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chol

  

compute the Cholesky factorization of a MapleMatrix or MatlabMatrix in MATLAB(R), where R'*R = X, and P is nonzero only if X is positive definite

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

chol(X)

chol(X, output=R)

chol(X, output=RP)

Parameters

X

-

square MapleMatrix, or MatlabMatrix

output

-

specify the form of the output (optional)

R

-

return only unitary Q matrix

RP

-

return Q and upper decomposed R matrix

Description

• 

The commands Matlab[chol](X) and Matlab[chol](X, 'output'='R') use MATLAB® to compute the Cholesky factorization, R, of a MapleMatrix or MatlabMatrix, where transpose(R)*(R) = X. If X is not positive definite, then an error is returned.

• 

When you specify the optional parameter, 'output'='RP', two values are returned.  The second value, P, is zero if X is positive definite; otherwise, P is 1+dimension(R).  The first value, R, is the largest dimension matrix such that transpose(R)*(R) = XX, where XX is the upper left corner of X, of dimension P.

• 

For further details on the chol command, see the MATLAB® documentation.

Examples

withMatlab:

Define the Maple matrix

aMatrix1,0,0,3

a:=1003

(1)

Compute the factorization

Matlab[chol]a

[1.            0.         ]

[                         ]

[0.    1.73205080756887720]

An example of the RP option

bMatrix3,1,3,5,1,6,4,2,6,7,8,1,3,3,7,3

b:=3135164267813373

(2)

r,pMatlab[chol]b,'output'='RP'

        [1.73205080756887720    0.577350269189625842    1.73205080756887742]

        [                                                                  ]

r, p := [        0.             2.38047614284761665     1.26025207562520891], 4.

        [                                                                  ]

        [        0.                      0.             1.84709629036559763]

See Also

LinearAlgebra[MatrixInverse]

Matlab

Matlab[det]

Matlab[evalM]

Matlab[inv]

MatlabMatrix

 


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