how to solve error using integral

clear all

clc

qu=linspace(-2*pi,2*pi,126);

x=linspace(-2,2,126);

y=2*x;

psi=(-x./sqrt(qu/2)+sqrt(y)/sqrt(exp(-2*asinh(sin(qu/2)))+1));

ket=diff(psi);

bras=psi';

bras=bras(1:end-1);

for i=1:length(qu)-1

f(i)=bras(i)*ket(i);

end

phase=1i*integral(f,qu,-pi,pi)

% i am getting the following error:

Error using integral (line 82)

First input argument must be a function handle.

Error in test (line 15)

phase=1i*integral(f,qu,-pi,pi)

how can i solve this error?

thank you in advance

Answer 1

[Star Strider]

Not certain what the desired result is, however everything here are arrays or vectors, so use trapz instead, since there are no functions defined —

qu=linspace(-pi,pi,126);
x=linspace(-2,2,126);
y=2*x;
psi=(-x./sqrt(qu/2)+sqrt(y)/sqrt(exp(-2*asinh(sin(qu/2)))+1));
ket=gradient(psi,(x(2)-x(1)));                                      % Use 'gradient' To Calculate The Numerical Derivative
bras=psi';
% bras=bras(1:end-1);
% for i=1:length(qu)-1
%     f(i)=bras(i)*ket(i);
% end
f = bras .* ket;

% phase=1i*integral(f,qu,-pi,pi)
phase_columns = 1i*trapz(qu,f)

phase_columns = 
   0.7046 - 0.0743i   0.7075 - 0.0746i   0.7133 - 0.0752i   0.7193 - 0.0758i   0.7254 - 0.0765i   0.7317 - 0.0771i   0.7382 - 0.0778i   0.7448 - 0.0785i   0.7516 - 0.0792i   0.7586 - 0.0800i   0.7658 - 0.0807i   0.7732 - 0.0815i   0.7808 - 0.0823i   0.7886 - 0.0831i   0.7967 - 0.0840i   0.8051 - 0.0849i   0.8137 - 0.0858i   0.8226 - 0.0867i   0.8318 - 0.0877i   0.8413 - 0.0887i   0.8511 - 0.0897i   0.8613 - 0.0908i   0.8719 - 0.0919i   0.8829 - 0.0931i   0.8943 - 0.0943i   0.9061 - 0.0955i   0.9184 - 0.0968i   0.9313 - 0.0982i   0.9447 - 0.0996i   0.9587 - 0.1011i   0.9733 - 0.1026i   0.9887 - 0.1042i   1.0048 - 0.1059i   1.0217 - 0.1077i   1.0394 - 0.1096i   1.0582 - 0.1116i   1.0780 - 0.1136i   1.0989 - 0.1159i   1.1212 - 0.1182i   1.1448 - 0.1207i   1.1700 - 0.1233i   1.1969 - 0.1262i   1.2258 - 0.1292i   1.2568 - 0.1325i   1.2904 - 0.1360i   1.3268 - 0.1399i   1.3665 - 0.1441i   1.4100 - 0.1487i   1.4579 - 0.1537i   1.5111 - 0.1593i   1.5705 - 0.1656i   1.6376 - 0.1727i   1.7142 - 0.1807i   1.8026 - 0.1900i   1.9064 - 0.2010i   2.0305 - 0.2141i   2.1827 - 0.2301i   2.3757 - 0.2505i   2.6320 - 0.2775i   2.9971 - 0.3160i   3.5846 - 0.3779i   4.8494 - 0.5113i   7.2088 + 3.2068i   4.6396 + 6.3816i   0.5113 + 4.8494i   0.3779 + 3.5846i   0.3160 + 2.9971i   0.2775 + 2.6320i   0.2505 + 2.3757i   0.2301 + 2.1827i   0.2141 + 2.0305i   0.2010 + 1.9064i   0.1900 + 1.8026i   0.1807 + 1.7142i   0.1727 + 1.6376i   0.1656 + 1.5705i   0.1593 + 1.5111i   0.1537 + 1.4579i   0.1487 + 1.4100i   0.1441 + 1.3665i   0.1399 + 1.3268i   0.1360 + 1.2904i   0.1325 + 1.2568i   0.1292 + 1.2258i   0.1262 + 1.1969i   0.1233 + 1.1700i   0.1207 + 1.1448i   0.1182 + 1.1212i   0.1159 + 1.0989i   0.1136 + 1.0780i   0.1116 + 1.0582i   0.1096 + 1.0394i   0.1077 + 1.0217i   0.1059 + 1.0048i   0.1042 + 0.9887i   0.1026 + 0.9733i   0.1011 + 0.9587i   0.0996 + 0.9447i   0.0982 + 0.9313i   0.0968 + 0.9184i   0.0955 + 0.9061i   0.0943 + 0.8943i   0.0931 + 0.8829i   0.0919 + 0.8719i   0.0908 + 0.8613i   0.0897 + 0.8511i   0.0887 + 0.8413i   0.0877 + 0.8318i   0.0867 + 0.8226i   0.0858 + 0.8137i   0.0849 + 0.8051i   0.0840 + 0.7967i   0.0831 + 0.7886i   0.0823 + 0.7808i   0.0815 + 0.7732i   0.0807 + 0.7658i   0.0800 + 0.7586i   0.0792 + 0.7516i   0.0785 + 0.7448i   0.0778 + 0.7382i   0.0771 + 0.7317i   0.0765 + 0.7254i   0.0758 + 0.7193i   0.0752 + 0.7133i   0.0746 + 0.7075i   0.0743 + 0.7046i

phase_rows = 1i*trapz(qu,f,2)

phase_rows = 
   2.1086 - 3.3722i
   2.0765 - 3.3401i
   2.0441 - 3.3077i
   2.0114 - 3.2750i
   1.9785 - 3.2421i
   1.9453 - 3.2088i
   1.9117 - 3.1753i
   1.8779 - 3.1415i
   1.8438 - 3.1074i
   1.8094 - 3.0730i
   1.7747 - 3.0382i
   1.7396 - 3.0032i
   1.7041 - 2.9677i
   1.6684 - 2.9320i
   1.6322 - 2.8958i
   1.5957 - 2.8593i
   1.5588 - 2.8224i
   1.5215 - 2.7851i
   1.4838 - 2.7474i
   1.4457 - 2.7092i
   1.4071 - 2.6707i
   1.3680 - 2.6316i
   1.3285 - 2.5921i
   1.2885 - 2.5521i
   1.2480 - 2.5116i
   1.2070 - 2.4706i
   1.1654 - 2.4290i
   1.1232 - 2.3868i
   1.0805 - 2.3441i
   1.0371 - 2.3007i
   0.9930 - 2.2566i
   0.9483 - 2.2119i
   0.9029 - 2.1665i
   0.8567 - 2.1203i
   0.8097 - 2.0733i
   0.7619 - 2.0255i
   0.7132 - 1.9768i
   0.6636 - 1.9272i
   0.6130 - 1.8766i
   0.5613 - 1.8249i
   0.5086 - 1.7722i
   0.4547 - 1.7182i
   0.3994 - 1.6630i
   0.3429 - 1.6065i
   0.2848 - 1.5484i
   0.2252 - 1.4888i
   0.1638 - 1.4274i
   0.1006 - 1.3642i
   0.0352 - 1.2988i
  -0.0324 - 1.2312i
  -0.1026 - 1.1610i
  -0.1756 - 1.0880i
  -0.2519 - 1.0117i
  -0.3319 - 0.9317i
  -0.4163 - 0.8473i
  -0.5058 - 0.7578i
  -0.6014 - 0.6621i
  -0.7048 - 0.5588i
  -0.8181 - 0.4455i
  -0.9448 - 0.3188i
  -1.0914 - 0.1722i
  -1.2717 + 0.0081i
  -1.5336 + 0.2700i
  -1.5336 + 0.9856i
  -1.2717 + 1.2475i
  -1.0914 + 1.4278i
  -0.9448 + 1.5744i
  -0.8181 + 1.7011i
  -0.7048 + 1.8144i
  -0.6014 + 1.9178i
  -0.5058 + 2.0135i
  -0.4163 + 2.1029i
  -0.3319 + 2.1873i
  -0.2519 + 2.2673i
  -0.1756 + 2.3436i
  -0.1026 + 2.4167i
  -0.0324 + 2.4868i
   0.0352 + 2.5545i
   0.1006 + 2.6198i
   0.1638 + 2.6831i
   0.2252 + 2.7444i
   0.2848 + 2.8041i
   0.3429 + 2.8621i
   0.3994 + 2.9187i
   0.4547 + 2.9739i
   0.5086 + 3.0278i
   0.5613 + 3.0806i
   0.6130 + 3.1322i
   0.6636 + 3.1828i
   0.7132 + 3.2324i
   0.7619 + 3.2811i
   0.8097 + 3.3289i
   0.8567 + 3.3759i
   0.9029 + 3.4221i
   0.9483 + 3.4675i
   0.9930 + 3.5123i
   1.0371 + 3.5563i
   1.0805 + 3.5997i
   1.1232 + 3.6424i
   1.1654 + 3.6846i
   1.2070 + 3.7262i
   1.2480 + 3.7672i
   1.2885 + 3.8078i
   1.3285 + 3.8478i
   1.3680 + 3.8873i
   1.4071 + 3.9263i
   1.4457 + 3.9649i
   1.4838 + 4.0030i
   1.5215 + 4.0407i
   1.5588 + 4.0780i
   1.5957 + 4.1149i
   1.6322 + 4.1515i
   1.6684 + 4.1876i
   1.7041 + 4.2234i
   1.7396 + 4.2588i
   1.7747 + 4.2939i
   1.8094 + 4.3286i
   1.8438 + 4.3631i
   1.8779 + 4.3972i
   1.9117 + 4.4310i
   1.9453 + 4.4645i
   1.9785 + 4.4977i
   2.0114 + 4.5306i
   2.0441 + 4.5633i
   2.0765 + 4.5957i
   2.1086 + 4.6278i

Experiment to get the desired result.

EDIT — (14 Oct 2021 at 12:42)

Originally forgot to multiply the trapz results by 1i, now included.

.

Answer 2

[Mathieu NOE]

hello

integral works on function (handles) not arrays

f is an array , not a function handle so use trapz to do numerical integration

clear all
clc
qu=linspace(-2*pi,2*pi,126);
x=linspace(-2,2,126);
y=2*x;
psi=(-x./sqrt(qu/2)+sqrt(y)./sqrt(exp(-2*asinh(sin(qu/2)))+1));
ket=diff(psi);
bras=psi;
bras=bras(1:end-1);

f = bras.*ket(1:length(qu)-1);

phase=1i*trapz(qu(1:length(qu)-1),f)