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ASL Basic Functions Vol.4 (for Fortran)
| Contents |
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Chapter 1 INTRODUCTION
- 1.1
- OVERVIEW
- 1.1.1
- Introduction to The Advanced Scientific Library ASL
- 1.1.2
- Distinctive Characteristics of ASL
- 1.2
- KINDS OF LIBRARIES
- 1.3
- ORGANIZATION
- 1.3.1
- Introduction
- 1.3.2
- Organization of Subroutine Description
- 1.3.3
- Contents of Each Item
- 1.4
- SUBROUTINE NAMES
- 1.5
- NOTES
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
- DKSNCS, RKSNCS
High-Order Simultaneous Ordinary Differential Equations (Speed Priority)- 2.2.2
- DKSNCA, RKSNCA
High-Order Simultaneous Ordinary Differential Equations (Precision Priority)- 2.2.3
- DKINCT, RKINCT
Implicit Simultaneous Ordinary Differential Equations- 2.2.4
- DKSSCA, RKSSCA
Stiff Problem High-Order Simultaneous Ordinary Differential Equations- 2.2.5
- DKFNCS, RKFNCS
Simultaneous Ordinary Differential Equations of the 1st Order- 2.2.6
- DKHNCS, RKHNCS
High-Order Ordinary Differential Equation- 2.2.7
- DKMNCN, RKMNCN
Ordinary Differential Equation of the Type My''+Cy'+Ky=p (x)- 2.3
- ORDINARY DIFFERENTIAL EQUATIONS (BOUNDARY VALUE PROBLEMS)
- 2.3.1
- DOSNNV, ROSNNV
High-Order Simultaneous Ordinary Differential Equations (Numerical Boundary Conditions)- 2.3.2
- DOSNNF, ROSNNF
High-Order Simultaneous Ordinary Differential Equations (Function Boundary Conditions)- 2.3.3
- DOFNNV, ROFNNV
First-Order Simultaneous Ordinary Differential Equations (Numerical Boundary Conditions)- 2.3.4
- DOFNNF, ROFNNF
First-Order Simultaneous Ordinary Differential Equations (Function Boundary Conditions)- 2.3.5
- DOHNNV, ROHNNV
High-Order Ordinary Differential Equation (Numerical Boundary Conditions)- 2.3.6
- DOHNNF, ROHNNF
High-Order Ordinary Differential Equation (Function Boundary Conditions)- 2.3.7
- DOHNLV, ROHNLV
High-Order Linear Ordinary Differential Equation- 2.3.8
- DOLNLV, ROLNLV
Second-Order Linear Ordinary Differential Equation- 2.4
- INTEGRAL EQUATIONS
- 2.5
- PARTIAL DIFFERENTIAL EQUATIONS
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
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
- DHEMNL, RHEMNL
Arbitrary Function- 4.2.2
- DHNSNL, RHNSNL
Smooth Function- 4.2.3
- DHNOFL, RHNOFL
Function of the Type f (x) (sinωx or cosωx)- 4.2.4
- DHNEFL, 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
- DHNIFL, RHNIFL
Function of the Type f (x) (1/ (x-c) )- 4.2.6
- DHNPNL, RHNPNL
General Oscillatory or Peak-Type Function- 4.2.7
- DHNENL, RHNENL
General Function Having an Endpoint Singularity- 4.2.8
- DHNINL, RHNINL
General Function Having Interior-Point Singularities- 4.2.9
- DHNANL, RHNANL
Singular Function for which Singularity Information is Unknown- 4.2.10
- DHBDFS, RHBDFS
Integral of Product with any Function f (x) and Bessel Function J0 (x)- 4.2.11
- DHBSFC, RHBSFC
Integral of the Product of Chebyshev Polynomial and Bessel Function of the Order 0- 4.3
- INTEGRATION OVER A SEMI-INFINITE INTERVAL
- 4.4
- INTEGRATION OVER A FULLY INFINITE INTERVAL
- 4.5
- INTEGRATION OVER A TWO-DIMENSIONAL FINITE INTERVAL
- 4.6
- MULTI-DIMENSIONAL INTEGRATION OVER A FINITE INTERVAL
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
- 5.3
- SURFACE INTERPOLATION
- 5.4
- LEAST SQUARES APPROXIMATION
- 5.5
- LEAST SQUARES SURFACE APPROXIMATION
- 5.6
- CHEBYSHEV APPROXIMATION
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
- DGISPC, RGISPC
Interpolation Values and Cubic Spline Coefficients- 6.2.2
- DGISSC, RGISSC
Smoothed Interpolation Values and Cubic Spline Coefficients- 6.2.3
- DGISMC, RGISMC
Least Squares Interpolation Values and Cubic Spline Coefficients- 6.2.4
- DGIDPC, RGIDPC
Derivative Values and Cubic Spline Coefficients- 6.2.5
- DGIDSC, RGIDSC
Smoothed Derivative Values and Cubic Spline Coefficients- 6.2.6
- DGIDMC, RGIDMC
Least Squares Method Derivative Values and Cubic Spline Coefficients- 6.2.7
- DGIIPC, RGIIPC
Integral Values and Cubic Spline Coefficients- 6.2.8
- DGIISC, RGIISC
Smoothed Integral Value and Cubic Spline Coefficients- 6.2.9
- DGIIMC, RGIIMC
Least Squares Method Integral Value and Cubic Spline Coefficients- 6.2.10
- DGICCP, RGICCP
Cubic Spline Coefficients (Endpoint Condition Input Unnecessary)- 6.2.11
- DGICCQ, RGICCQ
Cubic Spline Coefficients (Endpoint Conditions Are Input)- 6.2.12
- DGICCR, RGICCR
Cubic Spline Coefficients (Periodic Spline)- 6.2.13
- DGICCS, RGICCS
Cubic Spline Coefficients (Automatic Smoothing)- 6.2.14
- DGICCO, RGICCO
Cubic Spline Coefficients (Automatic Smoothing Periodic Conditions)- 6.2.15
- DGICCT, RGICCT
Cubic Spline Coefficients (Smoothing by Specifying a Control Variable)- 6.2.16
- DGICCM, RGICCM
Cubic Spline Coefficients (Least Squares Method When Knot Positions are Set Automatically)- 6.2.17
- DGICCN, RGICCN
Cubic Spline Coefficients (Least Squares Method When Knot Positions are Specified)- 6.2.18
- DGISCX, RGISCX
Interpolation Values According to Cubic Spline Coefficients- 6.2.19
- DGIDCY, RGIDCY
Derivative Values According to Cubic Spline Coefficients- 6.2.20
- DGIICZ, RGIICZ
Integral Value According to Cubic Spline Coefficients- 6.3
- BICUBIC SPLINE (CURVED SURFACE INTERPOLATION)
- 6.3.1
- DGISXB, RGISXB
Interpolation Values- 6.3.2
- DGIDYB, RGIDYB
Mixed Partial Derivative Values and Bicubic Spline Coefficients- 6.3.3
- DGIIZB, RGIIZB
Double Integral Value- 6.3.4
- DGICBP, RGICBP
Bicubic Spline Coefficients- 6.3.5
- DGISBX, RGISBX
Interpolation Values According to Bicubic Spline Coefficients- 6.3.6
- DGIDBY, RGIDBY
Mixed Partial Derivative Values According to Bicubic Spline Coefficients- 6.3.7
- DGIIBZ, RGIIBZ
Double Integral Value According to Bicubic Spline Coefficients- 6.4
- PLANE DATA INTERPOLATION
- 6.5
- B-SPLINE
- 6.5.1
- DGICBS, RGICBS
B-Spline Calculation- 6.5.2
- DGISI1, RGISI1
Interpolation Using a B-Spline (One-Dimensional Data)- 6.5.3
- DGISI2, RGISI2
Interpolation Using a B-Spline (Two-Dimensional Data)- 6.5.4
- DGISI3, RGISI3
Interpolation Using a B-Spline (Three-Dimensional Data)- 6.5.5
- DGISS1, RGISS1
B-Spline Smoothing (One-Dimensional Data)- 6.5.6
- DGISS2, RGISS2
B-Spline Smoothing (Two-Dimensional Data)- 6.5.7
- DGISS3, RGISS3
B-Spline Smoothing (Three-Dimensional Data)
Appendix
- Appendix A
- MACHINE CONSTANTS USED IN ASL
- A.1
- Units for Determining Error
- A.2
- Maximum and Minimum Values of Floating Point Data
