1 / 27

Multidimensional Arrays

Multidimensional Arrays. Multidimensional array is the array with two or more dimensions. For example: char box [3] [3] defines a two-dimensional array and box[2][1] is an element in row 2 , column 1 and char box[][3] can be used in the function prototype

jhamada
Download Presentation

Multidimensional Arrays

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Multidimensional Arrays Multidimensional array is the array with two or more dimensions. For example: char box [3] [3] defines a two-dimensional array and box[2][1] is an element in row 2 , column 1 and char box[][3] can be used in the function prototype note that only the first dimension can be omitted A.Abhari CPS125

  2. Multidimensional Arrays • For example : double table [NROWS][NCOLS]; Can be used as parameter in the function prototype as: void process_martrix( int in[ ][4], int out[ ][4], int nrows) A.Abhari CPS125

  3. Two Dimensional Array • Char box [3] [3] Column 0 1 2 Row 0 box [1] [2] 1 2 A.Abhari CPS125

  4. /* * Checks whether a box is completely filled */ int filled(char box[3][3]) /* input - box to check */ { int r,c, /* row and column subscripts */ ans; /* whether or not box is filled. */ /* Assumes box is filled until blank is found */ ans = 1; /* Resets ans to zero if a blank is found */ for (r = 0; r < 3; ++r) for (c = 0; c < 3; ++c) if (box[r][c] == ' ') ans = 0; return (ans); } A.Abhari CPS125

  5. Arrays with Several Dimensions • int soil_type[4] [7] [MAXDEPTH] A.Abhari CPS125

  6. Case Study: Cellular Telephone System • Problem: Finding the best way to build a cellular network. There is some marketing data that predicts the demand will be at tree time of interest. There are only 10 transmitters and there is a need for a program to help analyzing call demand data. A.Abhari CPS125

  7. Case Study: Cellular Telephone System • Analysis: There should be three matrices shows traffic density for each time of the day: Input: int commuters[GRID_SIZE][GRID_SIZE] int salesforce[GRID_SIZE][GRID_SIZE] int weekend[GRID_SIZE][GRID_SIZE] Output: int summed_data[GRID_SIZE][GRID_SIZE] int location_i, location_j A.Abhari CPS125

  8. Case Study: Cellular Telephone System • Design: initial algorithm: • Get traffic data for three time period • Get the weights from user • Multiply weight by each matrix entry and store the sum in the summed data • Find highest valued cells in the summed data and display them as the pair of location_i and location_j • Implementation A.Abhari CPS125

  9. Filling the multidimensional array /* Fills 3 GRID_SIZE x GRID_SIZE arrays with traffic data from TRAFFIC_FILE*/ void get_traffic_data(int commuters[GRID_SIZE][GRID_SIZE], /* output */ int salesforce[GRID_SIZE][GRID_SIZE], /* output */ int weekend[GRID_SIZE][GRID_SIZE]) /* output */ { int i, j; /* loop counters */ FILE *fp; /* file pointer */ fp = fopen(TRAFFIC_FILE, "r"); for (i = 0; i < GRID_SIZE; ++i) for (j = 0; j < GRID_SIZE; ++j) fscanf(fp, "%d", &commuters[i][j]); for (i = 0; i < GRID_SIZE; ++i) for (j = 0; j < GRID_SIZE; ++j) fscanf(fp, "%d", &salesforce[i][j]); for (i = 0; i < GRID_SIZE; ++i) for (j = 0; j < GRID_SIZE; ++j) fscanf(fp, "%d", &weekend[i][j]); fclose(fp); }

  10. Modifying the multidimensional array /* Computes and displays the weighted, summed_data */ for (i = 0; i < GRID_SIZE; ++i) for (j = 0; j < GRID_SIZE; ++j) summed_data[i][j] = commuter_weight* commuters[i][j] + salesforce_weight * salesforce[i][j] + weekend_weight * weekend[i][j]; A.Abhari CPS125

  11. Searching in the multidimensional array /* Finds the NUM_TRANSMITTERS highest values in the summed_data matrix.Temporarily stores the coordinates in location_i and location_j, and then displays the resulting locations */ printf("\n\nLocations of the %d transmitters:\n\n", NUM_TRANSMITTERS); for (tr = 1; tr <= NUM_TRANSMITTERS; ++tr) { current_max = SELECTED; /* Starts off our search with a value that is known to be too low. */ for (i = 0; i < GRID_SIZE; ++i) { for (j = 0; j < GRID_SIZE; ++j) { if (current_max < summed_data[i][j]) { current_max = summed_data[i][j]; location_i = i; location_j = j; } } }

  12. Printing the contents of multidimensional array /* * Displays contents of a GRID_SIZE x GRID_SIZE matrix of integers */ void print_matrix(int matrix[GRID_SIZE][GRID_SIZE]) { int i, j; /* loop counters */ for (i = 0; i < GRID_SIZE; ++i) { for (j = 0; j < GRID_SIZE; ++j) printf("%3d ", matrix[i][j]); printf("\n"); } } A.Abhari CPS125

  13. Vectors • Vector: a mathematical object consisting of a sequence of numbers. /* a vector <4, 12, 19> */ int vect[3] = {4, 12, 19}; • Differences between vector and array: 1- an n_dimensional vector is represented in C as a one dimensional array of size n. 2- vect3 is vect[2] in C A.Abhari CPS125

  14. Vectors • Calculating scalar product: <1,2,4>. <2,3,1> = 1*2 + 2*3 +4*1=12 In C: sum_prod = 0; for (k=0; k<n; k++) sum_prod += x[k] * w[k]; A.Abhari CPS125

  15. Matrices • Matrix: a mathematical object consisting of a rectangular arrangement of numbers called the element of matrix.. /* a matrix 3 6 4 5 int x[2][2] = {{3, 6}, {4, 5}}; 3 6 x 4 5 A.Abhari CPS125

  16. Matrices • Multiplying a matrix by a vector A * X = V 1 1 1 5 2 3 1 1 10 multiplication 1 -1 -1 * 2 = -3 on 0 1 2 26 the right • In C for each member of V: v[i] = 0; for (k=0; k<n; k++) v[k] += a[i][k] * x[k]; A.Abhari CPS125

  17. /* Computes the product of M-by-N matrix a and the N-dimensional vector x. The result is stored in the output parameter v, an M-dimensional vector.*/ void mat_vec_prod(double v[], /* M-dimensional vector */ double a[M][N], /* M-by-N matrix */ double x[]) /* N-dimensional vector */ { int i, k; for (i = 0; i < M; ++i) { v[i] = 0; for (k = 0; k < N; ++k) { v[i] += a[i][k] * x[k]; } } } A.Abhari CPS125

  18. Matrix Multiplication 1 1 1 2 0 1 6 0 0 2 3 1 * 1 -1 0 = 10 -2 1 1 -1 -1 3 1 -1 -2 0 2 for ( i=0; i< m , ++i) { for (j=0; j<p; ++j) { …….. compute c[i][j]…. } } A.Abhari CPS125

  19. /* Multiplies matrices A and B yielding product matrix C */ void mat_prod(double c[M][P], /* output - M by P matrix */ double a[M][N], /* input - M by N matrix */ double b[N][P]) /* input - N by P matrix */ { int i, j, k; for (i = 0; i < M; ++i) { for (j = 0; j < P; ++j) { c[i][j] = 0; for (k = 0; k < N; ++k) c[i][j] += a[i][k] * b[k][j]; } } } A.Abhari CPS125

  20. Solving System of Linear Equations • To solve many problems such as force equation in three-dimensional system we need to solve a three linear equations: A X = Y 1 1 1 x1 4 2 3 1 * x2 =9 1 -1 -1 x3 -2 It is multiplication of a matrix by a vector on the right A.Abhari CPS125

  21. Gaussian Elimination • Gaussian elimination can be used to solve a linear equation. • The algorithm for Gussian elimination is: • Transform the original system into scaled triangular form. • Solve for xi by back substitution A.Abhari CPS125

  22. Gaussian Elimination triangular form 1 1 1 x1 4 0 1 -1 * x2 =1 0 0 1 x3 1 back substitution x1 + x2 + x3 = 4 x2 - x3 = 1 x3 = 1 A.Abhari CPS125

  23. Gaussian Elimination • For doing that we need to triangularizing the augmented matrix by following operations: • Multiply any row of aug by nonzero number • Add to any row of aug a multiple of other rows • Swap any two rows • If system has a unique solution, we can get the system into desired form by this three operations. A.Abhari CPS125

  24. /* * Performs pivoting with respect to the pth row and the pth column * If no nonzero pivot can be found, FALSE is sent back through piv_foundp */ void pivot(double aug[N][N+1], /* input/output - augmented matrix */ int p, /* input - current row */ int *piv_foundp) /* output - whether or not nonzero pivot found */ { double xmax, xtemp; int j, k, max_row; /* Finds maximum pivot */ xmax = fabs(aug[p][p]); max_row = p; for (j = p+1; j < N; ++j) { if (fabs(aug[j][p]) > xmax) { xmax = fabs(aug[j][p]); max_row = j; } } A.Abhari CPS125

  25. /* Swaps rows if nonzero pivot was found */ if (xmax == 0) { *piv_foundp = FALSE; } else { *piv_foundp = TRUE; if (max_row != p) { /* swap rows */ for (k = p; k < N+1; ++k) { xtemp = aug[p][k]; aug[p][k] = aug[max_row][k]; aug[max_row][k] = xtemp; } } } } A.Abhari CPS125

  26. /* * Performs back substitution to compute a solution vector to a system of * linear equations represented by the augmented matrix aug. Assumes that * the coefficient portion of the augmented matrix has been triangularized, * and its diagonal values are all 1. */ void back_sub(double aug[N][N+1], /* input - scaled, triangularized augmented matrix */ double x[N]) /* output - solution vector */ { double sum; int i, j; x[N - 1] = aug[N - 1][N]; for (i = N - 2; i >= 0; --i) { sum = 0; for (j = i + 1; j < N; ++j) sum += aug[i][j] * x[j]; x[i] = aug[i][N] - sum; } }

  27. Common Programming Errors • Use constants for each dimension’s size when declaring multidimensional array • When declaring the array as a parameter of a function if you omit the first dimension all other dimensions must be supplied • Since access to the elements of a multidimensional array requires nested counting loops it is easy to make out-of-range error. • Since using multidimensional arrays as local variables requires large memory space, you may need to tell to operating system to increase stack size when the program is running A.Abhari CPS125

More Related