Topic 6. Computing an antrophic footprint 1.Matlab basics 2.Multiregional Database: WIOD 3.Input-Output analysis with Matlab 4.Graphic Analysis

Topic 6. Computing an antrophic footprint

1. Matlab basics

2. Multiregional Database: WIOD

3. Input-Output analysis with Matlab

4. Graphic Analysis

1. Matlab Basics2. Multiregional Database3. Input-Output analysis with Matlab4. Graphic Analysis

Workspace

Declaración de variables Operaciones basicas


Vectores

>> x=[1,2,3,4,5]; [1 2 3 4 5]

>> y=[1 2 3 4 5]; [1 2 3 4 5]

>> Z=[1:5]; [1 2 3 4 5]

>> pares=2:2:10; [2 4 6 8 10]

>> imp_down=9:-2:1; [9 7 5 3 2 1]

>> Xc=[1;2;3;4;5];

>> Xt=[1,2,3,4,5]‘


Declaración de matrices

>> M=[1 2 3; 4 5 6; 7 8 9];

>> I=eye(4);

>> unos=ones(5,4);

>> ceros=zeros(2,3);

>> M2=[10 20 30; M]

>> Xd=diag(x)


Operaciones con matrices


Cambiar elementos de una matriz

A(3, 2) = 7 coloca un 7 en el elemento (3, 2).

A(3,:)=v sustituye los valores de la tercera fila por los de v.

A(:, 2)=ww sustituye los valores de la segunda columna por los del vector w.

A([2 3],:) = A([3 2],:) intercambia las filas 2 y 3 de A.

Símbolo dos puntos “:” significa todo (todas las columnas o todas las filas).


Cambiar elementos de una matriz

A(i, j) muestra el elemento (i, j) de la matriz A (escalar = matriz de 1 × 1).

A(i, :) muestra la fila i-ésima de A (vector fila).

A(:, j) muestra la columna j-ésima de A (vector columna).

A(2: 4,3: 7) muestra las filas de la 2 a la 4 y las columnas de la 3 a la 7 (en forma de matriz de 3 × 5).

A([2 4],:) muestra las filas 2 y 4 y todas las columnas (en forma de matriz de 2 × n).

A(:) muestra una sola columna larga formada a partir de las columnas de A (matriz de mn × 1).


Otras funciones relevantes (ejemplos)

>> B=reshape(A,9,1) reordena la matriz A, en un vector fila

>> C=sum(A(:,2)) suma todos los elementos de la segunda columnaC=15

>> D=sum(sum(A)) suma todos los elementos de la matrizD=45

>> xlsread(filename,sheet,Range) Lee los elementos del archive “filename”, de la hoja “sheet”, en el rango de celdas que le indiquemos

>> xlswrite(filename,A,sheet,Range) Exporta la variable “A”, al rango de la hoja de excel que le indiquemos


Resumen funciones básicas Análisis IO

eye (x) Crea una matriz identidad de dimensión x

diag (v) Diagonaliza el vector v

inv (A) Invierte la matriz (A)

(inv(I-A))*diag(Y)Multiplica la inversa de Leontieff por un vector de demanda final diagonalizado

reshape (A,m,n)Redimensiona la matriz A en “m” filas y “n” columnas.

sum (A)Suma los elementos de la primera dimensión de A. Podemos acotar los elementos indicando los elementos de la fila y/o de la columna

sum(sum(A)) Suma los elementos totales de la matriz

xlsread Lee los elementos de una hoja excel

xlswrite Exporta los resultados a una hoja excel



World Input-Output Tables


Satellite accounts


“Countries”_EU

HCOAL BCOAL COKE CRUDE DIESEL GASOLINEJETFUEL LFO HFO NAPHTA OTHPETRONATGAS OTHGAS WASTE BIOGASOLBIODIESELBIOGAS OTHRENEWELECTR HEATPRODNUCLEAR HYDRO GEOTHERMSOLAR WIND OTHSOURCLOSS TOTALAgriculture, Hunting, Forestry and FishingsecAtB 4672.234 10788.65 76935.59 3095.373 107.9776 62.2528 37.36711 1602.377 6251.02 103552.8Mining and Quarrying secC 4213.0931 230.86015 1861.116 2517.92 2809.687 114082.8 1405.76 20711.27 200821.8 1014.294 33.54875 20.13756 71687.42 982.9769 422392.7Food, Beverages and Tobacco sec15t16 10221.863 109.736 2298.832 2565.212 1064.996 638.9894 3140.353 31275.98 134.9824 30.62961 18.38536 83361.99 27670.72 162532.7Textiles and Textile Products sec17t18 380.16813 153.4525 369.7949 597.1245 666.3171 33.07082 66.17416 387.5708 3802.234 7.956081 4.775621 2017.199 8485.838Leather, Leather and Footwear sec19 109.31065 44.12257 106.328 50.71644 56.59327 9.508933 19.02722 78.10104 1093.265 0.675745 0.405615 578.6972 2146.752Wood and Products of Wood and Corksec20 635.9692 709.6629 468.5867 622.3037 38.34815 8.473647 5.086289 16824.61 14.10301 19327.14Pulp, Paper, Paper , Printing and Publishingsec21t22 8363.6773 1507.332 1681.996 766.8124 2194.936 19173.53 20.08368 12.05518 31674.36 21739.07 87133.85Coke, Refined Petroleum and Nuclear Fuelsec23 41209.577 5500.995 1203752 71.51646 79.80351 2395.215 51671.65 18529.31 3933.169 0.952885 0.571967 7055.797 1334201Chemicals and Chemical Productssec24 2245.9251 6342.625 769.49197 563.6951 629.014 4132.204 638.9894 53746.63 77466.14 2176.466 3732.281 7.510668 4.508263 895.8077 15146.84 168498.1Rubber and Plastics sec25 457.0811 510.0459 465.0124 37.01636 6.090144 3.655596 351.3364 1830.238Other Non-Metallic Mineral sec26 30043.179 18.63126 256.48337 492.196 549.2298 1576.205 468.5867 6962.499 54130.34 267.8296 6.558015 3.936435 14692.38 109468.1Basic Metals and Fabricated Metalsec27t28 129481.44 464.2743 22730.684 779.0797 2051.788 2289.541 10176.77 34752 734.4066 5551.936 149537.2 22584.81 27.338 16.40958 2406.531 211104.6 594688.7Machinery, Nec sec29 757.2846 845.0359 188.0582 572.708 443.3199 10.09005 6.056533 1934.873 4757.426Electrical and Optical Equipment sec30t33 766.4167 855.2261 72.15477 366.7325 164.1351 10.21173 6.129568 766.9118 3007.918Transport Equipment sec34t35 1288.526 1437.835 657.3074 107.9108 17.1683 10.30524 510.4891 4029.542Manufacturing, Nec; Recycling sec36t37 1234.769 1377.85 453.8892 61.50426 16.45206 9.875311 126.2468 3280.587Electricity, Gas and Water SupplysecE 1425002.1 661956.9 3073.027 1134.214 1265.642 12854.67 4899.457 5256.86 358300.6 14479.49 15.11225 9.071097 15397.04 18056.54 83065.25 44028.72 29.75161 13704.07 61243.42 2723772Construction secF 13066.55 14580.65 20362.79 468.5867 53286.15 2745.117 174.0986 104.5023 437.0549 105225.5Sale, Maintenance and Repair of Motor Vehicles and Motorcycles; Retail Sale of Fuelsec50 3535.77 3945.481 2114.192 12.45902 1324.564 373.2911 13.53107 47.11056 28.27802 0.919339 18848.5 26.2409 30270.34Wholesale Trade and Commission Trade, Except of Motor Vehicles and Motorcyclessec51 184.07762 210.4859 5744.632 6410.298 2659.267 15.67117 2023.559 1849.901 10.30838 76.54141 45.94382 95.73606 14392.46 19.9911 33738.87Retail Trade, Except of Motor Vehicles and Motorcycles; Repair of Household Goodssec52 15.230871 17.41594 16604.48 18528.55 2078.664 12.24965 4920.1 29414.48 3.589419 221.238 132.7976 7.094109 5170.001 6.960983 77132.85Hotels and Restaurants secH 5902.277 6586.211 1493.725 8.80258 1873.943 3199.097 13.01989 78.64188 47.20462 78.694 18163.56 25.24955 37470.42Inland Transport sec60 112084.9 32375.98 17439.7 896.421 8866.378 171663.4Water Transport sec61 3733.4114 22992.6 30896.21 38.11522 57660.34Air Transport sec62 238000 238000Other Supporting and Auxiliary Transport Activities; Activities of Travel Agenciessec63 40429.99 1767.118 10.4137 292.7027 250.2142 11.47665 323.3468 2.102938 15974.12 22.25675 59083.74Post and Telecommunications sec64 41815.59 1905.436 11.22881 315.6135 1348.123 5.089514 334.4284 0.420325 7101.8 9.870126 52847.6Financial Intermediation secJ 5398.25 6023.779 26.79568 0.157908 1492.066 13.00378 0.951066 71.92623 43.17357 0.304243 1380.701 1.844409 14452.95Real Estate Activities sec70 1838.472 2051.508 472.1125 2.782179 584.8386 360.8536 5.948669 24.49579 14.70354 4.744006 8289.451 11.53629 13661.45Renting of M&Eq and Other Business Activitiessec71t74 15709.44 17529.79 4921.653 29.0035 5144.356 1651.37 27.84302 209.3124 125.6393 20.92063 38876.25 53.99614 84299.57Public Admin and Defence; Compulsory Social SecuritysecL 245.62127 280.8588 6165.965 6880.454 1563.59 9.214301 1958.182 693.4997 7.307254 82.15526 49.31352 8.158579 10225.04 14.171 28183.53Education secM 21.779164 24.90367 9851.743 10993.33 22.90832 0.135 2718.697 750.4158 19.64123 131.2645 78.79125 0.585238 27411.03 38.09037 52063.31Health and Social Work secN 23.118029 26.43461 15025.6 16766.71 1161.118 6.842515 4333.017 1725.853 7.120373 200.2009 120.1702 2.070716 10061.4 13.80859 49473.45Other Community, Social and Personal ServicessecO 20.563494 23.51359 9331.12 10412.37 1422.148 8.380776 2806.993 543.2056 10.38802 124.3278 74.62747 830.8286 77.18106 14542.1 20.14556 40247.9Private Households with Employed PersonssecPExtra-territorial organizations and bodiessecQTotal intermediate consumption secTOT 1655514.1 675174.3 23987.519 1209941 323602.4 149826.5 238000 318934.7 77543.15 734.4066 239048 977448.8 44592.27 3867.263 1722.418 2588.074 16227.87 155121.1 664452.8 44028.72 1276.89 13704.07 61243.42 6898580

Final consumption expenditure by householdsFC_HH 43.91953 30355.91 445676.4 1107.618 34638.94 125820.1 255.5204 5321.547 242.7774 56979.04 213709.3 7961.451 922112.5

Grand Total total 1655514.1 675218.3 23987.519 1209941 353958.3 595502.9 238000 320042.3 77543.15 734.4066 273687 1103269 44847.79 3867.263 7043.965 2830.851 16227.87 212100.2 878162 44028.72 9238.342 13704.07 61243.42 7820693

Sectors TerajoulesEnergy commodities


“Countries”_AIR

CO2 CH4 N2O NOX SOX CO NMVOC NH3Agriculture, Hunting, Forestry and FishingsecAtB 6652.8409 3109523 62940.137 204924.8 20246.88 1532993 391710.8 405677Mining and Quarrying secC 24083.361 1356674 129.95862 175190.3 48297.81 733534 246876.1 458.3612Food, Beverages and Tobacco sec15t16 3275.2122 1187.6 512.76442 69994.8 45571.22 226423.1 140881.9 112.3612Textiles and Textile Products sec17t18 361.34002 36.50625 9.6254013 3537.704 975.3014 14812.61 4985.29 4.321472Leather, Leather and Footwear sec19 84.018429 5.425845 1.1986245 878.0899 242.0785 3676.623 1237.393 0.450689Wood and Products of Wood and Corksec20 139.22675 59.84164 13.686951 8974.765 2474.232 37577.96 12647.13 13.36715Pulp, Paper, Paper , Printing and Publishingsec21t22 2084.7863 178.1463 106.62063 35828.29 26351.93 81202.99 28347.75 48.4207Coke, Refined Petroleum and Nuclear Fuelsec23 7511.6266 16680.3 164.59384 16766.91 133126.7 50434.45 58474.03 4.150877Chemicals and Chemical Productssec24 7942.2157 722.8645 10906.609 31147.6 82707.89 354901.5 94788.59 366.9926Rubber and Plastics sec25 77.009592 19.56157 5.9940233 625.5728 172.4627 2619.317 881.5495 4.748654Other Non-Metallic Mineral sec26 12594.922 211.6941 37.698312 71573.18 76261.09 270654.9 26930.69 209.2123Basic Metals and Fabricated Metalsec27t28 31146.258 2867.937 175.19487 144403.2 339883.1 9164422 72468.05 241.9092Machinery, Nec sec29 171.9593 35.11355 10.374022 1708.216 470.934 7152.419 2407.197 9.716806Electrical and Optical Equipment sec30t33 143.86362 33.42591 10.153122 1204.393 332.0362 5042.875 1697.215 6.180915Transport Equipment sec34t35 217.27547 54.69213 16.823164 1651.089 455.1847 6913.222 2326.694 8.327355Manufacturing, Nec; Recycling sec36t37 206.05652 51.98281 16.051232 1475.983 406.9103 6180.044 2079.937 13.0341Electricity, Gas and Water SupplysecE 206645.9 154161.5 2162.8719 570340.4 1503614 844408.8 61598.19 6.516183Construction secF 3765.9934 593.6648 176.99859 115105.5 12768.41 331242.1 199452.5 133.8213Sale, Maintenance and Repair of Motor Vehicles and Motorcycles; Retail Sale of Fuelsec50 773.88889 135.4476 44.497049 9906.773 2731.175 41480.34 13960.5 149.12Wholesale Trade and Commission Trade, Except of Motor Vehicles and Motorcyclessec51 1292.9532 218.7972 71.830725 12617.16 3478.395 52828.93 17779.95 110.7954Retail Trade, Except of Motor Vehicles and Motorcycles; Repair of Household Goodssec52 4413.9769 632.0474 207.48573 35448.34 9772.67 148424.7 49953.37 116.6974Hotels and Restaurants secH 1257.2022 224.9947 73.872734 13493.75 3720.059 56499.25 19015.22 27.1795Inland Transport sec60 10994.97 13403.15 716.58497 232676.6 5361.383 275758.2 29711.88 146.2132Water Transport sec61 4211.9265 6227.502 148.37011 232593.8 201885.1 2026634 124935.5 3.979026Air Transport sec62 16564.8 111.223 482.09429 195122.8 20750.14 392989.1 16127.4Other Supporting and Auxiliary Transport Activities; Activities of Travel Agenciessec63 2984.119 721.3307 236.56499 24292.89 6697.25 101716 34233.25 126.6484Post and Telecommunications sec64 3148.4602 745.438 244.4474 23439.89 6462.087 98144.43 33031.2 199.2641Financial Intermediation secJ 889.93273 203.6697 66.790278 6544.14 1804.138 27400.76 9221.922 48.9757Real Estate Activities sec70 359.56562 70.19897 23.052952 4522.777 1246.874 18937.18 6373.441 37.55362Renting of M&Eq and Other Business Activitiessec71t74 3070.4526 596.9918 195.94007 30830.95 8499.712 129091.3 43446.6 303.65Public Admin and Defence; Compulsory Social SecuritysecL 1224.8253 233.9069 76.755266 10967.67 3023.651 45922.39 15455.51 83.82856Education secM 1664.3677 373.9852 122.73111 18231.36 5026.16 76335.96 25691.41 31.13866Health and Social Work secN 2657.5719 567.9602 186.2947 21130.74 5825.482 88475.85 29777.17 132.84Other Community, Social and Personal ServicessecO 1711.9979 648733.9 1501.4981 15676.81 4321.901 65639.87 22091.56 117.3505Private Households with Employed PersonssecPExtra-territorial organizations and bodiessecQTotal intermediate consumption secTOT 364324.88 5316297 81796.164 2342827 2584965 17320471 1840597 408954.2

Final consumption expenditure by householdsFC_HH 41143.219 50916.66 2883.6364 390155.9 58656.3 7881056 609631.6 20316.89

Grand Total total 405468.09 5367214 84679.801 2732983 2643621 25201526 2450229 429271.1

𝐶𝑂2𝑒𝑞=𝐶𝑂2+211000

𝐶𝐻4+3101000

𝑁2𝑂


Satellite accounts


“Countries”_MAT

1000 tonnesBiomass_animals_UsedBiomass_feed_UsedBiomass_food_UsedBiomass_forestry_UsedBiomass_other_UsedFossil_coal_UsedFossil_gas_UsedFossil_oil_UsedFossil_other_UsedMinerals_construction_UsedMinerals_industrial_UsedMinerals_metals_UsedBiomass_animals_UnusedBiomass_feed_UnusedBiomass_food_UnusedBiomass_forestry_UnusedBiomass_other_UnusedFossil_coal_UnusedFossil_gas_UnusedFossil_oil_UnusedFossil_other_UnusedMinerals_construction_UnusedMinerals_industrial_UnusedMinerals_metals_UnusedTotalsecAtB 224.7532 324291.94 88714.518 18758.916 722.65 33.528858 149.8645 19683.681 2813.837 143.12 455536.8secC 291002 30932.136 15755 69830.635 27280.757 450717.08 4435369 3178.159 3466.1 2562.306 50981.15 440043.4 5821118

sec15t16 0sec17t18 0

sec19 0sec20 0

sec21t22 0sec23 0sec24 0sec25 0sec26 0

sec27t28 0sec29 0

sec30t33 0sec34t35 0sec36t37 0

secE 0secF 0sec50 0sec51 0sec52 0secH 0sec60 0sec61 0sec62 0sec63 0sec64 0secJ 0

sec70 0sec71t74 0

secL 0secM 0secN 0secO 0secP 0secQ 0

FC_HH 0

total 224.7532 324291.94 88714.518 18758.916 722.65 291002 30932.136 15755 0 69830.635 27280.757 450717.08 33.528858 149.8645 19683.681 2813.837 143.12 4435369 3178.159 3466.1 0 2562.306 50981.15 440043.4 6276655


“Countries”_WAT 1000 m3 water_bluewater_greenwater_greyTotalsecAtB 10576108 1.12E+08 7431085 130130642secC 0

sec15t16 36964.42 91302.12 128266.54sec17t18 6547.631 16172.65 22720.278

sec19 0sec20 0

sec21t22 31105.56 76830.74 107936.3sec23 0sec24 13438.93 33194.17 46633.101sec25 0sec26 4958.024 12246.32 17204.344

sec27t28 26223.38 64771.75 90995.132sec29 0

sec30t33 0sec34t35 0sec36t37 0

secE 2993953 0.190706 2993953.5secF 0sec50 0sec51 0sec52 0secH 0sec60 0sec61 0sec62 0sec63 0sec64 0secJ 0

sec70 0sec71t74 0

secL 0secM 0.047155 0.116473 0.1636283secN 0.056783 0.140254 0.1970367secO 0secP 0secQ 0

FC_HH 399408.6 865157.4 1264566.1

total 14088708 1.12E+08 8590761 134802918


Satellite accounts


“Countries”_SEAWIOD Socio Economic AccountsBasic data on output and employmentSource: WIOD database, July 2014 release

Countries Variables

Acronym Name Values DescriptionAUS Australia GO Gross output by industry at current basic prices (in millions of national currency)

AUT Austria II Intermediate inputs at current purchasers' prices (in millions of national currency)

BEL Belgium VA Gross value added at current basic prices (in millions of national currency)

BRA Brazil COMP Compensation of employees (in millions of national currency)

BGR Bulgaria LAB Labour compensation (in millions of national currency)

CAN Canada CAP Capital compensation (in millions of national currency)

CHN China GFCF Nominal gross fixed capital formation (in millions of national currency)

CYP Cyprus EMP Number of persons engaged (thousands)

CZE Czech Republic EMPE Number of employees (thousands)

DNK Denmark H_EMP Total hours worked by persons engaged (millions)

EST Estonia H_EMPE Total hours worked by employees (millions)

FIN FinlandFRA France Prices

DEU Germany GO_P Price levels gross output, 1995=100

GRC Greece II_P Price levels of intermediate inputs, 1995=100

HUN Hungary VA_P Price levels of gross value added, 1995=100

IND India GFCF_P Price levels of gross fixed capital formation, 1995=100

IDN IndonesiaIRL Ireland Volumes

ITA Italy GO_QI Gross output, volume indices, 1995 = 100

JPN Japan II_QI Intermediate inputs, volume indices, 1995 = 100

KOR Korea, Republic of VA_QI Gross value added, volume indices, 1995 = 100

LVA Latvia K_GFCF Real fixed capital stock, 1995 prices

LTU LithuaniaLUX Luxembourg Additional variables

MLT Malta LABHS High-skilled labour compensation (share in total labour compensation)

MEX Mexico LABMS Medium-skilled labour compensation (share in total labour compensation)

NLD Netherlands LABLS Low-skilled labour compensation (share in total labour compensation)

POL Poland H_HS Hours worked by high-skilled persons engaged (share in total hours)

PRT Portugal H_MS Hours worked by medium-skilled persons engaged (share in total hours)

ROU Romania H_LS Hours worked by low-skilled persons engaged (share in total hours)

RUS RussiaSVK Slovak RepublicSVN SloveniaESP SpainSWE SwedenTWN TaiwanTUR TurkeyGBR United KingdomUSA United States


Input-output basic equation

The basic equatio𝑛❑⇒ | 𝐴𝑋+𝑌=𝑋𝑋− 𝐴𝑋=𝑌

( 𝐼− 𝐴 )𝑋=𝑌❑⇒

𝑿=( 𝑰−𝑨 )−𝟏 ·𝒀

𝑀𝑎𝑡𝑟𝑖𝑧 𝑑𝑒𝑐𝑜𝑒𝑓𝑖𝑐𝑖𝑒𝑛𝑡𝑒𝑠𝑡 é 𝑐𝑛𝑖𝑐𝑜𝑠❑⇒ { 𝑎𝑖𝑗=

𝑍 𝑖𝑗𝑄 𝑗

𝐴=𝑍∗𝑞𝑑 1

¿ 𝑍𝑖𝑗∗𝑖𝑛𝑣 (𝑄𝑑 𝑗 )¿

𝑆𝑜𝑙𝑢𝑐𝑖 ó𝑛𝑠𝑖𝑠𝑡𝑒𝑚𝑎𝑒𝑐𝑢𝑎𝑐𝑖𝑜𝑛𝑒𝑠❑⇒ { 𝐴𝑥=𝑏❑

⇒

𝑥=𝑖𝑛𝑣 (𝐴 )∗𝑏

¿ 𝑦𝐵=𝑐❑⇒

𝑦=𝑐 ∗𝑖𝑛𝑣 (𝐵 )

𝑀𝑎𝑡𝑙𝑎𝑏⇒

𝐴=𝑍 𝑖𝑗/ (𝑄𝑑 𝑗 )


𝑥=𝐴 ¿


𝑦=𝑐 /B


Factor contents

𝑭=𝐟 (𝑰 −𝑨)−𝟏𝒀

yAIx 1)( Output

𝑽=𝒗𝒂(𝑰− 𝑨)−𝟏 �̂�=𝑉𝐴 𝒚 Value Added

LabourL

EmissionsE

WaterW


Practice 01.- Technical Coefficients

IO (Z) industry A industry B industry C DF (qd) Outputindustry A 0 20 45 35 100industry B 30 0 30 140 200inudstry C 0 80 0 70 150VA 70 100 75output 100 200 150

Coeficientes técnicos por división0,0 0,1 0,30,3 0,0 0,20,0 0,4 0,0

1 0 0Identidad 0 1 0

0 0 1

[I-A] 1,0 -0,1 -0,3-0,3 1,0 -0,20,0 -0,4 1,0

Inversa 1,077 0,258 0,3750,351 1,171 0,3400,141 0,468 1,136

0,0 0,1 0,30,3 0,0 0,20,0 0,4 0,0


Practice 02.- Spanish Emissions (C02eq) 2009

𝐶𝑂2𝑒𝑞=𝐶𝑂2+211000

𝐶𝐻4+3101000

𝑁2𝑂


WIOT_Data

Sec

tors

(1-

35)

Countries (1-41)year

s


Practice 03.- Emissions CO2eq MRIO

Tarea Comando/Operación Ecuación Cargamos los datos WIOD_2009 “xlsread” Cargamos los datos de Emisiones “Load” Para Calcular la matriz de coeficientes técnicos:

1ˆ· xZA

- Tomar los datos de consumos intermedios - Tomamos los datos de la producción

Extraer submatriz Z Extraer vector X

- Diagonalizar vector de output “Diag “ - Postmultiplicamos la inversa del output diagonalizado

por los consumos intermedios. Dividir “/”

Para Calcular la matriz de coeficientes de emisiones

1^

ˆ xEe

- Transformamos la matriz en un vector, para poder diagonalizarlo

“reshape” Reshape(variable,m,n)

- Postmultiplicamos la inversa del output diagonalizado por las emisiones diagonalizadas

Dividir “/”

Para calcular el Output Total

^1)( yAIx

- Tomamos los datos de la demanda final y sumamos por filas

For i=1:41… end Sum(variable,2)

- Premultiplicamos la inversa de Leontief por la demanda final

Dividir_invertida “\”

Calculamos las emisiones Multiplicar “*” ^1)(ˆ yAIeF

Para agregar los resultados - Cargamos la matriz de agregación AGM6 “Load” - Premultiplicamos los resultados por la matriz de

agregación y postmultiplicamos por la traspuesta AG*x*AG’

Exportamos los resultados a excel xlswrite


Research

Huella

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Topic 6. Computing an antrophic footprint 1.Matlab basics 2.Multiregional Database: WIOD 3.Input-Output analysis with Matlab 4.Graphic Analysis