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Not quite enough abstraction



This is a side comment about this SRFI.

I'm working with fMRI data, which consists of a time series of volumes,
of slices, of rows, of pixels, of complex numbers.  Just what an
array SRFI should help with.

Until now, I've been doing the following operations on the data (in place).

1.  Two-D FFT's on slices.
2.  Complex (as in complex numbers) wavelet transforms in the various
     coordinate directions.
3.  Various nonlinear operations on the wavelet coefficients to smooth the
    images.
4, 5, 6. ...  The reverse of all these operations.

Now I have to do time-series analysis of pixels and wavelet coefficients,
moving around quadrants of slices (take a two-d slice (image), and swap the
pixels in opposite diagonal quadrants), turning out pbm images of statistically
significant pixels, merging pgm images of complex magnitudes of pixels and pbm
images of the location of significant pixels, etc.  My low-level approach up to
this point is beginning to fail me.  (When the low level operations are rather
complex, like FFTs and wavelet transforms, you tend not to notice the control
flow code around the basic algorithms.)

So I looked at Alan Bawden's code and this SRFI.  And it turns out that
neither is at a high enough abstraction level to really simplify my life.
Both work too much at the "move a word around" level of programming.
Both assume that there are underlying arrays that are mutable, you can
set! elements of the arrays, the underlying arrays are generic
containers (vectors, not f64vectors or f32vectors, ...), etc.

So then I remembered code for an abstract-vector abstraction I wrote
several years ago for another rather complex image processing problem
(genetic programming to derive image processing algorithms).  In my
implementation, an abstract vector s just a mapping whose domain is a
subset 0..n-1 of the integers and whose range is the set of all Scheme values.
That is, they have a dimension n and a function (mapping) from 0..n-1
to Scheme objects.  That's it.  The code was written so that Scheme
vectors are also abstract vectors, but so also can be f64vectors, etc.

And I see now that a multi-dimensional version of abstract-vector is
what I need for my current purposes.  It's unfortunate that the
current SRFI can't fulfill my needs as usefully, but that's the
way things go.

To make things precise, I've included my old code at the end of this
message.  It uses the define-structure extension of Gambit-C and
a few Gambit-C declarations to speed things up.  As you can see, there
are no low-level (word level) operations, but for the most part, you
don't really need them.  Note also abstract-vector->vector, which
fixes a concrete representation of an abstract-vector so that one
can use a fixed, precomputed, representation of an abstract vector.

Brad Lucier

(define-structure avec dimension mapping)

(define (dimension av)
  (cond ((avec?   av) (avec-dimension av))
	((vector? av) (vector-length av))
	(else (error "dimension: argument is not an abstract vector"))))

(define (mapping av)
  (cond ((avec?   av) (avec-mapping av))
	((vector? av) (lambda (i) (vector-ref av i)))
	(else (error "mapping: argument is not an abstract vector"))))

(define (abstract-vector? av)
  (or (avec? av) (vector? av)))

(define (abstract-vector-map f)
  (lambda args
    (cond ((null? args) (error "abstract-vector-map: argument list is empty"))
	  ((let loop ((first (car args)) (rest (cdr args)))
	     (and (abstract-vector? first) 
                  (or (null? rest) (loop (car rest) (cdr rest)))))
	   (let ((dimensions (map dimension args)))
	     (if (apply = dimensions)
		 (let ((n (car dimensions))
		       (mappings (map mapping args)))
		   (case (length dimensions)
		     ((1) (let ((g (car mappings)))
			    (make-avec n (lambda (i) (f (g i))))))
		     ((2) (let ((g1 (car mappings))
				(g2 (cadr mappings)))
			    (make-avec n (lambda (i) (f (g1 i) (g2 i))))))
		     ((3) (let ((g1 (car mappings))
				(g2 (cadr mappings))
				(g3 (caddr mappings)))
			    (make-avec n (lambda (i) (f (g1 i) (g2 i) (g3 i))))))
		     ((4) (let ((g1 (car mappings))
				(g2 (cadr mappings))
				(g3 (caddr mappings))
				(g4 (cadddr mappings)))
			    (make-avec n (lambda (i) (f (g1 i) (g2 i) (g3 i) (g4 i))))))
		     (else (make-avec n (lambda (i) (apply f (map (lambda (g) (g i)) mappings)))))))
		 (error "abstract-vector-map: arguments have different dimensions"))))
	  (else (error "abstract-vector-map: arguments are not abstract vectors")))))

(define (abstract-vector->avec av)                ; a copying implementation
  (if (abstract-vector? av)
      (make-avec (dimension av) (mapping av))
      (error "abstract-vector->avec: not an abstract vector")))

(declare (inline) (inlining-limit 10000))

(define (abstract-vector-reduce f identity av)
  (if (abstract-vector? av)
      (let ((n (dimension av))
	    (g (mapping av)))
	(declare (fixnum))
	(do ((i 0 (+ i 1))
	     (result identity (f result (g i))))
	    ((= i n) result)))
      (error "abstract-vector-reduce: argument is not an abstract vector")))

(define (abstract-vector->vector av)              ; a copying implementation
  (if (abstract-vector? av)
      (let* ((n (dimension av))
	     (f (mapping av))
	     (v (make-vector n)))
	(declare (fixnum))
	(do ((i 0 (+ i 1)))
	    ((= i n) v)
	  (vector-set! v i (f i))))
      (error "abstract-vector->vector: argument is not an abstract vector")))

(define (abstract-vector-for-each av)
  (if (abstract-vector? av)
      (let ((n (dimension av))
	    (f (mapping av)))
	(declare (fixnum))
	(do ((i 0 (+ i 1)))
	    ((= i n) (void))
	  (f i)))
      (error "abstract-vector-for-each: argument is not an abstract vector")))

(declare (not inline) (inlining-limit 0))