vector gives 0 integral

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

Answer 1

[Star Strider]

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.

See the documentation on trapz.

.

[John D'Errico]

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]

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.

However, if ‘z’ is a function, use the integral funciton:

int_y = integral(@(x)sin(2*pi*x).^2, 0, 20)                 % 'z' Is A Function

int_y = 10.0000

.

[Gavin Seddon]

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]

I have no idea.

Another possibility is that there were no values in that range.

[Gavin Seddon]

Hello

int(y,183,306)

is -179

Thanks

G

[Star Strider]

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]

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

[Star Strider]

Thank you!

.

[Gavin Seddon]

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]

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.

.

[Gavin Seddon]

Thanks, is this a regular itegral

If so may I use syms?

int(y)

Thx again.

G.

[Star Strider]

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 = 

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]

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

[Gavin Seddon]

tnt a diff is the mol motion

g

[Star Strider]

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]

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]

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]

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]

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 = 

figure
fplot(int_y, [0 100])
grid

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]

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]

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.

.

[Gavin Seddon]

Thanks

g

[Gavin Seddon]

How do I get output of

v0 = 6.3303e-04

verbatim

thx

g

[Star Strider]

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]

Hello

PERFECT and a useful command.

G.

[Star Strider]

Thank you!

[Gavin Seddon]

Hello

how's this fixed

'Error using fprintf

Conversion to double from sym is not possible.

>> '

g.

[Star Strider]

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]

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 - 1689/2000)*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))/931322574615478515625000000000000000000 + (124416147043984741323121230200088077514254108203110635030193939*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((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)*sin((16940918583*cos((16940918583*cos((16940918583*cos((3573*x)/10000 + 13/8))/10000000000 + 13/8))/10000000000 + 13/8))/10000000000 + 13/8)^2)/303164900590976093750000000000000000000000000000000000000000 - (837720112467010304758087863435089978401527*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)*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)*sin((16940918583*cos((16940918583*cos((16940918583*cos((3573*x)/10000 + 13/8))/10000000000 + 13/8))/10000000000 + 13/8))/10000000000 + 13/8))/12126596023639043750000000000000000000000))/1250 + (96471*cos((724311742502702996928*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]

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’.

.

Answer 2

[Gavin Seddon]

Hello

Yes John is correct, I tried with no parenth and I see the fun integral not its value which is wht I need.

[Gavin Seddon]

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]

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]

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.

[Star Strider]

Thank you!

Just curious as to what you are integrating.

.

Answer 3

[Gavin Seddon]

Hello

When I searched 'vector integration' the trapezoid method came-up

yet is this correct?

Answer 4

[Gavin Seddon]

Hello

I am integrating the number of molecular motions in 10e-15s.

[Star Strider]

Interesting!

.