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Release calc version 2.11.1

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Landon Curt Noll
1999-12-14 01:33:40 -08:00
parent 2c9b160dc5
commit 867002aa77
519 changed files with 18131 additions and 4296 deletions
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help/mat
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@@ -14,7 +14,7 @@ SYNOPSIS
TYPES
index-range-list range_1 [, range_2, ...] up to 4 ranges
range_1, ... integer, or integer_1 : integer_2
value, value_1, ... any
value, value_1, ... any
variable_1 ... lvalue
decl declarator = global, static or local
id_1, ... identifier
@@ -32,7 +32,7 @@ DESCRIPTION
If a variable is specified by an expression that is not a symbol with
possibly object element specifiers, the expression should be enclosed
in parentheses. For example, parentheses are required in
mat (A[2]) [3] and mat (*p) [3] but mat P.x [3] is acceptable.
mat (A[2]) [3] and mat (*p) [3] but mat P.x [3] is acceptable.
When an index-range is specified as integer_1 : integer_2, where
integer_1 and integer_2 are expressions which evaluate to integers,
@@ -64,18 +64,18 @@ DESCRIPTION
is p + i as long as A exists and a new value is not assigned to A.
When a matrix is created, each element is initially assigned the
value zero. Other values may be assigned then or later using the
value zero. Other values may be assigned then or later using the
"= {...}" assignment operation. Thus
A = {value_0, value_1, ...}
assigns the values value_0, value_1, ... to the elements A[[0]],
A[[1]], ... Any blank "value" is passed over. For example,
A[[1]], ... Any blank "value" is passed over. For example,
A = {1, , 2}
will assign the value 1 to A[[0]], 2 to A[[2]] and leave all other
elements unchanged. Values may also be assigned to elements by
elements unchanged. Values may also be assigned to elements by
simple assignments, as in A[0,0] = 1, A[0,2] = 2;
If the index-range is left blank but an initializer list is specified
@@ -87,16 +87,16 @@ DESCRIPTION
the matrix created is one-dimensional. If the list contains a
positive number n of values or blanks, the result is as if the
range were specified by [n], i.e. the range of indices is from
0 to n - 1. In the above examples, A is of size 2 with A[0] = 1
0 to n - 1. In the above examples, A is of size 2 with A[0] = 1
and A[1] = 2; B is of size 4 with B[0] = 1, B[1] = B[3] = 0,
B[2] = 3. The specification mat[] = { } creates the same as mat[1].
If the index-range is left blank and no initializer list is specified,
as in mat C[] or C = mat[], the matrix assigned to C has zero
dimension; this has one element C[]. To assign a value using "= { ...}"
dimension; this has one element C[]. To assign a value using "= { ...}"
at the same time as creating C, parentheses are required as in
(mat[]) = {value} or (mat C[]) = {value}. Later a value may be
assigned to C[] by C[] = value or C = {value}.
(mat[]) = {value} or (mat C[]) = {value}. Later a value may be
assigned to C[] by C[] = value or C = {value}.
The value assigned at any time to any element of a matrix can be of
any type - number, string, list, matrix, object of previously specified
@@ -106,7 +106,7 @@ DESCRIPTION
If an element of a matrix is a structure for which indices or an
object element specifier is required, an element of that structure is
referred to by appropriate uses of [ ] or ., and so on if an element
of that element is required. For example, one may have an expressions
of that element is required. For example, one may have an expressions
like
A[1,2][3].alpha[2];
@@ -116,14 +116,14 @@ DESCRIPTION
type mat[4] and A is a mat[2,3] matrix. When an element of a matrix
is a matrix and the total number of indices does not exceed 4, the
indices can be combined into one list, e.g. the A[1,2][3] in the
above example can be shortened to A[1,2,3]. (Unlike C, A[1,2] cannot
above example can be shortened to A[1,2,3]. (Unlike C, A[1,2] cannot
be expressed as A[1][2].)
The function ismat(V) returns 1 if V is a matrix, 0 otherwise.
isident(V) returns 1 if V is a square matrix with diagonal elements 1,
off-diagonal elements zero, or a zero- or one-dimensional matrix with
every element 1; otherwise zero is returned. Thus isident(V) = 1
every element 1; otherwise zero is returned. Thus isident(V) = 1
indicates that for V * A and A * V where A is any matrix of
for which either product is defined and the elements of A are real
or complex numbers, that product will equal A.
@@ -166,7 +166,7 @@ DESCRIPTION
matrices as determined by the later index-range-lists. For
example mat[2][3] is a 2-element matrix, each of whose elements has
as its value a 3-element matrix. Values may be assigned to the
elements of the innermost matrices by nested = {...} operations as in
elements of the innermost matrices by nested = {...} operations as in
mat [2][3] = {{1,2,3},{4,5,6}}
@@ -187,7 +187,7 @@ DESCRIPTION
matmax(A,i) - matmin(A,i) == matmax(B,i) - matmin(B,i),
One consequence of being the same shape is that the matrices will
have the same size. Elements "correspond" if they have the same
have the same size. Elements "correspond" if they have the same
double-bracket indices; thus A == B implies that A[[i]] == B[[i]]
for 0 <= i < size(A) == size(B).
@@ -195,7 +195,7 @@ DESCRIPTION
A - B
These are defined A and B have the same shape, the element
with double-bracket index j being evaluated by A[[j]] + B[[j]] and
A[[j]] - B[[j]], respectively. The index-ranges for the results
A[[j]] - B[[j]], respectively. The index-ranges for the results
are those for the matrix A.
A[i,j]
@@ -208,7 +208,7 @@ DESCRIPTION
A * B
Multiplication is defined provided certain conditions by the
dimensions and shapes of A and B are satisfied. If both have
dimensions and shapes of A and B are satisfied. If both have
dimension 2 and the column-index-list for A is the same as
the row-index-list for B, C = A * B is defined in the usual
way so that for i in the row-index-list of A and j in the
@@ -243,7 +243,7 @@ DESCRIPTION
on the left by the corresponding element of A.
If A is of dimension 2 and B is of dimension 1, A * B is defined
if number of columns in A is the same as the size of A. The
if number of columns in A is the same as the size of A. The
result has the same index-lists as A; each column of A is
multiplied on the right by the corresponding element of B.
@@ -251,7 +251,7 @@ DESCRIPTION
and two-dimensional matrices is particularly simple when all the
elements are real or complex numbers and all the index-lists are
the same, as occurs, for example, if for some positive integer n,
all the matrices start as mat [n] or mat [n,n].
all the matrices start as mat [n] or mat [n,n].
det(A)
If A is a square, det(A) is evaluated by an algorithm that returns
@@ -265,7 +265,7 @@ DESCRIPTION
The following functions are defined to return matrices with the same
index-ranges as A and the specified operations performed on all
elements of A. Here num is an arbitrary complex number (nonzero
elements of A. Here num is an arbitrary complex number (nonzero
when it is a divisor), int an integer, rnd a rounding-type
specifier integer, real a real number.
@@ -276,8 +276,8 @@ DESCRIPTION
conj(A)
A << int, A >> int
scale(A, int)
round(A, int, rnd)
bround(A, int, rnd)
round(A, int, rnd)
bround(A, int, rnd)
appr(A, real, rnd)
int(A)
frac(A)
@@ -290,7 +290,7 @@ DESCRIPTION
elements.
If A and B are one-dimension and of size 3, cp(A, B) returns their
cross-product.
cross-product.
randperm(A) returns a matrix indexed the same as A in which the elements
of A have been randomly permuted.
@@ -300,7 +300,7 @@ DESCRIPTION
If A is an lvalue whose current value is a matrix, matfill(A, v)
assigns the value v to every element of A, and if also, A is
square, matfill(A, v1, v2) assigns v1 to the off-diagonal elements,
square, matfill(A, v1, v2) assigns v1 to the off-diagonal elements,
v2 to the diagonal elements. To create and assign to A the unit
n * n matrix, one may use matfill(mat A[n,n], 0, 1).
@@ -310,7 +310,7 @@ DESCRIPTION
For a two-dimensional matrix A, mattrans(A) returns the transpose
of A, i.e. if A is mat[m,n], it returns a mat[n,m] matrix with
[i,j] element equal to A[j,i]. For zero- or one-dimensional A,
[i,j] element equal to A[j,i]. For zero- or one-dimensional A,
mattrace(A) returns a matrix with the same value as A.
The functions search(A, value, start, end]) and
@@ -388,10 +388,36 @@ LIMITS
second to invert a 10 * 10 matrix, it will probably take about 1000
times as long to invert a 100 * 100 matrix.
LIBRARY
LINK LIBRARY
n/a
SEE ALSO
ismat, matdim, matmax, matmin, mattrans, mattrace, matsum, det, inverse,
isident, test, config, search, rsearch, reverse, copy, blkcpy, dp, cp,
randperm, sort
## Copyright (C) 1999 Landon Curt Noll
##
## Calc is open software; you can redistribute it and/or modify it under
## the terms of the version 2.1 of the GNU Lesser General Public License
## as published by the Free Software Foundation.
##
## Calc is distributed in the hope that it will be useful, but WITHOUT
## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
## or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General
## Public License for more details.
##
## A copy of version 2.1 of the GNU Lesser General Public License is
## distributed with calc under the filename COPYING-LGPL. You should have
## received a copy with calc; if not, write to Free Software Foundation, Inc.
## 59 Temple Place, Suite 330, Boston, MA 02111-1307, USA.
##
## @(#) $Revision: 29.1 $
## @(#) $Id: mat,v 29.1 1999/12/14 09:15:58 chongo Exp $
## @(#) $Source: /usr/local/src/cmd/calc/help/RCS/mat,v $
##
## Under source code control: 1991/07/21 04:37:22
## File existed as early as: 1991
##
## chongo <was here> /\oo/\ http://reality.sgi.com/chongo/
## Share and enjoy! :-) http://reality.sgi.com/chongo/tech/comp/calc/