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Question: building a matrix from a bivariable function

Question:building a matrix from a bivariable function

Giulianot 25 Maple 2015
matrix multivariate
November 22 2016
0

h1_y_h2.mw
 

(-9.481411*10^(-6)*(T__1(t)+T__1s(t))^2+2.1356735*10^(-3)*(T__1(t)+T__1s(t))+.5599920949)*(.825+.387*(((-(9.8*.11^3*4190)*(4.216485*10^(-2)-7.097451*10^(-3)*(T__1(t)+T__1s(t))+2.63217825*10^(-5)*(T__1(t)+T__1s(t))^2-4.9518879*10^(-8)*(T__1(t)+T__1s(t))^3)/(999.9399+2.1082425*10^(-2)*(T__1(t)+T__1s(t))-1.77436275*10^(-3)*(T__1(t)+T__1s(t))^2+.438696375*10^(-5)*(T__1(t)+T__1s(t))^3-.6189861563*10^(-8)*(T__1(t)+T__1s(t))^4))*((999.9399+2.1082425*10^(-2)*(T__1(t)+T__1s(t))-1.77436275*10^(-3)*(T__1(t)+T__1s(t))^2+.438696375*10^(-5)*(T__1(t)+T__1s(t))^3-.6189861563*10^(-8)*(T__1(t)+T__1s(t))^4)^2))*(T__1(t)-T__1s(t))/((0.178910466924394e-2-(0.593656020810955e-4*(1/2))*(T__1(t)+T__1s(t))+(0.130419399687942e-5*(1/4))*(T__1(t)+T__1s(t))^2-(1.79236416162215*(1/8))*10^(-8)*(T__1(t)+T__1s(t))^3+(1.33479173942873*(1/16))*10^(-10)*(T__1(t)+T__1s(t))^4-(4.03880841196434*(1/32))*10^(-13)*(T__1(t)+T__1s(t))^5)*(-9.481411*10^(-6)*(T__1(t)+T__1s(t))^2+2.1356735*10^(-3)*(T__1(t)+T__1s(t))+.5599920949)))^(1/6)/(1+((.492*(-9.481411*10^(-6)*(T__1(t)+T__1s(t))^2+2.1356735*10^(-3)*(T__1(t)+T__1s(t))+.5599920949))/(4190*(0.178910466924394e-2-(0.593656020810955e-4*(1/2))*(T__1(t)+T__1s(t))+(0.130419399687942e-5*(1/4))*(T__1(t)+T__1s(t))^2-(1.79236416162215*(1/8))*10^(-8)*(T__1(t)+T__1s(t))^3+(1.33479173942873*(1/16))*10^(-10)*(T__1(t)+T__1s(t))^4-(4.03880841196434*(1/32))*10^(-13)*(T__1(t)+T__1s(t))^5)))^(9/16))^(8/27))^2/(.11)

subs({T__1(t) = T__1, T__1s(t) = T__1s}, (-9.481411*10^(-6)*(T__1(t)+T__1s(t))^2+2.1356735*10^(-3)*(T__1(t)+T__1s(t))+.5599920949)*(.825+.387*(((-(9.8*.11^3*4190)*(4.216485*10^(-2)-7.097451*10^(-3)*(T__1(t)+T__1s(t))+2.63217825*10^(-5)*(T__1(t)+T__1s(t))^2-4.9518879*10^(-8)*(T__1(t)+T__1s(t))^3)/(999.9399+2.1082425*10^(-2)*(T__1(t)+T__1s(t))-1.77436275*10^(-3)*(T__1(t)+T__1s(t))^2+.438696375*10^(-5)*(T__1(t)+T__1s(t))^3-.6189861563*10^(-8)*(T__1(t)+T__1s(t))^4))*((999.9399+2.1082425*10^(-2)*(T__1(t)+T__1s(t))-1.77436275*10^(-3)*(T__1(t)+T__1s(t))^2+.438696375*10^(-5)*(T__1(t)+T__1s(t))^3-.6189861563*10^(-8)*(T__1(t)+T__1s(t))^4)^2))*(T__1(t)-T__1s(t))/((0.178910466924394e-2-(0.593656020810955e-4*(1/2))*(T__1(t)+T__1s(t))+(0.130419399687942e-5*(1/4))*(T__1(t)+T__1s(t))^2-(1.79236416162215*(1/8))*10^(-8)*(T__1(t)+T__1s(t))^3+(1.33479173942873*(1/16))*10^(-10)*(T__1(t)+T__1s(t))^4-(4.03880841196434*(1/32))*10^(-13)*(T__1(t)+T__1s(t))^5)*(-9.481411*10^(-6)*(T__1(t)+T__1s(t))^2+2.1356735*10^(-3)*(T__1(t)+T__1s(t))+.5599920949)))^(1/6)/(1+((.492*(-9.481411*10^(-6)*(T__1(t)+T__1s(t))^2+2.1356735*10^(-3)*(T__1(t)+T__1s(t))+.5599920949))/(4190*(0.178910466924394e-2-(0.593656020810955e-4*(1/2))*(T__1(t)+T__1s(t))+(0.130419399687942e-5*(1/4))*(T__1(t)+T__1s(t))^2-(1.79236416162215*(1/8))*10^(-8)*(T__1(t)+T__1s(t))^3+(1.33479173942873*(1/16))*10^(-10)*(T__1(t)+T__1s(t))^4-(4.03880841196434*(1/32))*10^(-13)*(T__1(t)+T__1s(t))^5)))^(9/16))^(8/27))^2/(.11))

9.090909091*(-0.9481411000e-5*(T__1+T__1s)^2+0.2135673500e-2*T__1+0.2135673500e-2*T__1s+.5599920949)*(.825+.387*(-54.6535220*(0.4216485000e-1-0.7097451000e-2*T__1-0.7097451000e-2*T__1s+0.2632178250e-4*(T__1+T__1s)^2-0.4951887900e-7*(T__1+T__1s)^3)*(999.9399+0.2108242500e-1*T__1+0.2108242500e-1*T__1s-0.1774362750e-2*(T__1+T__1s)^2+0.4386963750e-5*(T__1+T__1s)^3-0.6189861563e-8*(T__1+T__1s)^4)*(T__1-T__1s)/((0.178910466924394e-2-0.2968280104e-4*T__1-0.2968280104e-4*T__1s+0.3260484992e-6*(T__1+T__1s)^2-0.2240455202e-8*(T__1+T__1s)^3+0.8342448369e-11*(T__1+T__1s)^4-0.1262127629e-13*(T__1+T__1s)^5)*(-0.9481411000e-5*(T__1+T__1s)^2+0.2135673500e-2*T__1+0.2135673500e-2*T__1s+.5599920949)))^(1/6)/(1+.6710121288*((-0.9481411000e-5*(T__1+T__1s)^2+0.2135673500e-2*T__1+0.2135673500e-2*T__1s+.5599920949)/(7.496348563-.1243709364*T__1-.1243709364*T__1s+0.1366143212e-2*(T__1+T__1s)^2-0.9387507296e-5*(T__1+T__1s)^3+0.3495485867e-7*(T__1+T__1s)^4-0.5288314766e-10*(T__1+T__1s)^5))^(9/16))^(8/27))^2

 (1)

h__1 := proc (T__1, T__1s) options operator, arrow; (-0.9481411000e-5*(T__1+T__1s)^2+0.2135673500e-2*T__1+0.2135673500e-2*T__1s+.5599920949)*(.825+.387*((0.4216485000e-1-0.7097451000e-2*T__1-0.7097451000e-2*T__1s+0.2632178250e-4*(T__1+T__1s)^2-0.4951887900e-7*(T__1+T__1s)^3)*(999.9399+0.2108242500e-1*T__1+0.2108242500e-1*T__1s-0.1774362750e-2*(T__1+T__1s)^2+0.4386963750e-5*(T__1+T__1s)^3-0.6189861563e-8*(T__1+T__1s)^4)*(T__1-T__1s)*(-54.6535220)/((0.178910466924394e-2-0.2968280104e-4*T__1-0.2968280104e-4*T__1s+0.3260484992e-6*(T__1+T__1s)^2-0.2240455202e-8*(T__1+T__1s)^3+0.8342448369e-11*(T__1+T__1s)^4-0.1262127629e-13*(T__1+T__1s)^5)*(-0.9481411000e-5*(T__1+T__1s)^2+0.2135673500e-2*T__1+0.2135673500e-2*T__1s+.5599920949)))^(1/6)/(1+.6710121288*((-0.9481411000e-5*(T__1+T__1s)^2+0.2135673500e-2*T__1+0.2135673500e-2*T__1s+.5599920949)/(7.496348563-.1243709364*T__1-.1243709364*T__1s+0.1366143212e-2*(T__1+T__1s)^2-0.9387507296e-5*(T__1+T__1s)^3+0.3495485867e-7*(T__1+T__1s)^4-0.5288314766e-10*(T__1+T__1s)^5))^(9/16))^(8/27))^2*9.090909091 end proc

proc (T__1, T__1s) options operator, arrow; (-0.9481411000e-5*((T__1+T__1s)^2)+0.2135673500e-2*T__1+0.2135673500e-2*T__1s+.5599920949)*(.825+.387*(((0.4216485000e-1-0.7097451000e-2*T__1-0.7097451000e-2*T__1s+0.2632178250e-4*((T__1+T__1s)^2)-0.4951887900e-7*((T__1+T__1s)^3))*(999.9399+0.2108242500e-1*T__1+0.2108242500e-1*T__1s-0.1774362750e-2*((T__1+T__1s)^2)+0.4386963750e-5*((T__1+T__1s)^3)-0.6189861563e-8*((T__1+T__1s)^4))*(T__1-T__1s)*(-1)*54.6535220/(((0.178910466924394e-2-0.2968280104e-4*T__1-0.2968280104e-4*T__1s+0.3260484992e-6*((T__1+T__1s)^2)-0.2240455202e-8*((T__1+T__1s)^3)+0.8342448369e-11*((T__1+T__1s)^4)-0.1262127629e-13*((T__1+T__1s)^5))*(-0.9481411000e-5*((T__1+T__1s)^2)+0.2135673500e-2*T__1+0.2135673500e-2*T__1s+.5599920949))))^(1/6))/(((1+.6710121288*(((-0.9481411000e-5*((T__1+T__1s)^2)+0.2135673500e-2*T__1+0.2135673500e-2*T__1s+.5599920949)/(7.496348563-.1243709364*T__1-.1243709364*T__1s+0.1366143212e-2*((T__1+T__1s)^2)-0.9387507296e-5*((T__1+T__1s)^3)+0.3495485867e-7*((T__1+T__1s)^4)-0.5288314766e-10*((T__1+T__1s)^5)))^(9/16)))^(8/27))))^2*9.090909091 end proc

 (2)

(-9.481411*10^(-6)*(T__2(t)+T__2s(t))^2+2.1356735*10^(-3)*(T__2(t)+T__2s(t))+.5599920949)*(.825+.387*(((-(9.8*.11^3*4190)*(4.216485*10^(-2)-7.097451*10^(-3)*(T__2(t)+T__2s(t))+2.63217825*10^(-5)*(T__2(t)+T__2s(t))^2-4.9518879*10^(-8)*(T__2(t)+T__2s(t))^3)/(999.9399+2.1082425*10^(-2)*(T__2(t)+T__2s(t))-1.77436275*10^(-3)*(T__2(t)+T__2s(t))^2+.438696375*10^(-5)*(T__2(t)+T__2s(t))^3-.6189861563*10^(-8)*(T__2(t)+T__2s(t))^4))*((999.9399+2.1082425*10^(-2)*(T__2(t)+T__2s(t))-1.77436275*10^(-3)*(T__2(t)+T__2s(t))^2+.438696375*10^(-5)*(T__2(t)+T__2s(t))^3-.6189861563*10^(-8)*(T__2(t)+T__2s(t))^4)^2))*(T__2s(t)-T__2(t))/((0.178910466924394e-2-(0.593656020810955e-4*(1/2))*(T__2(t)+T__2s(t))+(0.130419399687942e-5*(1/4))*(T__2(t)+T__2s(t))^2-(1.79236416162215*(1/8))*10^(-8)*(T__2(t)+T__2s(t))^3+(1.33479173942873*(1/16))*10^(-10)*(T__2(t)+T__2s(t))^4-(4.03880841196434*(1/32))*10^(-13)*(T__2(t)+T__2s(t))^5)*(-9.481411*10^(-6)*(T__2(t)+T__2s(t))^2+2.1356735*10^(-3)*(T__2(t)+T__2s(t))+.5599920949)))^(1/6)/(1+((.492*(-9.481411*10^(-6)*(T__2(t)+T__2s(t))^2+2.1356735*10^(-3)*(T__2(t)+T__2s(t))+.5599920949))/(4190*(0.178910466924394e-2-(0.593656020810955e-4*(1/2))*(T__2(t)+T__2s(t))+(0.130419399687942e-5*(1/4))*(T__2(t)+T__2s(t))^2-(1.79236416162215*(1/8))*10^(-8)*(T__2(t)+T__2s(t))^3+(1.33479173942873*(1/16))*10^(-10)*(T__2(t)+T__2s(t))^4-(4.03880841196434*(1/32))*10^(-13)*(T__2(t)+T__2s(t))^5)))^(9/16))^(8/27))^2/(.11)

subs({T__2(t) = T__2, T__2s(t) = T__2s}, (-9.481411*10^(-6)*(T__2(t)+T__2s(t))^2+2.1356735*10^(-3)*(T__2(t)+T__2s(t))+.5599920949)*(.825+.387*(((-(9.8*.11^3*4190)*(4.216485*10^(-2)-7.097451*10^(-3)*(T__2(t)+T__2s(t))+2.63217825*10^(-5)*(T__2(t)+T__2s(t))^2-4.9518879*10^(-8)*(T__2(t)+T__2s(t))^3)/(999.9399+2.1082425*10^(-2)*(T__2(t)+T__2s(t))-1.77436275*10^(-3)*(T__2(t)+T__2s(t))^2+.438696375*10^(-5)*(T__2(t)+T__2s(t))^3-.6189861563*10^(-8)*(T__2(t)+T__2s(t))^4))*((999.9399+2.1082425*10^(-2)*(T__2(t)+T__2s(t))-1.77436275*10^(-3)*(T__2(t)+T__2s(t))^2+.438696375*10^(-5)*(T__2(t)+T__2s(t))^3-.6189861563*10^(-8)*(T__2(t)+T__2s(t))^4)^2))*(T__2s(t)-T__2(t))/((0.178910466924394e-2-(0.593656020810955e-4*(1/2))*(T__2(t)+T__2s(t))+(0.130419399687942e-5*(1/4))*(T__2(t)+T__2s(t))^2-(1.79236416162215*(1/8))*10^(-8)*(T__2(t)+T__2s(t))^3+(1.33479173942873*(1/16))*10^(-10)*(T__2(t)+T__2s(t))^4-(4.03880841196434*(1/32))*10^(-13)*(T__2(t)+T__2s(t))^5)*(-9.481411*10^(-6)*(T__2(t)+T__2s(t))^2+2.1356735*10^(-3)*(T__2(t)+T__2s(t))+.5599920949)))^(1/6)/(1+((.492*(-9.481411*10^(-6)*(T__2(t)+T__2s(t))^2+2.1356735*10^(-3)*(T__2(t)+T__2s(t))+.5599920949))/(4190*(0.178910466924394e-2-(0.593656020810955e-4*(1/2))*(T__2(t)+T__2s(t))+(0.130419399687942e-5*(1/4))*(T__2(t)+T__2s(t))^2-(1.79236416162215*(1/8))*10^(-8)*(T__2(t)+T__2s(t))^3+(1.33479173942873*(1/16))*10^(-10)*(T__2(t)+T__2s(t))^4-(4.03880841196434*(1/32))*10^(-13)*(T__2(t)+T__2s(t))^5)))^(9/16))^(8/27))^2/(.11))

9.090909091*(-0.9481411000e-5*(T__2+T__2s)^2+0.2135673500e-2*T__2+0.2135673500e-2*T__2s+.5599920949)*(.825+.387*(-54.6535220*(0.4216485000e-1-0.7097451000e-2*T__2-0.7097451000e-2*T__2s+0.2632178250e-4*(T__2+T__2s)^2-0.4951887900e-7*(T__2+T__2s)^3)*(999.9399+0.2108242500e-1*T__2+0.2108242500e-1*T__2s-0.1774362750e-2*(T__2+T__2s)^2+0.4386963750e-5*(T__2+T__2s)^3-0.6189861563e-8*(T__2+T__2s)^4)*(T__2s-T__2)/((0.178910466924394e-2-0.2968280104e-4*T__2-0.2968280104e-4*T__2s+0.3260484992e-6*(T__2+T__2s)^2-0.2240455202e-8*(T__2+T__2s)^3+0.8342448369e-11*(T__2+T__2s)^4-0.1262127629e-13*(T__2+T__2s)^5)*(-0.9481411000e-5*(T__2+T__2s)^2+0.2135673500e-2*T__2+0.2135673500e-2*T__2s+.5599920949)))^(1/6)/(1+.6710121288*((-0.9481411000e-5*(T__2+T__2s)^2+0.2135673500e-2*T__2+0.2135673500e-2*T__2s+.5599920949)/(7.496348563-.1243709364*T__2-.1243709364*T__2s+0.1366143212e-2*(T__2+T__2s)^2-0.9387507296e-5*(T__2+T__2s)^3+0.3495485867e-7*(T__2+T__2s)^4-0.5288314766e-10*(T__2+T__2s)^5))^(9/16))^(8/27))^2

 (3)

h__2 := proc (T__2, T__2s) options operator, arrow; (-0.9481411000e-5*(T__2+T__2s)^2+0.2135673500e-2*T__2+0.2135673500e-2*T__2s+.5599920949)*(.825+.387*((0.4216485000e-1-0.7097451000e-2*T__2-0.7097451000e-2*T__2s+0.2632178250e-4*(T__2+T__2s)^2-0.4951887900e-7*(T__2+T__2s)^3)*(999.9399+0.2108242500e-1*T__2+0.2108242500e-1*T__2s-0.1774362750e-2*(T__2+T__2s)^2+0.4386963750e-5*(T__2+T__2s)^3-0.6189861563e-8*(T__2+T__2s)^4)*(T__2s-T__2)*(-54.6535220)/((0.178910466924394e-2-0.2968280104e-4*T__2-0.2968280104e-4*T__2s+0.3260484992e-6*(T__2+T__2s)^2-0.2240455202e-8*(T__2+T__2s)^3+0.8342448369e-11*(T__2+T__2s)^4-0.1262127629e-13*(T__2+T__2s)^5)*(-0.9481411000e-5*(T__2+T__2s)^2+0.2135673500e-2*T__2+0.2135673500e-2*T__2s+.5599920949)))^(1/6)/(1+.6710121288*((-0.9481411000e-5*(T__2+T__2s)^2+0.2135673500e-2*T__2+0.2135673500e-2*T__2s+.5599920949)/(7.496348563-.1243709364*T__2-.1243709364*T__2s+0.1366143212e-2*(T__2+T__2s)^2-0.9387507296e-5*(T__2+T__2s)^3+0.3495485867e-7*(T__2+T__2s)^4-0.5288314766e-10*(T__2+T__2s)^5))^(9/16))^(8/27))^2*9.090909091 end proc

proc (T__2, T__2s) options operator, arrow; (-0.9481411000e-5*((T__2+T__2s)^2)+0.2135673500e-2*T__2+0.2135673500e-2*T__2s+.5599920949)*(.825+.387*(((0.4216485000e-1-0.7097451000e-2*T__2-0.7097451000e-2*T__2s+0.2632178250e-4*((T__2+T__2s)^2)-0.4951887900e-7*((T__2+T__2s)^3))*(999.9399+0.2108242500e-1*T__2+0.2108242500e-1*T__2s-0.1774362750e-2*((T__2+T__2s)^2)+0.4386963750e-5*((T__2+T__2s)^3)-0.6189861563e-8*((T__2+T__2s)^4))*(T__2s-T__2)*(-1)*54.6535220/(((0.178910466924394e-2-0.2968280104e-4*T__2-0.2968280104e-4*T__2s+0.3260484992e-6*((T__2+T__2s)^2)-0.2240455202e-8*((T__2+T__2s)^3)+0.8342448369e-11*((T__2+T__2s)^4)-0.1262127629e-13*((T__2+T__2s)^5))*(-0.9481411000e-5*((T__2+T__2s)^2)+0.2135673500e-2*T__2+0.2135673500e-2*T__2s+.5599920949))))^(1/6))/(((1+.6710121288*(((-0.9481411000e-5*((T__2+T__2s)^2)+0.2135673500e-2*T__2+0.2135673500e-2*T__2s+.5599920949)/(7.496348563-.1243709364*T__2-.1243709364*T__2s+0.1366143212e-2*((T__2+T__2s)^2)-0.9387507296e-5*((T__2+T__2s)^3)+0.3495485867e-7*((T__2+T__2s)^4)-0.5288314766e-10*((T__2+T__2s)^5)))^(9/16)))^(8/27))))^2*9.090909091 end proc

 (4)

``

``

im trying to build a matrix starting from a function, so i can later use this matrix to get a more simple function using linearfit from the statistics package, like a kind of regression.

i want to get a matrix starting from h__1(T1,T__1s) so it has to be a 3 columns matrix (T__1,T__1s,h__1). so as you can see, i have got the functions h__1 and h__2, but i need to evaluate it at differents values for T__1 and T__1s and building a kind of value-table in matrix form.

for h__1, T__1 must be higher than T__1s, or you could get imaginary values, don't know if that important for building the matrix.

thank you very much for your help.

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