简单的 gnuplot 峰值查找器
比较 3 个连续数据点是寻找最大值/峰值的简单方法。
if y(i-1) < y(i) > y(i+1) then you have a maximum/peak at x(i).
但是，如果您有嘈杂的曲线（如通常的实验光谱），您将获得太多“峰值”。
以下 gnuplot 代码允许为被视为峰值的内容设置阈值。该代码基本上为每个峰值计算一个数字，这是峰值“独立性”的度量。（参见https://en.wikipedia.org/wiki/Topographic_prominence）。该代码使用数据块，因此需要 gnuplot >=5.2。欢迎提出意见和改进。
测试数据：
Spectrum.dat
# x y
6.02 153.33
9.59 154.03
9.59 154.03
9.59 154.03
9.83 153.66
10.58 153.22
10.62 153.85
11.32 152.33
11.53 153.67
11.88 153.27
13.28 153.97
13.42 154.35
14.56 152.99
14.75 153.50
15.23 153.91
15.59 153.58
16.56 153.85
16.70 154.49
16.97 153.98
17.23 154.49
17.37 153.73
17.90 154.24
17.93 154.91
18.80 154.23
18.83 154.64
20.37 153.59
20.48 153.99
21.70 153.19
22.29 154.36
22.41 153.38
23.34 155.04
23.41 155.38
24.38 154.71
24.58 154.96
25.40 155.13
25.41 154.70
26.20 154.21
26.36 154.84
26.55 154.11
26.79 154.73
27.02 154.13
27.54 154.51
27.55 155.17
28.08 155.42
28.33 154.97
28.61 155.17
29.06 155.10
29.12 154.26
29.61 153.61
30.03 154.84
30.58 155.30
30.68 154.72
31.21 155.82
31.99 155.83
32.58 156.56
33.03 156.23
33.51 156.79
33.73 158.88
34.00 157.85
34.17 159.82
34.32 161.24
34.55 160.78
34.85 162.58
35.14 163.84
35.50 168.07
35.85 168.40
36.55 180.70
36.75 179.27
37.16 178.78
38.15 168.93
38.29 170.52
38.83 164.96
39.63 161.39
40.17 158.67
40.48 159.22
40.88 159.75
40.95 158.77
41.45 160.86
41.58 160.33
41.84 161.12
42.51 162.83
43.33 165.09
43.43 164.20
43.63 164.56
44.22 164.76
44.92 162.58
45.71 159.40
45.98 159.84
47.03 157.01
47.53 157.15
47.95 155.48
48.08 156.21
48.56 154.51
48.64 155.11
49.14 153.69
49.31 154.27
49.86 154.71
50.14 154.13
50.33 155.83
50.37 155.36
51.00 154.60
51.37 154.75
52.00 154.91
52.01 154.34
54.28 153.83
54.46 154.33
54.83 153.19
55.58 155.30
55.86 154.95
55.92 156.48
56.40 155.89
56.59 155.16
57.56 155.96
57.64 155.21
58.31 155.36
58.38 156.08
58.92 155.84
59.00 155.28
59.57 155.96
59.94 155.37
61.31 156.07
61.32 156.78
61.96 157.34
62.37 156.89
63.14 159.45
63.54 159.51
63.80 161.03
63.93 161.56
64.17 161.12
64.84 162.38
65.14 166.28
65.64 168.07
66.22 169.06
66.42 167.70
66.56 168.40
67.10 167.20
67.24 168.00
67.77 166.82
68.04 165.80
68.15 166.88
68.43 164.98
68.86 166.28
69.33 166.55
70.43 179.11
70.93 198.16
71.62 208.09
72.01 216.42
72.43 223.37
72.79 226.74
72.84 231.24
73.07 229.85
73.15 222.04
73.32 224.49
73.58 211.26
73.71 215.36
73.98 201.60
73.98 208.75
74.25 202.93
74.53 189.70
74.90 184.01
75.18 184.80
76.67 173.29
77.05 173.82
77.15 170.94
77.27 177.13
77.52 175.20
77.70 179.76
78.17 179.96
78.36 183.33
78.73 187.05
78.86 184.67
79.03 189.90
79.38 189.70
79.59 190.62
79.88 189.17
80.59 186.52
80.60 183.61
81.26 177.53
81.67 173.69
82.07 173.69
82.90 165.37
83.94 164.04
84.25 164.42
85.01 161.26
85.22 162.18
85.77 161.19
85.89 159.97
86.46 160.72
86.56 161.78
87.06 160.56
87.19 161.53
87.74 159.60
87.89 160.64
88.30 158.74
88.56 159.27
88.98 158.08
89.25 158.70
90.12 159.15
90.14 158.34
90.99 159.59
91.06 158.86
91.72 159.01
91.74 158.48
92.43 157.68
92.48 158.34
93.15 157.68
93.54 158.34
93.72 157.61
94.20 158.00
94.39 158.64
94.82 157.83
95.00 158.40
95.43 156.77
95.66 157.39
95.81 155.44
95.84 156.25
96.53 157.70
96.55 156.70
97.22 159.14
97.47 158.13
97.53 156.75
98.57 157.83
98.85 157.40
98.92 158.45
99.35 158.25
99.40 157.77
100.04 158.33
100.14 157.91
101.00 158.30
101.04 157.80
101.94 157.48
102.02 158.20
102.53 156.56
102.58 157.84
103.23 157.75
103.38 156.82
103.39 158.93
103.75 158.60
104.05 159.26
104.30 158.14
104.55 158.56
104.85 157.15
105.17 160.09
105.21 158.41
105.52 161.78
105.80 160.00
105.92 160.86
106.11 159.54
106.31 159.93
106.86 160.99
107.20 160.88
107.42 162.05
107.62 160.33
107.80 161.16
108.39 159.90
108.79 162.25
109.08 161.85
109.46 163.77
109.73 163.42
109.96 165.16
111.02 170.08
111.30 173.56
111.69 173.56
112.35 180.08
112.61 189.04
112.89 193.53
113.28 193.67
113.81 210.73
113.94 206.63
114.20 213.11
114.46 219.60
115.00 230.44
115.12 236.95
115.27 234.68
115.78 238.78
116.11 239.57
116.40 238.51
116.43 239.90
117.90 230.31
118.18 221.32
118.42 222.51
118.70 217.48
118.83 211.13
119.25 210.34
119.37 204.51
119.65 205.18
120.08 200.28
120.12 198.96
120.84 204.18
120.95 201.87
121.24 206.49
121.50 203.01
121.64 204.44
121.73 201.74
121.84 202.53
122.14 203.72
122.19 202.40
122.44 203.59
122.45 204.91
122.64 201.61
122.76 203.17
123.08 200.79
123.10 200.15
123.34 199.51
123.39 200.81
123.88 200.28
124.25 196.58
124.26 194.06
124.53 193.67
125.18 188.77
125.81 182.16
126.10 182.55
127.32 171.71
127.70 171.18
127.96 168.27
128.22 168.66
128.62 165.71
128.89 166.24
129.30 163.94
129.56 164.47
129.96 162.22
130.21 162.72
130.53 160.83
130.93 160.61
131.15 161.24
131.84 160.06
131.93 161.12
132.71 159.87
133.06 163.17
133.38 162.73
134.17 166.97
134.31 172.37
134.85 180.83
135.38 193.01
135.62 190.09
135.64 200.81
135.75 204.05
136.16 206.10
136.80 200.22
137.21 199.36
138.29 175.41
138.56 176.73
139.98 163.09
140.03 161.92
140.32 164.53
140.55 163.80
140.85 166.25
141.24 165.81
141.45 167.92
141.59 166.51
141.99 170.65
142.25 170.19
142.76 177.79
142.91 174.95
143.72 187.66
143.79 185.37
144.65 179.11
144.91 180.32
145.71 175.74
145.84 174.80
146.54 177.73
146.74 180.57
147.30 181.11
147.42 180.30
148.33 181.23
148.38 180.68
148.93 181.19
149.09 181.74
149.24 178.43
149.49 179.03
149.96 174.55
150.69 173.48
151.83 168.06
151.89 169.39
152.41 168.27
152.96 169.45
153.02 168.53
153.47 169.42
153.71 168.78
153.91 169.44
154.08 167.74
154.54 168.92
154.65 168.20
155.61 168.79
156.78 165.75
157.06 166.08
157.54 162.68
157.84 163.40
158.51 162.73
158.57 161.85
159.45 161.27
159.57 160.33
160.11 158.81
160.24 159.81
160.90 159.27
160.90 158.08
161.17 158.48
161.43 158.10
161.59 158.72
161.83 157.91
162.44 158.48
162.61 157.94
163.41 158.75
163.43 158.19
163.94 158.99
163.96 158.33
164.60 158.23
164.87 158.74
165.81 158.50
166.10 158.08
166.74 158.91
167.02 158.48
167.67 159.68
167.96 159.28
168.90 159.81
168.96 160.34
169.57 159.77
169.76 161.28
170.00 160.75
171.01 163.77
171.12 163.13
171.79 163.71
172.83 169.14
173.19 169.13
173.52 171.06
173.73 170.38
173.87 171.65
174.27 171.90
174.41 175.94
174.94 177.39
175.20 183.48
175.71 185.07
175.84 190.49
176.48 193.27
176.51 196.84
177.34 201.47
177.62 207.30
177.69 205.18
177.87 203.26
178.08 204.46
178.45 199.43
178.76 199.62
179.02 193.53
179.43 192.08
179.96 178.98
180.21 176.40
180.56 176.57
180.57 176.20
181.14 176.43
181.24 175.51
181.68 174.93
181.74 177.13
181.97 178.85
182.05 176.93
182.14 179.78
182.30 177.53
182.59 178.72
182.72 176.93
183.04 177.67
183.21 178.76
183.33 177.92
183.75 179.99
184.06 179.78
184.28 182.07
184.71 182.49
185.40 187.78
185.61 184.01
186.02 183.86
186.20 180.07
186.79 178.72
186.97 175.44
187.34 175.15
188.45 167.65
188.84 166.25
189.08 166.77
189.50 164.08
189.90 163.69
189.92 161.67
190.37 162.04
190.41 162.90
190.90 161.40
190.93 162.58
192.29 159.27
192.33 158.79
193.23 160.21
193.34 159.73
193.78 161.15
194.07 160.20
194.54 160.43
194.93 159.64
195.39 159.82
195.98 160.86
196.08 160.05
196.45 161.78
197.00 158.90
197.03 159.95
197.70 157.15
198.07 160.13
198.10 158.48
198.83 159.67
198.85 160.46
199.27 159.80
199.46 159.46
200.46 161.78
200.73 161.38
201.38 162.37
201.92 159.72
202.06 160.52
203.14 157.67
203.52 157.95
203.93 157.02
204.13 157.55
204.39 156.66
204.63 157.15
206.35 155.53
206.57 156.00
207.21 156.57
207.33 155.76
208.23 157.93
208.52 157.68
208.92 157.15
209.21 157.56
209.41 156.62
209.88 156.89
211.48 154.50
211.70 155.00
212.39 155.37
212.51 154.53
212.84 154.31
212.92 155.17
213.26 154.38
213.44 155.24
213.70 154.57
214.15 154.97
214.24 155.71
215.55 155.20
215.65 156.01
216.28 156.16
216.55 156.87
216.73 155.56
216.95 156.23
217.25 156.03
217.47 155.46
217.93 155.50
218.26 155.83
218.56 155.04
219.31 154.73
219.97 154.72
220.10 155.61
220.79 154.23
220.87 154.94
221.87 154.64
222.07 154.12
222.58 154.47
222.69 155.02
223.21 154.51
223.24 155.22
223.86 154.54
223.90 155.22
224.48 154.29
224.54 155.04
225.22 154.73
225.28 153.86
225.54 154.13
225.76 154.72
225.84 153.93
226.52 154.23
226.60 154.94
226.98 154.02
227.78 153.89
228.29 154.67
228.62 154.29
229.12 154.90
229.46 154.16
229.83 154.48
230.28 153.54
230.50 154.06
230.91 153.03
231.18 153.63
231.79 153.99
231.97 153.45
232.70 154.86
代码：
### a simple gnuplot peak-finder
# requires gnuplot >=5.2
reset session
FILE = "Spectrum.dat"
set table $Data
plot FILE u 1:2 with table
unset table
ColX=1
ColY=2
# extract all peaks
y2=y1=NaN
set print $Peaks
do for [i=2:|$Data|-1] {
if ( word($Data[i-1],ColY)<word($Data[i],ColY) && word($Data[i+1],ColY)<word($Data[i],ColY) ) \
{ print sprintf("%d %s %s", i, word($Data[i],ColX), word($Data[i],ColY)) }
}
set print
# determine prominence
set print $PeakInfo
do for [i=1:|$Peaks|] {
PeakIndex = int(word($Peaks[i],1))
PeakX = real(word($Data[PeakIndex],ColX))
PeakY = real(word($Data[PeakIndex],ColY))
MinY1 = PeakY
do for [j=PeakIndex+1:|$Data|] { # search for higher peak to the right
if ( word($Data[j],ColY) > PeakY ) { break }
else { MinY1 = word($Data[j],ColY) < MinY1 ? word($Data[j],ColY) : MinY1 }
}
MinY2 = PeakY
do for [j=PeakIndex-1:1:-1] { # search for higher peak to the left
if ( word($Data[j],ColY) > PeakY ) { break }
else { MinY2 = word($Data[j],ColY) < MinY2 ? word($Data[j],ColY) : MinY2 }
}
Prominence = MinY1 > MinY2 ? PeakY-MinY1 : PeakY-MinY2
NormalizedProminence = 100.*Prominence/PeakY
print sprintf("%2 d %6 .1f %6 .1f %6 .2f", i, PeakX, PeakY, NormalizedProminence )
}
set print
# print $PeakInfo
set yrange[150:250]
Threshold = 2.4
set label 1 at graph 0.05, 0.9 sprintf("Threshold: %g",Threshold)
plot $Data u 1:2 w lp pt 7 ps 0.5 lc rgb "red" not, \
$PeakInfo u ($4>Threshold?$2:NaN):3 w p pt 7 lc rgb "blue" not, \
$PeakInfo u ($4>Threshold?$2:NaN):3:2 w labels offset 0,0.8 not, \
$PeakInfo u ($4>Threshold?$2:NaN):3 w impulses lc rgb "black" not
### end of code
结果：（对于不同的阈值）
它可以完成,我很无聊,这样做.我生成了以下一组随机数据:
5191
29375
23222
32118
3185
32355
17173
8734
28850
20811
5956
6950
28560
25770
4630
28272
10035
7209
19428
26187
30784
20326
12865
23288
20924
根据列表中的位置绘制值如下所示:
您可以从上图中发现局部最大值.现在我可以处理存储临时变量中两个先前值(x和y坐标)的数据点,当我确定最大值时,我绘制数据点:
# Select the columns of your data file that contain x and y data
# (usually 1 and 2 respectively)
xcolumn=0
ycolumn=1
plot "data" u (column(xcolumn)):(column(ycolumn)) w l, \
"data" u (column(0)==0 ? (last2y=column(ycolumn), \
last2x=column(xcolumn), 1/0) : column(0)==1 ? (lasty=column(ycolumn), \
lastx=column(xcolumn), 1/0) : lastx) \
: \
( column(0) < 2 ? 1/0 : (last2y < lasty && \
column(ycolumn) < lasty) ? (value=lasty, last2y=lasty, last2x=lastx, \
lasty=column(ycolumn), lastx=column(xcolumn), value) : (last2y=lasty, \
last2x=lastx, lasty=column(ycolumn), lastx=column(xcolumn), 1/0)) pt 7
