How to add function argument for nthroot() ?

Question

Life is Wonderful 2021-11-28

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1597564-how-to-add-function-argument-for-nthroot

评论： Walter Roberson 2021-12-15

采纳的回答： Walter Roberson

在 MATLAB Online 中打开

Hi

I want to calculate nthroot() for 'embedded.fi', following is the code.

I don't understand , how to fix rem(n(:),2) ? / reminder after division

There is claimed fix https://in.mathworks.com/matlabcentral/answers/100386-why-do-i-receive-an-error-when-i-use-the-nthroot-function-within-matlab#answer_109734 from MathWorks Staff

x = fi(1,0,32,31);
n = fi(1,0,32,31);
if isreal(x) || isreal(n)
    nroot = nthroot(x, n);
end
Check for incorrect argument data type or missing argument in call to function 'rem'.

Error in nthroot (line 27)
if any((x(:) < 0) & (n(:) ~= fix(n(:)) | rem(n(:),2)==0))
rem(1,1) is 0 

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Walter Roberson 2021-11-28

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1597564-how-to-add-function-argument-for-nthroot#answer_842024

在 MATLAB Online 中打开

That fix you link to has no relationship to your current difficulty.

https://www.mathworks.com/help/matlab/ref/nthroot.html#buchym2-X

Data Types: single | double

Notice that fi is not listed. The nthroot() function is not defined for fixed point objects.

x = fi(1,0,32,31);
n = fi(1,0,32,31);
if isreal(x) && isreal(n)
   nroot = sign(x) .* abs(x).^(1./n);
else
   nroot = x .^ (1./n);
end
nroot
nroot = 
     1

          DataTypeMode: Fixed-point: binary point scaling
            Signedness: Signed
            WordLength: 40
        FractionLength: 31

16 个评论
显示 14更早的评论隐藏 14更早的评论

Walter Roberson 2021-11-29

在 MATLAB Online 中打开

If the root to be taken is not fixed, and is not one out of a small list, then:

If you know your maximum range of x values, and your maximum root, you can use a taylor expansion on x^(1/n) to get any desired (fixed) degree of accuracy, in the form of a polynomial. For example,

syms x real

syms n integer

assumeAlso(n, 'positive');

T = taylor(x^(1/n), x, 'ExpansionPoint', 512, 'Order', 10)

T =

Tx = collect(simplify(T), x)

Tx =

misfit = subs(Tx, n, 10) - x^(1/sym(10))

misfit =

fplot(misfit, [0 1024])

vpa(subs(misfit,x,1))

ans =

0.3975946820153549595981366392819

You can see that degree 10 expansion with n = 10 is not all that accurate for x = 1 (and is worse at 0) so you might need to use a higher order polynomial in the taylor expansion; also a higher order would probably be needed if your maximum n is above 10, or if your range of values is more than 1000.

The main benefit of this approach is that it fixes the amount of work to be done, which could be important for VHDL purposes.

You could probably get a more accurate result faster using some kind of loop.

Life is Wonderful 2021-11-29

编辑：Life is Wonderful 2021-11-29

在 MATLAB Online 中打开

Sorry, I didn't understand fixed vs dynamic!!

I consider root as square ,cube and it goes on from Max to Min number . Return root needs fixed word length otherwise we have truncated value

WL = 32;
fprintf('%10s|%30s|\n----------+------------------------------+\n','power', 'root');
     power|                          root|
----------+------------------------------+
for i = 1:WL % Num bits in Wordlength
        fprintf('%10d|%30.10f|\n',i, nthroot(2^WL,i))
end
         1|         4294967296.0000000000|
         2|              65536.0000000000|
         3|               1625.4986772154|
         4|                256.0000000000|
         5|                 84.4485062895|
         6|                 40.3174735966|
         7|                 23.7759086262|
         8|                 16.0000000000|
         9|                 11.7578759382|
        10|                  9.1895868400|
        11|                  7.5114472853|
        12|                  6.3496042079|
        13|                  5.5080378048|
        14|                  4.8760546168|
        15|                  4.3872999188|
        16|                  4.0000000000|
        17|                  3.6867585638|
        18|                  3.4289759314|
        19|                  3.2136449063|
        20|                  3.0314331330|
        21|                  2.8754933949|
        22|                  2.7407019694|
        23|                  2.6231573457|
        24|                  2.5198420998|
        25|                  2.4283897688|
        26|                  2.3469209200|
        27|                  2.2739258102|
        28|                  2.2081790273|
        29|                  2.1486764788|
        30|                  2.0945882456|
        31|                  2.0452228712|
        32|                  2.0000000000|

Another question is , for negative base value

example nthroot(-1 * (2^32),i) - what is the formula

Walter Roberson 2021-12-14

在 MATLAB Online 中打开

What? No!

Preparation, not to be deployed

syms x real
syms n integer
assumeAlso(n, 'positive');
T = taylor(x^(1/n), x, 'ExpansionPoint', 512, 'Order', 10);
Tfun = matlabFunction(T, 'vars', x, 'File', 'nthrootTaylor.m', 'optimize', false);
Tfun_opt = matlabFunction(T, 'vars', x, 'File', 'nthrootTaylor_opt.m', 'optimize', true);
x_example = fi(0,0,32,27);    % x can be negative as well, but start with positive numbers
n_example = fi(0,0,32,30);           % n can be negative as well, but start with positive numbers
codegen nthrootTaylor.m -args {x_example, n_example} ...
    -o nthrootTaylor_fixedpoint_mex -config:mex
codegen nthrootTaylor_opt.m -args {x_example, n_example} ...
    -o nthrootTaylor_opt_fixedpoint_mex -config:mex

Once code is generated then for deployment

x = fi(linspace(0,31.99999,10),0,32,27);    % x can be negative as well, but start with positive numbers
n = fi(linspace(0,3,10),0,32,30);           % n can be negative as well, but start with positive numbers
num_x = length(x);
num_n = length(n);
results = fi(zeros(num_x, num_n),0,32,30);
results_opt = fi(zeros(num_x, num_n),0,32,30);
for nidx = 1 : num_n
    for xidx = 1 : num_x
        results(xidx,nidx) = nthrootTaylor(x(xidx), n(nidx) );
        results_opt(xidx,nidx) = nthrootTaylor_opt(x(xidx), n(nidx) );
    end
end

now compare results to results_opt to verify whether the optimized version produces results that are acceptable quality compared to the non-optimized version.

At the moment, I do not know whether the code that would be generated would have looped over vector n and vector x -- and I didn't want to have to look up how to signal to codegen to expect arrays.

At the moment i do not know what fi would be used for the results, so I had to fill in something.

Life is Wonderful 2021-12-14

编辑：Life is Wonderful 2021-12-14

在 MATLAB Online 中打开

Still no success in codegen !! Also I have think fi object is not working

syms x real
syms n integer
assumeAlso(n, 'positive');
T = taylor(x^(1/n), x, 'ExpansionPoint', 512, 'Order', 10);
Tfun = matlabFunction(T, 'vars', x, 'File', 'nthrootTaylor.m', 'optimize', false);
Error using sym/matlabFunction>checkVarsSubset (line 253)
Free variable 'n' must be included in 'Vars' value.

Error in sym/matlabFunction>checkVars (line 240)
checkVarsSubset(vexpanded,funvars);

Error in sym/matlabFunction (line 158)
vars = checkVars(funvars,opts);
Tfun_opt = matlabFunction(T, 'vars', x, 'File', 'nthrootTaylor_opt.m', 'optimize', true);
x_example = fi(0,0,32,27);    % x can be negative as well, but start with positive numbers
n_example = fi(0,0,32,30);           % n can be negative as well, but start with positive numbers
codegen nthrootTaylor.m -args {x_example, n_example} ...
    -o nthrootTaylor_fixedpoint_mex -config:mex
codegen nthrootTaylor_opt.m -args {x_example, n_example} ...
    -o nthrootTaylor_opt_fixedpoint_mex -config:mex

x = fi(linspace(0,31.99999,10),0,32,27);    % x can be negative as well, but start with positive numbers
n = fi(linspace(0,3,10),0,32,30);           % n can be negative as well, but start with positive numbers
num_x = length(x);
num_n = length(n);
results = fi(zeros(num_x, num_n),0,32,30);
results_opt = fi(zeros(num_x, num_n),0,32,30);
for nidx = 1 : num_n
    for xidx = 1 : num_x
        results(xidx,nidx) = nthrootTaylor(x(xidx), n(nidx) );
        results_opt(xidx,nidx) = nthrootTaylor_opt(x(xidx), n(nidx) );
    end
end

I tried with and without fi object verification . I think there is an issue

Output argument "Tfun" (and possibly others) not assigned a value in the execution with "pow_taylor_v1>nthrootTaylor" function.

Error in pow_taylor_v1 (line 14)

results(xidx,nidx) = nthrootTaylor(x(xidx), n(nidx) );

clearvars;clc;
x = fi(linspace(0,31.99999,10),0,32,27);    % x can be negative as well, but start with positive numbers
n = fi(linspace(0,3,10),0,32,30);           % n can be negative as well, but start with positive numbers
% x = linspace(0,31.99999,10)
% n = linspace(0,3,10)
num_x = length(x);
num_n = length(n);
results = fi(zeros(num_x, num_n),0,32,30);
results_opt = fi(zeros(num_x, num_n),0,32,30);
for nidx = 1 : num_n
    for xidx = 1 : num_x
        results(xidx,nidx) = nthrootTaylor(x(xidx), n(nidx) );
%         results(xidx,nidx) = nthroot(x(xidx), n(nidx) )
%         results_opt(xidx,nidx) = nthrootTaylor_opt(x(xidx), n(nidx) );
    end
end
function [Tfun] = nthrootTaylor(x,n)
% syms x real
% syms n integer
% assumeAlso(n, 'positive');
T = taylor(x^(1/n), x, 'ExpansionPoint', 512, 'Order', 10);
end

Life is Wonderful 2021-12-14

编辑：Life is Wonderful 2021-12-14

在 MATLAB Online 中打开

still there is an issue!! codegen is unsuccessful

Please ignore the editor error since it is unsupported

syms x real
syms n integer
assumeAlso(n, 'positive');
T = taylor(x^(1/n), x, 'ExpansionPoint', 512, 'Order', 12);
Tfun = matlabFunction(T, 'vars', {x, n}, 'File', 'nthrootTaylor.m', 'optimize', false);
Tfun_opt = matlabFunction(T, 'vars', {x, n}, 'File', 'nthrootTaylor_opt.m', 'optimize', true);
x_example = fi(0,0,32,27);    % x can be negative as well, but start with positive numbers
n_example = fi(0,0,32,30);           % n can be negative as well, but start with positive numbers

codegen nthrootTaylor.m -args {x_example, n_example} ...
    -o nthrootTaylor_fixedpoint_mex -config:mex
??? The computed word length of the result is 142 bits. This exceeds the maximum supported wordlength of 128 bits.
Unable to run the 'fevalJSON' function because it calls the 'codegen' function, which is not supported for this product offering.
codegen nthrootTaylor_opt.m -args {x_example, n_example} ...
    -o nthrootTaylor_opt_fixedpoint_mex -config:mex
??? Function 'exp' is not defined for values of class 'embedded.fi'.

Walter Roberson 2021-12-15

This does not astonish me. When you have a series of expressions that are not being stored into a variable with defined fixed point characteristics, then the Fixed Point Toolbox dynamically expands the word length in order to try to preserve precision.

I suspect it might be possible to attach behaviour to the fi() so that the output results of expressions does not automatically expand for precision, but that is not something I have researched.

One approach would be to break up the expression into smaller segments that you assign into variables that you have set the precision for.

For example if you were to take children(T) then you would get a cell array of terms that are to be added together. You could then vertcat() the cell expansion to turn it into a vector, and you could compute the vector in the generated code, and fi() the results and sum() them.

You would still have some difficulty -- the individual term for the derivative to the 9th power would want to blow up the precision.

Probably it would be more rigourous to calculate the terms in a loop, applying fi() at each step.

But... really I think this approach is a dead end. Look at the precision loss near 0 or 1 !!!

请先登录，再进行评论。

How to add function argument for nthroot() ?

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

采纳的回答

16 个评论
显示 14更早的评论隐藏 14更早的评论

更多回答（0 个）

另请参阅

类别

标签

产品

版本

Community Treasure Hunt

How to add function argument for nthroot() ?

0 个评论 显示 -2更早的评论隐藏 -2更早的评论

采纳的回答

16 个评论 显示 14更早的评论隐藏 14更早的评论

更多回答（0 个）

另请参阅

类别

标签

产品

版本

Community Treasure Hunt

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

16 个评论
显示 14更早的评论隐藏 14更早的评论