~mdw / mLib / blame
| Commit | Line | Data |
|---|---|---|
| adec5584 MW |
1 | .\" -*-nroff-*- |
| 2 | .TH linreg 3 "9 March 2024" "Straylight/Edgeware" "mLib utilities library" | |
| 3 | .\" @linreg_init | |
| 4 | .\" @linreg_update | |
| 5 | .\" @linreg_fit | |
| 6 | .\" @LINREG_INIT | |
| 7 | . | |
| 8 | .SH SYNOPSIS | |
| 9 | .nf | |
| 10 | .B "#include <mLib/linreg.h>" | |
| d056fbdf | 11 | .PP |
| adec5584 MW |
12 | .B "struct linreg { ...\& };" |
| 13 | .B "#define LINREG_INIT ..." | |
| d056fbdf | 14 | .PP |
| adec5584 MW |
15 | .BI "void linreg_init(struct linreg *" lr ); |
| 16 | .BI "void linreg_update(struct linreg *" lr ", double " x ", double " y ); | |
| 17 | .ta \w'void linreg_fit('u | |
| 18 | .BI "void linreg_fit(struct linreg *" lr , | |
| 19 | .BI " double *" m_out ", double *" c_out ", double *" r_out ); | |
| 20 | .fi | |
| 21 | . | |
| 22 | .SH DESCRIPTION | |
| 23 | The functions declared in the | |
| 24 | .B <mLib/linreg.h> | |
| 25 | header perform simple linear regression. | |
| 26 | .PP | |
| 27 | The state for a linear regression is held in a | |
| 28 | .BR "struct linreg" . | |
| 29 | Such a structure can be initialized statically, | |
| 30 | using the | |
| 31 | .B LINREG_INIT macro, | |
| 32 | or dynamically, by calling the | |
| 33 | .B linreg_init | |
| 34 | function. | |
| 35 | .PP | |
| 36 | Once a state is initialized, | |
| 37 | points | |
| 38 | .RI ( x ",\ " y ) | |
| 39 | can be added by calling | |
| 40 | .BR linreg_update . | |
| 41 | Each call just performs a small and constant amount of computation; | |
| 42 | the linear regression state uses a constant amount of storage | |
| 43 | independent of the number of points. | |
| 44 | .P | |
| 45 | Finally, the | |
| 46 | .B linreg_fit | |
| 47 | function will return the results of the regression. | |
| 48 | It calculates quantities | |
| 49 | .I m | |
| 50 | and | |
| 51 | .I c | |
| 52 | such that the line | |
| 53 | .IR y "\ =\ " m "\ " x "\ +\ " c | |
| 54 | is a reasonable approximation to the data points provided, | |
| 55 | and a correlation coefficient | |
| 56 | .I r | |
| 57 | quantifying how good this approximation is. | |
| 58 | These quantities are stored in | |
| 59 | .BI * m_out \fR, | |
| 60 | .BI * c_out \fR, | |
| 61 | and | |
| 62 | .BI * r_out \fR, | |
| 63 | respectively; | |
| 64 | any (or all, but that wouldn't be useful) of these pointers may be null, | |
| 65 | to discard the corresponding output. | |
| 66 | .PP | |
| 67 | The linear regression state can be discarded without need for ceremony: | |
| 68 | it holds no external resources. | |
| 69 | .PP | |
| 70 | Any half-decent introduction to statistics will explain these concepts. | |
| 71 | . | |
| 72 | .SH AUTHOR | |
| 73 | Mark Wooding, <mdw@distorted.org.uk> |