113. Multiplying matrices via the Vector API

Let’s consider two matrices of 4x4 denoted as X and Y. Z=X*Y is as follows:

Figure 5.10: Multiplying two matrices (X * Y = Z)

Multiplying X with Y means multiplying the first row from X with the first column from Y, the second row from X with the second column from Y, and so on. For instance, (1 x 3) + (2 x 7) + (5 x 5) + (4 x 5) = 3 + 14 + 25 + 20 = 62. Basically, we repeatedly apply FMA computation and fill up Z with the results.

In this context, and based on the previous problem about computing FMA, we can produce the following code for multiplying X with Y:

private static final VectorSpecies<Float> VS 
  = FloatVector.SPECIES_PREFERRED;
public static float[] mulMatrix(
    float[] x, float[] y, int size) {
  final int upperBound = VS.loopBound(size);
  float[] z = new float[size * size];
  for (int i = 0; i < size; i++) {
    for (int k = 0; k < size; k++) {
      float elem = x[i * size + k];
      FloatVector eVector = FloatVector.broadcast(VS, elem);
      for (int j = 0; j < upperBound; j += VS.length()) {
        FloatVector yVector = FloatVector.fromArray(
            VS, y, k * size + j);
        FloatVector zVector = FloatVector.fromArray(
            VS, z, i * size + j);
        zVector = eVector.fma(yVector, zVector);
        zVector.intoArray(z, i * size + j);
      }
    }
  }
  return z;
}

In the bundled code, you can find this example next to another one using SPECIES_512.