fr.cnes.sirius.patrius.math.analysis.differentiation

Class DSCompiler

java.lang.Object

fr.cnes.sirius.patrius.math.analysis.differentiation.DSCompiler

public final 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 theur 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, df/dxdx, df/dy, df/dxdy and df/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)];
 
 

Since:

3.1

Version:

$Id: DSCompiler.java 18108 2017-10-04 06:45:27Z bignon $

See Also:

DerivativeStructure

Method Summary

Modifier and Type	Method and Description
void	acos(double[] operand, int operandOffset, double[] 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.
void	add(double[] lhs, int lhsOffset, double[] rhs, int rhsOffset, double[] 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.
void	asinh(double[] operand, int operandOffset, double[] 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.
void	atan2(double[] y, int yOffset, double[] x, int xOffset, double[] 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.
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.
void	cos(double[] operand, int operandOffset, double[] 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.
void	divide(double[] lhs, int lhsOffset, double[] rhs, int rhsOffset, double[] 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.
void	expm1(double[] operand, int operandOffset, double[] 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.
protected int[][][]	getCompIndirection() Returns indirection arrays for function composition.
int	getFreeParameters() Get the number of free parameters.
protected int[][][]	getMultIndirection() Returns indirection arrays for multiplication.
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	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.
void	log(double[] operand, int operandOffset, double[] 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.
void	log1p(double[] operand, int operandOffset, double[] 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.
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.
void	remainder(double[] lhs, int lhsOffset, double[] rhs, int rhsOffset, double[] result, int resultOffset) Perform remainder of two derivative structures.
void	rootN(double[] operand, int operandOffset, int n, double[] result, int resultOffset) Compute nth root of a derivative structure.
void	sin(double[] operand, int operandOffset, double[] result, int resultOffset) Compute sine of a derivative structure.
void	sinh(double[] operand, int operandOffset, double[] result, int resultOffset) Compute hyperbolic sine of a derivative structure.
void	subtract(double[] lhs, int lhsOffset, double[] rhs, int rhsOffset, double[] 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.
void	tanh(double[] operand, int operandOffset, double[] 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.

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)

Get the compiler for number of free parameters and order.

Parameters:

parameters - number of free parameters

order - derivation order

Returns:

cached rules set

getPartialDerivativeIndex

public int getPartialDerivativeIndex(int... orders)

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 incresing 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:

DimensionMismatchException - if the numbers of parameters does not match the instance

NumberIsTooLargeException - 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:

orders derivation orders with respect to each parameter

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 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 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

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

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

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

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

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

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

Since:

3.3

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 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 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

taylor

public double taylor(double[] ds,
                     int dsOffset,
                     double... delta)

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, ...

checkCompatibility

public void checkCompatibility(DSCompiler compiler)

Check rules set compatibility.

Parameters:

compiler - other compiler to check against instance

Throws:

DimensionMismatchException - if number of free parameters or orders are inconsistent

getMultIndirection

protected int[][][] getMultIndirection()

Returns indirection arrays for multiplication.

Returns:

indirection arrays for multiplication

getCompIndirection

protected int[][][] getCompIndirection()

Returns indirection arrays for function composition.

Returns:

indirection arrays for function composition