arrayfire.lapack module¶
Dense Linear Algebra functions (solve, inverse, etc).
arrayfire.lapack.cholesky(A,is_upper=True)[source]¶Cholesky decomposition
- Parameters
- A: af.Array
A 2 dimensional, symmetric, positive definite matrix.
- is_upper: optional: bool. default: True
Specifies if outputR is upper triangular (if True) or lower triangular (if False).
- Returns
- (R,info): tuple of af.Array, int.
R - triangular matrix.
info - 0 if decomposition sucessful.
arrayfire.lapack.cholesky_inplace(A,is_upper=True)[source]¶In place Cholesky decomposition.
- Parameters
- A: af.Array
a 2 dimensional, symmetric, positive definite matrix.
Trinangular matrix on exit.
- is_upper: optional: bool. default: True.
Specifies if outputR is upper triangular (if True) or lower triangular (if False).
- Returns
- infoint.
0 if decomposition sucessful.
arrayfire.lapack.det(A)[source]¶Determinant of a matrix.
- Parameters
- A: af.Array
A 2 dimensional arrayfire array
- Returns
- res: scalar
Determinant of the matrix.
arrayfire.lapack.inverse(A,options=<MATPROP.NONE:0>)[source]¶Invert a matrix.
- Parameters
- A: af.Array
A 2 dimensional arrayfire array
- options: optional: af.MATPROP. default: af.MATPROP.NONE.
Additional options to speed up computations.
Currently needs to be one ofaf.MATPROP.NONE.
- Returns
- AI: af.Array
A 2 dimensional array that is the inverse ofA
arrayfire.lapack.is_lapack_available()[source]¶Function to check if the arrayfire library was built with lapack support.
arrayfire.lapack.lu(A)[source]¶LU decomposition.
- Parameters
- A: af.Array
A 2 dimensional arrayfire array.
- Returns
- (L,U,P): tuple of af.Arrays
L - Lower triangular matrix.
U - Upper triangular matrix.
P - Permutation array.
arrayfire.lapack.lu_inplace(A,pivot='lapack')[source]¶In place LU decomposition.
- Parameters
- A: af.Array
a 2 dimensional arrayfire array on entry.
Contains L in the lower triangle on exit.
Contains U in the upper triangle on exit.
- Returns
- P: af.Array
Permutation array.
arrayfire.lapack.norm(A,norm_type=<NORM.VECTOR_2:2>,p=1.0,q=1.0)[source]¶Norm of an array or a matrix.
- Parameters
- A: af.Array
A 1 or 2 dimensional arrayfire array
- norm_type: optional: af.NORM. default: af.NORM.EUCLID.
Type of norm to be calculated.
- p: scalar. default 1.0.
Used only ifnorm_type is one ofaf.NORM.VECTOR_P,af.NORM_MATRIX_L_PQ
- q: scalar. default 1.0.
Used only ifnorm_type isaf.NORM_MATRIX_L_PQ
- Returns
- res: scalar
norm of the input
arrayfire.lapack.pinverse(A,tol=1e-06,options=<MATPROP.NONE:0>)[source]¶Find pseudo-inverse(Moore-Penrose) of a matrix.
- Parameters
- A: af.Array
A 2 dimensional arrayfire input matrix array
- tol: optional: scalar. default: 1E-6.
Tolerance for calculating rank
- options: optional: af.MATPROP. default: af.MATPROP.NONE.
Currently needs to beaf.MATPROP.NONE.
Additional options may speed up computation in the future
- Returns
- AI: af.Array
A 2 dimensional array that is the pseudo-inverse ofA
arrayfire.lapack.qr(A)[source]¶QR decomposition.
- Parameters
- A: af.Array
A 2 dimensional arrayfire array.
- Returns
- (Q,R,T): tuple of af.Arrays
Q - Orthogonal matrix.
R - Upper triangular matrix.
T - Vector containing additional information to solve a least squares problem.
arrayfire.lapack.qr_inplace(A)[source]¶In place QR decomposition.
- Parameters
- A: af.Array
a 2 dimensional arrayfire array on entry.
Packed Q and R matrices on exit.
- Returns
- T: af.Array
Vector containing additional information to solve a least squares problem.
arrayfire.lapack.rank(A,tol=1e-05)[source]¶Rank of a matrix.
- Parameters
- A: af.Array
A 2 dimensional arrayfire array
- tol: optional: scalar. default: 1E-5.
Tolerance for calculating rank
- Returns
- r: int
Rank ofA within the given tolerance
arrayfire.lapack.solve(A,B,options=<MATPROP.NONE:0>)[source]¶Solve a system of linear equations.
- Parameters
- A: af.Array
A 2 dimensional arrayfire array representing the coefficients of the system.
- B: af.Array
A 1 or 2 dimensional arrayfire array representing the constants of the system.
- options: optional: af.MATPROP. default: af.MATPROP.NONE.
Additional options to speed up computations.
Currently needs to be one ofaf.MATPROP.NONE,af.MATPROP.LOWER,af.MATPROP.UPPER.
- Returns
- X: af.Array
A 1 or 2 dimensional arrayfire array representing the unknowns in the system.
arrayfire.lapack.solve_lu(A,P,B,options=<MATPROP.NONE:0>)[source]¶Solve a system of linear equations, using LU decomposition.
- Parameters
- A: af.Array
A 2 dimensional arrayfire array representing the coefficients of the system.
This matrix should be decomposed previously usinglu_inplace(A).
- P: af.Array
Permutation array.
This array is the output of an earlier call tolu_inplace(A)
- B: af.Array
A 1 or 2 dimensional arrayfire array representing the constants of the system.
- Returns
- X: af.Array
A 1 or 2 dimensional arrayfire array representing the unknowns in the system.
