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1678 lines
50 KiB
EmacsLisp
1678 lines
50 KiB
EmacsLisp
;;; calc-vec.el --- vector functions for Calc
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;; Copyright (C) 1990-1993, 2001-2016 Free Software Foundation, Inc.
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;; Author: David Gillespie <daveg@synaptics.com>
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;; This file is part of GNU Emacs.
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;; GNU Emacs is free software: you can redistribute it and/or modify
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;; it under the terms of the GNU General Public License as published by
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;; the Free Software Foundation, either version 3 of the License, or
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;; (at your option) any later version.
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;; GNU Emacs is distributed in the hope that it will be useful,
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;; but WITHOUT ANY WARRANTY; without even the implied warranty of
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;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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;; GNU General Public License for more details.
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;; You should have received a copy of the GNU General Public License
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;; along with GNU Emacs. If not, see <http://www.gnu.org/licenses/>.
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;;; Commentary:
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;;; Code:
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;; This file is autoloaded from calc-ext.el.
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(require 'calc-ext)
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(require 'calc-macs)
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;; Declare functions which are defined elsewhere.
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(declare-function math-read-expr-level "calc-aent" (exp-prec &optional exp-term))
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(defun calc-display-strings (n)
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(interactive "P")
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(calc-wrapper
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(message (if (calc-change-mode 'calc-display-strings n t t)
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"Displaying vectors of integers as quoted strings"
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"Displaying vectors of integers normally"))))
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(defun calc-pack (n)
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(interactive "P")
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(calc-wrapper
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(let* ((nn (if n 1 2))
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(mode (if n (prefix-numeric-value n) (calc-top-n 1)))
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(mode (if (and (Math-vectorp mode) (cdr mode)) (cdr mode)
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(if (integerp mode) mode
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(error "Packing mode must be an integer or vector of integers"))))
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(num (calc-pack-size mode))
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(items (calc-top-list num nn)))
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(calc-enter-result (+ nn num -1) "pack" (calc-pack-items mode items)))))
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(defun calc-pack-size (mode)
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(cond ((consp mode)
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(let ((size 1))
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(while mode
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(or (integerp (car mode)) (error "Vector of integers expected"))
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(setq size (* size (calc-pack-size (car mode)))
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mode (cdr mode)))
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(if (= size 0)
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(error "Zero dimensions not allowed")
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size)))
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((>= mode 0) mode)
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(t (or (cdr (assq mode '((-3 . 3) (-13 . 1) (-14 . 3) (-15 . 6))))
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2))))
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(defun calc-pack-items (mode items)
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(cond ((consp mode)
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(if (cdr mode)
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(let* ((size (calc-pack-size (cdr mode)))
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(len (length items))
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(new nil)
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p row)
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(while (> len 0)
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(setq p (nthcdr (1- size) items)
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row items
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items (cdr p)
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len (- len size))
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(setcdr p nil)
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(setq new (cons (calc-pack-items (cdr mode) row) new)))
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(calc-pack-items (car mode) (nreverse new)))
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(calc-pack-items (car mode) items)))
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((>= mode 0)
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(cons 'vec items))
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((= mode -3)
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(if (and (math-objvecp (car items))
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(math-objvecp (nth 1 items))
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(math-objvecp (nth 2 items)))
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(if (and (math-num-integerp (car items))
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(math-num-integerp (nth 1 items)))
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(if (math-realp (nth 2 items))
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(cons 'hms items)
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(error "Seconds must be real"))
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(error "Hours and minutes must be integers"))
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(math-normalize (list '+
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(list '+
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(if (eq calc-angle-mode 'rad)
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(list '* (car items)
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'(hms 1 0 0))
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(car items))
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(list '* (nth 1 items) '(hms 0 1 0)))
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(list '* (nth 2 items) '(hms 0 0 1))))))
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((= mode -13)
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(if (math-realp (car items))
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(cons 'date items)
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(if (eq (car-safe (car items)) 'date)
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(car items)
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(if (math-objvecp (car items))
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(error "Date value must be real")
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(cons 'calcFunc-date items)))))
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((memq mode '(-14 -15))
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(let ((p items))
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(while (and p (math-objvecp (car p)))
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(or (math-integerp (car p))
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(error "Components must be integers"))
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(setq p (cdr p)))
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(if p
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(cons 'calcFunc-date items)
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(list 'date (math-dt-to-date items)))))
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((or (eq (car-safe (car items)) 'vec)
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(eq (car-safe (nth 1 items)) 'vec))
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(let* ((x (car items))
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(vx (eq (car-safe x) 'vec))
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(y (nth 1 items))
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(vy (eq (car-safe y) 'vec))
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(z nil)
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(n (1- (length (if vx x y)))))
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(and vx vy
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(/= n (1- (length y)))
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(error "Vectors must be the same length"))
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(while (>= (setq n (1- n)) 0)
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(setq z (cons (calc-pack-items
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mode
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(list (if vx (car (setq x (cdr x))) x)
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(if vy (car (setq y (cdr y))) y)))
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z)))
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(cons 'vec (nreverse z))))
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((= mode -1)
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(if (and (math-realp (car items)) (math-realp (nth 1 items)))
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(cons 'cplx items)
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(if (and (math-objectp (car items)) (math-objectp (nth 1 items)))
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(error "Components must be real"))
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(math-normalize (list '+ (car items)
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(list '* (nth 1 items) '(cplx 0 1))))))
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((= mode -2)
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(if (and (math-realp (car items)) (math-anglep (nth 1 items)))
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(cons 'polar items)
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(if (and (math-objectp (car items)) (math-objectp (nth 1 items)))
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(error "Components must be real"))
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(math-normalize (list '* (car items)
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(if (math-anglep (nth 1 items))
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(list 'polar 1 (nth 1 items))
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(list 'calcFunc-exp
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(list '*
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(math-to-radians-2
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(nth 1 items))
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(list 'polar
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1
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(math-quarter-circle
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nil)))))))))
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((= mode -4)
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(let ((x (car items))
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(sigma (nth 1 items)))
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(if (or (math-scalarp x) (not (math-objvecp x)))
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(if (or (math-anglep sigma) (not (math-objvecp sigma)))
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(math-make-sdev x sigma)
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(error "Error component must be real"))
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(error "Mean component must be real or complex"))))
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((= mode -5)
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(let ((a (car items))
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(m (nth 1 items)))
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(if (and (math-anglep a) (math-anglep m))
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(if (math-posp m)
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(math-make-mod a m)
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(error "Modulus must be positive"))
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(if (and (math-objectp a) (math-objectp m))
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(error "Components must be real"))
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(list 'calcFunc-makemod a m))))
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((memq mode '(-6 -7 -8 -9))
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(let ((lo (car items))
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(hi (nth 1 items)))
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(if (and (or (math-anglep lo) (eq (car lo) 'date)
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(not (math-objvecp lo)))
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(or (math-anglep hi) (eq (car hi) 'date)
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(not (math-objvecp hi))))
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(math-make-intv (+ mode 9) lo hi)
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(error "Components must be real"))))
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((eq mode -10)
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(if (math-zerop (nth 1 items))
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(error "Denominator must not be zero")
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(if (and (math-integerp (car items)) (math-integerp (nth 1 items)))
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(math-normalize (cons 'frac items))
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(if (and (math-objectp (car items)) (math-objectp (nth 1 items)))
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(error "Components must be integers"))
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(cons 'calcFunc-fdiv items))))
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((memq mode '(-11 -12))
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(if (and (math-realp (car items)) (math-integerp (nth 1 items)))
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(calcFunc-scf (math-float (car items)) (nth 1 items))
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(if (and (math-objectp (car items)) (math-objectp (nth 1 items)))
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(error "Components must be integers"))
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(math-normalize
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(list 'calcFunc-scf
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(list 'calcFunc-float (car items))
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(nth 1 items)))))
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(t
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(error "Invalid packing mode: %d" mode))))
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(defvar calc-unpack-with-type nil)
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(defun calc-unpack (mode)
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(interactive "P")
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(calc-wrapper
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(let ((calc-unpack-with-type t))
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(calc-pop-push-record-list 1 "unpk" (calc-unpack-item
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(and mode
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(prefix-numeric-value mode))
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(calc-top))))))
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(defun calc-unpack-type (item)
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(cond ((eq (car-safe item) 'vec)
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(1- (length item)))
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((eq (car-safe item) 'intv)
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(- (nth 1 item) 9))
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(t
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(or (cdr (assq (car-safe item) '( (cplx . -1) (polar . -2)
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(hms . -3) (sdev . -4) (mod . -5)
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(frac . -10) (float . -11)
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(date . -13) )))
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(error "Argument must be a composite object")))))
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(defun calc-unpack-item (mode item)
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(cond ((not mode)
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(if (or (and (not (memq (car-safe item) '(frac float cplx polar vec
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hms date sdev mod
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intv)))
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(math-objvecp item))
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(eq (car-safe item) 'var))
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(error "Argument must be a composite object or function call"))
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(if (eq (car item) 'intv)
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(cdr (cdr item))
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(cdr item)))
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((> mode 0)
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(let ((dims nil)
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type new row)
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(setq item (list item))
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(while (> mode 0)
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(setq type (calc-unpack-type (car item))
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dims (cons type dims)
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new (calc-unpack-item nil (car item)))
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(while (setq item (cdr item))
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(or (= (calc-unpack-type (car item)) type)
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(error "Inconsistent types or dimensions in vector elements"))
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(setq new (append new (calc-unpack-item nil (car item)))))
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(setq item new
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mode (1- mode)))
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(if (cdr dims) (setq dims (list (cons 'vec (nreverse dims)))))
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(cond ((eq calc-unpack-with-type 'pair)
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(list (car dims) (cons 'vec item)))
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(calc-unpack-with-type
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(append item dims))
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(t item))))
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((eq calc-unpack-with-type 'pair)
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(let ((calc-unpack-with-type nil))
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(list mode (cons 'vec (calc-unpack-item mode item)))))
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((= mode -3)
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(if (eq (car-safe item) 'hms)
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(cdr item)
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(error "Argument must be an HMS form")))
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((= mode -13)
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(if (eq (car-safe item) 'date)
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(cdr item)
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(error "Argument must be a date form")))
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((= mode -14)
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(if (eq (car-safe item) 'date)
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(math-date-to-dt (math-floor (nth 1 item)))
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(error "Argument must be a date form")))
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((= mode -15)
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(if (eq (car-safe item) 'date)
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(append (math-date-to-dt (nth 1 item))
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(and (not (math-integerp (nth 1 item)))
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(list 0 0 0)))
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(error "Argument must be a date form")))
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((eq (car-safe item) 'vec)
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(let ((x nil)
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(y nil)
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res)
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(while (setq item (cdr item))
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(setq res (calc-unpack-item mode (car item))
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x (cons (car res) x)
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y (cons (nth 1 res) y)))
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(list (cons 'vec (nreverse x))
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(cons 'vec (nreverse y)))))
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((= mode -1)
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(if (eq (car-safe item) 'cplx)
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(cdr item)
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(if (eq (car-safe item) 'polar)
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(cdr (math-complex item))
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(if (Math-realp item)
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(list item 0)
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(error "Argument must be a complex number")))))
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((= mode -2)
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(if (or (memq (car-safe item) '(cplx polar))
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(Math-realp item))
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(cdr (math-polar item))
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(error "Argument must be a complex number")))
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((= mode -4)
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(if (eq (car-safe item) 'sdev)
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(cdr item)
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(list item 0)))
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((= mode -5)
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(if (eq (car-safe item) 'mod)
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(cdr item)
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(error "Argument must be a modulo form")))
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((memq mode '(-6 -7 -8 -9))
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(if (eq (car-safe item) 'intv)
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(cdr (cdr item))
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(list item item)))
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((= mode -10)
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(if (eq (car-safe item) 'frac)
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(cdr item)
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(if (Math-integerp item)
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(list item 1)
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(error "Argument must be a rational number"))))
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((= mode -11)
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(if (eq (car-safe item) 'float)
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(list (nth 1 item) (math-normalize (nth 2 item)))
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(error "Expected a floating-point number")))
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((= mode -12)
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(if (eq (car-safe item) 'float)
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(list (calcFunc-mant item) (calcFunc-xpon item))
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(error "Expected a floating-point number")))
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(t
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(error "Invalid unpacking mode: %d" mode))))
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(defun calc-diag (n)
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(interactive "P")
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(calc-wrapper
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(calc-enter-result 1 "diag" (if n
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(list 'calcFunc-diag (calc-top-n 1)
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(prefix-numeric-value n))
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(list 'calcFunc-diag (calc-top-n 1))))))
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(defun calc-ident (n)
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(interactive "NDimension of identity matrix = ")
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(calc-wrapper
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(calc-enter-result 0 "idn" (if (eq n 0)
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'(calcFunc-idn 1)
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(list 'calcFunc-idn 1
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(prefix-numeric-value n))))))
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(defun calc-index (n &optional stack)
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(interactive "NSize of vector = \nP")
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(calc-wrapper
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(if (consp stack)
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(calc-enter-result 3 "indx" (cons 'calcFunc-index (calc-top-list-n 3)))
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(calc-enter-result 0 "indx" (list 'calcFunc-index
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(prefix-numeric-value n))))))
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(defun calc-build-vector (n)
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(interactive "NSize of vector = ")
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(calc-wrapper
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(calc-enter-result 1 "bldv" (list 'calcFunc-cvec
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(calc-top-n 1)
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(prefix-numeric-value n)))))
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(defun calc-cons (arg)
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(interactive "P")
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(calc-wrapper
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(if (calc-is-hyperbolic)
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(calc-binary-op "rcns" 'calcFunc-rcons arg)
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(calc-binary-op "cons" 'calcFunc-cons arg))))
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(defun calc-head (arg)
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(interactive "P")
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(calc-wrapper
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(if (calc-is-inverse)
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(if (calc-is-hyperbolic)
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(calc-unary-op "rtai" 'calcFunc-rtail arg)
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(calc-unary-op "tail" 'calcFunc-tail arg))
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(if (calc-is-hyperbolic)
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(calc-unary-op "rhed" 'calcFunc-rhead arg)
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(calc-unary-op "head" 'calcFunc-head arg)))))
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(defun calc-tail (arg)
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(interactive "P")
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(calc-invert-func)
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(calc-head arg))
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(defun calc-vlength (arg)
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(interactive "P")
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(calc-wrapper
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(if (calc-is-hyperbolic)
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(calc-unary-op "dims" 'calcFunc-mdims arg)
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(calc-unary-op "len" 'calcFunc-vlen arg))))
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(defun calc-arrange-vector (n)
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(interactive "NNumber of columns = ")
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(calc-wrapper
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(calc-enter-result 1 "arng" (list 'calcFunc-arrange (calc-top-n 1)
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(prefix-numeric-value n)))))
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(defun calc-vector-find (arg)
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(interactive "P")
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(calc-wrapper
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(let ((func (cons 'calcFunc-find (calc-top-list-n 2))))
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(calc-enter-result
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2 "find"
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(if arg (append func (list (prefix-numeric-value arg))) func)))))
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(defun calc-subvector ()
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(interactive)
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(calc-wrapper
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(if (calc-is-inverse)
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(calc-enter-result 3 "rsvc" (cons 'calcFunc-rsubvec
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(calc-top-list-n 3)))
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(calc-enter-result 3 "svec" (cons 'calcFunc-subvec (calc-top-list-n 3))))))
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(defun calc-reverse-vector (arg)
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(interactive "P")
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(calc-wrapper
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(calc-unary-op "rev" 'calcFunc-rev arg)))
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(defun calc-mask-vector (arg)
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(interactive "P")
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(calc-wrapper
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(calc-binary-op "vmsk" 'calcFunc-vmask arg)))
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(defun calc-expand-vector (arg)
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(interactive "P")
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(calc-wrapper
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(if (calc-is-hyperbolic)
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(calc-enter-result 3 "vexp" (cons 'calcFunc-vexp (calc-top-list-n 3)))
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(calc-binary-op "vexp" 'calcFunc-vexp arg))))
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(defun calc-sort ()
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(interactive)
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(calc-slow-wrapper
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(if (calc-is-inverse)
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(calc-enter-result 1 "rsrt" (list 'calcFunc-rsort (calc-top-n 1)))
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(calc-enter-result 1 "sort" (list 'calcFunc-sort (calc-top-n 1))))))
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(defun calc-grade ()
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(interactive)
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(calc-slow-wrapper
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(if (calc-is-inverse)
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(calc-enter-result 1 "rgrd" (list 'calcFunc-rgrade (calc-top-n 1)))
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(calc-enter-result 1 "grad" (list 'calcFunc-grade (calc-top-n 1))))))
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(defun calc-histogram (n)
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(interactive "P")
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(unless (natnump n)
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(setq n (math-read-expr (read-string "Centers of bins: "))))
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(calc-slow-wrapper
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(if calc-hyperbolic-flag
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(calc-enter-result 2 "hist" (list 'calcFunc-histogram
|
|
(calc-top-n 2)
|
|
(calc-top-n 1)
|
|
n))
|
|
(calc-enter-result 1 "hist" (list 'calcFunc-histogram
|
|
(calc-top-n 1)
|
|
n)))))
|
|
|
|
(defun calc-transpose (arg)
|
|
(interactive "P")
|
|
(calc-wrapper
|
|
(calc-unary-op "trn" 'calcFunc-trn arg)))
|
|
|
|
(defun calc-conj-transpose (arg)
|
|
(interactive "P")
|
|
(calc-wrapper
|
|
(calc-unary-op "ctrn" 'calcFunc-ctrn arg)))
|
|
|
|
(defun calc-cross (arg)
|
|
(interactive "P")
|
|
(calc-wrapper
|
|
(calc-binary-op "cros" 'calcFunc-cross arg)))
|
|
|
|
(defun calc-kron (arg)
|
|
(interactive "P")
|
|
(calc-wrapper
|
|
(calc-binary-op "kron" 'calcFunc-kron arg)))
|
|
|
|
(defun calc-remove-duplicates (arg)
|
|
(interactive "P")
|
|
(calc-wrapper
|
|
(calc-unary-op "rdup" 'calcFunc-rdup arg)))
|
|
|
|
(defun calc-set-union (arg)
|
|
(interactive "P")
|
|
(calc-wrapper
|
|
(calc-binary-op "unio" 'calcFunc-vunion arg '(vec) 'calcFunc-rdup)))
|
|
|
|
(defun calc-set-intersect (arg)
|
|
(interactive "P")
|
|
(calc-wrapper
|
|
(calc-binary-op "intr" 'calcFunc-vint arg '(vec) 'calcFunc-rdup)))
|
|
|
|
(defun calc-set-difference (arg)
|
|
(interactive "P")
|
|
(calc-wrapper
|
|
(calc-binary-op "diff" 'calcFunc-vdiff arg '(vec) 'calcFunc-rdup)))
|
|
|
|
(defun calc-set-xor (arg)
|
|
(interactive "P")
|
|
(calc-wrapper
|
|
(calc-binary-op "xor" 'calcFunc-vxor arg '(vec) 'calcFunc-rdup)))
|
|
|
|
(defun calc-set-complement (arg)
|
|
(interactive "P")
|
|
(calc-wrapper
|
|
(calc-unary-op "cmpl" 'calcFunc-vcompl arg)))
|
|
|
|
(defun calc-set-floor (arg)
|
|
(interactive "P")
|
|
(calc-wrapper
|
|
(calc-unary-op "vflr" 'calcFunc-vfloor arg)))
|
|
|
|
(defun calc-set-enumerate (arg)
|
|
(interactive "P")
|
|
(calc-wrapper
|
|
(calc-unary-op "enum" 'calcFunc-venum arg)))
|
|
|
|
(defun calc-set-span (arg)
|
|
(interactive "P")
|
|
(calc-wrapper
|
|
(calc-unary-op "span" 'calcFunc-vspan arg)))
|
|
|
|
(defun calc-set-cardinality (arg)
|
|
(interactive "P")
|
|
(calc-wrapper
|
|
(calc-unary-op "card" 'calcFunc-vcard arg)))
|
|
|
|
(defun calc-unpack-bits (arg)
|
|
(interactive "P")
|
|
(calc-wrapper
|
|
(if (calc-is-inverse)
|
|
(calc-unary-op "bpck" 'calcFunc-vpack arg)
|
|
(calc-unary-op "bupk" 'calcFunc-vunpack arg))))
|
|
|
|
(defun calc-pack-bits (arg)
|
|
(interactive "P")
|
|
(calc-invert-func)
|
|
(calc-unpack-bits arg))
|
|
|
|
|
|
(defun calc-rnorm (arg)
|
|
(interactive "P")
|
|
(calc-wrapper
|
|
(calc-unary-op "rnrm" 'calcFunc-rnorm arg)))
|
|
|
|
(defun calc-cnorm (arg)
|
|
(interactive "P")
|
|
(calc-wrapper
|
|
(calc-unary-op "cnrm" 'calcFunc-cnorm arg)))
|
|
|
|
(defun calc-mrow (n &optional nn)
|
|
(interactive "NRow number: \nP")
|
|
(calc-wrapper
|
|
(if (consp nn)
|
|
(calc-enter-result 2 "mrow" (cons 'calcFunc-mrow (calc-top-list-n 2)))
|
|
(setq n (prefix-numeric-value n))
|
|
(if (= n 0)
|
|
(calc-enter-result 1 "getd" (list 'calcFunc-getdiag (calc-top-n 1)))
|
|
(if (< n 0)
|
|
(calc-enter-result 1 "rrow" (list 'calcFunc-mrrow
|
|
(calc-top-n 1) (- n)))
|
|
(calc-enter-result 1 "mrow" (list 'calcFunc-mrow
|
|
(calc-top-n 1) n)))))))
|
|
|
|
(defun calc-mcol (n &optional nn)
|
|
(interactive "NColumn number: \nP")
|
|
(calc-wrapper
|
|
(if (consp nn)
|
|
(calc-enter-result 2 "mcol" (cons 'calcFunc-mcol (calc-top-list-n 2)))
|
|
(setq n (prefix-numeric-value n))
|
|
(if (= n 0)
|
|
(calc-enter-result 1 "getd" (list 'calcFunc-getdiag (calc-top-n 1)))
|
|
(if (< n 0)
|
|
(calc-enter-result 1 "rcol" (list 'calcFunc-mrcol
|
|
(calc-top-n 1) (- n)))
|
|
(calc-enter-result 1 "mcol" (list 'calcFunc-mcol
|
|
(calc-top-n 1) n)))))))
|
|
|
|
|
|
;;;; Vectors.
|
|
|
|
(defun calcFunc-mdims (m)
|
|
(or (math-vectorp m)
|
|
(math-reject-arg m 'vectorp))
|
|
(cons 'vec (math-mat-dimens m)))
|
|
|
|
|
|
;;; Apply a function elementwise to vector A. [V X V; N X N] [Public]
|
|
(defun math-map-vec (f a)
|
|
(if (math-vectorp a)
|
|
(cons 'vec (mapcar f (cdr a)))
|
|
(funcall f a)))
|
|
|
|
(defun math-dimension-error ()
|
|
(calc-record-why "*Dimension error")
|
|
(signal 'wrong-type-argument nil))
|
|
|
|
|
|
;;; Build a vector out of a list of objects. [Public]
|
|
(defun calcFunc-vec (&rest objs)
|
|
(cons 'vec objs))
|
|
|
|
|
|
;;; Build a constant vector or matrix. [Public]
|
|
(defun calcFunc-cvec (obj &rest dims)
|
|
(math-make-vec-dimen obj dims))
|
|
|
|
(defun math-make-vec-dimen (obj dims)
|
|
(if dims
|
|
(if (natnump (car dims))
|
|
(if (or (cdr dims)
|
|
(not (math-numberp obj)))
|
|
(cons 'vec (copy-sequence
|
|
(make-list (car dims)
|
|
(math-make-vec-dimen obj (cdr dims)))))
|
|
(cons 'vec (make-list (car dims) obj)))
|
|
(math-reject-arg (car dims) 'fixnatnump))
|
|
obj))
|
|
|
|
(defun calcFunc-head (vec)
|
|
(if (and (Math-vectorp vec)
|
|
(cdr vec))
|
|
(nth 1 vec)
|
|
(calc-record-why 'vectorp vec)
|
|
(list 'calcFunc-head vec)))
|
|
|
|
(defun calcFunc-tail (vec)
|
|
(if (and (Math-vectorp vec)
|
|
(cdr vec))
|
|
(cons 'vec (cdr (cdr vec)))
|
|
(calc-record-why 'vectorp vec)
|
|
(list 'calcFunc-tail vec)))
|
|
|
|
(defun calcFunc-cons (head tail)
|
|
(if (Math-vectorp tail)
|
|
(cons 'vec (cons head (cdr tail)))
|
|
(calc-record-why 'vectorp tail)
|
|
(list 'calcFunc-cons head tail)))
|
|
|
|
(defun calcFunc-rhead (vec)
|
|
(if (and (Math-vectorp vec)
|
|
(cdr vec))
|
|
(let ((vec (copy-sequence vec)))
|
|
(setcdr (nthcdr (- (length vec) 2) vec) nil)
|
|
vec)
|
|
(calc-record-why 'vectorp vec)
|
|
(list 'calcFunc-rhead vec)))
|
|
|
|
(defun calcFunc-rtail (vec)
|
|
(if (and (Math-vectorp vec)
|
|
(cdr vec))
|
|
(nth (1- (length vec)) vec)
|
|
(calc-record-why 'vectorp vec)
|
|
(list 'calcFunc-rtail vec)))
|
|
|
|
(defun calcFunc-rcons (head tail)
|
|
(if (Math-vectorp head)
|
|
(append head (list tail))
|
|
(calc-record-why 'vectorp head)
|
|
(list 'calcFunc-rcons head tail)))
|
|
|
|
|
|
|
|
;;; Apply a function elementwise to vectors A and B. [O X O O] [Public]
|
|
(defun math-map-vec-2 (f a b)
|
|
(if (math-vectorp a)
|
|
(if (math-vectorp b)
|
|
(let ((v nil))
|
|
(while (setq a (cdr a))
|
|
(or (setq b (cdr b))
|
|
(math-dimension-error))
|
|
(setq v (cons (funcall f (car a) (car b)) v)))
|
|
(if a (math-dimension-error))
|
|
(cons 'vec (nreverse v)))
|
|
(let ((v nil))
|
|
(while (setq a (cdr a))
|
|
(setq v (cons (funcall f (car a) b) v)))
|
|
(cons 'vec (nreverse v))))
|
|
(if (math-vectorp b)
|
|
(let ((v nil))
|
|
(while (setq b (cdr b))
|
|
(setq v (cons (funcall f a (car b)) v)))
|
|
(cons 'vec (nreverse v)))
|
|
(funcall f a b))))
|
|
|
|
|
|
|
|
;;; "Reduce" a function over a vector (left-associatively). [O X V] [Public]
|
|
(defun math-reduce-vec (f a)
|
|
(if (math-vectorp a)
|
|
(if (cdr a)
|
|
(let ((accum (car (setq a (cdr a)))))
|
|
(while (setq a (cdr a))
|
|
(setq accum (funcall f accum (car a))))
|
|
accum)
|
|
0)
|
|
a))
|
|
|
|
;;; Reduce a function over the columns of matrix A. [V X V] [Public]
|
|
(defun math-reduce-cols (f a)
|
|
(if (math-matrixp a)
|
|
(cons 'vec (math-reduce-cols-col-step f (cdr a) 1 (length (nth 1 a))))
|
|
a))
|
|
|
|
(defun math-reduce-cols-col-step (f a col cols)
|
|
(and (< col cols)
|
|
(cons (math-reduce-cols-row-step f (nth col (car a)) col (cdr a))
|
|
(math-reduce-cols-col-step f a (1+ col) cols))))
|
|
|
|
(defun math-reduce-cols-row-step (f tot col a)
|
|
(if a
|
|
(math-reduce-cols-row-step f
|
|
(funcall f tot (nth col (car a)))
|
|
col
|
|
(cdr a))
|
|
tot))
|
|
|
|
|
|
|
|
(defun math-dot-product (a b)
|
|
(if (setq a (cdr a) b (cdr b))
|
|
(let ((accum (math-mul (car a) (car b))))
|
|
(while (setq a (cdr a) b (cdr b))
|
|
(setq accum (math-add accum (math-mul (car a) (car b)))))
|
|
accum)
|
|
0))
|
|
|
|
|
|
;;; Return the number of elements in vector V. [Public]
|
|
(defun calcFunc-vlen (v)
|
|
(if (math-vectorp v)
|
|
(1- (length v))
|
|
(if (math-objectp v)
|
|
0
|
|
(list 'calcFunc-vlen v))))
|
|
|
|
;;; Get the Nth row of a matrix.
|
|
(defun calcFunc-mrow (mat n) ; [Public]
|
|
(if (Math-vectorp n)
|
|
(math-map-vec (function (lambda (x) (calcFunc-mrow mat x))) n)
|
|
(if (and (eq (car-safe n) 'intv) (math-constp n))
|
|
(calcFunc-subvec mat
|
|
(math-add (nth 2 n) (if (memq (nth 1 n) '(2 3)) 0 1))
|
|
(math-add (nth 3 n) (if (memq (nth 1 n) '(1 3)) 1 0)))
|
|
(or (and (integerp (setq n (math-check-integer n)))
|
|
(> n 0))
|
|
(math-reject-arg n 'fixposintp))
|
|
(or (Math-vectorp mat)
|
|
(math-reject-arg mat 'vectorp))
|
|
(or (nth n mat)
|
|
(math-reject-arg n "*Index out of range")))))
|
|
|
|
(defun calcFunc-subscr (mat n &optional m)
|
|
(if (eq (car-safe mat) 'var) nil
|
|
(setq mat (calcFunc-mrow mat n))
|
|
(if m
|
|
(if (math-num-integerp n)
|
|
(calcFunc-mrow mat m)
|
|
(calcFunc-mcol mat m))
|
|
mat)))
|
|
|
|
;;; Get the Nth column of a matrix.
|
|
(defun math-mat-col (mat n)
|
|
(cons 'vec (mapcar (function (lambda (x) (elt x n))) (cdr mat))))
|
|
|
|
(defun calcFunc-mcol (mat n) ; [Public]
|
|
(if (Math-vectorp n)
|
|
(calcFunc-trn
|
|
(math-map-vec (function (lambda (x) (calcFunc-mcol mat x))) n))
|
|
(if (and (eq (car-safe n) 'intv) (math-constp n))
|
|
(if (math-matrixp mat)
|
|
(math-map-vec (function (lambda (x) (calcFunc-mrow x n))) mat)
|
|
(calcFunc-mrow mat n))
|
|
(or (and (integerp (setq n (math-check-integer n)))
|
|
(> n 0))
|
|
(math-reject-arg n 'fixposintp))
|
|
(or (Math-vectorp mat)
|
|
(math-reject-arg mat 'vectorp))
|
|
(or (if (math-matrixp mat)
|
|
(and (< n (length (nth 1 mat)))
|
|
(math-mat-col mat n))
|
|
(nth n mat))
|
|
(math-reject-arg n "*Index out of range")))))
|
|
|
|
;;; Remove the Nth row from a matrix.
|
|
(defun math-mat-less-row (mat n)
|
|
(if (<= n 0)
|
|
(cdr mat)
|
|
(cons (car mat)
|
|
(math-mat-less-row (cdr mat) (1- n)))))
|
|
|
|
(defun calcFunc-mrrow (mat n) ; [Public]
|
|
(and (integerp (setq n (math-check-integer n)))
|
|
(> n 0)
|
|
(< n (length mat))
|
|
(math-mat-less-row mat n)))
|
|
|
|
;;; Remove the Nth column from a matrix.
|
|
(defun math-mat-less-col (mat n)
|
|
(cons 'vec (mapcar (function (lambda (x) (math-mat-less-row x n)))
|
|
(cdr mat))))
|
|
|
|
(defun calcFunc-mrcol (mat n) ; [Public]
|
|
(and (integerp (setq n (math-check-integer n)))
|
|
(> n 0)
|
|
(if (math-matrixp mat)
|
|
(and (< n (length (nth 1 mat)))
|
|
(math-mat-less-col mat n))
|
|
(math-mat-less-row mat n))))
|
|
|
|
(defun calcFunc-getdiag (mat) ; [Public]
|
|
(if (math-square-matrixp mat)
|
|
(cons 'vec (math-get-diag-step (cdr mat) 1))
|
|
(calc-record-why 'square-matrixp mat)
|
|
(list 'calcFunc-getdiag mat)))
|
|
|
|
(defun math-get-diag-step (row n)
|
|
(and row
|
|
(cons (nth n (car row))
|
|
(math-get-diag-step (cdr row) (1+ n)))))
|
|
|
|
(defun math-transpose (mat) ; [Public]
|
|
(let ((m nil)
|
|
(col (length (nth 1 mat))))
|
|
(while (> (setq col (1- col)) 0)
|
|
(setq m (cons (math-mat-col mat col) m)))
|
|
(cons 'vec m)))
|
|
|
|
(defun calcFunc-trn (mat)
|
|
(if (math-vectorp mat)
|
|
(if (math-matrixp mat)
|
|
(math-transpose mat)
|
|
(math-col-matrix mat))
|
|
(if (math-numberp mat)
|
|
mat
|
|
(math-reject-arg mat 'matrixp))))
|
|
|
|
(defun calcFunc-ctrn (mat)
|
|
(calcFunc-conj (calcFunc-trn mat)))
|
|
|
|
(defun calcFunc-pack (mode els)
|
|
(or (Math-vectorp els) (math-reject-arg els 'vectorp))
|
|
(if (and (Math-vectorp mode) (cdr mode))
|
|
(setq mode (cdr mode))
|
|
(or (integerp mode) (math-reject-arg mode 'fixnump)))
|
|
(condition-case err
|
|
(if (= (calc-pack-size mode) (1- (length els)))
|
|
(calc-pack-items mode (cdr els))
|
|
(math-reject-arg els "*Wrong number of elements"))
|
|
(error (math-reject-arg els (nth 1 err)))))
|
|
|
|
(defun calcFunc-unpack (mode thing)
|
|
(or (integerp mode) (math-reject-arg mode 'fixnump))
|
|
(condition-case err
|
|
(cons 'vec (calc-unpack-item mode thing))
|
|
(error (math-reject-arg thing (nth 1 err)))))
|
|
|
|
(defun calcFunc-unpackt (mode thing)
|
|
(let ((calc-unpack-with-type 'pair))
|
|
(calcFunc-unpack mode thing)))
|
|
|
|
(defun calcFunc-arrange (vec cols) ; [Public]
|
|
(setq cols (math-check-fixnum cols t))
|
|
(if (math-vectorp vec)
|
|
(let* ((flat (math-flatten-vector vec))
|
|
(mat (list 'vec))
|
|
next)
|
|
(if (<= cols 0)
|
|
(nconc mat flat)
|
|
(while (>= (length flat) cols)
|
|
(setq next (nthcdr cols flat))
|
|
(setcdr (nthcdr (1- cols) flat) nil)
|
|
(setq mat (nconc mat (list (cons 'vec flat)))
|
|
flat next))
|
|
(if flat
|
|
(setq mat (nconc mat (list (cons 'vec flat)))))
|
|
mat))))
|
|
|
|
(defun math-flatten-vector (vec) ; [L V]
|
|
(if (math-vectorp vec)
|
|
(apply 'append (mapcar 'math-flatten-vector (cdr vec)))
|
|
(list vec)))
|
|
|
|
(defun calcFunc-vconcat (a b)
|
|
(math-normalize (list '| a b)))
|
|
|
|
(defun calcFunc-vconcatrev (a b)
|
|
(math-normalize (list '| b a)))
|
|
|
|
(defun calcFunc-append (v1 v2)
|
|
(if (and (math-vectorp v1) (math-vectorp v2))
|
|
(append v1 (cdr v2))
|
|
(list 'calcFunc-append v1 v2)))
|
|
|
|
(defun calcFunc-appendrev (v1 v2)
|
|
(calcFunc-append v2 v1))
|
|
|
|
|
|
;;; Copy a matrix. [Public]
|
|
(defun math-copy-matrix (m)
|
|
(if (math-vectorp (nth 1 m))
|
|
(cons 'vec (mapcar 'copy-sequence (cdr m)))
|
|
(copy-sequence m)))
|
|
|
|
;;; Convert a scalar or vector into an NxN diagonal matrix. [Public]
|
|
(defun calcFunc-diag (a &optional n)
|
|
(and n (not (integerp n))
|
|
(setq n (math-check-fixnum n)))
|
|
(if (math-vectorp a)
|
|
(if (and n (/= (length a) (1+ n)))
|
|
(list 'calcFunc-diag a n)
|
|
(if (math-matrixp a)
|
|
(if (and n (/= (length (elt a 1)) (1+ n)))
|
|
(list 'calcFunc-diag a n)
|
|
a)
|
|
(cons 'vec (math-diag-step (cdr a) 0 (1- (length a))))))
|
|
(if n
|
|
(cons 'vec (math-diag-step (make-list n a) 0 n))
|
|
(list 'calcFunc-diag a))))
|
|
|
|
(defun calcFunc-idn (a &optional n)
|
|
(if n
|
|
(if (math-vectorp a)
|
|
(math-reject-arg a 'numberp)
|
|
(calcFunc-diag a n))
|
|
(if (integerp calc-matrix-mode)
|
|
(calcFunc-idn a calc-matrix-mode)
|
|
(list 'calcFunc-idn a))))
|
|
|
|
(defun math-mimic-ident (a m)
|
|
(if (math-square-matrixp m)
|
|
(calcFunc-idn a (1- (length m)))
|
|
(if (math-vectorp m)
|
|
(if (math-zerop a)
|
|
(cons 'vec (mapcar (function (lambda (x)
|
|
(if (math-vectorp x)
|
|
(math-mimic-ident a x)
|
|
a)))
|
|
(cdr m)))
|
|
(math-dimension-error))
|
|
(calcFunc-idn a))))
|
|
|
|
(defun math-diag-step (a n m)
|
|
(if (< n m)
|
|
(cons (cons 'vec
|
|
(nconc (make-list n 0)
|
|
(cons (car a)
|
|
(make-list (1- (- m n)) 0))))
|
|
(math-diag-step (cdr a) (1+ n) m))
|
|
nil))
|
|
|
|
;;; Create a vector of consecutive integers. [Public]
|
|
(defun calcFunc-index (n &optional start incr)
|
|
(if (math-messy-integerp n)
|
|
(math-float (calcFunc-index (math-trunc n) start incr))
|
|
(and (not (integerp n))
|
|
(setq n (math-check-fixnum n)))
|
|
(let ((vec nil))
|
|
(if start
|
|
(progn
|
|
(if (>= n 0)
|
|
(while (>= (setq n (1- n)) 0)
|
|
(setq vec (cons start vec)
|
|
start (math-add start (or incr 1))))
|
|
(while (<= (setq n (1+ n)) 0)
|
|
(setq vec (cons start vec)
|
|
start (math-mul start (or incr 2)))))
|
|
(setq vec (nreverse vec)))
|
|
(if (>= n 0)
|
|
(while (> n 0)
|
|
(setq vec (cons n vec)
|
|
n (1- n)))
|
|
(let ((i -1))
|
|
(while (>= i n)
|
|
(setq vec (cons i vec)
|
|
i (1- i))))))
|
|
(cons 'vec vec))))
|
|
|
|
;;; Find an element in a vector.
|
|
(defun calcFunc-find (vec x &optional start)
|
|
(setq start (if start (math-check-fixnum start t) 1))
|
|
(if (< start 1) (math-reject-arg start 'posp))
|
|
(setq vec (nthcdr start vec))
|
|
(let ((n start))
|
|
(while (and vec (not (Math-equal x (car vec))))
|
|
(setq n (1+ n)
|
|
vec (cdr vec)))
|
|
(if vec n 0)))
|
|
|
|
;;; Return a subvector of a vector.
|
|
(defun calcFunc-subvec (vec start &optional end)
|
|
(setq start (math-check-fixnum start t)
|
|
end (math-check-fixnum (or end 0) t))
|
|
(or (math-vectorp vec) (math-reject-arg vec 'vectorp))
|
|
(let ((len (1- (length vec))))
|
|
(if (<= start 0)
|
|
(setq start (+ len start 1)))
|
|
(if (<= end 0)
|
|
(setq end (+ len end 1)))
|
|
(if (or (> start len)
|
|
(<= end start))
|
|
'(vec)
|
|
(setq vec (nthcdr start vec))
|
|
(if (<= end len)
|
|
(let ((chop (nthcdr (- end start 1) (setq vec (copy-sequence vec)))))
|
|
(setcdr chop nil)))
|
|
(cons 'vec vec))))
|
|
|
|
;;; Remove a subvector from a vector.
|
|
(defun calcFunc-rsubvec (vec start &optional end)
|
|
(setq start (math-check-fixnum start t)
|
|
end (math-check-fixnum (or end 0) t))
|
|
(or (math-vectorp vec) (math-reject-arg vec 'vectorp))
|
|
(let ((len (1- (length vec))))
|
|
(if (<= start 0)
|
|
(setq start (+ len start 1)))
|
|
(if (<= end 0)
|
|
(setq end (+ len end 1)))
|
|
(if (or (> start len)
|
|
(<= end start))
|
|
vec
|
|
(let ((tail (nthcdr end vec))
|
|
(chop (nthcdr (1- start) (setq vec (copy-sequence vec)))))
|
|
(setcdr chop nil)
|
|
(append vec tail)))))
|
|
|
|
;;; Reverse the order of the elements of a vector.
|
|
(defun calcFunc-rev (vec)
|
|
(if (math-vectorp vec)
|
|
(cons 'vec (reverse (cdr vec)))
|
|
(math-reject-arg vec 'vectorp)))
|
|
|
|
;;; Compress a vector according to a mask vector.
|
|
(defun calcFunc-vmask (mask vec)
|
|
(if (math-numberp mask)
|
|
(if (math-zerop mask)
|
|
'(vec)
|
|
vec)
|
|
(or (math-vectorp mask) (math-reject-arg mask 'vectorp))
|
|
(or (math-constp mask) (math-reject-arg mask 'constp))
|
|
(or (math-vectorp vec) (math-reject-arg vec 'vectorp))
|
|
(or (= (length mask) (length vec)) (math-dimension-error))
|
|
(let ((new nil))
|
|
(while (setq mask (cdr mask) vec (cdr vec))
|
|
(or (math-zerop (car mask))
|
|
(setq new (cons (car vec) new))))
|
|
(cons 'vec (nreverse new)))))
|
|
|
|
;;; Expand a vector according to a mask vector.
|
|
(defun calcFunc-vexp (mask vec &optional filler)
|
|
(or (math-vectorp mask) (math-reject-arg mask 'vectorp))
|
|
(or (math-constp mask) (math-reject-arg mask 'constp))
|
|
(or (math-vectorp vec) (math-reject-arg vec 'vectorp))
|
|
(let ((new nil)
|
|
(fvec (and filler (math-vectorp filler))))
|
|
(while (setq mask (cdr mask))
|
|
(if (math-zerop (car mask))
|
|
(setq new (cons (or (if fvec
|
|
(car (setq filler (cdr filler)))
|
|
filler)
|
|
(car mask)) new))
|
|
(setq vec (cdr vec)
|
|
new (cons (or (car vec) (car mask)) new))))
|
|
(cons 'vec (nreverse new))))
|
|
|
|
|
|
;;; Compute the row and column norms of a vector or matrix. [Public]
|
|
(defun calcFunc-rnorm (a)
|
|
(if (and (Math-vectorp a)
|
|
(math-constp a))
|
|
(if (math-matrixp a)
|
|
(math-reduce-vec 'math-max (math-map-vec 'calcFunc-cnorm a))
|
|
(math-reduce-vec 'math-max (math-map-vec 'math-abs a)))
|
|
(calc-record-why 'vectorp a)
|
|
(list 'calcFunc-rnorm a)))
|
|
|
|
(defun calcFunc-cnorm (a)
|
|
(if (and (Math-vectorp a)
|
|
(math-constp a))
|
|
(if (math-matrixp a)
|
|
(math-reduce-vec 'math-max
|
|
(math-reduce-cols 'math-add-abs a))
|
|
(math-reduce-vec 'math-add-abs a))
|
|
(calc-record-why 'vectorp a)
|
|
(list 'calcFunc-cnorm a)))
|
|
|
|
(defun math-add-abs (a b)
|
|
(math-add (math-abs a) (math-abs b)))
|
|
|
|
|
|
;;; Sort the elements of a vector into increasing order.
|
|
(defun calcFunc-sort (vec) ; [Public]
|
|
(if (math-vectorp vec)
|
|
(cons 'vec (sort (copy-sequence (cdr vec)) 'math-beforep))
|
|
(math-reject-arg vec 'vectorp)))
|
|
|
|
(defun calcFunc-rsort (vec) ; [Public]
|
|
(if (math-vectorp vec)
|
|
(cons 'vec (nreverse (sort (copy-sequence (cdr vec)) 'math-beforep)))
|
|
(math-reject-arg vec 'vectorp)))
|
|
|
|
;; The variable math-grade-vec is local to calcFunc-grade and
|
|
;; calcFunc-rgrade, but is used by math-grade-beforep, which is called
|
|
;; by calcFunc-grade and calcFunc-rgrade.
|
|
(defvar math-grade-vec)
|
|
|
|
(defun calcFunc-grade (math-grade-vec)
|
|
(if (math-vectorp math-grade-vec)
|
|
(let* ((len (1- (length math-grade-vec))))
|
|
(cons 'vec (sort (cdr (calcFunc-index len)) 'math-grade-beforep)))
|
|
(math-reject-arg math-grade-vec 'vectorp)))
|
|
|
|
(defun calcFunc-rgrade (math-grade-vec)
|
|
(if (math-vectorp math-grade-vec)
|
|
(let* ((len (1- (length math-grade-vec))))
|
|
(cons 'vec (nreverse (sort (cdr (calcFunc-index len))
|
|
'math-grade-beforep))))
|
|
(math-reject-arg math-grade-vec 'vectorp)))
|
|
|
|
(defun math-grade-beforep (i j)
|
|
(math-beforep (nth i math-grade-vec) (nth j math-grade-vec)))
|
|
|
|
|
|
;;; Compile a histogram of data from a vector.
|
|
(defun calcFunc-histogram (vec wts &optional n)
|
|
(or n (setq n wts wts 1))
|
|
(or (Math-vectorp vec)
|
|
(math-reject-arg vec 'vectorp))
|
|
(if (Math-vectorp wts)
|
|
(or (= (length vec) (length wts))
|
|
(math-dimension-error)))
|
|
(cond ((natnump n)
|
|
(let ((res (make-vector n 0))
|
|
(vp vec)
|
|
(wvec (Math-vectorp wts))
|
|
(wp wts)
|
|
bin)
|
|
(while (setq vp (cdr vp))
|
|
(setq bin (car vp))
|
|
(or (natnump bin)
|
|
(setq bin (math-floor bin)))
|
|
(and (natnump bin)
|
|
(< bin n)
|
|
(aset res bin
|
|
(math-add (aref res bin)
|
|
(if wvec (car (setq wp (cdr wp))) wts)))))
|
|
(cons 'vec (append res nil))))
|
|
((Math-vectorp n) ;; n is a vector of midpoints
|
|
(let* ((bds (math-vector-avg n))
|
|
(res (make-vector (1- (length n)) 0))
|
|
(vp (cdr vec))
|
|
(wvec (Math-vectorp wts))
|
|
(wp wts)
|
|
num)
|
|
(while vp
|
|
(setq num (car vp))
|
|
(let ((tbds (cdr bds))
|
|
(i 0))
|
|
(while (and tbds (Math-lessp (car tbds) num))
|
|
(setq i (1+ i))
|
|
(setq tbds (cdr tbds)))
|
|
(aset res i
|
|
(math-add (aref res i)
|
|
(if wvec (car (setq wp (cdr wp))) wts))))
|
|
(setq vp (cdr vp)))
|
|
(cons 'vec (append res nil))))
|
|
(t
|
|
(math-reject-arg n "*Expecting an integer or vector"))))
|
|
|
|
;;; Replace a vector [a b c ...] with a vector of averages
|
|
;;; [(a+b)/2 (b+c)/2 ...]
|
|
(defun math-vector-avg (vec)
|
|
(let ((vp (sort (copy-sequence (cdr vec)) 'math-beforep))
|
|
(res nil))
|
|
(while (and vp (cdr vp))
|
|
(setq res (cons (math-div (math-add (car vp) (cadr vp)) 2) res)
|
|
vp (cdr vp)))
|
|
(cons 'vec (reverse res))))
|
|
|
|
|
|
;;; Set operations.
|
|
|
|
(defun calcFunc-vunion (a b)
|
|
(if (Math-objectp a)
|
|
(setq a (list 'vec a))
|
|
(or (math-vectorp a) (math-reject-arg a 'vectorp)))
|
|
(if (Math-objectp b)
|
|
(setq b (list b))
|
|
(or (math-vectorp b) (math-reject-arg b 'vectorp))
|
|
(setq b (cdr b)))
|
|
(calcFunc-rdup (append a b)))
|
|
|
|
(defun calcFunc-vint (a b)
|
|
(if (and (math-simple-set a) (math-simple-set b))
|
|
(progn
|
|
(setq a (cdr (calcFunc-rdup a)))
|
|
(setq b (cdr (calcFunc-rdup b)))
|
|
(let ((vec (list 'vec)))
|
|
(while (and a b)
|
|
(if (math-beforep (car a) (car b))
|
|
(setq a (cdr a))
|
|
(if (Math-equal (car a) (car b))
|
|
(setq vec (cons (car a) vec)
|
|
a (cdr a)))
|
|
(setq b (cdr b))))
|
|
(nreverse vec)))
|
|
(calcFunc-vcompl (calcFunc-vunion (calcFunc-vcompl a)
|
|
(calcFunc-vcompl b)))))
|
|
|
|
(defun calcFunc-vdiff (a b)
|
|
(if (and (math-simple-set a) (math-simple-set b))
|
|
(progn
|
|
(setq a (cdr (calcFunc-rdup a)))
|
|
(setq b (cdr (calcFunc-rdup b)))
|
|
(let ((vec (list 'vec)))
|
|
(while a
|
|
(while (and b (math-beforep (car b) (car a)))
|
|
(setq b (cdr b)))
|
|
(if (and b (Math-equal (car a) (car b)))
|
|
(setq a (cdr a)
|
|
b (cdr b))
|
|
(setq vec (cons (car a) vec)
|
|
a (cdr a))))
|
|
(nreverse vec)))
|
|
(calcFunc-vcompl (calcFunc-vunion (calcFunc-vcompl a) b))))
|
|
|
|
(defun calcFunc-vxor (a b)
|
|
(if (and (math-simple-set a) (math-simple-set b))
|
|
(progn
|
|
(setq a (cdr (calcFunc-rdup a)))
|
|
(setq b (cdr (calcFunc-rdup b)))
|
|
(let ((vec (list 'vec)))
|
|
(while (or a b)
|
|
(if (and a
|
|
(or (not b)
|
|
(math-beforep (car a) (car b))))
|
|
(setq vec (cons (car a) vec)
|
|
a (cdr a))
|
|
(if (and a (Math-equal (car a) (car b)))
|
|
(setq a (cdr a))
|
|
(setq vec (cons (car b) vec)))
|
|
(setq b (cdr b))))
|
|
(nreverse vec)))
|
|
(let ((ca (calcFunc-vcompl a))
|
|
(cb (calcFunc-vcompl b)))
|
|
(calcFunc-vunion (calcFunc-vcompl (calcFunc-vunion ca b))
|
|
(calcFunc-vcompl (calcFunc-vunion a cb))))))
|
|
|
|
(defun calcFunc-vcompl (a)
|
|
(setq a (math-prepare-set a))
|
|
(let ((vec (list 'vec))
|
|
(prev '(neg (var inf var-inf)))
|
|
(closed 2))
|
|
(while (setq a (cdr a))
|
|
(or (and (equal (nth 2 (car a)) '(neg (var inf var-inf)))
|
|
(memq (nth 1 (car a)) '(2 3)))
|
|
(setq vec (cons (list 'intv
|
|
(+ closed
|
|
(if (memq (nth 1 (car a)) '(0 1)) 1 0))
|
|
prev
|
|
(nth 2 (car a)))
|
|
vec)))
|
|
(setq prev (nth 3 (car a))
|
|
closed (if (memq (nth 1 (car a)) '(0 2)) 2 0)))
|
|
(or (and (equal prev '(var inf var-inf))
|
|
(= closed 0))
|
|
(setq vec (cons (list 'intv (+ closed 1)
|
|
prev '(var inf var-inf))
|
|
vec)))
|
|
(math-clean-set (nreverse vec))))
|
|
|
|
(defun calcFunc-vspan (a)
|
|
(setq a (math-prepare-set a))
|
|
(if (cdr a)
|
|
(let ((last (nth (1- (length a)) a)))
|
|
(math-make-intv (+ (logand (nth 1 (nth 1 a)) 2)
|
|
(logand (nth 1 last) 1))
|
|
(nth 2 (nth 1 a))
|
|
(nth 3 last)))
|
|
'(intv 2 0 0)))
|
|
|
|
(defun calcFunc-vfloor (a &optional always-vec)
|
|
(setq a (math-prepare-set a))
|
|
(let ((vec (list 'vec)) (p a) (prev nil) b mask)
|
|
(while (setq p (cdr p))
|
|
(setq mask (nth 1 (car p))
|
|
a (nth 2 (car p))
|
|
b (nth 3 (car p)))
|
|
(and (memq mask '(0 1))
|
|
(not (math-infinitep a))
|
|
(setq mask (logior mask 2))
|
|
(math-num-integerp a)
|
|
(setq a (math-add a 1)))
|
|
(setq a (math-ceiling a))
|
|
(and (memq mask '(0 2))
|
|
(not (math-infinitep b))
|
|
(setq mask (logior mask 1))
|
|
(math-num-integerp b)
|
|
(setq b (math-sub b 1)))
|
|
(setq b (math-floor b))
|
|
(if (and prev (Math-equal (math-sub a 1) (nth 3 prev)))
|
|
(setcar (nthcdr 3 prev) b)
|
|
(or (Math-lessp b a)
|
|
(setq vec (cons (setq prev (list 'intv mask a b)) vec)))))
|
|
(setq vec (nreverse vec))
|
|
(math-clean-set vec always-vec)))
|
|
|
|
(defun calcFunc-vcard (a)
|
|
(setq a (calcFunc-vfloor a t))
|
|
(or (math-constp a) (math-reject-arg a "*Set must be finite"))
|
|
(let ((count 0))
|
|
(while (setq a (cdr a))
|
|
(if (eq (car-safe (car a)) 'intv)
|
|
(setq count (math-add count (math-sub (nth 3 (car a))
|
|
(nth 2 (car a))))))
|
|
(setq count (math-add count 1)))
|
|
count))
|
|
|
|
(defun calcFunc-venum (a)
|
|
(setq a (calcFunc-vfloor a t))
|
|
(or (math-constp a) (math-reject-arg a "*Set must be finite"))
|
|
(let* ((prev a) (this (cdr prev)) this-val next this-last)
|
|
(while this
|
|
(setq next (cdr this)
|
|
this-val (car this))
|
|
(if (eq (car-safe this-val) 'intv)
|
|
(progn
|
|
(setq this (cdr (calcFunc-index (math-add
|
|
(math-sub (nth 3 this-val)
|
|
(nth 2 this-val))
|
|
1)
|
|
(nth 2 this-val))))
|
|
(setq this-last (last this))
|
|
(setcdr this-last next)
|
|
(setcdr prev this)
|
|
(setq prev this-last))
|
|
(setq prev this))
|
|
(setq this next)))
|
|
a)
|
|
|
|
(defun calcFunc-vpack (a)
|
|
(setq a (calcFunc-vfloor a t))
|
|
(if (and (cdr a)
|
|
(math-negp (if (eq (car-safe (nth 1 a)) 'intv)
|
|
(nth 2 (nth 1 a))
|
|
(nth 1 a))))
|
|
(math-reject-arg (nth 1 a) 'posp))
|
|
(let ((accum 0))
|
|
(while (setq a (cdr a))
|
|
(if (eq (car-safe (car a)) 'intv)
|
|
(if (equal (nth 3 (car a)) '(var inf var-inf))
|
|
(setq accum (math-sub accum
|
|
(math-power-of-2 (nth 2 (car a)))))
|
|
(setq accum (math-add accum
|
|
(math-sub
|
|
(math-power-of-2 (1+ (nth 3 (car a))))
|
|
(math-power-of-2 (nth 2 (car a)))))))
|
|
(setq accum (math-add accum (math-power-of-2 (car a))))))
|
|
accum))
|
|
|
|
(defun calcFunc-vunpack (a &optional w)
|
|
(or (math-num-integerp a) (math-reject-arg a 'integerp))
|
|
(if w (setq a (math-clip a w)))
|
|
(if (math-messy-integerp a) (setq a (math-trunc a)))
|
|
(let* ((calc-number-radix 2)
|
|
(calc-twos-complement-mode nil)
|
|
(neg (math-negp a))
|
|
(aa (if neg (math-sub -1 a) a))
|
|
(str (if (eq aa 0)
|
|
""
|
|
(if (consp aa)
|
|
(math-format-bignum-binary (cdr aa))
|
|
(math-format-binary aa))))
|
|
(zero (if neg ?1 ?0))
|
|
(one (if neg ?0 ?1))
|
|
(len (length str))
|
|
(vec (list 'vec))
|
|
(pos (1- len)) pos2)
|
|
(while (>= pos 0)
|
|
(if (eq (aref str pos) zero)
|
|
(setq pos (1- pos))
|
|
(setq pos2 pos)
|
|
(while (and (>= pos 0) (eq (aref str pos) one))
|
|
(setq pos (1- pos)))
|
|
(setq vec (cons (if (= pos (1- pos2))
|
|
(- len pos2 1)
|
|
(list 'intv 3 (- len pos2 1) (- len pos 2)))
|
|
vec))))
|
|
(if neg
|
|
(setq vec (cons (list 'intv 2 len '(var inf var-inf)) vec)))
|
|
(math-clean-set (nreverse vec))))
|
|
|
|
(defun calcFunc-rdup (a)
|
|
(if (math-simple-set a)
|
|
(progn
|
|
(and (Math-objectp a) (setq a (list 'vec a)))
|
|
(or (math-vectorp a) (math-reject-arg a 'vectorp))
|
|
(setq a (sort (copy-sequence (cdr a)) 'math-beforep))
|
|
(let ((p a))
|
|
(while (cdr p)
|
|
(if (Math-equal (car p) (nth 1 p))
|
|
(setcdr p (cdr (cdr p)))
|
|
(setq p (cdr p)))))
|
|
(cons 'vec a))
|
|
(math-clean-set (math-prepare-set a))))
|
|
|
|
(defun math-prepare-set (a)
|
|
(if (Math-objectp a)
|
|
(setq a (list 'vec a))
|
|
(or (math-vectorp a) (math-reject-arg a 'vectorp))
|
|
(setq a (cons 'vec (sort (copy-sequence (cdr a)) 'math-beforep))))
|
|
(let ((p a) res)
|
|
|
|
;; Convert all elements to non-empty intervals.
|
|
(while (cdr p)
|
|
(if (eq (car-safe (nth 1 p)) 'intv)
|
|
(if (math-intv-constp (nth 1 p))
|
|
(if (and (memq (nth 1 (nth 1 p)) '(0 1 2))
|
|
(Math-equal (nth 2 (nth 1 p)) (nth 3 (nth 1 p))))
|
|
(setcdr p (cdr (cdr p)))
|
|
(setq p (cdr p)))
|
|
(math-reject-arg (nth 1 p) 'constp))
|
|
(or (Math-anglep (nth 1 p))
|
|
(eq (car (nth 1 p)) 'date)
|
|
(equal (nth 1 p) '(var inf var-inf))
|
|
(equal (nth 1 p) '(neg (var inf var-inf)))
|
|
(math-reject-arg (nth 1 p) 'realp))
|
|
(setcar (cdr p) (list 'intv 3 (nth 1 p) (nth 1 p)))
|
|
(setq p (cdr p))))
|
|
|
|
;; Combine redundant intervals.
|
|
(setq p a)
|
|
(while (cdr (cdr p))
|
|
(if (or (memq (setq res (math-compare (nth 3 (nth 1 p))
|
|
(nth 2 (nth 2 p))))
|
|
'(-1 2))
|
|
(and (eq res 0)
|
|
(memq (nth 1 (nth 1 p)) '(0 2))
|
|
(memq (nth 1 (nth 2 p)) '(0 1))))
|
|
(setq p (cdr p))
|
|
(setq res (math-compare (nth 3 (nth 1 p)) (nth 3 (nth 2 p))))
|
|
(setcdr p (cons (list 'intv
|
|
(+ (logand (logior (nth 1 (nth 1 p))
|
|
(if (Math-equal
|
|
(nth 2 (nth 1 p))
|
|
(nth 2 (nth 2 p)))
|
|
(nth 1 (nth 2 p))
|
|
0))
|
|
2)
|
|
(logand (logior (if (memq res '(1 0 2))
|
|
(nth 1 (nth 1 p)) 0)
|
|
(if (memq res '(-1 0 2))
|
|
(nth 1 (nth 2 p)) 0))
|
|
1))
|
|
(nth 2 (nth 1 p))
|
|
(if (eq res 1)
|
|
(nth 3 (nth 1 p))
|
|
(nth 3 (nth 2 p))))
|
|
(cdr (cdr (cdr p))))))))
|
|
a)
|
|
|
|
(defun math-clean-set (a &optional always-vec)
|
|
(let ((p a) res)
|
|
(while (cdr p)
|
|
(if (and (eq (car-safe (nth 1 p)) 'intv)
|
|
(Math-equal (nth 2 (nth 1 p)) (nth 3 (nth 1 p))))
|
|
(setcar (cdr p) (nth 2 (nth 1 p))))
|
|
(setq p (cdr p)))
|
|
(if (and (not (cdr (cdr a)))
|
|
(eq (car-safe (nth 1 a)) 'intv)
|
|
(not always-vec))
|
|
(nth 1 a)
|
|
a)))
|
|
|
|
(defun math-simple-set (a)
|
|
(or (and (Math-objectp a)
|
|
(not (eq (car-safe a) 'intv)))
|
|
(and (Math-vectorp a)
|
|
(progn
|
|
(while (and (setq a (cdr a))
|
|
(not (eq (car-safe (car a)) 'intv))))
|
|
(null a)))))
|
|
|
|
|
|
|
|
|
|
;;; Compute a right-handed vector cross product. [O O O] [Public]
|
|
(defun calcFunc-cross (a b)
|
|
(if (and (eq (car-safe a) 'vec)
|
|
(= (length a) 4))
|
|
(if (and (eq (car-safe b) 'vec)
|
|
(= (length b) 4))
|
|
(list 'vec
|
|
(math-sub (math-mul (nth 2 a) (nth 3 b))
|
|
(math-mul (nth 3 a) (nth 2 b)))
|
|
(math-sub (math-mul (nth 3 a) (nth 1 b))
|
|
(math-mul (nth 1 a) (nth 3 b)))
|
|
(math-sub (math-mul (nth 1 a) (nth 2 b))
|
|
(math-mul (nth 2 a) (nth 1 b))))
|
|
(math-reject-arg b "*Three-vector expected"))
|
|
(math-reject-arg a "*Three-vector expected")))
|
|
|
|
|
|
;;; Compute a Kronecker product
|
|
(defun calcFunc-kron (x y &optional nocheck)
|
|
"The Kronecker product of objects X and Y.
|
|
The objects X and Y may be scalars, vectors or matrices.
|
|
The type of the result depends on the types of the operands;
|
|
the product of two scalars is a scalar,
|
|
of one scalar and a vector is a vector,
|
|
of two vectors is a vector.
|
|
of one vector and a matrix is a matrix,
|
|
of two matrices is a matrix."
|
|
(unless nocheck
|
|
(cond ((or (math-matrixp x)
|
|
(math-matrixp y))
|
|
(unless (math-matrixp x)
|
|
(setq x (if (math-vectorp x)
|
|
(list 'vec x)
|
|
(list 'vec (list 'vec x)))))
|
|
(unless (math-matrixp y)
|
|
(setq y (if (math-vectorp y)
|
|
(list 'vec y)
|
|
(list 'vec (list 'vec y))))))
|
|
((or (math-vectorp x)
|
|
(math-vectorp y))
|
|
(unless (math-vectorp x)
|
|
(setq x (list 'vec x)))
|
|
(unless (math-vectorp y)
|
|
(setq y (list 'vec y))))))
|
|
(if (math-vectorp x)
|
|
(let (ret)
|
|
(dolist (v (cdr x))
|
|
(dolist (w (cdr y))
|
|
(setq ret (cons (calcFunc-kron v w t) ret))))
|
|
(cons 'vec (nreverse ret)))
|
|
(math-mul x y)))
|
|
|
|
|
|
;; The variable math-rb-close is local to math-read-brackets, but
|
|
;; is used by math-read-vector, which is called (directly and
|
|
;; indirectly) by math-read-brackets.
|
|
(defvar math-rb-close)
|
|
|
|
;; The next few variables are local to math-read-exprs in calc-aent.el
|
|
;; and math-read-expr in calc-ext.el, but are set in functions they call.
|
|
(defvar math-exp-pos)
|
|
(defvar math-exp-str)
|
|
(defvar math-exp-old-pos)
|
|
(defvar math-exp-token)
|
|
(defvar math-exp-keep-spaces)
|
|
(defvar math-expr-data)
|
|
|
|
(defun math-read-brackets (space-sep math-rb-close)
|
|
(and space-sep (setq space-sep (not (math-check-for-commas))))
|
|
(math-read-token)
|
|
(while (eq math-exp-token 'space)
|
|
(math-read-token))
|
|
(if (or (equal math-expr-data math-rb-close)
|
|
(eq math-exp-token 'end))
|
|
(progn
|
|
(math-read-token)
|
|
'(vec))
|
|
(let ((save-exp-pos math-exp-pos)
|
|
(save-exp-old-pos math-exp-old-pos)
|
|
(save-exp-token math-exp-token)
|
|
(save-exp-data math-expr-data)
|
|
(vals (let ((math-exp-keep-spaces space-sep))
|
|
(if (or (equal math-expr-data "\\dots")
|
|
(equal math-expr-data "\\ldots"))
|
|
'(vec (neg (var inf var-inf)))
|
|
(catch 'syntax (math-read-vector))))))
|
|
(if (stringp vals)
|
|
(if space-sep
|
|
(let ((error-exp-pos math-exp-pos)
|
|
(error-exp-old-pos math-exp-old-pos)
|
|
vals2)
|
|
(setq math-exp-pos save-exp-pos
|
|
math-exp-old-pos save-exp-old-pos
|
|
math-exp-token save-exp-token
|
|
math-expr-data save-exp-data)
|
|
(let ((math-exp-keep-spaces nil))
|
|
(setq vals2 (catch 'syntax (math-read-vector))))
|
|
(if (and (not (stringp vals2))
|
|
(or (assoc math-expr-data '(("\\ldots") ("\\dots") (";")))
|
|
(equal math-expr-data math-rb-close)
|
|
(eq math-exp-token 'end)))
|
|
(setq space-sep nil
|
|
vals vals2)
|
|
(setq math-exp-pos error-exp-pos
|
|
math-exp-old-pos error-exp-old-pos)
|
|
(throw 'syntax vals)))
|
|
(throw 'syntax vals)))
|
|
(if (or (equal math-expr-data "\\dots")
|
|
(equal math-expr-data "\\ldots"))
|
|
(progn
|
|
(math-read-token)
|
|
(setq vals (if (> (length vals) 2)
|
|
(cons 'calcFunc-mul (cdr vals)) (nth 1 vals)))
|
|
(let ((exp2 (if (or (equal math-expr-data math-rb-close)
|
|
(equal math-expr-data ")")
|
|
(eq math-exp-token 'end))
|
|
'(var inf var-inf)
|
|
(math-read-expr-level 0))))
|
|
(setq vals
|
|
(list 'intv
|
|
(if (equal math-expr-data ")") 2 3)
|
|
vals
|
|
exp2)))
|
|
(if (not (or (equal math-expr-data math-rb-close)
|
|
(equal math-expr-data ")")
|
|
(eq math-exp-token 'end)))
|
|
(throw 'syntax "Expected `]'")))
|
|
(if (equal math-expr-data ";")
|
|
(let ((math-exp-keep-spaces space-sep))
|
|
(setq vals (cons 'vec (math-read-matrix (list vals))))))
|
|
(if (not (or (equal math-expr-data math-rb-close)
|
|
(eq math-exp-token 'end)))
|
|
(throw 'syntax "Expected `]'")))
|
|
(or (eq math-exp-token 'end)
|
|
(math-read-token))
|
|
vals)))
|
|
|
|
(defun math-check-for-commas (&optional balancing)
|
|
(let ((count 0)
|
|
(pos (1- math-exp-pos)))
|
|
(while (and (>= count 0)
|
|
(setq pos (string-match
|
|
(if balancing "[],[{}()<>]" "[],[{}()]")
|
|
math-exp-str (1+ pos)))
|
|
(or (/= (aref math-exp-str pos) ?,) (> count 0) balancing))
|
|
(cond ((memq (aref math-exp-str pos) '(?\[ ?\{ ?\( ?\<))
|
|
(setq count (1+ count)))
|
|
((memq (aref math-exp-str pos) '(?\] ?\} ?\) ?\>))
|
|
(setq count (1- count)))))
|
|
(if balancing
|
|
pos
|
|
(and pos (= (aref math-exp-str pos) ?,)))))
|
|
|
|
(defun math-read-vector ()
|
|
(let* ((val (list (math-read-expr-level 0)))
|
|
(last val))
|
|
(while (progn
|
|
(while (eq math-exp-token 'space)
|
|
(math-read-token))
|
|
(and (not (eq math-exp-token 'end))
|
|
(not (equal math-expr-data ";"))
|
|
(not (equal math-expr-data math-rb-close))
|
|
(not (equal math-expr-data "\\dots"))
|
|
(not (equal math-expr-data "\\ldots"))))
|
|
(if (equal math-expr-data ",")
|
|
(math-read-token))
|
|
(while (eq math-exp-token 'space)
|
|
(math-read-token))
|
|
(let ((rest (list (math-read-expr-level 0))))
|
|
(setcdr last rest)
|
|
(setq last rest)))
|
|
(cons 'vec val)))
|
|
|
|
(defun math-read-matrix (mat)
|
|
(while (equal math-expr-data ";")
|
|
(math-read-token)
|
|
(while (eq math-exp-token 'space)
|
|
(math-read-token))
|
|
(setq mat (nconc mat (list (math-read-vector)))))
|
|
mat)
|
|
|
|
(provide 'calc-vec)
|
|
|
|
;;; calc-vec.el ends here
|