[ English | Japanese ]

ASL Basic Functions Vol.4 (for C)

Go to Top

Chapter 1  INTRODUCTION

1.1
OVERVIEW
1.1.1
Introduction to The Advanced Scientific Library ASL C interface
1.1.2
Distinctive Characteristics of ASL C interface
1.2
KINDS OF LIBRARIES
1.3
ORGANIZATION
1.3.1
Introduction
1.3.2
Organization of Function Description
1.3.3
Contents of Each Item
1.4
FUNCTION NAMES
1.5
NOTES

Go to Top

Chapter 2  DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONS

2.1
INTRODUCTION
2.1.1
Notes
2.1.1.1
Ordinary Differential Equations (Initial Value Problems)
2.1.1.2
Ordinary Differential Equations (Boundary Value Problems)
2.1.1.3
Integral Equations
2.1.2
Algorithms Used
2.1.2.1
Ordinary Differential Equations (Initial Value Problems)
2.1.2.2
Ordinary Differential Equations (Boundary Value Problems)
2.1.2.3
Integral Equations
2.1.2.4
Partial Differential Equations
2.1.3
Reference Bibliography
2.2
ORDINARY DIFFERENTIAL EQUATIONS (INITIAL VALUE PROBLEMS)
2.2.1
ASL_dksncs, ASL_rksncs
High-Order Simultaneous Ordinary Differential Equations (Speed Priority)
2.2.2
ASL_dksnca, ASL_rksnca
High-Order Simultaneous Ordinary Differential Equations (Precision Priority)
2.2.3
ASL_dkinct, ASL_rkinct
Implicit Simultaneous Ordinary Differential Equations
2.2.4
ASL_dkssca, ASL_rkssca
Stiff Problem High-Order Simultaneous Ordinary Differential Equations
2.2.5
ASL_dkfncs, ASL_rkfncs
Simultaneous Ordinary Differential Equations of the 1st Order
2.2.6
ASL_dkhncs, ASL_rkhncs
High-Order Ordinary Differential Equation
2.2.7
ASL_dkmncn, ASL_rkmncn
Ordinary Differential Equation of the Type My''+Cy'+Ky=p (x)
2.3
ORDINARY DIFFERENTIAL EQUATIONS (BOUNDARY VALUE PROBLEMS)
2.3.1
ASL_dosnnv, ASL_rosnnv
High-Order Simultaneous Ordinary Differential Equations (Numerical Boundary Conditions)
2.3.2
ASL_dosnnf, ASL_rosnnf
High-Order Simultaneous Ordinary Differential Equations (Function Boundary Conditions)
2.3.3
ASL_dofnnv, ASL_rofnnv
First-Order Simultaneous Ordinary Differential Equations (Numerical Boundary Conditions)
2.3.4
ASL_dofnnf, ASL_rofnnf
First-Order Simultaneous Ordinary Differential Equations (Function Boundary Conditions)
2.3.5
ASL_dohnnv, ASL_rohnnv
High-Order Ordinary Differential Equation (Numerical Boundary Conditions)
2.3.6
ASL_dohnnf, ASL_rohnnf
High-Order Ordinary Differential Equation (Function Boundary Conditions)
2.3.7
ASL_dohnlv, ASL_rohnlv
High-Order Linear Ordinary Differential Equation
2.3.8
ASL_dolnlv, ASL_rolnlv
Second-Order Linear Ordinary Differential Equation
2.4
INTEGRAL EQUATIONS
2.4.1
ASL_doief2, ASL_roief2
Fredholm's Integral Equation of the Second Kind
2.4.2
ASL_doiev1, ASL_roiev1
Volterra's Integral Equation of the First Kind
2.5
PARTIAL DIFFERENTIAL EQUATIONS
2.5.1
ASL_dopdh2, ASL_ropdh2
Two-Dimensional Inhomogeneous Helmholtz Equation
2.5.2
ASL_dopdh3, ASL_ropdh3
Three-Dimensional Inhomogeneous Helmholtz Equation

Go to Top

Chapter 3  NUMERICAL DIFFERENTIALS

3.1
INTRODUCTION
3.1.1
Notes
3.1.2
Algorithms Used
3.1.2.1
Richardson's extrapolation
3.1.2.2
Numerical differentials of a function
3.1.2.3
Gradient vector of a function of many variables
3.1.2.4
Hessian matrix of a function of multiple variables
3.1.2.5
Jacobian matrix of a function of multiple variables
3.1.3
Reference Bibliography
3.2
NUMERICAL DIFFERENTIALS
3.2.1
ASL_dqfodx, ASL_rqfodx
Numerical Differentials of a Function
3.2.2
ASL_dqmogx, ASL_rqmogx
Gradient Vector of a Function of Many Variables
3.2.3
ASL_dqmohx, ASL_rqmohx
Hessian of a Function of Many Variables
3.2.4
ASL_dqmojx, ASL_rqmojx
Jacobian of Multiple Function of Many Variables

Go to Top

Chapter 4  NUMERICAL INTEGRATION

4.1
INTRODUCTION
4.1.1
Notes
4.1.2
Algorithms Used
4.1.2.1
Adaptive Newton-Cotes rule (Integration of arbitrary functions)
4.1.2.2
Gauss-Kronrod Method
4.1.2.3
Clenshaw-Curtis method (functions having a weight function)
4.1.2.4
varepsilon -algorithm
4.1.2.5
Double exponential formula (integrating a function having endpoint or interior-point singularities)
4.1.2.6
Integrating an oscillatory function over an infinite interval
4.1.2.7
Multi-dimensional integration over a finite interval
4.1.2.8
Integral of the product of arbitrary function and special functions
4.1.3
Reference Bibliography
4.2
INTEGRATION OVER A FINITE INTERVAL
4.2.1
ASL_dhemnl, ASL_rhemnl
Arbitrary Function
4.2.2
ASL_dhnsnl, ASL_rhnsnl
Smooth Function
4.2.3
ASL_dhnofl, ASL_rhnofl
Function of the Type f (x) (sinωx or cosωx)
4.2.4
ASL_dhnefl, ASL_rhnefl
Function of the Type f (x) ((x-a) α (b-x) β log (x-a) γ log (b-x) δ) (a<x<b; γ, δ=0, 1)
4.2.5
ASL_dhnifl, ASL_rhnifl
Function of the Type f (x) (1/ (x-c) )
4.2.6
ASL_dhnpnl, ASL_rhnpnl
General Oscillatory or Peak-Type Function
4.2.7
ASL_dhnenl, ASL_rhnenl
General Function Having an Endpoint Singularity
4.2.8
ASL_dhninl, ASL_rhninl
General Function Having Interior-Point Singularities
4.2.9
ASL_dhnanl, ASL_rhnanl
Singular Function for which Singularity Information is Unknown
4.2.10
ASL_dhbdfs, ASL_rhbdfs
Integral of Product with any Function f (x) and Bessel Function J0 (x)
4.2.11
ASL_dhbsfc, ASL_rhbsfc
Integral of the Product of Chebyshev Polynomial and Bessel Function of the Order 0
4.3
INTEGRATION OVER A SEMI-INFINITE INTERVAL
4.3.1
ASL_dhemnh, ASL_rhemnh
Arbitrary Function
4.3.2
ASL_dhnofh, ASL_rhnofh
Function of the Type f (x) (sinωx or cosωx)
4.3.3
ASL_dhnenh, ASL_rhnenh
General Function Having an Endpoint Singularity
4.3.4
ASL_dhninh, ASL_rhninh
General Function Having Interior-Point Singularities
4.4
INTEGRATION OVER A FULLY INFINITE INTERVAL
4.4.1
ASL_dhemni, ASL_rhemni
Arbitrary Function
4.4.2
ASL_dhnofi, ASL_rhnofi
Function of the Type f (x) (sinωx or cosωx)
4.4.3
ASL_dhnini, ASL_rhnini
Function Having Interior-Point Singularities
4.4.4
ASL_dh2int, ASL_rh2int
Function of the Type e^-x2f (x)
4.5
INTEGRATION OVER A TWO-DIMENSIONAL FINITE INTERVAL
4.5.1
ASL_dhnrnm, ASL_rhnrnm
Two-Dimensional Integration over a Rectangular Area
4.5.2
ASL_dhnfnm, ASL_rhnfnm
Two-Dimensional Integration over an Area Indicated by the Function
4.6
MULTI-DIMENSIONAL INTEGRATION OVER A FINITE INTERVAL
4.6.1
ASL_dhnrml, ASL_rhnrml
Multi-Dimensional Integration over a Hypercubic Space
4.6.2
ASL_dhnfml, ASL_rhnfml
Multi-Dimensional Integration over a Space Indicated by a Function

Go to Top

Chapter 5  APPROXIMATION AND INTERPOLATION

5.1
INTRODUCTION
5.1.1
Notes
5.1.2
Algorithms Used
5.1.2.1
Least squares approximation orthogonal polynomials
5.1.2.2
Nonlinear least square method
5.1.2.3
Two-dimensional arbitrary data least squares approximation polynomials
5.1.2.4
Two-dimensional lattice data least squares approximation polynomials
5.1.2.5
Unequally spaced discrete point interpolation value
5.1.2.6
Unequally spaced discrete point interpolation value and interpolation coefficients
5.1.2.7
Discrete point interpolation value on two-dimensional cross section lines
5.1.2.8
Discrete point interpolation value on two-dimensional lattice
5.1.2.9
Chebyshev approximation
5.1.3
Reference Bibliography
5.2
INTERPOLATION
5.2.1
ASL_dpdopl, ASL_rpdopl
Unequally Spaced Discrete Point Interpolation Value
5.2.2
ASL_dpdapn, ASL_rpdapn
Unequally Spaced Discrete Point Interpolation Value and Interpolation Coefficients
5.3
SURFACE INTERPOLATION
5.3.1
ASL_dplopl, ASL_rplopl
Discrete Point Interpolation Value on Two-Dimensional Cross Section Lines
5.3.2
ASL_dpgopl, ASL_rpgopl
Discrete Point Interpolation Value on a Two-Dimensional Lattice
5.4
LEAST SQUARES APPROXIMATION
5.4.1
ASL_dndaao, ASL_rndaao
Least Squares Approximation Orthogonal Polynomial Having Automatically Determined Degree
5.4.2
ASL_dndapo, ASL_rndapo
Least Squares Approximation Orthogonal Polynomials
5.4.3
ASL_dndanl, ASL_rndanl
Least Squares Approximation Nonlinear Functions
5.5
LEAST SQUARES SURFACE APPROXIMATION
5.5.1
ASL_dnrapl, ASL_rnrapl
Two-Dimensional Arbitrary Data Least Squares Approximation Polynomial
5.5.2
ASL_dngapl, ASL_rngapl
Two-Dimensional Lattice Data Least Squares Approximation Polynomial
5.6
CHEBYSHEV APPROXIMATION
5.6.1
ASL_dncbpo, ASL_rncbpo
Chebyshev Approximation

Go to Top

Chapter 6  SPLINE FUNCTIONS

6.1
INTRODUCTION
6.1.1
Notes
6.1.2
Algorithms Used
6.1.2.1
Cubic aperiodic spline function (inputting endpoint conditions)
6.1.2.2
Cubic periodic spline function
6.1.2.3
Cubic aperiodic spline functions (endpoint condition input is unnecessary)
6.1.2.4
Cubic spline smoothing by specifying a control variable
6.1.2.5
Cubic spline automatic smoothing
6.1.2.6
Cubic spline coefficients (least squares method with specification of knot locations)
6.1.2.7
Cubic spline coefficients (least squares method with knot positions automatically determined)
6.1.2.8
Interpolation values according to cubic spline coefficients
6.1.2.9
Derivatives according to cubic spline coefficients
6.1.2.10
Integrals according to cubic spline coefficients
6.1.2.11
Bicubic spline coefficients
6.1.2.12
Bicubic spline interpolation values
6.1.2.13
Bicubic spline mixed partial derivatives
6.1.2.14
Bicubic spline double integral
6.1.2.15
Plane data interpolation
6.1.2.16
Interpolation using a B-spline function (one-dimensional)
6.1.2.17
Interpolation using a B-spline function (multi-dimensional)
6.1.2.18
B-spline smoothing (one-dimensional data)
6.1.2.19
B-spline smoothing (multi-dimensional data)
6.1.3
Reference Bibliography
6.2
CUBIC SPLINE (CURVED LINE INTERPOLATION)
6.2.1
ASL_dgispc, ASL_rgispc
Interpolation Values and Cubic Spline Coefficients
6.2.2
ASL_dgissc, ASL_rgissc
Smoothed Interpolation Values and Cubic Spline Coefficients
6.2.3
ASL_dgismc, ASL_rgismc
Least Squares Interpolation Values and Cubic Spline Coefficients
6.2.4
ASL_dgidpc, ASL_rgidpc
Derivative Values and Cubic Spline Coefficients
6.2.5
ASL_dgidsc, ASL_rgidsc
Smoothed Derivative Values and Cubic Spline Coefficients
6.2.6
ASL_dgidmc, ASL_rgidmc
Least Squares Method Derivative Values and Cubic Spline Coefficients
6.2.7
ASL_dgiipc, ASL_rgiipc
Integral Values and Cubic Spline Coefficients
6.2.8
ASL_dgiisc, ASL_rgiisc
Smoothed Integral Value and Cubic Spline Coefficients
6.2.9
ASL_dgiimc, ASL_rgiimc
Least Squares Method Integral Value and Cubic Spline Coefficients
6.2.10
ASL_dgiccp, ASL_rgiccp
Cubic Spline Coefficients (Endpoint Condition Input Unnecessary)
6.2.11
ASL_dgiccq, ASL_rgiccq
Cubic Spline Coefficients (Endpoint Conditions Are Input)
6.2.12
ASL_dgiccr, ASL_rgiccr
Cubic Spline Coefficients (Periodic Spline)
6.2.13
ASL_dgiccs, ASL_rgiccs
Cubic Spline Coefficients (Automatic Smoothing)
6.2.14
ASL_dgicco, ASL_rgicco
Cubic Spline Coefficients (Automatic Smoothing Periodic Conditions)
6.2.15
ASL_dgicct, ASL_rgicct
Cubic Spline Coefficients (Smoothing by Specifying a Control Variable)
6.2.16
ASL_dgiccm, ASL_rgiccm
Cubic Spline Coefficients (Least Squares Method When Knot Positions are Set Automatically)
6.2.17
ASL_dgiccn, ASL_rgiccn
Cubic Spline Coefficients (Least Squares Method When Knot Positions are Specified)
6.2.18
ASL_dgiscx, ASL_rgiscx
Interpolation Values According to Cubic Spline Coefficients
6.2.19
ASL_dgidcy, ASL_rgidcy
Derivative Values According to Cubic Spline Coefficients
6.2.20
ASL_dgiicz, ASL_rgiicz
Integral Value According to Cubic Spline Coefficients
6.3
BICUBIC SPLINE (CURVED SURFACE INTERPOLATION)
6.3.1
ASL_dgisxb, ASL_rgisxb
Interpolation Values
6.3.2
ASL_dgidyb, ASL_rgidyb
Mixed Partial Derivative Values and Bicubic Spline Coefficients
6.3.3
ASL_dgiizb, ASL_rgiizb
Double Integral Value
6.3.4
ASL_dgicbp, ASL_rgicbp
Bicubic Spline Coefficients
6.3.5
ASL_dgisbx, ASL_rgisbx
Interpolation Values According to Bicubic Spline Coefficients
6.3.6
ASL_dgidby, ASL_rgidby
Mixed Partial Derivative Values According to Bicubic Spline Coefficients
6.3.7
ASL_dgiibz, ASL_rgiibz
Double Integral Value According to Bicubic Spline Coefficients
6.4
PLANE DATA INTERPOLATION
6.4.1
ASL_dgispo, ASL_rgispo
Open Curve Interpolation
6.4.2
ASL_dgispr, ASL_rgispr
Closed Curve Interpolation
6.4.3
ASL_dgisso, ASL_rgisso
Open Curve Smoothed Interpolation
6.4.4
ASL_dgissr, ASL_rgissr
Closed Curve Smoothed Interpolation
6.5
B-SPLINE
6.5.1
ASL_dgicbs, ASL_rgicbs
B-Spline Calculation
6.5.2
ASL_dgisi1, ASL_rgisi1
Interpolation Using a B-Spline (One-Dimensional Data)
6.5.3
ASL_dgisi2, ASL_rgisi2
Interpolation Using a B-Spline (Two-Dimensional Data)
6.5.4
ASL_dgisi3, ASL_rgisi3
Interpolation Using a B-Spline (Three-Dimensional Data)
6.5.5
ASL_dgiss1, ASL_rgiss1
B-Spline Smoothing (One-Dimensional Data)
6.5.6
ASL_dgiss2, ASL_rgiss2
B-Spline Smoothing (Two-Dimensional Data)
6.5.7
ASL_dgiss3, ASL_rgiss3
B-Spline Smoothing (Three-Dimensional Data)

Go to Top

Appendix

Appendix A
MACHINE CONSTANTS USED IN ASL C INTERFACE
A.1
Units for Determining Error
A.2
Maximum and Minimum Values of Floating Point Data