如何在Android中进行矩阵求逆和乘法？

Question

给定 2 个矩阵：

public float[] mRi = new float[16];  
public float[] mR = new float[16];  

的两个读数的输出

• 这些将是来自SensorManager.getRotationMatrix(mR, x, y, z) 和
• SensorManager.getRotationMatrix(mRi, x, y, z) code>

所以会有两个 4x4 矩阵，

我想得到以下方程的结果：

• ResultMtrix=inverse(mRi)*mR

事实上我知道它是否适用于 invertM() 和 multiplyMM() 但我不知道如何使用矩阵来做到这一点。

你能帮忙吗？

Answer 1

嘿伙计，我假设它们是 4x4 矩阵（16 个元素）...您可以使用高斯乔丹消除 http://en.wikipedia.org/wiki/Gauss%E2%80%93Jordan_elimination 用于反演。矩阵乘法的描述随处可见，甚至比矩阵求逆还要多。

Answer 2

您描述的矩阵实际上是一维向量，所以我假设您所说的逆实际上是转置。这种情况下的计算非常简单：

方法

// 1 row * 1 column
public static float scalarMultiplication (float[] m1, float[] m2) {
    if (m1.length != m2.length)
        throw new IllegalArgumentException("Vectors need to have the same length");
    float m = 0;
    for (int i=0; i<m1.length; i++)
        m += (m1[i]*m2[i]);
    return m;
}

// N rows * N columns
public static float[][] vectorMultiplication (float[] m1, float[] m2) {
    if (m1.length != m2.length)
        throw new IllegalArgumentException("Vectors need to have the same length");
    float[][] m = new float[m1.length][m1.length];
    for (int i=0; i<m1.length; i++)
        for (int j=0; j<m1.length; j++)
            m[i][j] = (m1[i]*m2[j]);
    return m;
}

测试

            float[] m1 = new float[16];
            float[] m2 = new float[16];

            for (int i=0; i<m1.length; i++) {
                m1[i]=i;
                m2[i]=i*i;
            }

            System.out.println ("Multiple is " + scalarMultiplication(m1, m2));
            float[][] m = vectorMultiplication(m1, m2);
            for (int i=0; i<m[0].length; i++) {
                for (int j=0; j<m[0].length; j++) {
                    System.out.print (m[i][j] +" ");
                }
                System.out.println();
            }

输出

Multiple is 14400.0
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 
0.0 1.0 4.0 9.0 16.0 25.0 36.0 49.0 64.0 81.0 100.0 121.0 144.0 169.0 196.0 225.0 
0.0 2.0 8.0 18.0 32.0 50.0 72.0 98.0 128.0 162.0 200.0 242.0 288.0 338.0 392.0 450.0 
0.0 3.0 12.0 27.0 48.0 75.0 108.0 147.0 192.0 243.0 300.0 363.0 432.0 507.0 588.0 675.0 
0.0 4.0 16.0 36.0 64.0 100.0 144.0 196.0 256.0 324.0 400.0 484.0 576.0 676.0 784.0 900.0 
0.0 5.0 20.0 45.0 80.0 125.0 180.0 245.0 320.0 405.0 500.0 605.0 720.0 845.0 980.0 1125.0 
0.0 6.0 24.0 54.0 96.0 150.0 216.0 294.0 384.0 486.0 600.0 726.0 864.0 1014.0 1176.0 1350.0 
0.0 7.0 28.0 63.0 112.0 175.0 252.0 343.0 448.0 567.0 700.0 847.0 1008.0 1183.0 1372.0 1575.0 
0.0 8.0 32.0 72.0 128.0 200.0 288.0 392.0 512.0 648.0 800.0 968.0 1152.0 1352.0 1568.0 1800.0 
0.0 9.0 36.0 81.0 144.0 225.0 324.0 441.0 576.0 729.0 900.0 1089.0 1296.0 1521.0 1764.0 2025.0 
0.0 10.0 40.0 90.0 160.0 250.0 360.0 490.0 640.0 810.0 1000.0 1210.0 1440.0 1690.0 1960.0 2250.0 
0.0 11.0 44.0 99.0 176.0 275.0 396.0 539.0 704.0 891.0 1100.0 1331.0 1584.0 1859.0 2156.0 2475.0 
0.0 12.0 48.0 108.0 192.0 300.0 432.0 588.0 768.0 972.0 1200.0 1452.0 1728.0 2028.0 2352.0 2700.0 
0.0 13.0 52.0 117.0 208.0 325.0 468.0 637.0 832.0 1053.0 1300.0 1573.0 1872.0 2197.0 2548.0 2925.0 
0.0 14.0 56.0 126.0 224.0 350.0 504.0 686.0 896.0 1134.0 1400.0 1694.0 2016.0 2366.0 2744.0 3150.0 
0.0 15.0 60.0 135.0 240.0 375.0 540.0 735.0 960.0 1215.0 1500.0 1815.0 2160.0 2535.0 2940.0 3375.0