C Numerical Library
™
User's Guide
VOLUME 1 of 4: C Math Library
™
[CHAPTERS 1-7]
VERSION 5.5
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IMSL
Fortran and C and Java
Application Development Tools
IMSL C/Math/Library Table of Contents · i
CMath Library /V1- Table of
Contents
Introduction ix
Chapter 1: Linear Systems 1
Chapter 2: Eigensystem Analysis 115
Chapter 3: Interpolation and Approximation 139
Chapter 4: Quadrature 235
Chapter 5: Differential Equations 289
Chapter 6: Transforms 339
Chapter 7: Nonlinear Equations 383
Appendix A: References A-1
Appendix B: Alphabetical Summary of Routines B-1
Index i
Introduction
IMSL C/Math/Library
The IMSL C/Math/Library is a library of C functions useful in scientific
programming. Each function is designed and documented to be used in research
activities as well as by technical specialists. A number of the example programs
also show graphs of resulting output.
Getting Started
To use any of the IMSL C/Math/Library functions, you first must write a program
in C to call the function. Each function conforms to established conventions in
programming and documentation. We give first priority in development to
efficient algorithms, clear documentation, and accurate results. The uniform
design of the functions makes it easy to use more than one function in a given
application. Also, you will find that the design consistency enables you to apply
your experience with one IMSL C/Math/Library function to all other IMSL
functions that you use.
ANSI C vs. Non-ANSI C
All of the examples in this user’s manual conform to ANSI C. If you are not using
ANSI C, you will need to modify your examples in which functions are declared
or in which arrays are initialized as the type float.
The following is an ANSI C program in which a function is declared. The
program estimates the value of the following:
()
1
1/ 2
0
ln 4xx dx
-
=-
ò
1 #include <math.h>
2 #include <imsl.h>
3
4 float fcn(float x);
5
6 main()
7 {
Introduction IMSL C/Math/Library · ix
x · Getting Started IMSL C/Math/ Library
8 float q, exact;
9 /* evaluate the integral */
10 q = imsl_f_int_fcn_sing (fcn, 0.0, 1.0, 0);
11 /* print the result and the exact answer */
12 exact = -4.0;
13 printf("integral = %10.3f\nexact = %10.3f\n", q, exact);
14 }
15
16 float fcn(float x)
17 {
18 return log(x)/sqrt(x);
19 }
If using non-ANSI C, you would need to modify lines 4 and 16 as follows:
4 float fcn(); /* function is not prototyped */
.
.
.
16 float fcn(x) /*Only variable of function defined here */
16a float x; /* Type of variable declared here */
Non-ANSI C does not allow for automatic aggregate initialization, and thus, all
auto arrays that are initialized as type float in ANSI C must be initialized as type
static float in non-ANSI C. The next program contains arrays that are initialized
as type float.
1 #include <imsl.h>
2
3 main()
4 {
5 int n = 3;
6 float *x;
7 float a[] = {1.0, 3.0, 3.0,
8 1.0, 3.0, 4.0,
9 1.0, 4.0, 3.0};
10
11 float b[] = {1.0, 4.0, -1.0};
12 /* Solve Ax = b for x */
13 x = imsl_f_lin_sol_gen (n, a, b, 0);
14 /* Print x */
15 imsl_f_write_matrix ("Solution, x, of Ax = b", 1, 3, x, 0);
16 }
If using non-ANSI C, you would need to modify lines 7 and 11 as follows:
7 static float a[] = {1.0, 3.0, 3.0,
.
.
.
11 static float b[] = {1.0, 4.0, -1.0};
The imsl.h File
The include file <imsl.h> is used in all of the examples in this manual. This file
contains prototypes for all IMSL-defined functions; the spline structures,
Imsl_f_ppoly, Imsl_d_ppoly, Imsl_f_spline, and Imsl_d_spline; enumerated data
