Powder Average Facilitator Functions

Page 63 out of 81 total pages , Page 6 out of 12 pages in this chapter

5.12 Powder Average Facilitator Functions

5.12.1 A0A, A20A

Usage:

row_vector IntG::A0A(int Ntheta)
row_vector IntG::A20A(int Ntheta)

Description:

The functions A0A and A20A are equivalent. They are used to obtain part of G interaction spatial tensor component

for a series of evenly incrmented

values.

Given a number of angle increments, Ntheta, a row vector of dimension Ntheta will be returned which contains the

independent terms of

at evenly spaced increments of

starting at the +z PAS (

) alignment and finishing at -z PAS (

) alignment.

Note that to obtain the full

terms (if they are

dependent) they must be properly combined with the values from the function A20B.

Return Value:

A vector.

Example:

IntG G(1.5, 3.e5, 0.2, 45.0, 45.0); // Make a G interaction.
row_vector A20s = G.A20A(720); // Get 720 A20A values spanning [0, 180]

See Also: A21A, A22A, A20B, A21B, A22B, A2As, A2Bs, A2s

5.12.2 A1A, A21A

Usage:

row_vector IntG::A1A(int Ntheta)
row_vector IntG::A21A(int Ntheta)

Description:

The functions A1A and A21A are equivalent. They are used to obtain part of G interaction spatial tensor component

for a series of evenly incrmented

values.

Given a number of angle increments, Ntheta, a row vector of dimension Ntheta will be returned which contains the

independent terms of

at evenly spaced increments of

starting at the +z PAS (

) alignment and finishing at -z PAS (

) alignment.

Note that to obtain the full

terms (if they are

dependent) they must be properly combined with the values from the function A21B.

Return Value:

A vector.

Example:

IntG G(1.5, 3.e5, 0.2); // Make a G interaction.
row_vector A21s = G.A21A(181); // Get 181 A20A values spanning [0, 180]

See Also: A20A, A22A, A20B, A21B, A22B, A2As, A2Bs, A2s

5.12.3 A2A, A221A

Usage:

row_vector IntG::A2A(int Ntheta)
row_vector IntG::A22A(int Ntheta)

Description:

The functions A2A and A22A are equivalent. They are used to obtain part of G interaction spatial tensor component

for a series of evenly incremented

values.

Given a number of angle increments, Ntheta, a row vector of dimension Ntheta will be returned which contains the

independent terms of

at evenly spaced increments of

starting at the +z PAS (

) alignment and finishing at -z PAS (

) alignment.

Note that to obtain the full

terms (if they are

dependent) they must be properly combined with the values from the function A22B.

Return Value:

A vector.

Example:

IntG G(1.5, 3.e5, 0.2); // Make a G interaction.
row_vector A22s = G.A22A(181); // Get 181 A22A values spanning [0, 180]

See Also: A20A, A21A, A20B, A21B, A22B, A2As, A2Bs, A2s

5.12.4 A0B, A20B

Usage:

row_vector IntG::A0B(int Nphi)
row_vector IntG::A20B(int Nphi)

Description:

The functions A0B and A20B are equivalent. They are used to obtain part of G interaction spatial tensor component

for a series of evenly incrmented

values.

Given a number of angle increments, Nphi, a row vector of dimension Nphi will be returned which contains

independent terms of

at evenly spaced increments of

starting at the +x PAS (

) alignment and finishing at +x PAS (

) alignment.

Note that to obtain the full

terms they must be properly combined with the values from the function A20A.

Return Value:

A vector.

Example:

IntG G(1.5, 3.e5, 0.2); // Make a G interaction.
row_vector A20s = G.A20B(120); // Get 120 A20B values spanning [0, 360)

See Also: A20A, A21A, A22A, A21B, A22B, A2As, A2Bs, A2s

5.12.5 A1B, A21B

Usage:

row_vector IntG::A1B(int Nphi)
row_vector IntG::A21B(int Nphi)

Description:

The functions A1B and A21B are equivalent. They are used to obtain part of G interaction spatial tensor component

for a series of evenly incrmented

values.

where

Given a number of angle increments, Nphi, a row vector of dimension Nphi will be returned which contains

independent terms of

at evenly spaced increments of

starting at the +x PAS (

) alignment and finishing at +x PAS (

) alignment.

Note that to obtain the full

terms they must be properly combined with the values from the function A21A.

Return Value:

A vector.

Example:

IntG G(1.5, 3.e5, 0.2); // Make a G interaction.
row_vector A21s = G.A21B(120); // Get 120 A21B values spanning [0, 360)

See Also: A20A, A21A, A22A, A20B, A22B, A2As, A2Bs, A2s

5.12.6 A2B, A22B

Usage:

row_vector IntG::A2B(int Nphi)
row_vector IntG::A22B(int Nphi)

Description:

The functions A1B and A21B are equivalent. They are used to obtain part of G interaction spatial tensor component

for a series of evenly incrmented

values.

where

Given a number of angle increments, Nphi, a row vector of dimension Nphi will be returned which contains

independent terms of

at evenly spaced increments of

starting at the +x PAS (

) alignment and finishing at +x PAS (

) alignment.

Note that to obtain the full

terms they must be properly combined with the values from the function A22A.

Return Value:

A vector.

Example:

IntG G(1.5, 3.e5, 0.2); // Make a G interaction.
row_vector A22s = G.A22B(120); // Get 120 A22B values spanning [0, 360)

See Also: A20A, A21A, A22A, A20B, A21B, A2As, A2Bs, A2s

5.12.7 A2s

Usage:

matrix IntG::A2s(int Ntheta, int Nphi)

Description:

The function A2s is used to construct the G interaction spatial tensor components

for a series of evenly incrmented

and

values. Given arguments for the number of angle increments, Ntheta and Nphi the function will return a matrix of dimenstion (8 x nc) where nc is the larger of the two input arguments. The matrix columns, indexed by j, will then correspond either to an angle

or an angle

where

depending upon which row is being accessed. Rows 0-2 of the array will correspond to the the

independent terms of

at evenly spaced increments of

starting at the +z PAS (

) alignment and finishing at -z PAS (

) alignment. Rows 3-5 of the array will correspond to

independent parts of the interaction spatial tensor components

at evenly spaced increments of

starting at the +x PAS (

) alignment and finishing at +x PAS (

) alignment. The final three array columns will contain

dependent terms that are used to blend with the other rows to form the full

values. Reconstruction of full

values is based on

A particular

can be reconstructed acconding to the analogous discrete equations.

The components with m negative are obtained from the relationship .

Return Value:

An array.

Example:

IntG G(1.5, 3.e5, 0.2); // Make a G interaction.
matrix As = G.A2x(720, 360); // Get array for values spanning [0, 180] & [0, 360)

See Also: A20A, A21A, A22A, A20B, A21B, A2As, A2Bs, A2s

Page 63 out of 81 total pages , Page 6 out of 12 pages in this chapter

No GAMMA WWW pages or GAMMA specific images therein may be reproduced or used in any manner outside of personal Web Browsers without permission from the copyright holders.
Send problems & suggestions to gamma@magnet.fsu.edu
Additonal GAMMA information can be found at http://gamma.magnet.fsu.edu