问题
I am a beginner in programming and just learned new concepts and started writing code for matrix multiplication but I got confused in pointers and others so I am uploading my code here in seek of guidelines.
#include <stdio.h>
#include <stdlib.h>
int **matrixMultiply(int A[][8], int B[][8], int row);
int main() {
int **A = allocate_matrix(A, 8, 8);
int **B = allocate_matrix(B, 8, 8);
int i, j;
for (i = 0; i < 8; i++) {
for (j = 0; j < 8; j++) {
A[i][j] = i + j;
A[i][j] = i + j;
}
}
int **C = allocate_matrix(C, 8, 8);
C = matrixMultiply(A, B, 8);
return 0;
}
int **matrixMultiply(int A[][8], int B[][8], int row) {
int **C = allocate_matrix(C, row, row);
if (row == 1) {
C[1][1] = A[1][1] * B[1][1];
} else {
int a11[row/2][row/2], a12[row/2][row/2], a21[row/2][row/2], a22[row/2][row/2];
int b11[row/2][row/2], b12[row/2][row/2], b21[row/2][row/2], b22[row/2][row/2];
int **c11 = allocate_matrix(c11, row/2, row/2);
int **c12 = allocate_matrix(c12, row/2, row/2);
int **c21 = allocate_matrix(c21, row/2, row/2);
int **c22 = allocate_matrix(c22, row/2, row/2);
int i, j;
for (i = 0; i < row/2; i++) {
for (j = 0; j < row/2; j++) {
a11[i][j] = A[i][j];
a12[i][j] = A[i][j + (row/2)];
a21[i][j] = A[i + (row/2)][j];
a22[i][j] = A[i + (row/2)][j + (row/2)];
b11[i][j] = B[i][j];
b12[i][j] = B[i][j + (row/2)];
b21[i][j] = B[i + (row/2)][j];
b22[i][j] = B[i + (row/2)][j + (row/2)];
c11[i][j] = C[i][j];
c12[i][j] = C[i][j + (row/2)];
c21[i][j] = C[i + (row/2)][j];
c22[i][j] = C[i + (row/2)][j + (row/2)];
}
}
c11 = addmatrix(matrixMultiply(a11, b11, row/2),
matrixMultiply(a12, b21, row/2), c11, row/2);
c12 = addmatrix(matrixMultiply(a11, b12, row/2),
matrixMultiply(a22, b22, row/2), c12, row/2);
c21 = addmatrix(matrixMultiply(a21, b11, row/2),
matrixMultiply(a22, b21, row/2), c21, row/2);
c22 = addmatrix(matrixMultiply(a21, b12, row/2),
matrixMultiply(a22, b22, row/2), c22, row/2);
// missing code???
return C;
}
}
int **allocate_matrix(int **matrix, int row, int column) {
matrix = (int **)malloc(row * sizeof(int*));
int i;
for (i = 0; i < row; i++) {
matrix[row] = (int *)malloc(row * sizeof(int));
}
return matrix;
}
void deallocate_matrix(int **matrix, int row) {
int i;
for (i = 0; i < row; i++) {
free(matrix[row]);
}
free(matrix);
}
int **addMatrix(int **a, int **b, int **c, int row) {
int i, j;
for (i = 0; i < row; i++) {
for (j = 0; j < row; j++) {
c[i][j] = a[i][j] + b[i][j];
}
}
return c;
}
回答1:
I reformatted your code so I could analyze it. Indent consistently with 4 spaces, insert spaces around binary operators, after , and ; separators and between keywords and (, this improves readability a lot.
There seems to be missing code in the matrixMultiply function: you allocate the resulting matrix C but you use it as an input to initialize the intermediary matrices c11, c21, c21 and c22, and never actually store anything into C except for the trivial 1x1 case.
The matrix multiplication code seems broken beyond this, the function takes 2 arguments of type int A[][8], int B[][8], but you recursively call it with local arrays a11 to b22 defined as int a11[row/2][row/2]. These types are different, I do not know how the code even compiles.
In the matrix allocation code, you allocate rows with in incorrect size row instead of column. You should use calloc for this so the matrix is initialized to 0, plus you should not pass the initial argument at all:
int **allocate_matrix(int row, int column) {
int **matrix = malloc(row * sizeof(*matrix));
for (int i = 0; i < row; i++) {
matrix[i] = calloc(column, sizeof(*matrix[row]));
}
return matrix;
}
There is also a mistake for the second submatrix multiplication, it should be
c12 = addmatrix(matrixMultiply(a11, b12, row/2),
matrixMultiply(a12, b22, row/2), c12, row/2);
Furthermore, you never free the temporary matrices used for intermediary results. Unlike java, C does not have a garbage collector, you are responsible for releasing blocks of memory when you no longer need them, before they become inaccessible.
Here is a corrected version, with extra functions to print the matrix data and verify the matrix multiplication correctness. I added timings: the recursive method is much slower than the direct method, mostly because of all the extra allocation/deallocation for the intermediary results.
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <time.h>
int **matrix_allocate(int row, int column) {
int **matrix = malloc(row * sizeof(*matrix));
for (int i = 0; i < row; i++) {
matrix[i] = calloc(column, sizeof(*matrix[i]));
}
return matrix;
}
void matrix_free(int **matrix, int row) {
for (int i = 0; i < row; i++) {
free(matrix[i]);
}
free(matrix);
}
void matrix_print(const char *str, int **a, int row) {
int min, max, w = 0, n1, n2, nw;
min = max = a[0][0];
for (int i = 0; i < row; i++) {
for (int j = 0; j < row; j++) {
if (min > a[i][j])
min = a[i][j];
if (max < a[i][j])
max = a[i][j];
}
}
n1 = snprintf(NULL, 0, "%d", min);
n2 = snprintf(NULL, 0, "%d", max);
nw = n1 > n2 ? n1 : n2;
for (int i = 0; i < row; i++) {
if (i == 0)
w = printf("%s = ", str);
else
printf("%*s", w, "");
for (int j = 0; j < row; j++) {
printf(" %*d", nw, a[i][j]);
}
printf("\n");
}
fflush(stdout);
}
int **matrix_add(int **a, int **b, int row, int deallocate) {
int **c = matrix_allocate(row, row);
for (int i = 0; i < row; i++) {
for (int j = 0; j < row; j++) {
c[i][j] = a[i][j] + b[i][j];
}
}
if (deallocate & 1) matrix_free(a, row);
if (deallocate & 2) matrix_free(b, row);
return c;
}
int **matrix_multiply(int **A, int **B, int row, int deallocate) {
int **C = matrix_allocate(row, row);
if (row == 1) {
C[0][0] = A[0][0] * B[0][0];
} else {
int row2 = row / 2;
int **a11 = matrix_allocate(row2, row2);
int **a12 = matrix_allocate(row2, row2);
int **a21 = matrix_allocate(row2, row2);
int **a22 = matrix_allocate(row2, row2);
int **b11 = matrix_allocate(row2, row2);
int **b12 = matrix_allocate(row2, row2);
int **b21 = matrix_allocate(row2, row2);
int **b22 = matrix_allocate(row2, row2);
for (int i = 0; i < row2; i++) {
for (int j = 0; j < row2; j++) {
a11[i][j] = A[i][j];
a12[i][j] = A[i][j + row2];
a21[i][j] = A[i + row2][j];
a22[i][j] = A[i + row2][j + row2];
b11[i][j] = B[i][j];
b12[i][j] = B[i][j + row2];
b21[i][j] = B[i + row2][j];
b22[i][j] = B[i + row2][j + row2];
}
}
int **c11 = matrix_add(matrix_multiply(a11, b11, row2, 0),
matrix_multiply(a12, b21, row2, 0), row2, 1+2);
int **c12 = matrix_add(matrix_multiply(a11, b12, row2, 1),
matrix_multiply(a12, b22, row2, 1), row2, 1+2);
int **c21 = matrix_add(matrix_multiply(a21, b11, row2, 2),
matrix_multiply(a22, b21, row2, 2), row2, 1+2);
int **c22 = matrix_add(matrix_multiply(a21, b12, row2, 1+2),
matrix_multiply(a22, b22, row2, 1+2), row2, 1+2);
for (int i = 0; i < row2; i++) {
for (int j = 0; j < row2; j++) {
C[i][j] = c11[i][j];
C[i][j + row2] = c12[i][j];
C[i + row2][j] = c21[i][j];
C[i + row2][j + row2] = c22[i][j];
}
}
matrix_free(c11, row2);
matrix_free(c12, row2);
matrix_free(c21, row2);
matrix_free(c22, row2);
}
if (deallocate & 1) matrix_free(A, row);
if (deallocate & 2) matrix_free(B, row);
return C;
}
int **matrix_multiply_direct(int **A, int **B, int row, int deallocate) {
int **C = matrix_allocate(row, row);
for (int i = 0; i < row; i++) {
for (int j = 0; j < row; j++) {
int x = 0;
for (int k = 0; k < row; k++) {
x += A[i][k] * B[k][j];
}
C[i][j] = x;
}
}
if (deallocate & 1) matrix_free(A, row);
if (deallocate & 2) matrix_free(B, row);
return C;
}
int main(int argc, char **argv) {
int n = argc < 2 ? 8 : atoi(argv[1]);
int **A = matrix_allocate(n, n);
int **B = matrix_allocate(n, n);
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
A[i][j] = i + j;
B[i][j] = i + j;
}
}
matrix_print("A", A, n);
matrix_print("B", B, n);
if ((n & (n - 1)) == 0) {
/* recursive method can be applied only to powers of 2 */
clock_t ticks = -clock();
int **C = matrix_multiply(A, B, n, 0);
ticks += clock();
matrix_print("C = A * B", C, n);
printf("%d ticks\n", ticks);
matrix_free(C, n);
}
clock_t ticks = -clock();
int **D = matrix_multiply_direct(A, B, n, 1+2);
ticks += clock();
matrix_print("D = A * B", D, n);
printf("%d ticks\n", ticks);
matrix_free(D, n);
return 0;
}
来源：https://stackoverflow.com/questions/34994405/matrix-multiplication-using-divide-and-conquer-approach