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CNL FUNCTON，即IMSL (International Matrix Software Library) C函数库，是一个广泛使用的数学和统计计算库，专为各种科学、工程和金融应用而设计。这个库在超过30年的历史中，已经建立了可靠性和高效性的声誉。下面将详细讨论CNL FUNCTON中包含的一些关键功能和章节。 1. **线性系统** (Chapter 1: Linear Systems) - 解决线性方程组，包括高斯消元法、LU分解、Cholesky分解、QR分解等。 - 矩阵求逆和行列式计算。 - 线性最小二乘问题的解决方案。 2. **特征值分析** (Chapter 2: Eigensystem Analysis) - 计算实对称矩阵和复矩阵的特征值和特征向量。 - 特征值分解，如Jacobi算法和QR迭代法。 3. **插值与逼近** (Chapter 3: Interpolation and Approximation) - 一维和多维插值方法，如线性插值、多项式插值（如拉格朗日插值和牛顿插值）和样条插值。 - 数据拟合，包括最小二乘曲线拟合和多项式曲线拟合。 4. **数值积分** (Chapter 4: Quadrature) - 一维数值积分，如梯形法则、辛普森法则和高斯积分。 - 多维积分方法，如蒙特卡洛积分和嵌套积分。 5. **微分方程** (Chapter 5: Differential Equations) - 常微分方程（ODEs）的数值解，包括欧拉方法、龙格-库塔方法和隐式方法。 - 偏微分方程（PDEs）的有限差分和有限元方法。 6. **变换** (Chapter 6: Transforms) -傅立叶变换，包括离散傅立叶变换（DFT）、快速傅立叶变换（FFT）和逆变换。 -拉普拉斯变换和Z变换用于信号处理和控制系统分析。 7. **非线性方程** (Chapter 7: Nonlinear Equations) - 非线性方程求解，如牛顿法、二分法和最速下降法。 - 非线性方程组的求解方法，如高斯-赛德尔迭代和雅可比迭代。 8. **优化** (Chapter 8: Optimization) - 无约束优化方法，如梯度下降法、牛顿法和拟牛顿法。 - 约束优化问题的解决，如拉格朗日乘子法和惩罚函数方法。 9. **特殊函数** (Chapter 9: Special Functions) - 幂级数、贝塞尔函数、伽马函数、正态分布函数、误差函数等。 - 这些函数在物理、统计和工程领域有广泛应用。 10. **统计与随机数生成** (Chapter 10: Statistics and Random Number Generation) - 统计分布函数，如正态分布、泊松分布、二项分布等。 - 随机数生成，支持多种分布，用于模拟和实验设计。 11. **打印函数** (Chapter 11: Printing Functions) - 提供数据可视化和结果输出的功能，方便用户进行数据分析和调试。 12. **实用工具** (Chapter 12: Utilities) - 数值工具，如矩阵操作、数值比较和精度控制。 - IMSL C/Stat/Library可能提供额外的统计特定功能，如假设检验、回归分析和时间序列分析。 CNL FUNCTON通过这些丰富的功能，为开发人员提供了强大的数学和统计计算能力，简化了复杂计算任务的实现，使得科研和工程计算更加高效。

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TABLE OF CONTENTS

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1

Mathematical Functionality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Statistical Functionality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

IMSL C/Math/Library . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Chapter 1:

Linear Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6

Chapter 2:

Eigensystem Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6

Chapter 3:

Interpolation and Approximation . . . . . . . . . . . . . . . . . . . . . . . . .7

Chapter 4:

Quadrature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7

Chapter 5:

Differential Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8

Chapter 6:

Transforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8

Chapter 7:

Nonlinear Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9

Chapter 8:

Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9

Chapter 9:

Special Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9

Chapter 10:

Statistics and Random Number Generation . . . . . . . . . . . . . . .12

Chapter 11:

Printing Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13

Chapter 12:

Utilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13

Numeric Utilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .14

IMSL C/Stat/Library . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .15

Chapter 1:

Basic Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Chapter 2:

Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Chapter 3:

Correlation and Covariance . . . . . . . . . . . . . . . . . . . . . . . . . . . .16

Chapter 4:

Analysis of Variance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16

Chapter 5:

Categorical and Discrete Data Analysis . . . . . . . . . . . . . . . . . . .16

Chapter 6:

Nonparametric Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16

Chapter 7:

Tests of Goodness of Fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .17

Chapter 8:

Time Series and Forecasting . . . . . . . . . . . . . . . . . . . . . . . . . . .17

Chapter 9:

Multivariate Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .17

Chapter 10:

Survival Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .17

Chapter 11:

Probability and Distribution Functions . . . . . . . . . . . . . . . . . . . .17

Chapter 12:

Random Number Generation . . . . . . . . . . . . . . . . . . . . . . . . . .18

Chapter 13:

Printing Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .19

Chapter 14:

Utilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .20

IMSL Fortran 90 MP Library . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .21

JNL - A Numerical Library for Java

™

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .21

IMSL C NUMERICAL LIBRARY

Written in C for C / C++ programmers and based on the world's most widely called

numerical subroutines.

The IMSL C Numerical Library ("CNL") is a comprehensive set of over 370 pre-built

mathematical and statistical analysis functions that C or C++ programmers can embed

directly into their numerical analysis applications. Many of CNL's functions are based

upon the same algorithms contained in the company's highly regarded IMSL Fortran 90

MP Library. Visual Numerics, Inc. has been providing algorithms for mathematical and

statistical computations under the IMSL name since 1970.

With CNL, we provide "building blocks" which eliminate the need to write code from

scratch. These prepackaged functions allow you to apply your industry-specific

expertise and reduce your development time.

CNL takes full advantage of the intrinsic characteristics and desirable features of the

C language. Variable argument lists simplify calling sequences. The concise set of

required arguments contains only information necessary for usage. Optional arguments

provide added functionality and power to each function.

CNL is thread safe. Thread safety allows CNL to be used in multithreaded applications

ranging from web-based applications to performing advanced data analysis in real time.

Which gives you increased throughput, better response time, conservation of system

resources and a natural programming structure. Performance benefits can be realized

through concurrent and/or parallel execution.

CNL has also been designed to take advantage of symmetric multiprocessor (SMP)

systems. Computationally intensive algorithms in areas such as linear algebra and fast

Fourier transforms will leverage SMP capabilities on a variety of systems. By allowing

you to replace the generic Basic Linear Algebra Subprograms ("BLAS") contained in

CNL with optimized BLAS from your hardware vendor, you can improve the

performance of your numerical calculations.

You can build applications that are portable across multiple platforms. CNL is available

for computer systems running UNIX and Windows operating systems.

Extensive online documentation provides powerful search capabilities with hundreds of

code examples.

Rely on the industry leader for software that is expertly developed, thoroughly tested,

meticulously maintained and well documented. Get reliable results EVERY TIME!

COST-EFFECTIVENESS AND VALUE

CNL significantly shortens program development time and promotes standardization. Variable argument

lists have been implemented to simplify calling sequences. You'll find that using CNL saves time in your

source code development and saves thousands of dollars in the design, development, documentation,

testing and maintenance of your applications.

ACCURATE, ROBUST AND RELIABLE

CNL uses descriptive, explanatory function names for intuitive programming. Reserved function names

begin with prefixes unique to each product.

Where appropriate, consistent variable names are used to:

• Make function names easy to identify and use and prevent conflicts with other software.

• Provide a common root name for numerical functions that offers the choice of multiple precisions.

ERROR HANDLING

Diagnostic error messages are clear and informative - designed not only to convey the error condition but

also to suggest corrective action if appropriate.

These error-handling features:

• Make it faster and easier for you to debug your programs.

• Provide for more productive programming and confidence that the algorithms are functioning

properly in your application.

PROGRAMMING INTERFACE FLEXIBILITY

CNL takes full advantage of the intrinsic characteristics and desirable features of the C language. The

functions support variable-length argument lists. The concise set of required arguments contains only

information necessary for usage. Optional arguments provide added functionality and power to each

function.

This flexibility:

• Reduces unnecessary code.

• Enables you to adapt each function call by activating optional arguments.

WIDE COMPATIBILITY AND UNIFORM OPERATION

The IMSL C Numerical Library is available for UNIX computing environments and Windows 98/2000/NT.

Visual Numerics' commitment to regular feature and enhancement updates:

• Ensures that your software will perform to the highest standards.

• Provides for portable applications.

• Assures that Visual Numerics will keep pace with the latest hardware and software innovations.

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