Optimising the Selection of MaxValue in AssociationOptimising 2D binning codeMathematica List Selectionselection based on values of other listConstructing lists in an efficient wayImproving a selection routineSelect Consecutive Association rows based on patternSelection based on truth tableHow to negate a boolean selection criteriaSorting an Association by FindMaximumOptimising Table wrapping over a Select
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Optimising the Selection of MaxValue in Association
Optimising 2D binning codeMathematica List Selectionselection based on values of other listConstructing lists in an efficient wayImproving a selection routineSelect Consecutive Association rows based on patternSelection based on truth tableHow to negate a boolean selection criteriaSorting an Association by FindMaximumOptimising Table wrapping over a Select
.everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty margin-bottom:0;
4
$begingroup$
Suppose I have the following Association:
f=<|"vanilla:veal" -> (353.073 x + 1137.02 x^2 + 2301.78 x^3 +
3771.09 x^4 + 5369.78 x^5 + 6302.43 x^6 + 6703.86 x^7 +
6518.57 x^8 + 5440.72 x^9 + 4612.02 x^10 + 3457.49 x^11 +
2654.9 x^12 + 2100.02 x^13 + 1521.13 x^14 + 1076.02 x^15 +
755.953 x^16 + 480.615 x^17 + 261.089 x^18 + 204.306 x^19 +
110.874 x^20 + 55.7565 x^21 + 28.2723 x^22 + 28.1937 x^23 +
19.6806 x^24 + 5.60733 x^25 + 3.72775 x^26 + 0.929319 x^27 +
1.8534 x^28 + 2.77225 x^29 + 0.921466 x^30 +
1.8377 x^31)/(354 x + 1143 x^2 + 2320 x^3 + 3811 x^4 +
5441 x^5 + 6403 x^6 + 6829 x^7 + 6658 x^8 + 5571 x^9 +
4737 x^10 + 3560 x^11 + 2741 x^12 + 2174 x^13 + 1579 x^14 +
1120 x^15 + 789 x^16 + 502 x^17 + 275 x^18 + 215 x^19 +
117 x^20 + 59 x^21 + 30 x^22 + 30 x^23 + 21 x^24 + 6 x^25 +
4 x^26 + x^27 + 2 x^28 + 3 x^29 + x^30 + 2 x^31),
"leek:white_wine" -> (353.073 x + 1137.02 x^2 + 2301.78 x^3 +
3772.08 x^4 + 5369.78 x^5 + 6306.37 x^6 + 6699.93 x^7 +
6523.46 x^8 + 5443.65 x^9 + 4606.18 x^10 + 3463.31 x^11 +
2651.02 x^12 + 2101.95 x^13 + 1520.17 x^14 + 1073.14 x^15 +
755.953 x^16 + 476.793 x^17 + 264.901 x^18 + 202.406 x^19 +
111.822 x^20 + 53.8665 x^21 + 29.2147 x^22 + 27.2539 x^23 +
19.6806 x^24 + 5.60733 x^25 + 3.72775 x^26 + 0.929319 x^27 +
1.8534 x^28 + 2.77225 x^29 + 0.921466 x^30 +
1.8377 x^31)/(354 x + 1143 x^2 + 2320 x^3 + 3811 x^4 +
5441 x^5 + 6403 x^6 + 6829 x^7 + 6658 x^8 + 5571 x^9 +
4737 x^10 + 3560 x^11 + 2741 x^12 + 2174 x^13 + 1579 x^14 +
1120 x^15 + 789 x^16 + 502 x^17 + 275 x^18 + 215 x^19 +
117 x^20 + 59 x^21 + 30 x^22 + 30 x^23 + 21 x^24 + 6 x^25 +
4 x^26 + x^27 + 2 x^28 + 3 x^29 + x^30 + 2 x^31),
"orange:shiitake" -> (353.073 x + 1137.02 x^2 + 2301.78 x^3 +
3771.09 x^4 + 5369.78 x^5 + 6302.43 x^6 + 6703.86 x^7 +
6518.57 x^8 + 5440.72 x^9 + 4612.02 x^10 + 3457.49 x^11 +
2655.86 x^12 + 2099.05 x^13 + 1521.13 x^14 + 1076.02 x^15 +
755.953 x^16 + 479.66 x^17 + 262.995 x^18 + 203.356 x^19 +
110.874 x^20 + 55.7565 x^21 + 28.2723 x^22 + 28.1937 x^23 +
19.6806 x^24 + 5.60733 x^25 + 3.72775 x^26 + 0.929319 x^27 +
1.8534 x^28 + 2.77225 x^29 + 0.921466 x^30 +
1.8377 x^31)/(354 x + 1143 x^2 + 2320 x^3 + 3811 x^4 +
5441 x^5 + 6403 x^6 + 6829 x^7 + 6658 x^8 + 5571 x^9 +
4737 x^10 + 3560 x^11 + 2741 x^12 + 2174 x^13 + 1579 x^14 +
1120 x^15 + 789 x^16 + 502 x^17 + 275 x^18 + 215 x^19 +
117 x^20 + 59 x^21 + 30 x^22 + 30 x^23 + 21 x^24 + 6 x^25 +
4 x^26 + x^27 + 2 x^28 + 3 x^29 + x^30 + 2 x^31),
"pepper:smoked_sausage" -> (353.073 x + 1137.02 x^2 + 2301.78 x^3 +
3773.07 x^4 + 5370.77 x^5 + 6303.41 x^6 + 6708.77 x^7 +
6522.48 x^8 + 5432.91 x^9 + 4612.02 x^10 + 3461.37 x^11 +
2650.05 x^12 + 2100.02 x^13 + 1520.17 x^14 + 1075.06 x^15 +
754.037 x^16 + 481.571 x^17 + 262.042 x^18 + 203.356 x^19 +
109.927 x^20 + 55.7565 x^21 + 28.2723 x^22 + 28.1937 x^23 +
19.6806 x^24 + 5.60733 x^25 + 3.72775 x^26 + 0.929319 x^27 +
1.8534 x^28 + 2.77225 x^29 + 0.921466 x^30 +
1.8377 x^31)/(354 x + 1143 x^2 + 2320 x^3 + 3811 x^4 +
5441 x^5 + 6403 x^6 + 6829 x^7 + 6658 x^8 + 5571 x^9 +
4737 x^10 + 3560 x^11 + 2741 x^12 + 2174 x^13 + 1579 x^14 +
1120 x^15 + 789 x^16 + 502 x^17 + 275 x^18 + 215 x^19 +
117 x^20 + 59 x^21 + 30 x^22 + 30 x^23 + 21 x^24 + 6 x^25 +
4 x^26 + x^27 + 2 x^28 + 3 x^29 + x^30 + 2 x^31),
"carrot:celery" -> (353.073 x + 1137.02 x^2 + 2301.78 x^3 +
3787.92 x^4 + 5375.7 x^5 + 6322.12 x^6 + 6740.18 x^7 +
6545.98 x^8 + 5464.16 x^9 + 4600.34 x^10 + 3451.66 x^11 +
2659.74 x^12 + 2084.56 x^13 + 1512.46 x^14 + 1049.12 x^15 +
733.916 x^16 + 467.238 x^17 + 254.419 x^18 + 199.555 x^19 +
107.084 x^20 + 47.2513 x^21 + 31.0995 x^22 + 23.4948 x^23 +
18.7435 x^24 + 5.60733 x^25 + 3.72775 x^26 + 0.929319 x^27 +
0.926702 x^28 + 2.77225 x^29 + 1.84293 x^30 +
0.918848 x^31)/(354 x + 1143 x^2 + 2320 x^3 + 3811 x^4 +
5441 x^5 + 6403 x^6 + 6829 x^7 + 6658 x^8 + 5571 x^9 +
4737 x^10 + 3560 x^11 + 2741 x^12 + 2174 x^13 + 1579 x^14 +
1120 x^15 + 789 x^16 + 502 x^17 + 275 x^18 + 215 x^19 +
117 x^20 + 59 x^21 + 30 x^22 + 30 x^23 + 21 x^24 + 6 x^25 +
4 x^26 + x^27 + 2 x^28 + 3 x^29 + x^30 + 2 x^31),
"cane_molasses:cumin" -> (353.073 x + 1137.02 x^2 + 2303.76 x^3 +
3769.12 x^4 + 5371.76 x^5 + 6304.4 x^6 + 6706.81 x^7 +
6518.57 x^8 + 5447.56 x^9 + 4618.84 x^10 + 3458.46 x^11 +
2655.86 x^12 + 2105.81 x^13 + 1514.39 x^14 + 1076.98 x^15 +
749.246 x^16 + 479.66 x^17 + 255.372 x^18 + 208.107 x^19 +
108.031 x^20 + 51.9764 x^21 + 24.5026 x^22 + 28.1937 x^23 +
18.7435 x^24 + 5.60733 x^25 + 2.79581 x^26 + 0.929319 x^27 +
2.7801 x^28 + 2.77225 x^29 + 1.8377 x^31)/(354 x + 1143 x^2 +
2320 x^3 + 3811 x^4 + 5441 x^5 + 6403 x^6 + 6829 x^7 +
6658 x^8 + 5571 x^9 + 4737 x^10 + 3560 x^11 + 2741 x^12 +
2174 x^13 + 1579 x^14 + 1120 x^15 + 789 x^16 + 502 x^17 +
275 x^18 + 215 x^19 + 117 x^20 + 59 x^21 + 30 x^22 + 30 x^23 +
21 x^24 + 6 x^25 + 4 x^26 + x^27 + 2 x^28 + 3 x^29 + x^30 +
2 x^31),
"lettuce:turnip" -> (353.073 x + 1137.02 x^2 + 2301.78 x^3 +
3771.09 x^4 + 5369.78 x^5 + 6302.43 x^6 + 6703.86 x^7 +
6519.54 x^8 + 5438.77 x^9 + 4612.99 x^10 + 3457.49 x^11 +
2654.9 x^12 + 2100.02 x^13 + 1521.13 x^14 + 1076.02 x^15 +
755.953 x^16 + 479.66 x^17 + 262.042 x^18 + 204.306 x^19 +
110.874 x^20 + 55.7565 x^21 + 28.2723 x^22 + 28.1937 x^23 +
19.6806 x^24 + 5.60733 x^25 + 3.72775 x^26 + 0.929319 x^27 +
1.8534 x^28 + 2.77225 x^29 + 0.921466 x^30 +
1.8377 x^31)/(354 x + 1143 x^2 + 2320 x^3 + 3811 x^4 +
5441 x^5 + 6403 x^6 + 6829 x^7 + 6658 x^8 + 5571 x^9 +
4737 x^10 + 3560 x^11 + 2741 x^12 + 2174 x^13 + 1579 x^14 +
1120 x^15 + 789 x^16 + 502 x^17 + 275 x^18 + 215 x^19 +
117 x^20 + 59 x^21 + 30 x^22 + 30 x^23 + 21 x^24 + 6 x^25 +
4 x^26 + x^27 + 2 x^28 + 3 x^29 + x^30 + 2 x^31),
"corn_grit:pork_sausage" -> (353.073 x + 1137.02 x^2 + 2302.77 x^3 +
3771.09 x^4 + 5371.76 x^5 + 6301.45 x^6 + 6701.9 x^7 +
6519.54 x^8 + 5439.75 x^9 + 4612.99 x^10 + 3457.49 x^11 +
2654.9 x^12 + 2100.98 x^13 + 1519.2 x^14 + 1076.02 x^15 +
755.953 x^16 + 479.66 x^17 + 262.042 x^18 + 204.306 x^19 +
110.874 x^20 + 55.7565 x^21 + 28.2723 x^22 + 28.1937 x^23 +
19.6806 x^24 + 5.60733 x^25 + 3.72775 x^26 + 0.929319 x^27 +
2.7801 x^28 + 1.84817 x^29 + 0.921466 x^30 +
1.8377 x^31)/(354 x + 1143 x^2 + 2320 x^3 + 3811 x^4 +
5441 x^5 + 6403 x^6 + 6829 x^7 + 6658 x^8 + 5571 x^9 +
4737 x^10 + 3560 x^11 + 2741 x^12 + 2174 x^13 + 1579 x^14 +
1120 x^15 + 789 x^16 + 502 x^17 + 275 x^18 + 215 x^19 +
117 x^20 + 59 x^21 + 30 x^22 + 30 x^23 + 21 x^24 + 6 x^25 +
4 x^26 + x^27 + 2 x^28 + 3 x^29 + x^30 + 2 x^31),
"avocado:pumpkin" -> (353.073 x + 1137.02 x^2 + 2301.78 x^3 +
3771.09 x^4 + 5369.78 x^5 + 6303.41 x^6 + 6702.88 x^7 +
6518.57 x^8 + 5440.72 x^9 + 4612.02 x^10 + 3457.49 x^11 +
2654.9 x^12 + 2100.02 x^13 + 1521.13 x^14 + 1076.02 x^15 +
755.953 x^16 + 479.66 x^17 + 262.042 x^18 + 204.306 x^19 +
110.874 x^20 + 55.7565 x^21 + 28.2723 x^22 + 28.1937 x^23 +
19.6806 x^24 + 5.60733 x^25 + 3.72775 x^26 + 0.929319 x^27 +
1.8534 x^28 + 2.77225 x^29 + 0.921466 x^30 +
1.8377 x^31)/(354 x + 1143 x^2 + 2320 x^3 + 3811 x^4 +
5441 x^5 + 6403 x^6 + 6829 x^7 + 6658 x^8 + 5571 x^9 +
4737 x^10 + 3560 x^11 + 2741 x^12 + 2174 x^13 + 1579 x^14 +
1120 x^15 + 789 x^16 + 502 x^17 + 275 x^18 + 215 x^19 +
117 x^20 + 59 x^21 + 30 x^22 + 30 x^23 + 21 x^24 + 6 x^25 +
4 x^26 + x^27 + 2 x^28 + 3 x^29 + x^30 + 2 x^31),
"chive:mandarin_peel" -> (353.073 x + 1137.02 x^2 + 2301.78 x^3 +
3771.09 x^4 + 5369.78 x^5 + 6302.43 x^6 + 6704.84 x^7 +
6517.59 x^8 + 5439.75 x^9 + 4612.99 x^10 + 3457.49 x^11 +
2654.9 x^12 + 2100.02 x^13 + 1521.13 x^14 + 1076.02 x^15 +
755.953 x^16 + 479.66 x^17 + 262.042 x^18 + 204.306 x^19 +
110.874 x^20 + 55.7565 x^21 + 28.2723 x^22 + 28.1937 x^23 +
19.6806 x^24 + 5.60733 x^25 + 3.72775 x^26 + 0.929319 x^27 +
1.8534 x^28 + 2.77225 x^29 + 0.921466 x^30 +
1.8377 x^31)/(354 x + 1143 x^2 + 2320 x^3 + 3811 x^4 +
5441 x^5 + 6403 x^6 + 6829 x^7 + 6658 x^8 + 5571 x^9 +
4737 x^10 + 3560 x^11 + 2741 x^12 + 2174 x^13 + 1579 x^14 +
1120 x^15 + 789 x^16 + 502 x^17 + 275 x^18 + 215 x^19 +
117 x^20 + 59 x^21 + 30 x^22 + 30 x^23 + 21 x^24 + 6 x^25 +
4 x^26 + x^27 + 2 x^28 + 3 x^29 + x^30 + 2 x^31),
"anise_seed:coconut" -> (353.073 x + 1137.02 x^2 + 2301.78 x^3 +
3771.09 x^4 + 5369.78 x^5 + 6302.43 x^6 + 6703.86 x^7 +
6518.57 x^8 + 5439.75 x^9 + 4612.99 x^10 + 3457.49 x^11 +
2654.9 x^12 + 2100.98 x^13 + 1521.13 x^14 + 1075.06 x^15 +
755.953 x^16 + 479.66 x^17 + 262.042 x^18 + 204.306 x^19 +
110.874 x^20 + 55.7565 x^21 + 28.2723 x^22 + 28.1937 x^23 +
19.6806 x^24 + 5.60733 x^25 + 3.72775 x^26 + 0.929319 x^27 +
1.8534 x^28 + 2.77225 x^29 + 0.921466 x^30 +
1.8377 x^31)/(354 x + 1143 x^2 + 2320 x^3 + 3811 x^4 +
5441 x^5 + 6403 x^6 + 6829 x^7 + 6658 x^8 + 5571 x^9 +
4737 x^10 + 3560 x^11 + 2741 x^12 + 2174 x^13 + 1579 x^14 +
1120 x^15 + 789 x^16 + 502 x^17 + 275 x^18 + 215 x^19 +
117 x^20 + 59 x^21 + 30 x^22 + 30 x^23 + 21 x^24 + 6 x^25 +
4 x^26 + x^27 + 2 x^28 + 3 x^29 + x^30 + 2 x^31)|>
which contains rational functions. I want to select the ones that have y value above 1 for a specific range of x, so I do:
Select[f, MaxValue[#, 2/382 <= x <= 1, x] > 1 &] // AbsoluteTiming
in this case none of them are, so I get:
1.80393, <
The point is that my original list contains 30000 of these polynomials and the command I have for selection is taking a lot of time. For 10 of them as above it took 1.8 seconds. I wonder how can I break this time down without losing the dictionary, namely what key is related to what polynomial?
I know if I only look at values the time would be reduced, but then I will not know the output would belong to which key from the association.
list-manipulation filtering maximum
edited Jul 17 at 17:18
Carl Woll
88.3k3 gold badges117 silver badges227 bronze badges
asked Jul 17 at 15:26
WilliamWilliam
1,0156 silver badges8 bronze badges
$endgroup$
add a comment |
4
$begingroup$
Suppose I have the following Association:
f=<|"vanilla:veal" -> (353.073 x + 1137.02 x^2 + 2301.78 x^3 +
3771.09 x^4 + 5369.78 x^5 + 6302.43 x^6 + 6703.86 x^7 +
6518.57 x^8 + 5440.72 x^9 + 4612.02 x^10 + 3457.49 x^11 +
2654.9 x^12 + 2100.02 x^13 + 1521.13 x^14 + 1076.02 x^15 +
755.953 x^16 + 480.615 x^17 + 261.089 x^18 + 204.306 x^19 +
110.874 x^20 + 55.7565 x^21 + 28.2723 x^22 + 28.1937 x^23 +
19.6806 x^24 + 5.60733 x^25 + 3.72775 x^26 + 0.929319 x^27 +
1.8534 x^28 + 2.77225 x^29 + 0.921466 x^30 +
1.8377 x^31)/(354 x + 1143 x^2 + 2320 x^3 + 3811 x^4 +
5441 x^5 + 6403 x^6 + 6829 x^7 + 6658 x^8 + 5571 x^9 +
4737 x^10 + 3560 x^11 + 2741 x^12 + 2174 x^13 + 1579 x^14 +
1120 x^15 + 789 x^16 + 502 x^17 + 275 x^18 + 215 x^19 +
117 x^20 + 59 x^21 + 30 x^22 + 30 x^23 + 21 x^24 + 6 x^25 +
4 x^26 + x^27 + 2 x^28 + 3 x^29 + x^30 + 2 x^31),
"leek:white_wine" -> (353.073 x + 1137.02 x^2 + 2301.78 x^3 +
3772.08 x^4 + 5369.78 x^5 + 6306.37 x^6 + 6699.93 x^7 +
6523.46 x^8 + 5443.65 x^9 + 4606.18 x^10 + 3463.31 x^11 +
2651.02 x^12 + 2101.95 x^13 + 1520.17 x^14 + 1073.14 x^15 +
755.953 x^16 + 476.793 x^17 + 264.901 x^18 + 202.406 x^19 +
111.822 x^20 + 53.8665 x^21 + 29.2147 x^22 + 27.2539 x^23 +
19.6806 x^24 + 5.60733 x^25 + 3.72775 x^26 + 0.929319 x^27 +
1.8534 x^28 + 2.77225 x^29 + 0.921466 x^30 +
1.8377 x^31)/(354 x + 1143 x^2 + 2320 x^3 + 3811 x^4 +
5441 x^5 + 6403 x^6 + 6829 x^7 + 6658 x^8 + 5571 x^9 +
4737 x^10 + 3560 x^11 + 2741 x^12 + 2174 x^13 + 1579 x^14 +
1120 x^15 + 789 x^16 + 502 x^17 + 275 x^18 + 215 x^19 +
117 x^20 + 59 x^21 + 30 x^22 + 30 x^23 + 21 x^24 + 6 x^25 +
4 x^26 + x^27 + 2 x^28 + 3 x^29 + x^30 + 2 x^31),
"orange:shiitake" -> (353.073 x + 1137.02 x^2 + 2301.78 x^3 +
3771.09 x^4 + 5369.78 x^5 + 6302.43 x^6 + 6703.86 x^7 +
6518.57 x^8 + 5440.72 x^9 + 4612.02 x^10 + 3457.49 x^11 +
2655.86 x^12 + 2099.05 x^13 + 1521.13 x^14 + 1076.02 x^15 +
755.953 x^16 + 479.66 x^17 + 262.995 x^18 + 203.356 x^19 +
110.874 x^20 + 55.7565 x^21 + 28.2723 x^22 + 28.1937 x^23 +
19.6806 x^24 + 5.60733 x^25 + 3.72775 x^26 + 0.929319 x^27 +
1.8534 x^28 + 2.77225 x^29 + 0.921466 x^30 +
1.8377 x^31)/(354 x + 1143 x^2 + 2320 x^3 + 3811 x^4 +
5441 x^5 + 6403 x^6 + 6829 x^7 + 6658 x^8 + 5571 x^9 +
4737 x^10 + 3560 x^11 + 2741 x^12 + 2174 x^13 + 1579 x^14 +
1120 x^15 + 789 x^16 + 502 x^17 + 275 x^18 + 215 x^19 +
117 x^20 + 59 x^21 + 30 x^22 + 30 x^23 + 21 x^24 + 6 x^25 +
4 x^26 + x^27 + 2 x^28 + 3 x^29 + x^30 + 2 x^31),
"pepper:smoked_sausage" -> (353.073 x + 1137.02 x^2 + 2301.78 x^3 +
3773.07 x^4 + 5370.77 x^5 + 6303.41 x^6 + 6708.77 x^7 +
6522.48 x^8 + 5432.91 x^9 + 4612.02 x^10 + 3461.37 x^11 +
2650.05 x^12 + 2100.02 x^13 + 1520.17 x^14 + 1075.06 x^15 +
754.037 x^16 + 481.571 x^17 + 262.042 x^18 + 203.356 x^19 +
109.927 x^20 + 55.7565 x^21 + 28.2723 x^22 + 28.1937 x^23 +
19.6806 x^24 + 5.60733 x^25 + 3.72775 x^26 + 0.929319 x^27 +
1.8534 x^28 + 2.77225 x^29 + 0.921466 x^30 +
1.8377 x^31)/(354 x + 1143 x^2 + 2320 x^3 + 3811 x^4 +
5441 x^5 + 6403 x^6 + 6829 x^7 + 6658 x^8 + 5571 x^9 +
4737 x^10 + 3560 x^11 + 2741 x^12 + 2174 x^13 + 1579 x^14 +
1120 x^15 + 789 x^16 + 502 x^17 + 275 x^18 + 215 x^19 +
117 x^20 + 59 x^21 + 30 x^22 + 30 x^23 + 21 x^24 + 6 x^25 +
4 x^26 + x^27 + 2 x^28 + 3 x^29 + x^30 + 2 x^31),
"carrot:celery" -> (353.073 x + 1137.02 x^2 + 2301.78 x^3 +
3787.92 x^4 + 5375.7 x^5 + 6322.12 x^6 + 6740.18 x^7 +
6545.98 x^8 + 5464.16 x^9 + 4600.34 x^10 + 3451.66 x^11 +
2659.74 x^12 + 2084.56 x^13 + 1512.46 x^14 + 1049.12 x^15 +
733.916 x^16 + 467.238 x^17 + 254.419 x^18 + 199.555 x^19 +
107.084 x^20 + 47.2513 x^21 + 31.0995 x^22 + 23.4948 x^23 +
18.7435 x^24 + 5.60733 x^25 + 3.72775 x^26 + 0.929319 x^27 +
0.926702 x^28 + 2.77225 x^29 + 1.84293 x^30 +
0.918848 x^31)/(354 x + 1143 x^2 + 2320 x^3 + 3811 x^4 +
5441 x^5 + 6403 x^6 + 6829 x^7 + 6658 x^8 + 5571 x^9 +
4737 x^10 + 3560 x^11 + 2741 x^12 + 2174 x^13 + 1579 x^14 +
1120 x^15 + 789 x^16 + 502 x^17 + 275 x^18 + 215 x^19 +
117 x^20 + 59 x^21 + 30 x^22 + 30 x^23 + 21 x^24 + 6 x^25 +
4 x^26 + x^27 + 2 x^28 + 3 x^29 + x^30 + 2 x^31),
"cane_molasses:cumin" -> (353.073 x + 1137.02 x^2 + 2303.76 x^3 +
3769.12 x^4 + 5371.76 x^5 + 6304.4 x^6 + 6706.81 x^7 +
6518.57 x^8 + 5447.56 x^9 + 4618.84 x^10 + 3458.46 x^11 +
2655.86 x^12 + 2105.81 x^13 + 1514.39 x^14 + 1076.98 x^15 +
749.246 x^16 + 479.66 x^17 + 255.372 x^18 + 208.107 x^19 +
108.031 x^20 + 51.9764 x^21 + 24.5026 x^22 + 28.1937 x^23 +
18.7435 x^24 + 5.60733 x^25 + 2.79581 x^26 + 0.929319 x^27 +
2.7801 x^28 + 2.77225 x^29 + 1.8377 x^31)/(354 x + 1143 x^2 +
2320 x^3 + 3811 x^4 + 5441 x^5 + 6403 x^6 + 6829 x^7 +
6658 x^8 + 5571 x^9 + 4737 x^10 + 3560 x^11 + 2741 x^12 +
2174 x^13 + 1579 x^14 + 1120 x^15 + 789 x^16 + 502 x^17 +
275 x^18 + 215 x^19 + 117 x^20 + 59 x^21 + 30 x^22 + 30 x^23 +
21 x^24 + 6 x^25 + 4 x^26 + x^27 + 2 x^28 + 3 x^29 + x^30 +
2 x^31),
"lettuce:turnip" -> (353.073 x + 1137.02 x^2 + 2301.78 x^3 +
3771.09 x^4 + 5369.78 x^5 + 6302.43 x^6 + 6703.86 x^7 +
6519.54 x^8 + 5438.77 x^9 + 4612.99 x^10 + 3457.49 x^11 +
2654.9 x^12 + 2100.02 x^13 + 1521.13 x^14 + 1076.02 x^15 +
755.953 x^16 + 479.66 x^17 + 262.042 x^18 + 204.306 x^19 +
110.874 x^20 + 55.7565 x^21 + 28.2723 x^22 + 28.1937 x^23 +
19.6806 x^24 + 5.60733 x^25 + 3.72775 x^26 + 0.929319 x^27 +
1.8534 x^28 + 2.77225 x^29 + 0.921466 x^30 +
1.8377 x^31)/(354 x + 1143 x^2 + 2320 x^3 + 3811 x^4 +
5441 x^5 + 6403 x^6 + 6829 x^7 + 6658 x^8 + 5571 x^9 +
4737 x^10 + 3560 x^11 + 2741 x^12 + 2174 x^13 + 1579 x^14 +
1120 x^15 + 789 x^16 + 502 x^17 + 275 x^18 + 215 x^19 +
117 x^20 + 59 x^21 + 30 x^22 + 30 x^23 + 21 x^24 + 6 x^25 +
4 x^26 + x^27 + 2 x^28 + 3 x^29 + x^30 + 2 x^31),
"corn_grit:pork_sausage" -> (353.073 x + 1137.02 x^2 + 2302.77 x^3 +
3771.09 x^4 + 5371.76 x^5 + 6301.45 x^6 + 6701.9 x^7 +
6519.54 x^8 + 5439.75 x^9 + 4612.99 x^10 + 3457.49 x^11 +
2654.9 x^12 + 2100.98 x^13 + 1519.2 x^14 + 1076.02 x^15 +
755.953 x^16 + 479.66 x^17 + 262.042 x^18 + 204.306 x^19 +
110.874 x^20 + 55.7565 x^21 + 28.2723 x^22 + 28.1937 x^23 +
19.6806 x^24 + 5.60733 x^25 + 3.72775 x^26 + 0.929319 x^27 +
2.7801 x^28 + 1.84817 x^29 + 0.921466 x^30 +
1.8377 x^31)/(354 x + 1143 x^2 + 2320 x^3 + 3811 x^4 +
5441 x^5 + 6403 x^6 + 6829 x^7 + 6658 x^8 + 5571 x^9 +
4737 x^10 + 3560 x^11 + 2741 x^12 + 2174 x^13 + 1579 x^14 +
1120 x^15 + 789 x^16 + 502 x^17 + 275 x^18 + 215 x^19 +
117 x^20 + 59 x^21 + 30 x^22 + 30 x^23 + 21 x^24 + 6 x^25 +
4 x^26 + x^27 + 2 x^28 + 3 x^29 + x^30 + 2 x^31),
"avocado:pumpkin" -> (353.073 x + 1137.02 x^2 + 2301.78 x^3 +
3771.09 x^4 + 5369.78 x^5 + 6303.41 x^6 + 6702.88 x^7 +
6518.57 x^8 + 5440.72 x^9 + 4612.02 x^10 + 3457.49 x^11 +
2654.9 x^12 + 2100.02 x^13 + 1521.13 x^14 + 1076.02 x^15 +
755.953 x^16 + 479.66 x^17 + 262.042 x^18 + 204.306 x^19 +
110.874 x^20 + 55.7565 x^21 + 28.2723 x^22 + 28.1937 x^23 +
19.6806 x^24 + 5.60733 x^25 + 3.72775 x^26 + 0.929319 x^27 +
1.8534 x^28 + 2.77225 x^29 + 0.921466 x^30 +
1.8377 x^31)/(354 x + 1143 x^2 + 2320 x^3 + 3811 x^4 +
5441 x^5 + 6403 x^6 + 6829 x^7 + 6658 x^8 + 5571 x^9 +
4737 x^10 + 3560 x^11 + 2741 x^12 + 2174 x^13 + 1579 x^14 +
1120 x^15 + 789 x^16 + 502 x^17 + 275 x^18 + 215 x^19 +
117 x^20 + 59 x^21 + 30 x^22 + 30 x^23 + 21 x^24 + 6 x^25 +
4 x^26 + x^27 + 2 x^28 + 3 x^29 + x^30 + 2 x^31),
"chive:mandarin_peel" -> (353.073 x + 1137.02 x^2 + 2301.78 x^3 +
3771.09 x^4 + 5369.78 x^5 + 6302.43 x^6 + 6704.84 x^7 +
6517.59 x^8 + 5439.75 x^9 + 4612.99 x^10 + 3457.49 x^11 +
2654.9 x^12 + 2100.02 x^13 + 1521.13 x^14 + 1076.02 x^15 +
755.953 x^16 + 479.66 x^17 + 262.042 x^18 + 204.306 x^19 +
110.874 x^20 + 55.7565 x^21 + 28.2723 x^22 + 28.1937 x^23 +
19.6806 x^24 + 5.60733 x^25 + 3.72775 x^26 + 0.929319 x^27 +
1.8534 x^28 + 2.77225 x^29 + 0.921466 x^30 +
1.8377 x^31)/(354 x + 1143 x^2 + 2320 x^3 + 3811 x^4 +
5441 x^5 + 6403 x^6 + 6829 x^7 + 6658 x^8 + 5571 x^9 +
4737 x^10 + 3560 x^11 + 2741 x^12 + 2174 x^13 + 1579 x^14 +
1120 x^15 + 789 x^16 + 502 x^17 + 275 x^18 + 215 x^19 +
117 x^20 + 59 x^21 + 30 x^22 + 30 x^23 + 21 x^24 + 6 x^25 +
4 x^26 + x^27 + 2 x^28 + 3 x^29 + x^30 + 2 x^31),
"anise_seed:coconut" -> (353.073 x + 1137.02 x^2 + 2301.78 x^3 +
3771.09 x^4 + 5369.78 x^5 + 6302.43 x^6 + 6703.86 x^7 +
6518.57 x^8 + 5439.75 x^9 + 4612.99 x^10 + 3457.49 x^11 +
2654.9 x^12 + 2100.98 x^13 + 1521.13 x^14 + 1075.06 x^15 +
755.953 x^16 + 479.66 x^17 + 262.042 x^18 + 204.306 x^19 +
110.874 x^20 + 55.7565 x^21 + 28.2723 x^22 + 28.1937 x^23 +
19.6806 x^24 + 5.60733 x^25 + 3.72775 x^26 + 0.929319 x^27 +
1.8534 x^28 + 2.77225 x^29 + 0.921466 x^30 +
1.8377 x^31)/(354 x + 1143 x^2 + 2320 x^3 + 3811 x^4 +
5441 x^5 + 6403 x^6 + 6829 x^7 + 6658 x^8 + 5571 x^9 +
4737 x^10 + 3560 x^11 + 2741 x^12 + 2174 x^13 + 1579 x^14 +
1120 x^15 + 789 x^16 + 502 x^17 + 275 x^18 + 215 x^19 +
117 x^20 + 59 x^21 + 30 x^22 + 30 x^23 + 21 x^24 + 6 x^25 +
4 x^26 + x^27 + 2 x^28 + 3 x^29 + x^30 + 2 x^31)|>
which contains rational functions. I want to select the ones that have y value above 1 for a specific range of x, so I do:
Select[f, MaxValue[#, 2/382 <= x <= 1, x] > 1 &] // AbsoluteTiming
in this case none of them are, so I get:
1.80393, <
The point is that my original list contains 30000 of these polynomials and the command I have for selection is taking a lot of time. For 10 of them as above it took 1.8 seconds. I wonder how can I break this time down without losing the dictionary, namely what key is related to what polynomial?
I know if I only look at values the time would be reduced, but then I will not know the output would belong to which key from the association.
list-manipulation filtering maximum
edited Jul 17 at 17:18
Carl Woll
88.3k3 gold badges117 silver badges227 bronze badges
asked Jul 17 at 15:26
WilliamWilliam
1,0156 silver badges8 bronze badges
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If you have 8 cores, and useParallelTable, that would take less than 12 minutes. Is that too long?
$endgroup$
– rhermans
Jul 17 at 16:14
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I have 4 so presume it will take 24', is there any way to chunk the code down into easier-to-handle part?
$endgroup$
– William
Jul 17 at 16:23
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For all of the polynomials you give, the maximum lies at the lower edge of your search interval. Maybe there's something generalizable here: maybe it's possible to exclude a large number of polynomials by just looking at the values (and derivatives) at the end points.
$endgroup$
– Roman
Jul 17 at 18:15
add a comment |
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Suppose I have the following Association:
f=<|"vanilla:veal" -> (353.073 x + 1137.02 x^2 + 2301.78 x^3 +
3771.09 x^4 + 5369.78 x^5 + 6302.43 x^6 + 6703.86 x^7 +
6518.57 x^8 + 5440.72 x^9 + 4612.02 x^10 + 3457.49 x^11 +
2654.9 x^12 + 2100.02 x^13 + 1521.13 x^14 + 1076.02 x^15 +
755.953 x^16 + 480.615 x^17 + 261.089 x^18 + 204.306 x^19 +
110.874 x^20 + 55.7565 x^21 + 28.2723 x^22 + 28.1937 x^23 +
19.6806 x^24 + 5.60733 x^25 + 3.72775 x^26 + 0.929319 x^27 +
1.8534 x^28 + 2.77225 x^29 + 0.921466 x^30 +
1.8377 x^31)/(354 x + 1143 x^2 + 2320 x^3 + 3811 x^4 +
5441 x^5 + 6403 x^6 + 6829 x^7 + 6658 x^8 + 5571 x^9 +
4737 x^10 + 3560 x^11 + 2741 x^12 + 2174 x^13 + 1579 x^14 +
1120 x^15 + 789 x^16 + 502 x^17 + 275 x^18 + 215 x^19 +
117 x^20 + 59 x^21 + 30 x^22 + 30 x^23 + 21 x^24 + 6 x^25 +
4 x^26 + x^27 + 2 x^28 + 3 x^29 + x^30 + 2 x^31),
"leek:white_wine" -> (353.073 x + 1137.02 x^2 + 2301.78 x^3 +
3772.08 x^4 + 5369.78 x^5 + 6306.37 x^6 + 6699.93 x^7 +
6523.46 x^8 + 5443.65 x^9 + 4606.18 x^10 + 3463.31 x^11 +
2651.02 x^12 + 2101.95 x^13 + 1520.17 x^14 + 1073.14 x^15 +
755.953 x^16 + 476.793 x^17 + 264.901 x^18 + 202.406 x^19 +
111.822 x^20 + 53.8665 x^21 + 29.2147 x^22 + 27.2539 x^23 +
19.6806 x^24 + 5.60733 x^25 + 3.72775 x^26 + 0.929319 x^27 +
1.8534 x^28 + 2.77225 x^29 + 0.921466 x^30 +
1.8377 x^31)/(354 x + 1143 x^2 + 2320 x^3 + 3811 x^4 +
5441 x^5 + 6403 x^6 + 6829 x^7 + 6658 x^8 + 5571 x^9 +
4737 x^10 + 3560 x^11 + 2741 x^12 + 2174 x^13 + 1579 x^14 +
1120 x^15 + 789 x^16 + 502 x^17 + 275 x^18 + 215 x^19 +
117 x^20 + 59 x^21 + 30 x^22 + 30 x^23 + 21 x^24 + 6 x^25 +
4 x^26 + x^27 + 2 x^28 + 3 x^29 + x^30 + 2 x^31),
"orange:shiitake" -> (353.073 x + 1137.02 x^2 + 2301.78 x^3 +
3771.09 x^4 + 5369.78 x^5 + 6302.43 x^6 + 6703.86 x^7 +
6518.57 x^8 + 5440.72 x^9 + 4612.02 x^10 + 3457.49 x^11 +
2655.86 x^12 + 2099.05 x^13 + 1521.13 x^14 + 1076.02 x^15 +
755.953 x^16 + 479.66 x^17 + 262.995 x^18 + 203.356 x^19 +
110.874 x^20 + 55.7565 x^21 + 28.2723 x^22 + 28.1937 x^23 +
19.6806 x^24 + 5.60733 x^25 + 3.72775 x^26 + 0.929319 x^27 +
1.8534 x^28 + 2.77225 x^29 + 0.921466 x^30 +
1.8377 x^31)/(354 x + 1143 x^2 + 2320 x^3 + 3811 x^4 +
5441 x^5 + 6403 x^6 + 6829 x^7 + 6658 x^8 + 5571 x^9 +
4737 x^10 + 3560 x^11 + 2741 x^12 + 2174 x^13 + 1579 x^14 +
1120 x^15 + 789 x^16 + 502 x^17 + 275 x^18 + 215 x^19 +
117 x^20 + 59 x^21 + 30 x^22 + 30 x^23 + 21 x^24 + 6 x^25 +
4 x^26 + x^27 + 2 x^28 + 3 x^29 + x^30 + 2 x^31),
"pepper:smoked_sausage" -> (353.073 x + 1137.02 x^2 + 2301.78 x^3 +
3773.07 x^4 + 5370.77 x^5 + 6303.41 x^6 + 6708.77 x^7 +
6522.48 x^8 + 5432.91 x^9 + 4612.02 x^10 + 3461.37 x^11 +
2650.05 x^12 + 2100.02 x^13 + 1520.17 x^14 + 1075.06 x^15 +
754.037 x^16 + 481.571 x^17 + 262.042 x^18 + 203.356 x^19 +
109.927 x^20 + 55.7565 x^21 + 28.2723 x^22 + 28.1937 x^23 +
19.6806 x^24 + 5.60733 x^25 + 3.72775 x^26 + 0.929319 x^27 +
1.8534 x^28 + 2.77225 x^29 + 0.921466 x^30 +
1.8377 x^31)/(354 x + 1143 x^2 + 2320 x^3 + 3811 x^4 +
5441 x^5 + 6403 x^6 + 6829 x^7 + 6658 x^8 + 5571 x^9 +
4737 x^10 + 3560 x^11 + 2741 x^12 + 2174 x^13 + 1579 x^14 +
1120 x^15 + 789 x^16 + 502 x^17 + 275 x^18 + 215 x^19 +
117 x^20 + 59 x^21 + 30 x^22 + 30 x^23 + 21 x^24 + 6 x^25 +
4 x^26 + x^27 + 2 x^28 + 3 x^29 + x^30 + 2 x^31),
"carrot:celery" -> (353.073 x + 1137.02 x^2 + 2301.78 x^3 +
3787.92 x^4 + 5375.7 x^5 + 6322.12 x^6 + 6740.18 x^7 +
6545.98 x^8 + 5464.16 x^9 + 4600.34 x^10 + 3451.66 x^11 +
2659.74 x^12 + 2084.56 x^13 + 1512.46 x^14 + 1049.12 x^15 +
733.916 x^16 + 467.238 x^17 + 254.419 x^18 + 199.555 x^19 +
107.084 x^20 + 47.2513 x^21 + 31.0995 x^22 + 23.4948 x^23 +
18.7435 x^24 + 5.60733 x^25 + 3.72775 x^26 + 0.929319 x^27 +
0.926702 x^28 + 2.77225 x^29 + 1.84293 x^30 +
0.918848 x^31)/(354 x + 1143 x^2 + 2320 x^3 + 3811 x^4 +
5441 x^5 + 6403 x^6 + 6829 x^7 + 6658 x^8 + 5571 x^9 +
4737 x^10 + 3560 x^11 + 2741 x^12 + 2174 x^13 + 1579 x^14 +
1120 x^15 + 789 x^16 + 502 x^17 + 275 x^18 + 215 x^19 +
117 x^20 + 59 x^21 + 30 x^22 + 30 x^23 + 21 x^24 + 6 x^25 +
4 x^26 + x^27 + 2 x^28 + 3 x^29 + x^30 + 2 x^31),
"cane_molasses:cumin" -> (353.073 x + 1137.02 x^2 + 2303.76 x^3 +
3769.12 x^4 + 5371.76 x^5 + 6304.4 x^6 + 6706.81 x^7 +
6518.57 x^8 + 5447.56 x^9 + 4618.84 x^10 + 3458.46 x^11 +
2655.86 x^12 + 2105.81 x^13 + 1514.39 x^14 + 1076.98 x^15 +
749.246 x^16 + 479.66 x^17 + 255.372 x^18 + 208.107 x^19 +
108.031 x^20 + 51.9764 x^21 + 24.5026 x^22 + 28.1937 x^23 +
18.7435 x^24 + 5.60733 x^25 + 2.79581 x^26 + 0.929319 x^27 +
2.7801 x^28 + 2.77225 x^29 + 1.8377 x^31)/(354 x + 1143 x^2 +
2320 x^3 + 3811 x^4 + 5441 x^5 + 6403 x^6 + 6829 x^7 +
6658 x^8 + 5571 x^9 + 4737 x^10 + 3560 x^11 + 2741 x^12 +
2174 x^13 + 1579 x^14 + 1120 x^15 + 789 x^16 + 502 x^17 +
275 x^18 + 215 x^19 + 117 x^20 + 59 x^21 + 30 x^22 + 30 x^23 +
21 x^24 + 6 x^25 + 4 x^26 + x^27 + 2 x^28 + 3 x^29 + x^30 +
2 x^31),
"lettuce:turnip" -> (353.073 x + 1137.02 x^2 + 2301.78 x^3 +
3771.09 x^4 + 5369.78 x^5 + 6302.43 x^6 + 6703.86 x^7 +
6519.54 x^8 + 5438.77 x^9 + 4612.99 x^10 + 3457.49 x^11 +
2654.9 x^12 + 2100.02 x^13 + 1521.13 x^14 + 1076.02 x^15 +
755.953 x^16 + 479.66 x^17 + 262.042 x^18 + 204.306 x^19 +
110.874 x^20 + 55.7565 x^21 + 28.2723 x^22 + 28.1937 x^23 +
19.6806 x^24 + 5.60733 x^25 + 3.72775 x^26 + 0.929319 x^27 +
1.8534 x^28 + 2.77225 x^29 + 0.921466 x^30 +
1.8377 x^31)/(354 x + 1143 x^2 + 2320 x^3 + 3811 x^4 +
5441 x^5 + 6403 x^6 + 6829 x^7 + 6658 x^8 + 5571 x^9 +
4737 x^10 + 3560 x^11 + 2741 x^12 + 2174 x^13 + 1579 x^14 +
1120 x^15 + 789 x^16 + 502 x^17 + 275 x^18 + 215 x^19 +
117 x^20 + 59 x^21 + 30 x^22 + 30 x^23 + 21 x^24 + 6 x^25 +
4 x^26 + x^27 + 2 x^28 + 3 x^29 + x^30 + 2 x^31),
"corn_grit:pork_sausage" -> (353.073 x + 1137.02 x^2 + 2302.77 x^3 +
3771.09 x^4 + 5371.76 x^5 + 6301.45 x^6 + 6701.9 x^7 +
6519.54 x^8 + 5439.75 x^9 + 4612.99 x^10 + 3457.49 x^11 +
2654.9 x^12 + 2100.98 x^13 + 1519.2 x^14 + 1076.02 x^15 +
755.953 x^16 + 479.66 x^17 + 262.042 x^18 + 204.306 x^19 +
110.874 x^20 + 55.7565 x^21 + 28.2723 x^22 + 28.1937 x^23 +
19.6806 x^24 + 5.60733 x^25 + 3.72775 x^26 + 0.929319 x^27 +
2.7801 x^28 + 1.84817 x^29 + 0.921466 x^30 +
1.8377 x^31)/(354 x + 1143 x^2 + 2320 x^3 + 3811 x^4 +
5441 x^5 + 6403 x^6 + 6829 x^7 + 6658 x^8 + 5571 x^9 +
4737 x^10 + 3560 x^11 + 2741 x^12 + 2174 x^13 + 1579 x^14 +
1120 x^15 + 789 x^16 + 502 x^17 + 275 x^18 + 215 x^19 +
117 x^20 + 59 x^21 + 30 x^22 + 30 x^23 + 21 x^24 + 6 x^25 +
4 x^26 + x^27 + 2 x^28 + 3 x^29 + x^30 + 2 x^31),
"avocado:pumpkin" -> (353.073 x + 1137.02 x^2 + 2301.78 x^3 +
3771.09 x^4 + 5369.78 x^5 + 6303.41 x^6 + 6702.88 x^7 +
6518.57 x^8 + 5440.72 x^9 + 4612.02 x^10 + 3457.49 x^11 +
2654.9 x^12 + 2100.02 x^13 + 1521.13 x^14 + 1076.02 x^15 +
755.953 x^16 + 479.66 x^17 + 262.042 x^18 + 204.306 x^19 +
110.874 x^20 + 55.7565 x^21 + 28.2723 x^22 + 28.1937 x^23 +
19.6806 x^24 + 5.60733 x^25 + 3.72775 x^26 + 0.929319 x^27 +
1.8534 x^28 + 2.77225 x^29 + 0.921466 x^30 +
1.8377 x^31)/(354 x + 1143 x^2 + 2320 x^3 + 3811 x^4 +
5441 x^5 + 6403 x^6 + 6829 x^7 + 6658 x^8 + 5571 x^9 +
4737 x^10 + 3560 x^11 + 2741 x^12 + 2174 x^13 + 1579 x^14 +
1120 x^15 + 789 x^16 + 502 x^17 + 275 x^18 + 215 x^19 +
117 x^20 + 59 x^21 + 30 x^22 + 30 x^23 + 21 x^24 + 6 x^25 +
4 x^26 + x^27 + 2 x^28 + 3 x^29 + x^30 + 2 x^31),
"chive:mandarin_peel" -> (353.073 x + 1137.02 x^2 + 2301.78 x^3 +
3771.09 x^4 + 5369.78 x^5 + 6302.43 x^6 + 6704.84 x^7 +
6517.59 x^8 + 5439.75 x^9 + 4612.99 x^10 + 3457.49 x^11 +
2654.9 x^12 + 2100.02 x^13 + 1521.13 x^14 + 1076.02 x^15 +
755.953 x^16 + 479.66 x^17 + 262.042 x^18 + 204.306 x^19 +
110.874 x^20 + 55.7565 x^21 + 28.2723 x^22 + 28.1937 x^23 +
19.6806 x^24 + 5.60733 x^25 + 3.72775 x^26 + 0.929319 x^27 +
1.8534 x^28 + 2.77225 x^29 + 0.921466 x^30 +
1.8377 x^31)/(354 x + 1143 x^2 + 2320 x^3 + 3811 x^4 +
5441 x^5 + 6403 x^6 + 6829 x^7 + 6658 x^8 + 5571 x^9 +
4737 x^10 + 3560 x^11 + 2741 x^12 + 2174 x^13 + 1579 x^14 +
1120 x^15 + 789 x^16 + 502 x^17 + 275 x^18 + 215 x^19 +
117 x^20 + 59 x^21 + 30 x^22 + 30 x^23 + 21 x^24 + 6 x^25 +
4 x^26 + x^27 + 2 x^28 + 3 x^29 + x^30 + 2 x^31),
"anise_seed:coconut" -> (353.073 x + 1137.02 x^2 + 2301.78 x^3 +
3771.09 x^4 + 5369.78 x^5 + 6302.43 x^6 + 6703.86 x^7 +
6518.57 x^8 + 5439.75 x^9 + 4612.99 x^10 + 3457.49 x^11 +
2654.9 x^12 + 2100.98 x^13 + 1521.13 x^14 + 1075.06 x^15 +
755.953 x^16 + 479.66 x^17 + 262.042 x^18 + 204.306 x^19 +
110.874 x^20 + 55.7565 x^21 + 28.2723 x^22 + 28.1937 x^23 +
19.6806 x^24 + 5.60733 x^25 + 3.72775 x^26 + 0.929319 x^27 +
1.8534 x^28 + 2.77225 x^29 + 0.921466 x^30 +
1.8377 x^31)/(354 x + 1143 x^2 + 2320 x^3 + 3811 x^4 +
5441 x^5 + 6403 x^6 + 6829 x^7 + 6658 x^8 + 5571 x^9 +
4737 x^10 + 3560 x^11 + 2741 x^12 + 2174 x^13 + 1579 x^14 +
1120 x^15 + 789 x^16 + 502 x^17 + 275 x^18 + 215 x^19 +
117 x^20 + 59 x^21 + 30 x^22 + 30 x^23 + 21 x^24 + 6 x^25 +
4 x^26 + x^27 + 2 x^28 + 3 x^29 + x^30 + 2 x^31)|>
which contains rational functions. I want to select the ones that have y value above 1 for a specific range of x, so I do:
Select[f, MaxValue[#, 2/382 <= x <= 1, x] > 1 &] // AbsoluteTiming
in this case none of them are, so I get:
1.80393, <
The point is that my original list contains 30000 of these polynomials and the command I have for selection is taking a lot of time. For 10 of them as above it took 1.8 seconds. I wonder how can I break this time down without losing the dictionary, namely what key is related to what polynomial?
I know if I only look at values the time would be reduced, but then I will not know the output would belong to which key from the association.
list-manipulation filtering maximum
edited Jul 17 at 17:18
Carl Woll
88.3k3 gold badges117 silver badges227 bronze badges
asked Jul 17 at 15:26
WilliamWilliam
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$endgroup$
Suppose I have the following Association:
f=<|"vanilla:veal" -> (353.073 x + 1137.02 x^2 + 2301.78 x^3 +
3771.09 x^4 + 5369.78 x^5 + 6302.43 x^6 + 6703.86 x^7 +
6518.57 x^8 + 5440.72 x^9 + 4612.02 x^10 + 3457.49 x^11 +
2654.9 x^12 + 2100.02 x^13 + 1521.13 x^14 + 1076.02 x^15 +
755.953 x^16 + 480.615 x^17 + 261.089 x^18 + 204.306 x^19 +
110.874 x^20 + 55.7565 x^21 + 28.2723 x^22 + 28.1937 x^23 +
19.6806 x^24 + 5.60733 x^25 + 3.72775 x^26 + 0.929319 x^27 +
1.8534 x^28 + 2.77225 x^29 + 0.921466 x^30 +
1.8377 x^31)/(354 x + 1143 x^2 + 2320 x^3 + 3811 x^4 +
5441 x^5 + 6403 x^6 + 6829 x^7 + 6658 x^8 + 5571 x^9 +
4737 x^10 + 3560 x^11 + 2741 x^12 + 2174 x^13 + 1579 x^14 +
1120 x^15 + 789 x^16 + 502 x^17 + 275 x^18 + 215 x^19 +
117 x^20 + 59 x^21 + 30 x^22 + 30 x^23 + 21 x^24 + 6 x^25 +
4 x^26 + x^27 + 2 x^28 + 3 x^29 + x^30 + 2 x^31),
"leek:white_wine" -> (353.073 x + 1137.02 x^2 + 2301.78 x^3 +
3772.08 x^4 + 5369.78 x^5 + 6306.37 x^6 + 6699.93 x^7 +
6523.46 x^8 + 5443.65 x^9 + 4606.18 x^10 + 3463.31 x^11 +
2651.02 x^12 + 2101.95 x^13 + 1520.17 x^14 + 1073.14 x^15 +
755.953 x^16 + 476.793 x^17 + 264.901 x^18 + 202.406 x^19 +
111.822 x^20 + 53.8665 x^21 + 29.2147 x^22 + 27.2539 x^23 +
19.6806 x^24 + 5.60733 x^25 + 3.72775 x^26 + 0.929319 x^27 +
1.8534 x^28 + 2.77225 x^29 + 0.921466 x^30 +
1.8377 x^31)/(354 x + 1143 x^2 + 2320 x^3 + 3811 x^4 +
5441 x^5 + 6403 x^6 + 6829 x^7 + 6658 x^8 + 5571 x^9 +
4737 x^10 + 3560 x^11 + 2741 x^12 + 2174 x^13 + 1579 x^14 +
1120 x^15 + 789 x^16 + 502 x^17 + 275 x^18 + 215 x^19 +
117 x^20 + 59 x^21 + 30 x^22 + 30 x^23 + 21 x^24 + 6 x^25 +
4 x^26 + x^27 + 2 x^28 + 3 x^29 + x^30 + 2 x^31),
"orange:shiitake" -> (353.073 x + 1137.02 x^2 + 2301.78 x^3 +
3771.09 x^4 + 5369.78 x^5 + 6302.43 x^6 + 6703.86 x^7 +
6518.57 x^8 + 5440.72 x^9 + 4612.02 x^10 + 3457.49 x^11 +
2655.86 x^12 + 2099.05 x^13 + 1521.13 x^14 + 1076.02 x^15 +
755.953 x^16 + 479.66 x^17 + 262.995 x^18 + 203.356 x^19 +
110.874 x^20 + 55.7565 x^21 + 28.2723 x^22 + 28.1937 x^23 +
19.6806 x^24 + 5.60733 x^25 + 3.72775 x^26 + 0.929319 x^27 +
1.8534 x^28 + 2.77225 x^29 + 0.921466 x^30 +
1.8377 x^31)/(354 x + 1143 x^2 + 2320 x^3 + 3811 x^4 +
5441 x^5 + 6403 x^6 + 6829 x^7 + 6658 x^8 + 5571 x^9 +
4737 x^10 + 3560 x^11 + 2741 x^12 + 2174 x^13 + 1579 x^14 +
1120 x^15 + 789 x^16 + 502 x^17 + 275 x^18 + 215 x^19 +
117 x^20 + 59 x^21 + 30 x^22 + 30 x^23 + 21 x^24 + 6 x^25 +
4 x^26 + x^27 + 2 x^28 + 3 x^29 + x^30 + 2 x^31),
"pepper:smoked_sausage" -> (353.073 x + 1137.02 x^2 + 2301.78 x^3 +
3773.07 x^4 + 5370.77 x^5 + 6303.41 x^6 + 6708.77 x^7 +
6522.48 x^8 + 5432.91 x^9 + 4612.02 x^10 + 3461.37 x^11 +
2650.05 x^12 + 2100.02 x^13 + 1520.17 x^14 + 1075.06 x^15 +
754.037 x^16 + 481.571 x^17 + 262.042 x^18 + 203.356 x^19 +
109.927 x^20 + 55.7565 x^21 + 28.2723 x^22 + 28.1937 x^23 +
19.6806 x^24 + 5.60733 x^25 + 3.72775 x^26 + 0.929319 x^27 +
1.8534 x^28 + 2.77225 x^29 + 0.921466 x^30 +
1.8377 x^31)/(354 x + 1143 x^2 + 2320 x^3 + 3811 x^4 +
5441 x^5 + 6403 x^6 + 6829 x^7 + 6658 x^8 + 5571 x^9 +
4737 x^10 + 3560 x^11 + 2741 x^12 + 2174 x^13 + 1579 x^14 +
1120 x^15 + 789 x^16 + 502 x^17 + 275 x^18 + 215 x^19 +
117 x^20 + 59 x^21 + 30 x^22 + 30 x^23 + 21 x^24 + 6 x^25 +
4 x^26 + x^27 + 2 x^28 + 3 x^29 + x^30 + 2 x^31),
"carrot:celery" -> (353.073 x + 1137.02 x^2 + 2301.78 x^3 +
3787.92 x^4 + 5375.7 x^5 + 6322.12 x^6 + 6740.18 x^7 +
6545.98 x^8 + 5464.16 x^9 + 4600.34 x^10 + 3451.66 x^11 +
2659.74 x^12 + 2084.56 x^13 + 1512.46 x^14 + 1049.12 x^15 +
733.916 x^16 + 467.238 x^17 + 254.419 x^18 + 199.555 x^19 +
107.084 x^20 + 47.2513 x^21 + 31.0995 x^22 + 23.4948 x^23 +
18.7435 x^24 + 5.60733 x^25 + 3.72775 x^26 + 0.929319 x^27 +
0.926702 x^28 + 2.77225 x^29 + 1.84293 x^30 +
0.918848 x^31)/(354 x + 1143 x^2 + 2320 x^3 + 3811 x^4 +
5441 x^5 + 6403 x^6 + 6829 x^7 + 6658 x^8 + 5571 x^9 +
4737 x^10 + 3560 x^11 + 2741 x^12 + 2174 x^13 + 1579 x^14 +
1120 x^15 + 789 x^16 + 502 x^17 + 275 x^18 + 215 x^19 +
117 x^20 + 59 x^21 + 30 x^22 + 30 x^23 + 21 x^24 + 6 x^25 +
4 x^26 + x^27 + 2 x^28 + 3 x^29 + x^30 + 2 x^31),
"cane_molasses:cumin" -> (353.073 x + 1137.02 x^2 + 2303.76 x^3 +
3769.12 x^4 + 5371.76 x^5 + 6304.4 x^6 + 6706.81 x^7 +
6518.57 x^8 + 5447.56 x^9 + 4618.84 x^10 + 3458.46 x^11 +
2655.86 x^12 + 2105.81 x^13 + 1514.39 x^14 + 1076.98 x^15 +
749.246 x^16 + 479.66 x^17 + 255.372 x^18 + 208.107 x^19 +
108.031 x^20 + 51.9764 x^21 + 24.5026 x^22 + 28.1937 x^23 +
18.7435 x^24 + 5.60733 x^25 + 2.79581 x^26 + 0.929319 x^27 +
2.7801 x^28 + 2.77225 x^29 + 1.8377 x^31)/(354 x + 1143 x^2 +
2320 x^3 + 3811 x^4 + 5441 x^5 + 6403 x^6 + 6829 x^7 +
6658 x^8 + 5571 x^9 + 4737 x^10 + 3560 x^11 + 2741 x^12 +
2174 x^13 + 1579 x^14 + 1120 x^15 + 789 x^16 + 502 x^17 +
275 x^18 + 215 x^19 + 117 x^20 + 59 x^21 + 30 x^22 + 30 x^23 +
21 x^24 + 6 x^25 + 4 x^26 + x^27 + 2 x^28 + 3 x^29 + x^30 +
2 x^31),
"lettuce:turnip" -> (353.073 x + 1137.02 x^2 + 2301.78 x^3 +
3771.09 x^4 + 5369.78 x^5 + 6302.43 x^6 + 6703.86 x^7 +
6519.54 x^8 + 5438.77 x^9 + 4612.99 x^10 + 3457.49 x^11 +
2654.9 x^12 + 2100.02 x^13 + 1521.13 x^14 + 1076.02 x^15 +
755.953 x^16 + 479.66 x^17 + 262.042 x^18 + 204.306 x^19 +
110.874 x^20 + 55.7565 x^21 + 28.2723 x^22 + 28.1937 x^23 +
19.6806 x^24 + 5.60733 x^25 + 3.72775 x^26 + 0.929319 x^27 +
1.8534 x^28 + 2.77225 x^29 + 0.921466 x^30 +
1.8377 x^31)/(354 x + 1143 x^2 + 2320 x^3 + 3811 x^4 +
5441 x^5 + 6403 x^6 + 6829 x^7 + 6658 x^8 + 5571 x^9 +
4737 x^10 + 3560 x^11 + 2741 x^12 + 2174 x^13 + 1579 x^14 +
1120 x^15 + 789 x^16 + 502 x^17 + 275 x^18 + 215 x^19 +
117 x^20 + 59 x^21 + 30 x^22 + 30 x^23 + 21 x^24 + 6 x^25 +
4 x^26 + x^27 + 2 x^28 + 3 x^29 + x^30 + 2 x^31),
"corn_grit:pork_sausage" -> (353.073 x + 1137.02 x^2 + 2302.77 x^3 +
3771.09 x^4 + 5371.76 x^5 + 6301.45 x^6 + 6701.9 x^7 +
6519.54 x^8 + 5439.75 x^9 + 4612.99 x^10 + 3457.49 x^11 +
2654.9 x^12 + 2100.98 x^13 + 1519.2 x^14 + 1076.02 x^15 +
755.953 x^16 + 479.66 x^17 + 262.042 x^18 + 204.306 x^19 +
110.874 x^20 + 55.7565 x^21 + 28.2723 x^22 + 28.1937 x^23 +
19.6806 x^24 + 5.60733 x^25 + 3.72775 x^26 + 0.929319 x^27 +
2.7801 x^28 + 1.84817 x^29 + 0.921466 x^30 +
1.8377 x^31)/(354 x + 1143 x^2 + 2320 x^3 + 3811 x^4 +
5441 x^5 + 6403 x^6 + 6829 x^7 + 6658 x^8 + 5571 x^9 +
4737 x^10 + 3560 x^11 + 2741 x^12 + 2174 x^13 + 1579 x^14 +
1120 x^15 + 789 x^16 + 502 x^17 + 275 x^18 + 215 x^19 +
117 x^20 + 59 x^21 + 30 x^22 + 30 x^23 + 21 x^24 + 6 x^25 +
4 x^26 + x^27 + 2 x^28 + 3 x^29 + x^30 + 2 x^31),
"avocado:pumpkin" -> (353.073 x + 1137.02 x^2 + 2301.78 x^3 +
3771.09 x^4 + 5369.78 x^5 + 6303.41 x^6 + 6702.88 x^7 +
6518.57 x^8 + 5440.72 x^9 + 4612.02 x^10 + 3457.49 x^11 +
2654.9 x^12 + 2100.02 x^13 + 1521.13 x^14 + 1076.02 x^15 +
755.953 x^16 + 479.66 x^17 + 262.042 x^18 + 204.306 x^19 +
110.874 x^20 + 55.7565 x^21 + 28.2723 x^22 + 28.1937 x^23 +
19.6806 x^24 + 5.60733 x^25 + 3.72775 x^26 + 0.929319 x^27 +
1.8534 x^28 + 2.77225 x^29 + 0.921466 x^30 +
1.8377 x^31)/(354 x + 1143 x^2 + 2320 x^3 + 3811 x^4 +
5441 x^5 + 6403 x^6 + 6829 x^7 + 6658 x^8 + 5571 x^9 +
4737 x^10 + 3560 x^11 + 2741 x^12 + 2174 x^13 + 1579 x^14 +
1120 x^15 + 789 x^16 + 502 x^17 + 275 x^18 + 215 x^19 +
117 x^20 + 59 x^21 + 30 x^22 + 30 x^23 + 21 x^24 + 6 x^25 +
4 x^26 + x^27 + 2 x^28 + 3 x^29 + x^30 + 2 x^31),
"chive:mandarin_peel" -> (353.073 x + 1137.02 x^2 + 2301.78 x^3 +
3771.09 x^4 + 5369.78 x^5 + 6302.43 x^6 + 6704.84 x^7 +
6517.59 x^8 + 5439.75 x^9 + 4612.99 x^10 + 3457.49 x^11 +
2654.9 x^12 + 2100.02 x^13 + 1521.13 x^14 + 1076.02 x^15 +
755.953 x^16 + 479.66 x^17 + 262.042 x^18 + 204.306 x^19 +
110.874 x^20 + 55.7565 x^21 + 28.2723 x^22 + 28.1937 x^23 +
19.6806 x^24 + 5.60733 x^25 + 3.72775 x^26 + 0.929319 x^27 +
1.8534 x^28 + 2.77225 x^29 + 0.921466 x^30 +
1.8377 x^31)/(354 x + 1143 x^2 + 2320 x^3 + 3811 x^4 +
5441 x^5 + 6403 x^6 + 6829 x^7 + 6658 x^8 + 5571 x^9 +
4737 x^10 + 3560 x^11 + 2741 x^12 + 2174 x^13 + 1579 x^14 +
1120 x^15 + 789 x^16 + 502 x^17 + 275 x^18 + 215 x^19 +
117 x^20 + 59 x^21 + 30 x^22 + 30 x^23 + 21 x^24 + 6 x^25 +
4 x^26 + x^27 + 2 x^28 + 3 x^29 + x^30 + 2 x^31),
"anise_seed:coconut" -> (353.073 x + 1137.02 x^2 + 2301.78 x^3 +
3771.09 x^4 + 5369.78 x^5 + 6302.43 x^6 + 6703.86 x^7 +
6518.57 x^8 + 5439.75 x^9 + 4612.99 x^10 + 3457.49 x^11 +
2654.9 x^12 + 2100.98 x^13 + 1521.13 x^14 + 1075.06 x^15 +
755.953 x^16 + 479.66 x^17 + 262.042 x^18 + 204.306 x^19 +
110.874 x^20 + 55.7565 x^21 + 28.2723 x^22 + 28.1937 x^23 +
19.6806 x^24 + 5.60733 x^25 + 3.72775 x^26 + 0.929319 x^27 +
1.8534 x^28 + 2.77225 x^29 + 0.921466 x^30 +
1.8377 x^31)/(354 x + 1143 x^2 + 2320 x^3 + 3811 x^4 +
5441 x^5 + 6403 x^6 + 6829 x^7 + 6658 x^8 + 5571 x^9 +
4737 x^10 + 3560 x^11 + 2741 x^12 + 2174 x^13 + 1579 x^14 +
1120 x^15 + 789 x^16 + 502 x^17 + 275 x^18 + 215 x^19 +
117 x^20 + 59 x^21 + 30 x^22 + 30 x^23 + 21 x^24 + 6 x^25 +
4 x^26 + x^27 + 2 x^28 + 3 x^29 + x^30 + 2 x^31)|>
which contains rational functions. I want to select the ones that have y value above 1 for a specific range of x, so I do:
Select[f, MaxValue[#, 2/382 <= x <= 1, x] > 1 &] // AbsoluteTiming
in this case none of them are, so I get:
1.80393, <
The point is that my original list contains 30000 of these polynomials and the command I have for selection is taking a lot of time. For 10 of them as above it took 1.8 seconds. I wonder how can I break this time down without losing the dictionary, namely what key is related to what polynomial?
I know if I only look at values the time would be reduced, but then I will not know the output would belong to which key from the association.
list-manipulation filtering maximum
list-manipulation filtering maximum
edited Jul 17 at 17:18
Carl Woll
88.3k3 gold badges117 silver badges227 bronze badges
asked Jul 17 at 15:26
WilliamWilliam
1,0156 silver badges8 bronze badges
edited Jul 17 at 17:18
Carl Woll
88.3k3 gold badges117 silver badges227 bronze badges
asked Jul 17 at 15:26
WilliamWilliam
1,0156 silver badges8 bronze badges
edited Jul 17 at 17:18
Carl Woll
88.3k3 gold badges117 silver badges227 bronze badges
edited Jul 17 at 17:18
Carl Woll
88.3k3 gold badges117 silver badges227 bronze badges
edited Jul 17 at 17:18
Carl Woll
88.3k3 gold badges117 silver badges227 bronze badges
88.3k3 gold badges117 silver badges227 bronze badges
asked Jul 17 at 15:26
WilliamWilliam
1,0156 silver badges8 bronze badges
asked Jul 17 at 15:26
WilliamWilliam
1,0156 silver badges8 bronze badges
asked Jul 17 at 15:26
WilliamWilliam
1,0156 silver badges8 bronze badges
1,0156 silver badges8 bronze badges
1
$begingroup$
If you have 8 cores, and useParallelTable, that would take less than 12 minutes. Is that too long?
$endgroup$
– rhermans
Jul 17 at 16:14
$begingroup$
I have 4 so presume it will take 24', is there any way to chunk the code down into easier-to-handle part?
$endgroup$
– William
Jul 17 at 16:23
$begingroup$
For all of the polynomials you give, the maximum lies at the lower edge of your search interval. Maybe there's something generalizable here: maybe it's possible to exclude a large number of polynomials by just looking at the values (and derivatives) at the end points.
$endgroup$
– Roman
Jul 17 at 18:15
add a comment |
1
$begingroup$
If you have 8 cores, and useParallelTable, that would take less than 12 minutes. Is that too long?
$endgroup$
– rhermans
Jul 17 at 16:14
$begingroup$
I have 4 so presume it will take 24', is there any way to chunk the code down into easier-to-handle part?
$endgroup$
– William
Jul 17 at 16:23
$begingroup$
For all of the polynomials you give, the maximum lies at the lower edge of your search interval. Maybe there's something generalizable here: maybe it's possible to exclude a large number of polynomials by just looking at the values (and derivatives) at the end points.
$endgroup$
– Roman
Jul 17 at 18:15
1
1
$begingroup$
If you have 8 cores, and use
ParallelTable, that would take less than 12 minutes. Is that too long?$endgroup$
– rhermans
Jul 17 at 16:14
$begingroup$
If you have 8 cores, and use
ParallelTable, that would take less than 12 minutes. Is that too long?$endgroup$
– rhermans
Jul 17 at 16:14
$begingroup$
I have 4 so presume it will take 24', is there any way to chunk the code down into easier-to-handle part?
$endgroup$
– William
Jul 17 at 16:23
$begingroup$
I have 4 so presume it will take 24', is there any way to chunk the code down into easier-to-handle part?
$endgroup$
– William
Jul 17 at 16:23
$begingroup$
For all of the polynomials you give, the maximum lies at the lower edge of your search interval. Maybe there's something generalizable here: maybe it's possible to exclude a large number of polynomials by just looking at the values (and derivatives) at the end points.
$endgroup$
– Roman
Jul 17 at 18:15
$begingroup$
For all of the polynomials you give, the maximum lies at the lower edge of your search interval. Maybe there's something generalizable here: maybe it's possible to exclude a large number of polynomials by just looking at the values (and derivatives) at the end points.
$endgroup$
– Roman
Jul 17 at 18:15
add a comment |
3 Answers
3
active
oldest
votes
4
$begingroup$
This would take less than 25 minutes with 4 cores.
LaunchKernels[];
maxlist = ParallelTable[
MaxValue[eq, 2/382 <= x <= 1, x]
, eq, List @@ f
];
Pick[
Keys[f],
Thread[Greater[maxlist, 1]]
]
My take on the answer by Carl Woll, which should bring you below 6 minutes.
trueFalseList = ParallelTable[
UnsameQ[
False,
Quiet[
Reduce[eq > 1 && 2/382 <= x <= 1, x]
, Reduce::ratnz]
], eq, List @@ f]
Pick[
Keys[f],
trueFalseList
]
answered Jul 17 at 16:33
rhermansrhermans
23.5k4 gold badges42 silver badges110 bronze badges
$endgroup$
$begingroup$
The second method is fabulously fast, thank you and Carl Woll.
$endgroup$
– William
Jul 18 at 11:14
add a comment |
6
$begingroup$
Maybe you can use Reduce instead of MaxValue. For instance, the "vanilla:veal" rational function is:
p = (353.073 x + 1137.02 x^2 + 2301.78 x^3 +
3771.09 x^4 + 5369.78 x^5 + 6302.43 x^6 + 6703.86 x^7 +
6518.57 x^8 + 5440.72 x^9 + 4612.02 x^10 + 3457.49 x^11 +
2654.9 x^12 + 2100.02 x^13 + 1521.13 x^14 + 1076.02 x^15 +
755.953 x^16 + 480.615 x^17 + 261.089 x^18 + 204.306 x^19 +
110.874 x^20 + 55.7565 x^21 + 28.2723 x^22 + 28.1937 x^23 +
19.6806 x^24 + 5.60733 x^25 + 3.72775 x^26 + 0.929319 x^27 +
1.8534 x^28 + 2.77225 x^29 + 0.921466 x^30 +
1.8377 x^31)/(354 x + 1143 x^2 + 2320 x^3 + 3811 x^4 +
5441 x^5 + 6403 x^6 + 6829 x^7 + 6658 x^8 + 5571 x^9 +
4737 x^10 + 3560 x^11 + 2741 x^12 + 2174 x^13 + 1579 x^14 +
1120 x^15 + 789 x^16 + 502 x^17 + 275 x^18 + 215 x^19 +
117 x^20 + 59 x^21 + 30 x^22 + 30 x^23 + 21 x^24 + 6 x^25 +
4 x^26 + x^27 + 2 x^28 + 3 x^29 + x^30 + 2 x^31)
Compare:
MaxValue[p, 2/382 <= x <= 1, x] //AbsoluteTiming
Quiet[Reduce[p > 1 && 2/382 <= x <= 1, x], Reduce::ratnz] //AbsoluteTiming
0.133098, 0.976077
0.041712, False
Another example where the result isn't false:
MaxValue[p+.5, 2/382 <= x <= 1, x] //AbsoluteTiming
Quiet[Reduce[p+.5 > 1 && 2/382 <= x <= 1, x], Reduce::ratnz] //AbsoluteTiming
0.128614, 1.47608
0.041923, 0.0390256 < x <= 1.
So, using Reduce is about 3 times faster. Combine it with a ParallelTable approach as in @rherman's answer.
answered Jul 17 at 17:03
Carl WollCarl Woll
88.3k3 gold badges117 silver badges227 bronze badges
$endgroup$
add a comment |
5
$begingroup$
The following is not the exact filter that you want, but a simple prefilter that apparently is quite good at filtering the given example ;) The point is that this check is much cheaper than computing the maxima, so it can be used to filter out (hopefully) many rational functions from your list f, so that filtering the resulting list becomes less expensive.
Here is the code:
a = 2./382;
b = 1.;
picker =
ParallelMap[
With[x = a + (b - a) z/(1 + z),
With[p = Together[#],
Min[CoefficientList[Denominator[r] - Numerator[r], z]] < 0.
]
] &,
Values[f]
]; // AbsoluteTiming // First
fpresieved = Pick[f, picker]
0.04817
<||>
Here is the idea behind the method.
Let $r(x)$ be a rational function from your list f.
First, we apply the substitution x = a + (b - a) z/(1 + z); The mapping $z mapsto x$ maps the $[0,infty]$ to the interval $[a,b]$.
Thus, $r = fracpq$ is a rational function on the positive real axis for which we want to check whether
$$r(x) = fracp(z)q(z) leq 1 quad textfor all $z geq 0$.$$
This is equivalent to
$$q(z) - p(z) geq 0 quad textfor all $z geq 0$.$$
A sufficient condition for this is that all coefficients of the polynomial $q(z) - p(z)$ are nonnegative. So a necessary condition for r(x) to be selected is that at least one coefficient of $q(z) - p(z)$ is negative. And precisely that is checked for in the code above.
answered Jul 17 at 18:33
Henrik SchumacherHenrik Schumacher
65.8k5 gold badges94 silver badges182 bronze badges
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4
$begingroup$
This would take less than 25 minutes with 4 cores.
LaunchKernels[];
maxlist = ParallelTable[
MaxValue[eq, 2/382 <= x <= 1, x]
, eq, List @@ f
];
Pick[
Keys[f],
Thread[Greater[maxlist, 1]]
]
My take on the answer by Carl Woll, which should bring you below 6 minutes.
trueFalseList = ParallelTable[
UnsameQ[
False,
Quiet[
Reduce[eq > 1 && 2/382 <= x <= 1, x]
, Reduce::ratnz]
], eq, List @@ f]
Pick[
Keys[f],
trueFalseList
]
answered Jul 17 at 16:33
rhermansrhermans
23.5k4 gold badges42 silver badges110 bronze badges
$endgroup$
$begingroup$
The second method is fabulously fast, thank you and Carl Woll.
$endgroup$
– William
Jul 18 at 11:14
add a comment |
4
$begingroup$
This would take less than 25 minutes with 4 cores.
LaunchKernels[];
maxlist = ParallelTable[
MaxValue[eq, 2/382 <= x <= 1, x]
, eq, List @@ f
];
Pick[
Keys[f],
Thread[Greater[maxlist, 1]]
]
My take on the answer by Carl Woll, which should bring you below 6 minutes.
trueFalseList = ParallelTable[
UnsameQ[
False,
Quiet[
Reduce[eq > 1 && 2/382 <= x <= 1, x]
, Reduce::ratnz]
], eq, List @@ f]
Pick[
Keys[f],
trueFalseList
]
answered Jul 17 at 16:33
rhermansrhermans
23.5k4 gold badges42 silver badges110 bronze badges
$endgroup$
$begingroup$
The second method is fabulously fast, thank you and Carl Woll.
$endgroup$
– William
Jul 18 at 11:14
add a comment |
4
4
4
$begingroup$
This would take less than 25 minutes with 4 cores.
LaunchKernels[];
maxlist = ParallelTable[
MaxValue[eq, 2/382 <= x <= 1, x]
, eq, List @@ f
];
Pick[
Keys[f],
Thread[Greater[maxlist, 1]]
]
My take on the answer by Carl Woll, which should bring you below 6 minutes.
trueFalseList = ParallelTable[
UnsameQ[
False,
Quiet[
Reduce[eq > 1 && 2/382 <= x <= 1, x]
, Reduce::ratnz]
], eq, List @@ f]
Pick[
Keys[f],
trueFalseList
]
answered Jul 17 at 16:33
rhermansrhermans
23.5k4 gold badges42 silver badges110 bronze badges
$endgroup$
This would take less than 25 minutes with 4 cores.
LaunchKernels[];
maxlist = ParallelTable[
MaxValue[eq, 2/382 <= x <= 1, x]
, eq, List @@ f
];
Pick[
Keys[f],
Thread[Greater[maxlist, 1]]
]
My take on the answer by Carl Woll, which should bring you below 6 minutes.
trueFalseList = ParallelTable[
UnsameQ[
False,
Quiet[
Reduce[eq > 1 && 2/382 <= x <= 1, x]
, Reduce::ratnz]
], eq, List @@ f]
Pick[
Keys[f],
trueFalseList
]
answered Jul 17 at 16:33
rhermansrhermans
23.5k4 gold badges42 silver badges110 bronze badges
edited Jul 17 at 17:52
answered Jul 17 at 16:33
rhermansrhermans
23.5k4 gold badges42 silver badges110 bronze badges
answered Jul 17 at 16:33
rhermansrhermans
23.5k4 gold badges42 silver badges110 bronze badges
answered Jul 17 at 16:33
rhermansrhermans
23.5k4 gold badges42 silver badges110 bronze badges
23.5k4 gold badges42 silver badges110 bronze badges
$begingroup$
The second method is fabulously fast, thank you and Carl Woll.
$endgroup$
– William
Jul 18 at 11:14
add a comment |
$begingroup$
The second method is fabulously fast, thank you and Carl Woll.
$endgroup$
– William
Jul 18 at 11:14
$begingroup$
The second method is fabulously fast, thank you and Carl Woll.
$endgroup$
– William
Jul 18 at 11:14
$begingroup$
The second method is fabulously fast, thank you and Carl Woll.
$endgroup$
– William
Jul 18 at 11:14
add a comment |
6
$begingroup$
Maybe you can use Reduce instead of MaxValue. For instance, the "vanilla:veal" rational function is:
p = (353.073 x + 1137.02 x^2 + 2301.78 x^3 +
3771.09 x^4 + 5369.78 x^5 + 6302.43 x^6 + 6703.86 x^7 +
6518.57 x^8 + 5440.72 x^9 + 4612.02 x^10 + 3457.49 x^11 +
2654.9 x^12 + 2100.02 x^13 + 1521.13 x^14 + 1076.02 x^15 +
755.953 x^16 + 480.615 x^17 + 261.089 x^18 + 204.306 x^19 +
110.874 x^20 + 55.7565 x^21 + 28.2723 x^22 + 28.1937 x^23 +
19.6806 x^24 + 5.60733 x^25 + 3.72775 x^26 + 0.929319 x^27 +
1.8534 x^28 + 2.77225 x^29 + 0.921466 x^30 +
1.8377 x^31)/(354 x + 1143 x^2 + 2320 x^3 + 3811 x^4 +
5441 x^5 + 6403 x^6 + 6829 x^7 + 6658 x^8 + 5571 x^9 +
4737 x^10 + 3560 x^11 + 2741 x^12 + 2174 x^13 + 1579 x^14 +
1120 x^15 + 789 x^16 + 502 x^17 + 275 x^18 + 215 x^19 +
117 x^20 + 59 x^21 + 30 x^22 + 30 x^23 + 21 x^24 + 6 x^25 +
4 x^26 + x^27 + 2 x^28 + 3 x^29 + x^30 + 2 x^31)
Compare:
MaxValue[p, 2/382 <= x <= 1, x] //AbsoluteTiming
Quiet[Reduce[p > 1 && 2/382 <= x <= 1, x], Reduce::ratnz] //AbsoluteTiming
0.133098, 0.976077
0.041712, False
Another example where the result isn't false:
MaxValue[p+.5, 2/382 <= x <= 1, x] //AbsoluteTiming
Quiet[Reduce[p+.5 > 1 && 2/382 <= x <= 1, x], Reduce::ratnz] //AbsoluteTiming
0.128614, 1.47608
0.041923, 0.0390256 < x <= 1.
So, using Reduce is about 3 times faster. Combine it with a ParallelTable approach as in @rherman's answer.
answered Jul 17 at 17:03
Carl WollCarl Woll
88.3k3 gold badges117 silver badges227 bronze badges
$endgroup$
add a comment |
6
$begingroup$
Maybe you can use Reduce instead of MaxValue. For instance, the "vanilla:veal" rational function is:
p = (353.073 x + 1137.02 x^2 + 2301.78 x^3 +
3771.09 x^4 + 5369.78 x^5 + 6302.43 x^6 + 6703.86 x^7 +
6518.57 x^8 + 5440.72 x^9 + 4612.02 x^10 + 3457.49 x^11 +
2654.9 x^12 + 2100.02 x^13 + 1521.13 x^14 + 1076.02 x^15 +
755.953 x^16 + 480.615 x^17 + 261.089 x^18 + 204.306 x^19 +
110.874 x^20 + 55.7565 x^21 + 28.2723 x^22 + 28.1937 x^23 +
19.6806 x^24 + 5.60733 x^25 + 3.72775 x^26 + 0.929319 x^27 +
1.8534 x^28 + 2.77225 x^29 + 0.921466 x^30 +
1.8377 x^31)/(354 x + 1143 x^2 + 2320 x^3 + 3811 x^4 +
5441 x^5 + 6403 x^6 + 6829 x^7 + 6658 x^8 + 5571 x^9 +
4737 x^10 + 3560 x^11 + 2741 x^12 + 2174 x^13 + 1579 x^14 +
1120 x^15 + 789 x^16 + 502 x^17 + 275 x^18 + 215 x^19 +
117 x^20 + 59 x^21 + 30 x^22 + 30 x^23 + 21 x^24 + 6 x^25 +
4 x^26 + x^27 + 2 x^28 + 3 x^29 + x^30 + 2 x^31)
Compare:
MaxValue[p, 2/382 <= x <= 1, x] //AbsoluteTiming
Quiet[Reduce[p > 1 && 2/382 <= x <= 1, x], Reduce::ratnz] //AbsoluteTiming
0.133098, 0.976077
0.041712, False
Another example where the result isn't false:
MaxValue[p+.5, 2/382 <= x <= 1, x] //AbsoluteTiming
Quiet[Reduce[p+.5 > 1 && 2/382 <= x <= 1, x], Reduce::ratnz] //AbsoluteTiming
0.128614, 1.47608
0.041923, 0.0390256 < x <= 1.
So, using Reduce is about 3 times faster. Combine it with a ParallelTable approach as in @rherman's answer.
answered Jul 17 at 17:03
Carl WollCarl Woll
88.3k3 gold badges117 silver badges227 bronze badges
$endgroup$
add a comment |
6
6
6
$begingroup$
Maybe you can use Reduce instead of MaxValue. For instance, the "vanilla:veal" rational function is:
p = (353.073 x + 1137.02 x^2 + 2301.78 x^3 +
3771.09 x^4 + 5369.78 x^5 + 6302.43 x^6 + 6703.86 x^7 +
6518.57 x^8 + 5440.72 x^9 + 4612.02 x^10 + 3457.49 x^11 +
2654.9 x^12 + 2100.02 x^13 + 1521.13 x^14 + 1076.02 x^15 +
755.953 x^16 + 480.615 x^17 + 261.089 x^18 + 204.306 x^19 +
110.874 x^20 + 55.7565 x^21 + 28.2723 x^22 + 28.1937 x^23 +
19.6806 x^24 + 5.60733 x^25 + 3.72775 x^26 + 0.929319 x^27 +
1.8534 x^28 + 2.77225 x^29 + 0.921466 x^30 +
1.8377 x^31)/(354 x + 1143 x^2 + 2320 x^3 + 3811 x^4 +
5441 x^5 + 6403 x^6 + 6829 x^7 + 6658 x^8 + 5571 x^9 +
4737 x^10 + 3560 x^11 + 2741 x^12 + 2174 x^13 + 1579 x^14 +
1120 x^15 + 789 x^16 + 502 x^17 + 275 x^18 + 215 x^19 +
117 x^20 + 59 x^21 + 30 x^22 + 30 x^23 + 21 x^24 + 6 x^25 +
4 x^26 + x^27 + 2 x^28 + 3 x^29 + x^30 + 2 x^31)
Compare:
MaxValue[p, 2/382 <= x <= 1, x] //AbsoluteTiming
Quiet[Reduce[p > 1 && 2/382 <= x <= 1, x], Reduce::ratnz] //AbsoluteTiming
0.133098, 0.976077
0.041712, False
Another example where the result isn't false:
MaxValue[p+.5, 2/382 <= x <= 1, x] //AbsoluteTiming
Quiet[Reduce[p+.5 > 1 && 2/382 <= x <= 1, x], Reduce::ratnz] //AbsoluteTiming
0.128614, 1.47608
0.041923, 0.0390256 < x <= 1.
So, using Reduce is about 3 times faster. Combine it with a ParallelTable approach as in @rherman's answer.
answered Jul 17 at 17:03
Carl WollCarl Woll
88.3k3 gold badges117 silver badges227 bronze badges
$endgroup$
Maybe you can use Reduce instead of MaxValue. For instance, the "vanilla:veal" rational function is:
p = (353.073 x + 1137.02 x^2 + 2301.78 x^3 +
3771.09 x^4 + 5369.78 x^5 + 6302.43 x^6 + 6703.86 x^7 +
6518.57 x^8 + 5440.72 x^9 + 4612.02 x^10 + 3457.49 x^11 +
2654.9 x^12 + 2100.02 x^13 + 1521.13 x^14 + 1076.02 x^15 +
755.953 x^16 + 480.615 x^17 + 261.089 x^18 + 204.306 x^19 +
110.874 x^20 + 55.7565 x^21 + 28.2723 x^22 + 28.1937 x^23 +
19.6806 x^24 + 5.60733 x^25 + 3.72775 x^26 + 0.929319 x^27 +
1.8534 x^28 + 2.77225 x^29 + 0.921466 x^30 +
1.8377 x^31)/(354 x + 1143 x^2 + 2320 x^3 + 3811 x^4 +
5441 x^5 + 6403 x^6 + 6829 x^7 + 6658 x^8 + 5571 x^9 +
4737 x^10 + 3560 x^11 + 2741 x^12 + 2174 x^13 + 1579 x^14 +
1120 x^15 + 789 x^16 + 502 x^17 + 275 x^18 + 215 x^19 +
117 x^20 + 59 x^21 + 30 x^22 + 30 x^23 + 21 x^24 + 6 x^25 +
4 x^26 + x^27 + 2 x^28 + 3 x^29 + x^30 + 2 x^31)
Compare:
MaxValue[p, 2/382 <= x <= 1, x] //AbsoluteTiming
Quiet[Reduce[p > 1 && 2/382 <= x <= 1, x], Reduce::ratnz] //AbsoluteTiming
0.133098, 0.976077
0.041712, False
Another example where the result isn't false:
MaxValue[p+.5, 2/382 <= x <= 1, x] //AbsoluteTiming
Quiet[Reduce[p+.5 > 1 && 2/382 <= x <= 1, x], Reduce::ratnz] //AbsoluteTiming
0.128614, 1.47608
0.041923, 0.0390256 < x <= 1.
So, using Reduce is about 3 times faster. Combine it with a ParallelTable approach as in @rherman's answer.
answered Jul 17 at 17:03
Carl WollCarl Woll
88.3k3 gold badges117 silver badges227 bronze badges
answered Jul 17 at 17:03
Carl WollCarl Woll
88.3k3 gold badges117 silver badges227 bronze badges
answered Jul 17 at 17:03
Carl WollCarl Woll
88.3k3 gold badges117 silver badges227 bronze badges
answered Jul 17 at 17:03
Carl WollCarl Woll
88.3k3 gold badges117 silver badges227 bronze badges
88.3k3 gold badges117 silver badges227 bronze badges
add a comment |
add a comment |
5
$begingroup$
The following is not the exact filter that you want, but a simple prefilter that apparently is quite good at filtering the given example ;) The point is that this check is much cheaper than computing the maxima, so it can be used to filter out (hopefully) many rational functions from your list f, so that filtering the resulting list becomes less expensive.
Here is the code:
a = 2./382;
b = 1.;
picker =
ParallelMap[
With[x = a + (b - a) z/(1 + z),
With[p = Together[#],
Min[CoefficientList[Denominator[r] - Numerator[r], z]] < 0.
]
] &,
Values[f]
]; // AbsoluteTiming // First
fpresieved = Pick[f, picker]
0.04817
<||>
Here is the idea behind the method.
Let $r(x)$ be a rational function from your list f.
First, we apply the substitution x = a + (b - a) z/(1 + z); The mapping $z mapsto x$ maps the $[0,infty]$ to the interval $[a,b]$.
Thus, $r = fracpq$ is a rational function on the positive real axis for which we want to check whether
$$r(x) = fracp(z)q(z) leq 1 quad textfor all $z geq 0$.$$
This is equivalent to
$$q(z) - p(z) geq 0 quad textfor all $z geq 0$.$$
A sufficient condition for this is that all coefficients of the polynomial $q(z) - p(z)$ are nonnegative. So a necessary condition for r(x) to be selected is that at least one coefficient of $q(z) - p(z)$ is negative. And precisely that is checked for in the code above.
answered Jul 17 at 18:33
Henrik SchumacherHenrik Schumacher
65.8k5 gold badges94 silver badges182 bronze badges
$endgroup$
add a comment |
5
$begingroup$
The following is not the exact filter that you want, but a simple prefilter that apparently is quite good at filtering the given example ;) The point is that this check is much cheaper than computing the maxima, so it can be used to filter out (hopefully) many rational functions from your list f, so that filtering the resulting list becomes less expensive.
Here is the code:
a = 2./382;
b = 1.;
picker =
ParallelMap[
With[x = a + (b - a) z/(1 + z),
With[p = Together[#],
Min[CoefficientList[Denominator[r] - Numerator[r], z]] < 0.
]
] &,
Values[f]
]; // AbsoluteTiming // First
fpresieved = Pick[f, picker]
0.04817
<||>
Here is the idea behind the method.
Let $r(x)$ be a rational function from your list f.
First, we apply the substitution x = a + (b - a) z/(1 + z); The mapping $z mapsto x$ maps the $[0,infty]$ to the interval $[a,b]$.
Thus, $r = fracpq$ is a rational function on the positive real axis for which we want to check whether
$$r(x) = fracp(z)q(z) leq 1 quad textfor all $z geq 0$.$$
This is equivalent to
$$q(z) - p(z) geq 0 quad textfor all $z geq 0$.$$
A sufficient condition for this is that all coefficients of the polynomial $q(z) - p(z)$ are nonnegative. So a necessary condition for r(x) to be selected is that at least one coefficient of $q(z) - p(z)$ is negative. And precisely that is checked for in the code above.
answered Jul 17 at 18:33
Henrik SchumacherHenrik Schumacher
65.8k5 gold badges94 silver badges182 bronze badges
$endgroup$
add a comment |
5
5
5
$begingroup$
The following is not the exact filter that you want, but a simple prefilter that apparently is quite good at filtering the given example ;) The point is that this check is much cheaper than computing the maxima, so it can be used to filter out (hopefully) many rational functions from your list f, so that filtering the resulting list becomes less expensive.
Here is the code:
a = 2./382;
b = 1.;
picker =
ParallelMap[
With[x = a + (b - a) z/(1 + z),
With[p = Together[#],
Min[CoefficientList[Denominator[r] - Numerator[r], z]] < 0.
]
] &,
Values[f]
]; // AbsoluteTiming // First
fpresieved = Pick[f, picker]
0.04817
<||>
Here is the idea behind the method.
Let $r(x)$ be a rational function from your list f.
First, we apply the substitution x = a + (b - a) z/(1 + z); The mapping $z mapsto x$ maps the $[0,infty]$ to the interval $[a,b]$.
Thus, $r = fracpq$ is a rational function on the positive real axis for which we want to check whether
$$r(x) = fracp(z)q(z) leq 1 quad textfor all $z geq 0$.$$
This is equivalent to
$$q(z) - p(z) geq 0 quad textfor all $z geq 0$.$$
A sufficient condition for this is that all coefficients of the polynomial $q(z) - p(z)$ are nonnegative. So a necessary condition for r(x) to be selected is that at least one coefficient of $q(z) - p(z)$ is negative. And precisely that is checked for in the code above.
answered Jul 17 at 18:33
Henrik SchumacherHenrik Schumacher
65.8k5 gold badges94 silver badges182 bronze badges
$endgroup$
The following is not the exact filter that you want, but a simple prefilter that apparently is quite good at filtering the given example ;) The point is that this check is much cheaper than computing the maxima, so it can be used to filter out (hopefully) many rational functions from your list f, so that filtering the resulting list becomes less expensive.
Here is the code:
a = 2./382;
b = 1.;
picker =
ParallelMap[
With[x = a + (b - a) z/(1 + z),
With[p = Together[#],
Min[CoefficientList[Denominator[r] - Numerator[r], z]] < 0.
]
] &,
Values[f]
]; // AbsoluteTiming // First
fpresieved = Pick[f, picker]
0.04817
<||>
Here is the idea behind the method.
Let $r(x)$ be a rational function from your list f.
First, we apply the substitution x = a + (b - a) z/(1 + z); The mapping $z mapsto x$ maps the $[0,infty]$ to the interval $[a,b]$.
Thus, $r = fracpq$ is a rational function on the positive real axis for which we want to check whether
$$r(x) = fracp(z)q(z) leq 1 quad textfor all $z geq 0$.$$
This is equivalent to
$$q(z) - p(z) geq 0 quad textfor all $z geq 0$.$$
A sufficient condition for this is that all coefficients of the polynomial $q(z) - p(z)$ are nonnegative. So a necessary condition for r(x) to be selected is that at least one coefficient of $q(z) - p(z)$ is negative. And precisely that is checked for in the code above.
answered Jul 17 at 18:33
Henrik SchumacherHenrik Schumacher
65.8k5 gold badges94 silver badges182 bronze badges
answered Jul 17 at 18:33
Henrik SchumacherHenrik Schumacher
65.8k5 gold badges94 silver badges182 bronze badges
answered Jul 17 at 18:33
Henrik SchumacherHenrik Schumacher
65.8k5 gold badges94 silver badges182 bronze badges
answered Jul 17 at 18:33
Henrik SchumacherHenrik Schumacher
65.8k5 gold badges94 silver badges182 bronze badges
65.8k5 gold badges94 silver badges182 bronze badges
add a comment |
add a comment |
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1
$begingroup$
If you have 8 cores, and use
ParallelTable, that would take less than 12 minutes. Is that too long?$endgroup$
– rhermans
Jul 17 at 16:14
$begingroup$
I have 4 so presume it will take 24', is there any way to chunk the code down into easier-to-handle part?
$endgroup$
– William
Jul 17 at 16:23
$begingroup$
For all of the polynomials you give, the maximum lies at the lower edge of your search interval. Maybe there's something generalizable here: maybe it's possible to exclude a large number of polynomials by just looking at the values (and derivatives) at the end points.
$endgroup$
– Roman
Jul 17 at 18:15