This is the command fitcirclegmt that can be run in the OnWorks free hosting provider using one of our multiple free online workstations such as Ubuntu Online, Fedora Online, Windows online emulator or MAC OS online emulator

**PROGRAM:**

**NAME**

fitcircle - find mean position and pole of best-fit great [or small] circle to points on a

sphere.

**SYNOPSIS**

**fitcircle**[

__table__]

__norm__[

__flags__] [ [

__lat__] ] [ [

__level__] ] [

**-bi**<binary> ] [

**-di**<nodata> ] [

**-f**<flags> ] [

**-g**<gaps> ] [

**-h**<headers> ] [

**-i**<flags> ] [

**-o**<flags> ] [

**-:**[

**i**|

**o**] ]

**Note:**No space is allowed between the option flag and the associated arguments.

**DESCRIPTION**

**fitcircle**reads lon,lat [or lat,lon] values from the first two columns on standard input

[or

__table__]. These are converted to Cartesian three-vectors on the unit sphere. Then two

locations are found: the mean of the input positions, and the pole to the great circle

which best fits the input positions. The user may choose one or both of two possible

solutions to this problem. The first is called

**-L1**and the second is called

**-L2**. When the

data are closely grouped along a great circle both solutions are similar. If the data have

large dispersion, the pole to the great circle will be less well determined than the mean.

Compare both solutions as a qualitative check.

The

**-L1**solution is so called because it approximates the minimization of the sum of

absolute values of cosines of angular distances. This solution finds the mean position as

the Fisher average of the data, and the pole position as the Fisher average of the

cross-products between the mean and the data. Averaging cross-products gives weight to

points in proportion to their distance from the mean, analogous to the "leverage" of

distant points in linear regression in the plane.

The

**-L2**solution is so called because it approximates the minimization of the sum of

squares of cosines of angular distances. It creates a 3 by 3 matrix of sums of squares of

components of the data vectors. The eigenvectors of this matrix give the mean and pole

locations. This method may be more subject to roundoff errors when there are thousands of

data. The pole is given by the eigenvector corresponding to the smallest eigenvalue; it is

the least-well represented factor in the data and is not easily estimated by either

method.

**REQUIRED** **ARGUMENTS**

**-L**

__norm__Specify the desired

__norm__as 1 or 2, or use

**-L**or

**-L3**to see both solutions.

**OPTIONAL** **ARGUMENTS**

__table__One or more ASCII [or binary, see

**-bi**] files containing lon,lat [or lat,lon; see

**-:**[

**i**|

**o**]] values in the first 2 columns. If no file is specified,

**fitcircle**will

read from standard input.

**-Ff|m|n|s|c**

Normally,

**fitcircle**will write its results in the form of a text report, with the

values intermingled with report sentences. Use

**-F**to only return data coordinates,

and append

__flags__to specify which coordinates you would like. You can choose from

**f**

(Flat Earth mean location),

**m**(mean location),

**n**(north pole of great circle),

**s**

(south pole of great circle), and

**c**

******

**(pole**

**of**

**small**

**circle**

**and**

**its**

**colatitude,**

**which**

**requires**

****-S**).

**-S[**

__lat__

**]**

Attempt to fit a small circle instead of a great circle. The pole will be

constrained to lie on the great circle connecting the pole of the best-fit great

circle and the mean location of the data. Optionally append the desired fixed

latitude of the small circle [Default will determine the latitude].

**-V[**

__level__

**]**

**(more**

**...)**

Select verbosity level [c].

**-bi[**

__ncols__

**][t]**

**(more**

**...)**

Select native binary input. [Default is 2 input columns].

**-di**

__nodata__

**(more**

**...)**

Replace input columns that equal

__nodata__with NaN.

**-f[i|o]**

__colinfo__

**(more**

**...)**

Specify data types of input and/or output columns.

**-g[a]x|y|d|X|Y|D|[**

__col__

**]z[+|-]**

__gap__

**[u]**

**(more**

**...)**

Determine data gaps and line breaks.

**-h[i|o][**

__n__

**][+c][+d][+r**

__remark__

**][+r**

__title__

**]**

**(more**

**...)**

Skip or produce header record(s).

**-i**

__cols__

**[l][s**

__scale__

**][o**

__offset__

**][,**

__...__

**]**

**(more**

**...)**

Select input columns (0 is first column).

**-o**

__cols__

**[,...]**

**(more**

**...)**

Select output columns (0 is first column).

**-:[i|o]**

**(more**

**...)**

Swap 1st and 2nd column on input and/or output.

**-^**

**or**

**just**

**-**

Print a short message about the syntax of the command, then exits (NOTE: on Windows

use just

**-**).

**-+**

**or**

**just**

**+**

Print an extensive usage (help) message, including the explanation of any

module-specific option (but not the GMT common options), then exits.

**-?**

**or**

**no**

**arguments**

Print a complete usage (help) message, including the explanation of options, then

exits.

**--version**

Print GMT version and exit.

**--show-datadir**

Print full path to GMT share directory and exit.

**ASCII** **FORMAT** **PRECISION**

The ASCII output formats of numerical data are controlled by parameters in your

**gmt.conf**

file. Longitude and latitude are formatted according to FORMAT_GEO_OUT, whereas other

values are formatted according to FORMAT_FLOAT_OUT. Be aware that the format in effect can

lead to loss of precision in the output, which can lead to various problems downstream. If

you find the output is not written with enough precision, consider switching to binary

output (

**-bo**if available) or specify more decimals using the FORMAT_FLOAT_OUT setting.

**EXAMPLES**

Suppose you have lon,lat,grav data along a twisty ship track in the file ship.xyg. You

want to project this data onto a great circle and resample it in distance, in order to

filter it or check its spectrum. Do the following:

gmt fitcircle ship.xyg -L2

gmt project ship.xyg -Cox/oy -Tpx/py -S -Fpz | sample1d -S-100 -I1 > output.pg

Here,

__ox__/

__oy__is the lon/lat of the mean from

**fitcircle**, and

__px__/

__py__is the lon/lat of the

pole. The file output.pg has distance, gravity data sampled every 1 km along the great

circle which best fits ship.xyg

If you have lon, lat points in the file data.txt and wish to return the northern

hemisphere great circle pole location using the L2 norm, try

gmt fitcircle data.txt -L2 -Fn > pole.txt

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