Calculate slope of a discrete points

Hi all,

Can anyone please help me to find the instantaneous gradient (slope) at each points from the following datasets.

data=[
% X             Y
%===================
0.7761	0.5715
0.794	        0.5729
0.8117	0.5744
0.8292	0.5762
0.8465	0.5782
0.8637	0.5804
0.8807	0.5828
0.8977	0.5853
0.9144	0.5879
0.9311	0.5907
0.9477	0.5937
0.9641	0.5968
0.9805	0.6
0.9967	0.6033
1.0129	0.6067
1.0289	0.6103
1.0449	0.6139
1.0608	0.6176
1.0767	0.6215
1.0924	0.6254
1.1081	0.6294
1.1238	0.6334
1.1393	0.6376
1.1548	0.6418
1.1703	0.6461
1.1857	0.6505
1.201	        0.6549
1.2163	0.6593
1.2316	0.6639
1.2468	0.6685
1.2619	0.6731
1.277	        0.6778
1.2921	0.6825
1.3071	0.6873
1.3221	0.6921
1.3371	0.697
1.352	        0.7019
1.3669	0.7069
1.3818	0.7119
1.3966	0.7169
1.4114	0.722
1.4262	0.727
1.441	        0.7322
1.4557	0.7373
1.4704	0.7425
1.4851	0.7477
1.4997	0.753
1.5143	0.7583
1.5289	0.7635
1.5435	0.7689
1.5581	0.7742
1.5726	0.7796
1.5872	0.785
1.6017	0.7904
1.6162	0.7958
1.6307	0.8013
1.6451	0.8067
1.6596	0.8122
1.674	        0.8178
1.6884	0.8233
1.7028	0.8288
1.7172	0.8344
1.7315	0.84
1.7459	0.8456
1.7602	0.8512
1.7746	0.8568
1.7889	0.8624
1.8032	0.8681
1.8175	0.8737
1.8318	0.8794
1.8461	0.8851
1.8603	0.8908
1.8746	0.8965
1.8888	0.9023
1.9031	0.908
1.9173	0.9137
1.9315	0.9195
1.9457	0.9253
1.9599	0.931
1.9741	0.9368
1.9883	0.9426
2.0025	0.9484
2.0166	0.9543
2.0308	0.9601
2.0449	0.9659
2.0591	0.9718
2.0732	0.9776
2.0874	0.9835
2.1015	0.9893
2.1156	0.9952
2.1297	1.0011
2.1438	1.007
2.1579	1.0128
2.172	        1.0187
2.1861	1.0247
2.2002	1.0306
2.2143	1.0365
2.2284	1.0424
2.2425	1.0483
2.2565	1.0543];

The plot of the dataset is shown below

I have calculated the slope based on the two neighboring points, the results is copied below.

the gradient (m) is calculated using the following formula:

and the angle is just the arc-tan of the result.

Now, is it possible to obtain the instantaneous slope (gradient) at each point without using any curve-fitting to find the equation of the dataset? How can we do this numerically?

out =[
% X	          Y	    m	            atan	atandeg
%================================================================
0.7761	0.5715			
0.794	        0.5729	0.078212291	0.078053394	4.472130064
0.8117	0.5744	0.084745763	0.084543756	4.844000375
0.8292	0.5762	0.102857143	0.102496699	5.872628281
0.8465	0.5782	0.115606936	0.115096	6.594515032
0.8637	0.5804	0.127906977	0.127216217	7.288952324
0.8807	0.5828	0.141176471	0.14024961	8.035710711
0.8977	0.5853	0.147058824	0.146012258	8.365886124
0.9144	0.5879	0.155688623	0.154448697	8.849258471
0.9311	0.5907	0.167664671	0.166119551	9.517949161
0.9477	0.5937	0.180722892	0.178793055	10.24408745
0.9641	0.5968	0.18902439	0.186820161	10.70400675
0.9805	0.6	0.195121951	0.192700759	11.04094018
0.9967	0.6033	0.203703704	0.200954264	11.51383118
1.0129	0.6067	0.209876543	0.206873949	11.85300417
1.0289	0.6103	0.225	0.221314442	12.68038349
1.0449	0.6139	0.225	0.221314442	12.68038349
1.0608	0.6176	0.232704403	0.228635393	13.09984308
1.0767	0.6215	0.245283019	0.240534248	13.78159724
1.0924	0.6254	0.248407643	0.243479414	13.95034281
1.1081	0.6294	0.25477707	0.249469651	14.29355811
1.1238	0.6334	0.25477707	0.249469651	14.29355811
1.1393	0.6376	0.270967742	0.264613602	15.16124258
1.1548	0.6418	0.270967742	0.264613602	15.16124258
1.1703	0.6461	0.277419355	0.270614072	15.50504418
1.1857	0.6505	0.285714286	0.278299659	15.9453959
1.201	0.6549	0.287581699	0.280025283	16.04426686
1.2163	0.6593	0.287581699	0.280025283	16.04426686
1.2316	0.6639	0.300653595	0.292056315	16.73359422
1.2468	0.6685	0.302631579	0.293869335	16.83747263
1.2619	0.6731	0.304635762	0.295704342	16.94261077
1.277	0.6778	0.311258278	0.30175322	17.28918598
1.2921	0.6825	0.311258278	0.30175322	17.28918598
1.3071	0.6873	0.32	0.309702945	17.74467163
1.3221	0.6921	0.32	0.309702945	17.74467163
1.3371	0.697	0.326666667	0.315738603	18.09048937
1.352	0.7019	0.32885906	0.317718318	18.20391871
1.3669	0.7069	0.33557047	0.323762624	18.55023193
1.3818	0.7119	0.33557047	0.323762624	18.55023193
1.3966	0.7169	0.337837838	0.325799115	18.66691427
1.4114	0.722	0.344594595	0.331851221	19.01367439
1.4262	0.727	0.337837838	0.325799115	18.66691427
1.441	0.7322	0.351351351	0.337878188	19.35899418
1.4557	0.7373	0.346938776	0.333945072	19.13364321
1.4704	0.7425	0.353741497	0.340004105	19.48080023
1.4851	0.7477	0.353741497	0.340004105	19.48080023
1.4997	0.753	0.363013699	0.348220949	19.95159069
1.5143	0.7583	0.363013699	0.348220949	19.95159069
1.5289	0.7635	0.356164384	0.342155885	19.60408815
1.5435	0.7689	0.369863014	0.354259423	20.29756977
1.5581	0.7742	0.363013699	0.348220949	19.95159069
1.5726	0.7796	0.372413793	0.356501385	20.42602476
1.5872	0.785	0.369863014	0.354259423	20.29756977
1.6017	0.7904	0.372413793	0.356501385	20.42602476
1.6162	0.7958	0.372413793	0.356501385	20.42602476
1.6307	0.8013	0.379310345	0.362544237	20.77225468
1.6451	0.8067	0.375	0.35877067	20.55604522
1.6596	0.8122	0.379310345	0.362544237	20.77225468
1.674	0.8178	0.388888889	0.370891289	21.25050551
1.6884	0.8233	0.381944444	0.364845007	20.90407908
1.7028	0.8288	0.381944444	0.364845007	20.90407908
1.7172	0.8344	0.388888889	0.370891289	21.25050551
1.7315	0.84	0.391608392	0.373251365	21.38572793
1.7459	0.8456	0.388888889	0.370891289	21.25050551
1.7602	0.8512	0.391608392	0.373251365	21.38572793
1.7746	0.8568	0.388888889	0.370891289	21.25050551
1.7889	0.8624	0.391608392	0.373251365	21.38572793
1.8032	0.8681	0.398601399	0.379300105	21.73229519
1.8175	0.8737	0.391608392	0.373251365	21.38572793
1.8318	0.8794	0.398601399	0.379300105	21.73229519
1.8461	0.8851	0.398601399	0.379300105	21.73229519
1.8603	0.8908	0.401408451	0.381719969	21.87094317
1.8746	0.8965	0.398601399	0.379300105	21.73229519
1.8888	0.9023	0.408450704	0.387770172	22.21759427
1.9031	0.908	0.398601399	0.379300105	21.73229519
1.9173	0.9137	0.401408451	0.381719969	21.87094317
1.9315	0.9195	0.408450704	0.387770172	22.21759427
1.9457	0.9253	0.408450704	0.387770172	22.21759427
1.9599	0.931	0.401408451	0.381719969	21.87094317
1.9741	0.9368	0.408450704	0.387770172	22.21759427
1.9883	0.9426	0.408450704	0.387770172	22.21759427
2.0025	0.9484	0.408450704	0.387770172	22.21759427
2.0166	0.9543	0.418439716	0.396300932	22.70637084
2.0308	0.9601	0.408450704	0.387770172	22.21759427
2.0449	0.9659	0.411347518	0.390250283	22.35969418
2.0591	0.9718	0.415492958	0.39379062	22.56254053
2.0732	0.9776	0.411347518	0.390250283	22.35969418
2.0874	0.9835	0.415492958	0.39379062	22.56254053
2.1015	0.9893	0.411347518	0.390250283	22.35969418
2.1156	0.9952	0.418439716	0.396300932	22.70637084
2.1297	1.0011	0.418439716	0.396300932	22.70637084
2.1438	1.007	0.418439716	0.396300932	22.70637084
2.1579	1.0128	0.411347518	0.390250283	22.35969418
2.172	1.0187	0.418439716	0.396300932	22.70637084
2.1861	1.0247	0.425531915	0.402321098	23.05130092
2.2002	1.0306	0.418439716	0.396300932	22.70637084
2.2143	1.0365	0.418439716	0.396300932	22.70637084
2.2284	1.0424	0.418439716	0.396300932	22.70637084
2.2425	1.0483	0.418439716	0.396300932	22.70637084
2.2565	1.0543	0.428571429	0.404891786	23.19859051];

[sisir regmi]

How did you get the plot as you have just two arrays of x and y points

Answer 1

[Star Strider]

I would use the gradient (link) function. Since the data need to be sampled regularly with respect to the independent variable (your data are not), you need to interpolate.

Try this:

data1 = linspace(min(data(:,1)), max(data(:,1)), size(data,1));
data2 = interp1(data(:,1),data(:,2),data1);
g = gradient(data2, diff(data1(1:2)));

figure
plot(data1, data2,    data1, g)
grid
legend('data', 'gradient', 'Location','NW')

EDIT —

Data and calculated slope plot:

[sisir regmi]

Can you please plot the x and y data finding the slopes of the points below? thank you

x=[0.06,.155,.180,.25,.28,.418,.554,1.737,1.822,1.823,1.824,2.029,2.062,2.073,2.075,2.091,2.108,2.11,2.157,3.12,3.26,3.37,3.44,3.54,3.56,3.58,3.92,4.08,4.17,4.19,4.36,4.38,4.39,4.45,4.456,4.44,4.46,4.35,4.55,4.69,5.138,5.28,5.40,5.54,5.67,5.78,5.80,5.81,5.900,5.9001,5.91,5.92,6.19,6.20,6.21,6.423,6.57,6.65,6.71,6.72,6.83,6.85,6.92,7.11,7.25]
y=[13.22,179.6,438.2,687.8,981.3,1152,931,91.24,80.37,37.61,12.09,70.55,96.34,125.6,73.59,57.15,88.75,80.1,111.6,258.1,40.66,42.7,60.61,236.8,239.8,212.1,128.4,46.09,40.58,47.62,90.86,174.5,244.2,316.9,482,614.4,775.3,923.3,782.3,486.9,75.65,35.83,31.34,35.01,28.84,36.18,31.63,16.6,11.6,4.97,11.38,10.54,9.34,13.16,21.86,28.17,73.86,148.5,469.1,763.6,914.6,301.9,192,118.5,79.65,49.06]

[Image Analyst]

Your vectors are not the same length. But the instantaneous slopes would be

slopes = diff(y) ./ diff(x)

[sisir regmi]

0.0600 13.22

0.1550 179.6

0.1800 438.2

0.2500 687.8

0.2800 981.3

0.4180 1152

0.5540 931

1.7370 91.24

1.8220 80.37

1.8230 37.61

1.8240 12.09

1.8250 70.55

2.0290 96.34

2.0620 125.6

2.0730 73.59

2.0750 57.15

2.0910 88.75

2.1080 80.1

2.1100 111.6

2.1570 258.1

3.1200 40.66

3.2600 42.7

3.3700 60.61

3.4400 236.8

3.5400 239.6

3.5600 212.1

3.5800 128.4

3.9200 46.09

4.0800 40.58

4.1700 47.02

4.1900 90.86

4.3600 174.5

4.3800 244.2

4.3900 316.9

4.4500 482

4.4560 614.4

4.4400 775.3

4.4600 923.3

4.3500 782.3

4.5500 486.9

4.6900 75.65

5.1380 35.83

5.2800 31.34

5.4000 35.01

5.5400 28.84

5.6700 36.18

5.7800 31.63

5.8000 16.6

5.8100 11.26

5.9000 4.97

5.9001 11.38

5.9100 10.54

5.9200 9.34

6.1900 13.16

6.2000 21.86

6.2100 28.86

6.4230 738.6

6.5700 148.5

6.6500 469.1

6.7100 763.6

6.7200 914.6

6.8300 301.9

6.8500 192

6.9200 118.5

7.1100 79.65

7.2500 49.06

now its the same length but when i give the command for slope it says matrix dimension must agree

Answer 2

[Image Analyst]

Try diff:

slopes = diff(out, 1)

[BeeTiaw]

I don't understand your answer. Which column of out are you referring to?

Please see the plot attached in the question.

The function diff will only give you the delta between two neighboring points, thus not the slope of the curve.

[Image Analyst]

It does it for all columns. The delta between two indexes IS the slope between two indexes (on the right side). Maybe the gradient function Star suggests does it on both sides and takes the average - I don't know, look it up.

[BeeTiaw]

I understand that, but it has nothing to do with slope of the curve. Please see the plot and the question.

It seems that you misunderstood the question here. But thanks for responding ;)

[Ghufran Aldawood]

Brilliant! Thank you!