This library can be used to generate cache efficient map/reduce operations for ndarrays.
For brevity, we will assume the following precedes each example:
//Import libraries
var cwise = require("cwise")
, ndarray = require("ndarray")The array equivalent of +=:
//Create operation
var addeq = cwise({
args: ["array", "array"],
body: function(a, b) {
a += b
}
})
//Create two 2D arrays
var X = ndarray(new Float32Array(128*128), [128,128])
var Y = ndarray(new Float32Array(128*128), [128,128])
//Add them together
addeq(X, Y)Formally, you can think of addeq(X,Y) as being something like the following for-loop, except optimized with respect to the dimension and order of X and Y:
for(var i=0; i<X.shape[0]; ++i) {
for(var j=0; j<X.shape[1]; ++j) {
X.set(i,j, X.get(i,j) + Y.get(i,j))
}
}var muls = cwise({
args: ["array", "scalar"],
body: function(a, s) {
a *= s
}
})
//Example usage:
muls(array, 2.0)var mgrid = cwise({
args: ["index", "array"],
body: function(i, a) {
a = i[0]
}
})
//Example usage:
var X = mgrid(ndarray(new Float32Array(128)))var norm2D = cwise({
args: ["array", {blockIndices: -1}],
body: function(o, i) {
o = Math.sqrt(i[0]*i[0] + i[1]*i[1])
}
})
//Example usage:
var o = ndarray([0, 0, 0], [3])
norm2D(o, ndarray([1, 2, 3, 4, 5, 6], [3,2]))
// o.data == [ 2.23606797749979, 5, 7.810249675906654 ]Note that in the above, i is not an actual Array, the indexing notation is just syntactic sugar.
var laplacian = cwise({
args:["array", "array", {offset:[0,1], array:1}, {offset:[0,-1], array:1}, {offset:[1,0], array:1}, {offset:[-1,0], array:1}],
body:function(a, c, n, s, e, w) {
a = 0.25 * (n + s + e + w) - c
}
})
laplacian(next, prev)var sum = cwise({
args: ["array"],
pre: function() {
this.sum = 0
},
body: function(a) {
this.sum += a
},
post: function() {
return this.sum
}
})
//Usage:
s = sum(array)Note that variables stored in this are common to all three code blocks. Also note that one should not treat this as an actual object (for example, one should not attempt to return this).
var any = cwise({
args: ["array"],
body: function(a) {
if(a) {
return true
}
},
post: function() {
return false
}
})
//Usage
if(any(array)) {
// ...
}var argmin = cwise({
args: ["index", "array"],
pre: function(index) {
this.min_v = Number.POSITIVE_INFINITY
this.min_index = index.slice(0)
},
body: function(index, a) {
if(a < this.min_v) {
this.min_v = a
for(var i=0; i<index.length; ++i) {
this.min_index[i] = index[i]
}
}
},
post: function() {
return this.min_index
}
})
//Usage:
argmin(X)Install using npm:
npm install cwise
To use the library, you pass it an object with the following fields:
args: (Required) An array describing the type of the arguments passed to the body. These may be one of the following:"array": Anndarray-type argument"scalar": A globally broadcasted scalar argument"index": (Hidden) An array representing the current index of the element being processed. Initially [0,0,...] in the pre block and set to some undefined value in the post block."shape": (Hidden) An array representing the shape of the arrays being processed- An object representing a "blocked" array (for example a colour image, an array of matrices, etc.):
blockIndicesThe number of indices (from the front of the array shape) to expose in the body (rather than iterating over them). Negative integers take indices from the back of the array shape.
- (Hidden) An object containing two properties representing an offset pointer from an array argument. Note that cwise does not implement any boundary conditions.
offsetAn array representing the relative offset of the objectarrayThe index of an array parameter
pre: A function to be executed before starting the loopbody: (Required) A function that gets applied to each element of the input arrayspost: Executed when loop completesprintCode: If this flag is set, then log all generated codeblockSize: The size of a block (default 32)funcName: The name to give to the generated procedure for debugging/profiling purposes. (Default isbody.name||"cwise")
The result is a procedure that you can call which executes these methods along the following lines:
function(a0, a1, ...) {
pre()
for(var i=0; i<a0.shape[0]; ++i) {
for(var j=0; j<a0.shape[1]; ++j) {
...
body(a0[i,j,...], a1[i,j,...], ... )
}
}
post()
}- To pass variables between the pre/body/post, use
this.* - The order in which variables get visited depends on the stride ordering if the input arrays. In general it is not safe to assume that elements get visited (co)lexicographically.
- If no return statement is specified, the first ndarray argument is returned
- All input arrays must have the same shape. If not, then the library will throw an error
If bundle size is an issue for you, it is possible to use cwise as a browserify transform, thus avoiding the potentially large parser dependencies. To do this, add the following lines to your package.json:
//Contents of package.json
{
// ...
"browserify": {
"transform": [ "cwise" ]
}
// ...
}Then when you use the module with browserify, only the cwise-compile submodule will get loaded into your script instead of all of esprima. Note that this step is optional and the library will still work in the browser even if you don't use a transform.
You can think of cwise as a type of macro language on top of JavaScript. Internally, cwise uses node-falafel to parse the functions you give it and sanitize their arguments. At run time, code for each array operation is generated lazily depending on the ordering and stride of the input arrays so that you get optimal cache performance. These compiled functions are then memoized for future calls to the same function. As a result, you should reuse array operations as much as possible to avoid wasting time and memory regenerating common functions.
(c) 2013 Mikola Lysenko. MIT License
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