FindMinimum does not free memory
- To: mathgroup at smc.vnet.net
- Subject: [mg128119] FindMinimum does not free memory
- From: dgolber at aol.com
- Date: Mon, 17 Sep 2012 00:21:48 -0400 (EDT)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
- Delivered-to: l-mathgroup@wolfram.com
- Delivered-to: mathgroup-newout@smc.vnet.net
- Delivered-to: mathgroup-newsend@smc.vnet.net
Mathematica 4 running on Windows XP.
The notebook below fits a 2-parameter curve (a simple Bezier curve) to some data.
The module "error" finds the total sum-of-squares of distances from the data points to a curve. The main cell (not a module) uses FindMinimum to vary the curve parameters to minimize the error.
The "error" module prints MemoryInUse each time it is entered.
The main cell is run twice (two completely distinct copies). The first time it is run, we see MemoryInUse building up from about one MB to 25 MB, as (I assume) FindMinimum builds up its search context.
The second time it is called, MemoryInUse starts aleady at 25 MB! In other words, even though the (first) use of FindMinimum is completely over, the memory it used is still shown in MemoryInUse.
What is going on?
Thank you
David Golber
===========
In[1]:=
dsq[p_, q_] := Module[{v}, v = p - q; Return[v.v]];
In[2]:=
data = {{-1.`, 0.07271879311326668`}, {-0.9795918367346939`,
0.40795711960412273`}, {-0.9591836734693877`,
0.7493968681691019`}, {-0.9387755102040817`,
1.0969831944328101`}, {-0.9183673469387755`,
1.4455797049857155`}, {-0.8979591836734694`,
1.7933577858764531`}, {-0.8775510204081632`,
2.1407781653548907`}, {-0.8571428571428571`,
2.4892086871775314`}, {-0.8367346938775511`,
2.835059096420477`}, {-0.8163265306122449`,
3.1747813234745452`}, {-0.7959183673469388`,
3.5099065199869566`}, {-0.7755102040816326`,
3.838416824535938`}, {-0.7551020408163265`,
4.160416099694797`}, {-0.7346938775510204`,
4.476709556785695`}, {-0.7142857142857143`,
4.784664350286133`}, {-0.6938775510204082`,
5.087323728777496`}, {-0.673469387755102`,
5.38696253472903`}, {-0.6530612244897959`,
5.6798465046806585`}, {-0.6326530612244898`,
5.964713365415807`}, {-0.6122448979591837`,
6.238632239548857`}, {-0.5918367346938775`,
6.501620953518743`}, {-0.5714285714285714`,
6.75656172280596`}, {-0.5510204081632653`,
7.002600506634537`}, {-0.5306122448979592`,
7.239968897142224`}, {-0.5102040816326531`,
7.467505798949419`}, {-0.4897959183673469`,
7.688899842449843`}, {-0.46938775510204084`,
7.895548159341792`}, {-0.4489795918367347`,
8.097377347460679`}, {-0.42857142857142855`,
8.2893341746341`}, {-0.40816326530612246`,
8.476144299078989`}, {-0.3877551020408163`,
8.652889973777224`}, {-0.3673469387755102`,
8.817374903757845`}, {-0.3469387755102041`,
8.976924242334949`}, {-0.32653061224489793`,
9.119591134252524`}, {-0.30612244897959184`,
9.248576791309134`}, {-0.2857142857142857`,
9.369588023769005`}, {-0.2653061224489796`,
9.482297547178607`}, {-0.24489795918367346`,
9.589139190122037`}, {-0.22448979591836735`,
9.689364983113595`}, {-0.20408163265306123`,
9.781452292825708`}, {-0.1836734693877551`,
9.860153881813591`}, {-0.16326530612244897`,
9.923011791745626`}, {-0.14285714285714285`,
9.976018300997982`}, {-0.12244897959183673`,
10.02452888876957`}, {-0.10204081632653061`,
10.070756998999077`}, {-0.08163265306122448`,
10.114970754465642`}, {-0.061224489795918366`,
10.15451548515944`}, {-0.04081632653061224`,
10.18522338591307`}, {-0.02040816326530612`,
10.202365464896314`}, {0.`,
10.208468465393292`}, {0.02040816326530612`,
10.202365464896314`}, {0.04081632653061224`,
10.18522338591307`}, {0.061224489795918366`,
10.15451548515944`}, {0.08163265306122448`,
10.114970754465642`}, {0.10204081632653061`,
10.070756998999077`}, {0.12244897959183673`,
10.02452888876957`}, {0.14285714285714285`,
9.976018300997982`}, {0.16326530612244897`,
9.923011791745626`}, {0.1836734693877551`,
9.860153881813591`}, {0.20408163265306123`,
9.781452292825708`}, {0.22448979591836735`,
9.689364983113595`}, {0.24489795918367346`,
9.589139190122037`}, {0.2653061224489796`,
9.482297547178607`}, {0.2857142857142857`,
9.369588023769005`}, {0.30612244897959184`,
9.248576791309134`}, {0.32653061224489793`,
9.119591134252524`}, {0.3469387755102041`,
8.976924242334949`}, {0.3673469387755102`,
8.817374903757845`}, {0.3877551020408163`,
8.652889973777224`}, {0.40816326530612246`,
8.476144299078989`}, {0.42857142857142855`,
8.2893341746341`}, {0.4489795918367347`,
8.097377347460679`}, {0.46938775510204084`,
7.895548159341792`}, {0.4897959183673469`,
7.688899842449843`}, {0.5102040816326531`,
7.467505798949419`}, {0.5306122448979592`,
7.239968897142224`}, {0.5510204081632653`,
7.002600506634537`}, {0.5714285714285714`,
6.75656172280596`}, {0.5918367346938775`,
6.501620953518743`}, {0.6122448979591837`,
6.238632239548857`}, {0.6326530612244898`,
5.964713365415807`}, {0.6530612244897959`,
5.6798465046806585`}, {0.673469387755102`,
5.38696253472903`}, {0.6938775510204082`,
5.087323728777496`}, {0.7142857142857143`,
4.784664350286133`}, {0.7346938775510204`,
4.476709556785695`}, {0.7551020408163265`,
4.160416099694797`}, {0.7755102040816326`,
3.838416824535938`}, {0.7959183673469388`,
3.5099065199869566`}, {0.8163265306122449`,
3.1747813234745452`}, {0.8367346938775511`,
2.835059096420477`}, {0.8571428571428571`,
2.4892086871775314`}, {0.8775510204081632`,
2.1407781653548907`}, {0.8979591836734694`,
1.7933577858764531`}, {0.9183673469387755`,
1.4455797049857155`}, {0.9387755102040817`,
1.0969831944328101`}, {0.9591836734693877`,
0.7493968681691019`}, {0.9795918367346939`,
0.40795711960412273`}, {1.`, 0.07271879311326668`}};
In[4]:=
bez[n_, i_, t_] := Binomial[n, i]((1 - t)^(i))( t^(n - i));
In[5]:=
t =.
In[6]:=
b1[t_] = bez[2, 2, t];
In[7]:=
b2[t_] = bez[2, 1, t];
In[8]:=
b3[t_] = bez[2, 0, t];
In[9]:=
Remove[t, y, w]
In[10]:=
curve[t_, y_, w_] = (b1[t]{-1, 0} + w b2[t]{0, y} + b3[t]{1, 0})/(
b1[t] + w b2[t] + b3[t]);
In[13]:=
error[y_, w_] :=
Module[
{i, j, dist, least, sum, ret, t, numStarts = 50},
Print["count= ", count, " memory in use = ", MemoryInUse[]];
count=count+1;
If[ValueQ[prev] == False || Length[prev] != Length[data],
Print["Building prev"];
prev = Table[Infinity, {Length[data]}];
For[i = 1, i <= Length[data], i++,
least = Infinity;
For[j = -numStarts, j <= numStarts - 1, j++,
dist = dsq[data[[i]], curve[j/numStarts, y, w]];
If[dist < least,
least = dist;
prev[[i]] = N[j/numStarts];
]; (* If this is a better values *)
]; (* Loop over j *)
]; (* Loop over data *)
Print["prev built"];
];
sum = 0;
For[i = 1, i <= Length[data], i++,
ret = FindMinimum[dsq[data[[i]], curve[t, y, w]], {t, prev[[i]]}];
prev[[i]] = t /. ret[[2]];
sum = sum + ret[[1]];
];
Return[sum];
];
In[14]:=
Print["Before call, memory usage = ", MemoryInUse[]];
count=0;
ret = FindMinimum[error[y, w], {y, 20.0, 21.0}, {w, 1.0, 1.1}];
Print["After call, memory usage = ", MemoryInUse[]];
(****** Output begins here *)
"Before call, memory usage = 1225448
"count= 0 memory in use = 1239968
"Building prev"
"prev built"
FindMinimum::"fmgz": "Encountered a vanishing gradient. The result returned \
may not be a minimum; it may be a maximum or a saddle point."
"count= 1 memory in use = 1707496
FindMinimum::"fmgz": "Encountered a vanishing gradient. The result returned \
may not be a minimum; it may be a maximum or a saddle point."
"count= 2 memory in use = 1902664
FindMinimum::"fmgz": "Encountered a vanishing gradient. The result returned \
may not be a minimum; it may be a maximum or a saddle point."
General::"stop": "Further output of \!\(FindMinimum :: \"fmgz\"\) will be \
suppressed during this calculation."
"count= 3 memory in use = 2097696
"count= 4 memory in use = 2292456
"count= 5 memory in use = 2487088
"count= 6 memory in use = 2681648
"count= 7 memory in use = 2876024
"count= 8 memory in use = 3070600
"count= 9 memory in use = 3264168
"count= 10 memory in use = 3457968
"count= 11 memory in use = 3651016
"count= 12 memory in use = 3844712
"count= 13 memory in use = 4037728
"count= 14 memory in use = 4231552
"count= 15 memory in use = 4424208
"count= 16 memory in use = 4615720
"count= 17 memory in use = 4807096
"count= 18 memory in use = 4999240
"count= 19 memory in use = 5192504
"count= 20 memory in use = 5384072
"count= 21 memory in use = 5575584
"count= 22 memory in use = 5766952
"count= 23 memory in use = 5958464
"count= 24 memory in use = 6150096
"count= 25 memory in use = 6339736
"count= 26 memory in use = 6529808
"count= 27 memory in use = 6719904
"count= 28 memory in use = 6910560
"count= 29 memory in use = 7099912
"count= 30 memory in use = 7291272
"count= 31 memory in use = 7480168
"count= 32 memory in use = 7669520
"count= 33 memory in use = 7856832
"count= 34 memory in use = 8046496
"count= 35 memory in use = 8232784
"count= 36 memory in use = 8420992
"count= 37 memory in use = 8607528
"count= 38 memory in use = 8793488
"count= 39 memory in use = 8979896
"count= 40 memory in use = 9166768
"count= 41 memory in use = 9352192
"count= 42 memory in use = 9536912
"count= 43 memory in use = 9721120
"count= 44 memory in use = 9906440
"count= 45 memory in use = 10091080
"count= 46 memory in use = 10276824
"count= 47 memory in use = 10460224
"count= 48 memory in use = 10643088
"count= 49 memory in use = 10824816
"count= 50 memory in use = 11005528
"count= 51 memory in use = 11186312
"count= 52 memory in use = 11365960
"count= 53 memory in use = 11546696
"count= 54 memory in use = 11724952
"count= 55 memory in use = 11902280
"count= 56 memory in use = 12082472
"count= 57 memory in use = 12263656
"count= 58 memory in use = 12439112
"count= 59 memory in use = 12612496
"count= 60 memory in use = 12789336
"count= 61 memory in use = 12968496
"count= 62 memory in use = 13142584
"count= 63 memory in use = 13315872
"count= 64 memory in use = 13488904
"count= 65 memory in use = 13662816
"count= 66 memory in use = 13833824
>From In[14]:=
"count= 67 memory in use = 14002480
"count= 68 memory in use = 14171952
"count= 69 memory in use = 14344992
"count= 70 memory in use = 14515592
"count= 71 memory in use = 14684272
"count= 72 memory in use = 14848096
"count= 73 memory in use = 15010280
"count= 74 memory in use = 15174344
"count= 75 memory in use = 15338456
"count= 76 memory in use = 15501752
"count= 77 memory in use = 15663360
"count= 78 memory in use = 15827800
"count= 79 memory in use = 15986144
"count= 80 memory in use = 16147072
"count= 81 memory in use = 16304808
"count= 82 memory in use = 16466384
"count= 83 memory in use = 16620688
"count= 84 memory in use = 16779712
"count= 85 memory in use = 16932376
"count= 86 memory in use = 17081544
"count= 87 memory in use = 17233104
"count= 88 memory in use = 17378920
"count= 89 memory in use = 17520152
"count= 90 memory in use = 17666496
"count= 91 memory in use = 17812840
"count= 92 memory in use = 17956456
"count= 93 memory in use = 18104704
"count= 94 memory in use = 18248224
"count= 95 memory in use = 18387720
"count= 96 memory in use = 18529160
"count= 97 memory in use = 18670144
"count= 98 memory in use = 18800800
"count= 99 memory in use = 18938520
"count= 100 memory in use = 19075880
"count= 101 memory in use = 19213720
"count= 102 memory in use = 19348320
"count= 103 memory in use = 19485704
"count= 104 memory in use = 19616288
"count= 105 memory in use = 19755288
"count= 106 memory in use = 19882520
"count= 107 memory in use = 20012928
"count= 108 memory in use = 20144808
"count= 109 memory in use = 20259688
"count= 110 memory in use = 20382632
"count= 111 memory in use = 20498720
"count= 112 memory in use = 20613944
"count= 113 memory in use = 20727200
"count= 114 memory in use = 20845816
"count= 115 memory in use = 20951960
"count= 116 memory in use = 21060424
"count= 117 memory in use = 21165032
"count= 118 memory in use = 21271600
"count= 119 memory in use = 21361088
"count= 120 memory in use = 21465360
"count= 121 memory in use = 21559656
"count= 122 memory in use = 21666072
"count= 123 memory in use = 21771952
"count= 124 memory in use = 21862912
"count= 125 memory in use = 21950960
"count= 126 memory in use = 22045144
"count= 127 memory in use = 22131944
"count= 128 memory in use = 22233512
"count= 129 memory in use = 22316544
"count= 130 memory in use = 22411368
"count= 131 memory in use = 22501280
"count= 132 memory in use = 22592208
"count= 133 memory in use = 22670376
"count= 134 memory in use = 22739256
"count= 135 memory in use = 22819144
"count= 136 memory in use = 22888808
"count= 137 memory in use = 22950168
"count= 138 memory in use = 23022288
"count= 139 memory in use = 23085400
"count= 140 memory in use = 23133304
"count= 141 memory in use = 23178552
"count= 142 memory in use = 23224584
"count= 143 memory in use = 23284600
"count= 144 memory in use = 23348720
"count= 145 memory in use = 23410224
"count= 146 memory in use = 23470128
"count= 147 memory in use = 23521400
"count= 148 memory in use = 23564960
"count= 149 memory in use = 23611424
"count= 150 memory in use = 23657136
"count= 151 memory in use = 23711472
"count= 152 memory in use = 23758904
"count= 153 memory in use = 23813872
"count= 154 memory in use = 23863992
"count= 155 memory in use = 23920648
"count= 156 memory in use = 23963944
"count= 157 memory in use = 24001040
"count= 158 memory in use = 24047040
"count= 159 memory in use = 24082488
"count= 160 memory in use = 24126096
"count= 161 memory in use = 24154760
"count= 162 memory in use = 24190232
"count= 163 memory in use = 24217392
"count= 164 memory in use = 24260216
"count= 165 memory in use = 24288496
"count= 166 memory in use = 24322592
"count= 167 memory in use = 24353848
"count= 168 memory in use = 24382096
"count= 169 memory in use = 24410232
"count= 170 memory in use = 24438688
"count= 171 memory in use = 24443984
"count= 172 memory in use = 24468616
"count= 173 memory in use = 24474616
"count= 174 memory in use = 24496032
"count= 175 memory in use = 24520464
"count= 176 memory in use = 24541072
"count= 177 memory in use = 24542184
"count= 178 memory in use = 24555576
"count= 179 memory in use = 24574720
"count= 180 memory in use = 24595024
"count= 181 memory in use = 24619632
"count= 182 memory in use = 24637656
"count= 183 memory in use = 24663712
"count= 184 memory in use = 24678744
"count= 185 memory in use = 24691240
"count= 186 memory in use = 24697472
"count= 187 memory in use = 24697504
"count= 188 memory in use = 24716208
"count= 189 memory in use = 24729776
"count= 190 memory in use = 24727936
"count= 191 memory in use = 24753128
"count= 192 memory in use = 24755968
"count= 193 memory in use = 24768128
"count= 194 memory in use = 24782752
"count= 195 memory in use = 24773104
"count= 196 memory in use = 24784608
"count= 197 memory in use = 24795632
"count= 198 memory in use = 24808416
"count= 199 memory in use = 24803464
"count= 200 memory in use = 24816928
"count= 201 memory in use = 24810816
"count= 202 memory in use = 24820104
"count= 203 memory in use = 24827768
"count= 204 memory in use = 24841016
"count= 205 memory in use = 24849344
"count= 206 memory in use = 24857896
"count= 207 memory in use = 24862280
"count= 208 memory in use = 24855664
"count= 209 memory in use = 24862384
"count= 210 memory in use = 24864000
"count= 211 memory in use = 24885576
"count= 212 memory in use = 24871800
"count= 213 memory in use = 24880816
"count= 214 memory in use = 24882200
"count= 215 memory in use = 24892776
"count= 216 memory in use = 24902616
"count= 217 memory in use = 24915824
"count= 218 memory in use = 24916688
"count= 219 memory in use = 24934600
"count= 220 memory in use = 24936656
"count= 221 memory in use = 24939296
"count= 222 memory in use = 24940008
"count= 223 memory in use = 24938608
"count= 224 memory in use = 24944200
"count= 225 memory in use = 24956728
"count= 226 memory in use = 24962000
"count= 227 memory in use = 24974056
"count= 228 memory in use = 24976080
"count= 229 memory in use = 24984928
"count= 230 memory in use = 24985072
"count= 231 memory in use = 24980320
"count= 232 memory in use = 24984888
"count= 233 memory in use = 25004288
"count= 234 memory in use = 25004760
"count= 235 memory in use = 25008752
"count= 236 memory in use = 25011760
"After call, memory usage = 25034144
In[18]:=
Print["Before call, memory usage = ", MemoryInUse[]];
count = 0;
ret = FindMinimum[error[y, w],
{y, 20.0, 21.0}, {w, 1.0, 1.1}];
Print["After call, memory usage = ", MemoryInUse[]];
(***** Output from second call begins here *)
"Before call, memory usage = 25037896
"count= 0 memory in use = 25044160
FindMinimum::"fmgz": "Encountered a vanishing gradient. The result returned \
may not be a minimum; it may be a maximum or a saddle point."
"count= 1 memory in use = 25050656
FindMinimum::"fmgz": "Encountered a vanishing gradient. The result returned \
may not be a minimum; it may be a maximum or a saddle point."
"count= 2 memory in use = 25057184
FindMinimum::"fmgz": "Encountered a vanishing gradient. The result returned \
may not be a minimum; it may be a maximum or a saddle point."
General::"stop": "Further output of \!\(FindMinimum :: \"fmgz\"\) will be \
suppressed during this calculation."
"count= 3 memory in use = 25058368
"count= 4 memory in use = 25050936
"count= 5 memory in use = 25065848
"count= 6 memory in use = 25063536
"count= 7 memory in use = 25054328
"count= 8 memory in use = 25051024
"count= 9 memory in use = 25044360
"count= 10 memory in use = 25047544
"count= 11 memory in use = 25048608
"count= 12 memory in use = 25043368
"count= 13 memory in use = 25056912
"count= 14 memory in use = 25066216
"count= 15 memory in use = 25050536
"count= 16 memory in use = 25032928
"count= 17 memory in use = 25030640
"count= 18 memory in use = 25017408
"count= 19 memory in use = 25010048
"count= 20 memory in use = 25004928
"count= 21 memory in use = 25019328
"count= 22 memory in use = 25017448
"count= 23 memory in use = 25019000
"count= 24 memory in use = 25039024
"count= 25 memory in use = 25050520
"count= 26 memory in use = 25053568
"count= 27 memory in use = 25048512
"count= 28 memory in use = 25056008
"count= 29 memory in use = 25057920
"count= 30 memory in use = 25065904
"count= 31 memory in use = 25062808
"count= 32 memory in use = 25055656
"count= 33 memory in use = 25060008
"count= 34 memory in use = 25070984
"count= 35 memory in use = 25067688
"count= 36 memory in use = 25077576
"count= 37 memory in use = 25074736
"count= 38 memory in use = 25069536
"count= 39 memory in use = 25073848
"count= 40 memory in use = 25069112
"count= 41 memory in use = 25066920
"count= 42 memory in use = 25073144
"count= 43 memory in use = 25072560
"count= 44 memory in use = 25073384
"count= 45 memory in use = 25078976
"count= 46 memory in use = 25056224
"count= 47 memory in use = 25059704
"count= 48 memory in use = 25064056
"count= 49 memory in use = 25063600
"count= 50 memory in use = 25075904
"count= 51 memory in use = 25073992
"count= 52 memory in use = 25073464
"count= 53 memory in use = 25052664
"count= 54 memory in use = 25042008
"count= 55 memory in use = 25041792
"count= 56 memory in use = 25037880
"count= 57 memory in use = 25031200
"count= 58 memory in use = 25033752
"count= 59 memory in use = 25023304
"count= 60 memory in use = 25027464
"count= 61 memory in use = 25026664
"count= 62 memory in use = 25032600
"count= 63 memory in use = 25033976
"count= 64 memory in use = 25016712
"count= 65 memory in use = 25029440
"count= 66 memory in use = 25029736
"count= 67 memory in use = 25031008
"count= 68 memory in use = 25025976
"count= 69 memory in use = 25034296
"count= 70 memory in use = 25046608
"count= 71 memory in use = 25045792
"count= 72 memory in use = 25041568
"count= 73 memory in use = 25030928
"count= 74 memory in use = 25032248
"count= 75 memory in use = 25041480
"count= 76 memory in use = 25037248
"count= 77 memory in use = 25043984
"count= 78 memory in use = 25047128
"count= 79 memory in use = 25048608
"count= 80 memory in use = 25030704
"count= 81 memory in use = 25033504
"count= 82 memory in use = 25024664
"count= 83 memory in use = 25025920
"count= 84 memory in use = 25026976
"count= 85 memory in use = 25027304
"count= 86 memory in use = 25040200
"count= 87 memory in use = 25029584
"count= 88 memory in use = 25018320
"count= 89 memory in use = 25035344
"count= 90 memory in use = 25039568
"count= 91 memory in use = 25049168
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"count= 98 memory in use = 25067496
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"count= 100 memory in use = 25066968
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"count= 130 memory in use = 25043320
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"count= 132 memory in use = 25042000
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"count= 190 memory in use = 25032736
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"count= 230 memory in use = 24993056
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"count= 234 memory in use = 25022776
"count= 235 memory in use = 25032592
"After call, memory usage = 25040120