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4.3.5.2 map-grid
— Function: grid:map-grid &key source source-affi source-dims destination destination-affi destination-specification initial-element element-function combination-function

Make a new grid by mapping on an existing grid or on indices. :source The source grid; if not a grid, it is taken as a function to apply to the grid indices to make the element of the destination; if this is supplied, source is ignored and element-function is only applied to the default value.

:source-affi The affi to be used for extraction; defaults to
making an affi from source-dims, then destination-specification.
:source-dims The dimensions of the source if source not supplied;
if nil, dimensions are taken from destination-specification.
:destination The destination grid, if not supplied, it will be made
according to destination-affi and destination-specification.
:destination-affi The affi for injection, defaults to (affi destination)
if destination is supplied, then makes an affi if destination-specification is supplied, otherwise source-affi.
:destination-specification The specification to use for the destination to be make,
defaults to the specification of source.
:initial-element The default value to set in a newly-created destination.
:element-function The function to apply to each element of the source; defaults
to coercing element to the element type of the destination.
:combination-function
A designator for a function of two arguments, or nil (default). If a function, it will be funcalled on the destination element and the transformed source element. If nil, the destination element is overwritten.
Although this function has other uses, it can be used to create a grid using a function of the index values. For example, in the file antik/grid/tests/grids.lisp is a function index-fill-decadal that multiplies increasing powers of ten by each argument in succession, and adds the result. The array *array-3-4-double-float* is created with this function: 
     (defparameter *array-3-4-double-float*
       (map-grid :source 'index-fill-decadal :source-dims '(3 4)))

which gives 

     *array-3-4-double-float*
     #2A((0.0d0 1.0d0 2.0d0 3.0d0)
         (10.0d0 11.0d0 12.0d0 13.0d0)
         (20.0d0 21.0d0 22.0d0 23.0d0))

(see also the function 'test-grid-double-float).

Take the square root of every element of an array: 

     (map-grid :source #m((0.0d0 1.0d0 2.0d0) (10.0d0 11.0d0 12.0d0) (20.0d0 21.0d0 22.0d0)) :element-function 'sqrt)

Make a foreign vector with each element the square root of its index: 

     (map-grid :source 'sqrt :destination-specification '((foreign-array 6) double-float))