linalg(deprecated)/forwardsub - Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : linalg(deprecated)/forwardsub

linalg(deprecated)

  

forwardsub

  

forward substitution on a matrix

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

forwardsub(L)

forwardsub(L, b, v)

Parameters

L

-

lower row reduced matrix

b

-

vector or matrix

v

-

(optional) name

Description

• 

Important: The linalg package has been deprecated. Use the superseding packages LinearAlgebra[ForwardSubstitute], instead.

  

- For information on migrating linalg code to the new packages, see examples/LinearAlgebraMigration.

• 

forwardsub generates a solution vector x to the equation Lx=b.

• 

If b is omitted, or b is 'false' then L is assumed to be an augmented matrix and the last column of L is used in place of b.

• 

If b is a matrix, then x (the solution) will also be a matrix with the same number of columns.

• 

If L is the result of applying Gaussian elimination to the augmented matrix of a system of linear equations, as might be obtained from LUdecomp, forwardsub completes the solution by forward substitution.  If a solution exists, it is returned as a vector. If no solution exists, an error will be generated.

• 

If the solution is not unique, it will be parameterized in terms of the symbols v[1], v[2], ..., etc. or v[1,k], v[2,k], ... as in the case where b is a matrix. If the third argument v is not specified, the global variable _t will be used.

• 

The input matrix must be in row-echelon form with all zero rows grouped at the top. Such a matrix is produced by obtaining the LU decomposition.

• 

The command with(linalg,forwardsub) allows the use of the abbreviated form of this command.

Examples

Important: The linalg package has been deprecated. Use the superseding packages LinearAlgebra[ForwardSubstitute], instead.

withlinalg:

Aarray1..3,1..4,1,2,3,1,2,k,6,6,1,3,k3,0:

LUdecompA,L='l',U='u'

12310k+40400kkk+4

(1)

b123:

v1forwardsubl,b

v1104

(2)

v2backsubu,v1

v2k2_t1k2+9k_t1+8k+48k+4k4_t1k+4k_t14k16k+4k_t1

(3)

mapnormal,evalmbA &* v2

000

(4)

See Also

linalg(deprecated)[backsub]

linalg(deprecated)[gausselim]

linalg(deprecated)[gaussjord]

linalg(deprecated)[linsolve]

linalg(deprecated)[LUdecomp]

LinearAlgebra