how to solve error using integral

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Rabih Sokhen
Rabih Sokhen on 14 Oct 2021
Edited: Star Strider on 14 Oct 2021
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

Answers (2)

Star Strider
Star Strider on 14 Oct 2021
Edited: Star Strider on 14 Oct 2021
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.
.

Mathieu NOE
Mathieu NOE on 14 Oct 2021
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)

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