Reference Guide
3-42 Full Command and Function Reference
The constant value is a real or complex number taken from argument 2/level 1. The resulting
array is either a new array, or an existing array with its elements replaced by the constant,
depending on the object in argument 1/level 2.
•
Creating a new array: If argument 1/level 2 contains a list of one or two integers, CON returns
a new array. If the list contains a single integer n
columns
, CON returns a constant vector with n
elements. If the list contains two integers n
rows
and m
columns
, CON returns a constant matrix with
n rows and m columns.
•
Replacing the elements of an existing array: If argument 1/level 2 contains an array, CON
returns an array of the same dimensions, with each element equal to the constant. If the
constant is a complex number, the original array must also be complex.
•
If argument 1/level 2 contains a name, the name must identify a variable that contains an array.
In this case, the elements of the array are replaced by the constant. If the constant is a complex
number, the original array must also be complex.
Access: !´
MATRIX MAKE CON
( ´ is the left-shift of the Pkey).
!Ø
CREATE CON
( Ø is the left-shift of the 5key).
Input/Output:
Level 2/Argument 1 Level 1/Argument 2 Level 1/Item 1
{ n
columns
}
z
constant
→
[ vector
constant
]
{ n
rows
m
columns
}
z
constant
→
[[ matrix
constant
]]
[ R-array ]
x
constant
→
[ R-array
constant
]
[ C-array ]
z
constant
→
[ C-array
constant
]
'name'
z
constant
→
Example 1:
{ 2 2 } 6 CON
returns the matrix
[[ 6 6 ][ 6 6 ]]
.
Example 2:
[ (2,4) (7,9) ] 3 CON
returns the complex vector
[ (3,0) (3,0) ]
.
See also: IDN
COND
Type: Command
Description: Condition Number Command: Returns the 1-norm (column norm) condition number of a square
matrix.
The condition number of a matrix is the product of the norm of the matrix and the norm of the
inverse of the matrix. COND uses the 1-norm and computes the condition number of the matrix
without computing the inverse of the matrix.
The condition number expresses the sensitivity of the problem of solving a system of linear
equations having coefficients represented by the elements of the matrix (this includes inverting
the matrix). That is, it indicates how much an error in the inputs may be magnified in the outputs
of calculations using the matrix.
In many linear algebra computations, the base 10 logarithm of the condition number of the matrix
is an estimate of the number of digits of precision that might be lost in computations using that
matrix. A reasonable rule of thumb is that the number of digits of accuracy in the result is
approximately MIN(12,15–log
10
(COND)).
Access: !´
MATRIX NORMALIZE COND
( ´ is the left-shift of the Pkey).
!Ø
OPERATIONS COND
( Ø is the left-shift of the 5key).
Input/Output:
Level 1/Argument 1 Level 1/Item 1
[[ matrix ]]
m×n
→
x
conditionnumber