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vector gives 0 integral
조회 수: 1 (최근 30일)
이전 댓글 표시
Hello
I have plotted a vector which has 3 planes.. When I integrate the integral is 0. There are negative regions, yet I expect a number. I us
sd = trapz((z),0,20)
sd =
0
will someone tell me if there is an error with my use of trapz?
sr
채택된 답변
Star Strider
2021년 7월 28일
There quite definitely is!
In your call to it:
sd = trapz((z),0,20)
the function interprets ‘z’ (the parentheses aren’t necessary) as the indepdent variable ‘x’, 0 as the dependent variable ‘y’, and 20 as the dimension. Integrating 0 produces 0 as the result.
.
댓글 수: 30
John D'Errico
2021년 7월 28일
My guess is, @Gavin Seddon was thinking the 0 and 20 were the limits of integration. Of course that is not how trapz works.
Star Strider
2021년 7월 29일
If you want to define a range of integration with trapz (or cumtrapz), do something like this:
x = linspace(-50, 50, 250);
z = sin(2*pi*x).^2; % 'z' Is A Vector
intRange = (x>=0) & (x<=20);
int_y = trapz(x(intRange), z(intRange))
int_y = 9.6166
or something similar.
int_y = integral(@(x)sin(2*pi*x).^2, 0, 20) % 'z' Is A Function
int_y = 10.0000
.
Gavin Seddon
2021년 8월 22일
Hello
When I
x = linspace(-50, 50, 350);
>>
>> int_y = trapz(x(intRange), z(intRange))
int_y =
0
Is this becausse my originall fun is scala r?
Gav
Star Strider
2021년 8월 22일
I have no idea.
Another possibility is that there were no values in that range.
Star Strider
2021년 8월 23일
I have no idea what ‘y’ is, or what ‘z’ is.
In any event, trapz integrates vectors, and int integrates symbolic functions.
A bit more information would be helpful.
.
Gavin Seddon
2021년 8월 24일
Hello StSt
Yes that is what I meat by a I n"scaler" fun and so not a vector.
This is actually encouraging since it assists the explanation.
As usual your comment was helpful.
G
Gavin Seddon
2021년 10월 19일
Hello
When I try tog do a func
int_y = integral(@(x)(x*6.4985e-4-x^2*2.8208e-7+x^3*3.9742e-11+2.4178), 0, 5000)
Error using ^ (line 51)
Incorrect dimensions for raising a matrix to a power. Check that the matrix is square and the power is a
scalar. To perform elementwise matrix powers, use '.^'.
Error in @(x)(x*6.4985e-4-x^2*2.8208e-7+x^3*3.9742e-11+2.4178)
Error in integralCalc/iterateScalarValued (line 314)
fx = FUN(t);
Error in integralCalc/vadapt (line 132)
[q,errbnd] = iterateScalarValued(u,tinterval,pathlen);
Error in integralCalc (line 75)
[q,errbnd] = vadapt(@AtoBInvTransform,interval);
Error in integral (line 87)
Q = integralCalc(fun,a,b,opstruct);
>> G
Star Strider
2021년 10월 19일
Try this —
int_y = integral(@(x)(x*6.4985e-4-x.^2*2.8208e-7+x.^3*3.9742e-11+2.4178), 0, 5000)
int_y = 1.4668e+04
Note — All the (^) are now (.^). No other element-wise operations are necessary. See Array vs. MAtrix Operations for an extended discussion.
.
Star Strider
2021년 10월 20일
As always, my pleasure!
You can use syms if you wish, however I see no significant advantage to doing that.
syms x
int_y = int((x*6.4985e-4-x^2*2.8208e-7+x^3*3.9742e-11+2.4178), x, 0, 5000)
int_y =
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/773113/image.png)
int_y = vpa(int_y, 42)
int_y =
14668.4791666666669207137336884483073976583
int_y = vpaintegral((x*6.4985e-4-x^2*2.8208e-7+x^3*3.9742e-11+2.4178), x, 0, 5000)
int_y =
14668.5
.
Gavin Seddon
2021년 10월 21일
Yes you see I store all sym
I tried
vpa int_y
ans =
int_y
>> int_y = vpa(int_y, 42)
int_y =
0.00000000000993550000000000022516417793009971867052021*x^4 - 0.0000000940266666666666651222878924957597016979586*x^3 + 0.000324924999999999996810884361764237837633118*x^2 + 2.4178*x
>>
>> but I need the 14668.5 only as ans
also
is it valid to int adiff this has mu ch biochem relevance?
thank you
g
Star Strider
2021년 10월 21일
The integrand must be different from what was originally posted.
The integral should not also be a function of ‘x’, if it was integrated with respect to ‘x’.
What changed, and what is the objective?
Should this be a double integral, and if so, with respect to what variables?
Details — and the code that created those results — are important.
I cannot go farther with this until I have more information about it.
.
Gavin Seddon
2021년 10월 22일
Hello
y is the deviation change
v is its diff (==motion)
y_int its int
v_int is the total amount of motion
g
Star Strider
2021년 10월 22일
I still do not understand this Comment. I have no idea how those results were calculated, so I cannot help with the code to get the desired result.
What integrand produced that integrated result? What were the limits of integration?
Post that code and I will see if I can produce the desired result. Note that the elements of that vector are all functions of ‘x’ so the integral must have been with respect to a different variable.
.
Gavin Seddon
2021년 10월 23일
The code is here, I neeed to get nums for the syms.The bioPhys is ok. My apologiies the params were forgtfully modified.
g
Star Strider
2021년 10월 23일
I’m sorry, however I still don’t understand.
It would appear that it is only necessary to provide values for whatever ‘x’ is to create numerical data from the ‘int_v’ and ‘int_y’ expressions. I have no idea what those ‘x’ values would be, however creating them as symbolic functions would make this straightforward (and avoids the use of the subs function) —
syms x
int_y(x) = 0.00000000000993550000000000022516417793009971867052021*x^4-0.000000094026666666666665122288924957597016979586*x^3 + 0.000324924999999999996810884361764237837633118*x^2 + 2.4178*x;
x = sym(0:10:100);
int_y_val = vpa(int_y(x), 5)
int_y_val = ![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/776513/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/776513/image.png)
figure
fplot(int_y, [0 100])
grid
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/776518/image.png)
I have no idea if this is the desired direction for this problem, however it is the only one I can think of.
.
Gavin Seddon
2021년 10월 24일
Hello
It is perfectly ok, you have helped alot and provided new considderations.
I havve now reproduced your calc. Your plot is familiar.
Another calc yields interesting results,
x=30;
>> diff(y)
ans =
(4612332472619961*x^2)/38685626227668133590597632 - (2664170274975739*x)/4722366482869645213696 + 1498452079537519/2305843009213693952
>> v0=diff(y)
v0 =
(4612332472619961*x^2)/38685626227668133590597632 - (2664170274975739*x)/4722366482869645213696 + 1498452079537519/2305843009213693952
>> vpa(v0)
ans =
0.0000000001192260000000000027019701351612*x^2 - 0.00000056415999999999999073372735497456*x + 0.00064984999999999999362176872352848
>> how do I make tthis an integer?
g.
Star Strider
2021년 10월 24일
It is not possible to make it an integer as long as it has symbolic variables in it. They have to be evaluated first.
x=30;
% >> diff(y)
%
% ans =
%
% (4612332472619961*x^2)/38685626227668133590597632 - (2664170274975739*x)/4722366482869645213696 + 1498452079537519/2305843009213693952
%
% >> v0=diff(y)
v0 = (4612332472619961*x^2)/38685626227668133590597632 - (2664170274975739*x)/4722366482869645213696 + 1498452079537519/2305843009213693952
v0 = 6.3303e-04
Result = vpa(v0) % Substitution For 'x' Is Implied, So Is Done Automatically
Result =
0.00063303250340000002255314015542353
% ans =
%
% 0.0000000001192260000000000027019701351612*x^2 - 0.00000056415999999999999073372735497456*x + 0.00064984999999999999362176872352848
This produces both double and symbolic results.
.
Star Strider
2021년 10월 25일
That value of ‘v0’ exists in the workspace.
x=30;
v0 = (4612332472619961*x^2)/38685626227668133590597632 - (2664170274975739*x)/4722366482869645213696 + 1498452079537519/2305843009213693952
v0 = 6.3303e-04
To print it using the largest available precision, use —
fprintf('%23.15E',v0)
6.330325034000000E-04
There are any number of ways to write it to a file. Please refer to the appropriate parts of the documentation for that.
.
Gavin Seddon
2021년 11월 3일
Hello
how's this fixed
'Error using fprintf
Conversion to double from sym is not possible.
>> '
g.
Star Strider
2021년 11월 3일
I’m not certain what argument to fprintf is throuwing that error. One possible fix is to use the double funciton, however that won’t work if there are any symbolic variables in the expression to be printed. In that evernt, evaluate the expression first, with numeric values of all the variables previously defined.
.
Gavin Seddon
2021년 11월 3일
Thx
the result is
con = eval(vecInt)
con =
344*sin((500436125687261696*sin((16940918583*cos((16940918583*cos((16940918583*cos((153639*cos((144125604197931365568*cos((1484049123*cos((16940918583*cos((16940918583*cos((16940918583*cos((3573*x)/10000 + 13/8))/10000000000 + 13/8))/10000000000 + 13/8))/10000000000 + 13/8))/200000000 - 1689/2000)*sin((16940918583*cos((16940918583*cos((3573*x)/10000 + 13/8))/10000000000 + 13/8))/10000000000 + 13/8)*sin((16940918583*cos((16940918583*cos((16940918583*cos((3573*x)/10000 + 13/8))/10000000000 + 13/8))/10000000000 + 13/8))/10000000000 + 13/8))/59604644775390625 + (3267773954505189164*sin((16940918583*cos((16940918583*cos((3573*x)/10000 + 13/8))/10000000000 + 13/8))/10000000000 + 13/8)*cos((8766794979*cos((16940918583*cos((16940918583*cos((16940918583*cos((3573*x)/10000 + 13/8))/10000000000 + 13/8))/10000000000 + 13/8))/10000000000 + 13/8))/2500000000 + 441/250)*sin((16940918583*cos((16940918583*cos((16940918583*cos((3573*x)/10000 + 13/8))/10000000000 + 13/8))/10000000000 + 13/8))/10000000000 + 13/8))/48506384094556175 + (5685004955689819712*sin((16940918583*cos((16940918583*cos((3573*x)/10000 + 13/8))/10000000000 + 13/8))/10000000000 + 13/8)*sin((16940918583*cos((16940918583*cos((16940918583*cos((3573*x)/10000 + 13/8))/10000000000 + 13/8))/10000000000 + 13/8))/10000000000 + 13/8)*cos((7458176583*cos((16940918583*cos((16940918583*cos((16940918583*cos((3573*x)/10000 + 13/8))/10000000000 + 13/8))/10000000000 + 13/8))/10000000000 + 13/8))/1000000000 + 1153/500))/2384185791015625 - 1689/2000)*((39120558738952133773605350221763784105679225592077737*sin((16940918583*cos((3573*x)/10000 + 13/8))/10000000000 + 13/8)*cos((1484049123*cos((16940918583*cos((16940918583*cos((16940918583*cos((3573*x)/10000 + 13/8))/10000000000 + 13/8))/10000000000 + 13/8))/10000000000 + 13/8))/200000000 - 1689/2000)*sin((16940918583*cos((16940918583*cos((3573*x)/10000 + 13/8))/10000000000 + 13/8))/10000000000 + 13/8)^2*sin((3573*x)/10000 + 13/8)*cos((16940918583*cos((16940918583*cos((16940918583*cos((3573*x)/10000 + 13/8))/10000000000 + 13/8))/10000000000 + 13/8))/10000000000 + 13/8))/9313225746154785156250000000000000000000000000000 + (11508730420873628018762065388876926714218419394751687105048989*sin((16940918583*cos((3573*x)/10000 + 13/8))/10000000000 + 13/8)*sin((16940918583*cos((16940918583*cos((3573*x)/10000 + 13/8))/10000000000 + 13/8))/10000000000 + 13/8)^2*sin((3573*x)/10000 + 13/8)*sin((16940918583*cos((16940918583*cos((16940918583*cos((3573*x)/10000 + 13/8))/10000000000 + 13/8))/10000000000 + 13/8))/10000000000 + 13/8)^2*sin((7458176583*cos((16940918583*cos((16940918583*cos((16940918583*cos((3573*x)/10000 + 13/8))/10000000000 + 13/8))/10000000000 + 13/8))/10000000000 + 13/8))/1000000000 + 1153/500))/372529029846191406250000000000000000000000000000000000000 - (91087294002736535382844815295133583863901*sin((16940918583*cos((3573*x)/10000 + 13/8))/10000000000 + 13/8)*cos((16940918583*cos((16940918583*cos((3573*x)/10000 + 13/8))/10000000000 + 13/8))/10000000000 + 13/8)*sin((3573*x)/10000 + 13/8)*sin((16940918583*cos((16940918583*cos((16940918583*cos((3573*x)/10000 + 13/8))/10000000000 + 13/8))/10000000000 + 13/8))/10000000000 + 13/8)*cos((7458176583*cos((16940918583*cos((16940918583*cos((16940918583*cos((3573*x)/10000 + 13/8))/10000000000 + 13/8))/10000000000 + 13/8))/10000000000 + 13/8))/1000000000 + 1153/500))/37252902984619140625000000000000000000 + (14191748220645224846328784005214282029379497389876241*sin((16940918583*cos((3573*x)/10000 + 13/8))/10000000000 + 13/8)*sin((16940918583*cos((16940918583*cos((3573*x)/10000 + 13/8))/10000000000 + 13/8))/10000000000 + 13/8)^2*cos((8766794979*cos((16940918583*cos((16940918583*cos((16940918583*cos((3573*x)/10000 + 13/8))/10000000000 + 13/8))/10000000000 + 13/8))/10000000000 + 13/8))/2500000000 + 441/250)*sin((3573*x)/10000 + 13/8)*cos((16940918583*cos((16940918583*cos((16940918583*cos((3573*x)/10000 + 13/8))/10000000000 + 13/8))/10000000000 + 13/8))/10000000000 + 13/8))/121265960236390437500000000000000000000000000000000 + (58056830887811900065697700544716399315194594059242121342674651*sin((16940918583*cos((3573*x)/10000 + 13/8))/10000000000 + 13/8)*sin((1484049123*cos((16940918583*cos((16940918583*cos((16940918583*cos((3573*x)/10000 + 13/8))/10000000000 + 13/8))/10000000000 + 13/8))/10000000000 + 13/8))/200000000 - 1689/2000)*sin((16940918583*cos((16940918583*cos((3573*x)/10000 + 13/8))/10000000000 + 13/8))/10000000000 + 13/8)^2*sin((3573*x)/10000 + 13/8)*sin((16940918583*cos((16940918583*cos((16940918583*cos((3573*x)/10000 + 13/8))/10000000000 + 13/8))/10000000000 + 13/8))/10000000000 + 13/8)^2)/1862645149230957031250000000000000000000000000000000000000 + (1543102431646143825120272750838531160347349393772283*sin((16940918583*cos((3573*x)/10000 + 13/8))/10000000000 + 13/8)*sin((16940918583*cos((16940918583*cos((3573*x)/10000 + 13/8))/10000000000 + 13/8))/10000000000 + 13/8)^2*sin((3573*x)/10000 + 13/8)*cos((16940918583*cos((16940918583*cos((16940918583*cos((3573*x)/10000 + 13/8))/10000000000 + 13/8))/10000000000 + 13/8))/10000000000 + 13/8)*cos((7458176583*cos((16940918583*cos((16940918583*cos((16940918583*cos((3573*x)/10000 + 13/8))/10000000000 + 13/8))/10000000000 + 13/8))/10000000000 + 13/8))/1000000000 + 1153/500))/372529029846191406250000000000000000000000000000 - (2309234800184278400153465292275986384491039*sin((16940918583*cos((3573*x)/10000 + 13/8))/10000000000 + 13/8)*cos((1484049123*cos((16940918583*cos((16940918583*cos((16940918583*cos((3573*x)/10000 + 13/8))/10000000000 + 13/8))/10000000000 + 13/8))/10000000000 + 13/8))/200000000 - 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1689/20... Output truncated. Text exceeds maximum line length for Command Window display.
>> fprintf('%23.15E',con)
Error using fprintf
Conversion to double from sym is not possible.
>>
Star Strider
2021년 11월 3일
That expression is a function of ‘x’, so provide a value for it (scalar, vector, using subs if necessary), evaluate it, then print the double result as a funciton of the values of ‘x’.
.
추가 답변 (3개)
Gavin Seddon
2021년 7월 29일
Hello
Yes John is correct, I tried with no parenth and I see the fun integral not its value which is wht I need.
댓글 수: 4
Gavin Seddon
2021년 7월 29일
Hello
Spot on, thank you. My integral is 9.6 which is + and I expected -. I assume the change is due to the measurement of multiple planes.
Star Strider
2021년 7월 29일
As always, my pleasure!
I am not certain what function you are integrating. The difference in the values in my example is due to the trapz function using trapezoidal integration on a finite-resolution vector, and the integral call doing a much finer adaptive numerical integration of the function provided to it.
.
Gavin Seddon
2021년 7월 29일
Hello
It is a cubic fun of an object moving in 3D space and from your description trapezoidal integration does a better job in 3D than int.
Gavin Seddon
2021년 7월 29일
Hello
When I searched 'vector integration' the trapezoid method came-up
yet is this correct?
Gavin Seddon
2021년 8월 4일
Hello
I am integrating the number of molecular motions in 10e-15s.
댓글 수: 1
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