{"id":358,"date":"2013-11-03T06:22:00","date_gmt":"2013-11-03T06:22:00","guid":{"rendered":"http:\/\/ahay.org\/blog\/?p=358"},"modified":"2015-08-30T17:50:22","modified_gmt":"2015-08-30T17:50:22","slug":"program-of-the-month-sfremap1","status":"publish","type":"post","link":"https:\/\/ahay.org\/blog\/2013\/11\/03\/program-of-the-month-sfremap1\/","title":{"rendered":"Program of the month: sfremap1"},"content":{"rendered":"

sfremap1<\/a> interpolates the input data to a different grid along the first axis. Here is an elementary example: making some data and interpolating it to a denser grid: <\/p>\n

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bash$ sfmath n1=5 o1=0 d1=1 output=x1 | sfdisfil \n0: 0 1 2 3 4 \nbash$ sfmath n1=5 o1=0 d1=1 output=x1 | sfremap1 n1=10 d1=0.5 | sfdisfil \n0: 0 0.5 1 1.5 2 \n5: 2.5 3 3.5 4 4.5\n<\/code><\/pre><\/div>\n
sfremap1<\/strong> uses ENO (essentially non-oscillatory) interpolation to prevent oscillations when interpolating discontinuous data:  <\/p>\n
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bash$ sergey$ sfspike n1=10 o1=0 d1=1 k1=6 | sfcausint | sfdisfil \n0: 0 0 0 0 0 \n5: 1 1 1 1 1 \nbash$ sfspike n1=10 o1=0 d1=1 k1=6 | sfcausint | sfremap1 n1=20 d1=0.5 | sfdisfil \n0: 0 0 0 0 0 \n5: 0 0 0 0 0.5 \n10: 1 1 1 1 1 \n15: 1 1 1 1 1\n<\/code><\/pre><\/div>\n
The ENO algorithm is described by Harten et al. (1987) and Shu and Osher (1988): <\/p>\n
A. Harten, B. Engquist, S. Osher, and S. R. Chakravarthy, 1987, Uniformly high order accurate essentially non-oscillatory schemes, III: Journal of Computational Physics,<\/em> 71(2), 231-303. <\/p>\n
C. W. Shu and S. Osher, 1988, Efficient implementation of essentially non-oscillatory shock-capturing schemes: Journal of Computational Physics<\/em>, 77(2), 439-471. <\/p>\n
The interpolation order is controlled by the order=<\/strong> parameter, order=2<\/strong> corresponds to linear interpolation, the default is order=3<\/strong>. The output grid can be specified either by n1=, o1=, d1= parameters or by providing an example file with the desired grid in pattern=<\/strong> parameter. Here is an example:  <\/p>\n
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bash$ sfmath n1=5 o1=0 d1=1 output=x1 > data.rsf\nbash$ sfspike n1=10 d1=0.5 > other.rsf\nbash$ < data.rsf sfremap1 pattern=other.rsf | sfdisfil\n   0:             0          0.5            1          1.5            2\n   5:           2.5            3          3.5            4          4.5\n<\/code><\/pre><\/div>\n
For an alternative method (cubic spline interpolation), see sfspline<\/a>. <\/p>\n
10 previous programs of the month:<\/h3>\n