I have a problem with my Negamax algorithm and hope someone could help me.
I'm writing it in Cython
my search method is a following:
cdef _search(self, object game_state, int depth, long alpha, long beta, int max_depth):
if depth == max_depth or game_state.is_terminated:
value = self.evaluator.evaluate(game_state) evaluates based on current player
return value, []
moves = self.prepare_moves(depth, game_state) # getting moves and sorting
max_value = LONG_MIN
for move in moves:
new_board = game_state.make_move(move)
value, pv_moves = self._search(new_board, depth + 1, -beta, -alpha, max_depth, event)
value = -value
if max_value < value:
max_value = value
best_move = move
best_pv_moves = pv_moves
if alpha < max_value:
alpha = max_value
if max_value >= beta:
return LONG_MAX, []
best_pv_moves.insert(0, best_move)
return alpha, best_pv_moves
In many examples you break after a cutoff is detected but when I do this the algorithm don't find the optimal solution. I'm testing against some chess puzzles and I was wondering why this is the case. If I return the maximum number after a cutoff is detected It works fine but I takes a long time (252sec for depth 6)...
Speed: Nodes pre Second : 21550.33203125
Or if you have other improvements let me know (I use transposition table, pvs and killer heuristics)
Turn out I used the c limits
cdef extern from "limits.h":
cdef long LONG_MAX
cdef long LONG_MIN
and when you try to invert LONG_MIN, with -LONG_MIN you get LONG_MIN, because of an overflow?
Related
I search a way to find all the vector from a np.meshgrid(xrange, xrange, xrange) that are related by k = -k.
For the moment I do that :
#numba.njit
def find_pairs(array):
boolean = np.ones(len(array), dtype=np.bool_)
pairs = []
idx = [i for i in range(len(array))]
while len(idx) > 1:
e1 = idx[0]
for e2 in idx:
if (array[e1] == -array[e2]).all():
boolean[e2] = False
pairs.append([e1, e2])
idx.remove(e1)
if e2 != e1:
idx.remove(e2)
break
return boolean, pairs
# Give array of 3D vectors
krange = np.fft.fftfreq(N)
comb_array = np.array(np.meshgrid(krange, krange, krange)).T.reshape(-1, 3)
# Take idx of the pairs k, -k vector and boolean selection that give position of -k vectors
boolean, pairs = find_pairs(array)
It works but the execution time grow rapidly with N...
Maybe someone has already deal with that?
The main problem is that comb_array has a shape of (R, 3) where R = N**3 and the nested loop in find_pairs runs at least in quadratic time since idx.remove runs in linear time and is called in the for loop. Moreover, there are cases where the for loop does not change the size of idx and the loop appear to run forever (eg. with N=4).
One solution to solve this problem in O(R log R) is to sort the array and then check for opposite values in linear time:
import numpy as np
import numba as nb
# Give array of 3D vectors
krange = np.fft.fftfreq(N)
comb_array = np.array(np.meshgrid(krange, krange, krange)).T.reshape(-1, 3)
# Sorting
packed = comb_array.view([('x', 'f8'), ('y', 'f8'), ('z', 'f8')])
idx = np.argsort(packed, axis=0).ravel()
sorted_comb = comb_array[idx]
# Find pairs
#nb.njit
def findPairs(sorted_comb, idx):
n = idx.size
boolean = np.zeros(n, dtype=np.bool_)
pairs = []
cur = n-1
for i in range(n):
while cur >= i:
if np.all(sorted_comb[i] == -sorted_comb[cur]):
boolean[idx[i]] = True
pairs.append([idx[i], idx[cur]])
cur -= 1
break
cur -= 1
return boolean, pairs
findPairs(sorted_comb, idx)
Note that the algorithm assume that for each row, there are only up to one valid matching pair. If there are several equal rows, they are paired 2 by two. If your goal is to extract all the combination of equal rows in this case, then please note that the output will grow exponentially (which is not reasonable IMHO).
This solution is pretty fast even for N = 100. Most of the time is spent in the sort that is not very efficient (unfortunately Numpy does not provide a way to do a lexicographic argsort of the row efficiently yet though this operation is fundamentally expensive).
I try to add the following constraints to my model. my problem: the function g() expects x as a binary numpy array. So the result arr_a depends on the current value of x in every step of the optimization!
Afterwards, I want the max of this array times x to be smaller than 50.
How can I add this constraint dynamically so that arr_a is always rightfully calculated with the value of x at each iteration while telling the model to keep the constraint arr_a * x <= 50 ? Currently I am getting an error when adding the constraint to the model because g() expects x as numpy array to calculate arr_a, arr_b, arr_c ( g uses np.where(x == 1) within its calculation).
#Init model
from ortools.sat.python import cp_model
model = cp_model.CpModel()
# Declare the variables
x = []
for i in range(self.ds.n_banks):
x.append(model.NewIntVar(0, 1, "x[%i]" % (i)))
#add bool vars
a = model.NewBoolVar('a')
arr_a, arr_b, arr_c = g(df1,df2,df3,x)
model.Add((arr_a.astype('int32') * x).max() <= 50).OnlyEnforceIf(a)
model.Add((arr_a.astype('int32') * x).max() > 50).OnlyEnforceIf(a.Not())
Afterwards i add the target function that naturally also depends on x.
model.Minimize(target(x))
def target(x):
arr_a, arr_b, arr_c = g(df1,df2,df3,x)
return (3 * arr_b * x + 2 * arr_c * x).sum()
EDIT:
My problem changed a bit and i managed to get it work without issues. Nevertheless, I experienced that the constraint is never actually met! self-defined-function is a highly non-linear function that expects the indices where x==1 and where x == 0 and returns a numpy array. Also it is not possible to re-build it with pre-defined functions of the sat.solver.
#Init model
model = cp_model.CpModel()
# Declare the variables
x = [model.NewIntVar(0, 1, "x[%i]" % (i)) for i in range(66)]
# add hints
[model.AddHint(x[i],np.random.choice(2, 1, p=[0.4, 0.6])[0]) for i in range(66)]
open_elements = [model.NewBoolVar("open_elements[%i]" % (i)) for i in range(66)]
closed_elements = [model.NewBoolVar("closed_elements[%i]" % (i)) for i in range(6)]
# open indices as bool vars
for i in range(66):
model.Add(x[i] == 1).OnlyEnforceIf(open_elements[i])
model.Add(x[i] != 1).OnlyEnforceIf(open_elements[i].Not())
model.Add(x[i] != 1).OnlyEnforceIf(closed_elements[i])
model.Add(x[i] == 1).OnlyEnforceIf(closed_elements[i].Not())
model.Add((self-defined-function(np.where(open_elements), np.where(closed_elements), some_array).astype('int32') * x - some_vector).all() <= 0)
Even when I apply a simpler function, it will not work properly.
model.Add((self-defined-function(x, some_array).astype('int32') * x - some_vector).all() <= 0)
I also tried the following:
arr_indices_open = []
arr_indices_closed = []
for i in range(66):
if open_elements[i] == True:
arr_indices_open.append(i)
else:
arr_indices_closed.append(i)
# final Constraint
arr_ = self-defined-function(arr_indices_open, arr_indices_closed, some_array)[0].astype('int32')
for i in range(66):
model.Add(arr_[i] * x[i] <= some_other_vector[i])
Some minimal example for the self-defined-function, with which I simply try to say that n_closed shall be smaller than 10. Even that condition is not met by the solver:
def self_defined_function(arr_indices_closed)
return len(arr_indices_closed)
arr_ = self-defined-function(arr_indices_closed)
for i in range(66):
model.Add(arr_ < 10)
I'm not sure I fully understand the question, but generally, if you want to optimize a function g(x), you'll have to implement it in using the solver's primitives (docs).
It's easier to do when your calculation coincides with an existing solver function, e.g.: if you're trying to calculate a linear expression; but could get harder to do when trying to calculate something more complex. However, I believe that's the only way.
For the following code, I want to generate random value but the value in dfCombined["TotalFreeSize"] can be up to 9.941458e+11, and it throws error for randint, what should I do?
And I can't find a randlong function..
# get average, std, and number of NaN values in col
average_age_test = dfCombined["TotalFreeSize"].mean()
std_age_test = dfCombined["TotalFreeSize"].std()
count_nan_age_test = dfCombined["TotalFreeSize"].isnull().sum()
rand_1 = np.random.randint(average_age_test - std_age_test, average_age_test + std_age_test, size = count_nan_age_test)
randint takes two values as parameters, both ints. a lower bound value and a higher bound value. it will than return an int between those values.
mean(), std() in the other hand return float values, as the mean and std of a set of values.
what you should do is give parameters that are int into the randint function.
you can:
average_age_test = int ( dfCombined["TotalFreeSize"].mean() )
std_age_test = int ( dfCombined["TotalFreeSize"].std() )
hope that helps! if it does please upvote :)
sample:
input:
A = int (9.941458e+11)
random.randint(0, A)
output:
153271550649L (type: long)
You can simply map random values from 0 to 1 (generated with random) to your max desired value, and python will cast it appropriately. This seems to work even for very large max values:
import random
max = 9.941458e91 # notice the '91' exponent here!
for i in xrange(10):
val = long(random.random() * max)
print val
print type(val)
print
Sample output (single value):
45525909158271540655933151699075210889481964268830820171688052775301692920778132706971090944
<type 'long'>
I am trying to code a java methods which returns a Boolean true if a point(x,y) is on a line segment and false if not.
I tried this:
public static boolean OnDistance(MyLocation a, MyLocation b, MyLocation queryPoint) {
double value = java.lang.Math.signum((a.mLongitude - b.mLongitude) * (queryPoint.mLatitude - a.mLatitude)
- (b.mLatitude - a.mLatitude) * (queryPoint.mLongitude - a.mLongitude));
double compare = 1;
if (value == compare) {
return true;
}
return false;
}
but it doesn't work.
I am not JAVA coder so I stick to math behind ... For starters let assume you are on plane (not sphere surface)
I would use Vector math so let:
a,b - be the line endpoints
q - queried point
c=q-a - queried line direction vector
d=b-a - line direction vector
use dot product for parameter extraction
t=dot(c,d)/(|c|*|d|)
t is line parameter <0,1> if out of range q is not inside line
|c|=sqrt(c.x*c.x+c.y*c.y) size of vector
dot(c,d)=c.x*d.x+c.y*d.y scalar vector multiply
now compute corresponding point on line
e=a+(t*d)
e is the closest point to q on the line ab
compute perpendicular distance of q and ab
l=|q-e|;
if (l>treshold) then q is not on line ab else it is on the line ab. The threshold is the max distance from line you are still accepting as inside line. No need to have l sqrt-ed the threshold constant can be powered by 2 instead for speed.
if you add all this to single equation
then some things will simplify itself (hope did not make some silly math mistake)
l=|(q-a)-(b-a)*(dot(q-a,b-a)/|b-a|^2)|;
return (l<=treshold);
or
l=|c-(d*dot(c,d)/|d|^2)|;
return (l<=treshold);
As you can see we do not even need sqrt for this :)
[Notes]
If you need spherical or ellipsoidal surface instead then you need to specify it closer which it is what are the semi axises. The line become arc/curve and need some corrections which depends on the shape of surface see
Projecting a point onto a path
but can be done also by approximation and may be also by binary search of point e see:
mine approx class in C++
The vector math used can be found here at the end:
Understanding 4x4 homogenous transform matrices
Here 3D C++ implementation (with different names):
double distance_point_axis(double *p,double *p0,double *dp)
{
int i;
double l,d,q[3];
for (i=0;i<3;i++) q[i]=p[i]-p0[i]; // q = p-p0
for (l=0.0,i=0;i<3;i++) l+=dp[i]*dp[i]; // l = |dp|^2
for (d=0.0,i=0;i<3;i++) d+=q[i]*dp[i]; // d = dot(q,dp)
if (l<1e-10) d=0.0; else d/=l; // d = dot(q,dp)/|dp|^2
for (i=0;i<3;i++) q[i]-=dp[i]*d; // q=q-dp*dot(q,dp)/|dp|^2
for (l=0.0,i=0;i<3;i++) l+=q[i]*q[i]; l=sqrt(l); // l = |q|
return l;
}
Where p0[3] is any point on axis and dp[3] is direction vector of axis. The p[3] is the queried point you want the distance to axis for.
I'm trying to calculate the average Luminance of an RGB image. To do this, I find the luminance of each pixel i.e.
L(r,g,b) = X*r + Y*g + Z*b (some linear combination).
And then find the average by summing up luminance of all pixels and dividing by width*height.
To speed this up, I'm using pyopencl.reduction.ReductionKernel
The array I pass to it is a Single Dimension Numpy Array so it works just like the example given.
import Image
import numpy as np
im = Image.open('image_00000001.bmp')
data = np.asarray(im).reshape(-1) # so data is a single dimension list
# data.dtype is uint8, data.shape is (w*h*3, )
I want to incorporate the following code from the example into it . i.e. I would make changes to datatype and the type of arrays I'm passing. This is the example:
a = pyopencl.array.arange(queue, 400, dtype=numpy.float32)
b = pyopencl.array.arange(queue, 400, dtype=numpy.float32)
krnl = ReductionKernel(ctx, numpy.float32, neutral="0",
reduce_expr="a+b", map_expr="x[i]*y[i]",
arguments="__global float *x, __global float *y")
my_dot_prod = krnl(a, b).get()
Except, my map_expr will work on each pixel and convert each pixel to its luminance value.
And reduce expr remains the same.
The problem is, it works on each element in the array, and I need it to work on each pixel which is 3 consecutive elements at a time (RGB ).
One solution is to have three different arrays, one for R, one for G and one for B ,which would work, but is there another way ?
Edit: I changed the program to illustrate the char4 usage instead of float4:
import numpy as np
import pyopencl as cl
import pyopencl.array as cl_array
deviceID = 0
platformID = 0
workGroup=(1,1)
N = 10
testData = np.zeros(N, dtype=cl_array.vec.char4)
dev = cl.get_platforms()[platformID].get_devices()[deviceID]
ctx = cl.Context([dev])
queue = cl.CommandQueue(ctx)
mf = cl.mem_flags
Data_In = cl.Buffer(ctx, mf.READ_WRITE, testData.nbytes)
prg = cl.Program(ctx, """
__kernel void Pack_Cmplx( __global char4* Data_In, int N)
{
int gid = get_global_id(0);
//Data_In[gid] = 1; // This would change all components to one
Data_In[gid].x = 1; // changing single component
Data_In[gid].y = 2;
Data_In[gid].z = 3;
Data_In[gid].w = 4;
}
""").build()
prg.Pack_Cmplx(queue, (N,1), workGroup, Data_In, np.int32(N))
cl.enqueue_copy(queue, testData, Data_In)
print testData
I hope it helps.