Matrix multiply transpose vs direct multiplication (v6)

Revision 6 of this benchmark created on

Description

Matrix multiplication normally and with transpose then dot product

Setup

var a = [
  [1, 2, 3, 4, 1, 2, 3, 4],
  [5, 6, 7, 8, 5, 6, 8, 8],
  [11, 12, 13, 14, 11, 12, 13, 14],
  [15, 16, 17, 18, 15, 16, 17, 18],
  [1, 2, 3, 4, 1, 2, 3, 4],
  [5, 6, 7, 8, 5, 6, 8, 8],
  [11, 12, 13, 14, 11, 12, 13, 14],
  [15, 16, 17, 18, 15, 16, 17, 18]
]
var b = [
  [21, 22, 23, 24, 21, 23, 24, 25],
  [35, 36, 37, 38, 35, 36, 37, 38],
  [41, 42, 43, 44, 41, 42, 43, 44],
  [45, 46, 47, 48, 45, 46, 47, 48],
  [21, 22, 23, 24, 21, 23, 24, 25],
  [35, 36, 37, 38, 35, 36, 37, 38],
  [41, 42, 43, 44, 41, 42, 43, 44],
  [45, 46, 47, 48, 45, 46, 47, 48]
]
const initialize = (rows, columns) => {
  let final = new Array(rows);
  for (let i = 0; i < rows; i++) {
    let temp = new Array(columns);
    for (let j = 0; j < columns; j++) {
      temp[j] = 0;
    }
    final[i] = temp;
  }
  return final
}
const dotProduct = (v1, v2) => {
  let sum = 0;
  for (let i = 0; i < v1.length; i++) {
    sum += v1[i] * v2[i]
  }
  return sum
}

function transpose(matrix) {
  for (var i = 0; i < matrix.length; i++) {
    for (var j = 0; j < i; j++) {
      const temp = matrix[i][j];
      matrix[i][j] = matrix[j][i];
      matrix[j][i] = temp;
    }
  }
}
const mult = (X, Y) => {
  let initial = initialize(X.length, Y[0].length)
  //let YTranspose = 
  transpose(Y)
  for (let i = 0; i < X.length; i++) {
    for (let j = 0; j < Y.length; j++) {
      initial[i][j] = dotProduct(X[i], Y[j])
    }
  }
  return initial
}

function proposed_multiply(a, b) {
  let aRows = a.length;
  let aCols = a[0].length;
  let bCols = b[0].length;
  let result = new Array(aRows);
  for (let r = 0; r < aRows; ++r) {
    const row = new Array(bCols);
    result[r] = row;
    const ar = a[r];
    for (let c = 0; c < bCols; ++c) {
      let sum = 0.;
      for (let i = 0; i < aCols; ++i) {
        sum += ar[i] * b[i][c];
      }
      row[c] = sum;
    }
  }
  return result;
}
//schoolbook matrix multiplication
function schoolbook_multiply(m1, m2) {
  var result = [];
  for (var i = 0; i < m1.length; i++) {
    result[i] = [];
    for (var j = 0; j < m2[0].length; j++) {
      var sum = 0;
      for (var k = 0; k < m1[0].length; k++) {
        sum += m1[i][k] * m2[k][j];
      }
      result[i][j] = sum;
    }
  }
  return result;
}

function matrixFunc(A, B) {
  let result = initialize(A.length, B[0].length)
  return result.map((row, i) => {
    return row.map((val, j) => {
      return A[i].reduce((sum, elm, k) => sum + (elm * B[k][j]), 0)
    })
  })
}
let matrixProdExp = (A, B) => A.map(
  (row, i) => B[0].map(
    (_, j) => row.reduce(
      (acc, _, n) => acc + A[i][n] * B[n][j], 0)));

Test runner

Ready to run.

Testing in
TestOps/sec
Plain multiply
schoolbook_multiply(a, b);
ready
Better plain multiply 
proposed_multiply(a,b);
ready
Transpose then dot product
mult(a, b);
ready
Map reduce
matrixFunc(a, b);
ready
Map reduce expression
matrixProdExp(a, b);
ready

Revisions

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