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 ncolumns, CON returns a constant vector with n elements. If the list contains two integers nrows and mcolumns, 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

 

 

 

 

 

 

 

 

{ ncolumns }

zconstant

→

[ vectorconstant ]

 

 

{ nrows mcolumns }

zconstant

→

[[ matrixconstant ]]

 

 

[ R-array ]

xconstant

→

[ R-arrayconstant]

 

 

[ C-array ]

zconstant

→

[ C-arrayconstant]

 

 

'name'

zconstant

→

 

 

{ 2 2 }

 

 

Example 1:

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

Command

 

 

 

Type:

 

 

 

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–log10(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

→

xconditionnumber

 

 

 

 

 

3-42 Full Command and Function Reference