Objective-C中的矩陣乘法

Question

這些是我在我的項目中進行矩陣計算的一些代碼。
它們是兩個類方法和一個實例方法，用於創建矩陣並進行矩陣乘法運算。
矩陣乘法的方法效果不好，它的結果是錯誤的。

+ (NSMutableArray *)arrayOfWidth:(NSInteger)width andHeight:(NSInteger)height { 
    return [[self alloc] initWithWidth:width andHeight:height]; 
} 

- (id)initWithWidth:(NSInteger)width andHeight:(NSInteger)height { 
    if((self = [self initWithCapacity:height])) { 
     for(int i = 0; i < height; i++) { 
      NSMutableArray *inner = [[NSMutableArray alloc] initWithCapacity:width]; 
      [self addObject:inner]; 
     } 
    } 
    return self; 
} 

+ (NSMutableArray *)matrixA:(NSMutableArray *)matrixA multiplyMatrixB:(NSMutableArray *)matrixB { 
    int aRow = [matrixA count]; 
    int aColumn = [[matrixA objectAtIndex:0] count]; 
    int bRow = [matrixB count]; 
    int bColumn = [[matrixB objectAtIndex:0] count]; 
    NSMutableArray *newArray = [NSMutableArray arrayOfWidth:aRow andHeight:bColumn]; 

    for (int i = 0; i < aRow; i++) { 
     for (int j = 0; j < bColumn; j++) { 
      double sum = 0.0; 
      for (int k = 0; k < aColumn; k++) { 
       NSMutableArray *innerA = [matrixA objectAtIndex:i]; 
       double numA = [[innerA objectAtIndex:k] doubleValue]; 
       NSMutableArray * innerB = [matrixB objectAtIndex:k]; 
       double numB = [[innerB objectAtIndex:j] doubleValue]; 
       sum += numA * numB; 
      } 
      NSNumber *result = [NSNumber numberWithDouble:sum]; 
      [[newArray objectAtIndex:i] insertObject:result atIndex:j]; 
     } 
    } 
    return newArray; 
} 

代碼有問題嗎？ 我該如何解決它？

---

//First, I create a array to hold the numbers 
    NSNumber *num11 = [NSNumber numberWithDouble:-2.0]; 
    NSNumber *num12 = [NSNumber numberWithDouble:1.0]; 
    NSNumber *num13 = [NSNumber numberWithDouble:-1.0]; 
    NSNumber *num14 = [NSNumber numberWithDouble:2.0]; 
    NSNumber *num21 = [NSNumber numberWithDouble:-7.0]; 
    NSNumber *num22 = [NSNumber numberWithDouble:0.0]; 
    NSNumber *num23 = [NSNumber numberWithDouble:-1.0]; 
    NSNumber *num24 = [NSNumber numberWithDouble:-4.0]; 
    NSNumber *num31 = [NSNumber numberWithDouble:-2.0]; 
    NSNumber *num32 = [NSNumber numberWithDouble:-1.0]; 
    NSNumber *num33 = [NSNumber numberWithDouble:0.0]; 
    NSNumber *num34 = [NSNumber numberWithDouble:-2.0]; 
    NSNumber *num41 = [NSNumber numberWithDouble:-3.0]; 
    NSNumber *num42 = [NSNumber numberWithDouble:-2.0]; 
    NSNumber *num43 = [NSNumber numberWithDouble:0.0]; 
    NSNumber *num44 = [NSNumber numberWithDouble:-3.0]; 

    NSMutableArray *temp = [NSMutableArray arrayWithObjects:num11, num12, num13, num14, num21, num22, num23, num24, num31, num32, num33, num34, num41, num42, num43, num44, nil]; 

    //Second, I create the matrix and get the elements from that array 
    for (int i = 0; i < 4; i++) { 
     for (int j = 0; j < 4; j++) { 
      double c = [[temp objectAtIndex:4*i+j] doubleValue]; 
      NSNumber *object = [NSNumber numberWithDouble:c]; 
      [[matrix objectAtIndex:i] insertObject:object atIndex:j]; 
     } 
    } 

    //Then, I do the multiplication for matrix and itself 
    NSMutableArray *multiMatrix = [NSMutableArray matrixA:matrix multiplyMatrixB:matrix]; 

    //get all the elements from the multiMatrix 
    double m11 = [[[multiMatrix objectAtIndex:0] objectAtIndex:0] doubleValue]; 
    double m12 = [[[multiMatrix objectAtIndex:0] objectAtIndex:1] doubleValue]; 
    double m13 = [[[multiMatrix objectAtIndex:0] objectAtIndex:2] doubleValue]; 
    double m14 = [[[multiMatrix objectAtIndex:0] objectAtIndex:3] doubleValue]; 

    double m21 = [[[multiMatrix objectAtIndex:1] objectAtIndex:0] doubleValue]; 
    double m22 = [[[multiMatrix objectAtIndex:1] objectAtIndex:1] doubleValue]; 
    double m23 = [[[multiMatrix objectAtIndex:1] objectAtIndex:2] doubleValue]; 
    double m24 = [[[multiMatrix objectAtIndex:1] objectAtIndex:3] doubleValue]; 

    double m31 = [[[multiMatrix objectAtIndex:2] objectAtIndex:0] doubleValue]; 
    double m32 = [[[multiMatrix objectAtIndex:2] objectAtIndex:1] doubleValue]; 
    double m33 = [[[multiMatrix objectAtIndex:2] objectAtIndex:2] doubleValue]; 
    double m34 = [[[multiMatrix objectAtIndex:2] objectAtIndex:3] doubleValue]; 

    double m41 = [[[multiMatrix objectAtIndex:3] objectAtIndex:0] doubleValue]; 
    double m42 = [[[multiMatrix objectAtIndex:3] objectAtIndex:1] doubleValue]; 
    double m43 = [[[multiMatrix objectAtIndex:3] objectAtIndex:2] doubleValue]; 
    double m44 = [[[multiMatrix objectAtIndex:3] objectAtIndex:3] doubleValue]; 

    //Or you can use the NSLog to check the result 
    NSString *lineOne = [NSString stringWithFormat:@"%f, %f, %f, %f", m11, m12, m13, m14]; 
    NSString *lineTwo= [NSString stringWithFormat:@"%f, %f, %f, %f", m21, m22, m23, m24]; 
    NSString *lineThree = [NSString stringWithFormat:@"%f, %f, %f, %f", m31, m32, m33, m34]; 
    NSString *lineFour = [NSString stringWithFormat:@"%f, %f, %f, %f", m41, m42, m43, m44]; 

@rooftop，這是所有的代碼

Answer 1

如果您熟悉MATLAB的向量運算（即使你沒有），我會建議你檢查Accelerate Framework，這是一個優化數字信號處理框架。

兩個很大的優勢：

• 他們有操作已經實現。
• 這是做更有效的方式，但顯然不是爲小矩陣，看到更詳細的評論。

這可能是你正在尋找的功能：

vDSP_mmul：執行兩個矩陣的外的地方繁殖;單精度。

void vDSP_mmul (
    float *__vDSP_a, 
    vDSP_Stride __vDSP_aStride, 
    float *__vDSP_b, 
    vDSP_Stride __vDSP_bStride, 
    float *__vDSP_c, 
    vDSP_Stride __vDSP_cStride, 
    vDSP_Length __vDSP_M, 
    vDSP_Length __vDSP_N, 
    vDSP_Length __vDSP_P 
); 
Parameters 
__vDSP_a 
Input matrix A. 
__vDSP_aStride 
The stride within __vDSP_a. For example if stride is 2, every second element is used. 
__vDSP_b 
Input matrix B. 
__vDSP_bStride 
The stride within __vDSP_b. For example if stride is 2, every second element is used. 
__vDSP_c 
The result matrix. 
__vDSP_M 
The number of rows in matrix A. 
__vDSP_N 
The number of columns in matrix B. 
__vDSP_P 
The number of columns in matrix A and the number of rows in matrix B. 
Discussion 
This function multiplies an M-by-P matrix (A) by a P-by-N matrix (B) and stores the results in an M-by-N matrix (C). 

此執行以下操作：

另一方面，如果寫自己有要求的方法，這個帖子不會幫你的。

Answer 2

如果你在iOS上，你可能要考慮矩陣例程GLKit

Answer 3

主要有兩種錯誤的位置：

1. 在主程序中，你沒有申報matrix。你知道如何解決這個問題。

2. 在創建matrix時，如果您已將矩陣初始化爲零，insertingObject將使矩陣的大小爲'4x8'，而不是'4x4'。

   [[matrix objectAtIndex:i] insertObject:object atIndex:j]; 
   

3. 在你的矩陣乘法的方法，你也insertObject到現有的矩陣，使得它的大小，而不是「4×4」×8'。

要解決此第二個問題，你需要更換方法insertObject:atIndex，與replaceObjectAtIndex:withObject。

這應該解決的問題。