

f  
filter  
Use a local interpolation algorithm (the cubic Bessel algorithm), so that spline can be used as a realtime filter. The slope of the interpolating curve at each point in a dataset will be chosen by fitting a quadratic function through that point and the two adjacent points in the dataset. If f is specified then the t option, otherwise optional, must be used as well. Also, if f is specified then the k, p, and T options may not be used.  
If f is not specified, then the default (global) interpolation algorithm will be used.  
k k  
boundarycondition k  
Set the boundary condition parameter for each constructed spline to be k. (The default value is 1.0.) In each of its components, the spline will satisfy the two boundary conditions y"[0]=ky"[1] and y"[n]=ky"[n1]. Here y[0] and y[1] signify the values of a specified component of the vectorvalued dependent variable y at the first two points of a dataset, and y[n1] and y[n] the values at the last two points. Setting k to zero will yield a "natural" spline, i.e., one that has zero curvature at the two ends of the dataset. The k option may not be used if f or p is specified.  
n n  
numberofintervals n  
Subdivide the interval over which interpolation occurs into n subintervals. The number of data points computed, and written to the output, will be n+1. The default value for n is 100.  
p  
periodic  
Construct a periodic spline. If this option is specified, the y values for the first and last points in each dataset must be equal. The f and k options may not be used if p is specified.  
T tension  
tension tension  
Each interpolating curve will be a spline under tension. This option sets the tension value (the default is 0.0).  
If tension equals zero, the curve will be a piecewise cubic spline. Increasing the tension above zero makes the curve "tighter", and reduces the likelihood of spurious inflection points. That is because between each pair of successive points in a dataset, the curve will satisfy the fourthorder differential equation y""=sgn(tension)*(tension^2)y" in each of its components. As tension increases to positive infinity, it will converge to a polygonal line. The T option may not be used if f is specified.  
t tmin tmax [tspacing]  
tspacing tmin tmax [tspacing]  
For each dataset, set the interval over which interpolation occurs to be the interval between tmin and tmax. If tspacing is not specified, the interval will be divided into the number of subintervals specified by the n option.  
If the t option is not used, the interval over which interpolation occurs will be the entire range of the independent variable in the dataset. The t option must always be used if the f option is used to request filterlike behavior (see above).  
d dimension ydimension dimension Set the dimensionality of the dependent variable y in the input and output files to be dimension. The default dimension is 1. I dataformat inputformat dataformat Set the data format for the input file(s) to be dataformat, which may be one of the following.
a ASCII format (the default). Each file is a sequence of floating point numbers, interpreted as the t and y coordinates of the successive data points in a dataset. If y is ddimensional, there will be d+1 numbers for each point. The t and y coordinates of a point need not appear on the same line, and points need not appear on different lines. But if a blank line occurs (i.e., two newlines in succession are seen), it is interpreted as the end of a dataset, and the beginning of the next. f Single precision binary format. Each file is a sequence of floating point numbers, interpreted as the t and y coordinates of the successive data points in a dataset. If y is ddimensional, there will be d+1 numbers for each point. Successive datasets are separated by a single occurrence of the quantity FLT_MAX, which is the largest possible single precision floating point number. On most machines this is approximately 3.4x10^38. d Double precision binary format. Each file is a sequence of double precision floating point numbers, interpreted as the t and y coordinates of the successive data points in a dataset. If y is ddimensional, there will be d+1 numbers for each point. Successive datasets are separated by a single occurrence of the quantity DBL_MAX, which is the largest possible double precision floating point number. On most machines this is approximately 1.8x10^308. i Integer binary format. Each file is a sequence of integers, interpreted as the t and y coordinates of the successive data points in a dataset. If y is ddimensional, there will be d+1 numbers for each point. Successive datasets are separated by a single occurrence of the quantity INT_MAX, which is the largest possible integer. On most machines this is 2^311. a [step_size [lower_limit]] autoabscissa [step_size [lower_limit]] Automatically generate values for t, the independent variable (the default values of step_size and lower_limit are 1.0 and 0.0, respectively). Irrespective of data format (‘a’, ‘f’, ‘d’, or ‘i’), this option specifies that the values of t are missing from the input file: the dataset(s) to be read contain only values of y, the dependent variable. So if y is ddimensional, there will be only d numbers for each point. The increment from each t value to the next will be step_size, and the first t value will be lower_limit. This option is useful, e.g., when interpolating curves rather than functions. A autodistabscissa Automatically generate values for t, the independent variable. This is a variant form of the a option. The increment from each t value to the next will be the distance in ddimensional space between the corresponding y values, and the first t value will be 0.0. That is, t will be "polygonal arclength". This option is useful when interpolating curves rather than functions. O dataformat outputformat dataformat Set the data format for the output file to be dataformat. The interpretation of dataformat is the same as for the I option. The default is ‘a’, i.e., ASCII format. P significantdigits precision significantdigits Set the numerical precision for the t and y values in the output file to be significantdigits. This takes effect only if the output file is written in ‘a’ format, i.e., in ASCII. significantdigits must be a positive integer (the default is 6). s suppressabscissa Omit the independent variable t from the output file; for each point, supply only the dependent variable y. If y is ddimensional, there will be only d numbers for each point, not d+1. This option is useful when interpolating curves rather than functions.
help Print a list of commandline options, and exit. version Print the version number of spline and the plotting utilities package, and exit.
Typing
echo 0 0 1 1 2 0  splinewill produce on standard output an interpolated dataset consisting of 101 data points. If graphed, this interpolated dataset will yield a parabola.
It is sometimes useful to interpolate between a sequence of arbitrarily placed points in ddimensional space, i.e., to "spline a curve" rather than a function. The a and s options are used for this. For example,
echo 0 0 1 0 1 1 0 1  spline d 2 a swill produce on standard output a 101point dataset that interpolates between the four points (0,0), (1,0), (1,1), and (0,1). The d 2 option specifies that the dependent variable y is twodimensional. The a option specifies that the t values are missing from the input and should be automatically generated. The s option specifies that the t values should be stripped from the output.
spline was written by Robert S. Maier (rsm@math.arizona.edu), starting with an earlier version by Rich Murphey (rich@freebsd.org). The algorithms for constructing splines under tension are similar to those used in the FITPACK subroutine library, and are ultimately due to Alan K. Cline (cline@cs.utexas.edu).
"The GNU Plotting Utilities Manual".
Email bug reports to buggnuutils@gnu.org.
FSF  SPLINE (1)  Dec 1998 
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