public class SparseGradient extends Object implements RealFieldElement<SparseGradient>, Serializable
This class plays a similar role to DerivativeStructure, with
a focus on efficiency when dealing with large number of independent variables
and most computation depend only on a few of them, and when only first derivative
is desired. When these conditions are met, this class should be much faster than
DerivativeStructure and use less memory.
| Modifier and Type | Method and Description |
|---|---|
SparseGradient |
abs()
absolute value.
|
SparseGradient |
acos()
Arc cosine operation.
|
SparseGradient |
acosh()
Inverse hyperbolic cosine operation.
|
SparseGradient |
add(double c)
'+' operator.
|
SparseGradient |
add(SparseGradient a)
Compute this + a.
|
void |
addInPlace(SparseGradient a)
Add in place.
|
SparseGradient |
asin()
Arc sine operation.
|
SparseGradient |
asinh()
Inverse hyperbolic sine operation.
|
SparseGradient |
atan()
Arc tangent operation.
|
SparseGradient |
atan2(SparseGradient x)
Two arguments arc tangent operation.
|
static SparseGradient |
atan2(SparseGradient y,
SparseGradient x)
Two arguments arc tangent operation.
|
SparseGradient |
atanh()
Inverse hyperbolic tangent operation.
|
SparseGradient |
cbrt()
Cubic root.
|
SparseGradient |
ceil()
Get the smallest whole number larger than instance.
|
SparseGradient |
compose(double f0,
double f1)
Compute composition of the instance by a univariate function.
|
SparseGradient |
copySign(double sign)
Returns the instance with the sign of the argument.
|
SparseGradient |
copySign(SparseGradient sign)
Returns the instance with the sign of the argument.
|
SparseGradient |
cos()
Cosine operation.
|
SparseGradient |
cosh()
Hyperbolic cosine operation.
|
static SparseGradient |
createConstant(double value)
Factory method creating a constant.
|
static SparseGradient |
createVariable(int idx,
double value)
Factory method creating an independent variable.
|
SparseGradient |
divide(double c)
'÷' operator.
|
SparseGradient |
divide(SparseGradient a)
Compute this ÷ a.
|
boolean |
equals(Object other)
Test for the equality of two sparse gradients.
|
SparseGradient |
exp()
Exponential.
|
SparseGradient |
expm1()
Exponential minus 1.
|
SparseGradient |
floor()
Get the largest whole number smaller than instance.
|
double |
getDerivative(int index)
Get the derivative with respect to a particular index variable.
|
Field<SparseGradient> |
getField()
Get the
Field to which the instance belongs. |
double |
getReal()
Get the real value of the number.
|
double |
getValue()
Get the value of the function.
|
int |
hashCode()
Get a hashCode for the derivative structure.
|
SparseGradient |
hypot(SparseGradient y)
Returns the hypotenuse of a triangle with sides
this and y
- sqrt(this2 +y2)
avoiding intermediate overflow or underflow. |
static SparseGradient |
hypot(SparseGradient x,
SparseGradient y)
Returns the hypotenuse of a triangle with sides
x and y
- sqrt(x2 +y2)
avoiding intermediate overflow or underflow. |
SparseGradient |
linearCombination(double[] a,
SparseGradient[] b)
Compute a linear combination.
|
SparseGradient |
linearCombination(double a1,
SparseGradient b1,
double a2,
SparseGradient b2)
Compute a linear combination.
|
SparseGradient |
linearCombination(double a1,
SparseGradient b1,
double a2,
SparseGradient b2,
double a3,
SparseGradient b3)
Compute a linear combination.
|
SparseGradient |
linearCombination(double a1,
SparseGradient b1,
double a2,
SparseGradient b2,
double a3,
SparseGradient b3,
double a4,
SparseGradient b4)
Compute a linear combination.
|
SparseGradient |
linearCombination(SparseGradient[] a,
SparseGradient[] b)
Compute a linear combination.
|
SparseGradient |
linearCombination(SparseGradient a1,
SparseGradient b1,
SparseGradient a2,
SparseGradient b2)
Compute a linear combination.
|
SparseGradient |
linearCombination(SparseGradient a1,
SparseGradient b1,
SparseGradient a2,
SparseGradient b2,
SparseGradient a3,
SparseGradient b3)
Compute a linear combination.
|
SparseGradient |
linearCombination(SparseGradient a1,
SparseGradient b1,
SparseGradient a2,
SparseGradient b2,
SparseGradient a3,
SparseGradient b3,
SparseGradient a4,
SparseGradient b4)
Compute a linear combination.
|
SparseGradient |
log()
Natural logarithm.
|
SparseGradient |
log10()
Base 10 logarithm.
|
SparseGradient |
log1p()
Shifted natural logarithm.
|
SparseGradient |
multiply(double c)
'×' operator.
|
SparseGradient |
multiply(int n)
Compute n × this.
|
SparseGradient |
multiply(SparseGradient a)
Compute this × a.
|
void |
multiplyInPlace(SparseGradient a)
Multiply in place.
|
SparseGradient |
negate()
Returns the additive inverse of
this element. |
int |
numVars()
Find the number of variables.
|
SparseGradient |
pow(double p)
Power operation.
|
static SparseGradient |
pow(double a,
SparseGradient x)
Compute ax where a is a double and x a
SparseGradient |
SparseGradient |
pow(int n)
Integer power operation.
|
SparseGradient |
pow(SparseGradient e)
Power operation.
|
SparseGradient |
reciprocal()
Returns the multiplicative inverse of
this element. |
SparseGradient |
remainder(double a)
IEEE remainder operator.
|
SparseGradient |
remainder(SparseGradient a)
IEEE remainder operator.
|
SparseGradient |
rint()
Get the whole number that is the nearest to the instance, or the even one if x is exactly half way between two integers.
|
SparseGradient |
rootN(int n)
Nth root.
|
long |
round()
Get the closest long to instance value.
|
SparseGradient |
scalb(int n)
Multiply the instance by a power of 2.
|
SparseGradient |
signum()
Compute the signum of the instance.
|
SparseGradient |
sin()
Sine operation.
|
SparseGradient |
sinh()
Hyperbolic sine operation.
|
SparseGradient |
sqrt()
Square root.
|
SparseGradient |
subtract(double c)
'-' operator.
|
SparseGradient |
subtract(SparseGradient a)
Compute this - a.
|
SparseGradient |
tan()
Tangent operation.
|
SparseGradient |
tanh()
Hyperbolic tangent operation.
|
double |
taylor(double... delta)
Evaluate Taylor expansion of a sparse gradient.
|
SparseGradient |
toDegrees()
Convert radians to degrees, with error of less than 0.5 ULP
|
SparseGradient |
toRadians()
Convert degrees to radians, with error of less than 0.5 ULP
|
public static SparseGradient createConstant(double value)
value - value of the constantpublic static SparseGradient createVariable(int idx, double value)
idx - index of the variablevalue - value of the variablepublic int numVars()
public double getDerivative(int index)
index - index to differentiate with.public double getValue()
public double getReal()
getReal in interface RealFieldElement<SparseGradient>public SparseGradient add(SparseGradient a)
add in interface FieldElement<SparseGradient>a - element to addpublic void addInPlace(SparseGradient a)
This method is designed to be faster when used multiple times in a loop.
The instance is changed here, in order to not change the
instance the add(SparseGradient) method should
be used.
a - instance to addpublic SparseGradient add(double c)
add in interface RealFieldElement<SparseGradient>c - right hand side parameter of the operatorpublic SparseGradient subtract(SparseGradient a)
subtract in interface FieldElement<SparseGradient>a - element to subtractpublic SparseGradient subtract(double c)
subtract in interface RealFieldElement<SparseGradient>c - right hand side parameter of the operatorpublic SparseGradient multiply(SparseGradient a)
multiply in interface FieldElement<SparseGradient>a - element to multiplypublic void multiplyInPlace(SparseGradient a)
This method is designed to be faster when used multiple times in a loop.
The instance is changed here, in order to not change the
instance the add(SparseGradient) method should
be used.
a - instance to multiplypublic SparseGradient multiply(double c)
multiply in interface RealFieldElement<SparseGradient>c - right hand side parameter of the operatorpublic SparseGradient multiply(int n)
multiply in interface FieldElement<SparseGradient>n - Number of times this must be added to itself.public SparseGradient divide(SparseGradient a)
divide in interface FieldElement<SparseGradient>a - element to divide bypublic SparseGradient divide(double c)
divide in interface RealFieldElement<SparseGradient>c - right hand side parameter of the operatorpublic SparseGradient negate()
this element.negate in interface FieldElement<SparseGradient>this.public Field<SparseGradient> getField()
Field to which the instance belongs.getField in interface FieldElement<SparseGradient>Field to which the instance belongspublic SparseGradient remainder(double a)
remainder in interface RealFieldElement<SparseGradient>a - right hand side parameter of the operatorpublic SparseGradient remainder(SparseGradient a)
remainder in interface RealFieldElement<SparseGradient>a - right hand side parameter of the operatorpublic SparseGradient abs()
abs in interface RealFieldElement<SparseGradient>public SparseGradient ceil()
ceil in interface RealFieldElement<SparseGradient>public SparseGradient floor()
floor in interface RealFieldElement<SparseGradient>public SparseGradient rint()
rint in interface RealFieldElement<SparseGradient>public long round()
round in interface RealFieldElement<SparseGradient>RealFieldElement.getReal()public SparseGradient signum()
signum in interface RealFieldElement<SparseGradient>public SparseGradient copySign(SparseGradient sign)
sign argument is treated as positive.copySign in interface RealFieldElement<SparseGradient>sign - the sign for the returned valuesign argumentpublic SparseGradient copySign(double sign)
sign argument is treated as positive.copySign in interface RealFieldElement<SparseGradient>sign - the sign for the returned valuesign argumentpublic SparseGradient scalb(int n)
scalb in interface RealFieldElement<SparseGradient>n - power of 2public SparseGradient hypot(SparseGradient y)
this and y
- sqrt(this2 +y2)
avoiding intermediate overflow or underflow.
hypot in interface RealFieldElement<SparseGradient>y - a valuepublic static SparseGradient hypot(SparseGradient x, SparseGradient y)
x and y
- sqrt(x2 +y2)
avoiding intermediate overflow or underflow.
x - a valuey - a valuepublic SparseGradient reciprocal()
this element.reciprocal in interface FieldElement<SparseGradient>reciprocal in interface RealFieldElement<SparseGradient>this.public SparseGradient sqrt()
sqrt in interface RealFieldElement<SparseGradient>public SparseGradient cbrt()
cbrt in interface RealFieldElement<SparseGradient>public SparseGradient rootN(int n)
rootN in interface RealFieldElement<SparseGradient>n - order of the rootpublic SparseGradient pow(double p)
pow in interface RealFieldElement<SparseGradient>p - power to applypublic SparseGradient pow(int n)
pow in interface RealFieldElement<SparseGradient>n - power to applypublic SparseGradient pow(SparseGradient e)
pow in interface RealFieldElement<SparseGradient>e - exponentpublic static SparseGradient pow(double a, SparseGradient x)
SparseGradienta - number to exponentiatex - power to applypublic SparseGradient exp()
exp in interface RealFieldElement<SparseGradient>public SparseGradient expm1()
expm1 in interface RealFieldElement<SparseGradient>public SparseGradient log()
log in interface RealFieldElement<SparseGradient>public SparseGradient log10()
public SparseGradient log1p()
log1p in interface RealFieldElement<SparseGradient>public SparseGradient cos()
cos in interface RealFieldElement<SparseGradient>public SparseGradient sin()
sin in interface RealFieldElement<SparseGradient>public SparseGradient tan()
tan in interface RealFieldElement<SparseGradient>public SparseGradient acos()
acos in interface RealFieldElement<SparseGradient>public SparseGradient asin()
asin in interface RealFieldElement<SparseGradient>public SparseGradient atan()
atan in interface RealFieldElement<SparseGradient>public SparseGradient atan2(SparseGradient x)
atan2 in interface RealFieldElement<SparseGradient>x - second argument of the arc tangentpublic static SparseGradient atan2(SparseGradient y, SparseGradient x)
y - first argument of the arc tangentx - second argument of the arc tangentpublic SparseGradient cosh()
cosh in interface RealFieldElement<SparseGradient>public SparseGradient sinh()
sinh in interface RealFieldElement<SparseGradient>public SparseGradient tanh()
tanh in interface RealFieldElement<SparseGradient>public SparseGradient acosh()
acosh in interface RealFieldElement<SparseGradient>public SparseGradient asinh()
asinh in interface RealFieldElement<SparseGradient>public SparseGradient atanh()
atanh in interface RealFieldElement<SparseGradient>public SparseGradient toDegrees()
public SparseGradient toRadians()
public double taylor(double... delta)
delta - parameters offsets (Δx, Δy, ...)public SparseGradient compose(double f0, double f1)
f0 - value of the function at (i.e. f(getValue()))f1 - first derivative of the function at
the current point (i.e. f'(getValue()))public SparseGradient linearCombination(SparseGradient[] a, SparseGradient[] b) throws DimensionMismatchException
linearCombination in interface RealFieldElement<SparseGradient>a - Factors.b - Factors.Σi ai bi.DimensionMismatchException - if arrays dimensions don't matchpublic SparseGradient linearCombination(double[] a, SparseGradient[] b)
linearCombination in interface RealFieldElement<SparseGradient>a - Factors.b - Factors.Σi ai bi.public SparseGradient linearCombination(SparseGradient a1, SparseGradient b1, SparseGradient a2, SparseGradient b2)
linearCombination in interface RealFieldElement<SparseGradient>a1 - first factor of the first termb1 - second factor of the first terma2 - first factor of the second termb2 - second factor of the second termRealFieldElement.linearCombination(Object, Object, Object, Object, Object, Object),
RealFieldElement.linearCombination(Object, Object, Object, Object, Object, Object, Object, Object)public SparseGradient linearCombination(double a1, SparseGradient b1, double a2, SparseGradient b2)
linearCombination in interface RealFieldElement<SparseGradient>a1 - first factor of the first termb1 - second factor of the first terma2 - first factor of the second termb2 - second factor of the second termRealFieldElement.linearCombination(double, Object, double, Object, double, Object),
RealFieldElement.linearCombination(double, Object, double, Object, double, Object, double, Object)public SparseGradient linearCombination(SparseGradient a1, SparseGradient b1, SparseGradient a2, SparseGradient b2, SparseGradient a3, SparseGradient b3)
linearCombination in interface RealFieldElement<SparseGradient>a1 - first factor of the first termb1 - second factor of the first terma2 - first factor of the second termb2 - second factor of the second terma3 - first factor of the third termb3 - second factor of the third termRealFieldElement.linearCombination(Object, Object, Object, Object),
RealFieldElement.linearCombination(Object, Object, Object, Object, Object, Object, Object, Object)public SparseGradient linearCombination(double a1, SparseGradient b1, double a2, SparseGradient b2, double a3, SparseGradient b3)
linearCombination in interface RealFieldElement<SparseGradient>a1 - first factor of the first termb1 - second factor of the first terma2 - first factor of the second termb2 - second factor of the second terma3 - first factor of the third termb3 - second factor of the third termRealFieldElement.linearCombination(double, Object, double, Object),
RealFieldElement.linearCombination(double, Object, double, Object, double, Object, double, Object)public SparseGradient linearCombination(SparseGradient a1, SparseGradient b1, SparseGradient a2, SparseGradient b2, SparseGradient a3, SparseGradient b3, SparseGradient a4, SparseGradient b4)
linearCombination in interface RealFieldElement<SparseGradient>a1 - first factor of the first termb1 - second factor of the first terma2 - first factor of the second termb2 - second factor of the second terma3 - first factor of the third termb3 - second factor of the third terma4 - first factor of the third termb4 - second factor of the third termRealFieldElement.linearCombination(Object, Object, Object, Object),
RealFieldElement.linearCombination(Object, Object, Object, Object, Object, Object)public SparseGradient linearCombination(double a1, SparseGradient b1, double a2, SparseGradient b2, double a3, SparseGradient b3, double a4, SparseGradient b4)
linearCombination in interface RealFieldElement<SparseGradient>a1 - first factor of the first termb1 - second factor of the first terma2 - first factor of the second termb2 - second factor of the second terma3 - first factor of the third termb3 - second factor of the third terma4 - first factor of the third termb4 - second factor of the third termRealFieldElement.linearCombination(double, Object, double, Object),
RealFieldElement.linearCombination(double, Object, double, Object, double, Object)public boolean equals(Object other)
Sparse gradients are considered equal if they have the same value and the same derivatives.
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