Mode

 

 

 

 

 

 

Result

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Rectangular (flag –16 clear)

 

 

 

[ x1

x2 x3 ]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Polar/Cylindrical (flag –15 clear and –16 set)

 

 

[ x1

x€theta xz ]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Polar/Spherical (flag –15 and –16 set)

 

 

[ x1

x€theta x€phi ]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Access:

!´VECTOR →V3

 

 

( ´is the left-shift of the Pkey).

 

 

 

 

 

 

Flags:

Coordinate System (–15 and –16)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Input/Output:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Level 3/Argument 1

Level 2/Argument 2 Level 1/Argument 3

 

Level 1/Item 1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

x1

x2

 

 

x3

→

[ x1 x2 x3 ]

 

 

 

 

 

x

1

x

theta

 

 

x

z

→

[ x

1

x

 

x

]

 

 

 

 

 

 

 

 

 

 

€ theta

 

 

z

 

 

 

 

x

1

x

theta

 

 

x

phi

→

[ x

1

x

x

phi

]

 

 

 

 

 

 

 

 

€ theta

 

 

 

Example 1: With flag –16 clear (Rectangular mode), 1 2 3 →V3 returns [ 1 2 3 ].

Example 2: With flag –15 clear and –16 set (Polar/Cylindrical mode), 1 2 3 →V3 returns [ 1 €2 3 ].

Example 3: With flags –15 and –16 set (Polar/Spherical mode), 1 2 3 →V3 returns [ 1 €2 €3 ].

See also:

V→, →V2

 

 

 

 

 

 

 

VANDERMONDE

 

 

 

 

Type:

Command

Description:

Builds the Vandermonde matrix (also called the alternant matrix) from a list of objects. That is,

 

for a list of n objects, the command creates an n × n matrix. The ith column in the matrix consists

 

of the list items raised to the power of (i–1). Sometimes the Vandermonde matrix is defined with

 

the ith row containing the items raised to the power of (i–1); to obtain this, transpose the result

 

with the command TRAN.

Access:

Matrices, !Ø CREATELL, !´MATRX MAKE LL

Input:

A list of objects. A vector is allowed too.

Output:

The corresponding Vandermonde matrix.

Flags:

Exact mode must be set (flag –105 clear).

 

Numeric mode must not be set (flag –3 clear).

Example:

Build the row version of the Vandermonde matrix from the following list of objects:

 

{x, y, z}

Command:

TRAN(VANDERMONDE({x,y,z}))

 

 

 

 

 

 

 

 

 

1

1

1

 

 

 

 

 

x

y

z

Result:

x2 y2 z2

See also: CON, HILBERT, IDN, RANM

VAR

Type: Command

Description: Variance Command: Calculates the sample variance of the coordinate values in each of the m columns in the current statistics matrix (ΣDAT).

Full Command and Function Reference 3-269