Class SparseGradient

Method Details

• createConstant

  public static SparseGradient createConstant(double value)

  Factory method creating a constant.

  Parameters:

  value - value of the constant

  Returns:

  a new instance

• createVariable

  public static SparseGradient createVariable(int idx, double value)

  Factory method creating an independent variable.

  Parameters:

  idx - index of the variable

  value - value of the variable

  Returns:

  a new instance

• numVars

  public int numVars()

  Find the number of variables.

  Returns:

  number of variables

• getDerivative

  public double getDerivative(int index)

  Get the derivative with respect to a particular index variable.

  Parameters:

  index - index to differentiate with.

  Returns:

  derivative with respect to a particular index variable

• getValue

  public double getValue()

  Get the value of the function.

  Returns:

  value of the function.

• getReal

  public double getReal()

  Get the real value of the number.

  Specified by:

  getReal in interface RealFieldElement<SparseGradient>

  Returns:

  real value

• add

  public SparseGradient add(SparseGradient a)

  Compute this + a.

  Specified by:

  add in interface FieldElement<SparseGradient>

  Parameters:

  a - element to add

  Returns:

  a new element representing this + a

• addInPlace

  public void addInPlace(SparseGradient a)

  Add in place.

  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.

  Parameters:

  a - instance to add

• add

  public SparseGradient add(double c)

  '+' operator.

  Specified by:

  add in interface RealFieldElement<SparseGradient>

  Parameters:

  c - right hand side parameter of the operator

  Returns:

  this+a

• subtract

  public SparseGradient subtract(SparseGradient a)

  Compute this - a.

  Specified by:

  subtract in interface FieldElement<SparseGradient>

  Parameters:

  a - element to subtract

  Returns:

  a new element representing this - a

• subtract

  public SparseGradient subtract(double c)

  '-' operator.

  Specified by:

  subtract in interface RealFieldElement<SparseGradient>

  Parameters:

  c - right hand side parameter of the operator

  Returns:

  this-a

• multiply

  public SparseGradient multiply(SparseGradient a)

  Compute this × a.

  Specified by:

  multiply in interface FieldElement<SparseGradient>

  Parameters:

  a - element to multiply

  Returns:

  a new element representing this × a

• multiplyInPlace

  public void multiplyInPlace(SparseGradient a)

  Multiply in place.

  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.

  Parameters:

  a - instance to multiply

• multiply

  public SparseGradient multiply(double c)

  '×' operator.

  Specified by:

  multiply in interface RealFieldElement<SparseGradient>

  Parameters:

  c - right hand side parameter of the operator

  Returns:

  this×a

• multiply

  public SparseGradient multiply(int n)

  Compute n × this. Multiplication by an integer number is defined as the following sum n × this = ∑_i=1ⁿ this.

  Specified by:

  multiply in interface FieldElement<SparseGradient>

  Parameters:

  n - Number of times this must be added to itself.

  Returns:

  A new element representing n × this.

• divide

  public SparseGradient divide(SparseGradient a)

  Compute this ÷ a.

  Specified by:

  divide in interface FieldElement<SparseGradient>

  Parameters:

  a - element to divide by

  Returns:

  a new element representing this ÷ a

• divide

  public SparseGradient divide(double c)

  '÷' operator.

  Specified by:

  divide in interface RealFieldElement<SparseGradient>

  Parameters:

  c - right hand side parameter of the operator

  Returns:

  this÷a

• negate

  public SparseGradient negate()

  Returns the additive inverse of this element.

  Specified by:

  negate in interface FieldElement<SparseGradient>

  Returns:

  the opposite of this.

• getField

  public Field<SparseGradient> getField()

  Get the Field to which the instance belongs.

  Specified by:

  getField in interface FieldElement<SparseGradient>

  Returns:

  Field to which the instance belongs

• remainder

  public SparseGradient remainder(double a)

  IEEE remainder operator.

  Specified by:

  remainder in interface RealFieldElement<SparseGradient>

  Parameters:

  a - right hand side parameter of the operator

  Returns:

  this - n × a where n is the closest integer to this/a (the even integer is chosen for n if this/a is halfway between two integers)

• remainder

  public SparseGradient remainder(SparseGradient a)

  IEEE remainder operator.

  Specified by:

  remainder in interface RealFieldElement<SparseGradient>

  Parameters:

  a - right hand side parameter of the operator

  Returns:

  this - n × a where n is the closest integer to this/a (the even integer is chosen for n if this/a is halfway between two integers)

• abs

  public SparseGradient abs()

  absolute value.

  Specified by:

  abs in interface RealFieldElement<SparseGradient>

  Returns:

  abs(this)

• ceil

  public SparseGradient ceil()

  Get the smallest whole number larger than instance.

  Specified by:

  ceil in interface RealFieldElement<SparseGradient>

  Returns:

  ceil(this)

• floor

  public SparseGradient floor()

  Get the largest whole number smaller than instance.

  Specified by:

  floor in interface RealFieldElement<SparseGradient>

  Returns:

  floor(this)

• rint

  public 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.

  Specified by:

  rint in interface RealFieldElement<SparseGradient>

  Returns:

  a double number r such that r is an integer r - 0.5 ≤ this ≤ r + 0.5

• round

  public long round()

  Get the closest long to instance value.

  Specified by:

  round in interface RealFieldElement<SparseGradient>

  Returns:

  closest long to RealFieldElement.getReal()

• signum

  public SparseGradient signum()

  Compute the signum of the instance. The signum is -1 for negative numbers, +1 for positive numbers and 0 otherwise

  Specified by:

  signum in interface RealFieldElement<SparseGradient>

  Returns:

  -1.0, -0.0, +0.0, +1.0 or NaN depending on sign of a

• copySign

  public SparseGradient copySign(SparseGradient sign)

  Returns the instance with the sign of the argument. A NaN sign argument is treated as positive.

  Specified by:

  copySign in interface RealFieldElement<SparseGradient>

  Parameters:

  sign - the sign for the returned value

  Returns:

  the instance with the same sign as the sign argument

• copySign

  public SparseGradient copySign(double sign)

  Returns the instance with the sign of the argument. A NaN sign argument is treated as positive.

  Specified by:

  copySign in interface RealFieldElement<SparseGradient>

  Parameters:

  sign - the sign for the returned value

  Returns:

  the instance with the same sign as the sign argument

• scalb

  public SparseGradient scalb(int n)

  Multiply the instance by a power of 2.

  Specified by:

  scalb in interface RealFieldElement<SparseGradient>

  Parameters:

  n - power of 2

  Returns:

  this × 2ⁿ

• hypot

  public SparseGradient hypot(SparseGradient y)

  Returns the hypotenuse of a triangle with sides this and y - sqrt(this² +y²) avoiding intermediate overflow or underflow.

  • If either argument is infinite, then the result is positive infinity.
  • else, if either argument is NaN then the result is NaN.

  Specified by:

  hypot in interface RealFieldElement<SparseGradient>

  Parameters:

  y - a value

  Returns:

  sqrt(this² +y²)

• hypot

  public 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.

  • If either argument is infinite, then the result is positive infinity.
  • else, if either argument is NaN then the result is NaN.

  Parameters:

  x - a value

  y - a value

  Returns:

  sqrt(x² +y²)

• reciprocal

  public SparseGradient reciprocal()

  Returns the multiplicative inverse of this element.

  Specified by:

  reciprocal in interface FieldElement<SparseGradient>

  Specified by:

  reciprocal in interface RealFieldElement<SparseGradient>

  Returns:

  the inverse of this.

• sqrt

  public SparseGradient sqrt()

  Square root.

  Specified by:

  sqrt in interface RealFieldElement<SparseGradient>

  Returns:

  square root of the instance

• cbrt

  public SparseGradient cbrt()

  Cubic root.

  Specified by:

  cbrt in interface RealFieldElement<SparseGradient>

  Returns:

  cubic root of the instance

• rootN

  public SparseGradient rootN(int n)

  N^th root.

  Specified by:

  rootN in interface RealFieldElement<SparseGradient>

  Parameters:

  n - order of the root

  Returns:

  n^th root of the instance

• pow

  public SparseGradient pow(double p)

  Power operation.

  Specified by:

  pow in interface RealFieldElement<SparseGradient>

  Parameters:

  p - power to apply

  Returns:

  this^p

• pow

  public SparseGradient pow(int n)

  Integer power operation.

  Specified by:

  pow in interface RealFieldElement<SparseGradient>

  Parameters:

  n - power to apply

  Returns:

  thisⁿ

• pow

  public SparseGradient pow(SparseGradient e)

  Power operation.

  Specified by:

  pow in interface RealFieldElement<SparseGradient>

  Parameters:

  e - exponent

  Returns:

  this^e

• pow

  public static SparseGradient pow(double a, SparseGradient x)

  Compute a^x where a is a double and x a SparseGradient

  Parameters:

  a - number to exponentiate

  x - power to apply

  Returns:

  a^x

• exp

  public SparseGradient exp()

  Exponential.

  Specified by:

  exp in interface RealFieldElement<SparseGradient>

  Returns:

  exponential of the instance

• expm1

  public SparseGradient expm1()

  Exponential minus 1.

  Specified by:

  expm1 in interface RealFieldElement<SparseGradient>

  Returns:

  exponential minus one of the instance

• log

  public SparseGradient log()

  Natural logarithm.

  Specified by:

  log in interface RealFieldElement<SparseGradient>

  Returns:

  logarithm of the instance

• log10

  public SparseGradient log10()

  Base 10 logarithm.

  Returns:

  base 10 logarithm of the instance

• log1p

  public SparseGradient log1p()

  Shifted natural logarithm.

  Specified by:

  log1p in interface RealFieldElement<SparseGradient>

  Returns:

  logarithm of one plus the instance

• cos

  public SparseGradient cos()

  Cosine operation.

  Specified by:

  cos in interface RealFieldElement<SparseGradient>

  Returns:

  cos(this)

• sin

  public SparseGradient sin()

  Sine operation.

  Specified by:

  sin in interface RealFieldElement<SparseGradient>

  Returns:

  sin(this)

• tan

  public SparseGradient tan()

  Tangent operation.

  Specified by:

  tan in interface RealFieldElement<SparseGradient>

  Returns:

  tan(this)

• acos

  public SparseGradient acos()

  Arc cosine operation.

  Specified by:

  acos in interface RealFieldElement<SparseGradient>

  Returns:

  acos(this)

• asin

  public SparseGradient asin()

  Arc sine operation.

  Specified by:

  asin in interface RealFieldElement<SparseGradient>

  Returns:

  asin(this)

• atan

  public SparseGradient atan()

  Arc tangent operation.

  Specified by:

  atan in interface RealFieldElement<SparseGradient>

  Returns:

  atan(this)

• atan2

  public SparseGradient atan2(SparseGradient x)

  Two arguments arc tangent operation.

  Specified by:

  atan2 in interface RealFieldElement<SparseGradient>

  Parameters:

  x - second argument of the arc tangent

  Returns:

  atan2(this, x)

• atan2

  public static SparseGradient atan2(SparseGradient y, SparseGradient x)

  Two arguments arc tangent operation.

  Parameters:

  y - first argument of the arc tangent

  x - second argument of the arc tangent

  Returns:

  atan2(y, x)

• cosh

  public SparseGradient cosh()

  Hyperbolic cosine operation.

  Specified by:

  cosh in interface RealFieldElement<SparseGradient>

  Returns:

  cosh(this)

• sinh

  public SparseGradient sinh()

  Hyperbolic sine operation.

  Specified by:

  sinh in interface RealFieldElement<SparseGradient>

  Returns:

  sinh(this)

• tanh

  public SparseGradient tanh()

  Hyperbolic tangent operation.

  Specified by:

  tanh in interface RealFieldElement<SparseGradient>

  Returns:

  tanh(this)

• acosh

  public SparseGradient acosh()

  Inverse hyperbolic cosine operation.

  Specified by:

  acosh in interface RealFieldElement<SparseGradient>

  Returns:

  acosh(this)

• asinh

  public SparseGradient asinh()

  Inverse hyperbolic sine operation.

  Specified by:

  asinh in interface RealFieldElement<SparseGradient>

  Returns:

  asin(this)

• atanh

  public SparseGradient atanh()

  Inverse hyperbolic tangent operation.

  Specified by:

  atanh in interface RealFieldElement<SparseGradient>

  Returns:

  atanh(this)

• toDegrees

  public SparseGradient toDegrees()

  Convert radians to degrees, with error of less than 0.5 ULP

  Returns:

  instance converted into degrees

• toRadians

  public SparseGradient toRadians()

  Convert degrees to radians, with error of less than 0.5 ULP

  Returns:

  instance converted into radians

• taylor

  public double taylor(double... delta)

  Evaluate Taylor expansion of a sparse gradient.

  Parameters:

  delta - parameters offsets (Δx, Δy, ...)

  Returns:

  value of the Taylor expansion at x + Δx, y + Δy, ...

• compose

  public SparseGradient compose(double f0, double f1)

  Compute composition of the instance by a univariate function.

  Parameters:

  f0 - value of the function at (i.e. f(getValue()))

  f1 - first derivative of the function at the current point (i.e. f'(getValue()))

  Returns:

  f(this)

• linearCombination

  public SparseGradient linearCombination(SparseGradient[] a, SparseGradient[] b) throws DimensionMismatchException

  Compute a linear combination.

  Specified by:

  linearCombination in interface RealFieldElement<SparseGradient>

  Parameters:

  a - Factors.

  b - Factors.

  Returns:

  Σi ai bi.

  Throws:

  DimensionMismatchException - if arrays dimensions don't match

• linearCombination

  public SparseGradient linearCombination(double[] a, SparseGradient[] b)

  Compute a linear combination.

  Specified by:

  linearCombination in interface RealFieldElement<SparseGradient>

  Parameters:

  a - Factors.

  b - Factors.

  Returns:

  Σi ai bi.

• linearCombination

  public SparseGradient linearCombination(SparseGradient a1, SparseGradient b1, SparseGradient a2, SparseGradient b2)

  Compute a linear combination.

  Specified by:

  linearCombination in interface RealFieldElement<SparseGradient>

  Parameters:

  a1 - first factor of the first term

  b1 - second factor of the first term

  a2 - first factor of the second term

  b2 - second factor of the second term

  Returns:

  a₁×b₁ + a₂×b₂

  See Also:

  • RealFieldElement.linearCombination(Object, Object, Object, Object, Object, Object)
  • RealFieldElement.linearCombination(Object, Object, Object, Object, Object, Object, Object, Object)

• linearCombination

  public SparseGradient linearCombination(double a1, SparseGradient b1, double a2, SparseGradient b2)

  Compute a linear combination.

  Specified by:

  linearCombination in interface RealFieldElement<SparseGradient>

  Parameters:

  a1 - first factor of the first term

  b1 - second factor of the first term

  a2 - first factor of the second term

  b2 - second factor of the second term

  Returns:

  a₁×b₁ + a₂×b₂

  See Also:

  • RealFieldElement.linearCombination(double, Object, double, Object, double, Object)
  • RealFieldElement.linearCombination(double, Object, double, Object, double, Object, double, Object)

• linearCombination

  public SparseGradient linearCombination(SparseGradient a1, SparseGradient b1, SparseGradient a2, SparseGradient b2, SparseGradient a3, SparseGradient b3)

  Compute a linear combination.

  Specified by:

  linearCombination in interface RealFieldElement<SparseGradient>

  Parameters:

  a1 - first factor of the first term

  b1 - second factor of the first term

  a2 - first factor of the second term

  b2 - second factor of the second term

  a3 - first factor of the third term

  b3 - second factor of the third term

  Returns:

  a₁×b₁ + a₂×b₂ + a₃×b₃

  See Also:

  • RealFieldElement.linearCombination(Object, Object, Object, Object)
  • RealFieldElement.linearCombination(Object, Object, Object, Object, Object, Object, Object, Object)

• linearCombination

  public SparseGradient linearCombination(double a1, SparseGradient b1, double a2, SparseGradient b2, double a3, SparseGradient b3)

  Compute a linear combination.

  Specified by:

  linearCombination in interface RealFieldElement<SparseGradient>

  Parameters:

  a1 - first factor of the first term

  b1 - second factor of the first term

  a2 - first factor of the second term

  b2 - second factor of the second term

  a3 - first factor of the third term

  b3 - second factor of the third term

  Returns:

  a₁×b₁ + a₂×b₂ + a₃×b₃

  See Also:

  • RealFieldElement.linearCombination(double, Object, double, Object)
  • RealFieldElement.linearCombination(double, Object, double, Object, double, Object, double, Object)

• linearCombination

  public SparseGradient linearCombination(SparseGradient a1, SparseGradient b1, SparseGradient a2, SparseGradient b2, SparseGradient a3, SparseGradient b3, SparseGradient a4, SparseGradient b4)

  Compute a linear combination.

  Specified by:

  linearCombination in interface RealFieldElement<SparseGradient>

  Parameters:

  a1 - first factor of the first term

  b1 - second factor of the first term

  a2 - first factor of the second term

  b2 - second factor of the second term

  a3 - first factor of the third term

  b3 - second factor of the third term

  a4 - first factor of the third term

  b4 - second factor of the third term

  Returns:

  a₁×b₁ + a₂×b₂ + a₃×b₃ + a₄×b₄

  See Also:

  • RealFieldElement.linearCombination(Object, Object, Object, Object)
  • RealFieldElement.linearCombination(Object, Object, Object, Object, Object, Object)

• linearCombination

  public SparseGradient linearCombination(double a1, SparseGradient b1, double a2, SparseGradient b2, double a3, SparseGradient b3, double a4, SparseGradient b4)

  Compute a linear combination.

  Specified by:

  linearCombination in interface RealFieldElement<SparseGradient>

  Parameters:

  a1 - first factor of the first term

  b1 - second factor of the first term

  a2 - first factor of the second term

  b2 - second factor of the second term

  a3 - first factor of the third term

  b3 - second factor of the third term

  a4 - first factor of the third term

  b4 - second factor of the third term

  Returns:

  a₁×b₁ + a₂×b₂ + a₃×b₃ + a₄×b₄

  See Also:

  • RealFieldElement.linearCombination(double, Object, double, Object)
  • RealFieldElement.linearCombination(double, Object, double, Object, double, Object)

• equals

  public boolean equals(Object other)

  Test for the equality of two sparse gradients.

  Sparse gradients are considered equal if they have the same value and the same derivatives.

  Overrides:

  equals in class Object

  Parameters:

  other - Object to test for equality to this

  Returns:

  true if two sparse gradients are equal

• hashCode

  public int hashCode()

  Get a hashCode for the derivative structure.

  Overrides:

  hashCode in class Object

  Returns:

  a hash code value for this object

  Since:

  3.2