如何在 Android 中对矩阵进行求逆和乘法？

Question

给定2个矩阵：

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

这些将是两个读数的输出

• SensorManager.getRotationMatrix(mR, x, y, z)和
• SensorManager.getRotationMatrix(mRi, x, y, z)

所以会有两个 4x4 矩阵，

我想得到以下等式的结果：

• 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。

你能帮我吗？

Answer 1

嘿家伙，我假设它们是 4x4 矩阵（16 个元素）......您可以使用 Gauss-Jordan 消除http://en.wikipedia.org/wiki/Gauss%E2%80%93Jordan_elimination进行反转。 矩阵乘法到处都有描述，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inverse实际上是transpose 。 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();
            }

Output

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