如何通过转置将给定的矩阵相乘？

Question

我必须创建一种方法，通过它的转置来乘以给定的矩阵。

​

​

假设我的矩阵是2d数组double [][] matrix;

public double[][] MultiplyByTranspose(double[][] matrix) 
{  
    return newMatrix;
}

如果需要我的矩阵类，请在answer of this question中检查它

Answer 1

最简单的方法就是实现转置和乘法。

当然，结合在一起时，可以提高效率，但我认为您需要在代码中将转置和乘法作为分离的例程(您已经询问了矩阵旋转的问题)。

public static Boolean IsRectangle(Double[][] value) {
  if (Object.ReferenceEquals(null, value))
    return false;
  else if (value.Length <= 0)
    return false;

  Double[] line = value[value.Length - 1];

  if (Object.ReferenceEquals(null, line))
    return false;

  int size = line.Length;

  for (int i = value.Length - 2; i >= 0; --i)
    if (Object.ReferenceEquals(null, value[i]))
      return false;
    else if (value[i].Length != size)
      return false;

  return true;
}

public static Double[][] Transpose(Double[][] value) {
  if (Object.ReferenceEquals(null, value))
    throw new ArgumentNullException("value");

  if (!IsRectangle(value))
    throw new ArgumentException("value should be a rectangular matrix.", "value");

  int colCount = value.Length;
  int rowCount = value[value.Length - 1].Length;

  Double[][] result = new Double[rowCount][];

  for (int i = rowCount - 1; i >= 0; --i) {
    Double[] line = new Double[colCount];
    result[i] = line;

    for (int j = colCount - 1; j >= 0; --j)
      line[j] = value[j][i];
  }

  return result;
}

// Simple quibic algorithm
public static Double[][] Multiply(Double[][] left, Double[][] right) {
  if (Object.ReferenceEquals(null, left))
    throw new ArgumentNullException("left");
  else if (Object.ReferenceEquals(null, right))
    throw new ArgumentNullException("right");

  if (!IsRectangle(left))
    throw new ArgumentException("left should be a rectangular matrix", "left");
  else if (!IsRectangle(right))
    throw new ArgumentException("right should be a rectangular matrix", "right");

  int leftRows = left.Length;
  int leftCols = left[0].Length;

  int rightRows = right.Length;
  int rightCols = right[0].Length;

  if (leftCols != rightRows)
    throw new ArgumentOutOfRangeException("right");

  Double[][] result = new Double[leftRows][];

  for (int r = leftRows - 1; r >= 0; --r) {
    Double[] leftLine = left[r];
    Double[] line = new Double[rightCols];
    result[r] = line;

    for (int c = rightCols - 1; c >= 0; --c) {
      Double s = 0.0;

      for (int i = leftCols - 1; i >= 0; --i)
        s += leftLine[i] * right[i][c];

      line[c] = s;
    }
  }

  return result;
}

...

public double[][] MultiplyByTranspose(double[][] matrix) {  
  //TODO: Check the order! Which matrix should be the first and which the second,
  // In Linear Algebra A * B != B * A 
  return Multiply(matrix, Transpose(matrix));
  // Or 
  // return Multiply(Transpose(matrix), matrix);
}