Description Usage Arguments Details Value Author(s) References See Also Examples

View source: R/profitCubaMoffat.R

Useful functions related to the Moffat profile. `profitCubaMoffat`

computes the exact 2D pixel integrals for a given Moffat model image. This is very slow compared to `profitMakeModel`

, but it is useful for checking model creation tuning (i.e. the degree to which speed can be increased without overly harming accuracy). Tests with this function were used to tune `profitMakeModel`

. `profitRadialMoffat`

computes the 1D radial flux intensity of the Moffat profile along the major axis of the profile.

1 2 3 | ```
profitCubaMoffat(xcen = dim[1]/2, ycen = dim[2]/2, mag = 15, fwhm = 3, con = 2, ang = 0,
axrat = 1, box = 0, dim = c(25, 25), rel.tol=1e-3, abs.tol= 1e-10)
profitRadialMoffat(r = 1, mag = 15, fwhm = 3, con = 2, ang = 0, axrat = 1, box = 0)
``` |

`xcen` |
Scalar; x centre of the 2D Sersic profile (can be fractional pixel positions). |

`ycen` |
Scalar; y centre of the 2D Sersic profile (can be fractional pixel positions). |

`r` |
Vector; the radius along the major axis at which to evalutate the flux intensity. |

`mag` |
Scalar; total magnitude of the 2D Moffat profile. Converted to flux using flux=10^(-0.4*(mag-magzero)). |

`fwhm` |
Scalar; full width half max of the Moffat function. |

`con` |
Scalar; concentration parameter for Moffat functions. Must be larger than 1. con=1 is pure Lorentzian and con=Inf is pure Normal. In practice con>5 starts to look very close to Normal. |

`ang` |
Scalar; the orientation of the major axis of the Sersic profile in degrees. When plotted as an R image the angle (theta) has the convention that 0= | (vertical), 45= \, 90= - (horizontal), 135= /, 180= | (vertical). Values outside the range 0 <= ang <= 180 are allowed, but these get recomputed as ang = ang. |

`axrat` |
Scalar; axial ratio of the Sersic profile defined as minor-axis/major-axis, i.e. 1 is a circle and 0 is a line. |

`box` |
Scalar; the boxiness of the Sersic profile that traces contours of iso-flux, defined such that r[mod]=(x^(2+box)+y^(2+box))^(1/(2+box)). When box=0 the iso-flux contours will be normal ellipses, but modifications between -1<box<1 will produce visually boxy distortions. Negative values have a pin-cushion effect, whereas positive values have a barrel effect (the major and minor axes staying fixed in all cases). |

`dim` |
Vector; The dimensions of the image to be generated. Typically this should be c(Nx,Ny). If length 1 then the value will be replicated for both dimenions. |

`rel.tol` |
Scalar; the requested relative accuracy. Default, 0.001. |

`abs.tol` |
Scalar; the requested absolute accuracy. The algorithm stops when either the relative or the absolute accuracies are met. Default, near 1e-10. |

This function uses the Cuba package to make an accurate (but expensive) cubature integral. This function was written to test the accuracy of Moffat models generated by `profitMakeModel`

.

By ProFit convention the bottom-left part of the bottom-left pixel when plotting the image matrix is c(0,0) and the top-right part of the bottom-left pixel is c(1,1), i.e. the mid-point of pixels are half integer values in x and y.

To confuse things a bit, when R plots an image of a matrix it is transposed and re-ordered vertically to how it appears if you print the matrix directly to screen, i.e. compare print(matrix(1:4,2,2)) and image(matrix(1:4,2,2)). The lowest value (1) is top-left when printed but bottom-left when displayed using image (the red pixel). Both are "correct": the issue is whether you consider the first element of a matrix to be the Cartesian x position (movement in x) or a row element (movement in y). Matrices in maths are always written top-left first where the first argument refers to row number, but images by convention are accessed in a Cartesian sense. Hence [3,4] in a maths matrix means 3 down and 4 right from the top-left, but 3 right and 4 up from the bottom-left in an image.

`profitCubaMoffat`

:
Matrix; contains the flux values of the specified model image. Dimensions dim.

`profitRadialMoffat`

:
Vector; same length as input r, specifying the flux intensity of the profile along the major axis.

Aaron Robotham

Moffat A. F. J., 1969, A\&A, 3, 455

`profitMakeModel`

, `profitSersic`

, `profitFerrer`

, `profitCoreSersic`

, `profitKing`

1 | ```
magimage(profitCubaMoffat(axrat=0.7, ang=30))
``` |

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