Home - News ( United States | United Kingdom | Italy | Germany ) - Football scores

Showing content from http://www.arrayfire.org/docs/group__lapack__factor__func__lu.htm below:

ArrayFire: lu

Perform LU decomposition. More...

Perform LU decomposition.

This function decomposes input matrix \(A\) into a lower triangle \(L\), an upper triangle \(U\) such that \(A = L * U\).

For stability, a permutation array \(P\) is also used to modify the formula in the following manner, \(A(P, span) = L * U\).

This operation can be performed in ArrayFire, using the following code snippet.

array l, u, pivot;

lu(l, u, pivot, a_orig);

The permuted version of the original matrix can be reconstructed, using the following snippet.

array a_recon = matmul(l, u);

array a_perm = a_orig(pivot, span);

The sample output for these operations can be seen below.

a_orig [3 3 1 1]

0.0000 3.0000 6.0000

1.0000 4.0000 7.0000

2.0000 5.0000 8.0000

l [3 3 1 1]

1.0000 0.0000 0.0000

0.0000 1.0000 0.0000

0.5000 0.5000 1.0000

u [3 3 1 1]

2.0000 5.0000 8.0000

0.0000 3.0000 6.0000

0.0000 0.0000 0.0000

pivot [3 1 1 1]

2

0

1

a_recon [3 3 1 1]

2.0000 5.0000 8.0000

0.0000 3.0000 6.0000

1.0000 4.0000 7.0000

a_perm [3 3 1 1]

2.0000 5.0000 8.0000

0.0000 3.0000 6.0000

1.0000 4.0000 7.0000

When memory is a concern, users can perform the LU decomposition in place as shown below.

array out = a_orig.copy();

array pivot2;

luInPlace(pivot2, out, false);

The lower and upper triangle matrices can be obtained if necessary in the following manner.

array l2 = lower(out, true);

array u2 = upper(out, false);

LU decompositions have many applications including solving a system of linear equations. Check af::solveLU for more information.

C Interface to perform LU decomposition.

Parameters

[out] lower lower triangular matrix of the LU decomposition [out] upper upper triangular matrix of the LU decomposition [out] pivot permutation indices mapping the input to the decomposition [in] in input array

Returns

AF_SUCCESS, if function returns successfully, else an af_err code is given

C Interface to perform in-place LU decomposition.

This function is not supported in GFOR.

Parameters

[out] pivot permutation indices mapping the input to the decomposition [in,out] in input array on entry; packed LU decomposition on exit [in] is_lapack_piv specifies if the pivot is returned in original LAPACK-compliant format

Returns

AF_SUCCESS, if function returns successfully, else an af_err code is given

C++ Interface to perform LU decomposition.

This function is not supported in GFOR.

Parameters

[out] lower lower triangular matrix of the LU decomposition [out] upper upper triangular matrix of the LU decomposition [out] pivot permutation indices mapping the input to the decomposition [in] in input array

C++ Interface to perform LU decomposition in packed format.

This function is not supported in GFOR.

Parameters

[out] out packed LU decomposition [out] pivot permutation indices mapping the input to the decomposition [in] in input array [in] is_lapack_piv specifies if the pivot is returned in original LAPACK compliant format

C++ Interface to perform in-place LU decomposition.

This function is not supported in GFOR.

Parameters

[out] pivot permutation indices mapping the input to the decomposition [in,out] in input array on entry; packed LU decomposition on exit [in] is_lapack_piv specifies if the pivot is returned in original LAPACK-compliant format

RetroSearch is an open source project built by @garambo | Open a GitHub Issue

Search and Browse the WWW like it's 1997 | Search results from DuckDuckGo

HTML: 3.2 | Encoding: UTF-8 | Version: 0.7.4