I am trying to use AMPL to optimize a log-utility function on some return data. The program reads in the data correctly but spits out the error
LOQO 6.07: LOQO ERROR(50): cannot evaluate obj and/or constraint at initial solution
My code is pretty simple:
set ASSETS; # asset names
set TIME; # dates
param R {TIME, ASSETS}; # return of asset A in month T
param w0:= 100; # initial wealth
var x{ASSETS} >=0; # amt of capital in each asset
maximize expected_utility:
sum {i in TIME} (1/card(TIME)) * log(sum {j in ASSETS} x[j]*(1+R[i,j])); # x*(1+r) = w
subject to tot_mass:
sum{j in ASSETS} x[j] <= w0; # amount in each asset must total to w0
data;
set ASSETS := VT SPY TLT EEM EFA GSG DBC DBV TIP;
set TIME := January-07 February-07 March-07 April-07 May-07 June-07 July-07 August-07 September-07 October-07 November-07 December-07 January-08 February-08 March-08 April-08 May-08 June-08;
param R: VT SPY TLT EEM EFA GSG DBC DBV TIP :=
January-07 0.01248713 0.015065017 -0.009943182 0.001149425 0.013974909 -0.025455453 -0.023718763 0.007237636 0.002407806
February-07 -0.013271444 -0.019606312 0.034002869 -0.032433984 -0.001252937 0.037131882 0.050759219 0.008383234 0.019721871
March-07 0.025685366 0.011552864 -0.017066741 0.053396618 0.029010507 0.024691358 0.006606111 0.023357086 0.003347384
April-07 0.040152115 0.044265911 0.009034444 0.037172627 0.037488571 0.004578313 0.007383101 0.021276596 0.006548869
May-07 0.031768575 0.033941771 -0.02308338 0.050773826 0.023501763 -0.011753418 -0.002035831 0.023863636 -0.013012521
June-07 -0.001752913 -0.01459002 -0.01016755 0.036692506 -0.00315729 0.03131068 0.007343941 0.027376989 -0.002238806
July-07 -0.021742556 -0.031314776 0.033130787 0.007228315 -0.022890872 0.047775947 0.019036047 -0.007922218 0.023061581
August-07 0.003843633 0.012839129 0.01792466 0.010393467 -0.006335642 -0.031895777 -0.019077901 -0.039564428 0.008163763
September-07 0.056778104 0.038708217 0.002338699 0.115601274 0.053232503 0.094431555 0.094003241 0.030234316 0.012811216
October-07 0.042289615 0.013511550 0.018116937 0.118770582 0.042376461 0.05999576 0.085185185 0.029713866 0.011694511
November-07 -0.043249736 -0.038704128 0.053518469 -0.076530612 -0.03619665 -0.00460000 -0.006143345 -0.034912718 0.041165369
December-07 -0.020039022 -0.011258574 -0.006269994 -0.014024649 -0.029848655 0.059674503 0.066964286 0.00036914 0.000566444
January-08 -0.07287025 -0.060478094 0.020988926 -0.089224138 -0.078434205 -0.004550626 0.029288703 -0.016605166 0.035665761
February-08 -0.011941005 -0.025844771 -0.004540295 0.019876952 -0.010188088 0.112571429 0.111319575 -0.007129456 0.01421231
March-08 -0.007344683 -0.00889841 0.021284683 -0.037587007 0.004117181 -0.009416196 -0.009285312 -0.041950113 -0.001401315
April-08 0.057279035 0.047634882 -0.024810818 0.091610415 0.054407822 0.08192188 0.060494178 0.038658777 -0.019753886
May-08 0.016184106 0.015156324 -0.026841369 0.031581272 0.011965301 0.084664537 0.069094804 0.017850361 0.0011012
June-08 -0.096123568 -0.08363949 0.026535948 -0.102975808 -0.104936447 0.103240059 0.104208417 -0.005597015 0.017929821
;
#display(ASSETS);
#display(TIME);
#display R;
solve;
display {i in ASSETS} x[i];
Any ideas?
Thanks again stackoverflow
Since you are not specifying initial values for the variables x[j], they are by default all being given initial values of 0. Thus your objective function involves a log of 0, which LOQO cannot evaluate. Try setting explicit initial values, for example
var x{ASSETS} >=0, := w0 / card(ASSETS);
Here all variables are initialized at equal shares of total assets, which might be a reasonable start.
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 wrote a script to convert the EELS map to EELS line scan data, and it works well with DM 2.0. I can deal with it as directly collected EELS line scan data with DM2.0. But it does not work with DM 3.0 and the above version. It looks DM 3.0 still recognizes it as an EELS map file. DM3.0 still tried to generate elemental maps with multiple windows from it not generate line scan profiles with one single window and said the display type is incorrect. Not sure what code/command I need to add to fit the DM 3.0 and above versions. Appreciate any suggestions/comments.
image source
source := getFrontImage()
number sizeX,sizeY,sizeZ
source.Get3Dsize(sizeX,sizeY,sizeZ)
Result( "Original size:"+ sizeX +"; "+ sizeY+"; "+sizeZ+""+"\n" )
image sum
number regionsizeX = 1
number regionsizeY = sizeY
number row,col
Result( "new size:"+ regionsizeX +"; "+ regionsizeY+"; "+row+""+row+" "+"\n" )
sum := RealImage("Line Scan of [0,0,"+regionSizeY+","+regionSizeX+"]",4,sizeX/regionSizeX,sizey/regionsizeY,sizeZ)
//sum := ImageClone(source)
sum = 0
for (row=0;row<regionsizeY;row++) for (col=0;col<regionSizeX;col++)
{
OpenAndSetProgressWindow("Doing sub-block","x = "+col," y = "+row)
sum += Slice3(source,col,row,0,0,sizeX/regionSizeX,regionsizeX,1,sizeY/regionSizeY,regionSizeY,2,sizez,1)
}
OpenAndSetProgressWindow("","","")
ImageCopyCalibrationFrom(sum, source)
sum.setdisplaytype (1)
sum.SetStringNote( "Meta Data:Format", "Spectrum image" )
sum.SetStringNote( "Meta Data:Signal", "EELS" )
showimage(sum)
I'm also a bit confused by your terminology. When you write "Convert a Map into a LineScan" do you mean:
a) Convert a 3D Spectrum-Image (xy scan, one spectral dimension) into a 2D Line-Scan Spectrum-Image (one spatial dimension, one spectral dimension)
or
b) Convert a 2D Map (xy scan, one value) in a 1D Line-Trace (one spatial dimension, one value per point) ?
I suppose you mean a) and answer to that.
I'm surprised if/that your script would work without issues in GMS 2.
Your final (supposedly line-scan SI) data is still a 3D dataset with the dispersion running in Z-direction. This is not the typical LineScan SI data format (which is dispersion in X, spatial dimension in Y, no Z dimension).
Am I right in thinking that you want to "collapse" your 3D data along the y-dimension (by summing) ?
If so, what you want to do is:
// Get Input
image src3D := GetFrontImage()
number sizeX,sizeY,sizeZ
if ( 3 != src3D.ImageGetNumDimensions() ) Throw( "Input not 3D")
src3D.Get3Dsize(sizeX,sizeY,sizeZ)
// Optional: Use Rect-ROI on image to specify area
// If no selection, will return full FOV
number t,l,b,r
src3D.GetSelection(t,l,b,r)
// Prepare output (for summing 3D of rect-selection along y)
// NB: 2D container has:
// X dimension (spatial) along Y
// Z dimension (energy) along X
number nSpatial = r - l
number nSpectral = sizeZ
number eOrig, eScale, sOrig, sScale
string eUnit, sUnit
src3D.ImageGetDimensionCalibration(0, sOrig, sScale, sUnit, 0)
src3D.ImageGetDimensionCalibration(2, eOrig, eScale, eUnit, 0)
string name
if ( nSpatial != sizeX )
name = "Y-projection of [" + t + "," + l + "," + b + "," + r + "] over " + (b-t) + " rows"
else
name = "Y-projection over " + sizeY + " rows"
image dst2D := RealImage( name, 4, nSpectral, nSpatial )
dst2D.ImageSetDimensionCalibration(0, eOrig, eScale, eUnit, 0)
dst2D.ImageSetDimensionCalibration(1, sOrig, sScale, sUnit, 0)
// Copy Tags (contains necessary meta tags! Meta Data Format & Signal)
dst2D.ImageGetTagGroup().TagGroupCopyTagsFrom( src3D.ImageGetTagGroup() )
// Display (with captions)
dst2D.ShowImage()
dst2D.ImageGetImageDisplay(0).ImageDisplaySetCaptionOn(1)
number doFAST = 0
if ( !doFAST )
{
// Perform actuall summing (projection) by summing "line by line"
// into the LinePlot SI. Note the flipping of input and output dimensions!
for( number y = t; y<b; y++ )
{
number lineNumber = y - t
dst2D.slice2( 0,0,0, 0,nSpectral,1, 1,nSpatial,1 ) += src3D.slice2( l,y,0, 2,nSpectral,1, 0,nSpatial,1)
}
}
else
{
// Alternative (faster) projection. Use dedicated projection command.
image proj := src3D[l,t,0,r,b,nSpectral].Project(1) // Outcome of projectsion is having x=x and y=z, so need flip axis
dst2D = proj.slice2(0,0,0, 1,nSpectral,1, 0,nSpatial,1 ) // Flip axis
}
// Display (with captions)
dst2D.ShowImage()
dst2D.ImageGetImageDisplay(0).ImageDisplaySetCaptionOn(1)
Note that iterating using slice blocks is fast, but not as fast as the dedicated 'Project' command available in latest GMS versions. The example uses either, but lines #51-56 might not be available in older GMS.
Edit to address comment below:
Other relevant meta data for spectra is also found in the tags. For EELS, in particular the collection & convergence angle as well as the HT is of importance. You can find out about the tag-path by checking the tags of a properly acquired EELS spectrum.
Or, you can find out about their tag-paths by "converting" an empty 1D line-plot into an EELS spectrum and then attempting a quantification. You will get the prompt to fill in the data. After doing so, check the tags of the image:
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.
I need to transform a AMPL code to JuMP.
param f;
set R := 1..N;
set R_OK := 1..M;
set V := 1..N;
param tMax;
set T := 1..tMax;
var primary{R,V}, binary;
var SendPrepReq{T,R,V}, binary;
"param f" would be an int. The varibles I know how to do. But what about the sets? What is its equivalent in JuMP?
One of the most relevant pieces of documentation may be the Quickstart guide to get the basics of how JuMP works.
For your example, you can just declare your parameters directly:
using JuMP
# declare some parameters
f = 3
N = 10
M = 5
R = 1:N
V = 1:N
R_OK = 1:M
Tmax = 33
T = 1:Tmax
# create the model
m = Model()
# add variables
#variable(m, primary[R,V], Bin)
#variable(m, SendPrepReq[T,R,V], Bin)
EDIT
One might want to provide parameters independently from the model declaration as in AMLP. The most straightforward way in Julia will be to build and solve the model in a function taking the problem parameters in argument:
function build_model(f, N, M, Tmax)
R = 1:N
V = 1:N
R_OK = 1:M
T = 1:Tmax
# create the model
m = Model()
# add variables
#variable(m, primary[R,V], Bin)
#variable(m, SendPrepReq[T,R,V], Bin)
return (m, primary, SendPrepReq)
end
Using Open SCAD, I have a module that, like cube(), has a size parameter that can be a single value or a vector of three values. Ultimately, I want a vector of three values.
If the caller passes a single value, I'd like all three values of the vector to be the same. I don't see anything in the language documentation about detecting the type of an argument. So I came up with this hack:
module my_cubelike_thing(size=1) {
dimensions = concat(size, size, size);
width = dimensions[0];
length = dimensions[1];
height = dimensions[2];
// ... use width, length, and height ...
}
When size is a single value, the result of the concat is exactly what I want: three copies of the value.
When size is a three-value vector, the result of the concat is nine-value vector, and my code just ignores the last six values.
It works but only because what I want in the single value case is to replicate the value. Is there a general way to switch on the argument type and do different things depending on that type?
If type of size only can be single value or a vector with 3 values, the type can helpwise be found by the special value undef:
a = [3,5,8];
// a = 5;
if (a[0] == undef) {
dimensions = concat(a, a, a);
// do something
cube(size=dimensions,center=false);
}
else {
dimensions = a;
// do something
cube(size=dimensions,center=false);
}
But assignments are only valid in the scope in which they are defined , documnetation of openscad.
So in each subtree much code is needed and i would prefere to validate the type of size in an external script (e.g. python3) and write the openscad-code with the assignment of variables to a file, which can be included in the openscad-file, here my short test-code:
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
import os
# size = 20
size = [20,15,10]
if type(size) == int:
dimensions = [size, size, size]
elif type(size) == list:
dimensions = size
else:
# if other types possible
pass
with open('variablen.scad', 'w') as wObj:
for i, v in enumerate(['l', 'w', 'h']):
wObj.write('{} = {};\n'.format(v, dimensions[i]))
os.system('openscad ./typeDef.scad')
content of variablen.scad:
l = 20;
w = 15;
h = 10;
and typeDef.scad can look like this
include <./variablen.scad>;
module my_cubelike_thing() {
linear_extrude(height=h, center=false) square(l, w);
}
my_cubelike_thing();