// (lim x->0) 1/sin(x)
public void CalculateLimit_AndReturnsCorrectLimit_8()
{
var numerator = new List <Summand>
{
new Summand()
};
var denominator = new List <Summand>
{
new Summand
{
Multiplicands = new List <IElementaryFunction>
{
new Sine {
Aparam = 1
}
}
}
};
var normalizedFunction = new NormalizedFunction
{
Numerator = numerator,
Denominator = denominator
};
var result = LimitCalculator.CalculateLimit(normalizedFunction, 0);
result.LimitResultType.Should().Be(LimitResultType.DoesNotExist);
}
// (lim x->-Pi) cos(0.5*x) = 0
public void CalculateLimit_MKD_68_25()
{
var numerator = new List <Summand>
{
new Summand
{
Coefficient = 1,
Multiplicands = new List <IElementaryFunction>
{
new Cosine {
Aparam = 0.5
}
}
},
};
var denominator = new List <Summand>
{
new Summand
{
Coefficient = 1
}
};
var normalizedFunction = new NormalizedFunction
{
Numerator = numerator,
Denominator = denominator
};
var result = LimitCalculator.CalculateLimit(normalizedFunction, -Math.PI);
result.LimitResultType.Should().Be(LimitResultType.RealNumber);
result.Value.Should().Be(0);
}
// (lim x->0) 1/x
public void CalculateLimit_AndReturnsCorrectLimit_6()
{
var numerator = new List <Summand>
{
new Summand()
};
var denominator = new List <Summand>
{
new Summand
{
PolynomialDegree = 1
}
};
var normalizedFunction = new NormalizedFunction
{
Numerator = numerator,
Denominator = denominator
};
var result = LimitCalculator.CalculateLimit(normalizedFunction, 0);
result.LimitResultType.Should().Be(LimitResultType.DoesNotExist);
}
// (lim x->0) 1/-(x^2)
public void CalculateLimit_AndReturnsCorrectLimit_7()
{
var numerator = new List <Summand>
{
new Summand()
};
var denominator = new List <Summand>
{
new Summand
{
Coefficient = -1,
PolynomialDegree = 2
}
};
var normalizedFunction = new NormalizedFunction
{
Numerator = numerator,
Denominator = denominator
};
var result = LimitCalculator.CalculateLimit(normalizedFunction, 0);
result.LimitResultType.Should().Be(LimitResultType.NegativeInfinity);
}
// (lim x->2) 1 / x = 0.5
public void CalculateLimit_MKD_67_2()
{
var numerator = new List <Summand>
{
new Summand
{
Coefficient = 1.0
}
};
var denominator = new List <Summand>
{
new Summand
{
Coefficient = 1.0,
PolynomialDegree = 1
}
};
var normalizedFunction = new NormalizedFunction
{
Numerator = numerator,
Denominator = denominator
};
var result = LimitCalculator.CalculateLimit(normalizedFunction, 2);
result.LimitResultType.Should().Be(LimitResultType.RealNumber);
result.Value.Should().Be(0.5);
}
// (lim x->1) (x^4 - x^3 + x^2 - 3x + 3) / (x^3 - x^2 - x + 1) = +INF
public void CalculateLimit_MKD_74_2()
{
var numerator = new List <Summand>
{
new Summand
{
PolynomialDegree = 4
},
new Summand
{
Coefficient = -1,
PolynomialDegree = 3
},
new Summand
{
PolynomialDegree = 2
},
new Summand
{
Coefficient = -3,
PolynomialDegree = 1
},
new Summand
{
Coefficient = 3,
}
};
var denominator = new List <Summand>
{
new Summand
{
PolynomialDegree = 3
},
new Summand
{
Coefficient = -1,
PolynomialDegree = 2
},
new Summand
{
Coefficient = -1,
PolynomialDegree = 1
},
new Summand
{
Coefficient = 1
}
};
var normalizedFunction = new NormalizedFunction
{
Numerator = numerator,
Denominator = denominator
};
var result = LimitCalculator.CalculateLimit(normalizedFunction, 1);
result.LimitResultType.Should().Be(LimitResultType.PositiveInfinity);
}
// (lim x->-infinity) (x^2+x) = +infinity
public void CalculatePoviloLimit4()
{
var numerator = new List <Summand>
{
new Summand
{
Coefficient = 1,
PolynomialDegree = 2,
},
new Summand
{
Coefficient = 1,
PolynomialDegree = 1,
}
};
var denominator = new List <Summand>
{
new Summand
{
Coefficient = 1
}
};
var normalizedFunction = new NormalizedFunction
{
Denominator = denominator,
Numerator = numerator,
};
var result = LimitCalculator.CalculateLimit(normalizedFunction, 10);
result.LimitResultType.Should().Be(LimitResultType.RealNumber);
result.Value.Should().Be(110.0);
}
// (lim x->1) sin(x - 1) = 0
public void CalculateLimit_MKD_67_4()
{
var numerator = new List <Summand>
{
new Summand
{
Coefficient = 1.0,
Multiplicands = new List <IElementaryFunction>
{
new Sine {
Aparam = 1.0, Bparam = -1.0
}
}
}
};
var denominator = new List <Summand>
{
new Summand
{
Coefficient = 1.0
}
};
var normalizedFunction = new NormalizedFunction
{
Numerator = numerator,
Denominator = denominator
};
var result = LimitCalculator.CalculateLimit(normalizedFunction, 1);
result.LimitResultType.Should().Be(LimitResultType.RealNumber);
result.Value.Should().Be(0.0);
}
// (lim x->11) ln(x) - ln(11) / x-11 = 1/11
public void Calculate_Antano_Limit_8_ln()
{
var numerator = new List <Summand>
{
new Summand
{
Coefficient = 1.0,
Multiplicands = new List <IElementaryFunction>
{
new LogarithmicFunction {
Aparam = 1, Bparam = 0
}
}
},
new Summand
{
Coefficient = -1.0,
Multiplicands = new List <IElementaryFunction>
{
new LogarithmicFunction {
Aparam = 0, Bparam = 11
}
}
}
};
var denominator = new List <Summand>
{
new Summand
{
Coefficient = 1.0,
PolynomialDegree = 1
},
new Summand
{
Coefficient = -11.0
}
};
var normalizedFunction = new NormalizedFunction
{
Numerator = numerator,
Denominator = denominator
};
var result = LimitCalculator.CalculateLimit(normalizedFunction, 11);
result.LimitResultType.Should().Be(LimitResultType.RealNumber);
result.Value.Should().Be(1.0 / 11.0);
}
public void CalculateLimit_MKD_69_30_StringParse()
{
string numeratorString = "sin(x)";
string denominatorString = "ln(1+2*x)";
var normalizedFunction = new NormalizedFunction
{
Numerator = StringToSummand.Parse(numeratorString),
Denominator = StringToSummand.Parse(denominatorString),
};
var result = LimitCalculator.CalculateLimit(normalizedFunction, 0.0);
result.LimitResultType.Should().Be(LimitResultType.RealNumber);
result.Value.Should().Be(0.5);
}
// (lim x->0) (ln(3*x + 5) - ln(5) - 3/5/1*x + 9/25/2*(x^2)) / (x^3) = 27/125/3
public void CalculateLimit_AndReturnsCorrectLimit_10()
{
var numerator = new List <Summand>
{
new Summand
{
Multiplicands = new List <IElementaryFunction>
{
new LogarithmicFunction {
Aparam = 3, Bparam = 5
}
}
},
new Summand
{
Coefficient = -Math.Log(5)
},
new Summand
{
Coefficient = -3.0 / 5,
PolynomialDegree = 1
},
new Summand
{
Coefficient = 9.0 / 25 / 2,
PolynomialDegree = 2
}
};
var denominator = new List <Summand>
{
new Summand
{
PolynomialDegree = 3
}
};
var normalizedFunction = new NormalizedFunction
{
Numerator = numerator,
Denominator = denominator
};
var result = LimitCalculator.CalculateLimit(normalizedFunction, 0);
result.LimitResultType.Should().Be(LimitResultType.RealNumber);
result.Value.Should().Be(27.0 / 125 / 3);
}
// (lim x->PI/2) 1-sinx / cosx^2 = 1/2
public void Calculate_Antano_Limit_12_sin()
{
var numerator = new List <Summand>
{
new Summand
{
Coefficient = -1.0,
Multiplicands = new List <IElementaryFunction>
{
new Sine {
Aparam = 1, Bparam = 0
}
}
},
new Summand
{
Coefficient = 1.0,
}
};
var denominator = new List <Summand>
{
new Summand
{
Coefficient = 1.0,
Multiplicands = new List <IElementaryFunction>
{
new Cosine {
Aparam = 1, Bparam = 0
},
new Cosine {
Aparam = 1, Bparam = 0
}
}
}
};
var normalizedFunction = new NormalizedFunction
{
Numerator = numerator,
Denominator = denominator
};
var result = LimitCalculator.CalculateLimit(normalizedFunction, Math.PI / 2);
result.LimitResultType.Should().Be(LimitResultType.RealNumber);
result.Value.Should().Be(0.5);
}
public void CalculateLimit_AndReturnsCorrectLimit_9_StringParse()
{
string numeratorString = "x^(1/5)";
string denominatorString = "x^(1/3)";
var normalizedFunction = new NormalizedFunction
{
Numerator = StringToSummand.Parse(numeratorString),
Denominator = StringToSummand.Parse(denominatorString),
};
var result = LimitCalculator.CalculateLimit(normalizedFunction, 0);
result.LimitResultType.Should().Be(LimitResultType.PositiveInfinity);
}
public void CalculateLimit_MKD_67_16_StringParse()
{
string numeratorString = "1-cos(Pi*x+2)";
string denominatorString = "1";
var normalizedFunction = new NormalizedFunction
{
Numerator = StringToSummand.Parse(numeratorString),
Denominator = StringToSummand.Parse(denominatorString),
};
var result = LimitCalculator.CalculateLimit(normalizedFunction, -2 / Math.PI);
result.LimitResultType.Should().Be(LimitResultType.RealNumber);
result.Value.Should().Be(0);
}
// (lim x->1) (x^101 - 101*x + 100)/ (x^2 - 2*x + 1) = 5050
public void CalculateLimit_MKD_74_1()
{
var numerator = new List <Summand>
{
new Summand
{
PolynomialDegree = 101
},
new Summand
{
Coefficient = -101,
PolynomialDegree = 1
},
new Summand
{
Coefficient = 100
}
};
var denominator = new List <Summand>
{
new Summand
{
PolynomialDegree = 2
},
new Summand
{
Coefficient = -2,
PolynomialDegree = 1
},
new Summand
{
Coefficient = 1
}
};
var normalizedFunction = new NormalizedFunction
{
Numerator = numerator,
Denominator = denominator
};
var result = LimitCalculator.CalculateLimit(normalizedFunction, 1);
result.LimitResultType.Should().Be(LimitResultType.RealNumber);
result.Value.Should().Be(5050);
}
// (lim x->0) (sin(x) - x) / (sin(x) * x) = 0
public void CalculateLimit_AndReturnsCorrectLimit_1()
{
var numerator = new List <Summand>
{
new Summand
{
Coefficient = 1.0,
Multiplicands = new List <IElementaryFunction>
{
new Sine {
Aparam = 1, Bparam = 0
}
}
},
new Summand
{
Coefficient = -1.0,
PolynomialDegree = 1
}
};
var denominator = new List <Summand>
{
new Summand
{
Coefficient = 1.0,
PolynomialDegree = 1,
Multiplicands = new List <IElementaryFunction>
{
new Sine {
Aparam = 1, Bparam = 0
}
}
}
};
var normalizedFunction = new NormalizedFunction
{
Numerator = numerator,
Denominator = denominator
};
var result = LimitCalculator.CalculateLimit(normalizedFunction, 0);
result.LimitResultType.Should().Be(LimitResultType.RealNumber);
result.Value.Should().Be(0.0);
}
// (lim x->0) (cos(3*x) - cos(7*x)) / x^2 = 20
public void CalculateLimit_MKD_69_27()
{
var numerator = new List <Summand>
{
new Summand
{
Coefficient = 1.0,
Multiplicands = new List <IElementaryFunction>
{
new Cosine {
Aparam = 3
}
}
},
new Summand
{
Coefficient = -1.0,
Multiplicands = new List <IElementaryFunction>
{
new Cosine {
Aparam = 7
}
}
}
};
var denominator = new List <Summand>
{
new Summand
{
Coefficient = 1.0,
PolynomialDegree = 2
}
};
var normalizedFunction = new NormalizedFunction
{
Numerator = numerator,
Denominator = denominator
};
var result = LimitCalculator.CalculateLimit(normalizedFunction, 0.0);
result.LimitResultType.Should().Be(LimitResultType.RealNumber);
result.Value.Should().Be(20);
}
private void CountLimit_Click(object sender, EventArgs e)
{
if (string.IsNullOrWhiteSpace(NuText.Text) || string.IsNullOrWhiteSpace(DeText.Text) || string.IsNullOrWhiteSpace(XgoTo.Text))
{
ErrorBox.Text = "Fields can't be empty";
return;
}
try
{
var normalizedFunction = new NormalizedFunction
{
Numerator = Stack_Numerator.ToList(),
Denominator = Stack_Denominator.ToList()
};
var result = LimitCalculator.CalculateLimit(normalizedFunction, Convert.ToDouble(XgoTo.Text));
if (result.LimitResultType == LimitResultType.RealNumber)
{
Limit_Answer.Text = Convert.ToString(result.Value);
}
if (result.LimitResultType == LimitResultType.DoesNotExist)
{
Limit_Answer.Text = "Not exist";
}
if (result.LimitResultType == LimitResultType.PositiveInfinity)
{
Limit_Answer.Text = "Positive infinity";
}
if (result.LimitResultType == LimitResultType.NegativeInfinity)
{
Limit_Answer.Text = "Negative infinity";
}
}
catch (LimitDoesNotExistException)
{
Limit_Answer.Text = "Not exist";
}
catch (Exception ex)
{
ErrorBox.Text = ex.Message;
}
finally
{
CountLimit.Enabled = false;
}
}
public void CalculateLimit_MKD_67_1_StringParse()
{
string numeratorString = "((5*x^2)-4*x-1)";
string denominatorString = "(x-1)";
// var a = StringToSummand.FindPolynomialDegree("(5*x^2)");
var normalizedFunction = new NormalizedFunction
{
Numerator = StringToSummand.Parse(numeratorString),
Denominator = StringToSummand.Parse(denominatorString)
};
var result = LimitCalculator.CalculateLimit(normalizedFunction, 1);
result.LimitResultType.Should().Be(LimitResultType.RealNumber);
result.Value.Should().Be(6.0);
}
// (lim x->-2) ((x - 6)^(1/3) + 2) / (x + 2) = 1/12
public void CalculateLimit_MKD_68_8()
{
var numerator = new List <Summand>
{
new Summand
{
Coefficient = 1.0,
Multiplicands = new List <IElementaryFunction>
{
new PowerFunction {
Aparam = 1.0, Bparam = -6, PowerNumerator = 1, PowerDenominator = 3
}
}
},
new Summand
{
Coefficient = 2.0
}
};
var denominator = new List <Summand>
{
new Summand
{
Coefficient = 1.0,
PolynomialDegree = 1
},
new Summand
{
Coefficient = 2.0,
}
};
var normalizedFunction = new NormalizedFunction
{
Numerator = numerator,
Denominator = denominator
};
var result = LimitCalculator.CalculateLimit(normalizedFunction, -2.0);
result.LimitResultType.Should().Be(LimitResultType.RealNumber);
result.Value.Should().Be(1.0 / 12.0);
}
// (lim x->-1)(x^2+6x+5) / (x^2-1) = -2
public void Calculate_Antano_Limit_3()
{
var numerator = new List <Summand>
{
new Summand
{
Coefficient = 1.0,
PolynomialDegree = 2
},
new Summand
{
Coefficient = 6.0,
PolynomialDegree = 1
},
new Summand
{
Coefficient = 5.0
}
};
var denominator = new List <Summand>
{
new Summand
{
Coefficient = 1.0,
PolynomialDegree = 2
},
new Summand
{
Coefficient = -1.0
}
};
var normalizedFunction = new NormalizedFunction
{
Numerator = numerator,
Denominator = denominator
};
var result = LimitCalculator.CalculateLimit(normalizedFunction, -1.0);
result.LimitResultType.Should().Be(LimitResultType.RealNumber);
result.Value.Should().Be(-2.0);
}
// (lim x->1) ((x - 1)^(1/2)) / ((x - 1)^(1/3) * (x + 1)^(1/3)) NOT EXISTS
public void CalculateLimit_MKD_68_10()
{
var numerator = new List <Summand>
{
new Summand
{
Coefficient = 1.0,
Multiplicands = new List <IElementaryFunction>
{
new PowerFunction {
Aparam = 1.0, Bparam = -1.0, PowerNumerator = 1, PowerDenominator = 2
}
}
}
};
var denominator = new List <Summand>
{
new Summand
{
Coefficient = 1.0,
Multiplicands = new List <IElementaryFunction>
{
new PowerFunction {
Aparam = 1.0, Bparam = -1.0, PowerNumerator = 1, PowerDenominator = 3
},
new PowerFunction {
Aparam = 1.0, Bparam = 1.0, PowerNumerator = 1, PowerDenominator = 3
}
}
}
};
var normalizedFunction = new NormalizedFunction
{
Numerator = numerator,
Denominator = denominator
};
var result = LimitCalculator.CalculateLimit(normalizedFunction, 1.0);
result.LimitResultType.Should().Be(LimitResultType.DoesNotExist);
}
// (lim x->0)(x) / ((4-x)^1/2)-2 = -4
public void Calculate_Antano_Limit_4()
{
var numerator = new List <Summand>
{
new Summand
{
PolynomialDegree = 1,
Coefficient = 1.0
}
};
var denominator = new List <Summand>
{
new Summand
{
Coefficient = 1.0,
Multiplicands = new List <IElementaryFunction>
{
new PowerFunction {
Aparam = -1, Bparam = 4, PowerNumerator = 1, PowerDenominator = 2
}
}
},
new Summand
{
Coefficient = -2.0
}
};
var normalizedFunction = new NormalizedFunction
{
Numerator = numerator,
Denominator = denominator
};
var result = LimitCalculator.CalculateLimit(normalizedFunction, 0);
result.LimitResultType.Should().Be(LimitResultType.RealNumber);
result.Value.Should().Be(-4.0);
}
// (lim x->1) 5x-x^0.5 = 4
public void CalculatePoviloLimit1()
{
var numerator = new List <Summand>
{
new Summand
{
Coefficient = -1.0,
Multiplicands = new List <IElementaryFunction>
{
new PowerFunction {
Aparam = 1, Bparam = 0, PowerNumerator = 1, PowerDenominator = 2
}
}
},
new Summand
{
Coefficient = 5.0,
PolynomialDegree = 1,
}
};
var denominator = new List <Summand>
{
new Summand
{
Coefficient = 1
}
};
var normalizedFunction = new NormalizedFunction
{
Numerator = numerator,
Denominator = denominator
};
var result = LimitCalculator.CalculateLimit(normalizedFunction, 1);
result.LimitResultType.Should().Be(LimitResultType.RealNumber);
result.Value.Should().Be(4);
}
// x->-1 (x^3+1)/sin(x+1)
public void Kuznecov_15_3()
{
var numerator = new List <Summand>
{
new Summand
{
Coefficient = 1.0,
PolynomialDegree = 3
},
new Summand
{
Coefficient = 1.0,
},
};
var denominator = new List <Summand>
{
new Summand
{
Coefficient = 1.0,
Multiplicands = new List <IElementaryFunction>
{
new Sine {
Aparam = 1.0, Bparam = 1.0
}
}
}
};
var normalizedFunction = new NormalizedFunction
{
Numerator = numerator,
Denominator = denominator
};
var result = LimitCalculator.CalculateLimit(normalizedFunction, -1);
result.LimitResultType.Should().Be(LimitResultType.RealNumber);
result.Value.Should().Be(3.0);
}
// (lim x->0) (x^(1/5)) / (x^(1/3)) = +INF
public void CalculateLimit_AndReturnsCorrectLimit_9()
{
var numerator = new List <Summand>
{
new Summand
{
Multiplicands = new List <IElementaryFunction>
{
new PowerFunction()
{
Aparam = 1, PowerNumerator = 1, PowerDenominator = 5
}
}
}
};
var denominator = new List <Summand>
{
new Summand
{
Multiplicands = new List <IElementaryFunction>
{
new PowerFunction {
Aparam = 1, PowerNumerator = 1, PowerDenominator = 3
}
}
}
};
var normalizedFunction = new NormalizedFunction
{
Numerator = numerator,
Denominator = denominator
};
var result = LimitCalculator.CalculateLimit(normalizedFunction, 0);
result.LimitResultType.Should().Be(LimitResultType.PositiveInfinity);
}
// (lim x->0) sin (x + 3) = sin(3) ~ 0.141120008059867
public void CalculateLimit_AndReturnsCorrectLimit_5()
{
var numerator = new List <Summand>
{
new Summand
{
Coefficient = 1.0,
Multiplicands = new List <IElementaryFunction>
{
new Sine()
{
Aparam = 1.0,
Bparam = 3
}
}
}
};
var denominator = new List <Summand>
{
new Summand
{
Coefficient = 1.0
}
};
var normalizedFunction = new NormalizedFunction
{
Numerator = numerator,
Denominator = denominator
};
var result = LimitCalculator.CalculateLimit(normalizedFunction, 0);
result.LimitResultType.Should().Be(LimitResultType.RealNumber);
MathHelper.AreApproximatelyEqual(result.Value, 0.141, 0.005).Should().BeTrue();
}
// (lim x->0) x / 2^x = 0
public void Calculate_Antano_Limit_9_EX()
{
var numerator = new List <Summand>
{
new Summand
{
Coefficient = 1.0,
PolynomialDegree = 1
}
};
var denominator = new List <Summand>
{
new Summand
{
Coefficient = 1.0,
Multiplicands = new List <IElementaryFunction>
{
new ExponentialFunction {
Aparam = 2, Bparam = 0
},
}
}
};
var normalizedFunction = new NormalizedFunction
{
Numerator = numerator,
Denominator = denominator
};
var result = LimitCalculator.CalculateLimit(normalizedFunction, 0);
result.LimitResultType.Should().Be(LimitResultType.RealNumber);
result.Value.Should().Be(0);
}
public static LimitResult CalculateLimit(NormalizedFunction normalizedFunction, double argument)
{
var raisedNumerator = normalizedFunction.Numerator.SelectMany(RaiseSumsToPower);
var raisedDenominator = normalizedFunction.Denominator.SelectMany(RaiseSumsToPower);
if (!MathHelper.IsZero(argument))
{
raisedNumerator = TransformArgumentToZero(raisedNumerator, argument);
raisedDenominator = TransformArgumentToZero(raisedDenominator, argument);
}
var expandedNumerator = PerformTaylorExpansion(raisedNumerator);
var expandedDenominator = PerformTaylorExpansion(raisedDenominator);
var numeratorMinPolynomialWithoutO = expandedNumerator.FirstOrDefault(s => s.LittleODegree == 0);
var denominatorMinPolynomialWithoutO = expandedDenominator.FirstOrDefault(s => s.LittleODegree == 0);
if (denominatorMinPolynomialWithoutO == null)
{
return(new LimitResult
{
LimitResultType = LimitResultType.DoesNotExist,
});
}
if (numeratorMinPolynomialWithoutO == null)
{
return(new LimitResult
{
LimitResultType = LimitResultType.RealNumber,
Value = 0
});
}
var degreeNumerator = numeratorMinPolynomialWithoutO.PolynomialDegree *
denominatorMinPolynomialWithoutO.PolynomialDegreeDenominator
-
denominatorMinPolynomialWithoutO.PolynomialDegree *
numeratorMinPolynomialWithoutO.PolynomialDegreeDenominator;
var degreeDenominator = denominatorMinPolynomialWithoutO.PolynomialDegreeDenominator *
numeratorMinPolynomialWithoutO.PolynomialDegreeDenominator;
if (degreeNumerator == 0)
{
return(new LimitResult
{
LimitResultType = LimitResultType.RealNumber,
Value = numeratorMinPolynomialWithoutO.Coefficient / denominatorMinPolynomialWithoutO.Coefficient
});
}
var gcd = MathHelper.GreatestCommonDivisor(degreeNumerator >= 0 ? degreeNumerator : -degreeNumerator,
degreeDenominator);
degreeNumerator /= gcd;
degreeDenominator /= gcd;
if (degreeNumerator > 0 && (degreeDenominator == 1 || degreeNumerator % 2 == 0))
{
return(new LimitResult
{
LimitResultType = LimitResultType.RealNumber,
Value = 0
});
}
if (degreeNumerator > 0 && degreeNumerator % 2 == 1)
{
return(new LimitResult
{
LimitResultType = LimitResultType.DoesNotExist,
});
}
degreeNumerator = -degreeNumerator;
if (degreeNumerator % 2 == 1)
{
return(new LimitResult {
LimitResultType = LimitResultType.DoesNotExist
});
}
if (numeratorMinPolynomialWithoutO.Coefficient * denominatorMinPolynomialWithoutO.Coefficient > 0)
{
return(new LimitResult {
LimitResultType = LimitResultType.PositiveInfinity
});
}
return(new LimitResult {
LimitResultType = LimitResultType.NegativeInfinity
});
}
private static int Main()
{
// The svm functions use column vectors to contain a lot of the data on which they
// operate. So the first thing we do here is declare a convenient typedef.
// This typedef declares a matrix with 2 rows and 1 column. It will be the object that
// contains each of our 2 dimensional samples. (Note that if you wanted more than 2
// features in this vector you can simply change the 2 to something else. Or if you
// don't know how many features you want until runtime then you can put a 0 here and
// use the matrix.set_size() member function)
//typedef matrix<double, 2, 1 > sample_type;
// This is a typedef for the type of kernel we are going to use in this example. In
// this case I have selected the radial basis kernel that can operate on our 2D
// sample_type objects
//typedef radial_basis_kernel<sample_type> kernel_type;
// Now we make objects to contain our samples and their respective labels.
var samples = new List <SampleType>();
var labels = new List <double>();
// Now let's put some data into our samples and labels objects. We do this by looping
// over a bunch of points and labeling them according to their distance from the
// origin.
for (var r = -20; r <= 20; ++r)
{
for (var c = -20; c <= 20; ++c)
{
var samp = new SampleType();
samp.SetSize(2, 1);
samp[0] = r;
samp[1] = c;
samples.Add(samp);
// if this point is less than 10 from the origin
if (Math.Sqrt((double)r * r + c * c) <= 10)
{
labels.Add(+1);
}
else
{
labels.Add(-1);
}
}
}
// Here we normalize all the samples by subtracting their mean and dividing by their
// standard deviation. This is generally a good idea since it often heads off
// numerical stability problems and also prevents one large feature from smothering
// others. Doing this doesn't matter much in this example so I'm just doing this here
// so you can see an easy way to accomplish this with the library.
using (var normalizer = new VectorNormalizer <SampleType>())
{
// let the normalizer learn the mean and standard deviation of the samples
normalizer.Train(samples);
// now normalize each sample
for (var i = 0; i < samples.Count; ++i)
{
var ret = normalizer.Operator(samples[i]);
samples[i].Dispose();
samples[i] = ret;
}
// Now that we have some data we want to train on it. However, there are two
// parameters to the training. These are the nu and gamma parameters. Our choice for
// these parameters will influence how good the resulting decision function is. To
// test how good a particular choice of these parameters is we can use the
// cross_validate_trainer() function to perform n-fold cross validation on our training
// data. However, there is a problem with the way we have sampled our distribution
// above. The problem is that there is a definite ordering to the samples. That is,
// the first half of the samples look like they are from a different distribution than
// the second half. This would screw up the cross validation process but we can fix it
// by randomizing the order of the samples with the following function call.
Dlib.RandomizeSamples(samples, labels);
// The nu parameter has a maximum value that is dependent on the ratio of the +1 to -1
// labels in the training data. This function finds that value.
double maxNu = Dlib.MaximumNu(labels);
// here we make an instance of the svm_nu_trainer object that uses our kernel type.
using (var trainer = new SvmNuTrainer <double, RadialBasisKernel <double, Matrix <double> > >())
{
// Now we loop over some different nu and gamma values to see how good they are. Note
// that this is a very simple way to try out a few possible parameter choices. You
// should look at the model_selection_ex.cpp program for examples of more sophisticated
// strategies for determining good parameter choices.
Console.WriteLine("doing cross validation");
for (var gamma = 0.00001; gamma <= 1; gamma *= 5)
{
for (var nu = 0.00001; nu < maxNu; nu *= 5)
{
// tell the trainer the parameters we want to use
using (var kernel = new RadialBasisKernel <double, Matrix <double> >(gamma, 0, 0))
{
trainer.Kernel = kernel;
trainer.Nu = nu;
Console.Write($"gamma: {gamma} nu: {nu}");
// Print out the cross validation accuracy for 3-fold cross validation using
// the current gamma and nu. cross_validate_trainer() returns a row vector.
// The first element of the vector is the fraction of +1 training examples
// correctly classified and the second number is the fraction of -1 training
// examples correctly classified.
using (var ret = Dlib.CrossValidateTrainer(trainer, samples, labels, 3))
Console.Write($" cross validation accuracy: {ret}");
}
}
}
// From looking at the output of the above loop it turns out that a good value for nu
// and gamma for this problem is 0.15625 for both. So that is what we will use.
// Now we train on the full set of data and obtain the resulting decision function. We
// use the value of 0.15625 for nu and gamma. The decision function will return values
// >= 0 for samples it predicts are in the +1 class and numbers < 0 for samples it
// predicts to be in the -1 class.
using (var kernel = new RadialBasisKernel <double, Matrix <double> >(0.15625, 0, 0))
{
trainer.Kernel = kernel;
trainer.Nu = 0.15625;
// Here we are making an instance of the normalized_function object. This object
// provides a convenient way to store the vector normalization information along with
// the decision function we are going to learn.
var learnedFunction = new NormalizedFunction <double, DecisionFunction <double, RadialBasisKernel <double, Matrix <double> > > >();
learnedFunction.Normalizer = normalizer; // save normalization information
using (var function = trainer.Train(samples, labels))
{
learnedFunction.Function = function; // perform the actual SVM training and save the results
// print out the number of support vectors in the resulting decision function
Console.WriteLine();
// ToDo: must support nested matrix
//Console.WriteLine($"number of support vectors in our learned_function is {learnedFunction.Function.basis_vectors.size()}");
}
// Now let's try this decision_function on some samples we haven't seen before.
using (var sample = new SampleType())
{
sample.SetSize(2, 1);
sample[0] = 3.123;
sample[1] = 2;
Console.WriteLine($"This is a +1 class example, the classifier output is {learnedFunction.Operator(sample)}");
sample[0] = 3.123;
sample[1] = 9.3545;
Console.WriteLine($"This is a +1 class example, the classifier output is {learnedFunction.Operator(sample)}");
sample[0] = 13.123;
sample[1] = 9.3545;
Console.WriteLine($"This is a -1 class example, the classifier output is {learnedFunction.Operator(sample)}");
sample[0] = 13.123;
sample[1] = 0;
Console.WriteLine($"This is a -1 class example, the classifier output is {learnedFunction.Operator(sample)}");
}
// We can also train a decision function that reports a well conditioned probability
// instead of just a number > 0 for the +1 class and < 0 for the -1 class. An example
// of doing that follows:
var learnedProbabilisticFunction = new NormalizedFunction <double, ProbabilisticDecisionFunction <double, RadialBasisKernel <double, Matrix <double> > > >();
learnedProbabilisticFunction.Normalizer = normalizer;
using (var function = Dlib.TrainProbabilisticDecisionFunction <double,
RadialBasisKernel <double, Matrix <double> >,
SvmNuTrainer <double, RadialBasisKernel <double, Matrix <double> > > >(trainer, samples, labels, 3))
{
learnedProbabilisticFunction.Function = function;
// Now we have a function that returns the probability that a given sample is of the +1 class.
// print out the number of support vectors in the resulting decision function.
// (it should be the same as in the one above)
Console.WriteLine();
// ToDo: must support nested matrix
//Console.WriteLine($"number of support vectors in our learned_pfunct is {learnedProbabilisticFunction.Function.DecisionFunct.BasisVectors.size()}");
}
using (var sample = new SampleType())
{
sample.SetSize(2, 1);
sample[0] = 3.123;
sample[1] = 2;
Console.WriteLine($"This +1 class example should have high probability. Its probability is: {learnedProbabilisticFunction.Operator(sample)}");
sample[0] = 3.123;
sample[1] = 9.3545;
Console.WriteLine($"This +1 class example should have high probability. Its probability is: {learnedProbabilisticFunction.Operator(sample)}");
sample[0] = 13.123;
sample[1] = 9.3545;
Console.WriteLine($"This -1 class example should have low probability. Its probability is: {learnedProbabilisticFunction.Operator(sample)}");
sample[0] = 13.123;
sample[1] = 0;
Console.WriteLine($"This -1 class example should have low probability. Its probability is: {learnedProbabilisticFunction.Operator(sample)}");
}
// Another thing that is worth knowing is that just about everything in dlib is
// serializable. So for example, you can save the learned_pfunct object to disk and
// recall it later like so:
NormalizedFunction <double, ProbabilisticDecisionFunction <double, RadialBasisKernel <double, Matrix <double> > > > .Serialize("saved_function.dat", learnedProbabilisticFunction);
// Now let's open that file back up and load the function object it contains.
learnedProbabilisticFunction.Dispose();
learnedProbabilisticFunction = NormalizedFunction <double, ProbabilisticDecisionFunction <double, RadialBasisKernel <double, Matrix <double> > > > .Deserialize("saved_function.dat");
// Note that there is also an example program that comes with dlib called
// the file_to_code_ex.cpp example. It is a simple program that takes a
// file and outputs a piece of C++ code that is able to fully reproduce the
// file's contents in the form of a std::string object. So you can use that
// along with the std::istringstream to save learned decision functions
// inside your actual C++ code files if you want.
// Note that there is also an example program that comes with dlib called the
// file_to_code_ex.cpp example. It is a simple program that takes a file and outputs a
// piece of C++ code that is able to fully reproduce the file's contents in the form of
// a std::string object. So you can use that along with the std::istringstream to save
// learned decision functions inside your actual C++ code files if you want.
// Lastly, note that the decision functions we trained above involved well over 200
// basis vectors. Support vector machines in general tend to find decision functions
// that involve a lot of basis vectors. This is significant because the more basis
// vectors in a decision function, the longer it takes to classify new examples. So
// dlib provides the ability to find an approximation to the normal output of a trainer
// using fewer basis vectors.
// Here we determine the cross validation accuracy when we approximate the output using
// only 10 basis vectors. To do this we use the reduced2() function. It takes a
// trainer object and the number of basis vectors to use and returns a new trainer
// object that applies the necessary post processing during the creation of decision
// function objects.
using (var reduced = Dlib.Reduced2 <double,
RadialBasisKernel <double, Matrix <double> >,
SvmNuTrainer <double, RadialBasisKernel <double, Matrix <double> > > >(trainer, 10))
{
Console.WriteLine();
using (var ret = Dlib.CrossValidateTrainer(reduced, samples, labels, 3))
Console.Write($"cross validation accuracy with only 10 support vectors: {ret}");
}
// Let's print out the original cross validation score too for comparison.
using (var ret2 = Dlib.CrossValidateTrainer(trainer, samples, labels, 3))
Console.Write($"cross validation accuracy with all the original support vectors: {ret2}");
// When you run this program you should see that, for this problem, you can reduce the
// number of basis vectors down to 10 without hurting the cross validation accuracy.
// To get the reduced decision function out we would just do this:
using (var reduced = Dlib.Reduced2 <double,
RadialBasisKernel <double, Matrix <double> >,
SvmNuTrainer <double, RadialBasisKernel <double, Matrix <double> > > >(trainer, 10))
using (var function = reduced.Train(samples, labels))
learnedFunction.Function = function;
// And similarly for the probabilistic_decision_function:
using (var reduced = Dlib.Reduced2 <double,
RadialBasisKernel <double, Matrix <double> >,
SvmNuTrainer <double, RadialBasisKernel <double, Matrix <double> > > >(trainer, 10))
using (var function = Dlib.TrainProbabilisticDecisionFunction(reduced, samples, labels, 3))
learnedProbabilisticFunction.Function = function;
learnedFunction.Dispose();
learnedProbabilisticFunction.Dispose();
}
}
}
return(0);
}
