lin.h File Reference

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## Data Structures

struct | linprm
| Linear transformation parameters. More...

## Macros

#define | LINLEN (sizeof(struct linprm)/sizeof(int))
| Size of the linprm struct in int units. More...
#define | linini_errmsg lin_errmsg
| Deprecated. More...
#define | lincpy_errmsg lin_errmsg
| Deprecated. More...
#define | linfree_errmsg lin_errmsg
| Deprecated. More...
#define | linprt_errmsg lin_errmsg
| Deprecated. More...
#define | linset_errmsg lin_errmsg
| Deprecated. More...
#define | linp2x_errmsg lin_errmsg
| Deprecated. More...
#define | linx2p_errmsg lin_errmsg
| Deprecated. More...

## Enumerations

enum | lin_errmsg_enum { LINERR_SUCCESS = 0 , LINERR_NULL_POINTER = 1 , LINERR_MEMORY = 2 , LINERR_SINGULAR_MTX = 3 , LINERR_DISTORT_INIT = 4 , LINERR_DISTORT = 5 , LINERR_DEDISTORT = 6 }

## Functions

int | linini (int alloc, int naxis, struct linprm *lin)
| Default constructor for the linprm struct. More...
int | lininit (int alloc, int naxis, struct linprm *lin, int ndpmax)
| Default constructor for the linprm struct. More...
int | lindis (int sequence, struct linprm *lin, struct disprm *dis)
| Assign a distortion to a linprm struct. More...
int | lindist (int sequence, struct linprm *lin, struct disprm *dis, int ndpmax)
| Assign a distortion to a linprm struct. More...
int | lincpy (int alloc, const struct linprm *linsrc, struct linprm *lindst)
| Copy routine for the linprm struct. More...
int | linfree (struct linprm *lin)
| Destructor for the linprm struct. More...
int | linsize (const struct linprm *lin, int sizes[2])
| Compute the size of a linprm struct. More...
int | linprt (const struct linprm *lin)
| Print routine for the linprm struct. More...
int | linperr (const struct linprm *lin, const char *prefix)
| Print error messages from a linprm struct. More...
int | linset (struct linprm *lin)
| Setup routine for the linprm struct. More...
int | linp2x (struct linprm *lin, int ncoord, int nelem, const double pixcrd[], double imgcrd[])
| Pixel-to-world linear transformation. More...
int | linx2p (struct linprm *lin, int ncoord, int nelem, const double imgcrd[], double pixcrd[])
| World-to-pixel linear transformation. More...
int | linwarp (struct linprm *lin, const double pixblc[], const double pixtrc[], const double pixsamp[], int *nsamp, double maxdis[], double *maxtot, double avgdis[], double *avgtot, double rmsdis[], double *rmstot)
| Compute measures of distortion. More...
int | matinv (int n, const double mat[], double inv[])
| Matrix inversion. More...

## Variables

const char * | lin_errmsg []
| Status return messages. More...

## Detailed Description

Routines in this suite apply the linear transformation defined by the FITS World Coordinate System (WCS) standard, as described in

"Representations of world coordinates in FITS",
Greisen, E.W., & Calabretta, M.R. 2002, A&A, 395, 1061 (WCS Paper I)

These routines are based on the linprm struct which contains all information needed for the computations. The struct contains some members that must be set by the user, and others that are maintained by these routines, somewhat like a C++ class but with no encapsulation.

Six routines, linini(), lininit(), lindis(), lindist() lincpy(), and linfree() are provided to manage the linprm struct, linsize() computes its total size including allocated memory, and linprt() prints its contents.

linperr() prints the error message(s) (if any) stored in a linprm struct, and the disprm structs that it may contain.

A setup routine, linset(), computes intermediate values in the linprm struct from parameters in it that were supplied by the user. The struct always needs to be set up by linset() but need not be called explicitly - refer to the explanation of linprm::flag.

linp2x() and linx2p() implement the WCS linear transformations.

An auxiliary routine, linwarp(), computes various measures of the distortion over a specified range of pixel coordinates.

An auxiliary matrix inversion routine, matinv(), is included. It uses LU-triangular factorization with scaled partial pivoting.

## Macro Definition Documentation

## LINLEN

#define LINLEN (sizeof(struct linprm)/sizeof(int))

Size of the linprm struct in int units, used by the Fortran wrappers.

## linini_errmsg

#define linini_errmsg lin_errmsg

Deprecated:
  Added for backwards compatibility, use lin_errmsg directly now instead.

## lincpy_errmsg

#define lincpy_errmsg lin_errmsg

Deprecated:
  Added for backwards compatibility, use lin_errmsg directly now instead.

## linfree_errmsg

#define linfree_errmsg lin_errmsg

Deprecated:
  Added for backwards compatibility, use lin_errmsg directly now instead.

## linprt_errmsg

#define linprt_errmsg lin_errmsg

Deprecated:
  Added for backwards compatibility, use lin_errmsg directly now instead.

## linset_errmsg

#define linset_errmsg lin_errmsg

Deprecated:
  Added for backwards compatibility, use lin_errmsg directly now instead.

## linp2x_errmsg

#define linp2x_errmsg lin_errmsg

Deprecated:
  Added for backwards compatibility, use lin_errmsg directly now instead.

## linx2p_errmsg

#define linx2p_errmsg lin_errmsg

Deprecated:
  Added for backwards compatibility, use lin_errmsg directly now instead.

## Enumeration Type Documentation

## lin_errmsg_enum

enum lin_errmsg_enum

Enumerator
LINERR_SUCCESS |
LINERR_NULL_POINTER |
LINERR_MEMORY |
LINERR_SINGULAR_MTX |
LINERR_DISTORT_INIT |
LINERR_DISTORT |
LINERR_DEDISTORT |

## Function Documentation

## linini()

int linini | ( | int | alloc,
|  | int | naxis,
|  | struct linprm * | lin
| ) |  |

linini() is a thin wrapper on lininit(). It invokes it with ndpmax set to -1 which causes it to use the value of the global variable NDPMAX. It is thereby potentially thread-unsafe if NDPMAX is altered dynamically via disndp(). Use lininit() for a thread-safe alternative in this case.

## lininit()

int lininit | ( | int | alloc,
|  | int | naxis,
|  | struct linprm * | lin,
|  | int | ndpmax
| ) |  |

lininit() allocates memory for arrays in a linprm struct and sets all members of the struct to default values.

PLEASE NOTE: every linprm struct must be initialized by lininit(), possibly repeatedly. On the first invokation, and only the first invokation, linprm::flag must be set to -1 to initialize memory management, regardless of whether lininit() will actually be used to allocate memory.

Parameters

  [in] | alloc | If true, allocate memory unconditionally for arrays in the linprm struct. If false, it is assumed that pointers to these arrays have been set by the user except if they are null pointers in which case memory will be allocated for them regardless. (In other words, setting alloc true saves having to initalize these pointers to zero.)
  [in] | naxis | The number of world coordinate axes, used to determine array sizes.
  [in,out] | lin | Linear transformation parameters. Note that, in order to initialize memory management linprm::flag should be set to -1 when lin is initialized for the first time (memory leaks may result if it had already been initialized).
  [in] | ndpmax | The number of DPja or DQia keywords to allocate space for. If set to -1, the value of the global variable NDPMAX will be used. This is potentially thread-unsafe if disndp() is being used dynamically to alter its value.

Returns
  Status return value:
  - 0: Success.
  - 1: Null linprm pointer passed.
  - 2: Memory allocation failed.
  For returns > 1, a detailed error message is set in linprm::err if enabled, see wcserr_enable().

## lindis()

int lindis | ( | int | sequence,
|  | struct linprm * | lin,
|  | struct disprm * | dis
| ) |  |

lindis() is a thin wrapper on lindist(). It invokes it with ndpmax set to -1 which causes the value of the global variable NDPMAX to be used (by disinit()). It is thereby potentially thread-unsafe if NDPMAX is altered dynamically via disndp(). Use lindist() for a thread-safe alternative in this case.

## lindist()

int lindist | ( | int | sequence,
|  | struct linprm * | lin,
|  | struct disprm * | dis,
|  | int | ndpmax
| ) |  |

lindist() may be used to assign the address of a disprm struct to linprm::dispre or linprm::disseq. The linprm struct must already have been initialized by lininit().

The disprm struct must have been allocated from the heap (e.g. using malloc(), calloc(), etc.). lindist() will immediately initialize it via a call to disini() using the value of linprm::naxis. Subsequently, it will be reinitialized by calls to lininit(), and freed by linfree(), neither of which would happen if the disprm struct was assigned directly.

If the disprm struct had previously been assigned via lindist(), it will be freed before reassignment. It is also permissable for a null disprm pointer to be assigned to disable the distortion correction.

Parameters

  [in]

  sequence

  Is it a prior or sequent distortion?
  - 1: Prior, the assignment is to linprm::dispre.
  - 2: Sequent, the assignment is to linprm::disseq.
  Anything else is an error.

  [in,out] | lin | Linear transformation parameters.
  [in,out] | dis | Distortion function parameters.
  [in] | ndpmax | The number of DPja or DQia keywords to allocate space for. If set to -1, the value of the global variable NDPMAX will be used. This is potentially thread-unsafe if disndp() is being used dynamically to alter its value.

Returns
  Status return value:
  - 0: Success.
  - 1: Null linprm pointer passed.
  - 4: Invalid sequence.

## lincpy()

int lincpy | ( | int | alloc,
|  | const struct linprm * | linsrc,
|  | struct linprm * | lindst
| ) |  |

lincpy() does a deep copy of one linprm struct to another, using lininit() to allocate memory for its arrays if required. Only the "information to be provided" part of the struct is copied; a call to linset() is required to initialize the remainder.

Parameters

  [in] | alloc | If true, allocate memory for the crpix, pc, and cdelt arrays in the destination. Otherwise, it is assumed that pointers to these arrays have been set by the user except if they are null pointers in which case memory will be allocated for them regardless.
  [in] | linsrc | Struct to copy from.
  [in,out] | lindst | Struct to copy to. linprm::flag should be set to -1 if lindst was not previously initialized (memory leaks may result if it was previously initialized).

Returns
  Status return value:
  - 0: Success.
  - 1: Null linprm pointer passed.
  - 2: Memory allocation failed.
  For returns > 1, a detailed error message is set in linprm::err if enabled, see wcserr_enable().

## linfree()

int linfree | ( | struct linprm * | lin | ) |

linfree() frees memory allocated for the linprm arrays by lininit() and/or linset(). lininit() keeps a record of the memory it allocates and linfree() will only attempt to free this.

PLEASE NOTE: linfree() must not be invoked on a linprm struct that was not initialized by lininit().

Parameters

  [in] | lin | Linear transformation parameters.

Returns
  Status return value:
  - 0: Success.
  - 1: Null linprm pointer passed.

## linsize()

int linsize | ( | const struct linprm * | lin,
|  | int | sizes[2]
| ) |  |

linsize() computes the full size of a linprm struct, including allocated memory.

Parameters

  [in] | lin | Linear transformation parameters. If NULL, the base size of the struct and the allocated size are both set to zero.

  [out]

  sizes

  The first element is the base size of the struct as returned by sizeof(struct linprm).
  The second element is the total size of memory allocated in the struct, in bytes, assuming that the allocation was done by linini(). This figure includes memory allocated for members of constituent structs, such as linprm::dispre.
  It is not an error for the struct not to have been set up via linset(), which normally results in additional memory allocation.

Returns
  Status return value:
  - 0: Success.

## linprt()

int linprt | ( | const struct linprm * | lin | ) |

linprt() prints the contents of a linprm struct using wcsprintf(). Mainly intended for diagnostic purposes.

Parameters

  [in] | lin | Linear transformation parameters.

Returns
  Status return value:
  - 0: Success.
  - 1: Null linprm pointer passed.

## linperr()

int linperr | ( | const struct linprm * | lin,
|  | const char * | prefix
| ) |  |

linperr() prints the error message(s) (if any) stored in a linprm struct, and the disprm structs that it may contain. If there are no errors then nothing is printed. It uses wcserr_prt(), q.v.

Parameters

  [in] | lin | Coordinate transformation parameters.
  [in] | prefix | If non-NULL, each output line will be prefixed with this string.

Returns
  Status return value:
  - 0: Success.
  - 1: Null linprm pointer passed.

## linset()

int linset | ( | struct linprm * | lin | ) |

linset(), if necessary, allocates memory for the linprm::piximg and linprm::imgpix arrays and sets up the linprm struct according to information supplied within it - refer to the explanation of linprm::flag.

Note that this routine need not be called directly; it will be invoked by linp2x() and linx2p() if the linprm::flag is anything other than a predefined magic value.

Parameters

  [in,out] | lin | Linear transformation parameters.

Returns
  Status return value:
  - 0: Success.
  - 1: Null linprm pointer passed.
  - 2: Memory allocation failed.
  - 3: `PCi_ja` matrix is singular.
  For returns > 1, a detailed error message is set in linprm::err if enabled, see wcserr_enable().

## linp2x()

int linp2x | ( | struct linprm * | lin,
|  | int | ncoord,
|  | int | nelem,
|  | const double | pixcrd[],
|  | double | imgcrd[]
| ) |  |

linp2x() transforms pixel coordinates to intermediate world coordinates.

Parameters

  [in,out] | lin | Linear transformation parameters.
  [in] | ncoord,nelem | The number of coordinates, each of vector length nelem but containing lin.naxis coordinate elements.
  [in] | pixcrd | Array of pixel coordinates.
  [out] | imgcrd | Array of intermediate world coordinates.

Returns
  Status return value:
  - 0: Success.
  - 1: Null linprm pointer passed.
  - 2: Memory allocation failed.
  - 3: `PCi_ja` matrix is singular.
  For returns > 1, a detailed error message is set in linprm::err if enabled, see wcserr_enable().

## linx2p()

int linx2p | ( | struct linprm * | lin,
|  | int | ncoord,
|  | int | nelem,
|  | const double | imgcrd[],
|  | double | pixcrd[]
| ) |  |

linx2p() transforms intermediate world coordinates to pixel coordinates.

Parameters

  [in,out] | lin | Linear transformation parameters.
  [in] | ncoord,nelem | The number of coordinates, each of vector length nelem but containing lin.naxis coordinate elements.
  [in] | imgcrd | Array of intermediate world coordinates.

  [out]

  pixcrd

  Array of pixel coordinates. Status return value:
  - 0: Success.
  - 1: Null linprm pointer passed.
  - 2: Memory allocation failed.
  - 3: `PCi_ja` matrix is singular.
  For returns > 1, a detailed error message is set in linprm::err if enabled, see wcserr_enable().

## linwarp()

int linwarp | ( | struct linprm * | lin,
|  | const double | pixblc[],
|  | const double | pixtrc[],
|  | const double | pixsamp[],
|  | int * | nsamp,
|  | double | maxdis[],
|  | double * | maxtot,
|  | double | avgdis[],
|  | double * | avgtot,
|  | double | rmsdis[],
|  | double * | rmstot
| ) |  |

linwarp() computes various measures of the distortion over a specified range of pixel coordinates.

All distortion measures are specified as an offset in pixel coordinates, as given directly by prior distortions. The offset in intermediate pixel coordinates given by sequent distortions is translated back to pixel coordinates by applying the inverse of the linear transformation matrix (`PCi_ja` or `CDi_ja`). The difference may be significant if the matrix introduced a scaling.

If all distortions are prior, then linwarp() uses diswarp(), q.v.

Parameters

  [in,out] | lin | Linear transformation parameters plus distortions.
  [in] | pixblc | Start of the range of pixel coordinates (i.e. "bottom left-hand corner" in the conventional FITS image display orientation). May be specified as a NULL pointer which is interpreted as (1,1,...).
  [in] | pixtrc | End of the range of pixel coordinates (i.e. "top right-hand corner" in the conventional FITS image display orientation).

  [in]

  pixsamp

  If positive or zero, the increment on the particular axis, starting at pixblc[]. Zero is interpreted as a unit increment. pixsamp may also be specified as a NULL pointer which is interpreted as all zeroes, i.e. unit increments on all axes.
  If negative, the grid size on the particular axis (the absolute value being rounded to the nearest integer). For example, if pixsamp is (-128.0,-128.0,...) then each axis will be sampled at 128 points between pixblc[] and pixtrc[] inclusive. Use caution when using this option on non-square images.

  [out] | nsamp | The number of pixel coordinates sampled. Can be specified as a NULL pointer if not required.
  [out] | maxdis | For each individual distortion function, the maximum absolute value of the distortion. Can be specified as a NULL pointer if not required.
  [out] | maxtot | For the combination of all distortion functions, the maximum absolute value of the distortion. Can be specified as a NULL pointer if not required.
  [out] | avgdis | For each individual distortion function, the mean value of the distortion. Can be specified as a NULL pointer if not required.
  [out] | avgtot | For the combination of all distortion functions, the mean value of the distortion. Can be specified as a NULL pointer if not required.
  [out] | rmsdis | For each individual distortion function, the root mean square deviation of the distortion. Can be specified as a NULL pointer if not required.
  [out] | rmstot | For the combination of all distortion functions, the root mean square deviation of the distortion. Can be specified as a NULL pointer if not required.

Returns
  Status return value:
  - 0: Success.
  - 1: Null linprm pointer passed.
  - 2: Memory allocation failed.
  - 3: Invalid parameter.
  - 4: Distort error.

## matinv()

matinv | ( | int | n,
|  | const double | mat[],
|  | double | inv[]
| ) |  |

matinv() performs matrix inversion using LU-triangular factorization with scaled partial pivoting.

Parameters

  [in] | n | Order of the matrix ( ).
  [in] | mat | Matrix to be inverted, stored as mat[ ] where and are the row and column indices respectively.
  [out] | inv | Inverse of mat with the same storage convention.

Returns
  Status return value:
  - 0: Success.
  - 2: Memory allocation failed.
  - 3: Singular matrix.

## Variable Documentation

## lin_errmsg

const char * lin_errmsg[]

extern

Error messages to match the status value returned from each function.