z=f(x,y) and w=f(x,y). I am trying to reverse the table to get x=f(z,w) and y=f(z,w).

Hello,

I have a 2 lookup tables with same X and Y but the outputs are Z and W. Basicaly I have a z=f(x,y) and w=f(x,y). I am trying to reverse the table to get x=f(z,w) and y=f(z,w). what is the best way of doing that in Matlab. the table data is in this format:

[Torsten]

Is your mapping, defined by the two functions (z,w) = ( f1(x,y), f2(x,y) ), invertible (like e.g. the transformation from cartesian to polar coordinates) ?

[Sobhi Zeidan]

This is motor current output as a function of flux. It's a 64x128 table

[Torsten]

This is motor current output as a function of flux.

And why do you have two inputs and two outputs then ? Sounds like one input and one output.

[Sobhi Zeidan]

2 inputs 1 output.

[Torsten]

FluxQ=Iq x Lq(inductance) FlusD= FluxPM + Id x Lq

If you have equations z = f1(x,y) and w = f2(x,y), why don't you solve for x and y given z and w ?

Two equations in two unknowns.

Answer 1

[John D'Errico]

In general, this is often impossible. That is so for good reasons too.

The problem is, IF you have any instances where the responses would not be a single valued function, then it would fail. For example:

syms x y
z = x.^2 + y.^2;
fsurf(z)

For any value of z and x, you can find two values of y. So the coutours of z here are circles in the (x,y) plane, and so there is no unique way to invert this function in a table.

But we can look at your problem. Does that data suffer from any issues that would cause failure? Some contour plots will help us there.

A=[17.9 18.0 18.1 18.2]';
B=[0.4  0.5  0.6  0.7];
C=[67   89   95   108
    74   92   110  123
    80   97   115  127
    84   106  119  135];
D=[40   65   80   95
    50   72   85  103
    60   93   97  110
    70   100  103  127];
contour(A,B,C)

contour(A,B,D)

So there are no overtly problematic contours that I see. There are no circular contours. There are no places where a contour is u-shaped. So does that mean a solution MUST exist? There are still problems.

We can use these contour plots to understand what is happening. I've picked out two contour levels that will be problematic for you.

contour(A,B,D,[80 80],'r')
hold on
contour(A,B,C,[100 100],'b')
hold off
legend('D == 80','C == 100')
grid on

Do you see what I did? The contour plot of D==80 and that of C==100, cross at TWO distinct points in the (A,B) plane. And that means there is no inverse for your problem. You CANNOT use a scattered interpolant here. There is no unique solution.

[Sobhi Zeidan]

Thank you for the response. Assuming the Data has a one to one correspondence , How do i get what I am looking for? This is random data that I put together. the equation is a linear equation and should have a one to one correspondence .

[Torsten]

the equation is a linear equation and should have a one to one correspondence .

As noted above, if you have equations, you can solve for the unknowns.

syms x y z w
eqn1 = z == 3*x+5*y+7;
eqn2 = w == -4*x+8*y-12;
solve([eqn1 eqn2],[x y])

ans = struct with fields:
    x: (2*z)/11 - (5*w)/44 - 29/11
    y: (3*w)/44 + z/11 + 2/11

Answer 2

[Star Strider]

Apparently, X, Y, Z and W are all equal-sized matrices. Assuming that there is essentially a one-to-one correspondence between the matrices, it could be possible to do this with the scatteredInterpolant function. Everything essentially depends on the functions that create Z and W.

[Sobhi Zeidan]

This is motor current output as a function of flux. It's a 64x128 table

[Star Strider]

Thank you.

What do the calculations involve that produce the Z, W output matrices from the X, Y input matrices?

What are the actual data in the matrices?

Please post a relevant example of the matrices and the calculations.

[Sobhi Zeidan]

X is fluxD and y is fluxQ. Z is Current Id and w is current Iq

FluxQ=Iq x Lq(inductance) FlusD= FluxPM + Id x Lq

FluxPM is a constant

I cannot post data. Thank you so much for the input

[Star Strider]

Can you post the code (or at least the equations) and a range of what the X, Y data should be?

[Sobhi Zeidan]

So after trying to understand how the data moves around with interp1 and interp2, I came up with this code. I am stuck at the final step of the code. I am trying to get the data in the format of X=f(z,w) and Y=f(z,w).

%%%%%%%%%%%%%%%%%%%

% --------------

% A-----> | |

% | |

% | |-----> C

% B-----> | |

% --------------

%

% --------------

% A-----> | |

% | |

% | |-----> D

% B-----> | |

% --------------

A=[17.9 18.0 18.1 18.2]';

B=[0.4 0.5 0.6 0.7];

C=[67 89 95 108

74 92 110 123

80 97 115 127

84 106 119 135];

D=[40 65 80 95

50 72 85 103

60 93 97 110

70 100 103 127];

%Min and Max of C data

C_Data = 67:4:135;

%Min and Max of D data

D_Data = 40:4:127;

%These for loops will get Data for

%%%%%%%%%%%%%%%%%%%

% --------------

% C-----> | |

% | |

% | |-----> A

% B-----> | |

% --------------

%

% --------------

% A-----> | |

% | |

% | |-----> B

% D-----> | |

% --------------

for i=1:length(B)

for j=1:length(C_Data)

%table Data for B column at given index. This gives the value of C

%for the specific B column

B_Data=interp2(A,B,C',A,B(1));

%get the value of A for the given B and C value

A_Data(j,i)=interp1(B_Data,A,C_Data(j),'linear','extrap');

end

end

A_Output=A_Data;

for i=1:length(A)

for j=1:length(D_Data)

%table Data for Row A at given index. This gives the value of D

%for the specific Row A

A_Data=interp2(A,B,C',A(i),B);

%get the value of B for the given A and D value

B_Data(i,j)=interp1(A_Data,B,D_Data(j),'linear','extrap');

end

end

B_Output=B_Data;

%How Can I get this Data

%%%%%%%%%%%%%%%%%%%

% --------------

% C-----> | |

% | |

% | |-----> A

% D-----> | |

% --------------

%

% --------------

% C-----> | |

% | |

% | |-----> B

% D-----> | |

%

[John D'Errico]

Sorry. There is no one-one correspondence for that data.