Dictionary of Satimage

Example

creatematrix v : create an array of real of size ncols*nrows

creatematrix string : "1": array of 1.0, "x": array of x values, "y": array of y values, "d": diagonal square matrix

ncols integer : or a list of real with the "x" option, will make an array with identical rows

nrows integer : or a list of real with the "y" option, will make an array with identical columns

[range list of real] : a range {min,max} for the "x" and "y" options

[diagonal array of real] : the diagonal values for the "d" option. You can also provide a real, in which case the matrix dimensions are specified by ncols=nrows. Default: 1.0 (identity matrix).

[as type] : array of real or matrix, default: array of real

→ array of real : or matrix

Example

randomarray v : create a random array of real

randomarray integer : the requested size of the array

[range list of real] : {min,max}

[seed integer]

Example

replacemissingvalue v : replace missing values (or NAN's) in a list, or an array of real, or a list of such.

replacemissingvalue array of real : or a list of arrays

with real

→ array of real : or a list of arrays

Example

extractitem v : (obsolete: use extractarray instead)

extractitem integer

[thru integer]

[step integer]

in array of real

[blocksize integer]

[as type]

extractarray v : extract values from an array of real

extractarray array of real

[at integer] : the first item to read or a list of indexes (in which case, the "for", "step" and "blocksize" parameters are not taken into account). 1-based. Default 1

[for integer] : the number of blocks to read. If <0 then read as many blocks as possible. Default 1

[blocksize integer] : size of the block to read at each step. blocksize must be smaller than step

[step integer] : the interval between the beginnings of successive blocks to read. Must be larger than blocksize. Default: blocksize

[as type] : default is array of real, you can provide small real or real for 1 item

Example

changearray v : change items in an array of real

changearray array of real : the array to modify

[at integer] : the index of the first item to change (1 based) or a list of indexes (in which case, the "step" and "blocksize" parameters are not taken into account). default: 1

into array of real : the new values

[blocksize integer] : size of the blocks to copy at each step. The "into" parameter must have a size multiple of blocksize. Default: 1

[step integer] : the interval between the beginnings of successive blocks to write. Must be larger than blocksize. Default: blocksize

Example

insertarray v : insert items into an array of real

insertarray array of real : the values to insert

into array of real : the array to modify

[at integer] : the index of the first item to insert (0: at the beginning) or a list of indexes of the same size as the direct parameter (in which case, the "for", "step" and "blocksize" parameters are not taken into account). default -1 (insert values at the end)

[for integer] : number of blocks to insert. default 1

[step integer] : the number of values between each insertion. default 0

[blocksize integer] : size of the blocks to insert after each step. The direct parameter must have a size multiple of blocksize. Default: 1 if "for" is defined, else the size of the direct parameter.

Example

resamplematrix v : resample a matrix. The incoming matrix is divided into rectangular blocks. Each block may be replaced by its mean value or by another statistical value.

resamplematrix matrix : the matrix to resample

blocksize list of integer : {i,j}, defines the horizontal and vertical sizes of the blocks used for resampling. i and j may be integers (identical blocks) or lists of integers (irregular grid, the items of the lists define the successive sizes of the blocks).

[wanted string] : the following strings or a list of such: "mean", "minimum", "maximum", "stdev", "missing value", "sum", "median", "dispersion". Specify the statistical function computed on each block. Default: "mean".

→ matrix : the resampled matrix, or a list of matrices if 'wanted' is a list. The dimensions of the resampled matrix correspond to the numbers of blocks defined with 'blocksize'.

Example

reversearray v : returns reverse of the direct parameter.

reversearray list of real : ... or an array of real

Example

multlist v : performs the product of the parameters. Each parameter may be a list, an array of real, a matrix or a number. multlist {x1,x2...} with {y1,y2...} returns {x1.y1, x2.y2, ...}; multlist x with {y1,y2...} returns {x.y1, x.y2, ...}

multlist list of real

divlist v : same as multlist, but for quotient

divlist list of real

addlist v : same as multlist, but for sums

addlist list of real

sublist v : same as multlist, but for subtraction

sublist list of real

runningsum v : returns the running sum of an array of real

runningsum array of real

Example

statlist v : returns as a record the min, max, min index, max index, mean, sum, standard deviation, variance.

statlist list of real : ... or an array of real

[kurtosis boolean] : if true, statlist compute also skewness, kurtosis and median calculations.

→ statsrecord

Example

histogram v : given an array of real numbers, return a list of 2 arrays : {sampling values,frequencies}

histogram array of real

samples integer : number of intervals

[minimum real] : lower bound of the intervals

[maximum real] : upper bound of the intervals

→ list of array of real : {sampling values,frequencies}

Example

evalformula v : apply C-like mathematical expressions to arrays of real. Ex: evalformula "a*x^2+y^2" with {"a",2.4,"x",anarray,"y",anotherarray} (or by using a record: evalformula "a*x^2+y^2" with {a:2.4,x:anarray,y:anotherarray})

evalformula string : the formula to compute

with list or record : the definition of the variables occurring in the formula. If a list, an alternation of reference names (strings) and data (number, list of numbers or array of real). Prefer lists because you can't use reserved words with records.

as type : matrix or array of real: the requested type if parameters are matrices. Default: array of real

→ array of real : or real

Example

Discussion

The expression of evalformula may include logical operators, yet all values remain real numbers: true expressions evaluate to 1.0, false expressions evaluate to 0.0. Conversely when implied in a logical expression any non null number is considered as true (1.0).
The direct parameter of evalformula may be a sequence of elementary expressions, provided they are separated with semi-colon ;. You can also use return as the separator, so in complex cases when the expression may require several intermediate steps you can easily use the contents of a text window as the expression. When you use such a composite construct evalformula will return the result of the last (rightmost) expression.
Instead of one expression you can pass a list of expressions to evalformula: evalformula will return a list of arrays of real.
Here is the list of the operators and functions that evalformula supports.
operators (higher precedence first)
- - (unary)
- * /, + -, ^ (exponentiation)
- >= > <= <== != (equal - not equal), & (logical AND), | (logical OR), ! (boolean not, evaluates to 1 if the operand is 0 and to 0 otherwise).
algebra
- sqr, sqrt, hypot, pow
- abs, ceil, floor, trunc, max, min
- mod (modulo), remainder
- isnan (test whether the quantity is a ``NAN''. NAN = Not A Number.)
transcendental
- ln or log (neperian), log10, exp
- cos, sin, tan, acos, asin, atan, atan2 (atan2(y,x))
- cosh, sinh, tanh, acosh, asinh, atanh
- erf, erfc, gamma, lgamma
functions on arrays
- norm and norm2, respectively the euclidian norm and its square (numbers),
- sum and runsum, respectively the sum (a number) and the running sum (an array),
- count, the number of elements (a number).

maskarray v : suppress items (or rows) out of an array of real (or a matrix) with respect to a mask of 0's and 1's.

maskarray array of real : the array(s) or matrix to be filtered. For a matrix, the rows are deleted.

with array of real : the filter: an array of real, 0's mean that the corresponding items are to be deleted in the direct object(s).

→ array of real : the resulting array(s) or matrix

Example

filter v

filter matrix

using array of real : a list of 9 real numbers representing the 3x3 convolution matrix

[reduced boolean] : the resulting matrix is smaller (the 2 extremal columns and rows are removed. Default true.)

→ matrix

evalpolynomial v

evalpolynomial list of real : the polynomial, given as the list of its coefficients, 0th degree (constant term) first. Or an array of real coerced with "as polynomial"

at real : or array of real

→ real

Example

roots of v

roots of list of real : the polynomial, given as the list of its coefficients, 0th degree (constant term) first

[complex boolean] : default : false. Also compute the complex roots

→ list of real : roots of the polynomial. Complex roots are returned as a list of 2 real numbers

Example

composepolynomial v : you can provide arrays of real instead of polynomials

composepolynomial polynomial : or an array of real: the polynomial P(X), given as the list of its coefficients, 0th degree (constant term) first.

with polynomial : Q(X)

→ polynomial : P(Q(X))

pade approximant v : given a polynomial P(X), compute the Padé approximant as the rational function NUM(X)/DEN(X). NUM and DEN are polynomials and the constant term of DEN is 1. syn pade

pade approximant polynomial : or an array of real: the polynomial P(X), given as the list of its coefficients, 0th degree (constant term) first.

numerator integer : the requested degree for NUM(X)

denominator integer : the requested degree for DEN(X)

→ list of polynomial : {NUM(X), DEN(X)}

fitpolynomial v : given two arrays of real {x,y} returns the best polynomial fit y=P(x)

fitpolynomial list of array of real : a list of two arrays of real {x,y}

degree integer : the degree of the resulting polynomial

[number formatting string] : the format string for the formula output. If you don't specify this parameter, no fit string will be provided in the result record.

→ fitrecord

Example

fitrational v : given two arrays of real {x,y} returns the best rational fit y=NUM(x)/DEN(x). NUM and DEN are polynomials and the constant term of DEN is 1.

fitrational list of array of real : a list of two arrays of real {x,y}

numerator integer : the requested degree for NUM(X)

denominator integer : the requested degree for DEN(X)

[number formatting string] : the format string for the formula output. If you don't specify this parameter, no fit string will be provided in the result record.

→ fitrecord : where fit result if a list of 2 polynomials.

read binary v : read a file of real or small real

read binary file specification : the file

as type : the format of the data file: real (8 bytes), small real (4 bytes), integer (4 bytes), small integer (2 bytes), or byte (1 byte)

[skip integer] : the number of leading bytes to skip

[step integer] : the offset between two consecutive readings

[blocksize integer] : the size of the blocks in the "as" unit. Default 1

[length integer] : the number of blocks to read

[big endian boolean] : is the file encoded as big endian or little endian? Default: system endianess (false on mac intel).

[signed boolean] : Only for integer types. Are they signed or unsigned? Default: true.