Integrating columns of a Matrix using R (Error)

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This is my matrix: 

funcao=structure(c(-14.7690673280818, -14.5543581356252, -12.1406211639974, 
-10.7200919648493, -9.55507848352318, -9.20790894914246, -8.74647670464071, 
-8.26548763467919, -7.3962484443768, -6.94590909664862, -6.63903257406218, 
-6.40598087538929, -6.09621085755895, -5.88245015332806, -5.69615454359131, 
-5.4543516801245, -5.24485270997044, -5.05729667581875, -4.7660441793448, 
-4.39683466679171, -4.30668996362841, -4.0828498417172, -3.95528199743041, 
-3.81741171570944, -3.66175435590196, -3.56271256245504, -3.49609868983868, 
-3.37586125647396, -3.0034966287813, -2.90517151506904, -2.72993249556762, 
-2.66092057836039, -2.4408738658527, -2.36547969703899, -2.09546783234301, 
-1.95526398213212, -1.88470374007828, -1.72750243012653, -1.60575660667247, 
-1.43542615745848, -1.29362975715702, -1.18449733575892, -0.98947894198681, 
-0.853386354928181, -0.63296867063245, -0.527486151545778, -0.361277864998242, 
-0.257665212366851, -0.109270291541468, 0, 0.109270291541468, 
0.257665212366851, 0.361277864998242, 0.527486151545778, 0.63296867063245, 
0.853386354928181, 0.98947894198681, 1.18449733575892, 1.29362975715702, 
1.43542615745848, 1.60575660667247, 1.72750243012653, 1.88470374007828, 
1.95526398213212, 2.09546783234301, 2.36547969703899, 2.4408738658527, 
2.66092057836039, 2.72993249556762, 2.90517151506904, 3.0034966287813, 
3.37586125647396, 3.49609868983868, 3.56271256245504, 3.66175435590196, 
3.81741171570944, 3.95528199743041, 4.0828498417172, 4.30668996362841, 
4.39683466679171, 4.7660441793448, 5.05729667581875, 5.24485270997044, 
5.4543516801245, 5.69615454359131, 5.88245015332806, 6.09621085755895, 
6.40598087538929, 6.63903257406218, 6.94590909664862, 7.3962484443768, 
8.26548763467919, 8.74647670464071, 9.20790894914246, 9.55507848352318, 
10.7200919648493, 12.1406211639974, 14.5543581356252, 14.7690673280818, 
-13.7079821475458, -13.4498703618915, -11.67838231268, -10.4589486406842, 
-8.9432388382521, -8.58312548137122, -8.14102991846389, -7.71079209128989, 
-6.95240042017031, -6.66414427349685, -6.40033205538623, -6.13816822549321, 
-5.77208382991545, -5.49527630669887, -5.33154964830415, -5.12782641892739, 
-4.93206161073643, -4.72556232300793, -4.52080276980657, -4.1694078333758, 
-4.03956026669583, -3.90869860153294, -3.79104380757601, -3.69124767313376, 
-3.47159857371935, -3.3643163654408, -3.29467696235366, -3.16605701449292, 
-2.84435464789616, -2.71650210221017, -2.59690597248341, -2.52388797476942, 
-2.34094207608544, -2.20427426100811, -1.83879580218285, -1.72737794398069, 
-1.6454056454373, -1.5042411957216, -1.38609220687676, -1.2432788707001, 
-1.1225617148797, -1.01318771357089, -0.90038209504245, -0.773284479514442, 
-0.640368323748707, -0.555178375238413, -0.377358821158776, -0.230347860323025, 
-0.110436162251717, 0, 0.110436162251717, 0.230347860323025, 
0.377358821158776, 0.555178375238413, 0.640368323748707, 0.773284479514442, 
0.90038209504245, 1.01318771357089, 1.1225617148797, 1.2432788707001, 
1.38609220687676, 1.5042411957216, 1.6454056454373, 1.72737794398069, 
1.83879580218285, 2.20427426100811, 2.34094207608544, 2.52388797476942, 
2.59690597248341, 2.71650210221017, 2.84435464789616, 3.16605701449292, 
3.29467696235366, 3.3643163654408, 3.47159857371935, 3.69124767313376, 
3.79104380757601, 3.90869860153294, 4.03956026669583, 4.1694078333758, 
4.52080276980657, 4.72556232300793, 4.93206161073643, 5.12782641892739, 
5.33154964830415, 5.49527630669887, 5.77208382991545, 6.13816822549321, 
6.40033205538623, 6.66414427349685, 6.95240042017031, 7.71079209128989, 
8.14102991846389, 8.58312548137122, 8.9432388382521, 10.4589486406842, 
11.67838231268, 13.4498703618915, 13.7079821475458, -14.358609077878, 
-14.1271105147046, -11.9618138886078, -10.6190742201334, -9.31840132054895, 
-8.96622474353695, -8.51227248333579, -8.05091545299969, -7.22455526958365, 
-6.83691436333096, -6.54669635165921, -6.30238324376159, -5.97082920578328, 
-5.73268017960003, -5.55511488901834, -5.32804232266972, -5.12385612117062, 
-4.92897229198519, -4.67117775232928, -4.30885942992513, -4.20335651783943, 
-4.0154831357938, -3.89174994433905, -3.76860783727992, -3.58819663306074, 
-3.48596721027473, -3.41818297549918, -3.29470294456033, -2.94193593581688, 
-2.83218876260999, -2.67847401240583, -2.60791242809822, -2.40221737689215, 
-2.3031208003073, -1.99617971268181, -1.86711111167336, -1.79213635811389, 
-1.64113856670334, -1.52078410227216, -1.36109806339877, -1.22745572081485, 
-1.11822984936273, -0.955013720375685, -0.822400646878094, -0.635831069171161, 
-0.538198299721656, -0.367498441110635, -0.24709807532094, -0.109721283846771, 
0, 0.109721283846771, 0.24709807532094, 0.367498441110635, 0.538198299721656, 
0.635831069171161, 0.822400646878094, 0.955013720375685, 1.11822984936273, 
1.22745572081485, 1.36109806339877, 1.52078410227216, 1.64113856670334, 
1.79213635811389, 1.86711111167336, 1.99617971268181, 2.3031208003073, 
2.40221737689215, 2.60791242809822, 2.67847401240583, 2.83218876260999, 
2.94193593581688, 3.29470294456033, 3.41818297549918, 3.48596721027473, 
3.58819663306074, 3.76860783727992, 3.89174994433905, 4.0154831357938, 
4.20335651783943, 4.30885942992513, 4.67117775232928, 4.92897229198519, 
5.12385612117062, 5.32804232266972, 5.55511488901834, 5.73268017960003, 
5.97082920578328, 6.30238324376159, 6.54669635165921, 6.83691436333096, 
7.22455526958365, 8.05091545299969, 8.51227248333579, 8.96622474353695, 
9.31840132054895, 10.6190742201334, 11.9618138886078, 14.1271105147046, 
14.358609077878, -14.5672256639001, -14.3442603466748, -12.0526932005212, 
-10.6704167793823, -9.43869316924387, -9.08906143604798, -8.63130745231583, 
-8.15997238138419, -7.31181881941087, -6.89231124997616, -6.59362650222709, 
-6.3550370379524, -6.03455479085867, -5.80880119944129, -5.62679869904323, 
-5.39223941682433, -5.1853529853784, -4.99419352909143, -4.7193938866676, 
-4.35357309705323, -4.255876038818, -4.04972245780601, -3.92404029302206, 
-3.79341254883719, -3.62558255722496, -3.52497325621722, -3.4577838613747, 
-3.33595188997765, -2.97322433504632, -2.86928245642403, -2.70462793445213, 
-2.63485397290467, -2.42186464857093, -2.33481488889686, -2.04664318502277, 
-1.91191506158551, -1.8391839961936, -1.68503324864501, -1.56397162198931, 
-1.39887553095015, -1.26108886508264, -1.15191048988921, -0.972530768371285, 
-0.838149222100249, -0.634376246882453, -0.532753819606308, -0.364336815412981, 
-0.252468853112474, -0.109492065710681, 0, 0.109492065710681, 
0.252468853112474, 0.364336815412981, 0.532753819606308, 0.634376246882453, 
0.838149222100249, 0.972530768371285, 1.15191048988921, 1.26108886508264, 
1.39887553095015, 1.56397162198931, 1.68503324864501, 1.8391839961936, 
1.91191506158551, 2.04664318502277, 2.33481488889686, 2.42186464857093, 
2.63485397290467, 2.70462793445213, 2.86928245642403, 2.97322433504632, 
3.33595188997765, 3.4577838613747, 3.52497325621722, 3.62558255722496, 
3.79341254883719, 3.92404029302206, 4.04972245780601, 4.255876038818, 
4.35357309705323, 4.7193938866676, 4.99419352909143, 5.1853529853784, 
5.39223941682433, 5.62679869904323, 5.80880119944129, 6.03455479085867, 
6.3550370379524, 6.59362650222709, 6.89231124997616, 7.31181881941087, 
8.15997238138419, 8.63130745231583, 9.08906143604798, 9.43869316924387, 
10.6704167793823, 12.0526932005212, 14.3442603466748, 14.5672256639001, 
-13.6245844768687, -13.3630613956461, -11.6420519179073, -10.4384236674326, 
-8.89515033208928, -8.53401963497411, -8.0934438691888, -7.66719491633901, 
-6.91751548158816, -6.64199852086489, -6.38157100998465, -6.11711906602055, 
-5.74660855271358, -5.46484576488352, -5.30289294897202, -5.10216264876024, 
-4.90747729878566, -4.69948913603343, -4.50152763272595, -4.15153286112639, 
-4.01856478499323, -3.89501090892983, -3.77813524686729, -3.68133161034538, 
-3.45665297878437, -3.34872310204811, -3.27884590260074, -3.14956711773407, 
-2.83184663180451, -2.70167333082681, -2.5864505421683, -2.51311768021067, 
-2.33308777876224, -2.19160406439047, -1.81862225736669, -1.70946687980764, 
-1.6265976326061, -1.48669362532537, -1.36882733539455, -1.22817675030816, 
-1.10911635110033, -0.999723362435733, -0.89337938721453, -0.766988745723311, 
-0.640949911207503, -0.557354889428034, -0.37862272938278, -0.228200809764493, 
-0.110527795707098, 0, 0.110527795707098, 0.228200809764493, 
0.37862272938278, 0.557354889428034, 0.640949911207503, 0.766988745723311, 
0.89337938721453, 0.999723362435733, 1.10911635110033, 1.22817675030816, 
1.36882733539455, 1.48669362532537, 1.6265976326061, 1.70946687980764, 
1.81862225736669, 2.19160406439047, 2.33308777876224, 2.51311768021067, 
2.5864505421683, 2.70167333082681, 2.83184663180451, 3.14956711773407, 
3.27884590260074, 3.34872310204811, 3.45665297878437, 3.68133161034538, 
3.77813524686729, 3.89501090892983, 4.01856478499323, 4.15153286112639, 
4.50152763272595, 4.69948913603343, 4.90747729878566, 5.10216264876024, 
5.30289294897202, 5.46484576488352, 5.74660855271358, 6.11711906602055, 
6.38157100998465, 6.64199852086489, 6.91751548158816, 7.66719491633901, 
8.0934438691888, 8.53401963497411, 8.89515033208928, 10.4384236674326, 
11.6420519179073, 13.3630613956461, 13.6245844768687, -13.7513240158161, 
-13.4949850845108, -11.6972632618919, -10.4696154936035, -8.96823049188587, 
-8.60864584793023, -8.16576044465774, -7.73344959477095, -6.97053016408726, 
-6.67565344738059, -6.41008219291174, -6.14910749861269, -5.78532336166338, 
-5.51109109533802, -5.34644256890291, -5.14116391069274, -4.94483810678764, 
-4.73911258917317, -4.53082008138683, -4.17869747763421, -4.05047164341461, 
-3.91581211159757, -3.79775240187192, -3.6964010627146, -3.47936581711638, 
-3.37242020290272, -3.30290438286576, -3.17462683337767, -2.85085507867997, 
-2.72420863226898, -2.60233967200701, -2.52948530961352, -2.34502396371101, 
-2.21085897720345, -1.84928001732781, -1.73668634525457, -1.65518019199163, 
-1.51336068884896, -1.39506478104353, -1.25112746056258, -1.1295492863675, 
-1.02018515280999, -0.904021410598258, -0.776556379825624, -0.640066072057238, 
-0.554047238235075, -0.376701966557133, -0.231463685042374, -0.110388540236378, 
0, 0.110388540236378, 0.231463685042374, 0.376701966557133, 0.554047238235075, 
0.640066072057238, 0.776556379825624, 0.904021410598258, 1.02018515280999, 
1.1295492863675, 1.25112746056258, 1.39506478104353, 1.51336068884896, 
1.65518019199163, 1.73668634525457, 1.84928001732781, 2.21085897720345, 
2.34502396371101, 2.52948530961352, 2.60233967200701, 2.72420863226898, 
2.85085507867997, 3.17462683337767, 3.30290438286576, 3.37242020290272, 
3.47936581711638, 3.6964010627146, 3.79775240187192, 3.91581211159757, 
4.05047164341461, 4.17869747763421, 4.53082008138683, 4.73911258917317, 
4.94483810678764, 5.14116391069274, 5.34644256890291, 5.51109109533802, 
5.78532336166338, 6.14910749861269, 6.41008219291174, 6.67565344738059, 
6.97053016408726, 7.73344959477095, 8.16576044465774, 8.60864584793023, 
8.96823049188587, 10.4696154936035, 11.6972632618919, 13.4949850845108, 
13.7513240158161, -13.5038153563633, -13.2373523390222, -11.5894414578226, 
-10.4087012189772, -8.82551281645418, -8.46290889731311, -8.02453396711809, 
-7.60406134878737, -6.86699820314081, -6.6099290032563, -6.3544029256183, 
-6.08663753750477, -5.70971751250438, -5.42077894932731, -5.26139485499848, 
-5.06499864973269, -4.87187647554418, -4.66173225584577, -4.47361508632088, 
-4.12564790942336, -3.98816098787005, -3.87518960476143, -3.75944221250401, 
-3.66697204643782, -3.43501009186589, -3.32614231903036, -3.2559207639547, 
-3.12568790968636, -2.81373363068119, -2.68019961742924, -2.57130991397796, 
-2.49752109350884, -2.32171388099973, -2.17325620779303, -1.78940871644707, 
-1.68352966297731, -1.59936153416788, -1.46128278798956, -1.34382587758861, 
-1.20630719708568, -1.08964596607244, -0.980225481600834, -0.88323868593752, 
-0.757871821632761, -0.641792114656659, -0.560506724513046, -0.380453009333927, 
-0.225091641300559, -0.110660491161603, 0, 0.110660491161603, 
0.225091641300559, 0.380453009333927, 0.560506724513046, 0.641792114656659, 
0.757871821632761, 0.88323868593752, 0.980225481600834, 1.08964596607244, 
1.20630719708568, 1.34382587758861, 1.46128278798956, 1.59936153416788, 
1.68352966297731, 1.78940871644707, 2.17325620779303, 2.32171388099973, 
2.49752109350884, 2.57130991397796, 2.68019961742924, 2.81373363068119, 
3.12568790968636, 3.2559207639547, 3.32614231903036, 3.43501009186589, 
3.66697204643782, 3.75944221250401, 3.87518960476143, 3.98816098787005, 
4.12564790942336, 4.47361508632088, 4.66173225584577, 4.87187647554418, 
5.06499864973269, 5.26139485499848, 5.42077894932731, 5.70971751250438, 
6.08663753750477, 6.3544029256183, 6.6099290032563, 6.86699820314081, 
7.60406134878737, 8.02453396711809, 8.46290889731311, 8.82551281645418, 
10.4087012189772, 11.5894414578226, 13.2373523390222, 13.5038153563633, 
-12.8877947524831, -12.5961340486959, -11.3210853809037, -10.2570925911286, 
-8.47030492676585, -8.10018637873416, -7.67303749757961, -7.28202887686486, 
-6.60931905266524, -6.44634841642492, -6.21582362929168, -5.93115698481963, 
-5.5215432443443, -5.19600239869575, -5.04972087076752, -4.87543206990054, 
-4.69028336184037, -4.46914150055587, -4.33123842894087, -3.99361363184664, 
-3.833076928421, -3.77408485453713, -3.6640925546724, -3.59372660759739, 
-3.32461379011727, -3.21096198541142, -3.13898393694403, -3.00388455382712, 
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-2.26369776447253, -2.07966723692233, -1.64375650300888, -1.54786821816088, 
-1.46043531083332, -1.33166687876378, -1.21629813646533, -1.09475471308712, 
-0.990331188483095, -0.880770453063485, -0.831512873094893, -0.711368103958197, 
-0.64608803628934, -0.576583643383317, -0.389788923647592, -0.219325408944189, 
-0.101244293663156, 0, 0.101244293663156, 0.219325408944189, 
0.389788923647592, 0.576583643383317, 0.64608803628934, 0.711368103958197, 
0.831512873094893, 0.880770453063485, 0.990331188483095, 1.09475471308712, 
1.21629813646533, 1.33166687876378, 1.46043531083332, 1.54786821816088, 
1.64375650300888, 2.07966723692233, 2.26369776447253, 2.41796583370138, 
2.49408041291093, 2.57066623804085, 2.72134261347931, 3.00388455382712, 
3.13898393694403, 3.21096198541142, 3.32461379011727, 3.59372660759739, 
3.6640925546724, 3.77408485453713, 3.833076928421, 3.99361363184664, 
4.33123842894087, 4.46914150055587, 4.69028336184037, 4.87543206990054, 
5.04972087076752, 5.19600239869575, 5.5215432443443, 5.93115698481963, 
6.21582362929168, 6.44634841642492, 6.60931905266524, 7.28202887686486, 
7.67303749757961, 8.10018637873416, 8.47030492676585, 10.2570925911286, 
11.3210853809037, 12.5961340486959, 12.8877947524831, -12.6000848203634, 
-12.2966556390103, -11.1957507602953, -10.1862843945321, -8.30440651819497, 
-7.93147284818737, -7.50817793772083, -7.13162491301438, -6.48897104737938, 
-6.36994876479492, -6.15110072929745, -5.85854042138457, -5.43365721329602, 
-5.09102141962306, -4.95085939235108, -4.78689576531572, -4.60547103236952, 
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4.71456527242172, 4.90078016073291, 5.07802507599128, 5.22605862710606, 
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8.51780191626772, 10.2773650952434, 11.3569688906404, 12.6818752140478, 
12.9701665831908), .Dim = c(99L, 11L))

In each column I want to integrate using the integrate function of R, and put the value of that integral in the integrais array. The problem I encounter is the error: 

Error in integrate(integrando.funcao.t, lower = 0.01, upper = 0.5, subdivisions = 1000) : 
  extremely bad integrand behaviour

integrais=matrix(0,11)

for (t in 1:11){


integrando.funcao.t = approxfun(thau,funcao[,t],rule=2)

integrais[t,1]=integrate(integrando.funcao.t, lower = 0.01, upper = 0.5,subdivisions = 1000)$value

}

Is there a way to work around this problem with the same integrate function? Or do I need to approach in a nonlinear way? If this is the case how do I do it?

Thank you

    
asked by anonymous 02.11.2016 / 20:16

1 answer

3

The integrate function is not used to calculate integrals in this way. To use this function specifically, you need to write the function to be built into R . In your case, since the function values are already calculated, what you should do is use something like the Simpson Formula, as shown in this answer right here in StackOverflow .

I plotted the contents of the object funcao and got the following: 

matplot(funcao, type="l", col="black", lty=1)

Given your question history here, these 11 functions each have quartile functions of the normal distribution. Ignore the x-axis numbers of this graph as they are only showing the position of the values within the data frame and therefore range from 1 to 99. Looking at this figure, I would say that the integrals are all zero. To test this, I have assumed two hypotheses that are not explicit in your original question:

The step between each line of the object funcao is constant, that is, the function in question was calculated at equidistant points

  • As I am suspicious that it is a quantile function, it should not be calculated between 0.01 and 0.50, but between 0.01 and 0.99

    • My answer is based on these two hypotheses and I may be wrong. If I am, please correct me. 

    # pacote para calcular as integrais pela Fórmula de Simpson
library(Bolstad) 

# vetor variando entre 0,01 e 0,99, com tamanho igual ao numero
# de linhas da matriz funcao
x <- seq(from=0.01, to=0.99, length.out=dim(funcao)[1])

# inicializa o vetor para guardar os resultados das integracoes
integrais <- 0

# loop para calcular um numero de integrais igual ao numero de 
# colunas da matriz funcao
# utilizo j como contador porque t eh uma funcao do R e nao eh
# interessante utilizar palavras reservadas da linguagem
# como nome de objetos
for (j in 1:dim(funcao)[2]){
    integrais[j] <- sintegral(x, funcao[, j])$value
}

# resultado
integrais
 [1] -5.149960e-16 -5.657367e-16 -5.128276e-16 -4.902762e-16
 [5] -5.373306e-16 -5.893723e-16 -5.306085e-16 -5.205255e-16
 [9] -5.434021e-16 -5.186823e-16 -5.606409e-16

    As I suspected, all integrals were equal to zero.

    An important observation to make is about the divergence of this function. It is not set to 0 and 1. So if you are interested in calculating the integral between 0.01 and 0.50, you will get a value. If you calculate between 0.001 and 0.500, you will get even greater value. If you calculate between 0.0001 and 0.5000, you will get even higher value. The more the function approaches its limits at 0 and 1, the more it will diverge.

        
    03.11.2016 / 01:07
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