arrayfire-python/_modules/arrayfire/lapack.html at gh-pages · arrayfire/arrayfire-python

Repository navigation

History

100

101

102

103

104

105

106

107

108

109

110

111

112

113

114

115

116

117

118

119

120

121

122

123

124

125

126

127

128

129

130

131

132

133

134

135

136

137

138

139

140

141

142

143

144

145

146

147

148

149

150

151

152

153

154

155

156

157

158

159

160

161

162

163

164

165

166

167

168

169

170

171

172

173

174

175

176

177

178

179

180

181

182

183

184

185

186

187

188

189

190

191

192

193

194

195

196

197

198

199

200

201

202

203

204

205

206

207

208

209

210

211

212

213

214

215

216

217

218

219

220

221

222

223

224

225

226

227

228

229

230

231

232

233

234

235

236

237

238

239

240

241

242

243

244

245

246

247

248

249

250

251

252

253

254

255

256

257

258

259

260

261

262

263

264

265

266

267

268

269

270

271

272

273

274

275

276

277

278

279

280

281

282

283

284

285

286

287

288

289

290

291

292

293

294

295

296

297

298

299

300

301

302

303

304

305

306

307

308

309

310

311

312

313

314

315

316

317

318

319

320

321

322

323

324

325

326

327

328

329

330

331

332

333

334

335

336

337

338

339

340

341

342

343

344

345

346

347

348

349

350

351

352

353

354

355

356

357

358

359

360

361

362

363

364

365

366

367

368

369

370

371

372

373

374

375

376

377

378

379

380

381

382

383

384

385

386

387

388

389

390

391

392

393

394

395

396

397

398

399

400

401

402

403

404

405

406

407

408

409

410

411

412

413

414

415

416

417

418

419

420

421

422

423

424

425

426

427

428

429

430

431

432

433

434

435

436

437

438

439

440

441

442

443

444

445

446

447

448

449

450

451

452

453

454

455

456

457

458

459

460

461

462

463

464

465

466

467

468

469

470

471

472

473

474

475

476

477

478

479

480

481

482

483

484

485

486

487

488

489

490

491

492

493

494

495

496

497

498

499

500

501

502

503

504

505

506

507

508

509

510

511

512

513

514

515

516

517

518

519

520

521

522

523

524

525

526

527

528

529

530

531

532

533

534

535

536

537

538

539

540

541

542

543

544

545

546

547

548

549

550

551

552

553

554

<!DOCTYPE html>

<html>

<head>

<title>arrayfire.lapack — ArrayFire Python documentation</title>

</head><body>

<h1>Source code for arrayfire.lapack</h1><div class="highlight"><pre>

#######################################################

#

# This file is distributed under 3-clause BSD license.

# The complete license agreement can be obtained at:

# http://arrayfire.com/licenses/BSD-3-Clause

########################################################

"""

Dense Linear Algebra functions (solve, inverse, etc).

"""

from .library import *

from .array import *

<div class="viewcode-block" id="lu"><a class="viewcode-back" href="../../arrayfire.lapack.html#arrayfire.lapack.lu">[docs]</a>def lu(A):

"""

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.

Note

----

The original matrix `A` can be reconstructed using the outputs in the following manner.

>>> A[P, :] = af.matmul(L, U)

"""

L = Array()

U = Array()

P = Array()

safe_call(backend.get().af_lu(c_pointer(L.arr), c_pointer(U.arr), c_pointer(P.arr), A.arr))

return L,U,P</div>

<div class="viewcode-block" id="lu_inplace"><a class="viewcode-back" href="../../arrayfire.lapack.html#arrayfire.lapack.lu_inplace">[docs]</a>def lu_inplace(A, pivot="lapack"):

"""

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.

Note

----

This function is primarily used with `af.solve_lu` to reduce computations.

"""

P = Array()

is_pivot_lapack = False if (pivot == "full") else True

return P</div>

<div class="viewcode-block" id="qr"><a class="viewcode-back" href="../../arrayfire.lapack.html#arrayfire.lapack.qr">[docs]</a>def qr(A):

"""

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.

Note

----

The outputs of this funciton have the following properties.

>>> A = af.matmul(Q, R)

>>> I = af.matmulNT(Q, Q) # Identity matrix

"""

Q = Array()

R = Array()

T = Array()

safe_call(backend.get().af_qr(c_pointer(Q.arr), c_pointer(R.arr), c_pointer(T.arr), A.arr))

return Q,R,T</div>

<div class="viewcode-block" id="qr_inplace"><a class="viewcode-back" href="../../arrayfire.lapack.html#arrayfire.lapack.qr_inplace">[docs]</a>def qr_inplace(A):

"""

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.

Note

----

This function is used to save space only when `R` is required.

"""

T = Array()

return T</div>

<div class="viewcode-block" id="cholesky"><a class="viewcode-back" href="../../arrayfire.lapack.html#arrayfire.lapack.cholesky">[docs]</a>def cholesky(A, is_upper=True):

"""

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

"""

R = Array()

info = c_int_t(0)

safe_call(backend.get().af_cholesky(c_pointer(R.arr), c_pointer(info), A.arr, is_upper))

return R, info.value</div>

<div class="viewcode-block" id="cholesky_inplace"><a class="viewcode-back" href="../../arrayfire.lapack.html#arrayfire.lapack.cholesky_inplace">[docs]</a>def cholesky_inplace(A, is_upper=True):

"""

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.

"""

info = c_int_t(0)

return info.value</div>

<div class="viewcode-block" id="solve"><a class="viewcode-back" href="../../arrayfire.lapack.html#arrayfire.lapack.solve">[docs]</a>def solve(A, B, options=MATPROP.NONE):

"""

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.

"""

X = Array()

safe_call(backend.get().af_solve(c_pointer(X.arr), A.arr, B.arr, options.value))

return X</div>

<div class="viewcode-block" id="solve_lu"><a class="viewcode-back" href="../../arrayfire.lapack.html#arrayfire.lapack.solve_lu">[docs]</a>def solve_lu(A, P, B, options=MATPROP.NONE):

"""

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.

"""

X = Array()

safe_call(backend.get().af_solve_lu(c_pointer(X.arr), A.arr, P.arr, B.arr, options.value))

return X</div>

<div class="viewcode-block" id="inverse"><a class="viewcode-back" href="../../arrayfire.lapack.html#arrayfire.lapack.inverse">[docs]</a>def inverse(A, options=MATPROP.NONE):

"""

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`

Note

----

`A` needs to be a square matrix.

"""

AI = Array()

safe_call(backend.get().af_inverse(c_pointer(AI.arr), A.arr, options.value))

return AI</div>

<div class="viewcode-block" id="pinverse"><a class="viewcode-back" href="../../arrayfire.lapack.html#arrayfire.lapack.pinverse">[docs]</a>def pinverse(A, tol=1E-6, options=MATPROP.NONE):

"""

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 be `af.MATPROP.NONE`.

- Additional options may speed up computation in the future

Returns

-------

AI: af.Array

- A 2 dimensional array that is the pseudo-inverse of `A`

Note

----

This function is not supported in GFOR

"""

AI = Array()

safe_call(backend.get().af_pinverse(c_pointer(AI.arr), A.arr, c_double_t(tol), options.value))

return AI</div>

<div class="viewcode-block" id="rank"><a class="viewcode-back" href="../../arrayfire.lapack.html#arrayfire.lapack.rank">[docs]</a>def rank(A, tol=1E-5):

"""

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

"""

r = c_uint_t(0)

return r.value</div>

<div class="viewcode-block" id="det"><a class="viewcode-back" href="../../arrayfire.lapack.html#arrayfire.lapack.det">[docs]</a>def det(A):

"""

Determinant of a matrix.

Parameters

----------

A: af.Array

- A 2 dimensional arrayfire array

Returns

-------

res: scalar

- Determinant of the matrix.

"""

re = c_double_t(0)

im = c_double_t(0)

re = re.value

im = im.value

return re if (im == 0) else re + im * 1j</div>

<div class="viewcode-block" id="norm"><a class="viewcode-back" href="../../arrayfire.lapack.html#arrayfire.lapack.norm">[docs]</a>def norm(A, norm_type=NORM.EUCLID, p=1.0, q=1.0):

"""

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

"""

res = c_double_t(0)

c_double_t(p), c_double_t(q)))

return res.value</div>

<div class="viewcode-block" id="svd"><a class="viewcode-back" href="../../arrayfire.lapack.html#arrayfire.lapack.svd">[docs]</a>def svd(A):

"""

Singular Value Decomposition

Parameters

----------

A: af.Array

A 2 dimensional arrayfire array.

Returns

-------

(U,S,Vt): tuple of af.Arrays

- U - A unitary matrix

- S - An array containing the elements of diagonal matrix

- Vt - A unitary matrix

Note

----

- The original matrix `A` is preserved and additional storage space is required for decomposition.

- If the original matrix `A` need not be preserved, use `svd_inplace` instead.

- The original matrix `A` can be reconstructed using the outputs in the following manner.

>>> Smat = af.diag(S, 0, False)

>>> A_recon = af.matmul(af.matmul(U, Smat), Vt)

"""

U = Array()

S = Array()

Vt = Array()

safe_call(backend.get().af_svd(c_pointer(U.arr), c_pointer(S.arr), c_pointer(Vt.arr), A.arr))

return U, S, Vt</div>

<div class="viewcode-block" id="svd_inplace"><a class="viewcode-back" href="../../arrayfire.lapack.html#arrayfire.lapack.svd_inplace">[docs]</a>def svd_inplace(A):

"""

Singular Value Decomposition

Parameters

----------

A: af.Array

A 2 dimensional arrayfire array.

Returns

-------

(U,S,Vt): tuple of af.Arrays

- U - A unitary matrix

- S - An array containing the elements of diagonal matrix

- Vt - A unitary matrix

Note

----

- The original matrix `A` is not preserved.

- If the original matrix `A` needs to be preserved, use `svd` instead.

- The original matrix `A` can be reconstructed using the outputs in the following manner.

>>> Smat = af.diag(S, 0, False)

>>> A_recon = af.matmul(af.matmul(U, Smat), Vt)

"""

U = Array()

S = Array()

Vt = Array()

safe_call(backend.get().af_svd_inplace(c_pointer(U.arr), c_pointer(S.arr), c_pointer(Vt.arr),

A.arr))

return U, S, Vt</div>

<div class="viewcode-block" id="is_lapack_available"><a class="viewcode-back" href="../../arrayfire.lapack.html#arrayfire.lapack.is_lapack_available">[docs]</a>def is_lapack_available():

"""

Function to check if the arrayfire library was built with lapack support.

"""

res = c_bool_t(False)

return res.value</div>

</pre></div>

</div>

</a>

<h1 class="logo"><a href="../../index.html">ArrayFire</a></h1>

<h3>Navigation</h3>

<h3>Related Topics</h3>

<ul>

<li><a href="../../index.html">Documentation overview</a><ul>

<li><a href="../index.html">Module code</a><ul>

</ul></li>

</ul>

</div>

<h3 id="searchlabel">Quick search</h3>

</form>

</div>

</div>

</div>

& <a href="https://github.com/bitprophet/alabaster">Alabaster 0.7.12</a>

</div>

</body>

</html>

FilesExpand file tree

lapack.html

Latest commit

History

lapack.html

File metadata and controls