CAAM 420 Fall 2012 Lecture 19. Robert T. Prevost

Transcription

1 CAAM 420 Fall 2012 Lecture 19 Robert T. Prevost October 14, 2012

2 Table of Contents 1 Two Dimensional Arrays in C The Stack The Heap Safe Programming Strings and Multidemnsional Arrays

3 1. Two Dimensional Arrays in C 1.1 The Stack First, we will initialize a two dimensional array in C on the stack. The main format for this declaration, provided the array s memory fits on the stack, is as follows: variable_ type variable_ name [ number_ of_ rows ][ number_ of_ columns ]; This will allow for a two dimensional array of variable type with number of rows times number of columns variables of this type. *variable name is a pointer to the first entry of this array and is of type variable type*. Using this initial pointer, we can access the elements of this array by offset from this pointer. However, there is a question of whether the linear memory of the array goes along the rows or the columns first, as computer memory is essentially stored in a linear fashion. The C programing language uses the convention of row-major ordering, meaning that the linear memory is stored along the rows first. This is in contrast to column-major ordering, which is the convention in languages such as Fortran and Matlab. Additional languages that use row-major or column-major ordering can be found at [5]. In regards to the C programing language, for an integer i, inclusively between 0 and number of rows minus 1, variable name[i] is the pointer to the first entry in row i of the array variable name. As variable name[i] is a pointer we can dereference this pointer in the various ways that we have seen before. For example, double A [ 5][ 4]; /* creates 5 by 4 array of doubles */ int i,j,k; k = 0; /* iterate over the rows and columns of A */ for (i =0;i <5;++ i){ for (j =0;j <4;++ j){ /* The following do the same assignment to the ( i, j)- th element of A to the linear index ( row - major ) */ k = 4*i+j; A[i][j] = k; /* In array notation */ *(A[i]+j) = k; /* As offset from the pointer to the i-th row */ *(A [0]+ k) = k; /* As offset from the pointer to the 0-th row or beginning of the array */ A [ 0][ k] = k; /* In array notation, as offset foam the pointer to the 0- th row or the beginning of the array */ (*A)[k] = k; /* In vector notation, as offset foam the pointer to the 0- th row or the beginning of the array */ *((* A)+k) = k; /* Similarly, without brackets */ printf ("A[%d][% d] = %f\n",i,j,a[i][j]); 3

4 1.2 The Heap Next, we will examine creating a two dimensional array on the heap, using dynamic memory allocation. This will be necessary in certain memory intensive cases, as there is only approximately 8 MB of total stack memory using the gcc compilier on Ubuntu [1] [3]. Two things must be done in order to create a two dimensional array on the stack: the memory for the row pointers must be allocated and the memory for all the elements in each row must be allocated. The following is an example of how to allocate an array of type variable type with an arbitrary number of rows and columns with contiguous linear memory. variable_type ** A = ( variable_type **) malloc ( sizeof ( variable_type *)* number_of_rows ); A [0] = ( variable_type *) malloc ( sizeof ( variable_type )* number_of_rows * number_of_columns ); for (i =1;i< number_of_rows ;++ i){ A[i] = A [0] + number_of_columns *i; Now, the entries of A can be populated as we had before. The following code will assign every entry in A to the linear index. int i,j; for (i =0;i< number_of_rows ;++ i){ for (j =0;j< number_of_columns ;++ j){ A[i][j] = number_of_columns *i+j; Finally, we need to free the memory in the arrays from the calls to malloc. free (A [0]) ; free (A); 1.3 Safe Programming In either case, allowing for direct use of pointers can easily lead to mistakes in programing. Additionally, in order to interface with vast library of Fortran programs written for computational science, there will need to be a way to easily exchange between the row-major and column-major styles of C and Fortran. Therefore, we d like to incorporate our two dimensional arrays into a new type, matrix, in order to control the accessing of elements in the two dimensional array as well as control the creation and destruction of these arrays. The type matrix contains the information for the number of rows and columns of the matrix as well as the pointers to the rows to the matrix and fixes the variable type of array. typedef struct { int Nrows, Ncolumns ; double ** row_ pointers ; matrix ; In the function matrix constructor, a matrix of size Nrows by Ncolumns of type double is initialized. 4

5 /* Initializes a variable of type matrix and initializes elements of the struct */ matrix matrix_ constructor ( int Nrows, int Ncolumns ){ /* Creates a variable of type matrix */ matrix A; /* Sets the pointer for the rows pointers array */ A. row_pointers = ( double **) malloc ( Nrows * sizeof ( double *)); /* Sets the pointers for the rows of the array */ A. row_pointers [0] = ( double *) malloc ( Nrows * Ncolumns * sizeof ( double )); for (i =1;i< Nrows ;++ i){ A. row_pointers [i] = A. row_pointers [0] + Ncolumns *i; /* Sets Nrows and Ncolumns */ A. Nrows = Nrows ; A. Ncolumns = Ncolumns ; return A; In the function matrix set, the (row, column) element of the matrix A is set to val. Notice that error checking is packaged into the function in order to avoid unwanted programing errors, especially in reading and writing to memory. /* Set the ( row, column ) element of the matrix A to val */ void matrix_ set ( matrix A, int row, int column, double val ){ /* first checks to see if call to malloc in matrix_ constructor was successful otherwise the value is not set and messages are printed to the screen */ if(a. row_pointers == NULL ){ printf (" matrix_ set matrix not allocated \ n"); /* then a check is made on whether the access to the elements of A can be performed by bounds checking the indices row and column. Only with appropriate indices can the value of the array be set to val */ if(row <A. Nrows && column <A. Ncolumns ){ if( row >=0 && column >=0){ A. row_pointers [ row ][ column ] = val ; else { printf (" matrix_set out of bounds access \n"); Other functions necessary to the manipulation and destruction of the type matrix need to be constructed as done in previous lectures for the type vector (see vector.c at EX12 [4]). Finally, in order to use the created functions and type matrix that we have created in other C functions, we will have to include all the source code for the matrix functions in a file called matrix.c and 5

6 all prototypes for these functions and the type definition for our double matrix in a header file, matrix.h. 1.4 Strings and Multidemnsional Arrays Two dimensional arrays were also used in earlier lectures to represent the second input to main, the string char** argv. However, in this case, each line of the array does not have necessarily the same number of characters. Instead, the end of each row of the array is ended by the terminating character \0 [2]. Additionally, multidimensional arrays can be created on the stack or heap using similar conventions to those used above, e.g a 5x4x3 array of doubles is given by the following: double A [5][4][3]; 6

7 Bibliography [1] Exact Geometric Computation Group. Stack overflow problems, [Online; accessed 14- October-2012]. [2] B.W. Kernighan and D.M. Ritchie. The C programming language. Prentice Hall, [3] LinuxQuestions.org. Default stack size on linux/glibc/pthreads?, [Online; accessed 14- October-2012]. [4] Dr. Timothy C. Warburton. Caam 420: Week 6: structures in c, [Online; accessed 14-October-2012]. [5] Wikipedia. Row-major order Wikipedia, The Free Encyclopedia [Online; accessed 14-October-2012]. 7