arrayfire.lapack module¶
Dense Linear Algebra functions (solve, inverse, etc).
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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 output R 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.
Note
The original matrix A can be reconstructed using the outputs in the following manner.
>>> A = af.matmulNT(R, R) #if R is upper triangular
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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 output R is upper triangular (if True) or lower triangular (if False).
Returns: info : int.
0 if decomposition sucessful.
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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.
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arrayfire.lapack.inverse(A, options=<arrayfire.library.MATPROP object>)[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 of af.MATPROP.NONE.
Returns: AI: af.Array
- A 2 dimensional array that is the inverse of A
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arrayfire.lapack.is_lapack_available()[source]¶ Function to check if the arrayfire library was built with lapack support.
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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.
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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.
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arrayfire.lapack.norm(A, norm_type=<arrayfire.library.NORM object>, 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 if norm_type is one of af.NORM.VECTOR_P, af.NORM_MATRIX_L_PQ
q: scalar. default 1.0.
- Used only if norm_type is af.NORM_MATRIX_L_PQ
Returns: res: scalar
- norm of the input
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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.
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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.
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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 of A within the given tolerance
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arrayfire.lapack.solve(A, B, options=<arrayfire.library.MATPROP object>)[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 of af.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.
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arrayfire.lapack.solve_lu(A, P, B, options=<arrayfire.library.MATPROP object>)[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 using lu_inplace(A).
P: af.Array
- Permutation array.
- This array is the output of an earlier call to lu_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.
