIdHasNegativeReverse()
? -1.0d / OrthonormalMetric[MaxBasisBladeId]
: 1.0d / OrthonormalMetric[MaxBasisBladeId]
);
}
public MathematicaScalar GetSymbolicInteger(int minLimit, int maxLimit)
{
return(MathematicaScalar.Create(SymbolicUtils.Cas, GetInteger(minLimit, maxLimit)));
}
public static void IsOpsTest()
{
TestUtils.AddTestStartingMessage("MathematicaScalar 'Is' Operations Test Started.");
var s1 = MathematicaScalar.Create(Cas, 0.0f);
TestUtils.AddTest("Try apply IsPossibleZero() to 0.0f ... ", s1.IsPossibleZero());
s1 = MathematicaScalar.CreateSymbol(Cas, "Pi");
TestUtils.AddTest("Try apply IsPossibleZero() to Pi ... ", s1.IsPossibleZero());
s1 = MathematicaScalar.Create(Cas, @"x - x");
TestUtils.AddTest("Try apply IsPossibleZero() to (x - x) ... ", s1.IsPossibleZero());
s1 = MathematicaScalar.Create(Cas, @"3 x ^ 2 + 2 Pi ^ x - Sin[x]");
TestUtils.AddTest("Try apply IsPossibleZero() to 3 x ^ 2 + 2 Pi ^ x - Sin[x] ... ", s1.IsPossibleZero());
s1 = MathematicaScalar.Create(Cas, 0.0f);
TestUtils.AddTest("Try apply IsEqualZero() to 0.0f ... ", s1.IsEqualZero());
s1 = MathematicaScalar.CreateSymbol(Cas, "Pi");
TestUtils.AddTest("Try apply IsEqualZero() to Pi ... ", s1.IsEqualZero());
s1 = MathematicaScalar.Create(Cas, @"x - x");
TestUtils.AddTest("Try apply IsEqualZero() to (x - x) ... ", s1.IsEqualZero());
s1 = MathematicaScalar.Create(Cas, @"3 x ^ 2 + 2 Pi ^ x - Sin[x]");
TestUtils.AddTest("Try apply IsEqualZero() to 3 x ^ 2 + 2 Pi ^ x - Sin[x] ... ", s1.IsEqualZero());
s1 = MathematicaScalar.Create(Cas, 5.0f);
var s2 = MathematicaScalar.Create(Cas, 5);
TestUtils.AddTest("Try apply IsPossibleScalar() to 5.0f with 5 ... ", s1.IsPossibleScalar(s2));
s1 = MathematicaScalar.Create(Cas, 5.1f);
s2 = MathematicaScalar.Create(Cas, 5);
TestUtils.AddTest("Try apply IsPossibleScalar() to 5.1f with 5 ... ", s1.IsPossibleScalar(s2));
s1 = MathematicaScalar.Create(Cas, 1.0f);
s2 = MathematicaScalar.Create(Cas, "Sin[Pi]");
TestUtils.AddTest("Try apply IsPossibleScalar() to 1.0f with Sin[Pi] ... ", s1.IsPossibleScalar(s2));
s1 = MathematicaScalar.Create(Cas, -1.0f);
s2 = MathematicaScalar.Create(Cas, "Cos[Pi]");
TestUtils.AddTest("Try apply IsPossibleScalar() to -1.0f with Cos[Pi] ... ", s1.IsPossibleScalar(s2));
s1 = MathematicaScalar.Create(Cas, 5.0f);
s2 = MathematicaScalar.Create(Cas, 5);
TestUtils.AddTest("Try apply IsEqualScalar() to 5.0f with 5 ... ", s1.IsEqualScalar(s2));
s1 = MathematicaScalar.Create(Cas, 5.1f);
s2 = MathematicaScalar.Create(Cas, 5);
TestUtils.AddTest("Try apply IsEqualScalar() to 5.1f with 5 ... ", s1.IsEqualScalar(s2));
s1 = MathematicaScalar.Create(Cas, 1.0f);
s2 = MathematicaScalar.Create(Cas, "Sin[Pi]");
TestUtils.AddTest("Try apply IsEqualScalar() to 1.0f with Sin[Pi] ... ", s1.IsEqualScalar(s2));
s1 = MathematicaScalar.Create(Cas, -1.0f);
s2 = MathematicaScalar.Create(Cas, "Cos[Pi]");
TestUtils.AddTest("Try apply IsEqualScalar() to -1.0f with Cos[Pi] ... ", s1.IsEqualScalar(s2));
s1 = MathematicaScalar.Create(Cas, -1.0f);
TestUtils.AddTest("Try apply IsConstant() to -1.0f ... ", s1.IsConstant());
s1 = MathematicaScalar.Create(Cas, "Sin[Pi]");
TestUtils.AddTest("Try apply IsConstant() to Sin[Pi] ... ", s1.IsConstant());
s1 = MathematicaScalar.Create(Cas, "Sin[x]");
TestUtils.AddTest("Try apply IsConstant() to Sin[x] ... ", s1.IsConstant());
s1 = MathematicaScalar.Create(Cas, "Sin[x - x]");
TestUtils.AddTest("Try apply IsConstant() to Sin[x - x] ... ", s1.IsConstant());
s1 = MathematicaScalar.Create(Cas, 0.0f);
TestUtils.AddTest("Try apply IsNonZeroRealConstant() to 0.0f ... ", s1.IsNonZeroRealConstant());
s1 = MathematicaScalar.Create(Cas, -1.0f);
TestUtils.AddTest("Try apply IsNonZeroRealConstant() to -1.0f ... ", s1.IsNonZeroRealConstant());
s1 = MathematicaScalar.Create(Cas, "Sin[Pi]");
TestUtils.AddTest("Try apply IsNonZeroRealConstant() to Sin[Pi] ... ", s1.IsNonZeroRealConstant());
s1 = MathematicaScalar.Create(Cas, "Sin[x]");
TestUtils.AddTest("Try apply IsNonZeroRealConstant() to Sin[x] ... ", s1.IsNonZeroRealConstant());
s1 = MathematicaScalar.Create(Cas, "Sin[x - x]");
TestUtils.AddTest("Try apply IsNonZeroRealConstant() to Sin[x - x] ... ", s1.IsNonZeroRealConstant());
s1 = MathematicaScalar.Create(Cas, "3 + i * Sin[Pi / 2]");
TestUtils.AddTest("Try apply IsNonZeroRealConstant() to 3 + i * Sin[Pi / 2] ... ", s1.IsNonZeroRealConstant());
TestUtils.AddTestCompletionMessage("MathematicaScalar 'Is' Operations Test Completed.");
}
public static void BasicOpsTest()
{
var s = MathematicaScalar.Create(Cas, -2);
var v = MathematicaVector.CreateFullVector(Cas, Cas.Constants.One, Cas.Constants.Pi, Cas.Constants.MinusOne);
var m1 = MathematicaMatrix.Create(Cas, "RandomInteger[{-5, 5}, {3, 4}]");
var m2 = MathematicaMatrix.CreateFullDiagonalMatrix(Cas, Cas.Constants.One, Cas.Constants.Pi, Cas.Constants.MinusOne);
var sm3 = MathematicaMatrix.Create(Cas, "SparseArray[{{1, 0, 0, 0}, {0, 2, 0, 4}, {0, 0, 0, 3}}]");
var sm4 = m2.ToMathematicaSparseMatrix();
TestUtils.AddTestStartingMessage("MathematicaMatrix Basic Operations Test Started.");
TestUtils.AddTest("Try get rows of full 3x4 matrix ... ", m1.RowCount);
TestUtils.AddTest("Try get columns of full 3x4 matrix ... ", m1.ColumnCount);
TestUtils.AddTest("Try get rows of sparse 3x4 matrix ... ", sm3.RowCount);
TestUtils.AddTest("Try get columns of sparse 3x4 matrix ... ", sm3.ColumnCount);
for (var i = 0; i < m1.RowCount; i++)
{
for (var j = 0; j < m1.ColumnCount; j++)
{
TestUtils.AddTest("Try get component (" + i + ", " + j + ") of full 3x4 matrix " + m1.ExpressionText + " ... ", m1[i, j]);
}
}
for (var i = 0; i < sm3.RowCount; i++)
{
for (var j = 0; j < sm3.ColumnCount; j++)
{
TestUtils.AddTest("Try get component (" + i + ", " + j + ") of sparse 3x4 matrix " + sm3.ToMathematicaFullMatrix().ExpressionText + " ... ", sm3[i, j]);
}
}
for (var i = 0; i < m1.RowCount; i++)
{
TestUtils.AddTest("Try get row " + i + " of full 3x4 matrix " + m1.ExpressionText + " ... ", m1.GetRow(i));
}
for (var i = 0; i < m1.ColumnCount; i++)
{
TestUtils.AddTest("Try get column " + i + " of full 3x4 matrix " + m1.ExpressionText + " ... ", m1.GetColumn(i));
}
for (var i = 0; i < sm3.RowCount; i++)
{
TestUtils.AddTest("Try get row " + i + " of sparse 3x4 matrix " + sm3.ToMathematicaFullMatrix().ExpressionText + " ... ", sm3.GetRow(i));
}
for (var i = 0; i < sm3.ColumnCount; i++)
{
TestUtils.AddTest("Try get column " + i + " of sparse 3x4 matrix " + sm3.ToMathematicaFullMatrix().ExpressionText + " ... ", sm3.GetColumn(i));
}
TestUtils.AddTest("Try get diagonal of full matrix " + m2.ExpressionText + " ... ", m2.GetDiagonal());
TestUtils.AddTest("Try get diagonal of sparse matrix " + sm4.ToMathematicaFullMatrix().ExpressionText + " ... ", sm4.GetDiagonal());
TestUtils.AddTest("Try negate matrix " + m2.ExpressionText + " ... ", -m2);
TestUtils.AddTest("Try add matrix " + m1.ExpressionText + " and " + sm3.ToMathematicaFullMatrix().ExpressionText + " ... ", m1 + sm3);
TestUtils.AddTest("Try subtract matrix " + m1.ExpressionText + " and " + sm3.ToMathematicaFullMatrix().ExpressionText + " ... ", m1 - sm3);
TestUtils.AddTest("Try multiply matrix " + m2.ExpressionText + " and " + m1.ToMathematicaFullMatrix().ExpressionText + " ... ", m2 * m1);
TestUtils.AddTest("Try multiply matrix " + m2.ExpressionText + " and scalar -2 ... ", m2 * s);
TestUtils.AddTest("Try multiply scalar -2 and matrix " + m2.ExpressionText + " ... ", s * m2);
TestUtils.AddTest("Try divide matrix " + m2.ExpressionText + " by scalar -2 ... ", m2 / s);
TestUtils.AddTest("Try multiply matrix " + m2.ExpressionText + " and vector " + v.ExpressionText + " ... ", m2.Times(v));
TestUtils.AddTest("Try multiply vector " + v.ExpressionText + " and matrix " + m2.ExpressionText + " ... ", v.Times(m2));
TestUtils.AddTest("Try transpose matrix " + m2.ExpressionText + " ... ", m2.Transpose());
TestUtils.AddTest("Try inverse matrix " + m2.ExpressionText + " ... ", m2.Inverse());
TestUtils.AddTest("Try inverse transpose matrix " + m2.ExpressionText + " ... ", m2.InverseTranspose());
m2 = MathematicaMatrix.Create(Cas, "{{1, -1, 0}, {-1, 2, -1}, {0, -1, 1}}");
TestUtils.AddTest("Try get eigen values (in a vector) of matrix " + m2.ExpressionText + " ... ", m2.EigenValues_InVector());
TestUtils.AddTest("Try get eigen values (in a matrix) of matrix " + m2.ExpressionText + " ... ", m2.EigenValues_InDiagonalMatrix());
TestUtils.AddTest("Try get eigen vectors (as rows of a matrix) of matrix " + m2.ExpressionText + " ... ", m2.EigenVectors(MathematicaMatrix.EigenVectorsSpecs.InMatrixRows));
TestUtils.AddTest("Try get eigen vectors (as columns of a matrix) of matrix " + m2.ExpressionText + " ... ", m2.EigenVectors(MathematicaMatrix.EigenVectorsSpecs.InMatrixColumns));
TestUtils.AddTest("Try get eigen vectors (as orthonormal rows of a matrix) of matrix " + m2.ExpressionText + " ... ", m2.EigenVectors(MathematicaMatrix.EigenVectorsSpecs.OrthogonalInMatrixRows));
TestUtils.AddTest("Try get eigen vectors (as orthonormal columns of a matrix) of matrix " + m2.ExpressionText + " ... ", m2.EigenVectors(MathematicaMatrix.EigenVectorsSpecs.OrthogonalInMatrixColumns));
MathematicaVector eval1;
MathematicaMatrix eval2;
MathematicaMatrix evec;
m2.EigenSystem(MathematicaMatrix.EigenVectorsSpecs.InMatrixRows, out eval1, out evec);
TestUtils.AddTest("Try get eigen system values (in a vector) of matrix " + m2.ExpressionText + " ... ", eval1);
m2.EigenSystem(MathematicaMatrix.EigenVectorsSpecs.InMatrixRows, out eval2, out evec);
TestUtils.AddTest("Try get eigen system values (in a matrix) of matrix " + m2.ExpressionText + " ... ", eval2);
m2.EigenSystem(MathematicaMatrix.EigenVectorsSpecs.InMatrixRows, out eval1, out evec);
TestUtils.AddTest("Try get eigen system vectors (as rows of a matrix) of matrix " + m2.ExpressionText + " ... ", evec);
m2.EigenSystem(MathematicaMatrix.EigenVectorsSpecs.InMatrixColumns, out eval1, out evec);
TestUtils.AddTest("Try get eigen system vectors (as columns of a matrix) of matrix " + m2.ExpressionText + " ... ", evec);
m2.EigenSystem(MathematicaMatrix.EigenVectorsSpecs.OrthogonalInMatrixRows, out eval1, out evec);
TestUtils.AddTest("Try get eigen system vectors (as orthonormal rows of a matrix) of matrix " + m2.ExpressionText + " ... ", evec);
m2.EigenSystem(MathematicaMatrix.EigenVectorsSpecs.OrthogonalInMatrixColumns, out eval1, out evec);
TestUtils.AddTest("Try get eigen system vectors (as orthonormal columns of a matrix) of matrix " + m2.ExpressionText + " ... ", evec);
TestUtils.AddTestCompletionMessage("MathematicaMatrix Basic Operations Test Completed.");
}
public MathematicaScalar ToSymbolicScalar(GaSymMultivectorTempTree mv1, GaSymMultivectorTempTree mv2)
{
return(MathematicaScalar.Create(SymbolicUtils.Cas, this[mv1, mv2]));
}
public static void BasicOpsTest()
{
var v1 = MathematicaVector.CreateFullVector(Cas, Cas.Constants.Zero, Cas.Constants.One, Cas.Constants.TwoPi);
var v2 = MathematicaVector.Create(Cas, @"{-1, x, Sin[t]}");
var sv3 = MathematicaVector.Create(Cas, "SparseArray[{Rule[1, Pi], Rule[5, -1]}]");
var s = MathematicaScalar.Create(Cas, "x");
TestUtils.AddTestStartingMessage("MathematicaVector Basic Operations Test Started.");
TestUtils.AddTest("Try get size of full vector {-1, x, Sin[t]} ... ", v2.Size);
TestUtils.AddTest("Try get 1st component of full vector {-1, x, Sin[t]} ... ", v2[0]);
TestUtils.AddTest("Try get 2nd component of full vector {-1, x, Sin[t]} ... ", v2[1]);
TestUtils.AddTest("Try get 3rd component of full vector {-1, x, Sin[t]} ... ", v2[2]);
TestUtils.AddTest("Try get size of sparse vector {Pi, 0, 0, 0, -1} ... ", sv3.Size);
TestUtils.AddTest("Try get 1st component of sparse vector {Pi, 0, 0, 0, -1} ... ", sv3[0]);
TestUtils.AddTest("Try get 3rd component of sparse vector {Pi, 0, 0, 0, -1} ... ", sv3[2]);
TestUtils.AddTest("Try get 5th component of sparse vector {Pi, 0, 0, 0, -1} ... ", sv3[4]);
TestUtils.AddTest("Try list components of full vector {-1, x, Sin[t]}", "");
var i = 0;
foreach (var scalar in v2)
{
TestUtils.AddTest(" Component " + i + " ... ", scalar);
i++;
}
TestUtils.AddTest("Try list components of sparse vector {Pi, 0, 0, 0, -1}", "");
i = 0;
foreach (var scalar in sv3)
{
TestUtils.AddTest(" Component " + i + " ... ", scalar);
i++;
}
TestUtils.AddTest("Try negate vector {-1, x, Sin[t]} ... ", -v2);
TestUtils.AddTest("Try add vectors {0, 1, 2 Pi} and {-1, x, Sin[t]} ... ", v1 + v2);
TestUtils.AddTest("Try subtract vectors {0, 1, 2 Pi} and {-1, x, Sin[t]} ... ", v1 - v2);
TestUtils.AddTest("Try find dot product of {0, 1, 2 Pi} and {-1, x, Sin[t]} ... ", v1 * v2);
TestUtils.AddTest("Try find product of vector {-1, x, Sin[t]} with scalar x ... ", v2 * s);
TestUtils.AddTest("Try find product of scalar x with vector {-1, x, Sin[t]} ... ", s * v2);
TestUtils.AddTest("Try divide vector {-1, x, Sin[t]} by scalar x ... ", v2 / s);
TestUtils.AddTest("Try apply Norm to vector {0, 1, 2 Pi} ... ", v1.Norm());
TestUtils.AddTest("Try apply Norm2 to vector {0, 1, 2 Pi} ... ", v1.Norm2());
var m = MathematicaMatrix.CreateFullDiagonalMatrix(Cas, Cas.Constants.One, Cas.Constants.Pi, Cas.Constants.MinusOne);
TestUtils.AddTest("Try find product of vector {-1, x, Sin[t]} with matrix DiagonalMatrix[{1, Pi, -1}] ... ", v2.Times(m));
TestUtils.AddTest("Try apply ToMathematicaVector() to full vector {0, 1, 2 Pi} ... ", v1.ToMathematicaVector());
TestUtils.AddTest("Try apply ToMathematicaFullVector() to full vector {0, 1, 2 Pi} ... ", v1.ToMathematicaFullVector());
TestUtils.AddTest("Try apply ToMathematicaSparseVector() to full vector {0, 1, 2 Pi} ... ", v1.ToMathematicaSparseVector());
TestUtils.AddTest("Try apply ToMathematicaVector() to sparse vector {Pi, 0, 0, 0, -1} ... ", sv3.ToMathematicaVector());
TestUtils.AddTest("Try apply ToMathematicaFullVector() to sparse vector {Pi, 0, 0, 0, -1} ... ", sv3.ToMathematicaFullVector());
TestUtils.AddTest("Try apply ToMathematicaSparseVector() to sparse vector {Pi, 0, 0, 0, -1} ... ", sv3.ToMathematicaSparseVector());
TestUtils.AddTestCompletionMessage("MathematicaVector Basic Operations Test Completed.");
}
