├── standalone ├── readme.MD ├── example.ino └── Quickstats.h ├── keywords.txt ├── library.properties ├── examples ├── filternan │ └── filternan.ino ├── slidingavg │ └── slidingavg.ino ├── regression │ └── regression.ino ├── statistics │ └── statistics.ino ├── filterread │ └── filterread.ino └── smoothread │ └── smoothread.ino ├── QuickStats.h ├── Readme.txt ├── README.md ├── QuickStats.cpp └── LICENSE /standalone/readme.MD: -------------------------------------------------------------------------------- 1 | Rather than install a .ZIP version of this library, this standalone version is a bit of a simpler idea. You just save "QuickStats.h" from this directory in the same directory as your sketch, it will load in a separate tab in the Arduino IDE, and then you can follow the syntax in "example.ino" to call the functions. 2 | -------------------------------------------------------------------------------- /keywords.txt: -------------------------------------------------------------------------------- 1 | QuickStats KEYWORD1 2 | average KEYWORD2 3 | g_average KEYWORD2 4 | minimum KEYWORD2 5 | maximum KEYWORD2 6 | stdev KEYWORD2 7 | stderror KEYWORD2 8 | CV KEYWORD2 9 | SNR KEYWORD2 10 | bubbleSort KEYWORD2 11 | median KEYWORD2 12 | mode KEYWORD2 13 | gmdn KEYWORD2 14 | slope KEYWORD2 15 | intercept KEYWORD2 16 | rsq KEYWORD2 17 | rsq_adj KEYWORD2 18 | filternan KEYWORD2 19 | f_round KEYWORD2 20 | -------------------------------------------------------------------------------- /library.properties: -------------------------------------------------------------------------------- 1 | name=QuickStats 2 | version=1.2.5 3 | author=David Dubins 4 | maintainer=David Dubins 5 | sentence=Descriptive Statistics for Arduino 6 | paragraph=Descriptive statistics such as mean, geometric mean, maximum, minimum, sample standard deviation and standard error, median, mode, coefficient of variation, and linear regression. Written for float arrays. 7 | category=Data Processing 8 | url=https://github.com/dndubins/QuickStats 9 | architectures=avr 10 | -------------------------------------------------------------------------------- /examples/filternan/filternan.ino: -------------------------------------------------------------------------------- 1 | // Example program for use with QuickStats.h 2 | // Filter out nan and inf values from a 1-dimensional matrix 3 | // Warning: the filternan function overwrites the original matrix and adjusts the matrix size integer 4 | // (destructive) 5 | 6 | #include "QuickStats.h" 7 | 8 | QuickStats stats; //initialize an instance of this class 9 | int NUMSAMPLES=10; // size of matrix 10 | //create a 1D array with a nan and inf value in it: 11 | float measurements[10]={1.0, 2.0, sqrt(-1), 4.0, 5.0/0.0, 6.0, 7.0, 8.0, 9.0, 10.0}; 12 | 13 | void setup() 14 | { 15 | Serial.begin(9600); 16 | stats.filternan(measurements,NUMSAMPLES); // filter out nan and inf values 17 | Serial.print(stats.average(measurements,NUMSAMPLES)); //calculate and print the average 18 | } 19 | 20 | void loop() 21 | { 22 | } -------------------------------------------------------------------------------- /examples/slidingavg/slidingavg.ino: -------------------------------------------------------------------------------- 1 | // Example program for use with QuickStats.h 2 | // Report sliding average with slope 3 | 4 | #include "QuickStats.h" 5 | 6 | #define NUMREADINGS 10 7 | 8 | byte vPin=A0; 9 | float readings[NUMREADINGS]; 10 | float times[NUMREADINGS]; 11 | int idx=NUMREADINGS; 12 | int count=0; 13 | 14 | QuickStats stats; //initialize an instance of this class 15 | 16 | void setup() 17 | { 18 | Serial.begin(9600); 19 | Serial.println("Reading, Sliding Average, Slope"); 20 | } 21 | 22 | void loop() 23 | { 24 | count++; 25 | idx++; 26 | if(idx>=NUMREADINGS){ 27 | idx=0; 28 | } 29 | times[idx]=millis(); 30 | readings[idx]=analogRead(vPin); 31 | if(count>NUMREADINGS){ 32 | Serial.print(readings[idx]); 33 | Serial.print(", "); 34 | Serial.print(stats.average(readings,NUMREADINGS)); 35 | Serial.print(", "); 36 | Serial.println(stats.slope(times,readings,NUMREADINGS),5); 37 | } 38 | delay(50); 39 | } 40 | -------------------------------------------------------------------------------- /examples/regression/regression.ino: -------------------------------------------------------------------------------- 1 | // Example program for use with QuickStats.h 2 | // Simple linear regression (y=ax+b) 3 | /* Expected Results: 4 | Linear Regression 5 | Slope: 8.12 6 | Intercept: 1.85 7 | r^2: 0.8972 8 | Adjusted r^2: 0.8629 9 | */ 10 | 11 | #include "QuickStats.h" 12 | 13 | int numreadings = 5; 14 | float readings[]={2.15, 3.25, 2.55, 4.64, 7.43}; 15 | float times[]={0.00, 0.10, 0.20, 0.41, 0.62}; 16 | 17 | QuickStats stats; //initialize an instance of this class 18 | 19 | void setup() 20 | { 21 | Serial.begin(9600); 22 | Serial.println("Linear Regression"); 23 | Serial.print("Slope: "); 24 | Serial.println(stats.slope(times,readings,numreadings)); 25 | Serial.print("Intercept: "); 26 | Serial.println(stats.intercept(times,readings,numreadings)); 27 | Serial.print("r^2: "); 28 | Serial.println(stats.rsq(times,readings,numreadings),4); 29 | Serial.print("Adjusted r^2: "); 30 | Serial.println(stats.rsq_adj(times,readings,numreadings),4); 31 | } 32 | 33 | void loop() 34 | { 35 | } 36 | -------------------------------------------------------------------------------- /QuickStats.h: -------------------------------------------------------------------------------- 1 | /* QuickStats.h version 1.2.3 - Library for quick descriptive statistics of an array samples[] of size m, 2 | * assuming a normal distribution. 3 | * Created by David Dubins, January 10th, 2016. 4 | * Last edited: 01-Apr-25. 5 | * https://github.com/dndubins/QuickStats/ 6 | * Released into the public domain. 7 | */ 8 | 9 | #ifndef QuickStats_h 10 | #define QuickStats_h 11 | 12 | #include 13 | 14 | class QuickStats { 15 | public: 16 | QuickStats(); 17 | ~QuickStats(); 18 | float average(float samples[],int m); 19 | float g_average(float samples[],int m); 20 | float minimum(float samples[],int m); 21 | float maximum(float samples[],int m); 22 | float stdev(float samples[],int m); 23 | float stderror(float samples[],int m); 24 | float CV(float samples[],int m); 25 | float SNR(float samples[],int m); 26 | void bubbleSort(float A[],int len); 27 | float fabs(float sample); 28 | float median(float samples[],int m); 29 | float mode(float samples[],int m,float epsilon); 30 | float gmdn(float samples[],int m,float epsilon); 31 | float slope(float x[],float samples[],int m); 32 | float intercept(float x[],float samples[],int m); 33 | float rsq(float x[],float samples[],int m); 34 | float rsq_adj(float x[],float samples[],int m); 35 | void filternan(float samples[],int &m); 36 | void f_round(float samples[], int m, int p); 37 | }; 38 | 39 | #endif 40 | -------------------------------------------------------------------------------- /standalone/example.ino: -------------------------------------------------------------------------------- 1 | // Example sketch for use with QuickStats.h standalone library 2 | // Author: D. Dubins 3 | // Date: 01-Apr-25 4 | // Copy QuickStats.h into the same directory as this sketch. 5 | // The program results should be as follows: 6 | /* 7 | Descriptive Statistics 8 | Average: 3.62 9 | Geometric mean: 3.11 10 | Minimum: 1.00 11 | Maximum: 7.00 12 | Standard Deviation: 2.00 13 | Standard Error: 0.67 14 | Coefficient of Variation (%): 55.23 15 | SNR: 1.81 16 | Median: 3.30 17 | Mode: 2.20 18 | */ 19 | 20 | #include "Quickstats.h" 21 | 22 | int numreadings = 9; 23 | float readings[]={1.0,2.2,4.8,3.3,6.1,2.2,3.8,7.0,2.2}; 24 | 25 | void setup() 26 | { 27 | Serial.begin(9600); 28 | Serial.println("Descriptive Statistics"); 29 | Serial.print("Average: "); 30 | Serial.println(average(readings,numreadings)); 31 | Serial.print("Geometric mean: "); 32 | Serial.println(g_average(readings,numreadings)); 33 | Serial.print("Minimum: "); 34 | Serial.println(minimum(readings,numreadings)); 35 | Serial.print("Maximum: "); 36 | Serial.println(maximum(readings,numreadings)); 37 | Serial.print("Standard Deviation: "); 38 | Serial.println(stdev(readings,numreadings)); 39 | Serial.print("Standard Error: "); 40 | Serial.println(stderror(readings,numreadings)); 41 | Serial.print("Coefficient of Variation (%): "); 42 | Serial.println(CV(readings,numreadings)); 43 | Serial.print("SNR: "); 44 | Serial.println(SNR(readings,numreadings)); 45 | Serial.print("Median: "); 46 | Serial.println(median(readings,numreadings)); 47 | Serial.print("Mode: "); 48 | Serial.println(mode(readings,numreadings,0.00001)); 49 | } 50 | 51 | void loop() 52 | { 53 | } 54 | -------------------------------------------------------------------------------- /examples/statistics/statistics.ino: -------------------------------------------------------------------------------- 1 | // Example program for use with QuickStats.h 2 | // Author: D. Dubins 3 | // Date: 01-Apr-25 4 | /* Expected Results: 5 | Descriptive Statistics 6 | Average: 3.62 7 | Geometric mean: 3.11 8 | Minimum: 1.00 9 | Maximum: 7.00 10 | Standard Deviation: 2.00 11 | Standard Error: 0.67 12 | Coefficient of Variation (%): 55.23 13 | SNR: 1.81 14 | Median: 3.30 15 | Mode: 2.20 16 | GMDN: 3.33 17 | */ 18 | 19 | #include "QuickStats.h" 20 | 21 | int numreadings = 9; 22 | float readings[]={1.0,2.2,4.8,3.3,6.1,2.2,3.8,7.0,2.2}; 23 | 24 | QuickStats stats; //initialize an instance of this class 25 | 26 | void setup() 27 | { 28 | Serial.begin(9600); 29 | Serial.println("Descriptive Statistics"); 30 | Serial.print("Average: "); 31 | Serial.println(stats.average(readings,numreadings)); 32 | Serial.print("Geometric mean: "); 33 | Serial.println(stats.g_average(readings,numreadings)); 34 | Serial.print("Minimum: "); 35 | Serial.println(stats.minimum(readings,numreadings)); 36 | Serial.print("Maximum: "); 37 | Serial.println(stats.maximum(readings,numreadings)); 38 | Serial.print("Standard Deviation: "); 39 | Serial.println(stats.stdev(readings,numreadings)); 40 | Serial.print("Standard Error: "); 41 | Serial.println(stats.stderror(readings,numreadings)); 42 | Serial.print("Coefficient of Variation (%): "); 43 | Serial.println(stats.CV(readings,numreadings)); 44 | Serial.print("SNR: "); 45 | Serial.println(stats.SNR(readings,numreadings)); 46 | Serial.print("Median: "); 47 | Serial.println(stats.median(readings,numreadings)); 48 | Serial.print("Mode: "); 49 | Serial.println(stats.mode(readings,numreadings,0.00001)); 50 | Serial.print("GMDN: "); 51 | Serial.println(stats.gmdn(readings,numreadings,0.00001)); 52 | } 53 | 54 | void loop() 55 | { 56 | } 57 | -------------------------------------------------------------------------------- /examples/filterread/filterread.ino: -------------------------------------------------------------------------------- 1 | // The following program is an example of data smoothing using the QuickStats.h library in Arduino. 2 | // This program filters out NaN values, and rejects measurements outside mean +/- 1.645*sd. 3 | // (~90% of measurements should be within 1.645*sd of mean if the data are normally distributed) 4 | 5 | #include "QuickStats.h" 6 | 7 | #define NUMSAMPLES 100 // number of measurements to make per data point 8 | byte sensorPin = A1; // declaring the analog input to be Pin A1 of Arduino board. 9 | float v = 0.0; // variable to store analog reading 10 | 11 | QuickStats stats; //initialize an instance of this class 12 | 13 | void setup() 14 | { 15 | Serial.begin(9600); // Start the serial monitor 16 | } 17 | 18 | void loop() 19 | { 20 | v=getMes(NUMSAMPLES); // get a measurement 21 | Serial.println(v,3); // Print smoothed value to serial monitor 22 | delay(250); // Change (or remove) this delay to alter the time between readings. 23 | } 24 | 25 | float getMes(int samples) { // routine that takes #samples, filters out NaN values, drops values outside 1.645*standard deviations of mean 26 | float mData[NUMSAMPLES]; // to hold measured data from thermocouple 27 | int cCount=0; // number actually collected 28 | for(int i=0;i 10 | 11 | void bubbleSort(float A[],int len) 12 | { 13 | unsigned long newn; 14 | unsigned long n=len; 15 | float temp=0.0; 16 | do { 17 | newn=1; 18 | for(int p=1;pA[p]){ 20 | temp=A[p]; //swap places in array 21 | A[p]=A[p-1]; 22 | A[p-1]=temp; 23 | newn=p; 24 | } //end if 25 | } //end for 26 | n=newn; 27 | } while(n>1); 28 | } 29 | 30 | float average(float samples[],int m) 31 | { 32 | float avg1=0.0; 33 | for(int i=0;imaxp){ // if this exceeds the largest frequency 167 | maxp=uniquect[p]; // record this number, it's the new mode 168 | maxidx=p; // store the index of the number with the highest freq 169 | } 170 | } else { 171 | p++; // found a new unique number 172 | unique[p]=sorted[i]; 173 | uniquect[p]=1; 174 | } 175 | } 176 | /*for(int i=0;i1) { 183 | return unique[maxidx]; //If there is more than one mode, return the lowest one. 184 | } else { 185 | return 0.0; //If there is no mode, return a zero. 186 | } 187 | } 188 | 189 | 190 | float slope(float x[],float samples[],int m) //calculate the slope (dsamples/dx) 191 | { 192 | float xavg=average(x,m); 193 | float yavg=average(samples,m); 194 | float numerator = 0.0; 195 | float denominator = 0.0; 196 | for(int i=0;i 12 | 13 | QuickStats::QuickStats(){/*nothing to construct*/} 14 | QuickStats::~QuickStats(){/*nothing to destruct*/} 15 | 16 | float QuickStats::average(float samples[],int m) 17 | { 18 | float avg1=0.0; 19 | for(int i=0;iA[p]){ 99 | temp=A[p]; //swap places in array 100 | A[p]=A[p-1]; 101 | A[p-1]=temp; 102 | newn=p; 103 | } //end if 104 | } //end for 105 | n=newn; 106 | } while(n>1); 107 | } 108 | 109 | float QuickStats::fabs(float sample) // calculate absolute value 110 | { 111 | if(sample<0.f){ 112 | return -sample; 113 | }else{ 114 | return sample; 115 | } 116 | } 117 | 118 | float QuickStats::median(float samples[],int m) //calculate the median 119 | { 120 | //First bubble sort the values: https://en.wikipedia.org/wiki/Bubble_sort 121 | float sorted[m]; //Define and initialize sorted array. 122 | float temp=0.0; //Temporary float for swapping elements 123 | /*Serial.println("Before:"); 124 | for(int j=0;jmaxp){ // if this exceeds the largest frequency 172 | maxp=uniquect[p]; // record this number, it's the new mode 173 | maxidx=p; // store the index of the number with the highest freq 174 | } 175 | } else { 176 | p++; // found a new unique number 177 | unique[p]=sorted[i]; 178 | uniquect[p]=1; 179 | } 180 | } 181 | /*for(int i=0;i1) { 188 | return unique[maxidx]; //If there is more than one mode, return the lowest one. 189 | } else { 190 | return 0.0; //If there is no mode, return a zero. 191 | } 192 | } 193 | 194 | float QuickStats::gmdn(float samples[], int m, float epsilon) //geothmetic meandian (https://bebac.at/articles/A-Rant-About-Nice-Numbers.phtml) 195 | { //epsilon is tolerance of conversion (where mean, geometric mean, and median considered equal) 196 | float c1[3]={0.0, 0.0, 0.0}; // to hold mean, geometric mean, median 197 | float c2[3]={0.0, 0.0, 0.0}; // to hold mean, geometric mean, median 198 | float delta=0.0; 199 | c1[0]=average(samples,m); // calculate the mean of the samples 200 | c1[1]=g_average(samples,m); // calculate the geometric mean of the samples 201 | c1[2]=median(samples,m); // calculate the median of the samples 202 | do{ 203 | c2[0]=average(c1,3); // calculate the mean of the three (mean, geometric mean, median) 204 | c2[1]=g_average(c1,3); // calculate the geometric mean of the three (mean, geometric mean, median) 205 | c2[2]=median(c1,3); // calculate the median 206 | delta=(c2[0]-c2[1])+(c2[0]-c2[2]); // calculate the difference between stats 207 | for(byte i=0;i<3;i++){ // write back c2 to c1 208 | c1[i]=c2[i]; 209 | } 210 | }while(delta>epsilon); // did these numbers converge? 211 | return c2[0]; // return converged value 212 | } 213 | 214 | float QuickStats::slope(float x[],float samples[],int m) //calculate the slope (dsamples/dx) 215 | { 216 | float xavg=average(x,m); 217 | float yavg=average(samples,m); 218 | float numerator = 0.0; 219 | float denominator = 0.0; 220 | for(int i=0;i 5 | Everyone is permitted to copy and distribute verbatim copies 6 | of this license document, but changing it is not allowed. 7 | 8 | Preamble 9 | 10 | The GNU General Public License is a free, copyleft license for 11 | software and other kinds of works. 12 | 13 | The licenses for most software and other practical works are designed 14 | to take away your freedom to share and change the works. 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Patents. 472 | 473 | A "contributor" is a copyright holder who authorizes use under this 474 | License of the Program or a work on which the Program is based. The 475 | work thus licensed is called the contributor's "contributor version". 476 | 477 | A contributor's "essential patent claims" are all patent claims 478 | owned or controlled by the contributor, whether already acquired or 479 | hereafter acquired, that would be infringed by some manner, permitted 480 | by this License, of making, using, or selling its contributor version, 481 | but do not include claims that would be infringed only as a 482 | consequence of further modification of the contributor version. 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"Knowingly relying" means you have 508 | actual knowledge that, but for the patent license, your conveying the 509 | covered work in a country, or your recipient's use of the covered work 510 | in a country, would infringe one or more identifiable patents in that 511 | country that you have reason to believe are valid. 512 | 513 | If, pursuant to or in connection with a single transaction or 514 | arrangement, you convey, or propagate by procuring conveyance of, a 515 | covered work, and grant a patent license to some of the parties 516 | receiving the covered work authorizing them to use, propagate, modify 517 | or convey a specific copy of the covered work, then the patent license 518 | you grant is automatically extended to all recipients of the covered 519 | work and works based on it. 520 | 521 | A patent license is "discriminatory" if it does not include within 522 | the scope of its coverage, prohibits the exercise of, or is 523 | conditioned on the non-exercise of one or more of the rights that are 524 | specifically granted under this License. You may not convey a covered 525 | work if you are a party to an arrangement with a third party that is 526 | in the business of distributing software, under which you make payment 527 | to the third party based on the extent of your activity of conveying 528 | the work, and under which the third party grants, to any of the 529 | parties who would receive the covered work from you, a discriminatory 530 | patent license (a) in connection with copies of the covered work 531 | conveyed by you (or copies made from those copies), or (b) primarily 532 | for and in connection with specific products or compilations that 533 | contain the covered work, unless you entered into that arrangement, 534 | or that patent license was granted, prior to 28 March 2007. 535 | 536 | Nothing in this License shall be construed as excluding or limiting 537 | any implied license or other defenses to infringement that may 538 | otherwise be available to you under applicable patent law. 539 | 540 | 12. No Surrender of Others' Freedom. 541 | 542 | If conditions are imposed on you (whether by court order, agreement or 543 | otherwise) that contradict the conditions of this License, they do not 544 | excuse you from the conditions of this License. If you cannot convey a 545 | covered work so as to satisfy simultaneously your obligations under this 546 | License and any other pertinent obligations, then as a consequence you may 547 | not convey it at all. For example, if you agree to terms that obligate you 548 | to collect a royalty for further conveying from those to whom you convey 549 | the Program, the only way you could satisfy both those terms and this 550 | License would be to refrain entirely from conveying the Program. 551 | 552 | 13. Use with the GNU Affero General Public License. 553 | 554 | Notwithstanding any other provision of this License, you have 555 | permission to link or combine any covered work with a work licensed 556 | under version 3 of the GNU Affero General Public License into a single 557 | combined work, and to convey the resulting work. The terms of this 558 | License will continue to apply to the part which is the covered work, 559 | but the special requirements of the GNU Affero General Public License, 560 | section 13, concerning interaction through a network will apply to the 561 | combination as such. 562 | 563 | 14. Revised Versions of this License. 564 | 565 | The Free Software Foundation may publish revised and/or new versions of 566 | the GNU General Public License from time to time. Such new versions will 567 | be similar in spirit to the present version, but may differ in detail to 568 | address new problems or concerns. 569 | 570 | Each version is given a distinguishing version number. If the 571 | Program specifies that a certain numbered version of the GNU General 572 | Public License "or any later version" applies to it, you have the 573 | option of following the terms and conditions either of that numbered 574 | version or of any later version published by the Free Software 575 | Foundation. If the Program does not specify a version number of the 576 | GNU General Public License, you may choose any version ever published 577 | by the Free Software Foundation. 578 | 579 | If the Program specifies that a proxy can decide which future 580 | versions of the GNU General Public License can be used, that proxy's 581 | public statement of acceptance of a version permanently authorizes you 582 | to choose that version for the Program. 583 | 584 | Later license versions may give you additional or different 585 | permissions. However, no additional obligations are imposed on any 586 | author or copyright holder as a result of your choosing to follow a 587 | later version. 588 | 589 | 15. Disclaimer of Warranty. 590 | 591 | THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY 592 | APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT 593 | HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY 594 | OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, 595 | THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR 596 | PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM 597 | IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF 598 | ALL NECESSARY SERVICING, REPAIR OR CORRECTION. 599 | 600 | 16. Limitation of Liability. 601 | 602 | IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING 603 | WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS 604 | THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY 605 | GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE 606 | USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF 607 | DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD 608 | PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), 609 | EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF 610 | SUCH DAMAGES. 611 | 612 | 17. Interpretation of Sections 15 and 16. 613 | 614 | If the disclaimer of warranty and limitation of liability provided 615 | above cannot be given local legal effect according to their terms, 616 | reviewing courts shall apply local law that most closely approximates 617 | an absolute waiver of all civil liability in connection with the 618 | Program, unless a warranty or assumption of liability accompanies a 619 | copy of the Program in return for a fee. 620 | 621 | END OF TERMS AND CONDITIONS 622 | 623 | How to Apply These Terms to Your New Programs 624 | 625 | If you develop a new program, and you want it to be of the greatest 626 | possible use to the public, the best way to achieve this is to make it 627 | free software which everyone can redistribute and change under these terms. 628 | 629 | To do so, attach the following notices to the program. It is safest 630 | to attach them to the start of each source file to most effectively 631 | state the exclusion of warranty; and each file should have at least 632 | the "copyright" line and a pointer to where the full notice is found. 633 | 634 | 635 | Copyright (C) 636 | 637 | This program is free software: you can redistribute it and/or modify 638 | it under the terms of the GNU General Public License as published by 639 | the Free Software Foundation, either version 3 of the License, or 640 | (at your option) any later version. 641 | 642 | This program is distributed in the hope that it will be useful, 643 | but WITHOUT ANY WARRANTY; without even the implied warranty of 644 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 645 | GNU General Public License for more details. 646 | 647 | You should have received a copy of the GNU General Public License 648 | along with this program. If not, see . 649 | 650 | Also add information on how to contact you by electronic and paper mail. 651 | 652 | If the program does terminal interaction, make it output a short 653 | notice like this when it starts in an interactive mode: 654 | 655 | Copyright (C) 656 | This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. 657 | This is free software, and you are welcome to redistribute it 658 | under certain conditions; type `show c' for details. 659 | 660 | The hypothetical commands `show w' and `show c' should show the appropriate 661 | parts of the General Public License. Of course, your program's commands 662 | might be different; for a GUI interface, you would use an "about box". 663 | 664 | You should also get your employer (if you work as a programmer) or school, 665 | if any, to sign a "copyright disclaimer" for the program, if necessary. 666 | For more information on this, and how to apply and follow the GNU GPL, see 667 | . 668 | 669 | The GNU General Public License does not permit incorporating your program 670 | into proprietary programs. If your program is a subroutine library, you 671 | may consider it more useful to permit linking proprietary applications with 672 | the library. If this is what you want to do, use the GNU Lesser General 673 | Public License instead of this License. But first, please read 674 | . 675 | --------------------------------------------------------------------------------