Gnu Scientific Library Reference Manual,9780954161705

Gnu Scientific Library Reference Manual

by ; ; ; ; ; ;
ISBN13: 9780954161705
ISBN10: 095416170X
Format: Paperback
Pub. Date: 2001-12-01
Publisher(s): Network Theory Ltd
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Summary

The GNU Scientific Library (GSL) is a free numerical library for C and C++ programmers. This reference manual is the definitive guide to the library.

Table of Contents

Preface 1(2)
Introduction
3(4)
Routines available in GSL
3(1)
GSL is Free Software
4(1)
Obtaining GSL
5(1)
An Example Program
5(1)
No Warranty
6(1)
Further Information
6(1)
Using the library
7(8)
ANSI C Compliance
7(1)
Compiling and Linking
7(1)
Shared Libraries
8(1)
Autoconf macros
8(2)
Inline functions
10(1)
Long double
10(1)
Portability functions
11(1)
Alternative optimized functions
12(1)
Support for different numeric types
12(2)
Compatibility with C++
14(1)
Aliasing of arrays
14(1)
Code Reuse
14(1)
Error Handling
15(6)
Error Reporting
15(2)
Error Handlers
17(2)
Using GSL error reporting in your own functions
19(2)
Mathematical Functions
21(6)
Mathematical Constants
21(1)
Infinities and Not-a-number
22(1)
Elementary Functions
22(1)
Small integer powers
23(1)
Testing the Sign of Numbers
24(1)
Testing for Odd and Even Numbers
24(1)
Maximum and Minimum functions
24(3)
Complex Numbers
27(10)
Complex Numbers
27(1)
Properties of complex numbers
28(1)
Complex arithmetic operators
29(2)
Elementary Complex Functions
31(1)
Complex Trigonometric Functions
32(1)
Inverse Complex Trigonometric Functions
32(2)
Complex Hyperbolic Functions
34(1)
Inverse Complex Hyperbolic Functions
35(1)
References and Further Reading
36(1)
Polynomials
37(6)
Polynomial Evaluation
37(1)
Divided Difference Representation of Polynomials
37(1)
Quadratic Equations
38(1)
Cubic Equations
39(1)
General Polynomial Equations
39(1)
Examples
40(1)
References and Further Reading
41(2)
Special Functions
43(54)
Usage
43(1)
The gsl_sf_result struct
44(1)
Modes
44(1)
Airy Functions and Derivatives
45(2)
Airy Functions
45(1)
Derivatives of Airy Functions
46(1)
Zeros of Airy Functions
47(1)
Zeros of Derivatives of Airy Functions
47(1)
Bessel Functions
47(11)
Regular Cylindrical Bessel Functions
48(1)
Irregular Cylindrical Bessel Functions
48(1)
Regular Modified Cylindrical Bessel Functions
49(1)
Irregular Modified Cylindrical Bessel Functions
50(2)
Regular Spherical Bessel Functions
52(1)
Irregular Spherical Bessel Functions
53(1)
Regular Modified Spherical Bessel Functions
54(1)
Irregular Modified Spherical Bessel Functions
55(1)
Regular Bessel Function - Fractional Order
56(1)
Irregular Bessel Function - Fractional Order
56(1)
Regular Modified Bessel Functions-Fractional Order
56(1)
Irregular Modified Bessel Functions-Fractional Order
57(1)
Zeros of Regular Bessel Functions
57(1)
Clausen Functions
58(1)
Coulomb Functions
58(3)
Normalized Hydrogenic Bound States
58(1)
Coulomb Wave Functions
59(1)
Coulomb Wave Function Normalization Constant
60(1)
Coupling Coefficients
61(1)
3-j Symbols
61(1)
6-j Symbols
61(1)
9-j Symbols
62(1)
Dawson Function
62(1)
Debye Functions
62(1)
Dilogarithm
63(1)
Real Argument
63(1)
Complex Argument
63(1)
Elementary Operations
64(1)
Elliptic Integrals
64(3)
Definition of Legendre Forms
64(1)
Definition of Carlson Forms
65(1)
Legendre Form of Complete Elliptic Integrals
65(1)
Legendre Form of Incomplete Elliptic Integrals
65(1)
Carlson Forms
66(1)
Elliptic Functions (Jacobi)
67(1)
Error Functions
67(2)
Error Function
67(1)
Complementary Error Function
68(1)
Log Complementary Error Function
68(1)
Probability functions
68(1)
Exponential Functions
69(2)
Exponential Function
69(1)
Relative Exponential Functions
69(1)
Exponentiation With Error Estimate
70(1)
Exponential Integrals
71(2)
Exponential Integral
71(1)
Ei(x)
71(1)
Hyperbolic Integrals
72(1)
Ei_3(x)
72(1)
Trigonometric Integrals
72(1)
Arctangent Integral
72(1)
Fermi-Dirac Function
73(2)
Complete Fermi-Dirac Integrals
73(1)
Incomplete Fermi-Dirac Integrals
74(1)
Gamma Function
75(4)
Gegenbauer Functions
79(1)
Hypergeometric Functions
80(2)
Laguerre Functions
82(1)
Lambert W Functions
82(1)
Legendre Functions and Spherical Harmonics
83(4)
Legendre Polynomials
83(1)
Associated Legendre Polynomials and Spherical Harmonics
84(1)
Conical Functions
85(1)
Radial Functions for Hyperbolic Space
86(1)
Logarithm and Related Functions
87(1)
Power Function
88(1)
Psi (Digamma) Function
88(1)
Digamma Function
88(1)
Trigamma Function
89(1)
Polygamma Function
89(1)
Synchrotron Functions
89(1)
Transport Functions
90(1)
Trigonometric Functions
90(3)
Circular Trigonometric Functions
91(1)
Trigonometric Functions for Complex Arguments
91(1)
Hyperbolic Trigonometric Functions
92(1)
Conversion Functions
92(1)
Restriction Functions
92(1)
Trigonometric Functions With Error Estimates
93(1)
Zeta Functions
93(1)
Riemann Zeta Function
93(1)
Hurwitz Zeta Function
94(1)
Eta Function
94(1)
Examples
94(1)
References and Further Reading
95(2)
Vectors and Matrices
97(32)
Data types
97(1)
Blocks
98(2)
Block allocation
98(1)
Reading and writing blocks
99(1)
Example programs for blocks
100(1)
Vectors
100(11)
Vector allocation
101(1)
Accessing vector elements
102(1)
Initializing vector elements
103(1)
Reading and writing vectors
103(1)
Vector views
104(3)
Copying vectors
107(1)
Exchanging elements
108(1)
Vector operations
108(1)
Finding maximum and minimum elements of vectors
109(1)
Vector properties
110(1)
Example programs for vectors
110(1)
Matrices
111(16)
Matrix allocation
112(1)
Accessing matrix elements
113(1)
Initializing matrix elements
114(1)
Reading and writing matrices
114(1)
Matrix views
115(4)
Creating row and column views
119(1)
Copying matrices
120(1)
Copying rows and columns
121(1)
Exchanging rows and columns
121(1)
Matrix operations
122(1)
Finding maximum and minimum elements of matrices
123(1)
Matrix properties
124(1)
Example programs for matrices
124(3)
References and Further Reading
127(2)
Permutations
129(8)
The Permutation struct
129(1)
Permutation allocation
129(1)
Accessing permutation elements
130(1)
Permutation properties
131(1)
Permutation functions
131(1)
Applying Permutations
132(1)
Reading and writing permutations
133(1)
Examples
134(1)
References and Further Reading
135(2)
Sorting
137(8)
Sorting objects
137(1)
Sorting vectors
138(2)
Selecting the k-th smallest or largest elements
140(1)
Computing the rank
141(1)
Examples
142(1)
References and Further Reading
143(2)
BLAS Support
145(18)
GSL BLAS Interface
146(15)
Level 1
147(4)
Level 2
151(4)
Level 3
155(6)
Examples
161(1)
References and Further Reading
162(1)
Linear Algebra
163(18)
LU Decomposition
163(3)
QR Decomposition
166(3)
QR Decomposition with Column Pivoting
169(2)
Singular Value Decomposition
171(1)
Cholesky Decomposition
172(1)
Tridiagonal Decomposition of Real Symmetric Matrices
173(1)
Tridiagonal Decomposition of Hermitian Matrices
174(1)
Bidiagonalization
175(1)
Householder solver for linear systems
176(1)
Tridiagonal Systems
176(1)
Examples
177(2)
References and Further Reading
179(2)
Eigensystems
181(6)
Real Symmetric Matrices
181(1)
Complex Hermitian Matrices
182(1)
Sorting Eigenvalues and Eigenvectors
183(1)
Examples
184(2)
References and Further Reading
186(1)
Fast Fourier Transforms (FFTs)
187(22)
Mathematical Definitions
187(1)
Overview of complex data FFTs
188(1)
Radix-2 FFT routines for complex data
189(4)
Mixed-radix FFT routines for complex data
193(4)
Overview of real data FFTs
197(2)
Radix-2 FFT routines for real data
199(1)
Mixed-radix FFT routines for real data
200(6)
References and Further Reading
206(3)
Numerical Integration
209(14)
Introduction
209(2)
QNG non-adaptive Gauss-Kronrod integration
211(1)
QAG adaptive integration
211(1)
QAGS adaptive integration with singularities
212(1)
QAGP adaptive integration with known singular points
213(1)
QAGI adaptive integration on infinite intervals
214(1)
QAWC adaptive integration for Cauchy principal values
215(1)
QAWS adaptive integration for singular functions
215(2)
QAWO adaptive integration for oscillatory functions
217(1)
QAWF adaptive integration for Fourier integrals
218(2)
Error codes
220(1)
Examples
220(1)
References and Further Reading
221(2)
Random Number Generation
223(22)
General comments on random numbers
223(1)
The Random Number Generator Interface
224(1)
Random number generator initialization
224(1)
Sampling from a random number generator
225(1)
Auxiliary random number generator functions
226(2)
Random number environment variables
228(1)
Saving and restoring random number generator state
229(1)
Random number generator algorithms
230(4)
Unix random number generators
234(1)
Numerical Recipes generators
235(1)
Other random number generators
236(5)
Random Number Generator Performance
241(1)
Examples
242(1)
References and Further Reading
243(1)
Acknowledgements
244(1)
Quasi-Random Sequences
245(4)
Quasi-random number generator initialization
245(1)
Sampling from a quasi-random number generator
245(1)
Auxiliary quasi-random number generator functions
246(1)
Saving and resorting quasi-random number generator state
246(1)
Quasi-random number generator algorithms
247(1)
Examples
247(1)
References
248(1)
Random Number Distributions
249(44)
The Gaussian Distribution
250(2)
The Gaussian Tail Distribution
252(2)
The Bivariate Gaussian Distribution
254(1)
The Exponential Distribution
255(1)
The Laplace Distribution
256(1)
The Exponential Power Distribution
257(1)
The Cauchy Distribution
258(1)
The Rayleigh Distribution
259(1)
The Rayleigh Tail Distribution
260(1)
The Landan Distribution
261(1)
The Levy alpha-Stable Distributions
262(1)
The Levy skew alpha-Stable Distribution
263(1)
The Gamma Distribution
264(1)
The Flat (Uniform) Distribution
265(1)
The Lognormal Distribution
266(1)
The Chi-squared Distribution
267(1)
The F-distribution
268(1)
The t-distribution
269(1)
The Beta Distribution
270(1)
The Logistic Distribution
271(1)
The Pareto Distribution
272(1)
The Spherical Distribution (2D & 3D)
273(2)
The Weibull Distribution
275(1)
The Type-1 Gumbel Distribution
276(1)
The Type-2 Gumbel Distribution
277(1)
General Discrete Distributions
278(2)
The Poisson Distribution
280(1)
The Bernoulli Distribution
281(1)
The Binomial Distribution
282(1)
The Negative Binomial Distribution
283(1)
The Pascal Distribution
284(1)
The Geometric Distribution
285(1)
The Hypergeometric Distribution
286(1)
The Logarithmic Distribution
287(1)
Shuffling and Sampling
288(1)
Examples
289(2)
References and Further Reading
291(2)
Statistics
293(14)
Mean, Standard Deviation and Variance
293(2)
Absolute deviation
295(1)
Higher moments (skewness and kurtosis)
295(2)
Autocorrelation
297(1)
Covariance
297(1)
Weighted Samples
298(3)
Maximum and Minimum values
301(1)
Median and Percentiles
302(1)
Example statistical programs
303(2)
References and Further Reading
305(2)
Histograms
307(24)
The histogram struct
307(1)
Histogram allocation
308(1)
Copying Histograms
309(1)
Updating and accessing histogram elements
310(1)
Searching histogram ranges
311(1)
Histogram Statistics
312(1)
Histogram Operations
313(1)
Reading and writing histograms
314(1)
Resampling from histograms
315(1)
The histogram probability distribution struct
315(2)
Example programs for histograms
317(2)
Two dimensional histograms
319(1)
The 2D histogram struct
319(1)
2D Histogram allocation
320(1)
Copying 2D Histograms
321(1)
Updating and accessing 2D histogram elements
321(2)
Searching 2D histogram ranges
323(1)
2D Histogram Statistics
324(1)
2D Histogram Operations
324(1)
Reading and writing 2D histograms
325(2)
Resampling from 2D histograms
327(2)
Example programs for 2D histograms
329(2)
N-tuples
331(8)
The ntuple struct
331(1)
Creating ntuples
331(1)
Opening an existing ntuple file
332(1)
Writing ntuples
332(1)
Reading ntuples
332(1)
Closing an ntuple file
332(1)
Histogramming ntuple values
333(1)
Example programs
334(3)
References and Further Reading
337(2)
Monte Carlo Integration
339(14)
Interface
339(2)
PLAIN Monte Carlo
341(1)
MISER
342(3)
VEGAS
345(4)
Examples
349(3)
References and Further Reading
352(1)
Simulated Annealing
353(10)
Simulated Annealing algorithm
353(1)
Simulated Annealing functions
354(2)
Examples with Simulated Annealing
356(7)
Trivial example
356(3)
Traveling Salesman Problem
359(4)
Ordinary Differential Equations
363(10)
Defining the ODE System
363(1)
Stepping Functions
364(2)
Adaptive Step-size Control
366(2)
Evolution
368(1)
Examples
369(3)
References and Further Reading
372(1)
Interpolation
373(8)
Introduction
373(1)
Interpolation Functions
373(1)
Interpolation Types
374(1)
Index Look-up and Acceleration
375(1)
Evaluation of interpolating functions
376(1)
Higher-level interface
377(1)
Examples
378(1)
References and Further Reading
379(2)
Numerical Differentiation
381(4)
Functions
381(1)
Example
382(1)
References and Further Reading
383(2)
Chebyshev Approximations
385(4)
The gsl_cheb_series struct
385(1)
Creation and Calculation of Chebyshev Series
385(1)
Chebyshev Series Evaluation
386(1)
Derivatives and Integrals
386(1)
Examples
387(1)
References and Further Reading
388(1)
Series Acceleration
389(6)
Acceleration functions
389(1)
Acceleration functions without error estimation
390(1)
Example of accelerating a series
391(2)
References and Further Reading
393(2)
Discrete Hankel Transforms
395(2)
Definitions
395(1)
Functions
396(1)
References and Further Reading
396(1)
One dimensional Root-Finding
397(18)
Overview
397(1)
Caveats
398(1)
Initializing the Solver
399(1)
Providing the function to solve
400(3)
Search Bounds and Guesses
403(1)
Iteration
403(1)
Search Stopping Parameters
404(1)
Root Bracketing Algorithms
405(2)
Root Finding Algorithms using Derivatives
407(2)
Examples
409(5)
References and Further Reading
414(1)
One dimensional Minimization
415(10)
Overview
415(1)
Caveats
416(1)
Initializing the Minimizer
417(1)
Providing the function to minimize
418(1)
Iteration
418(1)
Stopping Parameters
419(1)
Minimization Algorithms
420(1)
Examples
421(2)
References and Further Reading
423(2)
Multidimensional Root-Finding
425(18)
Overview
425(1)
Initializing the Solver
426(2)
Providing the function to solve
428(3)
Iteration
431(1)
Search Stopping Parameters
432(1)
Algorithms using Derivatives
433(2)
Algorithms without Derivatives
435(1)
Examples
436(5)
References and Further Reading
441(2)
Multidimensional Minimization
443(10)
Overview
443(1)
Caveats
444(1)
Initializing the Multidimensional Minimizer
444(1)
Providing a function to minimize
445(2)
Iteration
447(1)
Stopping Criteria
448(1)
Algorithms
449(1)
Examples
450(2)
References and Further Reading
452(1)
Least-Squares Fitting
453(12)
Linear regression
453(1)
Linear fitting without a constant term
454(1)
Multi-parameter fitting
455(2)
Examples
457(6)
References and Further Reading
463(2)
Nonlinear Least-Squares Fitting
465(14)
Overview
465(1)
Initializing the Solver
466(1)
Providing the Function to be Minimized
467(1)
Iteration
468(1)
Search Stopping Parameters
469(1)
Minimization Algorithms using Derivatives
470(1)
Minimization Algorithms without Derivatives
471(1)
Computing the covariance matrix of best fit parameters
472(1)
Examples
472(5)
References and Further Reading
477(2)
Physical Constants
479(8)
Fundamental Constants
479(1)
Astronomy and Astrophysics
480(1)
Atomic and Nuclear Physics
480(1)
Measurement of Time
481(1)
Imperial Units
481(1)
Nautical Units
482(1)
Printers Units
482(1)
Volume
482(1)
Mass and Weight
483(1)
Thermal Energy and Power
483(1)
Pressure
484(1)
Viscosity
484(1)
Light and Illumination
484(1)
Radioactivity
485(1)
Examples
485(1)
References and Further Reading
486(1)
IEEE floating-point arithmetic
487(8)
Representation of floating point numbers
487(2)
Setting up your IEEE environment
489(4)
References and Further Reading
493(2)
Appendix A Debugging Numerical Programs 495(6)
A.1 Using gdb
495(2)
A.2 Examining floating point registers
497(1)
A.3 Handling floating point exceptions
497(1)
A.4 GCC warning options for numerical programs
498(2)
A.5 References and Further Reading
500(1)
Appendix B Contributors to GSL 501(2)
Appendix C Autoconf Macros 503(2)
Appendix D GSL CBLAS Library 505(20)
D.1 Level 1
505(3)
D.2 Level 2
508(9)
D.3 Level 3
517(5)
D.4 Examples
522(3)
GNU General Public License 525(10)
Preamble
525(1)
Terms and Conditions for Copying, Distribution and Modification
526(6)
Appendix: How to Apply These Terms to Your New Programs
532(3)
GNU Free Documentation License 535(10)
Addendum: How to use this License for your documents
543(2)
Other Scientific Packages for the GNU System 545(4)
GNU Octave
545(1)
GNU R
545(2)
GNU Multiprecision Library
547(1)
GNU Linear Programming Kit
547(2)
Function Index 549(18)
Variable Index 567(2)
Type Index 569(2)
Concept Index 571

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