Derivatives with respect to three variables using gradent function. I am getting zero as answer for all values of varables

function f = objective_fun_full(x)

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% Input parameters------------------------------------------------
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Inj_Pr_min = 500; % Kpa
Inj_Pr_max = 8500; % Kpa

Injection_period_min = 0.5; % years
Injection_period_max= 8.5; % years

Solvolfrac_min = 0.01;% fraction
Solvolfrac_max = 0.410;% fraction

A = (Inj_Pr_min + Inj_Pr_max)/2;
B = (Injection_period_min+Injection_period_max)/2;
C = (Solvolfrac_min+Solvolfrac_max)/2;

a = (Inj_Pr_max - Inj_Pr_min)/2;
b = (Injection_period_max  - Injection_period_min)/2;
c = (Solvolfrac_max - Solvolfrac_min)/2;
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% Optimum conditions--------------------------------------
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Inj_Pr_Op_RF = 5400; 
Inj_Period_Op_RF = 5.4;
Solvent_frac_Op_RF = 0.255;

Inj_Pr_Op_cSOR = 600;
Inj_Period_Op_cSOR = 0.6;
Solvent_frac_Op_cSOR = 0.015;

Inj_Pr_Op_Solv_Reco = 6600;
Inj_Period_Op_Solv_Reco = 6.6;
Solvent_frac_Op_Solv_Reco = 0.315;

RF_Optimum =  (0.428612934) + (0.073578399) * ((Inj_Pr_Op_RF-A)/a) + (-0.028780801) * ((Inj_Period_Op_RF-B)/b) + (0.093376701) * ((Solvent_frac_Op_RF-C)/c) + (-0.022667198) * ((Inj_Pr_Op_RF-A)/a)*((Inj_Period_Op_RF-B)/b) + (-0.023206995) * ((Inj_Pr_Op_RF-A)/a)*((Solvent_frac_Op_RF-C)/c) + (-0.085392014) * ((Inj_Period_Op_RF-B)/b)*((Solvent_frac_Op_RF-C)/c) + (0.012506573) * ((Inj_Pr_Op_RF-A)/a)*((Inj_Period_Op_RF-B)/b)*((Solvent_frac_Op_RF-C)/c) + (-0.013395787) * ((Inj_Pr_Op_RF-A)/a)*((Inj_Pr_Op_RF-A)/a) + (-0.028069875) * ((Inj_Period_Op_RF-B)/b)*((Inj_Period_Op_RF-B)/b) + (-0.053102912) * ((Solvent_frac_Op_RF-C)/c)*((Solvent_frac_Op_RF-C)/c);
cSOR_Optimum = (2.485517241) + (0.21) * ((Inj_Pr_Op_RF-A)/a) + (0.436) * ((Inj_Period_Op_RF-B)/b) + (-0.048) * ((Solvent_frac_Op_RF-C)/c) + (-0.1075) * ((Inj_Pr_Op_RF-A)/a)*((Inj_Period_Op_RF-B)/b) + (0.045) * ((Inj_Pr_Op_RF-A)/a)*((Solvent_frac_Op_RF-C)/c) + (0.0925) * ((Inj_Period_Op_RF-B)/b)*((Solvent_frac_Op_RF-C)/c) + (0.3325) * ((Inj_Pr_Op_RF-A)/a)*((Inj_Period_Op_RF-B)/b)*((Solvent_frac_Op_RF-C)/c) + (0.071724138) * ((Inj_Pr_Op_RF-A)/a)*((Inj_Pr_Op_RF-A)/a) + (0.001724138) * ((Inj_Period_Op_RF-B)/b)*((Inj_Period_Op_RF-B)/b) + (0.051724138) * ((Solvent_frac_Op_RF-C)/c)*((Solvent_frac_Op_RF-C)/c);
Solv_Reco_Optimum = (1.00619478) + (-0.002832569) * ((Inj_Pr_Op_RF-A)/a) + (0.017820705) * ((Inj_Period_Op_RF-B)/b) + (0.015304436) * ((Solvent_frac_Op_RF-C)/c) + (0.005412352) * ((Inj_Pr_Op_RF-A)/a)*((Inj_Period_Op_RF-B)/b) + (0.003780369) * ((Inj_Pr_Op_RF-A)/a)*((Solvent_frac_Op_RF-C)/c) + (-0.016360606) * ((Inj_Period_Op_RF-B)/b)*((Solvent_frac_Op_RF-C)/c) + (-0.005467952) * ((Inj_Pr_Op_RF-A)/a)*((Inj_Period_Op_RF-B)/b)*((Solvent_frac_Op_RF-C)/c) + (-0.013667312) * ((Inj_Pr_Op_RF-A)/a)*((Inj_Pr_Op_RF-A)/a) + (-0.000849831) * ((Inj_Period_Op_RF-B)/b)*((Inj_Period_Op_RF-B)/b) + (-0.017202734) * ((Solvent_frac_Op_RF-C)/c)*((Solvent_frac_Op_RF-C)/c);
x=[2500 0.5 0.5]
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% Optimum conditions--------------------------------------
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RF1 = (0.428612934) + (0.073578399) * ((x(1)-A)/a) + (-0.028780801) * ((x(2)-B)/b) + (0.093376701) * ((x(3)-C)/c) + (-0.022667198) * ((x(1)-A)/a)*((x(2)-B)/b) + (-0.023206995) * ((x(1)-A)/a)*((x(3)-C)/c) + (-0.085392014) * ((x(2)-B)/b)*((x(3)-C)/c) + (0.012506573) * ((x(1)-A)/a)*((x(2)-B)/b)*((x(3)-C)/c) + (-0.013395787) * ((x(1)-A)/a)*((x(1)-A)/a) + (-0.028069875) * ((x(2)-B)/b)*((x(2)-B)/b) + (-0.053102912) * ((x(3)-C)/c)*((x(3)-C)/c);
cSOR1 = (2.485517241) + (0.21) * ((x(1)-A)/a) + (0.436) * ((x(2)-B)/b) + (-0.048) * ((x(3)-C)/c) + (-0.1075) * ((x(1)-A)/a)*((x(2)-B)/b) + (0.045) * ((x(1)-A)/a)*((x(3)-C)/c) + (0.0925) * ((x(2)-B)/b)*((x(3)-C)/c) + (0.3325) * ((x(1)-A)/a)*((x(2)-B)/b)*((x(3)-C)/c) + (0.071724138) * ((x(1)-A)/a)*((x(1)-A)/a) + (0.001724138) * ((x(2)-B)/b)*((x(2)-B)/b) + (0.051724138) * ((x(3)-C)/c)*((x(3)-C)/c);
Solv_Reco1 = (1.00619478) + (-0.002832569) * ((x(1)-A)/a) + (0.017820705) * ((x(2)-B)/b) + (0.015304436) * ((x(3)-C)/c) + (0.005412352) * ((x(1)-A)/a)*((x(2)-B)/b) + (0.003780369) * ((x(1)-A)/a)*((x(3)-C)/c) + (-0.016360606) * ((x(2)-B)/b)*((x(3)-C)/c) + (-0.005467952) * ((x(1)-A)/a)*((x(2)-B)/b)*((x(3)-C)/c) + (-0.013667312) * ((x(1)-A)/a)*((x(1)-A)/a) + (-0.000849831) * ((x(2)-B)/b)*((x(2)-B)/b) + (-0.017202734) * ((x(3)-C)/c)*((x(3)-C)/c);

distance=  sqrt((((RF1-RF_Optimum)^2)/RF_Optimum^2) + ((cSOR1 - cSOR_Optimum)^2/cSOR_Optimum^2)+(((Solv_Reco1-Solv_Reco_Optimum)^2)/Solv_Reco_Optimum^2))

f = gradient(distance)

Answer 1

[Alan Weiss]

The MATLAB gradient function calculates a numerical gradient as described here, not an analytic gradient. If you are looking for an analytic gradient, use Symbolic Math Toolbox and the jacobian or gradient function.

Alan Weiss

MATLAB mathematical toolbox documentation