Mathematica ® in the Laboratory

by Samuel Dick , Alfred Riddle , Douglas Stein

• ISBN13: 9780521581370
• ISBN10: 0521581370
• Format: Hardcover
• Copyright: 1997-05-28
• Publisher: Cambridge University Press

Summary

Mathematica®in the Laboratory is a hands-on guide which shows how to harness the power and flexibility of Mathematica in the control of data-acquisition equipment and the analysis of experimental data. It explains how to use Mathematica to import, manipulate, visualise and analyse data from existing files. The generation and export of test data are also covered. The control of laboratory equipment is dealt with in detail, including the use of Mathematica's MathLink® system in instrument control, data processing, and interfacing. Many practical examples are given, which can either be used directly or adapted to suit a particular application. The book sets out clearly how Mathematica can provide a truly unified data-handling environment, and will be invaluable to anyone who collects or analyses experimental data, including astronomers, biologists, chemists, mathematicians, geologists, physicists and engineers. The book is fully compatible with Mathematica 3.0.

Table of Contents

Preface	xv
1 Importing data from files	1	(38)
1.1 File operations in general	1	(3)
1.1.1 Locating files	2	(2)
1.2 File types	4	(1)
1.3 Data structures	4	(2)
1.4 Simple ASCII files	6	(16)
1.4.1 Numbers and strings from free-format ASCII files	6	(3)
1.4.2 String-number conversion	9	(1)
1.4.3 Files with embedded comments	10	(3)
1.4.4 Variably named files	13	(4)
1.4.5 File-content catalogs	17	(3)
1.4.6 Numbers and strings from fixed-format ASCII files	20	(2)
1.5 ASCII files created by spreadsheets	22	(6)
1.6 Mathematica files	28	(1)
1.7 DXF files	29	(6)
1.8 Binary files	35	(3)
1.9 References	38	(1)
2 Visualizing data	39	(48)
2.1 The art of visualization	39	(1)
2.2 Standard graph-plotting functions	40	(2)
2.3 Augmenting standard Mathematica graphs	42	(1)
2.4 Data fusion	43	(5)
2.5 Coping with awkward data	48	(8)
2.5.1 Axis reversal	48	(5)
2.5.2 Complex numbers	53	(1)
2.5.3 Unwrapping cyclic phase data	54	(2)
2.6 Making your own graphs	56	(18)
2.6.1 Polar surface plot	57	(7)
2.6.2 Bar charts and Manhattan plots	64	(10)
2.7 Acquisition-system problems	74	(5)
2.7.1 Glitch removal	74	(2)
2.7.2 Cyclic errors	76	(2)
2.7.3 Stuck ADC or encoder bits	78	(1)
2.8 Listening to your data	79	(8)
2.8.1 Simple waveforms	80	(2)
2.8.2 Listening to the inaudible: Using modulation	82	(4)
2.9 References	86	(1)
3 Data analysis	87	(55)
3.1 Statistical characteristics	87	(5)
3.1.1 Preparing data	89	(1)
3.1.2 Statistics without numbers	90	(2)
3.2 Comparing theory and data	92	(8)
3.2.1 Generating theoretical results	92	(2)
3.2.2 Plotting theory and data	94	(3)
3.2.3 Plotting theory-data differences	97	(3)
3.3 Fitting functions to data	100	(41)
3.3.1 Mathematica's built-in fitting functions	100	(7)
3.3.1.1 Linear fitting	101	(3)
3.3.1.2 Nonlinear fitting	104	(4)
3.3.2 Fitting functions to complex data	108	(11)
3.3.2.1 Simple RC filter	109	(3)
3.3.2.2 LC resonator	112	(7)
3.3.3 Spline-based fitting	119	(9)
3.3.4 Filtering data to remove noise	128	(13)
3.3.4.1 Rejecting outliers	128	(5)
3.3.4.2 Smoothing and filtering	133	(8)
3.4 References	141	(1)
4 Generating test data	142	(16)
4.1 Creating perfect data	142	(3)
4.2 Creating random numbers	145	(12)
4.2.1 Adding noise to simulated data	146	(6)
4.2.2 Random numbers from custom distributions	152	(5)
4.3 References	157	(1)
5 Exporting data	158	(11)
5.1 Basic file operations	158	(1)
5.2 Mathematica output to ASCII files	158	(6)
5.2.1 Evaluated and unevaluated expressions	159	(1)
5.2.2 Definitions	159	(1)
5.2.3 Expressions in C/FORTRAN/TeX forms	160	(1)
5.2.4 Formatted numbers	161	(3)
5.3 Mathematica output to binary files	164	(4)
5.3.1 Numbers	165	(2)
5.3.2 Strings	167	(1)
5.4 References	168	(1)
6 Introduction to instrument control and data acquisition	169	(21)
6.1 Anatomy of an instrument data acquisition system	170	(5)
6.1.1 Standards in instrumentation	170	(2)
6.1.2 Designing your software	172	(1)
6.1.3 Layerology	173	(2)
6.1.3.1 Top (application) layer	173	(1)
6.1.3.2 Hardware assessment layer	173	(1)
6.1.3.3 The computing layer	174	(1)
6.2 Coping with your data	175	(13)
6.2.1 Data assessment	176	(1)
6.2.2 Transmission time	176	(1)
6.2.3 Compression	177	(10)
6.2.4 Binary and ASCII forms	187	(1)
6.3 Safety in laboratory systems	188	(1)
6.4 References	189	(1)
7 Understanding MathLink	190	(35)
7.1 The pons asinorum: addtwo	192	(3)
7.2 Using :Evaluate: to include Mathematica code	195	(1)
7.3 Puting and geting arguments manually	196	(2)
7.4 Passing lists and arrays	198	(4)
7.5 Passing arbitrary expressions	202	(2)
7.6 Requesting evaluations by the kernel	204	(2)
7.7 Handling and recovery of MathLink errors	206	(2)
7.8 Handling and recovery of other errors	208	(8)
7.9 Troubleshooting and debugging	216	(2)
7.10 Large projects	218	(2)
7.11 Special topics	220	(4)
7.11.1 Unknown result length from your program	220	(2)
7.11.1.1 Loopback links	220	(2)
7.11.2 Making your function abortable	222	(2)
7.12 References	224	(1)
8 Interfacing I: a simple serial link	225	(24)
8.1 The serial port hardware	226	(4)
8.1.1 Electrical connections	226	(2)
8.1.2 Serial port parameters	228	(2)
8.2 Software specification	230	(1)
8.3 The Macintosh software	230	(12)
8.3.1 Creating the rs232.XXX project	231	(1)
8.3.2 The application C code	231	(6)
8.3.3 The MathLink template file	237	(2)
8.3.4 Building the executable program	239	(1)
8.3.5 The Mathematica code	239	(3)
8.4 The PC/Linux software	242	(4)
8.4.1 Port configuration	242	(1)
8.4.2 Port use	243	(3)
8.5 Problems?	246	(2)
8.5.1 Checking the hardware	246	(1)
8.5.2 Debugging the C code	247	(1)
8.5.3 Response times	248	(1)
8.6 References	248	(1)
9 Interfacing II: more advanced links	249	(51)
9.1 Design issues	249	(4)
9.1.1 Layers	249	(1)
9.1.2 Polling versus synchronous function calls	250	(2)
9.1.2.1 Mathematica code	251	(1)
9.1.2.2 Macintosh Toolbox	251	(1)
9.1.2.3 Drivers	251	(1)
9.1.2.4 Summary	251	(1)
9.1.3 Looping	252	(1)
9.1.4 Latency	252	(1)
9.2 Handling bare hardware (no support libraries)	253	(8)
9.2.1 The template file: SerialDataAcquisition.tm	254	(1)
9.2.2 The C code: SerialDataAcquisition.c	255	(5)
9.2.3 Using SerialDataAcquisition	260	(1)
9.3 Handling hardware with vendor libraries	261	(30)
9.3.1 One-shot oscilloscope	262	(6)
9.3.1.1 The template file: OneShotScope.tm	262	(1)
9.3.1.2 The C code: OneShotScope.c	262	(4)
9.3.1.3 Using OneShotScope	266	(1)
9.3.1.4 Moving on	267	(1)
9.3.2 Continuous acquisition (one channel)	268	(8)
9.3.2.1 The template file: Oscilloscope.tm	269	(1)
9.3.2.2 The C code: Oscilloscope.c	270	(4)
9.3.2.3 Using Oscilloscope	274	(2)
9.3.3 Streaming data to disk	276	(7)
9.3.3.1 The template file: StreamToDisk.tm	277	(1)
9.3.3.2 The C code: StreamToDisk.c	277	(5)
9.3.3.3 Using StreamToDisk	282	(1)
9.3.3.4 Moving on	282	(1)
9.3.4 Generating a waveform	283	(7)
9.3.4.1 The template file: Generate-Waveform.tm	283	(1)
9.3.4.2 The C code: GenerateWaveform.c	284	(4)
9.3.4.3 Using GenerateWaveform	288	(1)
9.3.4.4 Moving on	289	(1)
9.3.5 Additional projects	290	(1)
9.3.5.1 Counting LEDs	290	(1)
9.3.5.2 Times Square (block character generator)	290	(1)
9.3.5.3 Home heating controls	290	(1)
9.3.5.4 Elevator controls	291	(1)
9.3.5.5 Dream away	291	(1)
9.4 Utility routines	291	(8)
9.4.1 The template file: MitlMain.tm	291	(2)
9.4.2 The C code: MitlUtil.c	293	(6)
9.5 References	299	(1)
10 Interface hardware design	300	(11)
10.1 Simple buffer circuits	301	(3)
10.1.1 Attenuators	301	(1)
10.1.2 Amplifiers	302	(2)
10.1.2.1 Inverting-summing amplifier	302	(1)
10.1.2.2 Differential amplifier	303	(1)
10.1.2.3 Going on	304	(1)
10.2 Noise control	304	(5)
10.2.1 Noise in general	305	(1)
10.2.2 Reducing true noise	306	(1)
10.2.3 Switch debounce	307	(1)
10.2.4 Level detection	307	(2)
10.3 Signal generator	309	(1)
10.4 References	310	(1)
Appendix	311	(1)
A.1 Defining your own functions: a brief summary	311	(1)
A.2 Pure anonymous functions	312	(5)
Index	317