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ndarray.js
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2307 lines (2132 loc) · 67.4 KB
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/**
* Numpy like n-dimensional array proccessing class
* http://docs.scipy.org/doc/numpy/reference/arrays.ndarray.html
*
* @author pissang (https://github.com/pissang/)
*/
define(function(require) {
'use strict';
var kwargs = require('./kwargs');
var ArraySlice = Array.prototype.slice;
// Polyfill of Typed Array
this.Int32Array = window.Int32Array || Array;
this.Int16Array = window.Int16Array || Array;
this.Int8Array = window.Int8Array || Array;
this.Uint32Array = window.Uint32Array || Array;
this.Uint16Array = window.Uint16Array || Array;
this.Uint8Array = window.Uint8Array || Array;
this.Float32Array = window.Float32Array || Array;
this.Float64Array = window.Float64Array || Array;
// Map of numpy dtype and typed array
// http://docs.scipy.org/doc/numpy/reference/arrays.dtypes.html#arrays-dtypes
// http://www.khronos.org/registry/typedarray/specs/latest/
var ArrayConstructor = {
'int32' : this.Int32Array,
'int16' : this.Int16Array,
'int8' : this.Int8Array,
'uint32' : this.Uint32Array,
'uint16' : this.Uint16Array,
'uint8' : this.Uint8Array,
// 'uint8c' is not existed in numpy
'uint8c' : this.Uint8ClampedArray,
'float32' : this.Float32Array,
'float64' : this.Float64Array,
'number' : Array
};
var dTypeStrideMap = {
'int32' : 4,
'int16' : 2,
'int8' : 1,
'uint32' : 4,
'uint16' : 2,
'uint8' : 1,
'uint8c' : 1,
'float32' : 4,
'float64' : 8,
// Consider array stride is 1
'number' : 1
};
var E_ADD = 0;
var E_SUB = 1;
var E_MUL = 2;
var E_DIV = 3;
var E_MOD = 4;
var E_AND = 5;
var E_OR = 6;
var E_XOR = 7;
var E_EQL = 8;
function guessDataType(arr) {
if (typeof(arr) === 'undefined') {
return 'number';
}
switch(Object.prototype.toString.call(arr)) {
case '[object Int32Array]':
return 'int32';
case '[object Int16Array]':
return 'int16';
case '[object Int8Array]':
return 'int8';
case '[object Uint32Array]':
return 'uint32';
case '[object Uint16Array]':
return 'uint16';
case '[object Uint8Array]':
return 'uint8';
case '[object Uint8ClampedArray]':
return 'uint8c';
case '[object Float32Array]':
return 'float32';
case '[object Float64Array]':
return 'float64';
default:
return 'number';
}
}
/**
* NDArray
* @param {Array|NDArray} array
* @param {String} dtype
*/
var NDArray = function(array) {
// Last argument describe the data type of ndarray
var dtype = arguments[arguments.length-1];
if (typeof(dtype) == 'string') {
this._dtype = dtype;
} else {
// Normal array
this._dtype = guessDataType(array);
}
if (array && typeof(array) !== 'string') {
if (array instanceof NDArray) {
array._dtype = this._dtype;
return array;
} else if (typeof(array.length) !== 'undefined') {
// Init from array
this.initFromArray(array);
} else if(typeof(array) === 'number') {
// Init from shape
this.initFromShape.apply(this, arguments);
}
} else {
/**
* _array
* Initialized with an empty array
* Data is continuous one-dimensional array, row-major
* A [2, 2] dim empty array is stored like
* [0,0, 0,0]
* TODO : Consider column majors ?
* @type {ArrayConstructor}
*/
this._array = new ArrayConstructor[this._dtype]();
/**
* _shape
* a tuple array describe the dimension and size of each dimension
* [10, 10] means a 10x10 array
* @type {Array}
*/
this._shape = [0];
/**
* _size
* size of the storage array length
* @type {Number}
*/
this._size = 0;
}
};
NDArray.prototype = {
/**
* Initialize from a normal js array.
*
* @param {Array} input
* @return {NDArray} this
*/
initFromArray : function(input) {
var dim = getDimension(input);
var cursor = 0;
function flatten(axis, _out, _in) {
var len = _in.length;
for (var i = 0; i < len; i++) {
if (axis < dim-1) {
flatten(axis+1, _out, _in[i]);
} else {
_out[cursor++] = _in[i];
}
}
}
var shape = getShape(input);
var size = getSize(shape);
this._array = new ArrayConstructor[this._dtype](size);
flatten(0, this._array, input);
this._shape = shape;
this._size = size;
return this;
},
/**
* Initialize from the given shape description.
* @param {Array} shape
* @return {NDArray} this
*/
initFromShape : function(shape) {
if (typeof(shape) == 'number') {
shape = Array.prototype.slice.call(arguments);
}
if(shape) {
var size = getSize(shape);
if (this._dtype === 'number') {
this._array = [];
var data = this._array;
for (var i = 0; i < size; i++) {
data[i] = 0;
}
} else {
this._array = new ArrayConstructor[this._dtype](size);
}
}
this._shape = shape;
this._size = getSize(shape);
return this;
},
/**
* Fill the array with the given value.
* @param {Number} value
* @return {NDArray} this
*/
fill : function(value) {
var data = this._array;
for (var i = 0; i < data.length; i++) {
data[i] = value;
}
return this;
},
/**
* Get ndarray shape copy.
* @return {Array}
*/
shape : function() {
// Create a copy
return this._shape.slice();
},
/**
* Get array size
* @return {Number}
*/
size : function() {
return this._size;
},
/**
* Get array data type.
* 'int32'
* 'int16'
* 'int8'
* 'uint32'
* 'uint16'
* 'uint8'
* 'float32'
* 'float64'
* @return {String}
*/
dtype : function() {
return this._dtype;
},
/**
* Get array dimension.
* @return {[type]} [description]
*/
dimension : function() {
return this._shape.length;
},
/**
* Tuple of bytes to step in each dimension when traversing an array.
* @return {Array}
*/
strides : function() {
var strides = calculateDimStrides(this._shape);
var dTypeStride = dTypeStrideMap[this._dtype];
for (var i = 0; i < strides.length; i++) {
strides[i] *= dTypeStride;
}
return strides;
},
/**
* Gives a new shape to an array without changing its data.
* @param {Array} shape
* @return {NDArray}
*/
reshape : function(shape) {
if (typeof(shape) == 'number') {
shape = Array.prototype.slice.call(arguments);
}
if (this._isShapeValid(shape)) {
this._shape = shape;
} else {
throw new Error('Total size of new array must be unchanged');
}
return this;
},
_isShapeValid : function(shape) {
return getSize(shape) === this._size;
},
/**
* Change shape and size of array in-place.
* @param {Array} shape
* @return {NDArray}
*/
resize : function(shape) {
if (typeof(shape) == 'number') {
shape = Array.prototype.slice.call(arguments);
}
var len = getSize(shape);
if (len < this._size) {
if (this._dtype === 'number') {
this._array.length = len;
}
} else {
if (this._dtype === 'number') {
for (var i = this._array.length; i < len; i++) {
// Fill the rest with zero
this._array[i] = 0;
}
} else {
// Reallocate new buffer
var newArr = new ArrayConstructor[this._dtype](len);
var originArr = this._array;
// Copy data
for (var i = 0; i < originArr.length; i++) {
newArr[i] = originArr[i];
}
this._array = newArr;
}
}
this._shape = shape;
this._size = len;
return this;
},
/**
* Returns a new array with axes transposed.
* @param {Array} [axes]
* @param {NDArray} [out]
* @return {NDArray}
*/
transpose : kwargs(function(axes, out) {
var originAxes = [];
for (var i = 0; i < this._shape.length; i++) {
originAxes.push(i);
}
if (typeof(axes) === 'undefined') {
axes = originAxes.slice();
}
// Check if any axis is out of bounds
for (var i = 0; i < axes.length; i++) {
if (axes[i] >= this._shape.length) {
throw new Error(axisOutofBoundsErrorMsg(axes[i]));
}
}
// Has no effect on 1-D transpose
if (axes.length <= 1) {
return this;
}
var targetAxes = originAxes.slice();
for (var i = 0; i < Math.floor(axes.length / 2); i++) {
for (var j = axes.length-1; j >= Math.ceil(axes.length / 2) ; j--) {
// Swap axes
targetAxes[axes[i]] = axes[j];
targetAxes[axes[j]] = axes[i];
}
}
return this._transposelike(targetAxes, out);
}),
/**
* Return a new array with axis1 and axis2 interchanged.
* @param {Number} axis1
* @param {Number} axis2
* @param {NDArray} out
* @return {NDArray}
*/
swapaxes : kwargs(function(axis1, axis2, out) {
return this.transpose([axis1, axis2], out);
}),
/**
* Roll the specified axis backwards, until it lies in a given position.
* @param {Number} axis
* @param {Number} [start=0]
* @param {NDArray} out
* @return {NDArray}
*/
rollaxis : kwargs(function(axis, start, out) {
if (axis >= this._shape.length) {
throw new Error(axisOutofBoundsErrorMsg(axis));
}
var axes = [];
for (var i = 0; i < this._shape.length; i++) {
axes.push(i);
}
axes.splice(axis, 1);
axes.splice(start, 0, axis);
return this._transposelike(axes, out);
}, { start : 0}),
// Base function for transpose-like operations
_transposelike : function(axes, out) {
var source = this._array;
var shape = this._shape.slice();
var strides = calculateDimStrides(this._shape);
var dim = shape.length;
// Swap
var tmpStrides = [];
var tmpShape = [];
for (var i = 0; i < axes.length; i++) {
var axis = axes[i];
// swap to target axis
tmpShape[i] = shape[axis];
tmpStrides[i] = strides[axis];
}
strides = tmpStrides;
shape = tmpShape;
this._shape = shape;
var transposedStrides = calculateDimStrides(this._shape);
if (!out) {
out = new NDArray();
out._shape = this._shape.slice();
out._dtype = this._dtype;
out._size = this._size;
}
// FIXME in-place transpose?
var transposedData = new ArrayConstructor[this._dtype](this._size);
out._array = transposedData;
// @param Item offset in current axis offset of the original array
// @param Item offset in current axis offset of the transposed array
function transpose(axis, offset, transposedOffset) {
var size = shape[axis];
// strides in orginal array
var stride = strides[axis];
// strides in transposed array
var transposedStride = transposedStrides[axis];
if (axis < dim-1) {
for (var i = 0; i < size; i++) {
transpose(
axis+1,
offset + stride * i,
transposedOffset + transposedStride * i
);
}
} else {
for (var i = 0; i < size; i++) {
// offset + stride * i is the index of the original array
// transposedOffset + i is the index of the transposed array
transposedData[transposedOffset + i]
= source[offset + stride * i];
}
}
}
transpose(0, 0, 0);
return out;
},
/**
* Repeat elements of an array along axis
* @param {Number} repeats
* The number of repetitions for each element.
* repeats is broadcasted to fit the shape of the given axis.
* @param {Number} [axis]
* The axis along which to repeat values.
* By default, use the flattened input array,
* and return a flat output array.
* @param {NDArray} [out]
* @return {NDArray}
*/
repeat : kwargs(function(repeats, axis, out) {
var shape;
// flattened input array
if (typeof(axis) === 'undefined') {
shape = [this._size];
axis = 0;
} else {
shape = this._shape.slice();
}
var originShape = shape.slice();
shape[axis] *= repeats;
if (!out) {
out = new NDArray(this._dtype);
out.initFromShape(shape);
} else {
if (!arrayEqual(shape, out._shape)) {
throw new Error(broadcastErrorMsg(shape, out._shape));
}
}
var data = out._array;
var stride = calculateDimStride(originShape, axis);
var axisSize = originShape[axis];
var source = this._array;
var offsetStride = stride * axisSize;
for (var offset = 0; offset < this._size; offset+=offsetStride) {
for (var k = 0; k < stride; k++) {
var idx = offset + k;
var idxRepeated = offset * repeats + k;
for (var i = 0; i < axisSize; i++) {
for (var j = 0; j < repeats; j++) {
data[idxRepeated] = source[idx];
idxRepeated += stride;
}
idx += stride;
}
}
}
return out;
}),
choose : function() {
console.warn('TODO');
},
take : function() {
console.warn('TODO');
},
tile : function() {
console.warn('TODO');
},
/**
* Preprocess for array calculation
* max, min, argmax, argmin, sum, ptp, val, mean
* Which will reduce one axis if the axis is given
*
* @param {Number} axis
* @param {NDArray} out
* @param {Function} funcWithAxis
* @param {Function} funcFlatten
* @return {Number|NDArray}
*/
_withPreprocess1 : function(axis, out, funcWithAxis, funcFlatten) {
var source = this._array;
if (!this._size) {
return;
}
if (typeof(axis)!=='undefined') {
if (axis < 0) {
axis = this._shape.length + axis;
}
if (axis >= this._shape.length || axis < 0) {
throw new Error(axisOutofBoundsErrorMsg(axis));
}
var shape = this._shape.slice();
shape.splice(axis, 1);
if (out && !arrayEqual(shape, out._shape)) {
throw new Error(broadcastErrorMsg(shape, out._shape));
}
if (!out) {
out = new NDArray(this._dtype);
out.initFromShape(shape);
}
var data = out._array;
var stride = calculateDimStride(this._shape, axis);
var axisSize = this._shape[axis];
var offsetStride = stride * axisSize;
funcWithAxis.call(
this, data, source, offsetStride, axisSize, stride
);
return out;
} else {
return funcFlatten.call(this, source);
}
},
/**
* Preprocess for array calculation cumsum, cumprod
* Which will keep the shape if axis is given
* and flatten if axis is undefined
* @param {Number} axis
* @param {NDArray} out
* @param {Function} funcWithAxis
* @param {Function} funcFlatten
* @return {NDArray}
*/
_withPreprocess2 : function(axis, out, funcWithAxis, funcFlatten) {
var source = this._array;
if (!this._size) {
return;
}
if (out && !arrayEqual(this._shape, out._shape)) {
throw new Error(broadcastErrorMsg(this._shape, out._shape));
}
if (!out) {
out = new NDArray(this._dtype);
out.initFromShape(this._shape);
}
var data = out._array;
if (typeof(axis)!=='undefined') {
if (axis < 0) {
axis = this._shape.length + axis;
}
if (axis >= this._shape.length || axis < 0) {
throw new Error(axisOutofBoundsErrorMsg(axis));
}
if (axis >= this._shape.length) {
throw new Error(axisOutofBoundsErrorMsg(axis));
}
var stride = calculateDimStride(this._shape, axis);
var axisSize = this._shape[axis];
var offsetStride = stride * axisSize;
funcWithAxis.call(
this, data, source, offsetStride, axisSize, stride
);
} else {
out.reshape([this._size]);
funcFlatten.call(this, data, source);
}
return out;
},
/**
* Get the max value of ndarray
* If the axis is given, the max is only calculate in this dimension
* Example, for the given ndarray
* [[3, 9],
* [4, 8]]
* >>> max(0)
* [4, 9]
* >>> max(1)
* [9, 8]
*
* @param {Number} [axis]
* @param {NDArray} out
* @return {NDArray}
*/
max : kwargs((function() {
function withAxis(data, source, offsetStride, axisSize, stride) {
var cursor = 0;
for (var offset = 0; offset < this._size; offset+=offsetStride) {
for (var i = 0; i < stride; i++) {
var idx = i + offset;
var max = source[idx];
for (var j = 0; j < axisSize; j++) {
var d = source[idx];
if (d > max) {
max = d;
}
idx += stride;
}
data[cursor++] = max;
}
}
}
function withFlatten(source) {
var max = source[0];
for (var i = 1; i < this._size; i++) {
if (source[i] > max) {
max = source[i];
}
}
return max;
}
return function(axis, out) {
return this._withPreprocess1(
axis, out,
withAxis, withFlatten
);
};
})()),
/**
* Return the minimum of an array or minimum along an axis.
* @param {Number} [axis]
* @param {NDArray} out
* @return {NDArray}
*/
min : kwargs((function() {
function withAxis(data, source, offsetStride, axisSize, stride) {
var cursor = 0;
for (var offset = 0; offset < this._size; offset+=offsetStride) {
for (var i = 0; i < stride; i++) {
var idx = i + offset;
var min = source[idx];
for (var j = 0; j < axisSize; j++) {
var d = source[idx];
if (d < min) {
min = d;
}
idx += stride;
}
data[cursor++] = min;
}
}
}
function withFlatten(source) {
var min = source[0];
for (var i = 1; i < this._size; i++) {
if (source[i] < min) {
min = source[i];
}
}
return min;
}
return function(axis, out) {
return this._withPreprocess1(
axis, out,
withAxis, withFlatten
);
};
})()),
/**
* Return indices of the maximum values along an axis.
* @param {Number} [axis]
* @param {NDArray} out
* @return {NDArray}
*/
argmax : kwargs((function() {
function withAxis(data, source, offsetStride, axisSize, stride) {
var cursor = 0;
for (var offset = 0; offset < this._size; offset+=offsetStride) {
for (var i = 0; i < stride; i++) {
var dataIdx = 0;
var idx = i + offset;
var max = source[idx];
for (var j = 0; j < axisSize; j++) {
var d = source[idx];
if (d > max) {
max = d;
dataIdx = j;
}
idx += stride;
}
data[cursor++] = dataIdx;
}
}
}
function withFlatten(source) {
var max = source[0];
var idx = 0;
for (var i = 1; i < this._size; i++) {
if (source[i] > max) {
idx = i;
max = source[i];
}
}
return idx;
}
return function(axis, out) {
return this._withPreprocess1(
axis, out,
withAxis, withFlatten
);
};
})()),
/**
* Indices of the minimum values along an axis.
* @param {Number} [axis]
* @param {NDArray} out
* @return {NDArray}
*/
argmin : kwargs((function() {
function withAxis(data, source, offsetStride, axisSize, stride) {
var cursor = 0;
for (var offset = 0; offset < this._size; offset+=offsetStride) {
for (var i = 0; i < stride; i++) {
var dataIdx = 0;
var idx = i + offset;
var min = source[idx];
for (var j = 0; j < axisSize; j++) {
var d = source[idx];
if (d < min) {
min = d;
dataIdx = j;
}
idx += stride;
}
data[cursor++] = dataIdx;
}
}
}
function withFlatten(source) {
var min = source[0];
var idx = 0;
for (var i = 1; i < this._size; i++) {
if (source[i] < min) {
idx = i;
min = source[i];
}
}
return idx;
}
return function(axis, out) {
return this._withPreprocess1(
axis, out,
withAxis, withFlatten
);
};
})()),
/**
* Return the sum of the array elements over the given axis.
* @param {Number} [axis]
* @param {NDArray} out
* @return {NDArray}
*/
sum : kwargs((function() {
function withAxis(data, source, offsetStride, axisSize, stride) {
var cursor = 0;
for (var offset = 0; offset < this._size; offset+=offsetStride) {
for (var i = 0; i < stride; i++) {
var sum = 0;
var idx = i + offset;
for (var j = 0; j < axisSize; j++) {
sum += source[idx];
idx += stride;
}
data[cursor++] = sum;
}
}
}
function withFlatten(source) {
var sum = 0;
for (var i = 0; i < this._size; i++) {
sum += source[i];
}
return sum;
}
return function(axis, out) {
return this._withPreprocess1(
axis, out,
withAxis, withFlatten
);
};
})()),
/**
* Return the product of the array elements over the given axis.
* @param {Number} [axis]
* @param {NDArray} out
* @return {NDArray}
*/
prod : kwargs((function() {
function withAxis(data, source, offsetStride, axisSize, stride) {
var cursor = 0;
for (var offset = 0; offset < this._size; offset+=offsetStride) {
for (var i = 0; i < stride; i++) {
var prod = 1;
var idx = i + offset;
for (var j = 0; j < axisSize; j++) {
prod *= source[idx];
idx += stride;
}
data[cursor++] = prod;
}
}
}
function withFlatten(source) {
var prod = 1;
for (var i = 0; i < this._size; i++) {
prod *= source[i];
}
return prod;
}
return function(axis, out) {
return this._withPreprocess1(
axis, out,
withAxis, withFlatten
);
};
})()),
/**
* Returns the average of the array elements along given axis.
* @param {Number} [axis]
* @param {NDArray} out
* @return {NDArray}
*/
mean : kwargs((function() {
function withAxis(data, source, offsetStride, axisSize, stride) {
var cursor = 0;
for (var offset = 0; offset < this._size; offset+=offsetStride) {
for (var i = 0; i < stride; i++) {
var sum = 0;
var idx = i + offset;
for (var j = 0; j < axisSize; j++) {
sum += source[idx];
idx += stride;
}
var mean = sum / axisSize;
data[cursor++] = mean;
}
}
}
function withFlatten(source) {
var sum = 0;
var len = source.length;
for (var i = 0; i < len; i++) {
sum += source[i];
}
var mean = sum / len;
return mean;
}
return function(axis, out) {
return this._withPreprocess1(
axis, out,
withAxis, withFlatten
);
};
})()),
/**
* Return the variance of the array elements over the given axis.
* @param {Number} [axis]
* @param {NDArray} out
* @return {NDArray}
*/
'var' : kwargs((function() {
function withAxis(data, source, offsetStride, axisSize, stride) {
var cursor = 0;
for (var offset = 0; offset < this._size; offset+=offsetStride) {
for (var i = 0; i < stride; i++) {
var sum = 0;
var idx = i + offset;
for (var j = 0; j < axisSize; j++) {
sum += source[idx];
idx += stride;
}
var mean = sum / axisSize;
var moments = 0;
idx = i + offset;
for (var j = 0; j < axisSize; j++) {
var diff = source[idx] - mean;
moments += diff * diff;
idx += stride;
}
data[cursor++] = moments / axisSize;
}
}
}
function withFlatten(source) {
var sum = 0;
var len = source.length;
for (var i = 0; i < len; i++) {
sum += source[i];
}
var mean = sum / len;
var moments = 0;
for (var i = 0; i < len; i++) {
var diff = source[i] - mean;
moments += diff * diff;
}
return moments / len;
}
return function(axis, out) {
return this._withPreprocess1(
axis, out,
withAxis, withFlatten
);
};
})()),
/**
* Return the standard derivatione of the array elements
* over the given axis.
* @param {Number} [axis]
* @param {NDArray} out
* @return {NDArray}
*/
std : kwargs((function() {
function withAxis(data, source, offsetStride, axisSize, stride) {
var cursor = 0;
for (var offset = 0; offset < this._size; offset+=offsetStride) {
for (var i = 0; i < stride; i++) {
var sum = 0;
var idx = i + offset;
for (var j = 0; j < axisSize; j++) {
sum += source[idx];
idx += stride;
}
var mean = sum / axisSize;