DSCompiler (Hipparchus 2.2 API)

java.lang.Object
- org.hipparchus.analysis.differentiation.DSCompiler

```
public class DSCompiler
extends Object
```
Class holding "compiled" computation rules for derivative structures.
This class implements the computation rules described in Dan Kalman's paper Doubly Recursive Multivariate Automatic Differentiation, Mathematics Magazine, vol. 75, no. 3, June 2002. However, in order to avoid performances bottlenecks, the recursive rules are "compiled" once in an unfold form. This class does this recursion unrolling and stores the computation rules as simple loops with pre-computed indirection arrays.

This class maps all derivative computation into single dimension arrays that hold the value and partial derivatives. The class does not hold these arrays, which remains under the responsibility of the caller. For each combination of number of free parameters and derivation order, only one compiler is necessary, and this compiler will be used to perform computations on all arrays provided to it, which can represent hundreds or thousands of different parameters kept together with all their partial derivatives.

The arrays on which compilers operate contain only the partial derivatives together with the 0^th derivative, i.e. the value. The partial derivatives are stored in a compiler-specific order, which can be retrieved using methods getPartialDerivativeIndex and getPartialDerivativeOrders(int). The value is guaranteed to be stored as the first element (i.e. the getPartialDerivativeIndex method returns 0 when called with 0 for all derivation orders and getPartialDerivativeOrders returns an array filled with 0 when called with 0 as the index).

Note that the ordering changes with number of parameters and derivation order. For example given 2 parameters x and y, df/dy is stored at index 2 when derivation order is set to 1 (in this case the array has three elements: f, df/dx and df/dy). If derivation order is set to 2, then df/dy will be stored at index 3 (in this case the array has six elements: f, df/dx, d²f/dxdx, df/dy, d²f/dxdy and d²f/dydy).

Given this structure, users can perform some simple operations like adding, subtracting or multiplying constants and negating the elements by themselves, knowing if they want to mutate their array or create a new array. These simple operations are not provided by the compiler. The compiler provides only the more complex operations between several arrays.

This class is mainly used as the engine for scalar variable DerivativeStructure. It can also be used directly to hold several variables in arrays for more complex data structures. User can for example store a vector of n variables depending on three x, y and z free parameters in one array as follows:
```
   // parameter 0 is x, parameter 1 is y, parameter 2 is z
   int parameters = 3;
   DSCompiler compiler = DSCompiler.getCompiler(parameters, order);
   int size = compiler.getSize();

   // pack all elements in a single array
   double[] array = new double[n * size];
   for (int i = 0; i < n; ++i) {

     // we know value is guaranteed to be the first element
     array[i * size] = v[i];

     // we don't know where first derivatives are stored, so we ask the compiler
     array[i * size + compiler.getPartialDerivativeIndex(1, 0, 0) = dvOnDx[i][0];
     array[i * size + compiler.getPartialDerivativeIndex(0, 1, 0) = dvOnDy[i][0];
     array[i * size + compiler.getPartialDerivativeIndex(0, 0, 1) = dvOnDz[i][0];

     // we let all higher order derivatives set to 0

   }
 
```
Then in another function, user can perform some operations on all elements stored in the single array, such as a simple product of all variables:
```
   // compute the product of all elements
   double[] product = new double[size];
   prod[0] = 1.0;
   for (int i = 0; i < n; ++i) {
     double[] tmp = product.clone();
     compiler.multiply(tmp, 0, array, i * size, product, 0);
   }

   // value
   double p = product[0];

   // first derivatives
   double dPdX = product[compiler.getPartialDerivativeIndex(1, 0, 0)];
   double dPdY = product[compiler.getPartialDerivativeIndex(0, 1, 0)];
   double dPdZ = product[compiler.getPartialDerivativeIndex(0, 0, 1)];

   // cross derivatives (assuming order was at least 2)
   double dPdXdX = product[compiler.getPartialDerivativeIndex(2, 0, 0)];
   double dPdXdY = product[compiler.getPartialDerivativeIndex(1, 1, 0)];
   double dPdXdZ = product[compiler.getPartialDerivativeIndex(1, 0, 1)];
   double dPdYdY = product[compiler.getPartialDerivativeIndex(0, 2, 0)];
   double dPdYdZ = product[compiler.getPartialDerivativeIndex(0, 1, 1)];
   double dPdZdZ = product[compiler.getPartialDerivativeIndex(0, 0, 2)];
 
```
See Also:

DerivativeStructure, FieldDerivativeStructure

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`void`	`acos(double[] operand, int operandOffset, double[] result, int resultOffset)` Compute arc cosine of a derivative structure.
`<T extends CalculusFieldElement<T>> void`	`acos(T[] operand, int operandOffset, T[] result, int resultOffset)` Compute arc cosine of a derivative structure.
`void`	`acosh(double[] operand, int operandOffset, double[] result, int resultOffset)` Compute inverse hyperbolic cosine of a derivative structure.
`<T extends CalculusFieldElement<T>> void`	`acosh(T[] operand, int operandOffset, T[] result, int resultOffset)` Compute inverse hyperbolic cosine of a derivative structure.
`void`	`add(double[] lhs, int lhsOffset, double[] rhs, int rhsOffset, double[] result, int resultOffset)` Perform addition of two derivative structures.
`<T extends CalculusFieldElement<T>> void`	`add(T[] lhs, int lhsOffset, T[] rhs, int rhsOffset, T[] result, int resultOffset)` Perform addition of two derivative structures.
`void`	`asin(double[] operand, int operandOffset, double[] result, int resultOffset)` Compute arc sine of a derivative structure.
`<T extends CalculusFieldElement<T>> void`	`asin(T[] operand, int operandOffset, T[] result, int resultOffset)` Compute arc sine of a derivative structure.
`void`	`asinh(double[] operand, int operandOffset, double[] result, int resultOffset)` Compute inverse hyperbolic sine of a derivative structure.
`<T extends CalculusFieldElement<T>> void`	`asinh(T[] operand, int operandOffset, T[] result, int resultOffset)` Compute inverse hyperbolic sine of a derivative structure.
`void`	`atan(double[] operand, int operandOffset, double[] result, int resultOffset)` Compute arc tangent of a derivative structure.
`<T extends CalculusFieldElement<T>> void`	`atan(T[] operand, int operandOffset, T[] result, int resultOffset)` Compute arc tangent of a derivative structure.
`void`	`atan2(double[] y, int yOffset, double[] x, int xOffset, double[] result, int resultOffset)` Compute two arguments arc tangent of a derivative structure.
`<T extends CalculusFieldElement<T>> void`	`atan2(T[] y, int yOffset, T[] x, int xOffset, T[] result, int resultOffset)` Compute two arguments arc tangent of a derivative structure.
`void`	`atanh(double[] operand, int operandOffset, double[] result, int resultOffset)` Compute inverse hyperbolic tangent of a derivative structure.
`<T extends CalculusFieldElement<T>> void`	`atanh(T[] operand, int operandOffset, T[] result, int resultOffset)` Compute inverse hyperbolic tangent of a derivative structure.
`void`	`checkCompatibility(DSCompiler compiler)` Check rules set compatibility.
`void`	`compose(double[] operand, int operandOffset, double[] f, double[] result, int resultOffset)` Compute composition of a derivative structure by a function.
`<T extends CalculusFieldElement<T>> void`	`compose(T[] operand, int operandOffset, double[] f, T[] result, int resultOffset)` Compute composition of a derivative structure by a function.
`<T extends CalculusFieldElement<T>> void`	`compose(T[] operand, int operandOffset, T[] f, T[] result, int resultOffset)` Compute composition of a derivative structure by a function.
`void`	`cos(double[] operand, int operandOffset, double[] result, int resultOffset)` Compute cosine of a derivative structure.
`<T extends CalculusFieldElement<T>> void`	`cos(T[] operand, int operandOffset, T[] result, int resultOffset)` Compute cosine of a derivative structure.
`void`	`cosh(double[] operand, int operandOffset, double[] result, int resultOffset)` Compute hyperbolic cosine of a derivative structure.
`<T extends CalculusFieldElement<T>> void`	`cosh(T[] operand, int operandOffset, T[] result, int resultOffset)` Compute hyperbolic cosine of a derivative structure.
`void`	`divide(double[] lhs, int lhsOffset, double[] rhs, int rhsOffset, double[] result, int resultOffset)` Perform division of two derivative structures.
`<T extends CalculusFieldElement<T>> void`	`divide(T[] lhs, int lhsOffset, T[] rhs, int rhsOffset, T[] result, int resultOffset)` Perform division of two derivative structures.
`void`	`exp(double[] operand, int operandOffset, double[] result, int resultOffset)` Compute exponential of a derivative structure.
`<T extends CalculusFieldElement<T>> void`	`exp(T[] operand, int operandOffset, T[] result, int resultOffset)` Compute exponential of a derivative structure.
`void`	`expm1(double[] operand, int operandOffset, double[] result, int resultOffset)` Compute exp(x) - 1 of a derivative structure.
`<T extends CalculusFieldElement<T>> void`	`expm1(T[] operand, int operandOffset, T[] result, int resultOffset)` Compute exp(x) - 1 of a derivative structure.
`static DSCompiler`	`getCompiler(int parameters, int order)` Get the compiler for number of free parameters and order.
`int`	`getFreeParameters()` Get the number of free parameters.
`int`	`getOrder()` Get the derivation order.
`int`	`getPartialDerivativeIndex(int... orders)` Get the index of a partial derivative in the array.
`int[]`	`getPartialDerivativeOrders(int index)` Get the derivation orders for a specific index in the array.
`int`	`getPartialDerivativeOrdersSum(int index)` Get the sum of derivation orders for a specific index in the array.
`int`	`getSize()` Get the array size required for holding partial derivatives data.
`void`	`linearCombination(double a1, double[] c1, int offset1, double a2, double[] c2, int offset2, double[] result, int resultOffset)` Compute linear combination.
`void`	`linearCombination(double a1, double[] c1, int offset1, double a2, double[] c2, int offset2, double a3, double[] c3, int offset3, double[] result, int resultOffset)` Compute linear combination.
`void`	`linearCombination(double a1, double[] c1, int offset1, double a2, double[] c2, int offset2, double a3, double[] c3, int offset3, double a4, double[] c4, int offset4, double[] result, int resultOffset)` Compute linear combination.
`<T extends CalculusFieldElement<T>> void`	`linearCombination(double a1, T[] c1, int offset1, double a2, T[] c2, int offset2, double a3, T[] c3, int offset3, double a4, T[] c4, int offset4, T[] result, int resultOffset)` Compute linear combination.
`<T extends CalculusFieldElement<T>> void`	`linearCombination(double a1, T[] c1, int offset1, double a2, T[] c2, int offset2, double a3, T[] c3, int offset3, T[] result, int resultOffset)` Compute linear combination.
`<T extends CalculusFieldElement<T>> void`	`linearCombination(double a1, T[] c1, int offset1, double a2, T[] c2, int offset2, T[] result, int resultOffset)` Compute linear combination.
`<T extends CalculusFieldElement<T>> void`	`linearCombination(T a1, T[] c1, int offset1, T a2, T[] c2, int offset2, T[] result, int resultOffset)` Compute linear combination.
`<T extends CalculusFieldElement<T>> void`	`linearCombination(T a1, T[] c1, int offset1, T a2, T[] c2, int offset2, T a3, T[] c3, int offset3, T[] result, int resultOffset)` Compute linear combination.
`<T extends CalculusFieldElement<T>> void`	`linearCombination(T a1, T[] c1, int offset1, T a2, T[] c2, int offset2, T a3, T[] c3, int offset3, T a4, T[] c4, int offset4, T[] result, int resultOffset)` Compute linear combination.
`void`	`log(double[] operand, int operandOffset, double[] result, int resultOffset)` Compute natural logarithm of a derivative structure.
`<T extends CalculusFieldElement<T>> void`	`log(T[] operand, int operandOffset, T[] result, int resultOffset)` Compute natural logarithm of a derivative structure.
`void`	`log10(double[] operand, int operandOffset, double[] result, int resultOffset)` Computes base 10 logarithm of a derivative structure.
`<T extends CalculusFieldElement<T>> void`	`log10(T[] operand, int operandOffset, T[] result, int resultOffset)` Computes base 10 logarithm of a derivative structure.
`void`	`log1p(double[] operand, int operandOffset, double[] result, int resultOffset)` Computes shifted logarithm of a derivative structure.
`<T extends CalculusFieldElement<T>> void`	`log1p(T[] operand, int operandOffset, T[] result, int resultOffset)` Computes shifted logarithm of a derivative structure.
`void`	`multiply(double[] lhs, int lhsOffset, double[] rhs, int rhsOffset, double[] result, int resultOffset)` Perform multiplication of two derivative structures.
`<T extends CalculusFieldElement<T>> void`	`multiply(T[] lhs, int lhsOffset, T[] rhs, int rhsOffset, T[] result, int resultOffset)` Perform multiplication of two derivative structures.
`void`	`pow(double[] x, int xOffset, double[] y, int yOffset, double[] result, int resultOffset)` Compute power of a derivative structure.
`void`	`pow(double[] operand, int operandOffset, double p, double[] result, int resultOffset)` Compute power of a derivative structure.
`void`	`pow(double[] operand, int operandOffset, int n, double[] result, int resultOffset)` Compute integer power of a derivative structure.
`void`	`pow(double a, double[] operand, int operandOffset, double[] result, int resultOffset)` Compute power of a double to a derivative structure.
`<T extends CalculusFieldElement<T>> void`	`pow(double a, T[] operand, int operandOffset, T[] result, int resultOffset)` Compute power of a double to a derivative structure.
`<T extends CalculusFieldElement<T>> void`	`pow(T[] operand, int operandOffset, double p, T[] result, int resultOffset)` Compute power of a derivative structure.
`<T extends CalculusFieldElement<T>> void`	`pow(T[] operand, int operandOffset, int n, T[] result, int resultOffset)` Compute integer power of a derivative structure.
`<T extends CalculusFieldElement<T>> void`	`pow(T[] x, int xOffset, T[] y, int yOffset, T[] result, int resultOffset)` Compute power of a derivative structure.
`void`	`rebase(double[] ds, int dsOffset, DSCompiler baseCompiler, double[] p, double[] result, int resultOffset)` Rebase derivative structure with respect to low level parameter functions.
`<T extends CalculusFieldElement<T>> void`	`rebase(T[] ds, int dsOffset, DSCompiler baseCompiler, T[] p, T[] result, int resultOffset)` Rebase derivative structure with respect to low level parameter functions.
`void`	`remainder(double[] lhs, int lhsOffset, double[] rhs, int rhsOffset, double[] result, int resultOffset)` Perform remainder of two derivative structures.
`<T extends CalculusFieldElement<T>> void`	`remainder(T[] lhs, int lhsOffset, T[] rhs, int rhsOffset, T[] result, int resultOffset)` Perform remainder of two derivative structures.
`void`	`rootN(double[] operand, int operandOffset, int n, double[] result, int resultOffset)` Compute n^th root of a derivative structure.
`<T extends CalculusFieldElement<T>> void`	`rootN(T[] operand, int operandOffset, int n, T[] result, int resultOffset)` Compute n^th root of a derivative structure.
`void`	`sin(double[] operand, int operandOffset, double[] result, int resultOffset)` Compute sine of a derivative structure.
`<T extends CalculusFieldElement<T>> void`	`sin(T[] operand, int operandOffset, T[] result, int resultOffset)` Compute sine of a derivative structure.
`void`	`sinCos(double[] operand, int operandOffset, double[] sin, int sinOffset, double[] cos, int cosOffset)` Compute combined sine and cosine of a derivative structure.
`<T extends CalculusFieldElement<T>> void`	`sinCos(T[] operand, int operandOffset, T[] sin, int sinOffset, T[] cos, int cosOffset)` Compute combined sine and cosine of a derivative structure.
`void`	`sinh(double[] operand, int operandOffset, double[] result, int resultOffset)` Compute hyperbolic sine of a derivative structure.
`<T extends CalculusFieldElement<T>> void`	`sinh(T[] operand, int operandOffset, T[] result, int resultOffset)` Compute hyperbolic sine of a derivative structure.
`void`	`sinhCosh(double[] operand, int operandOffset, double[] sinh, int sinhOffset, double[] cosh, int coshOffset)` Compute combined hyperbolic sine and cosine of a derivative structure.
`<T extends CalculusFieldElement<T>> void`	`sinhCosh(T[] operand, int operandOffset, T[] sinh, int sinhOffset, T[] cosh, int coshOffset)` Compute combined hyperbolic sine and cosine of a derivative structure.
`void`	`subtract(double[] lhs, int lhsOffset, double[] rhs, int rhsOffset, double[] result, int resultOffset)` Perform subtraction of two derivative structures.
`<T extends CalculusFieldElement<T>> void`	`subtract(T[] lhs, int lhsOffset, T[] rhs, int rhsOffset, T[] result, int resultOffset)` Perform subtraction of two derivative structures.
`void`	`tan(double[] operand, int operandOffset, double[] result, int resultOffset)` Compute tangent of a derivative structure.
`<T extends CalculusFieldElement<T>> void`	`tan(T[] operand, int operandOffset, T[] result, int resultOffset)` Compute tangent of a derivative structure.
`void`	`tanh(double[] operand, int operandOffset, double[] result, int resultOffset)` Compute hyperbolic tangent of a derivative structure.
`<T extends CalculusFieldElement<T>> void`	`tanh(T[] operand, int operandOffset, T[] result, int resultOffset)` Compute hyperbolic tangent of a derivative structure.
`double`	`taylor(double[] ds, int dsOffset, double... delta)` Evaluate Taylor expansion of a derivative structure.
`<T extends CalculusFieldElement<T>> T`	`taylor(T[] ds, int dsOffset, double... delta)` Evaluate Taylor expansion of a derivative structure.
`<T extends CalculusFieldElement<T>> T`	`taylor(T[] ds, int dsOffset, T... delta)` Evaluate Taylor expansion of a derivative structure.

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Method Detail
  - getCompiler
```
public static DSCompiler getCompiler(int parameters,
                                     int order)
                              throws MathIllegalArgumentException
```
    Get the compiler for number of free parameters and order.
    
    Parameters:
    
    parameters - number of free parameters
    
    order - derivation order
    
    Returns:
    
    cached rules set
    
    Throws:
    
    MathIllegalArgumentException - if order is too large
  - getPartialDerivativeIndex
```
public int getPartialDerivativeIndex(int... orders)
                              throws MathIllegalArgumentException
```
    Get the index of a partial derivative in the array.
    If all orders are set to 0, then the 0^th order derivative is returned, which is the value of the function.
    
    The indices of derivatives are between 0 and getSize() - 1. Their specific order is fixed for a given compiler, but otherwise not publicly specified. There are however some simple cases which have guaranteed indices:
    - the index of 0^th order derivative is always 0
    - if there is only 1 free parameter, then the derivatives are sorted in increasing derivation order (i.e. f at index 0, df/dp at index 1, d²f/dp² at index 2 ... d^kf/dp^k at index k),
    - if the derivation order is 1, then the derivatives are sorted in increasing free parameter order (i.e. f at index 0, df/dx₁ at index 1, df/dx₂ at index 2 ... df/dx_k at index k),
    - all other cases are not publicly specified
    This method is the inverse of method getPartialDerivativeOrders(int)
    Parameters:
    
    orders - derivation orders with respect to each parameter
    
    Returns:
    
    index of the partial derivative
    
    Throws:
    
    MathIllegalArgumentException - if the numbers of parameters does not match the instance
    
    MathIllegalArgumentException - if sum of derivation orders is larger than the instance limits
    
    See Also:
    
    getPartialDerivativeOrders(int)
  - getPartialDerivativeOrders
```
public int[] getPartialDerivativeOrders(int index)
```
    Get the derivation orders for a specific index in the array.
    This method is the inverse of getPartialDerivativeIndex(int...).
    
    Parameters:
    
    index - of the partial derivative
    
    Returns:
    
    derivation orders with respect to each parameter
    
    See Also:
    
    getPartialDerivativeIndex(int...)
  - getPartialDerivativeOrdersSum
```
public int getPartialDerivativeOrdersSum(int index)
```
    Get the sum of derivation orders for a specific index in the array.
    This method return the sum of the elements returned by getPartialDerivativeIndex(int...), using precomputed values
    
    Parameters:
    
    index - of the partial derivative
    
    Returns:
    
    sum of derivation orders with respect to each parameter
    
    Since:
    
    2.2
    
    See Also:
    
    getPartialDerivativeIndex(int...)
  - getFreeParameters
```
public int getFreeParameters()
```
    Get the number of free parameters.
    
    Returns:
    
    number of free parameters
  - getOrder
```
public int getOrder()
```
    Get the derivation order.
    
    Returns:
    
    derivation order
  - getSize
```
public int getSize()
```
    Get the array size required for holding partial derivatives data.
    This number includes the single 0 order derivative element, which is guaranteed to be stored in the first element of the array.
    
    Returns:
    
    array size required for holding partial derivatives data
  - linearCombination
```
public void linearCombination(double a1,
                              double[] c1,
                              int offset1,
                              double a2,
                              double[] c2,
                              int offset2,
                              double[] result,
                              int resultOffset)
```
    Compute linear combination. The derivative structure built will be a1 * ds1 + a2 * ds2
    
    Parameters:
    
    a1 - first scale factor
    
    c1 - first base (unscaled) component
    
    offset1 - offset of first operand in its array
    
    a2 - second scale factor
    
    c2 - second base (unscaled) component
    
    offset2 - offset of second operand in its array
    
    result - array where result must be stored (it may be one of the input arrays)
    
    resultOffset - offset of the result in its array
  - linearCombination
```
public <T extends CalculusFieldElement<T>> void linearCombination(T a1,
                                                                  T[] c1,
                                                                  int offset1,
                                                                  T a2,
                                                                  T[] c2,
                                                                  int offset2,
                                                                  T[] result,
                                                                  int resultOffset)
```
    Compute linear combination. The derivative structure built will be a1 * ds1 + a2 * ds2
    
    Type Parameters:
    
    T - the type of the function parameters and value
    
    Parameters:
    
    a1 - first scale factor
    
    c1 - first base (unscaled) component
    
    offset1 - offset of first operand in its array
    
    a2 - second scale factor
    
    c2 - second base (unscaled) component
    
    offset2 - offset of second operand in its array
    
    result - array where result must be stored (it may be one of the input arrays)
    
    resultOffset - offset of the result in its array
  - linearCombination
```
public <T extends CalculusFieldElement<T>> void linearCombination(double a1,
                                                                  T[] c1,
                                                                  int offset1,
                                                                  double a2,
                                                                  T[] c2,
                                                                  int offset2,
                                                                  T[] result,
                                                                  int resultOffset)
```
    Compute linear combination. The derivative structure built will be a1 * ds1 + a2 * ds2
    
    Type Parameters:
    
    T - the type of the function parameters and value
    
    Parameters:
    
    a1 - first scale factor
    
    c1 - first base (unscaled) component
    
    offset1 - offset of first operand in its array
    
    a2 - second scale factor
    
    c2 - second base (unscaled) component
    
    offset2 - offset of second operand in its array
    
    result - array where result must be stored (it may be one of the input arrays)
    
    resultOffset - offset of the result in its array
  - linearCombination
```
public void linearCombination(double a1,
                              double[] c1,
                              int offset1,
                              double a2,
                              double[] c2,
                              int offset2,
                              double a3,
                              double[] c3,
                              int offset3,
                              double[] result,
                              int resultOffset)
```
    Compute linear combination. The derivative structure built will be a1 * ds1 + a2 * ds2 + a3 * ds3 + a4 * ds4
    
    Parameters:
    
    a1 - first scale factor
    
    c1 - first base (unscaled) component
    
    offset1 - offset of first operand in its array
    
    a2 - second scale factor
    
    c2 - second base (unscaled) component
    
    offset2 - offset of second operand in its array
    
    a3 - third scale factor
    
    c3 - third base (unscaled) component
    
    offset3 - offset of third operand in its array
    
    result - array where result must be stored (it may be one of the input arrays)
    
    resultOffset - offset of the result in its array
  - linearCombination
```
public <T extends CalculusFieldElement<T>> void linearCombination(T a1,
                                                                  T[] c1,
                                                                  int offset1,
                                                                  T a2,
                                                                  T[] c2,
                                                                  int offset2,
                                                                  T a3,
                                                                  T[] c3,
                                                                  int offset3,
                                                                  T[] result,
                                                                  int resultOffset)
```
    Compute linear combination. The derivative structure built will be a1 * ds1 + a2 * ds2 + a3 * ds3 + a4 * ds4
    
    Type Parameters:
    
    T - the type of the function parameters and value
    
    Parameters:
    
    a1 - first scale factor
    
    c1 - first base (unscaled) component
    
    offset1 - offset of first operand in its array
    
    a2 - second scale factor
    
    c2 - second base (unscaled) component
    
    offset2 - offset of second operand in its array
    
    a3 - third scale factor
    
    c3 - third base (unscaled) component
    
    offset3 - offset of third operand in its array
    
    result - array where result must be stored (it may be one of the input arrays)
    
    resultOffset - offset of the result in its array
  - linearCombination
```
public <T extends CalculusFieldElement<T>> void linearCombination(double a1,
                                                                  T[] c1,
                                                                  int offset1,
                                                                  double a2,
                                                                  T[] c2,
                                                                  int offset2,
                                                                  double a3,
                                                                  T[] c3,
                                                                  int offset3,
                                                                  T[] result,
                                                                  int resultOffset)
```
    Compute linear combination. The derivative structure built will be a1 * ds1 + a2 * ds2 + a3 * ds3 + a4 * ds4
    
    Type Parameters:
    
    T - the type of the function parameters and value
    
    Parameters:
    
    a1 - first scale factor
    
    c1 - first base (unscaled) component
    
    offset1 - offset of first operand in its array
    
    a2 - second scale factor
    
    c2 - second base (unscaled) component
    
    offset2 - offset of second operand in its array
    
    a3 - third scale factor
    
    c3 - third base (unscaled) component
    
    offset3 - offset of third operand in its array
    
    result - array where result must be stored (it may be one of the input arrays)
    
    resultOffset - offset of the result in its array
  - linearCombination
```
public void linearCombination(double a1,
                              double[] c1,
                              int offset1,
                              double a2,
                              double[] c2,
                              int offset2,
                              double a3,
                              double[] c3,
                              int offset3,
                              double a4,
                              double[] c4,
                              int offset4,
                              double[] result,
                              int resultOffset)
```
    Compute linear combination. The derivative structure built will be a1 * ds1 + a2 * ds2 + a3 * ds3 + a4 * ds4
    
    Parameters:
    
    a1 - first scale factor
    
    c1 - first base (unscaled) component
    
    offset1 - offset of first operand in its array
    
    a2 - second scale factor
    
    c2 - second base (unscaled) component
    
    offset2 - offset of second operand in its array
    
    a3 - third scale factor
    
    c3 - third base (unscaled) component
    
    offset3 - offset of third operand in its array
    
    a4 - fourth scale factor
    
    c4 - fourth base (unscaled) component
    
    offset4 - offset of fourth operand in its array
    
    result - array where result must be stored (it may be one of the input arrays)
    
    resultOffset - offset of the result in its array
  - linearCombination
```
public <T extends CalculusFieldElement<T>> void linearCombination(T a1,
                                                                  T[] c1,
                                                                  int offset1,
                                                                  T a2,
                                                                  T[] c2,
                                                                  int offset2,
                                                                  T a3,
                                                                  T[] c3,
                                                                  int offset3,
                                                                  T a4,
                                                                  T[] c4,
                                                                  int offset4,
                                                                  T[] result,
                                                                  int resultOffset)
```
    Compute linear combination. The derivative structure built will be a1 * ds1 + a2 * ds2 + a3 * ds3 + a4 * ds4
    
    Type Parameters:
    
    T - the type of the function parameters and value
    
    Parameters:
    
    a1 - first scale factor
    
    c1 - first base (unscaled) component
    
    offset1 - offset of first operand in its array
    
    a2 - second scale factor
    
    c2 - second base (unscaled) component
    
    offset2 - offset of second operand in its array
    
    a3 - third scale factor
    
    c3 - third base (unscaled) component
    
    offset3 - offset of third operand in its array
    
    a4 - fourth scale factor
    
    c4 - fourth base (unscaled) component
    
    offset4 - offset of fourth operand in its array
    
    result - array where result must be stored (it may be one of the input arrays)
    
    resultOffset - offset of the result in its array
  - linearCombination
```
public <T extends CalculusFieldElement<T>> void linearCombination(double a1,
                                                                  T[] c1,
                                                                  int offset1,
                                                                  double a2,
                                                                  T[] c2,
                                                                  int offset2,
                                                                  double a3,
                                                                  T[] c3,
                                                                  int offset3,
                                                                  double a4,
                                                                  T[] c4,
                                                                  int offset4,
                                                                  T[] result,
                                                                  int resultOffset)
```
    Compute linear combination. The derivative structure built will be a1 * ds1 + a2 * ds2 + a3 * ds3 + a4 * ds4
    
    Type Parameters:
    
    T - the type of the function parameters and value
    
    Parameters:
    
    a1 - first scale factor
    
    c1 - first base (unscaled) component
    
    offset1 - offset of first operand in its array
    
    a2 - second scale factor
    
    c2 - second base (unscaled) component
    
    offset2 - offset of second operand in its array
    
    a3 - third scale factor
    
    c3 - third base (unscaled) component
    
    offset3 - offset of third operand in its array
    
    a4 - fourth scale factor
    
    c4 - fourth base (unscaled) component
    
    offset4 - offset of fourth operand in its array
    
    result - array where result must be stored (it may be one of the input arrays)
    
    resultOffset - offset of the result in its array
  - add
```
public void add(double[] lhs,
                int lhsOffset,
                double[] rhs,
                int rhsOffset,
                double[] result,
                int resultOffset)
```
    Perform addition of two derivative structures.
    
    Parameters:
    
    lhs - array holding left hand side of addition
    
    lhsOffset - offset of the left hand side in its array
    
    rhs - array right hand side of addition
    
    rhsOffset - offset of the right hand side in its array
    
    result - array where result must be stored (it may be one of the input arrays)
    
    resultOffset - offset of the result in its array
  - add
```
public <T extends CalculusFieldElement<T>> void add(T[] lhs,
                                                    int lhsOffset,
                                                    T[] rhs,
                                                    int rhsOffset,
                                                    T[] result,
                                                    int resultOffset)
```
    Perform addition of two derivative structures.
    
    Type Parameters:
    
    T - the type of the function parameters and value
    
    Parameters:
    
    lhs - array holding left hand side of addition
    
    lhsOffset - offset of the left hand side in its array
    
    rhs - array right hand side of addition
    
    rhsOffset - offset of the right hand side in its array
    
    result - array where result must be stored (it may be one of the input arrays)
    
    resultOffset - offset of the result in its array
  - subtract
```
public void subtract(double[] lhs,
                     int lhsOffset,
                     double[] rhs,
                     int rhsOffset,
                     double[] result,
                     int resultOffset)
```
    Perform subtraction of two derivative structures.
    
    Parameters:
    
    lhs - array holding left hand side of subtraction
    
    lhsOffset - offset of the left hand side in its array
    
    rhs - array right hand side of subtraction
    
    rhsOffset - offset of the right hand side in its array
    
    result - array where result must be stored (it may be one of the input arrays)
    
    resultOffset - offset of the result in its array
  - subtract
```
public <T extends CalculusFieldElement<T>> void subtract(T[] lhs,
                                                         int lhsOffset,
                                                         T[] rhs,
                                                         int rhsOffset,
                                                         T[] result,
                                                         int resultOffset)
```
    Perform subtraction of two derivative structures.
    
    Type Parameters:
    
    T - the type of the function parameters and value
    
    Parameters:
    
    lhs - array holding left hand side of subtraction
    
    lhsOffset - offset of the left hand side in its array
    
    rhs - array right hand side of subtraction
    
    rhsOffset - offset of the right hand side in its array
    
    result - array where result must be stored (it may be one of the input arrays)
    
    resultOffset - offset of the result in its array
  - multiply
```
public void multiply(double[] lhs,
                     int lhsOffset,
                     double[] rhs,
                     int rhsOffset,
                     double[] result,
                     int resultOffset)
```
    Perform multiplication of two derivative structures.
    
    Parameters:
    
    lhs - array holding left hand side of multiplication
    
    lhsOffset - offset of the left hand side in its array
    
    rhs - array right hand side of multiplication
    
    rhsOffset - offset of the right hand side in its array
    
    result - array where result must be stored (for multiplication the result array cannot be one of the input arrays)
    
    resultOffset - offset of the result in its array
  - multiply
```
public <T extends CalculusFieldElement<T>> void multiply(T[] lhs,
                                                         int lhsOffset,
                                                         T[] rhs,
                                                         int rhsOffset,
                                                         T[] result,
                                                         int resultOffset)
```
    Perform multiplication of two derivative structures.
    
    Type Parameters:
    
    T - the type of the function parameters and value
    
    Parameters:
    
    lhs - array holding left hand side of multiplication
    
    lhsOffset - offset of the left hand side in its array
    
    rhs - array right hand side of multiplication
    
    rhsOffset - offset of the right hand side in its array
    
    result - array where result must be stored (for multiplication the result array cannot be one of the input arrays)
    
    resultOffset - offset of the result in its array
  - divide
```
public void divide(double[] lhs,
                   int lhsOffset,
                   double[] rhs,
                   int rhsOffset,
                   double[] result,
                   int resultOffset)
```
    Perform division of two derivative structures.
    
    Parameters:
    
    lhs - array holding left hand side of division
    
    lhsOffset - offset of the left hand side in its array
    
    rhs - array right hand side of division
    
    rhsOffset - offset of the right hand side in its array
    
    result - array where result must be stored (for division the result array cannot be one of the input arrays)
    
    resultOffset - offset of the result in its array
  - divide
```
public <T extends CalculusFieldElement<T>> void divide(T[] lhs,
                                                       int lhsOffset,
                                                       T[] rhs,
                                                       int rhsOffset,
                                                       T[] result,
                                                       int resultOffset)
```
    Perform division of two derivative structures.
    
    Type Parameters:
    
    T - the type of the function parameters and value
    
    Parameters:
    
    lhs - array holding left hand side of division
    
    lhsOffset - offset of the left hand side in its array
    
    rhs - array right hand side of division
    
    rhsOffset - offset of the right hand side in its array
    
    result - array where result must be stored (for division the result array cannot be one of the input arrays)
    
    resultOffset - offset of the result in its array
  - remainder
```
public void remainder(double[] lhs,
                      int lhsOffset,
                      double[] rhs,
                      int rhsOffset,
                      double[] result,
                      int resultOffset)
```
    Perform remainder of two derivative structures.
    
    Parameters:
    
    lhs - array holding left hand side of remainder
    
    lhsOffset - offset of the left hand side in its array
    
    rhs - array right hand side of remainder
    
    rhsOffset - offset of the right hand side in its array
    
    result - array where result must be stored (it may be one of the input arrays)
    
    resultOffset - offset of the result in its array
  - remainder
```
public <T extends CalculusFieldElement<T>> void remainder(T[] lhs,
                                                          int lhsOffset,
                                                          T[] rhs,
                                                          int rhsOffset,
                                                          T[] result,
                                                          int resultOffset)
```
    Perform remainder of two derivative structures.
    
    Type Parameters:
    
    T - the type of the function parameters and value
    
    Parameters:
    
    lhs - array holding left hand side of remainder
    
    lhsOffset - offset of the left hand side in its array
    
    rhs - array right hand side of remainder
    
    rhsOffset - offset of the right hand side in its array
    
    result - array where result must be stored (it may be one of the input arrays)
    
    resultOffset - offset of the result in its array
  - pow
```
public void pow(double a,
                double[] operand,
                int operandOffset,
                double[] result,
                int resultOffset)
```
    Compute power of a double to a derivative structure.
    
    Parameters:
    
    a - number to exponentiate
    
    operand - array holding the power
    
    operandOffset - offset of the power in its array
    
    result - array where result must be stored (for power the result array cannot be the input array)
    
    resultOffset - offset of the result in its array
  - pow
```
public <T extends CalculusFieldElement<T>> void pow(double a,
                                                    T[] operand,
                                                    int operandOffset,
                                                    T[] result,
                                                    int resultOffset)
```
    Compute power of a double to a derivative structure.
    
    Type Parameters:
    
    T - the type of the function parameters and value
    
    Parameters:
    
    a - number to exponentiate
    
    operand - array holding the power
    
    operandOffset - offset of the power in its array
    
    result - array where result must be stored (for power the result array cannot be the input array)
    
    resultOffset - offset of the result in its array
  - pow
```
public void pow(double[] operand,
                int operandOffset,
                double p,
                double[] result,
                int resultOffset)
```
    Compute power of a derivative structure.
    
    Parameters:
    
    operand - array holding the operand
    
    operandOffset - offset of the operand in its array
    
    p - power to apply
    
    result - array where result must be stored (for power the result array cannot be the input array)
    
    resultOffset - offset of the result in its array
  - pow
```
public <T extends CalculusFieldElement<T>> void pow(T[] operand,
                                                    int operandOffset,
                                                    double p,
                                                    T[] result,
                                                    int resultOffset)
```
    Compute power of a derivative structure.
    
    Type Parameters:
    
    T - the type of the function parameters and value
    
    Parameters:
    
    operand - array holding the operand
    
    operandOffset - offset of the operand in its array
    
    p - power to apply
    
    result - array where result must be stored (for power the result array cannot be the input array)
    
    resultOffset - offset of the result in its array
  - pow
```
public void pow(double[] operand,
                int operandOffset,
                int n,
                double[] result,
                int resultOffset)
```
    Compute integer power of a derivative structure.
    
    Parameters:
    
    operand - array holding the operand
    
    operandOffset - offset of the operand in its array
    
    n - power to apply
    
    result - array where result must be stored (for power the result array cannot be the input array)
    
    resultOffset - offset of the result in its array
  - pow
```
public <T extends CalculusFieldElement<T>> void pow(T[] operand,
                                                    int operandOffset,
                                                    int n,
                                                    T[] result,
                                                    int resultOffset)
```
    Compute integer power of a derivative structure.
    
    Type Parameters:
    
    T - the type of the function parameters and value
    
    Parameters:
    
    operand - array holding the operand
    
    operandOffset - offset of the operand in its array
    
    n - power to apply
    
    result - array where result must be stored (for power the result array cannot be the input array)
    
    resultOffset - offset of the result in its array
  - pow
```
public void pow(double[] x,
                int xOffset,
                double[] y,
                int yOffset,
                double[] result,
                int resultOffset)
```
    Compute power of a derivative structure.
    
    Parameters:
    
    x - array holding the base
    
    xOffset - offset of the base in its array
    
    y - array holding the exponent
    
    yOffset - offset of the exponent in its array
    
    result - array where result must be stored (for power the result array cannot be the input array)
    
    resultOffset - offset of the result in its array
  - pow
```
public <T extends CalculusFieldElement<T>> void pow(T[] x,
                                                    int xOffset,
                                                    T[] y,
                                                    int yOffset,
                                                    T[] result,
                                                    int resultOffset)
```
    Compute power of a derivative structure.
    
    Type Parameters:
    
    T - the type of the function parameters and value
    
    Parameters:
    
    x - array holding the base
    
    xOffset - offset of the base in its array
    
    y - array holding the exponent
    
    yOffset - offset of the exponent in its array
    
    result - array where result must be stored (for power the result array cannot be the input array)
    
    resultOffset - offset of the result in its array
  - rootN
```
public void rootN(double[] operand,
                  int operandOffset,
                  int n,
                  double[] result,
                  int resultOffset)
```
    Compute n^th root of a derivative structure.
    
    Parameters:
    
    operand - array holding the operand
    
    operandOffset - offset of the operand in its array
    
    n - order of the root
    
    result - array where result must be stored (for n^th root the result array cannot be the input array)
    
    resultOffset - offset of the result in its array
  - rootN
```
public <T extends CalculusFieldElement<T>> void rootN(T[] operand,
                                                      int operandOffset,
                                                      int n,
                                                      T[] result,
                                                      int resultOffset)
```
    Compute n^th root of a derivative structure.
    
    Type Parameters:
    
    T - the type of the function parameters and value
    
    Parameters:
    
    operand - array holding the operand
    
    operandOffset - offset of the operand in its array
    
    n - order of the root
    
    result - array where result must be stored (for n^th root the result array cannot be the input array)
    
    resultOffset - offset of the result in its array
  - exp
```
public void exp(double[] operand,
                int operandOffset,
                double[] result,
                int resultOffset)
```
    Compute exponential of a derivative structure.
    
    Parameters:
    
    operand - array holding the operand
    
    operandOffset - offset of the operand in its array
    
    result - array where result must be stored (for exponential the result array cannot be the input array)
    
    resultOffset - offset of the result in its array
  - exp
```
public <T extends CalculusFieldElement<T>> void exp(T[] operand,
                                                    int operandOffset,
                                                    T[] result,
                                                    int resultOffset)
```
    Compute exponential of a derivative structure.
    
    Type Parameters:
    
    T - the type of the function parameters and value
    
    Parameters:
    
    operand - array holding the operand
    
    operandOffset - offset of the operand in its array
    
    result - array where result must be stored (for exponential the result array cannot be the input array)
    
    resultOffset - offset of the result in its array
  - expm1
```
public void expm1(double[] operand,
                  int operandOffset,
                  double[] result,
                  int resultOffset)
```
    Compute exp(x) - 1 of a derivative structure.
    
    Parameters:
    
    operand - array holding the operand
    
    operandOffset - offset of the operand in its array
    
    result - array where result must be stored (for exponential the result array cannot be the input array)
    
    resultOffset - offset of the result in its array
  - expm1
```
public <T extends CalculusFieldElement<T>> void expm1(T[] operand,
                                                      int operandOffset,
                                                      T[] result,
                                                      int resultOffset)
```
    Compute exp(x) - 1 of a derivative structure.
    
    Type Parameters:
    
    T - the type of the function parameters and value
    
    Parameters:
    
    operand - array holding the operand
    
    operandOffset - offset of the operand in its array
    
    result - array where result must be stored (for exponential the result array cannot be the input array)
    
    resultOffset - offset of the result in its array
  - log
```
public void log(double[] operand,
                int operandOffset,
                double[] result,
                int resultOffset)
```
    Compute natural logarithm of a derivative structure.
    
    Parameters:
    
    operand - array holding the operand
    
    operandOffset - offset of the operand in its array
    
    result - array where result must be stored (for logarithm the result array cannot be the input array)
    
    resultOffset - offset of the result in its array
  - log
```
public <T extends CalculusFieldElement<T>> void log(T[] operand,
                                                    int operandOffset,
                                                    T[] result,
                                                    int resultOffset)
```
    Compute natural logarithm of a derivative structure.
    
    Type Parameters:
    
    T - the type of the function parameters and value
    
    Parameters:
    
    operand - array holding the operand
    
    operandOffset - offset of the operand in its array
    
    result - array where result must be stored (for logarithm the result array cannot be the input array)
    
    resultOffset - offset of the result in its array
  - log1p
```
public void log1p(double[] operand,
                  int operandOffset,
                  double[] result,
                  int resultOffset)
```
    Computes shifted logarithm of a derivative structure.
    
    Parameters:
    
    operand - array holding the operand
    
    operandOffset - offset of the operand in its array
    
    result - array where result must be stored (for shifted logarithm the result array cannot be the input array)
    
    resultOffset - offset of the result in its array
  - log1p
```
public <T extends CalculusFieldElement<T>> void log1p(T[] operand,
                                                      int operandOffset,
                                                      T[] result,
                                                      int resultOffset)
```
    Computes shifted logarithm of a derivative structure.
    
    Type Parameters:
    
    T - the type of the function parameters and value
    
    Parameters:
    
    operand - array holding the operand
    
    operandOffset - offset of the operand in its array
    
    result - array where result must be stored (for shifted logarithm the result array cannot be the input array)
    
    resultOffset - offset of the result in its array
  - log10
```
public void log10(double[] operand,
                  int operandOffset,
                  double[] result,
                  int resultOffset)
```
    Computes base 10 logarithm of a derivative structure.
    
    Parameters:
    
    operand - array holding the operand
    
    operandOffset - offset of the operand in its array
    
    result - array where result must be stored (for base 10 logarithm the result array cannot be the input array)
    
    resultOffset - offset of the result in its array
  - log10
```
public <T extends CalculusFieldElement<T>> void log10(T[] operand,
                                                      int operandOffset,
                                                      T[] result,
                                                      int resultOffset)
```
    Computes base 10 logarithm of a derivative structure.
    
    Type Parameters:
    
    T - the type of the function parameters and value
    
    Parameters:
    
    operand - array holding the operand
    
    operandOffset - offset of the operand in its array
    
    result - array where result must be stored (for base 10 logarithm the result array cannot be the input array)
    
    resultOffset - offset of the result in its array
  - cos
```
public void cos(double[] operand,
                int operandOffset,
                double[] result,
                int resultOffset)
```
    Compute cosine of a derivative structure.
    
    Parameters:
    
    operand - array holding the operand
    
    operandOffset - offset of the operand in its array
    
    result - array where result must be stored (for cosine the result array cannot be the input array)
    
    resultOffset - offset of the result in its array
  - cos
```
public <T extends CalculusFieldElement<T>> void cos(T[] operand,
                                                    int operandOffset,
                                                    T[] result,
                                                    int resultOffset)
```
    Compute cosine of a derivative structure.
    
    Type Parameters:
    
    T - the type of the function parameters and value
    
    Parameters:
    
    operand - array holding the operand
    
    operandOffset - offset of the operand in its array
    
    result - array where result must be stored (for cosine the result array cannot be the input array)
    
    resultOffset - offset of the result in its array
  - sin
```
public void sin(double[] operand,
                int operandOffset,
                double[] result,
                int resultOffset)
```
    Compute sine of a derivative structure.
    
    Parameters:
    
    operand - array holding the operand
    
    operandOffset - offset of the operand in its array
    
    result - array where result must be stored (for sine the result array cannot be the input array)
    
    resultOffset - offset of the result in its array
  - sin
```
public <T extends CalculusFieldElement<T>> void sin(T[] operand,
                                                    int operandOffset,
                                                    T[] result,
                                                    int resultOffset)
```
    Compute sine of a derivative structure.
    
    Type Parameters:
    
    T - the type of the function parameters and value
    
    Parameters:
    
    operand - array holding the operand
    
    operandOffset - offset of the operand in its array
    
    result - array where result must be stored (for sine the result array cannot be the input array)
    
    resultOffset - offset of the result in its array
  - sinCos
```
public void sinCos(double[] operand,
                   int operandOffset,
                   double[] sin,
                   int sinOffset,
                   double[] cos,
                   int cosOffset)
```
    Compute combined sine and cosine of a derivative structure.
    
    Parameters:
    
    operand - array holding the operand
    
    operandOffset - offset of the operand in its array
    
    sin - array where sine must be stored (for sine the result array cannot be the input array)
    
    sinOffset - offset of the result in its array
    
    cos - array where cosine must be stored (for cosine the result array cannot be the input array)
    
    cosOffset - offset of the result in its array
    
    Since:
    
    1.4
  - sinCos
```
public <T extends CalculusFieldElement<T>> void sinCos(T[] operand,
                                                       int operandOffset,
                                                       T[] sin,
                                                       int sinOffset,
                                                       T[] cos,
                                                       int cosOffset)
```
    Compute combined sine and cosine of a derivative structure.
    
    Type Parameters:
    
    T - the type of the function parameters and value
    
    Parameters:
    
    operand - array holding the operand
    
    operandOffset - offset of the operand in its array
    
    sin - array where sine must be stored (for sine the result array cannot be the input array)
    
    sinOffset - offset of the result in its array
    
    cos - array where cosine must be stored (for cosine the result array cannot be the input array)
    
    cosOffset - offset of the result in its array
    
    Since:
    
    1.4
  - tan
```
public void tan(double[] operand,
                int operandOffset,
                double[] result,
                int resultOffset)
```
    Compute tangent of a derivative structure.
    
    Parameters:
    
    operand - array holding the operand
    
    operandOffset - offset of the operand in its array
    
    result - array where result must be stored (for tangent the result array cannot be the input array)
    
    resultOffset - offset of the result in its array
  - tan
```
public <T extends CalculusFieldElement<T>> void tan(T[] operand,
                                                    int operandOffset,
                                                    T[] result,
                                                    int resultOffset)
```
    Compute tangent of a derivative structure.
    
    Type Parameters:
    
    T - the type of the function parameters and value
    
    Parameters:
    
    operand - array holding the operand
    
    operandOffset - offset of the operand in its array
    
    result - array where result must be stored (for tangent the result array cannot be the input array)
    
    resultOffset - offset of the result in its array
  - acos
```
public void acos(double[] operand,
                 int operandOffset,
                 double[] result,
                 int resultOffset)
```
    Compute arc cosine of a derivative structure.
    
    Parameters:
    
    operand - array holding the operand
    
    operandOffset - offset of the operand in its array
    
    result - array where result must be stored (for arc cosine the result array cannot be the input array)
    
    resultOffset - offset of the result in its array
  - acos
```
public <T extends CalculusFieldElement<T>> void acos(T[] operand,
                                                     int operandOffset,
                                                     T[] result,
                                                     int resultOffset)
```
    Compute arc cosine of a derivative structure.
    
    Type Parameters:
    
    T - the type of the function parameters and value
    
    Parameters:
    
    operand - array holding the operand
    
    operandOffset - offset of the operand in its array
    
    result - array where result must be stored (for arc cosine the result array cannot be the input array)
    
    resultOffset - offset of the result in its array
  - asin
```
public void asin(double[] operand,
                 int operandOffset,
                 double[] result,
                 int resultOffset)
```
    Compute arc sine of a derivative structure.
    
    Parameters:
    
    operand - array holding the operand
    
    operandOffset - offset of the operand in its array
    
    result - array where result must be stored (for arc sine the result array cannot be the input array)
    
    resultOffset - offset of the result in its array
  - asin
```
public <T extends CalculusFieldElement<T>> void asin(T[] operand,
                                                     int operandOffset,
                                                     T[] result,
                                                     int resultOffset)
```
    Compute arc sine of a derivative structure.
    
    Type Parameters:
    
    T - the type of the function parameters and value
    
    Parameters:
    
    operand - array holding the operand
    
    operandOffset - offset of the operand in its array
    
    result - array where result must be stored (for arc sine the result array cannot be the input array)
    
    resultOffset - offset of the result in its array
  - atan
```
public void atan(double[] operand,
                 int operandOffset,
                 double[] result,
                 int resultOffset)
```
    Compute arc tangent of a derivative structure.
    
    Parameters:
    
    operand - array holding the operand
    
    operandOffset - offset of the operand in its array
    
    result - array where result must be stored (for arc tangent the result array cannot be the input array)
    
    resultOffset - offset of the result in its array
  - atan
```
public <T extends CalculusFieldElement<T>> void atan(T[] operand,
                                                     int operandOffset,
                                                     T[] result,
                                                     int resultOffset)
```
    Compute arc tangent of a derivative structure.
    
    Type Parameters:
    
    T - the type of the function parameters and value
    
    Parameters:
    
    operand - array holding the operand
    
    operandOffset - offset of the operand in its array
    
    result - array where result must be stored (for arc tangent the result array cannot be the input array)
    
    resultOffset - offset of the result in its array
  - atan2
```
public void atan2(double[] y,
                  int yOffset,
                  double[] x,
                  int xOffset,
                  double[] result,
                  int resultOffset)
```
    Compute two arguments arc tangent of a derivative structure.
    
    Parameters:
    
    y - array holding the first operand
    
    yOffset - offset of the first operand in its array
    
    x - array holding the second operand
    
    xOffset - offset of the second operand in its array
    
    result - array where result must be stored (for two arguments arc tangent the result array cannot be the input array)
    
    resultOffset - offset of the result in its array
  - atan2
```
public <T extends CalculusFieldElement<T>> void atan2(T[] y,
                                                      int yOffset,
                                                      T[] x,
                                                      int xOffset,
                                                      T[] result,
                                                      int resultOffset)
```
    Compute two arguments arc tangent of a derivative structure.
    
    Type Parameters:
    
    T - the type of the function parameters and value
    
    Parameters:
    
    y - array holding the first operand
    
    yOffset - offset of the first operand in its array
    
    x - array holding the second operand
    
    xOffset - offset of the second operand in its array
    
    result - array where result must be stored (for two arguments arc tangent the result array cannot be the input array)
    
    resultOffset - offset of the result in its array
  - cosh
```
public void cosh(double[] operand,
                 int operandOffset,
                 double[] result,
                 int resultOffset)
```
    Compute hyperbolic cosine of a derivative structure.
    
    Parameters:
    
    operand - array holding the operand
    
    operandOffset - offset of the operand in its array
    
    result - array where result must be stored (for hyperbolic cosine the result array cannot be the input array)
    
    resultOffset - offset of the result in its array
  - cosh
```
public <T extends CalculusFieldElement<T>> void cosh(T[] operand,
                                                     int operandOffset,
                                                     T[] result,
                                                     int resultOffset)
```
    Compute hyperbolic cosine of a derivative structure.
    
    Type Parameters:
    
    T - the type of the function parameters and value
    
    Parameters:
    
    operand - array holding the operand
    
    operandOffset - offset of the operand in its array
    
    result - array where result must be stored (for hyperbolic cosine the result array cannot be the input array)
    
    resultOffset - offset of the result in its array
  - sinh
```
public void sinh(double[] operand,
                 int operandOffset,
                 double[] result,
                 int resultOffset)
```
    Compute hyperbolic sine of a derivative structure.
    
    Parameters:
    
    operand - array holding the operand
    
    operandOffset - offset of the operand in its array
    
    result - array where result must be stored (for hyperbolic sine the result array cannot be the input array)
    
    resultOffset - offset of the result in its array
  - sinh
```
public <T extends CalculusFieldElement<T>> void sinh(T[] operand,
                                                     int operandOffset,
                                                     T[] result,
                                                     int resultOffset)
```
    Compute hyperbolic sine of a derivative structure.
    
    Type Parameters:
    
    T - the type of the function parameters and value
    
    Parameters:
    
    operand - array holding the operand
    
    operandOffset - offset of the operand in its array
    
    result - array where result must be stored (for hyperbolic sine the result array cannot be the input array)
    
    resultOffset - offset of the result in its array
  - sinhCosh
```
public void sinhCosh(double[] operand,
                     int operandOffset,
                     double[] sinh,
                     int sinhOffset,
                     double[] cosh,
                     int coshOffset)
```
    Compute combined hyperbolic sine and cosine of a derivative structure.
    
    Parameters:
    
    operand - array holding the operand
    
    operandOffset - offset of the operand in its array
    
    sinh - array where hyperbolic sine must be stored (for sine the result array cannot be the input array)
    
    sinhOffset - offset of the result in its array
    
    cosh - array where hyperbolic cannot be the input array)
    
    coshOffset - offset of the result in its array
    
    Since:
    
    2.0
  - sinhCosh
```
public <T extends CalculusFieldElement<T>> void sinhCosh(T[] operand,
                                                         int operandOffset,
                                                         T[] sinh,
                                                         int sinhOffset,
                                                         T[] cosh,
                                                         int coshOffset)
```
    Compute combined hyperbolic sine and cosine of a derivative structure.
    
    Type Parameters:
    
    T - the type of the function parameters and value
    
    Parameters:
    
    operand - array holding the operand
    
    operandOffset - offset of the operand in its array
    
    sinh - array where hyperbolic sine must be stored (for sine the result array cannot be the input array)
    
    sinhOffset - offset of the result in its array
    
    cosh - array where hyperbolic cosine must be stored (for cosine the result array cannot be the input array)
    
    coshOffset - offset of the result in its array
    
    Since:
    
    1.4
  - tanh
```
public void tanh(double[] operand,
                 int operandOffset,
                 double[] result,
                 int resultOffset)
```
    Compute hyperbolic tangent of a derivative structure.
    
    Parameters:
    
    operand - array holding the operand
    
    operandOffset - offset of the operand in its array
    
    result - array where result must be stored (for hyperbolic tangent the result array cannot be the input array)
    
    resultOffset - offset of the result in its array
  - tanh
```
public <T extends CalculusFieldElement<T>> void tanh(T[] operand,
                                                     int operandOffset,
                                                     T[] result,
                                                     int resultOffset)
```
    Compute hyperbolic tangent of a derivative structure.
    
    Type Parameters:
    
    T - the type of the function parameters and value
    
    Parameters:
    
    operand - array holding the operand
    
    operandOffset - offset of the operand in its array
    
    result - array where result must be stored (for hyperbolic tangent the result array cannot be the input array)
    
    resultOffset - offset of the result in its array
  - acosh
```
public void acosh(double[] operand,
                  int operandOffset,
                  double[] result,
                  int resultOffset)
```
    Compute inverse hyperbolic cosine of a derivative structure.
    
    Parameters:
    
    operand - array holding the operand
    
    operandOffset - offset of the operand in its array
    
    result - array where result must be stored (for inverse hyperbolic cosine the result array cannot be the input array)
    
    resultOffset - offset of the result in its array
  - acosh
```
public <T extends CalculusFieldElement<T>> void acosh(T[] operand,
                                                      int operandOffset,
                                                      T[] result,
                                                      int resultOffset)
```
    Compute inverse hyperbolic cosine of a derivative structure.
    
    Type Parameters:
    
    T - the type of the function parameters and value
    
    Parameters:
    
    operand - array holding the operand
    
    operandOffset - offset of the operand in its array
    
    result - array where result must be stored (for inverse hyperbolic cosine the result array cannot be the input array)
    
    resultOffset - offset of the result in its array
  - asinh
```
public void asinh(double[] operand,
                  int operandOffset,
                  double[] result,
                  int resultOffset)
```
    Compute inverse hyperbolic sine of a derivative structure.
    
    Parameters:
    
    operand - array holding the operand
    
    operandOffset - offset of the operand in its array
    
    result - array where result must be stored (for inverse hyperbolic sine the result array cannot be the input array)
    
    resultOffset - offset of the result in its array
  - asinh
```
public <T extends CalculusFieldElement<T>> void asinh(T[] operand,
                                                      int operandOffset,
                                                      T[] result,
                                                      int resultOffset)
```
    Compute inverse hyperbolic sine of a derivative structure.
    
    Type Parameters:
    
    T - the type of the function parameters and value
    
    Parameters:
    
    operand - array holding the operand
    
    operandOffset - offset of the operand in its array
    
    result - array where result must be stored (for inverse hyperbolic sine the result array cannot be the input array)
    
    resultOffset - offset of the result in its array
  - atanh
```
public void atanh(double[] operand,
                  int operandOffset,
                  double[] result,
                  int resultOffset)
```
    Compute inverse hyperbolic tangent of a derivative structure.
    
    Parameters:
    
    operand - array holding the operand
    
    operandOffset - offset of the operand in its array
    
    result - array where result must be stored (for inverse hyperbolic tangent the result array cannot be the input array)
    
    resultOffset - offset of the result in its array
  - atanh
```
public <T extends CalculusFieldElement<T>> void atanh(T[] operand,
                                                      int operandOffset,
                                                      T[] result,
                                                      int resultOffset)
```
    Compute inverse hyperbolic tangent of a derivative structure.
    
    Type Parameters:
    
    T - the type of the function parameters and value
    
    Parameters:
    
    operand - array holding the operand
    
    operandOffset - offset of the operand in its array
    
    result - array where result must be stored (for inverse hyperbolic tangent the result array cannot be the input array)
    
    resultOffset - offset of the result in its array
  - compose
```
public void compose(double[] operand,
                    int operandOffset,
                    double[] f,
                    double[] result,
                    int resultOffset)
```
    Compute composition of a derivative structure by a function.
    
    Parameters:
    
    operand - array holding the operand
    
    operandOffset - offset of the operand in its array
    
    f - array of value and derivatives of the function at the current point (i.e. at operand[operandOffset]).
    
    result - array where result must be stored (for composition the result array cannot be the input array)
    
    resultOffset - offset of the result in its array
  - compose
```
public <T extends CalculusFieldElement<T>> void compose(T[] operand,
                                                        int operandOffset,
                                                        T[] f,
                                                        T[] result,
                                                        int resultOffset)
```
    Compute composition of a derivative structure by a function.
    
    Type Parameters:
    
    T - the type of the function parameters and value
    
    Parameters:
    
    operand - array holding the operand
    
    operandOffset - offset of the operand in its array
    
    f - array of value and derivatives of the function at the current point (i.e. at operand[operandOffset]).
    
    result - array where result must be stored (for composition the result array cannot be the input array)
    
    resultOffset - offset of the result in its array
  - compose
```
public <T extends CalculusFieldElement<T>> void compose(T[] operand,
                                                        int operandOffset,
                                                        double[] f,
                                                        T[] result,
                                                        int resultOffset)
```
    Compute composition of a derivative structure by a function.
    
    Type Parameters:
    
    T - the type of the function parameters and value
    
    Parameters:
    
    operand - array holding the operand
    
    operandOffset - offset of the operand in its array
    
    f - array of value and derivatives of the function at the current point (i.e. at operand[operandOffset]).
    
    result - array where result must be stored (for composition the result array cannot be the input array)
    
    resultOffset - offset of the result in its array
  - taylor
```
public double taylor(double[] ds,
                     int dsOffset,
                     double... delta)
              throws MathRuntimeException
```
    Evaluate Taylor expansion of a derivative structure.
    
    Parameters:
    
    ds - array holding the derivative structure
    
    dsOffset - offset of the derivative structure in its array
    
    delta - parameters offsets (Δx, Δy, ...)
    
    Returns:
    
    value of the Taylor expansion at x + Δx, y + Δy, ...
    
    Throws:
    
    MathRuntimeException - if factorials becomes too large
  - taylor
```
@SafeVarargs
public final <T extends CalculusFieldElement<T>> T taylor(T[] ds,
                                                                       int dsOffset,
                                                                       T... delta)
                                                                throws MathRuntimeException
```
    Evaluate Taylor expansion of a derivative structure.
    
    Type Parameters:
    
    T - the type of the function parameters and value
    
    Parameters:
    
    ds - array holding the derivative structure
    
    dsOffset - offset of the derivative structure in its array
    
    delta - parameters offsets (Δx, Δy, ...)
    
    Returns:
    
    value of the Taylor expansion at x + Δx, y + Δy, ...
    
    Throws:
    
    MathRuntimeException - if factorials becomes too large
  - taylor
```
public <T extends CalculusFieldElement<T>> T taylor(T[] ds,
                                                    int dsOffset,
                                                    double... delta)
                                             throws MathRuntimeException
```
    Evaluate Taylor expansion of a derivative structure.
    
    Type Parameters:
    
    T - the type of the function parameters and value
    
    Parameters:
    
    ds - array holding the derivative structure
    
    dsOffset - offset of the derivative structure in its array
    
    delta - parameters offsets (Δx, Δy, ...)
    
    Returns:
    
    value of the Taylor expansion at x + Δx, y + Δy, ...
    
    Throws:
    
    MathRuntimeException - if factorials becomes too large
  - rebase
```
public void rebase(double[] ds,
                   int dsOffset,
                   DSCompiler baseCompiler,
                   double[] p,
                   double[] result,
                   int resultOffset)
```
    Rebase derivative structure with respect to low level parameter functions.
    
    Parameters:
    
    ds - array holding the derivative structure
    
    dsOffset - offset of the derivative structure in its array
    
    baseCompiler - compiler associated with the low level parameter functions
    
    p - array holding the low level parameter functions (one flat array)
    
    result - array where result must be stored (for composition the result array cannot be the input
    
    resultOffset - offset of the result in its array
    
    Since:
    
    2.2
  - rebase
```
public <T extends CalculusFieldElement<T>> void rebase(T[] ds,
                                                       int dsOffset,
                                                       DSCompiler baseCompiler,
                                                       T[] p,
                                                       T[] result,
                                                       int resultOffset)
```
    Rebase derivative structure with respect to low level parameter functions.
    
    Type Parameters:
    
    T - type of the field elements
    
    Parameters:
    
    ds - array holding the derivative structure
    
    dsOffset - offset of the derivative structure in its array
    
    baseCompiler - compiler associated with the low level parameter functions
    
    p - array holding the low level parameter functions (one flat array)
    
    result - array where result must be stored (for composition the result array cannot be the input
    
    resultOffset - offset of the result in its array
    
    Since:
    
    2.2
  - checkCompatibility
```
public void checkCompatibility(DSCompiler compiler)
                        throws MathIllegalArgumentException
```
    Check rules set compatibility.
    
    Parameters:
    
    compiler - other compiler to check against instance
    
    Throws:
    
    MathIllegalArgumentException - if number of free parameters or orders are inconsistent

Class DSCompiler

Method Summary

Methods inherited from class java.lang.Object

Method Detail

getCompiler

getPartialDerivativeIndex

getPartialDerivativeOrders

getPartialDerivativeOrdersSum

getFreeParameters

getOrder

getSize

linearCombination

linearCombination

linearCombination

linearCombination

linearCombination

linearCombination

linearCombination

linearCombination

linearCombination

add

add

subtract

subtract

multiply

multiply

divide

divide

remainder

remainder

pow

pow

pow

pow

pow

pow

pow

pow

rootN

rootN

exp

exp

expm1

expm1

log

log

log1p

log1p

log10

log10

cos

cos

sin

sin

sinCos

sinCos

tan

tan

acos

acos

asin

asin

atan

atan

atan2

atan2

cosh

cosh

sinh

sinh

sinhCosh

sinhCosh

tanh

tanh

acosh

acosh

asinh

asinh

atanh

atanh