úÎRXNÜ0      !"#$%&'()*+,-./portable experimental-Aleksey Khudyakov <alexey.skladnoy@gmail.com>Result of numeric integration. Integraion result %Rough estimate of attained precision Number of iterations >Integration parameters for numerical routines. Note that each E additional iteration doubles number of function evaluation required  to compute integral. &Number of iterations is capped at 30. Relative precision of answer Maximum number of iterations 0 -Default parameters for integration functions # Maximum number of iterations = 20  Precision is 10 { y >Integration of using trapezoids. This is robust algorithm and A place and useful for not very smooth. But it is very slow. It  hundreds times slower then   if function is  sufficiently smooth.  Parameters Integration limits Function to integrate AIntegration using Simpson rule. It should be more efficient than   1 if function being integrated have finite fourth  derivative.  Parameters Integration limits Function to integrate BIntegration using Romberg rule. For sufficiently smooth functions  (e.g. analytic) it's a fastest of three.  Parameters Integration limits Function to integrate 12     portable experimental-Aleksey Khudyakov <alexey.skladnoy@gmail.com> Differentiation result Derivative value Rough error estimate 3&Calculate derivative using Richaradson's deferred approach to A limit. This is a preferred method for numeric differentiation  since it'5s most precise. Function could be evaluated up to 20  times. BInitial step size should be chosen fairly big. Too small one will @ result reduced precision, too big one in nonsensical answer.  Function Delta %Point at which evaluate differential ;Simplest form of differentiation. Should be used only when > function evaluation is prohibitively expensive and already  computed value at point x should be reused.  f'(x) = f(x+h) - f(x) / h Function to differentiate Delta ,Coordinate and function value at this point ;Simple differentiation. It uses simmetric rule and provide  reasonable accuracy. It''s suitable when function evaluation is 6 expensive and precision could be traded for speed.  f'(x) = f(x-h) + f(x+h) / 2h Function to differentiate Delta %Point at which evaluate differential  For number x and small h return such h' that x+h' and x  differ by representable number x  small delta    portable experimental-Aleksey Khudyakov <alexey.skladnoy@gmail.com>Solve equation f(x) = 0% using bisection method. Function is E must be continous. If function has different signs at the ends of / initial interval answer is always returned. 4 is returned ( if function fails to find an answer. Required absolute precision Range  Equation 5portable experimental-Aleksey Khudyakov <alexey.skladnoy@gmail.com>2Type class for array-like data type which support O(1) access ( by integer index starting from zero. Size of table. O(1)$ Index table without range cheking. O(1)6 Safe indexing. Calls error if index is out of range. Check that index is valid portable experimental-Aleksey Khudyakov <alexey.skladnoy@gmail.com>  Uniform mesh 67Distance between points 87Class for 1-dimensional meshes. Mesh is ordered set of ? points. Each instance must guarantee that every next point is ? greater that previous and there is at least 2 points in mesh. Low bound of mesh Upper bound of mesh !Find such index for value that  ! mesh ! i <= x && mesh ! i+1 > x 4Will return invalid index if value is out of range. "Create uniform mesh Lower and upper bound Number of points  !" !" ! !"portable experimental-Aleksey Khudyakov <alexey.skladnoy@gmail.com>#3For function which act much like for loop in the C Staring index value  Condition Function to modify index Action to perform $Specialized for loop. Akin to:  for( i = 0; i < 10; i++) { ... Starting index  Maximal index value not reached Action to perfor, #$#$#$portable experimental-Aleksey Khudyakov <alexey.skladnoy@gmail.com>%Natural cubic splines 9:;<&Data for linear interpolation =>?'#Interpolation for arbitraty meshes (8Interpolate function at some point. Function should not A fail outside of mesh however it may and most likely will give  nonsensical results )Tabulate function *@Use table of already evaluated function and mesh. Sizes of mesh ! and table must coincide but it's not checked. Do not use this  function use - instead. + Get mesh. ,Get table of function values -@Use table of already evaluated function and mesh. Sizes of mesh  and table must coincide. .Function used to fix types @/Function used to fix types ABC !"%&'()*+,-./ '()*+,-&.%/ %&'()*+,()*+,-./D       !"#$%&'()*+,-./0123456789:;<!=>*?@A+BCDEFGHnumeric-tools-0.1.0.0Numeric.Tools.IntegrationNumeric.Tools.DifferentiationNumeric.Tools.EquationNumeric.Classes.IndexingNumeric.Tools.MeshControl.Monad.NumericNumeric.Tools.InterpolationQuadResquadRes quadPrecEst quadNIter QuadParam quadPrecision quadMaxIterdefQuad quadTrapezoid quadSimpson quadRombergDiffResdiffRes diffPrecisiondiffRichardson diffSimple diffSimmetricrepresentableDeltasolveBisection IndexableIndexValsize unsafeIndex! validIndex UniformMeshuniformMeshStepMeshmeshLowerBoundmeshUpperBound meshFindIndex uniformMeshforGenfor CubicSpline LinearInterp Interpolationat tabulateFununsafeTabulateinterpolationMeshinterpolationTabletabulate linearInterp cubicSplinemaxIter trapGuess nextTrapezoidrepresentableDeltaFFIbase Data.MaybeNothingbisectionWorkeruniformMeshFromuniformMeshSizecubicSplineMeshcubicSplineTable cubicSplineY2linearInterpMeshlinearInterpTablelinearInterpolationmakeCubicSplinedelta safeFindIndex