1SPLINE(1) GNU Plotting Utilities SPLINE(1)
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6 spline - interpolate datasets using splines under tension
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9 spline [ options ] [ files ]
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12 spline reads datasets from standard input or from one or more files,
13 and fits a smooth curve (a "spline") through each dataset. An interpo‐
14 lated version of each dataset, consisting of points from the smooth
15 curve, is written to standard output.
16 Unless the -a or -A options are used (see below), each dataset should
18 be a sequence of values for a vector-valued function of a single scalar
19 variable. That is, each dataset should be a sequence of data points,
20 given as alternating t and y values. t is a scalar independent vari‐
21 able, and y is a vector-valued dependent variable. The dimensionality
22 of y is specified with the -d option (the default dimensionality is 1).
23 Between each data point and the next, t should increase.
24 An input file may contain more than a single dataset. If an input file
26 is in ASCII format (the default), its datasets should be separated by
27 blank lines. The t and y values of the data points in each dataset may
28 be arranged arbitrarily, so long as they are separated by white space.
29 Besides datasets, an input file may contain any number of comment
30 lines, which should begin with the comment character `#'. Comment
31 lines are ignored. They are not treated as blank, i.e., they do not
32 interrupt a dataset in progress.
33 Options and file names may be interspersed on the command line, but the
35 options are processed before the file names are read. If -- is seen,
36 it is interpreted as the end of the options. If no file names are
37 specified, or the file name - is encountered, the standard input is
38 read.
39 The type of interpolation, and the format of the input and output
41 files, may be selected by command-line options.
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44 Interpolation-Related Options
45 -f
46 --filter
47 Use a local interpolation algorithm (the cubic Bessel algo‐
48 rithm), so that spline can be used as a real-time filter. The
49 slope of the interpolating curve at each point in a dataset will
50 be chosen by fitting a quadratic function through that point and
51 the two adjacent points in the dataset. If -f is specified then
52 the -t option, otherwise optional, must be used as well. Also,
53 if -f is specified then the -k, -p, and -T options may not be
54 used.
55 If -f is not specified, then the default (global) interpolation
57 algorithm will be used.
58 -k k
60 --boundary-condition k
61 Set the boundary condition parameter for each constructed spline
62 to be k. (The default value is 1.0.) In each of its compo‐
63 nents, the spline will satisfy the two boundary conditions
64 y"[0]=ky"[1] and y"[n]=ky"[n-1]. Here y[0] and y[1] signify the
65 values of a specified component of the vector-valued dependent
66 variable y at the first two points of a dataset, and y[n-1] and
67 y[n] the values at the last two points. Setting k to zero will
68 yield a "natural" spline, i.e., one that has zero curvature at
69 the two ends of the dataset. The -k option may not be used if
70 -f or -p is specified.
71 -n n
73 --number-of-intervals n
74 Subdivide the interval over which interpolation occurs into n
75 subintervals. The number of data points computed, and written
76 to the output, will be n+1. The default value for n is 100.
77 -p
79 --periodic
80 Construct a periodic spline. If this option is specified, the y
81 values for the first and last points in each dataset must be
82 equal. The -f and -k options may not be used if -p is speci‐
83 fied.
84 -T tension
86 --tension tension
87 Each interpolating curve will be a spline under tension. This
88 option sets the tension value (the default is 0.0).
89 If tension equals zero, the curve will be a piecewise cubic
91 spline. Increasing the tension above zero makes the curve
92 "tighter", and reduces the likelihood of spurious inflection
93 points. That is because between each pair of successive points
94 in a dataset, the curve will satisfy the fourth-order differen‐
95 tial equation y""=sgn(tension)*(tension^2)y" in each of its com‐
96 ponents. As tension increases to positive infinity, it will
97 converge to a polygonal line. The -T option may not be used if
98 -f is specified.
99 -t tmin tmax [tspacing]
101 --t-spacing tmin tmax [tspacing]
102 For each dataset, set the interval over which interpolation
103 occurs to be the interval between tmin and tmax. If tspacing is
104 not specified, the interval will be divided into the number of
105 subintervals specified by the -n option.
106 If the -t option is not used, the interval over which interpola‐
108 tion occurs will be the entire range of the independent variable
109 in the dataset. The -t option must always be used if the -f
110 option is used to request filter-like behavior (see above).
111 Format-Related Options
113 -d dimension
114 --y-dimension dimension
115 Set the dimensionality of the dependent variable y in the input
116 and output files to be dimension. The default dimension is 1.
117 -I data-format
119 --input-format data-format
120 Set the data format for the input file(s) to be data-format,
121 which may be one of the following.
122 a ASCII format (the default). Each file is a sequence of
124 floating point numbers, interpreted as the t and y coor‐
125 dinates of the successive data points in a dataset. If y
126 is d-dimensional, there will be d+1 numbers for each
127 point. The t and y coordinates of a point need not
128 appear on the same line, and points need not appear on
129 different lines. But if a blank line occurs (i.e., two
130 newlines in succession are seen), it is interpreted as
131 the end of a dataset, and the beginning of the next.
132 f Single precision binary format. Each file is a sequence
134 of floating point numbers, interpreted as the t and y
135 coordinates of the successive data points in a dataset.
136 If y is d-dimensional, there will be d+1 numbers for each
137 point. Successive datasets are separated by a single
138 occurrence of the quantity FLT_MAX, which is the largest
139 possible single precision floating point number. On most
140 machines this is approximately 3.4x10^38.
141 d Double precision binary format. Each file is a sequence
143 of double precision floating point numbers, interpreted
144 as the t and y coordinates of the successive data points
145 in a dataset. If y is d-dimensional, there will be d+1
146 numbers for each point. Successive datasets are sepa‐
147 rated by a single occurrence of the quantity DBL_MAX,
148 which is the largest possible double precision floating
149 point number. On most machines this is approximately
150 1.8x10^308.
151 i Integer binary format. Each file is a sequence of inte‐
153 gers, interpreted as the t and y coordinates of the suc‐
154 cessive data points in a dataset. If y is d-dimensional,
155 there will be d+1 numbers for each point. Successive
156 datasets are separated by a single occurrence of the
157 quantity INT_MAX, which is the largest possible integer.
158 On most machines this is 2^31-1.
159 -a [step_size [lower_limit]]
161 --auto-abscissa [step_size [lower_limit]]
162 Automatically generate values for t, the independent variable
163 (the default values of step_size and lower_limit are 1.0 and
164 0.0, respectively).
165 Irrespective of data format (`a', `f', `d', or `i'), this option
167 specifies that the values of t are missing from the input file:
168 the dataset(s) to be read contain only values of y, the depen‐
169 dent variable. So if y is d-dimensional, there will be only d
170 numbers for each point. The increment from each t value to the
171 next will be step_size, and the first t value will be
172 lower_limit. This option is useful, e.g., when interpolating
173 curves rather than functions.
174 -A
176 --auto-dist-abscissa
177 Automatically generate values for t, the independent variable.
178 This is a variant form of the -a option. The increment from
179 each t value to the next will be the distance in d-dimensional
180 space between the corresponding y values, and the first t value
181 will be 0.0. That is, t will be "polygonal arclength". This
182 option is useful when interpolating curves rather than func‐
183 tions.
184 -O data-format
186 --output-format data-format
187 Set the data format for the output file to be data-format. The
188 interpretation of data-format is the same as for the -I option.
189 The default is `a', i.e., ASCII format.
190 -P significant-digits
192 --precision significant-digits
193 Set the numerical precision for the t and y values in the output
194 file to be significant-digits. This takes effect only if the
195 output file is written in `a' format, i.e., in ASCII. signifi‐
196 cant-digits must be a positive integer (the default is 6).
197 -s
199 --suppress-abscissa
200 Omit the independent variable t from the output file; for each
201 point, supply only the dependent variable y. If y is d-dimen‐
202 sional, there will be only d numbers for each point, not d+1.
203 This option is useful when interpolating curves rather than
204 functions.
205 Informational Options
207 --help Print a list of command-line options, and exit.
208 --version
210 Print the version number of spline and the plotting utilities
211 package, and exit.
212
214 Typing
215 echo 0 0 1 1 2 0 | spline
217 will produce on standard output an interpolated dataset consisting of
219 101 data points. If graphed, this interpolated dataset will yield a
220 parabola.
221 It is sometimes useful to interpolate between a sequence of arbitrarily
223 placed points in d-dimensional space, i.e., to "spline a curve" rather
224 than a function. The -a and -s options are used for this. For exam‐
225 ple,
226 echo 0 0 1 0 1 1 0 1 | spline -d 2 -a -s
228 will produce on standard output a 101-point dataset that interpolates
230 between the four points (0,0), (1,0), (1,1), and (0,1). The -d 2
231 option specifies that the dependent variable y is two-dimensional. The
232 -a option specifies that the t values are missing from the input and
233 should be automatically generated. The -s option specifies that the t
234 values should be stripped from the output.
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237 spline was written by Robert S. Maier (rsm@math.arizona.edu), starting
238 with an earlier version by Rich Murphey (rich@freebsd.org). The algo‐
239 rithms for constructing splines under tension are similar to those used
240 in the FITPACK subroutine library, and are ultimately due to Alan K.
241 Cline (cline@cs.utexas.edu).
242
244 "The GNU Plotting Utilities Manual".
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247 Email bug reports to bug-gnu-utils@gnu.org.
248FSF Dec 1998 SPLINE(1)