Libctl User Reference
From AbInitio
Revision as of 23:36, 15 October 2005 (edit) Stevenj (Talk | contribs) (→Miscellaneous utilities) ← Previous diff |
Revision as of 23:51, 15 October 2005 (edit) Stevenj (Talk | contribs) (→Miscellaneous utilities) Next diff → |
||
Line 142: | Line 142: | ||
: Return a function wrapping around the function <code>''func''</code> that "memoizes" its arguments and return values. That is, it returns the same thing as <code>''func''</code>, but if passed the same arguments as a previous call it returns a cached return value from the previous call instead of recomputing it. | : Return a function wrapping around the function <code>''func''</code> that "memoizes" its arguments and return values. That is, it returns the same thing as <code>''func''</code>, but if passed the same arguments as a previous call it returns a cached return value from the previous call instead of recomputing it. | ||
- | {{Category:libctl}} | + | [[Category:libctl]] |
Revision as of 23:51, 15 October 2005
libctl |
Manual: Introduction |
Basic User Experience |
Advanced User Experience |
User Reference |
Developer Experience |
Guile and Scheme links |
License and Copyright |
In this section, we list all of the special functions provided for users by libctl. We do not attempt to document standard Scheme functions, with a couple of exceptions below, since there are plenty of good Scheme references [guile-links.html elsewhere].
Of course, the most important function is:
-
(help)
- Outputs a listing of all the available classes, their properties, default values, and types. Also lists the input and output variables.
Remember, Guile lets you enter expressions and see their values interactively. This is the best way to learn how to use anything that confuses you—just try it and see how it works!
Contents |
Basic Scheme functions
-
(set! variable value)
- Change the value of
variable
tovalue
. -
(define variable value)
- Define new
variable
with initialvalue
. -
(list [ element1 element2 ... ])
- Returns a list consisting of zero or more elements.
-
(append [ list1 list2 ... ])
- Concatenates zero or more lists into a single list.
-
(function [ arg1 arg2 ... ])
- This is how you call a Scheme
function
in general. -
(define (function [ arg1 arg2 ... ]) body)
- Define a new
function
with zero or more arguments that returns the result of givenbody
when it is invoked.
Command-line parameters
-
(define-param name default-value)
- Define a variable
name
whose value can be set from the command line, and which assumes a valuedefault-value
if it is not set. To set the value on the command-line, includename=value
on the command-line when the program is executed. In all other respects,name
is an ordinary Scheme variable. -
(set-param! name new-default-value)
- Like
set!
, but does nothing ifname
was set on the command line.
Complex numbers
Scheme includes full support for complex numbers and arithmetic; all of the ordinary operations (+
, *
, sqrt
, etcetera) just work. For the same reason, you can freely use complex numbers in libctl's vector and matrix functions, below.
To specify a complex number a+bi, you simply use the syntax a+bi
if a and b are constants, and (make-rectangular a b)
otherwise. (You can also specify numbers in "polar" format a*eib by the syntax a@b
or (make-polar a b)
.)
There are a few special functions provided by Scheme to manipulate complex numbers. (real-part z)
and (imag-part z)
return the real and imaginary parts of z
, respectively. (magnitude z)
returns the absolute value and (angle z)
returns the phase angle. libctl also provides a (conj z)
function, below, to return the complex conjugate.
3-vector functions
-
(vector3 x [y z]
) - Create a new 3-vector with the given components. If the
y
orz
value is omitted, it is set to zero. -
(vector3-x v)
-
(vector3-y v)
-
(vector3-z v)
- Return the corresponding component of the vector
v
. -
(vector3+ v1 v2)
-
(vector3- v1 v2)
-
(vector3-cross v1 v2)
- Return the sum, difference, or cross product of the two vectors.
-
(vector3* a b)
- If
a
andb
are both vectors, returns their dot product. If one of them is a number and the other is a vector, then scales the vector by the number. -
(vector3-dot v1 v2)
- Returns the dot product of
v1
andv2
. -
(vector3-cross v1 v2)
- Returns the cross product of
v1
andv2
. -
(vector3-cdot v1 v2)
- Returns the conjugated dot product: v1* dot v2.
-
(vector3-norm v)
- Returns the length
(sqrt (vector3-cdot v v))
of the given vector. -
(unit-vector3 x [y z]
) -
(unit-vector3 v)
- Given a vector or, alternatively, one or more components, returns a unit vector in that direction.
-
(vector3-close? v1 v2 tolerance)
- Returns whether or not the corresponding components of the two vectors are within
tolerance
of each other. -
(vector3= v1 v2)
- Returns whether or not the two vectors are numerically equal. Beware of using this function after operations that may have some error due to the finite precision of floating-point numbers; use
vector3-close?
instead. -
(rotate-vector3 axis theta v)
- Returns the vector
v
rotated by an angletheta
(in radians) in the right-hand direction around theaxis
vector (whose length is ignored). You may find the functions(deg->rad theta-deg)
and(rad->deg theta-rad)
useful to convert angles between degrees and radians.
3x3 matrix functions
-
(matrix3x3 c1 c2 c3)
- Creates a 3x3 matrix with the given 3-vectors as its columns.
-
(matrix3x3-transpose m)
-
(matrix3x3-adjoint m)
-
(matrix3x3-determinant m)
-
(matrix3x3-inverse m)
- Return the transpose, adjoint (conjugate transpose), determinant, or inverse of the given matrix.
-
(matrix3x3+ m1 m2)
-
(matrix3x3- m1 m2)
-
(matrix3x3* m1 m2)
- Return the sum, difference, or product of the given matrices.
-
(matrix3x3* v m)
-
(matrix3x3* m v)
- Returns the (3-vector) product of the matrix
m
by the vectorv
, with the vector multiplied on the left or the right respectively. -
(matrix3x3* s m)
-
(matrix3x3* m s)
- Scales the matrix
m
by the numbers
. -
(rotation-matrix3x3 axis theta)
- Like
rotate-vector3
, except returns the (unitary) rotation matrix that performs the given rotation. i.e.,(matrix3x3* (rotation-matrix3x3 axis theta) v)
produces the same result as(rotate-vector3 axis theta v)
.
Objects (members of classes)
-
(make class [ properties ... ])
- Make an object of the given
class
. Each property is of the form(property-name property-value)
. A property need not be specified if it has a default value, and properties may be given in any order. -
(object-property-value object property-name)
- Return the value of the property whose name (symbol) is
property-name
inobject
. For example,(object-property-value a-circle-object 'radius)
. (Returnsfalse
ifproperty-name
is not a property ofobject
.)
Miscellaneous utilities
-
(conj x)
- Return the complex conjugate of a number
x
(for some reason, Scheme doesn't provide such a function). -
(interpolate n list)
- Given a
list
of numbers or 3-vectors, linearly interpolates between them to addn
new evenly-spaced values between each pair of consecutive values in the original list. -
(print expressions...)
- Calls the Scheme
display
function on each of its arguments from left to right (printing them to standard output). Note that, likedisplay
, it does not append a newline to the end of the outputs; you have to do this yourself by including the"\n"
string at the end of the expression list. In addition, there is a global variableprint-ok?
, defaulting totrue
, that controls whetherprint
does anything; by settingprint-ok?
to false, you can disable all output. -
(begin-time message-string statements...)
- Like the Scheme
(begin ...)
construct, this executes the given sequence of statements one by one. In addition, however, it measures the elapsed time for the statements and outputs it asmessage-string
, followed by the time, followed by a newline. The return value ofbegin-time
is the elapsed time in seconds. -
(minimize function tolerance)
- Given a
function
of one (number) argument, finds its minimum within the specified fractionaltolerance
. If the return value ofminimize
is assigned to a variableresult
, then(min-arg result)
and(min-val result)
give the argument and value of the function at its minimum. If you can, you should use one of the variant forms ofminimize
, described below. -
(minimize function tolerance guess)
- The same as above, but you supply an initial
guess
for where the minimum is located. -
(minimize function tolerance arg-min arg-max)
- The same as above, but you supply the minimum and maximum function argument values within which to search for the minimum. This is the most preferred form of
minimize
, and is faster and more robust than the other two variants. -
(minimize-multiple function tolerance arg1 .. argN)
- Minimize a
function
of N numeric arguments within the specified fractionaltolerance
.arg1
..argN
are an initial guess for the function arguments. Returns both the arguments and value of the function at its minimum. A list of the arguments at the minimum are retrieved viamin-arg
, and the value viamin-val
. -
maximize
,maximize-multiple
- These are the same as the
minimize
functions except that they maximizes the function instead of minimizing it. The functionsmax-arg
andmax-val
are provided instead ofmin-arg
andmin-val
. -
(find-root function tolerance arg-min arg-max)
- Find a root of the given
function
to within the specified fractionaltolerance
.arg-min
andarg-max
bracket the desired root; the function must have opposite signs at these two points! -
(find-root-deriv function tolerance arg-min arg-max [arg-guess])
- As
find-root
, butfunction
should return acons
pair of (function-value . function-derivative); the derivative information is exploited to achieve faster convergence via Newton's method, compared tofind-root
. The optional argumentarg-guess
should be an initial guess for the root location. -
(derivative function x [dx tolerance])
-
(deriv function x [dx tolerance])
-
(derivative2 function x [dx tolerance])
-
(deriv2 function x [dx tolerance])
- Compute the numerical derivative of the given
function
atx
to within at best the specified fractionaltolerance
(defaulting to the maximum achievable tolerance), using Ridder's method of polynomial extrapolation.dx
should be a maximum displacement inx
for derivative evaluation; thefunction
should change by a significant amount (much larger than the numerical precision) overdx
.dx
defaults to 1% ofx
or0.01
, whichever is larger. - If the return value of
derivative
is assigned to a variableresult
, then(derivative-df result)
and(derivative-df-err result)
give the derivative of the function and an estimate of the numerical error in the derivative, respectively. - The
derivative2
function computes both the first and second derivatives, using minimal extra function evaluations; the second derivative and its error are then obtained by(derivative-d2f result)
and(derivative-d2f-err result)
. deriv
andderiv2
are identical toderivative
andderivative2
, except that they directly return the value of the first and second derivatives, respectively (no need to callderivative-df
orderivative-d2f
). (They don't provide the error estimate, however, or the ability to compute first and second derivatives simulataneously.)-
(integrate f a b tolerance)
- Return the definite integral of the function
f
froma
tob
, to within the specified fractionaltolerance
, using an adaptive trapezoidal rule. - This function can compute multi-dimensional integrals, in which case
f
is a function of N variables anda
andb
are either lists or vectors of length N, giving the (constant) integration bounds in each dimension. (Non-constant integration bounds, i.e. non-rectilinear integration domains, can be handled by an appropriate mapping of the functionf
.) -
(fold-left op init list)
- Combine the elements of
list
using the binary "operator" function(op x y)
, with initial valueinit
, associating from the left of the list. That is, iflist
consist of the elements(a b c d)
, then(fold-left op init list)
computes(op (op (op (op init a) b) c) d)
. For example, iflist
contains numbers, then(fold-left + 0 list)
returns the sum of the elements oflist
. -
(fold-right op init list)
- As
fold-left
, but associate from the right. For example,(op a (op b (op c (op d init))))
. -
(memoize func)
- Return a function wrapping around the function
func
that "memoizes" its arguments and return values. That is, it returns the same thing asfunc
, but if passed the same arguments as a previous call it returns a cached return value from the previous call instead of recomputing it.