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## IDENTIFY Database

The IDENTIFY database specified by the parameter *database* is a directory of
simple text files. The text files have names beginning with 'id' followed
by the entry name, usually the name of the image. The database text files
consist of a number of records. A record begins with a line starting with the
keyword "`begin`". The rest of the line is the record identifier. Records
read and written by **identify** have "`identify`" as the first word of the
identifier. Following this is a name which may be specified following the
"`:read`" or "`:write`" commands. If no name is specified then the image name
is used. For 1D spectra the database entry includes the aperture number
and so to read a solution from a aperture different than the current image
and aperture number must be specified. For 2D/3D images the entry name
has the 1D image section which is what is specified to read the entry.
The lines following the record identifier contain
the feature information and dispersion function coefficients.

The dispersion function is saved in the database as a series of
coefficients. The section containing the coefficients starts with the
keyword "`coefficients`" and the number of coefficients.

The first four coefficients define the type of function, the order or number of spline pieces, and the range of the independent variable (the line or column coordinate along the dispersion). The first coefficient is the function type code with values:

Code Type 1 Chebyshev polynomial 2 Legendre polynomial 3 Cubic spline 4 Linear spline

The second coefficient is the order (actually the number of terms) of the polynomial or the number of pieces in the spline.

The next two coefficients are the range of the independent variable over which the function is defined. These values are used to normalize the input variable to the range -1 to 1 in the polynomial functions. If the independent variable is x and the normalized variable is n, then

n = (2 * x - (xmax + xmin)) / (xmax - xmin)

where xmin and xmax are the two coefficients.

The spline functions divide the range into the specified number of pieces. A spline coordinate s and the nearest integer below s, denoted as j, are defined by

s = (x - xmin) / (xmax - xmin) * npieces j = integer part of s

where npieces are the number of pieces.

The remaining coefficients are those for the appropriate function. The number of coefficients is either the same as the function order for the polynomials, npieces+1 for the linear spline, or npieces + 3 for the cubic spline.

1. Chebyshev Polynomial

The polynomial can be expressed as the sum

y = sum from i=1 to order {c_i * z_i}

where the the c_i are the coefficients and the z_i are defined interactively as:

z_1 = 1 z_2 = n z_i = 2 * n * z_{i-1} - z_{i-2}

2. Legendre Polynomial

The polynomial can be expressed as the sum

y = sum from i=1 to order {c_i * z_i}

where the the c_i are the coefficients and the z_i are defined interactively as:

z_1 = 1 z_2 = n z_i = ((2*i-3) * n * z_{i-1} - (i-2) * z_{i-2}) / (i-1)

3. Linear Spline

The linear spline is evaluated as

y = c_j * a + c_{j+1} * b

where j is as defined earlier and a and b are fractional difference between s and the nearest integers above and below

a = (j + 1) - s b = s - j

4. Cubic Spline

The cubic spline is evaluated as

y = sum from i=0 to 3 {c_{i+j} * z_i}

where j is as defined earlier. The term z_i are computed from a and b, as defined earlier, as follows

z_0 = a**3 z_1 = 1 + 3 * a * (1 + a * b) z_2 = 1 + 3 * b * (1 + a * b) z_3 = b**3