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"Command"
.
Trailing spaces in a caption are ignored.
x
is a matrix with m
rows and n
columns,
and v
is a vector corresponding to column major ordering of the
elements of x
v(1) = x(1, 1)
v(2) = x(2, 1)
. .
. .
. .
v(m) = x(m, 1)
v(m + 1) = x(1, 2)
. .
. .
. .
v(m * n - 1) = x(m - 1, n)
v(m * n) = x(m, n)
Conjugate Symmetric
setcontrol
and getcontrol
.
v[x]
is
n-1 n-2 n-3
v[x] = v x + v x + v x + ... + v
1 2 3 n
(see also Polynomial
.)
real(x) | single-precision version of real part of x |
double(x) | double-precision version of real part of x |
imag(x) | double-precision version of imaginary part of x |
O>
or
DEBUG>
.
The prompt DEBUG>
is referred to a the Debugger prompt.
It signals that commands typed at the command line will be sent
to the debugger.
const
,
dll
,
global
,
include
,
label
,
load
,
or
save
.
A function definition is a also a directive but a function assignment
is not. For example,
function f(x) begin
return x^2
end
is a directive but
function h = f()
is not a directive.
f(x)
, or a unary operator,
acts element-by-element
if the value of element (i,j)
of f(x)
only depends on the value of x(i,j)
.
The type and dimension for f(x)
are the same as for x
.
This notation extends to binary operators.
Either one operand is a scalar or they have the same dimensions.
If both operands are scalars,
the return value is a scalar.
Otherwise the dimension of the return value
is the same as for the operand that is not a scalar.
The type of the return value is the type that results from
coercion
between the operands.
This notation also extends to
functions with more than one argument.
Each argument must either be a scalar or have the same
dimensions as the other arguments that are not scalars.
If all the arguments are scalars,
the return value is a scalar.
Otherwise the dimension of the return value
is the same as for the arguments that are not scalars.
The type of the return value is the type that results from
coercion
between the arguments.
sin
) in which case the intrinsic function is not available
for use where the identifier is defined.
It cannot use the same name as a
keyword
(such as while
).
An identifier list is a set of identifiers separated by commas.
For example,
x, y1, z_2
is an identifier list.
INF
, is the result of 1./0.
.
It is greater than any finite value.
Minus infinity, -INF
, is less than any finite value.
Not a number, NAN
, is the result of 0./0.
.
It is also the result of any unary or binary operation in which one of the
operands is not a number (for example 1 + NAN
).
It is not defined for any logical comparison
operators (such as ==
).
You should use the function isnan
to check if a value is not a number.
1, x, x + y
is a list of three values.
X
is lower triangular
if all the elements above the diagonal of the matrix are zero;
i.e. if X(i, j)
is zero whenever i < j
.
Thus the matrix has the form
/ X_11 0 0 ... 0 \
| X_21 X_22 0 ... . |
| X_31 X_32 X_33 ... . |
| . . . . . |
| . . . . 0 |
| . |
\ X_M1 X_M2 X_M3 ... X_MN /
x
is monotone increasing if
x(i) < x(i+1)
for each i
such that i
and i+1
are valid indices of the vector.
A vector is monotone decreasing if
x(i) > x(i+1)
.
If the inequalities above are replaced by strict inequalities
(equal not allowed), the vector is referred to as
strictly monotone increasing and
strictly monotone decreasing respectively.
O>
, M>
, or
DEBUG>
.
The O>
prompt is referred to as the O-Matrix prompt.
O-Matrix language commands can be submitted at this prompt for execution.
v[x]
is
1 2 n-1
v[x] = v + v x + v x + ... + v x
1 2 3 n
(see also Descending Polynomial
.)
The largest scope corresponds to intrinsic functions.
These always have the same definition even after a clear
command.
The next level of scope is global scope.
and refers to all the source code between O-Matrix clear
commands.
A variable has global scope if it is
created outside of any function
by an assignment statement that does not begin with the local
option.
A function has global scope if its
definition
does not begin with the local
option.
The memory connected with such a variable
or function is freed when a clear
command is executed.
The next level of scope if file scope and refers to all
of the source code in one O-Matrix file.
A variable has file scope if it is created outside of any function
by an assignment statement that begins with the local
option.
A function has file scope if its
definition
begins with the local
option.
The memory connected with such a variable
current value is freed when the clear
command is executed.
The smallest scope is function scope and refers to all
of the source code within one function.
A variable that is created within a function has this scope
(functions cannot have this scope).
The memory connected with such a variable is freed when the function
returns; i.e., its value is not remembered between function calls.
X
is upper triangular
if all the elements below the diagonal of the matrix are zero;
i.e. if X(i, j)
is zero whenever i > j
.
Thus the matrix has the form
/ X_11 X_12 X_13 ... X_1N \
| 0 X_22 X_23 ... X_2N |
| . 0 X_33 ... X_3N |
| . . 0 . . |
| . . . . . |
| . . |
\ 0 0 0 ... X_MN /