Michael Shimniok / Mbed 2 deprecated AVC_2012

Code for autonomous ground vehicle, Data Bus, 3rd place winner in 2012 Sparkfun AVC.

Dependencies:   Watchdog mbed Schedule SimpleFilter LSM303DLM PinDetect DebounceIn Servo

Estimation/Matrix/Matrix.cpp@0:826c6171fc1b, 2012-06-20 (annotated)

Committer:
shimniok
Date:
Wed Jun 20 14:57:48 2012 +0000
Revision:
0:826c6171fc1b
Updated documentation

Who changed what in which revision?

UserRevisionLine numberNew contents of line
shimniok 0:826c6171fc1b 1 #include <stdio.h>
shimniok 0:826c6171fc1b 2 #include "Matrix.h"
shimniok 0:826c6171fc1b 3
shimniok 0:826c6171fc1b 4 unsigned int matrix_error = 0;
shimniok 0:826c6171fc1b 5
shimniok 0:826c6171fc1b 6 void Vector_Cross_Product(float C[3], float A[3], float B[3])
shimniok 0:826c6171fc1b 7 {
shimniok 0:826c6171fc1b 8 C[0] = (A[1] * B[2]) - (A[2] * B[1]);
shimniok 0:826c6171fc1b 9 C[1] = (A[2] * B[0]) - (A[0] * B[2]);
shimniok 0:826c6171fc1b 10 C[2] = (A[0] * B[1]) - (A[1] * B[0]);
shimniok 0:826c6171fc1b 11
shimniok 0:826c6171fc1b 12 return;
shimniok 0:826c6171fc1b 13 }
shimniok 0:826c6171fc1b 14
shimniok 0:826c6171fc1b 15 void Vector_Scale(float C[3], float A[3], float b)
shimniok 0:826c6171fc1b 16 {
shimniok 0:826c6171fc1b 17 for (int m = 0; m < 3; m++)
shimniok 0:826c6171fc1b 18 C[m] = A[m] * b;
shimniok 0:826c6171fc1b 19
shimniok 0:826c6171fc1b 20 return;
shimniok 0:826c6171fc1b 21 }
shimniok 0:826c6171fc1b 22
shimniok 0:826c6171fc1b 23 float Vector_Dot_Product(float A[3], float B[3])
shimniok 0:826c6171fc1b 24 {
shimniok 0:826c6171fc1b 25 float result = 0.0;
shimniok 0:826c6171fc1b 26
shimniok 0:826c6171fc1b 27 for (int i = 0; i < 3; i++) {
shimniok 0:826c6171fc1b 28 result += A[i] * B[i];
shimniok 0:826c6171fc1b 29 }
shimniok 0:826c6171fc1b 30
shimniok 0:826c6171fc1b 31 return result;
shimniok 0:826c6171fc1b 32 }
shimniok 0:826c6171fc1b 33
shimniok 0:826c6171fc1b 34 void Vector_Add(float C[3], float A[3], float B[3])
shimniok 0:826c6171fc1b 35 {
shimniok 0:826c6171fc1b 36 for (int m = 0; m < 3; m++)
shimniok 0:826c6171fc1b 37 C[m] = A[m] + B[m];
shimniok 0:826c6171fc1b 38
shimniok 0:826c6171fc1b 39 return;
shimniok 0:826c6171fc1b 40 }
shimniok 0:826c6171fc1b 41
shimniok 0:826c6171fc1b 42 void Vector_Add(float C[3][3], float A[3][3], float B[3][3])
shimniok 0:826c6171fc1b 43 {
shimniok 0:826c6171fc1b 44 for (int m = 0; m < 3; m++)
shimniok 0:826c6171fc1b 45 for (int n = 0; n < 3; n++)
shimniok 0:826c6171fc1b 46 C[m][n] = A[m][n] + B[m][n];
shimniok 0:826c6171fc1b 47 }
shimniok 0:826c6171fc1b 48
shimniok 0:826c6171fc1b 49 void Matrix_Add(float C[3][3], float A[3][3], float B[3][3])
shimniok 0:826c6171fc1b 50 {
shimniok 0:826c6171fc1b 51 for (int i = 0; i < 3; i++) {
shimniok 0:826c6171fc1b 52 for (int j = 0; j < 3; j++) {
shimniok 0:826c6171fc1b 53 C[i][j] = A[i][j] + B[i][j];
shimniok 0:826c6171fc1b 54 }
shimniok 0:826c6171fc1b 55 }
shimniok 0:826c6171fc1b 56 }
shimniok 0:826c6171fc1b 57
shimniok 0:826c6171fc1b 58 void Matrix_Add(int n, int m, float *C, float *A, float *B)
shimniok 0:826c6171fc1b 59 {
shimniok 0:826c6171fc1b 60 for (int i = 0; i < n*m; i++) {
shimniok 0:826c6171fc1b 61 C[i] = A[i] + B[i];
shimniok 0:826c6171fc1b 62 }
shimniok 0:826c6171fc1b 63 }
shimniok 0:826c6171fc1b 64
shimniok 0:826c6171fc1b 65 void Matrix_Subtract(int n, int m, float *C, float *A, float *B)
shimniok 0:826c6171fc1b 66 {
shimniok 0:826c6171fc1b 67 for (int i = 0; i < n*m; i++) {
shimniok 0:826c6171fc1b 68 C[i] = A[i] - B[i];
shimniok 0:826c6171fc1b 69 }
shimniok 0:826c6171fc1b 70 }
shimniok 0:826c6171fc1b 71
shimniok 0:826c6171fc1b 72
shimniok 0:826c6171fc1b 73
shimniok 0:826c6171fc1b 74 // grabbed from MatrixMath library for Arduino
shimniok 0:826c6171fc1b 75 // http://arduino.cc/playground/Code/MatrixMath
shimniok 0:826c6171fc1b 76 // E.g., the equivalent Octave script:
shimniok 0:826c6171fc1b 77 // A=[x; y; z];
shimniok 0:826c6171fc1b 78 // B=[xx xy xz; yx yy yz; zx xy zz];
shimniok 0:826c6171fc1b 79 // C=A*B;
shimniok 0:826c6171fc1b 80 // Would be called like this:
shimniok 0:826c6171fc1b 81 // Matrix_Mulitply(1, 3, 3, C, A, B);
shimniok 0:826c6171fc1b 82 //
shimniok 0:826c6171fc1b 83 void Matrix_Multiply(int m, int p, int n, float *C, float *A, float *B)
shimniok 0:826c6171fc1b 84 {
shimniok 0:826c6171fc1b 85 // A = input matrix (m x p)
shimniok 0:826c6171fc1b 86 // B = input matrix (p x n)
shimniok 0:826c6171fc1b 87 // m = number of rows in A
shimniok 0:826c6171fc1b 88 // p = number of columns in A = number of rows in B
shimniok 0:826c6171fc1b 89 // n = number of columns in B
shimniok 0:826c6171fc1b 90 // C = output matrix = A*B (m x n)
shimniok 0:826c6171fc1b 91 for (int i=0; i < m; i++) {
shimniok 0:826c6171fc1b 92 for(int j=0; j < n; j++) {
shimniok 0:826c6171fc1b 93 C[n*i+j] = 0;
shimniok 0:826c6171fc1b 94 for (int k=0; k < p; k++) {
shimniok 0:826c6171fc1b 95 C[i*n+j] += A[i*p+k] * B[k*n+j];
shimniok 0:826c6171fc1b 96 }
shimniok 0:826c6171fc1b 97 }
shimniok 0:826c6171fc1b 98 }
shimniok 0:826c6171fc1b 99
shimniok 0:826c6171fc1b 100 return;
shimniok 0:826c6171fc1b 101 }
shimniok 0:826c6171fc1b 102
shimniok 0:826c6171fc1b 103 void Matrix_Multiply(float C[3][3], float A[3][3], float B[3][3])
shimniok 0:826c6171fc1b 104 {
shimniok 0:826c6171fc1b 105 for (int i = 0; i < 3; i++) {
shimniok 0:826c6171fc1b 106 for (int j = 0; j < 3; j++) {
shimniok 0:826c6171fc1b 107 C[i][j] = 0;
shimniok 0:826c6171fc1b 108 for (int k = 0; k < 3; k++) {
shimniok 0:826c6171fc1b 109 C[i][j] += A[i][k] * B[k][j];
shimniok 0:826c6171fc1b 110 }
shimniok 0:826c6171fc1b 111 }
shimniok 0:826c6171fc1b 112 }
shimniok 0:826c6171fc1b 113 }
shimniok 0:826c6171fc1b 114
shimniok 0:826c6171fc1b 115
shimniok 0:826c6171fc1b 116 void Matrix_Transpose(int n, int m, float *C, float *A)
shimniok 0:826c6171fc1b 117 {
shimniok 0:826c6171fc1b 118 for (int i=0; i < n; i++) {
shimniok 0:826c6171fc1b 119 for (int j=0; j < m; j++) {
shimniok 0:826c6171fc1b 120 C[j*n+i] = A[i*m+j];
shimniok 0:826c6171fc1b 121 }
shimniok 0:826c6171fc1b 122 }
shimniok 0:826c6171fc1b 123 }
shimniok 0:826c6171fc1b 124
shimniok 0:826c6171fc1b 125 #define fabs(x) (((x) < 0) ? -x : x)
shimniok 0:826c6171fc1b 126
shimniok 0:826c6171fc1b 127 // grabbed from MatrixMath library for Arduino
shimniok 0:826c6171fc1b 128 // http://arduino.cc/playground/Code/MatrixMath
shimniok 0:826c6171fc1b 129 //Matrix Inversion Routine
shimniok 0:826c6171fc1b 130 // * This function inverts a matrix based on the Gauss Jordan method.
shimniok 0:826c6171fc1b 131 // * Specifically, it uses partial pivoting to improve numeric stability.
shimniok 0:826c6171fc1b 132 // * The algorithm is drawn from those presented in
shimniok 0:826c6171fc1b 133 // NUMERICAL RECIPES: The Art of Scientific Computing.
shimniok 0:826c6171fc1b 134 // * NOTE: The argument is ALSO the result matrix, meaning the input matrix is REPLACED
shimniok 0:826c6171fc1b 135 void Matrix_Inverse(int n, float *A)
shimniok 0:826c6171fc1b 136 {
shimniok 0:826c6171fc1b 137 // A = input matrix AND result matrix
shimniok 0:826c6171fc1b 138 // n = number of rows = number of columns in A (n x n)
shimniok 0:826c6171fc1b 139 int pivrow=0; // keeps track of current pivot row
shimniok 0:826c6171fc1b 140 int k,i,j; // k: overall index along diagonal; i: row index; j: col index
shimniok 0:826c6171fc1b 141 int pivrows[n]; // keeps track of rows swaps to undo at end
shimniok 0:826c6171fc1b 142 float tmp; // used for finding max value and making column swaps
shimniok 0:826c6171fc1b 143
shimniok 0:826c6171fc1b 144 for (k = 0; k < n; k++) {
shimniok 0:826c6171fc1b 145 // find pivot row, the row with biggest entry in current column
shimniok 0:826c6171fc1b 146 tmp = 0;
shimniok 0:826c6171fc1b 147 for (i = k; i < n; i++) {
shimniok 0:826c6171fc1b 148 if (fabs(A[i*n+k]) >= tmp) { // 'Avoid using other functions inside abs()?'
shimniok 0:826c6171fc1b 149 tmp = fabs(A[i*n+k]);
shimniok 0:826c6171fc1b 150 pivrow = i;
shimniok 0:826c6171fc1b 151 }
shimniok 0:826c6171fc1b 152 }
shimniok 0:826c6171fc1b 153
shimniok 0:826c6171fc1b 154 // check for singular matrix
shimniok 0:826c6171fc1b 155 if (A[pivrow*n+k] == 0.0f) {
shimniok 0:826c6171fc1b 156 matrix_error |= SINGULAR_MATRIX;
shimniok 0:826c6171fc1b 157 //fprintf(stdout, "Inversion failed due to singular matrix");
shimniok 0:826c6171fc1b 158 return;
shimniok 0:826c6171fc1b 159 }
shimniok 0:826c6171fc1b 160
shimniok 0:826c6171fc1b 161 // Execute pivot (row swap) if needed
shimniok 0:826c6171fc1b 162 if (pivrow != k) {
shimniok 0:826c6171fc1b 163 // swap row k with pivrow
shimniok 0:826c6171fc1b 164 for (j = 0; j < n; j++) {
shimniok 0:826c6171fc1b 165 tmp = A[k*n+j];
shimniok 0:826c6171fc1b 166 A[k*n+j] = A[pivrow*n+j];
shimniok 0:826c6171fc1b 167 A[pivrow*n+j] = tmp;
shimniok 0:826c6171fc1b 168 }
shimniok 0:826c6171fc1b 169 }
shimniok 0:826c6171fc1b 170 pivrows[k] = pivrow; // record row swap (even if no swap happened)
shimniok 0:826c6171fc1b 171
shimniok 0:826c6171fc1b 172 tmp = 1.0f/A[k*n+k]; // invert pivot element
shimniok 0:826c6171fc1b 173 A[k*n+k] = 1.0f; // This element of input matrix becomes result matrix
shimniok 0:826c6171fc1b 174
shimniok 0:826c6171fc1b 175 // Perform row reduction (divide every element by pivot)
shimniok 0:826c6171fc1b 176 for (j = 0; j < n; j++) {
shimniok 0:826c6171fc1b 177 A[k*n+j] = A[k*n+j]*tmp;
shimniok 0:826c6171fc1b 178 }
shimniok 0:826c6171fc1b 179
shimniok 0:826c6171fc1b 180 // Now eliminate all other entries in this column
shimniok 0:826c6171fc1b 181 for (i = 0; i < n; i++) {
shimniok 0:826c6171fc1b 182 if (i != k) {
shimniok 0:826c6171fc1b 183 tmp = A[i*n+k];
shimniok 0:826c6171fc1b 184 A[i*n+k] = 0.0f; // The other place where in matrix becomes result mat
shimniok 0:826c6171fc1b 185 for (j = 0; j < n; j++) {
shimniok 0:826c6171fc1b 186 A[i*n+j] = A[i*n+j] - A[k*n+j]*tmp;
shimniok 0:826c6171fc1b 187 }
shimniok 0:826c6171fc1b 188 }
shimniok 0:826c6171fc1b 189 }
shimniok 0:826c6171fc1b 190 }
shimniok 0:826c6171fc1b 191
shimniok 0:826c6171fc1b 192 // Done, now need to undo pivot row swaps by doing column swaps in reverse order
shimniok 0:826c6171fc1b 193 for (k = n-1; k >= 0; k--) {
shimniok 0:826c6171fc1b 194 if (pivrows[k] != k) {
shimniok 0:826c6171fc1b 195 for (i = 0; i < n; i++) {
shimniok 0:826c6171fc1b 196 tmp = A[i*n+k];
shimniok 0:826c6171fc1b 197 A[i*n+k] = A[i*n+pivrows[k]];
shimniok 0:826c6171fc1b 198 A[i*n+pivrows[k]] = tmp;
shimniok 0:826c6171fc1b 199 }
shimniok 0:826c6171fc1b 200 }
shimniok 0:826c6171fc1b 201 }
shimniok 0:826c6171fc1b 202 return;
shimniok 0:826c6171fc1b 203 }
shimniok 0:826c6171fc1b 204
shimniok 0:826c6171fc1b 205
shimniok 0:826c6171fc1b 206 void Matrix_Copy(int n, int m, float *C, float *A)
shimniok 0:826c6171fc1b 207 {
shimniok 0:826c6171fc1b 208 for (int i=0; i < n*m; i++)
shimniok 0:826c6171fc1b 209 C[i] = A[i];
shimniok 0:826c6171fc1b 210 }
shimniok 0:826c6171fc1b 211
shimniok 0:826c6171fc1b 212 void Matrix_print(int n, int m, float *A, const char *name)
shimniok 0:826c6171fc1b 213 {
shimniok 0:826c6171fc1b 214 fprintf(stdout, "%s=[", name);
shimniok 0:826c6171fc1b 215 for (int i=0; i < n; i++) {
shimniok 0:826c6171fc1b 216 for (int j=0; j < m; j++) {
shimniok 0:826c6171fc1b 217 fprintf(stdout, "%5.5f", A[i*m+j]);
shimniok 0:826c6171fc1b 218 if (j < m-1) fprintf(stdout, ", ");
shimniok 0:826c6171fc1b 219 }
shimniok 0:826c6171fc1b 220 if (i < n-1) fprintf(stdout, "; ");
shimniok 0:826c6171fc1b 221 }
shimniok 0:826c6171fc1b 222 fprintf(stdout, "]\n");
shimniok 0:826c6171fc1b 223 }
shimniok 0:826c6171fc1b 224
shimniok 0:826c6171fc1b 225
shimniok 0:826c6171fc1b 226 void Vector_Print(float A[3], const char *name)
shimniok 0:826c6171fc1b 227 {
shimniok 0:826c6171fc1b 228 fprintf(stdout, "%s=[ ", name);
shimniok 0:826c6171fc1b 229 for (int i=0; i < 3; i++)
shimniok 0:826c6171fc1b 230 fprintf(stdout, "%5.5f ", A[i]);
shimniok 0:826c6171fc1b 231 fprintf(stdout, "]\n");
shimniok 0:826c6171fc1b 232
shimniok 0:826c6171fc1b 233 return;
shimniok 0:826c6171fc1b 234 }
shimniok 0:826c6171fc1b 235