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IntArrMath.py
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IntArrMath.py
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"""
IntArrMath.py by John Dorsey.
IntArrMath.py contains tools for analyzing or manipulating arrays, and must either take or return an array. Functions that both take a generator and return a generator should be put in IntSeqMath.py.
"""
import IntSeqMath
import IntDomainMath
import Curves
from PyGenTools import makeArr, zipGens
def intify(inputArr, roundNearest=False, weakly=False):
"""
recursively forces every number to be an int.
when roundNearest=True, numbers will be rounded to the nearest integer instead of being rounded down.
when weak=True, a number will only be converted if doing so does not change its value.
"""
for i,item in enumerate(inputArr):
if type(item) == list:
intify(item,roundNearest=roundNearest,weakly=weakly)
elif item != None:
if weakly:
if int(item) == item:
inputArr[i] = int(item)
else:
inputArr[i] = int(round(item)) if roundNearest else int(item)
def intified(inputArr, roundNearest=False, weakly=False):
result = [None for i in range(len(inputArr))]
for i,item in enumerate(inputArr):
if type(item) == list:
result[i] = intified(item,roundNearest=roundNearest,weakly=weakly)
elif item != None:
result[i] = (int(item) if int(item) == item else item) if weakly else (int(round(item)) if roundNearest else int(item))
return result
def floatify(inputArr):
for i,item in enumerate(inputArr):
if type(item) == list:
floatify(item)
elif item != None:
inputArr[i] = float(item)
def floatified(inputArr, listifiedContainers=False):
resultGen = (None for i in range(len(inputArr)))
if listifiedContainers or type(inputArr) == tuple:
result = list(resultGen)
else:
result = (type(inputArr))(resultGen)
if hasattr(inputArr, "__len__") and hasattr(result, "__len__"):
assert len(result) == len(inputArr)
for i,item in enumerate(inputArr):
if type(item) in {list, tuple, set}:
result[i] = floatified(item)
elif item is not None:
if type(item) not in [int, float]:
raise TypeError("won't convert item {} of type {} to float.".format(item, repr(type(item))))
result[i] = float(item)
return result
def is_sorted(inputArr):
#test whether the input array is sorted.
if len(inputArr) <= 1:
return True
for i in range(1,len(inputArr)):
if inputArr[i] < inputArr[i-1]:
return False
return True
def mean(inputArr):
#find the mean of the input array. Might mishandle long type items in python2.
inputArr = makeArr(inputArr)
if len(inputArr) == 0:
raise ValueError("can't find the mean of an empty list.")
inputArrSum = sum(inputArr)
if type(inputArrSum)==int and inputArrSum%len(inputArr) == 0:
return inputArrSum / len(inputArr)
else:
return float(inputArrSum) / len(inputArr)
def median(inputArr, middlePairHandlingFun=mean):
#find the median of the input array. Uses middlePairHandlingFun as the function to process the middle pair in even-length inputArrs to get the result.
inputArr = makeArr(inputArr)
if len(inputArr) == 0:
raise ValueError("can't find the median of an empty list.")
elif len(inputArr) == 1:
return inputArr[0]
elif len(inputArr) >= 2:
#this might be faster without unecessary sorting.
workingArr = sorted(inputArr)
if len(workingArr)%2 == 1:
return workingArr[len(workingArr)>>1]
else:
middlePair = workingArr[(len(workingArr)>>1)-1:(len(workingArr)>>1)+1]
return middlePairHandlingFun(middlePair)
assert False, "reality error."
def genInterlacedIndices(inputEndpoints, startWithEndpoints=True, midpointMode="fail"):
#This didn't need to be a generator, and probably doesn't save much memory by being a generator.
#works like this:
#1 2
#| 3 |
#| 4 | 5 |
#|6|8|7|9|
#|||||||||
#at the index n in the output, the horizontal position of the vertical line labled with the number n is given. This horizontal position counts up from the first endpoint to the second one, including both if includeEndpoints==True and neither otherwise.
#print("endpoints are " + str(inputEndpoints) + ".")
assert midpointMode in ["fail","round_down","round_up","unsubdivided"], "bad midpointMode."
if not inputEndpoints[0] <= inputEndpoints[1]:
#print("IntArrMath.genInterlacedIndices: the endpoints " + str(inputEndpoints) + " are in the wrong order, and nothing will be yielded. This is not always an error.")
return
domainSize = inputEndpoints[1]-inputEndpoints[0]+1
if domainSize == 1:
yield inputEndpoints[0]
elif startWithEndpoints:
yield inputEndpoints[0]
yield inputEndpoints[1]
if domainSize > 2:
for item in genInterlacedIndices((inputEndpoints[0]+1,inputEndpoints[1]-1),startWithEndpoints=False,midpointMode=midpointMode):
yield item
else:
perfectMidpoint = ((domainSize-1)%2 == 0)
if not perfectMidpoint:
if midpointMode == "fail":
assert False, "bad midpoint is not allowed when midpointMode=\"fail\""
elif midpointMode == "unsubdivided":
for i in range(inputEndpoints[0],inputEndpoints[1]+1):
yield i
return
midpoint = int((domainSize-1)/2 + inputEndpoints[0])
if midpointMode == "round_up" and not perfectMidpoint:
midpoint += 1
yield midpoint
for item in zipGens([genInterlacedIndices((inputEndpoints[0],midpoint-1),startWithEndpoints=False,midpointMode=midpointMode),genInterlacedIndices((midpoint+1,inputEndpoints[1]),startWithEndpoints=False,midpointMode=midpointMode)]):
yield item
def genReverseIndexMap(inputMap):
workingMap = makeArr(inputMap) #so that calls to .index works even if the input is a generator.
for i in range(len(workingMap)):
yield workingMap.index(i)
def applyIndexMap(inputArr,inputMap):
return [inputArr[index] for index in inputMap]
def applyIndexMapReversed(inputArr,inputMap):
#simply using return applyIndexMap(inputArr,genReverseIndexMap(inputMap)) would be O(N^2).
#the following version is O(N).
result = [None for i in range(len(inputArr))]
for i,inputIndex in enumerate(inputMap):
result[inputIndex] = inputArr[i]
return result
def rulerOPIntArrTranscode(inputIntArr, opMode, spline=None, interlacingProvider=None):
#ruler interlacing is what I call the method of interlacing described in IntArrMath.genInterlacedIndices.
#ruler interlacing is used to add values to the array in a helpful order (no clusters). Interpolation is used to guess what a new value will be. The _Focused_ integer functions in IntDomainMath are used to focus a new value around the prediction for it to make it easier to compress using a universal code.
#the interpolationProvider should be something like Curves.Spline WITH INTEGER OUTPUTS, such as by enabling the rounding output filter for Curves.Spline.
#the output could be made streamable.
assert opMode in ["encode","decode"]
if spline == None:
spline = Curves.Spline(interpolationMode="linear&round", size=[len(inputIntArr),None])
if interlacingProvider == None:
interlacingProvider = genInterlacedIndices((0, len(inputIntArr)-1), midpointMode="round_down")
result = []
for i,index in enumerate(interlacingProvider):
localFocus = spline[index]
assert type(localFocus) == int, "IntArrMath.rulerOPIntArrTranscode: Only integer foci are supported. Make sure the provided spline gives only integer outputs."
#print("(i,index,localFocus,inputIntArr[i]) is " + str((i,index,localFocus,inputIntArr[i])) + ".")
if opMode == "encode":
spline[index] = inputIntArr[index]
result.append(IntDomainMath.unfocusedOP_to_focusedOP(spline[index], localFocus))
#print("result is " + str(result) + ".")
else:
spline[index] = IntDomainMath.focusedOP_to_unfocusedOP(inputIntArr[i], localFocus)
#print("spline is " + str([item for item in spline]) + ".")
if opMode == "encode":
return result
else:
return [spline[i] for i in range(len(inputIntArr))]
def headingDeltadPaletteIntArrEncode(inputIntArr):
#store an integer array as a new array starting with a palette length, followed by a palette, followed by a finite sequence of palette indices.
#the output could be made streamable, even though the input is not.
values = [item for item in genRunless(sorted(inputIntArr))]
result = []
result.append(len(values))
result.extend(IntSeqMath.genDeltaEncode(values))
result.extend(values.index(item) for item in inputIntArr)
return result
def headingDeltadPaletteIntArrDecode(inputIntArr):
#both the output and the input could be made streamable.
paletteLength = inputIntArr[0]
palette = [item for item in IntSeqMath.genDeltaDecode(inputIntArr[1:1+paletteLength])]
return [palette[item] for item in inputIntArr[1+paletteLength:]]
def headingFloorIntArrEncode(inputIntArr):
#store an input integer array as a new array starting with a floor value, followed by each of the array's items minus that floor value.
floorVal = min(inputIntArr)
return [floorVal] + [item-floorVal for item in inputIntArr]
def headingFloorIntArrDecode(inputIntArr):
#the input and output could both be made streamable.
floorVal = inputIntArr[0]
return [item+floorVal for item in inputIntArr[1:]]
def headingMedianIntArrEncode(inputIntArr):
#store an input integer array as a new array starting with its median, followed by each of the input array's items minus that median.
medianVal = int(median(inputIntArr))
return [medianVal] + [item-medianVal for item in inputIntArr]
def headingMedianIntArrDecode(inputIntArr):
#the input and output could both be made streamable.
medianVal = inputIntArr[0]
return [item+medianVal for item in inputIntArr[1:]]
def headingMedianStaggerIntArrEncode(inputIntArr):
#like headingMedianIntArrEncode, but use staggering around the number line origin to format the output as an all-positive integer array.
medianVal = int(median(inputIntArr))
return [medianVal] + [IntDomainMath.NOP_to_OP(item-medianVal) for item in inputIntArr]
def headingMedianStaggerIntArrDecode(inputIntArr):
#the input and output could both be made streamable.
medianVal = inputIntArr[0]
return [IntDomainMath.OP_to_NOP(item)+medianVal for item in inputIntArr[1:]]
def headingMedianStaggerOPIntArrEncode(inputIntArr):
#like headingMedianStaggerIntArrEncode, but takes advantage of an input array's limited value range [0,inf) to make the output consist of smaller values.
medianVal = int(median(inputIntArr))
return [medianVal] + [IntDomainMath.unfocusedOP_to_focusedOP(item,medianVal) for item in inputIntArr]
def headingMedianStaggerOPIntArrDecode(inputIntArr):
#the input and output could both be made streamable.
medianVal = inputIntArr[0]
return [IntDomainMath.focusedOP_to_unfocusedOP(item,medianVal) for item in inputIntArr[1:]]
assert applyIndexMap("abcdefg",[0,5,6,3,2,1,4]) == ['a', 'f', 'g', 'd', 'c', 'b', 'e']
assert applyIndexMapReversed("afgdcbe",[0,5,6,3,2,1,4]) == ['a', 'b', 'c', 'd', 'e', 'f', 'g']