Question

I am making a curve fitting program using matrices in the form of a two dimensional arrays but the compiler throws out BAD_ACCESS errors at random such as Thread 1:EXC_BAD_ACCESS (code=1, address=0x13f800000). The program works sometimes and other times crashes. Any ideas would be appreciated. Thanks.

- (void)main {
    NSLog(@"Enter size");

    scanf("%i", &matrixSize);

    float* temp;

    matrix = (float**)calloc(matrixSize, sizeof(float*));
    temp = (float*)calloc(matrixSize+1, sizeof(float));

    for (int i = 0; i < matrixSize+1; i++) {
        matrix[i] = temp + (i*(matrixSize+1));
    }

    [self enterPoints];
    [self elimination];
    [self setNeedsDisplay:YES];
    free(matrix);
    free(temp);
}

//points entered here

- (void)enterPoints {
    CGPoint *points = (CGPoint *)malloc(matrixSize * sizeof(CGPoint));

    for (int i = 0; i < matrixSize; i++) {
        scanf("%lf", &points[i].x);
        scanf("%lf", &points[i].y);
    }

    for (int j = 0; j < matrixSize; j++) {
        for (int i = 0; i < matrixSize+1; i++) {
            if (i == (matrixSize)) {
                matrix[i][j] = points[j].y;
            }
            else {
                matrix[i][j] = pow(points[j].x, (matrixSize-1)-i);
            }
        }
    }
    free(points);
}

//matrix reduction occurs here

- (void)elimination {

    for (int j = 0; j < matrixSize; j++) {
        double divideValue = matrix[j][j];
        for (int i = 0; i < matrixSize+1; i++) {
            matrix[i][j] /= divideValue;
        }
        for (int j1 = 0; j1 < matrixSize; j1++) {
            if (j1 == j) {
                if (j1 == matrixSize-1) {
                    break;
                }
                else {
                    j1++;
                }
            }
            double subValue = matrix[j][j1];
            for (int i = 0; i < matrixSize+1; i++) {
                matrix[i][j1] -= matrix[i][j]*subValue;
            }
        }
    }
}

//drawing the polynomial 

- (void)drawRect:(NSRect)dirtyRect {
    NSGraphicsContext * GraphicsContext = [NSGraphicsContext currentContext];
    CGContextRef context = (CGContextRef) [GraphicsContext graphicsPort];

    CGContextSetRGBStrokeColor(context, 0.0, 0.0, 0.0, 1.0);

    CGContextSetLineWidth(context, 3.0);

    CGContextMoveToPoint(context, 0, matrix[matrixSize][0]*100 + 100);

    [GraphicsContext saveGraphicsState];

    CGMutablePathRef path;

    path = CGPathCreateMutable();

    for (float i = -matrixSize; i < matrixSize; i+=.01) {
        float y = 0;

        for (int j = 0; j < matrixSize; j++) {
             y += matrix[matrixSize][j]*pow(i, j);
        }

        CGContextAddLineToPoint(context, i*100 + 100, y*100 + 100);   
    }

    CGContextStrokePath(context);

    [GraphicsContext restoreGraphicsState];
}

Answer 1

You did not allocate enough memory for your matrix. This line sets up the entire data area, but you have only allocated matrixSize+1 elements, instead of matrixSize*(matrixSize+1):

temp = (float*)calloc(matrixSize+1, sizeof(float));

So, maintaining the matrixSize+1 columns and matrixSize rows:

matrix = (float**)calloc(matrixSize, sizeof(float*));
temp = (float*)calloc(matrixSize * (matrixSize+1), sizeof(float));

for (int i = 0; i < matrixSize; i++) {
    matrix[i] = temp + (i*(matrixSize+1));
}

When you use this later, be careful. You are addressing it wrong:

for (int j = 0; j < matrixSize; j++) {
    for (int i = 0; i < matrixSize+1; i++) {
        if (i == (matrixSize)) {
            matrix[i][j] = points[j].y;
        }
        else {
            matrix[i][j] = pow(points[j].x, (matrixSize-1)-i);
        }
    }
}

Notice that i goes to matrixSize+1 but you are using that as the row index (there are only matrixSize rows). I think you meant to use matrix[j][i] instead of matrix[i][j]. You also do this when you construct the initial matrix, but I’ve actually changed that to be in line with your allocation.

So there are two points of buffer overrun in your program that I see.