1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

61

62

63

64

65

66

67

68

69

70

71

72

73

74

75

76

77

78

79

80

81

82

83

84

85

86

87

88

89

90

91

92

93

94

95

96

97

98

99

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

555

556

557

558

559

560

561

562

563

564

565

566

567

568

569

570

571

572

573

574

575

576

577

578

579

580

581

582

583

584

585

586

587

588

589

590

591

592

593

594

595

596

597

598

599

600

601

602

603

604

605

606

607

608

609

610

611

612

613

614

615

616

617

618

619

620

621

622

623

624

625

626

627

628

629

630

631

632

633

634

635

636

637

638

639

640

641

642

643

644

645

646

647

648

649

650

651

652

653

654

655

656

657

658

659

660

661

662

663

664

665

666

667

668

669

670

671

672

673

674

675

676

677

678

679

680

681

682

683

684

685

686

687

688

689

690

691

692

693

694

695

696

697

698

699

700

701

702

703

704

705

706

707

708

709

710

711

712

713

714

715

716

717

718

719

720

721

722

723

724

725

726

727

728

729

730

731

732

733

734

735

736

737

738

739

740

741

742

743

744

745

746

747

748

749

750

751

752

753

754

755

756

757

758

759

760

761

762

763

764

765

766

767

768

769

770

771

772

773

774

775

776

777

778

779

780

781

782

783

784

785

786

787

788

789

790

791

792

793

794

795

796

797

798

799

800

801

802

803

804

805

806

807

808

809

810

811

812

813

814

815

816

817

818

819

820

821

822

823

824

825

826

827

828

829

830

831

832

833

834

835

836

837

838

"""Functions to construct sparse matrices 

""" 

from __future__ import division, print_function, absolute_import 

 

__docformat__ = "restructuredtext en" 

 

__all__ = ['spdiags', 'eye', 'identity', 'kron', 'kronsum', 

'hstack', 'vstack', 'bmat', 'rand', 'random', 'diags', 'block_diag'] 

 

 

import numpy as np 

 

from scipy._lib.six import xrange 

 

from .sputils import upcast, get_index_dtype, isscalarlike 

 

from .csr import csr_matrix 

from .csc import csc_matrix 

from .bsr import bsr_matrix 

from .coo import coo_matrix 

from .dia import dia_matrix 

 

from .base import issparse 

 

 

def spdiags(data, diags, m, n, format=None): 

""" 

Return a sparse matrix from diagonals. 

 

Parameters 

---------- 

data : array_like 

matrix diagonals stored row-wise 

diags : diagonals to set 

- k = 0 the main diagonal 

- k > 0 the k-th upper diagonal 

- k < 0 the k-th lower diagonal 

m, n : int 

shape of the result 

format : str, optional 

Format of the result. By default (format=None) an appropriate sparse 

matrix format is returned. This choice is subject to change. 

 

See Also 

-------- 

diags : more convenient form of this function 

dia_matrix : the sparse DIAgonal format. 

 

Examples 

-------- 

>>> from scipy.sparse import spdiags 

>>> data = np.array([[1, 2, 3, 4], [1, 2, 3, 4], [1, 2, 3, 4]]) 

>>> diags = np.array([0, -1, 2]) 

>>> spdiags(data, diags, 4, 4).toarray() 

array([[1, 0, 3, 0], 

[1, 2, 0, 4], 

[0, 2, 3, 0], 

[0, 0, 3, 4]]) 

 

""" 

return dia_matrix((data, diags), shape=(m,n)).asformat(format) 

 

 

def diags(diagonals, offsets=0, shape=None, format=None, dtype=None): 

""" 

Construct a sparse matrix from diagonals. 

 

Parameters 

---------- 

diagonals : sequence of array_like 

Sequence of arrays containing the matrix diagonals, 

corresponding to `offsets`. 

offsets : sequence of int or an int, optional 

Diagonals to set: 

- k = 0 the main diagonal (default) 

- k > 0 the k-th upper diagonal 

- k < 0 the k-th lower diagonal 

shape : tuple of int, optional 

Shape of the result. If omitted, a square matrix large enough 

to contain the diagonals is returned. 

format : {"dia", "csr", "csc", "lil", ...}, optional 

Matrix format of the result. By default (format=None) an 

appropriate sparse matrix format is returned. This choice is 

subject to change. 

dtype : dtype, optional 

Data type of the matrix. 

 

See Also 

-------- 

spdiags : construct matrix from diagonals 

 

Notes 

----- 

This function differs from `spdiags` in the way it handles 

off-diagonals. 

 

The result from `diags` is the sparse equivalent of:: 

 

np.diag(diagonals[0], offsets[0]) 

+ ... 

+ np.diag(diagonals[k], offsets[k]) 

 

Repeated diagonal offsets are disallowed. 

 

.. versionadded:: 0.11 

 

Examples 

-------- 

>>> from scipy.sparse import diags 

>>> diagonals = [[1, 2, 3, 4], [1, 2, 3], [1, 2]] 

>>> diags(diagonals, [0, -1, 2]).toarray() 

array([[1, 0, 1, 0], 

[1, 2, 0, 2], 

[0, 2, 3, 0], 

[0, 0, 3, 4]]) 

 

Broadcasting of scalars is supported (but shape needs to be 

specified): 

 

>>> diags([1, -2, 1], [-1, 0, 1], shape=(4, 4)).toarray() 

array([[-2., 1., 0., 0.], 

[ 1., -2., 1., 0.], 

[ 0., 1., -2., 1.], 

[ 0., 0., 1., -2.]]) 

 

 

If only one diagonal is wanted (as in `numpy.diag`), the following 

works as well: 

 

>>> diags([1, 2, 3], 1).toarray() 

array([[ 0., 1., 0., 0.], 

[ 0., 0., 2., 0.], 

[ 0., 0., 0., 3.], 

[ 0., 0., 0., 0.]]) 

""" 

# if offsets is not a sequence, assume that there's only one diagonal 

if isscalarlike(offsets): 

# now check that there's actually only one diagonal 

if len(diagonals) == 0 or isscalarlike(diagonals[0]): 

diagonals = [np.atleast_1d(diagonals)] 

else: 

raise ValueError("Different number of diagonals and offsets.") 

else: 

diagonals = list(map(np.atleast_1d, diagonals)) 

 

offsets = np.atleast_1d(offsets) 

 

# Basic check 

if len(diagonals) != len(offsets): 

raise ValueError("Different number of diagonals and offsets.") 

 

# Determine shape, if omitted 

if shape is None: 

m = len(diagonals[0]) + abs(int(offsets[0])) 

shape = (m, m) 

 

# Determine data type, if omitted 

if dtype is None: 

dtype = np.common_type(*diagonals) 

 

# Construct data array 

m, n = shape 

 

M = max([min(m + offset, n - offset) + max(0, offset) 

for offset in offsets]) 

M = max(0, M) 

data_arr = np.zeros((len(offsets), M), dtype=dtype) 

 

K = min(m, n) 

 

for j, diagonal in enumerate(diagonals): 

offset = offsets[j] 

k = max(0, offset) 

length = min(m + offset, n - offset, K) 

if length < 0: 

raise ValueError("Offset %d (index %d) out of bounds" % (offset, j)) 

try: 

data_arr[j, k:k+length] = diagonal[...,:length] 

except ValueError: 

if len(diagonal) != length and len(diagonal) != 1: 

raise ValueError( 

"Diagonal length (index %d: %d at offset %d) does not " 

"agree with matrix size (%d, %d)." % ( 

j, len(diagonal), offset, m, n)) 

raise 

 

return dia_matrix((data_arr, offsets), shape=(m, n)).asformat(format) 

 

 

def identity(n, dtype='d', format=None): 

"""Identity matrix in sparse format 

 

Returns an identity matrix with shape (n,n) using a given 

sparse format and dtype. 

 

Parameters 

---------- 

n : int 

Shape of the identity matrix. 

dtype : dtype, optional 

Data type of the matrix 

format : str, optional 

Sparse format of the result, e.g. format="csr", etc. 

 

Examples 

-------- 

>>> from scipy.sparse import identity 

>>> identity(3).toarray() 

array([[ 1., 0., 0.], 

[ 0., 1., 0.], 

[ 0., 0., 1.]]) 

>>> identity(3, dtype='int8', format='dia') 

<3x3 sparse matrix of type '<class 'numpy.int8'>' 

with 3 stored elements (1 diagonals) in DIAgonal format> 

 

""" 

return eye(n, n, dtype=dtype, format=format) 

 

 

def eye(m, n=None, k=0, dtype=float, format=None): 

"""Sparse matrix with ones on diagonal 

 

Returns a sparse (m x n) matrix where the k-th diagonal 

is all ones and everything else is zeros. 

 

Parameters 

---------- 

m : int 

Number of rows in the matrix. 

n : int, optional 

Number of columns. Default: `m`. 

k : int, optional 

Diagonal to place ones on. Default: 0 (main diagonal). 

dtype : dtype, optional 

Data type of the matrix. 

format : str, optional 

Sparse format of the result, e.g. format="csr", etc. 

 

Examples 

-------- 

>>> from scipy import sparse 

>>> sparse.eye(3).toarray() 

array([[ 1., 0., 0.], 

[ 0., 1., 0.], 

[ 0., 0., 1.]]) 

>>> sparse.eye(3, dtype=np.int8) 

<3x3 sparse matrix of type '<class 'numpy.int8'>' 

with 3 stored elements (1 diagonals) in DIAgonal format> 

 

""" 

if n is None: 

n = m 

m,n = int(m),int(n) 

 

if m == n and k == 0: 

# fast branch for special formats 

if format in ['csr', 'csc']: 

idx_dtype = get_index_dtype(maxval=n) 

indptr = np.arange(n+1, dtype=idx_dtype) 

indices = np.arange(n, dtype=idx_dtype) 

data = np.ones(n, dtype=dtype) 

cls = {'csr': csr_matrix, 'csc': csc_matrix}[format] 

return cls((data,indices,indptr),(n,n)) 

elif format == 'coo': 

idx_dtype = get_index_dtype(maxval=n) 

row = np.arange(n, dtype=idx_dtype) 

col = np.arange(n, dtype=idx_dtype) 

data = np.ones(n, dtype=dtype) 

return coo_matrix((data,(row,col)),(n,n)) 

 

diags = np.ones((1, max(0, min(m + k, n))), dtype=dtype) 

return spdiags(diags, k, m, n).asformat(format) 

 

 

def kron(A, B, format=None): 

"""kronecker product of sparse matrices A and B 

 

Parameters 

---------- 

A : sparse or dense matrix 

first matrix of the product 

B : sparse or dense matrix 

second matrix of the product 

format : str, optional 

format of the result (e.g. "csr") 

 

Returns 

------- 

kronecker product in a sparse matrix format 

 

 

Examples 

-------- 

>>> from scipy import sparse 

>>> A = sparse.csr_matrix(np.array([[0, 2], [5, 0]])) 

>>> B = sparse.csr_matrix(np.array([[1, 2], [3, 4]])) 

>>> sparse.kron(A, B).toarray() 

array([[ 0, 0, 2, 4], 

[ 0, 0, 6, 8], 

[ 5, 10, 0, 0], 

[15, 20, 0, 0]]) 

 

>>> sparse.kron(A, [[1, 2], [3, 4]]).toarray() 

array([[ 0, 0, 2, 4], 

[ 0, 0, 6, 8], 

[ 5, 10, 0, 0], 

[15, 20, 0, 0]]) 

 

""" 

B = coo_matrix(B) 

 

if (format is None or format == "bsr") and 2*B.nnz >= B.shape[0] * B.shape[1]: 

# B is fairly dense, use BSR 

A = csr_matrix(A,copy=True) 

 

output_shape = (A.shape[0]*B.shape[0], A.shape[1]*B.shape[1]) 

 

if A.nnz == 0 or B.nnz == 0: 

# kronecker product is the zero matrix 

return coo_matrix(output_shape) 

 

B = B.toarray() 

data = A.data.repeat(B.size).reshape(-1,B.shape[0],B.shape[1]) 

data = data * B 

 

return bsr_matrix((data,A.indices,A.indptr), shape=output_shape) 

else: 

# use COO 

A = coo_matrix(A) 

output_shape = (A.shape[0]*B.shape[0], A.shape[1]*B.shape[1]) 

 

if A.nnz == 0 or B.nnz == 0: 

# kronecker product is the zero matrix 

return coo_matrix(output_shape) 

 

# expand entries of a into blocks 

row = A.row.repeat(B.nnz) 

col = A.col.repeat(B.nnz) 

data = A.data.repeat(B.nnz) 

 

row *= B.shape[0] 

col *= B.shape[1] 

 

# increment block indices 

row,col = row.reshape(-1,B.nnz),col.reshape(-1,B.nnz) 

row += B.row 

col += B.col 

row,col = row.reshape(-1),col.reshape(-1) 

 

# compute block entries 

data = data.reshape(-1,B.nnz) * B.data 

data = data.reshape(-1) 

 

return coo_matrix((data,(row,col)), shape=output_shape).asformat(format) 

 

 

def kronsum(A, B, format=None): 

"""kronecker sum of sparse matrices A and B 

 

Kronecker sum of two sparse matrices is a sum of two Kronecker 

products kron(I_n,A) + kron(B,I_m) where A has shape (m,m) 

and B has shape (n,n) and I_m and I_n are identity matrices 

of shape (m,m) and (n,n) respectively. 

 

Parameters 

---------- 

A 

square matrix 

B 

square matrix 

format : str 

format of the result (e.g. "csr") 

 

Returns 

------- 

kronecker sum in a sparse matrix format 

 

Examples 

-------- 

 

 

""" 

A = coo_matrix(A) 

B = coo_matrix(B) 

 

if A.shape[0] != A.shape[1]: 

raise ValueError('A is not square') 

 

if B.shape[0] != B.shape[1]: 

raise ValueError('B is not square') 

 

dtype = upcast(A.dtype, B.dtype) 

 

L = kron(eye(B.shape[0],dtype=dtype), A, format=format) 

R = kron(B, eye(A.shape[0],dtype=dtype), format=format) 

 

return (L+R).asformat(format) # since L + R is not always same format 

 

 

def _compressed_sparse_stack(blocks, axis): 

""" 

Stacking fast path for CSR/CSC matrices 

(i) vstack for CSR, (ii) hstack for CSC. 

""" 

other_axis = 1 if axis == 0 else 0 

data = np.concatenate([b.data for b in blocks]) 

constant_dim = blocks[0].shape[other_axis] 

idx_dtype = get_index_dtype(arrays=[b.indptr for b in blocks], 

maxval=max(data.size, constant_dim)) 

indices = np.empty(data.size, dtype=idx_dtype) 

indptr = np.empty(sum(b.shape[axis] for b in blocks) + 1, dtype=idx_dtype) 

last_indptr = idx_dtype(0) 

sum_dim = 0 

sum_indices = 0 

for b in blocks: 

if b.shape[other_axis] != constant_dim: 

raise ValueError('incompatible dimensions for axis %d' % other_axis) 

indices[sum_indices:sum_indices+b.indices.size] = b.indices 

sum_indices += b.indices.size 

idxs = slice(sum_dim, sum_dim + b.shape[axis]) 

indptr[idxs] = b.indptr[:-1] 

indptr[idxs] += last_indptr 

sum_dim += b.shape[axis] 

last_indptr += b.indptr[-1] 

indptr[-1] = last_indptr 

if axis == 0: 

return csr_matrix((data, indices, indptr), 

shape=(sum_dim, constant_dim)) 

else: 

return csc_matrix((data, indices, indptr), 

shape=(constant_dim, sum_dim)) 

 

 

def hstack(blocks, format=None, dtype=None): 

""" 

Stack sparse matrices horizontally (column wise) 

 

Parameters 

---------- 

blocks 

sequence of sparse matrices with compatible shapes 

format : str 

sparse format of the result (e.g. "csr") 

by default an appropriate sparse matrix format is returned. 

This choice is subject to change. 

dtype : dtype, optional 

The data-type of the output matrix. If not given, the dtype is 

determined from that of `blocks`. 

 

See Also 

-------- 

vstack : stack sparse matrices vertically (row wise) 

 

Examples 

-------- 

>>> from scipy.sparse import coo_matrix, hstack 

>>> A = coo_matrix([[1, 2], [3, 4]]) 

>>> B = coo_matrix([[5], [6]]) 

>>> hstack([A,B]).toarray() 

array([[1, 2, 5], 

[3, 4, 6]]) 

 

""" 

return bmat([blocks], format=format, dtype=dtype) 

 

 

def vstack(blocks, format=None, dtype=None): 

""" 

Stack sparse matrices vertically (row wise) 

 

Parameters 

---------- 

blocks 

sequence of sparse matrices with compatible shapes 

format : str, optional 

sparse format of the result (e.g. "csr") 

by default an appropriate sparse matrix format is returned. 

This choice is subject to change. 

dtype : dtype, optional 

The data-type of the output matrix. If not given, the dtype is 

determined from that of `blocks`. 

 

See Also 

-------- 

hstack : stack sparse matrices horizontally (column wise) 

 

Examples 

-------- 

>>> from scipy.sparse import coo_matrix, vstack 

>>> A = coo_matrix([[1, 2], [3, 4]]) 

>>> B = coo_matrix([[5, 6]]) 

>>> vstack([A, B]).toarray() 

array([[1, 2], 

[3, 4], 

[5, 6]]) 

 

""" 

return bmat([[b] for b in blocks], format=format, dtype=dtype) 

 

 

def bmat(blocks, format=None, dtype=None): 

""" 

Build a sparse matrix from sparse sub-blocks 

 

Parameters 

---------- 

blocks : array_like 

Grid of sparse matrices with compatible shapes. 

An entry of None implies an all-zero matrix. 

format : {'bsr', 'coo', 'csc', 'csr', 'dia', 'dok', 'lil'}, optional 

The sparse format of the result (e.g. "csr"). By default an 

appropriate sparse matrix format is returned. 

This choice is subject to change. 

dtype : dtype, optional 

The data-type of the output matrix. If not given, the dtype is 

determined from that of `blocks`. 

 

Returns 

------- 

bmat : sparse matrix 

 

See Also 

-------- 

block_diag, diags 

 

Examples 

-------- 

>>> from scipy.sparse import coo_matrix, bmat 

>>> A = coo_matrix([[1, 2], [3, 4]]) 

>>> B = coo_matrix([[5], [6]]) 

>>> C = coo_matrix([[7]]) 

>>> bmat([[A, B], [None, C]]).toarray() 

array([[1, 2, 5], 

[3, 4, 6], 

[0, 0, 7]]) 

 

>>> bmat([[A, None], [None, C]]).toarray() 

array([[1, 2, 0], 

[3, 4, 0], 

[0, 0, 7]]) 

 

""" 

 

blocks = np.asarray(blocks, dtype='object') 

 

if blocks.ndim != 2: 

raise ValueError('blocks must be 2-D') 

 

M,N = blocks.shape 

 

# check for fast path cases 

if (N == 1 and format in (None, 'csr') and all(isinstance(b, csr_matrix) 

for b in blocks.flat)): 

A = _compressed_sparse_stack(blocks[:,0], 0) 

if dtype is not None: 

A = A.astype(dtype) 

return A 

elif (M == 1 and format in (None, 'csc') 

and all(isinstance(b, csc_matrix) for b in blocks.flat)): 

A = _compressed_sparse_stack(blocks[0,:], 1) 

if dtype is not None: 

A = A.astype(dtype) 

return A 

 

block_mask = np.zeros(blocks.shape, dtype=bool) 

brow_lengths = np.zeros(M, dtype=np.int64) 

bcol_lengths = np.zeros(N, dtype=np.int64) 

 

# convert everything to COO format 

for i in range(M): 

for j in range(N): 

if blocks[i,j] is not None: 

A = coo_matrix(blocks[i,j]) 

blocks[i,j] = A 

block_mask[i,j] = True 

 

if brow_lengths[i] == 0: 

brow_lengths[i] = A.shape[0] 

elif brow_lengths[i] != A.shape[0]: 

msg = ('blocks[{i},:] has incompatible row dimensions. ' 

'Got blocks[{i},{j}].shape[0] == {got}, ' 

'expected {exp}.'.format(i=i, j=j, 

exp=brow_lengths[i], 

got=A.shape[0])) 

raise ValueError(msg) 

 

if bcol_lengths[j] == 0: 

bcol_lengths[j] = A.shape[1] 

elif bcol_lengths[j] != A.shape[1]: 

msg = ('blocks[:,{j}] has incompatible row dimensions. ' 

'Got blocks[{i},{j}].shape[1] == {got}, ' 

'expected {exp}.'.format(i=i, j=j, 

exp=bcol_lengths[j], 

got=A.shape[1])) 

raise ValueError(msg) 

 

nnz = sum(block.nnz for block in blocks[block_mask]) 

if dtype is None: 

all_dtypes = [blk.dtype for blk in blocks[block_mask]] 

dtype = upcast(*all_dtypes) if all_dtypes else None 

 

row_offsets = np.append(0, np.cumsum(brow_lengths)) 

col_offsets = np.append(0, np.cumsum(bcol_lengths)) 

 

shape = (row_offsets[-1], col_offsets[-1]) 

 

data = np.empty(nnz, dtype=dtype) 

idx_dtype = get_index_dtype(maxval=max(shape)) 

row = np.empty(nnz, dtype=idx_dtype) 

col = np.empty(nnz, dtype=idx_dtype) 

 

nnz = 0 

ii, jj = np.nonzero(block_mask) 

for i, j in zip(ii, jj): 

B = blocks[i, j] 

idx = slice(nnz, nnz + B.nnz) 

data[idx] = B.data 

row[idx] = B.row + row_offsets[i] 

col[idx] = B.col + col_offsets[j] 

nnz += B.nnz 

 

return coo_matrix((data, (row, col)), shape=shape).asformat(format) 

 

 

def block_diag(mats, format=None, dtype=None): 

""" 

Build a block diagonal sparse matrix from provided matrices. 

 

Parameters 

---------- 

mats : sequence of matrices 

Input matrices. 

format : str, optional 

The sparse format of the result (e.g. "csr"). If not given, the matrix 

is returned in "coo" format. 

dtype : dtype specifier, optional 

The data-type of the output matrix. If not given, the dtype is 

determined from that of `blocks`. 

 

Returns 

------- 

res : sparse matrix 

 

Notes 

----- 

 

.. versionadded:: 0.11.0 

 

See Also 

-------- 

bmat, diags 

 

Examples 

-------- 

>>> from scipy.sparse import coo_matrix, block_diag 

>>> A = coo_matrix([[1, 2], [3, 4]]) 

>>> B = coo_matrix([[5], [6]]) 

>>> C = coo_matrix([[7]]) 

>>> block_diag((A, B, C)).toarray() 

array([[1, 2, 0, 0], 

[3, 4, 0, 0], 

[0, 0, 5, 0], 

[0, 0, 6, 0], 

[0, 0, 0, 7]]) 

 

""" 

nmat = len(mats) 

rows = [] 

for ia, a in enumerate(mats): 

row = [None]*nmat 

if issparse(a): 

row[ia] = a 

else: 

row[ia] = coo_matrix(a) 

rows.append(row) 

return bmat(rows, format=format, dtype=dtype) 

 

 

def random(m, n, density=0.01, format='coo', dtype=None, 

random_state=None, data_rvs=None): 

"""Generate a sparse matrix of the given shape and density with randomly 

distributed values. 

 

Parameters 

---------- 

m, n : int 

shape of the matrix 

density : real, optional 

density of the generated matrix: density equal to one means a full 

matrix, density of 0 means a matrix with no non-zero items. 

format : str, optional 

sparse matrix format. 

dtype : dtype, optional 

type of the returned matrix values. 

random_state : {numpy.random.RandomState, int}, optional 

Random number generator or random seed. If not given, the singleton 

numpy.random will be used. This random state will be used 

for sampling the sparsity structure, but not necessarily for sampling 

the values of the structurally nonzero entries of the matrix. 

data_rvs : callable, optional 

Samples a requested number of random values. 

This function should take a single argument specifying the length 

of the ndarray that it will return. The structurally nonzero entries 

of the sparse random matrix will be taken from the array sampled 

by this function. By default, uniform [0, 1) random values will be 

sampled using the same random state as is used for sampling 

the sparsity structure. 

 

Returns 

------- 

res : sparse matrix 

 

Examples 

-------- 

>>> from scipy.sparse import random 

>>> from scipy import stats 

>>> class CustomRandomState(object): 

... def randint(self, k): 

... i = np.random.randint(k) 

... return i - i % 2 

>>> rs = CustomRandomState() 

>>> rvs = stats.poisson(25, loc=10).rvs 

>>> S = random(3, 4, density=0.25, random_state=rs, data_rvs=rvs) 

>>> S.A 

array([[ 36., 0., 33., 0.], # random 

[ 0., 0., 0., 0.], 

[ 0., 0., 36., 0.]]) 

 

>>> from scipy.sparse import random 

>>> from scipy.stats import rv_continuous 

>>> class CustomDistribution(rv_continuous): 

... def _rvs(self, *args, **kwargs): 

... return self._random_state.randn(*self._size) 

>>> X = CustomDistribution(seed=2906) 

>>> Y = X() # get a frozen version of the distribution 

>>> S = random(3, 4, density=0.25, random_state=2906, data_rvs=Y.rvs) 

>>> S.A 

array([[ 0. , 1.9467163 , 0.13569738, -0.81205367], 

[ 0. , 0. , 0. , 0. ], 

[ 0. , 0. , 0. , 0. ]]) 

 

Notes 

----- 

Only float types are supported for now. 

""" 

if density < 0 or density > 1: 

raise ValueError("density expected to be 0 <= density <= 1") 

dtype = np.dtype(dtype) 

if dtype.char not in 'fdg': 

raise NotImplementedError("type %s not supported" % dtype) 

 

mn = m * n 

 

tp = np.intc 

if mn > np.iinfo(tp).max: 

tp = np.int64 

 

if mn > np.iinfo(tp).max: 

msg = """\ 

Trying to generate a random sparse matrix such as the product of dimensions is 

greater than %d - this is not supported on this machine 

""" 

raise ValueError(msg % np.iinfo(tp).max) 

 

# Number of non zero values 

k = int(density * m * n) 

 

if random_state is None: 

random_state = np.random 

elif isinstance(random_state, (int, np.integer)): 

random_state = np.random.RandomState(random_state) 

if data_rvs is None: 

data_rvs = random_state.rand 

 

# Use the algorithm from python's random.sample for k < mn/3. 

if mn < 3*k: 

ind = random_state.choice(mn, size=k, replace=False) 

else: 

ind = np.empty(k, dtype=tp) 

selected = set() 

for i in xrange(k): 

j = random_state.randint(mn) 

while j in selected: 

j = random_state.randint(mn) 

selected.add(j) 

ind[i] = j 

 

j = np.floor(ind * 1. / m).astype(tp) 

i = (ind - j * m).astype(tp) 

vals = data_rvs(k).astype(dtype) 

return coo_matrix((vals, (i, j)), shape=(m, n)).asformat(format) 

 

 

def rand(m, n, density=0.01, format="coo", dtype=None, random_state=None): 

"""Generate a sparse matrix of the given shape and density with uniformly 

distributed values. 

 

Parameters 

---------- 

m, n : int 

shape of the matrix 

density : real, optional 

density of the generated matrix: density equal to one means a full 

matrix, density of 0 means a matrix with no non-zero items. 

format : str, optional 

sparse matrix format. 

dtype : dtype, optional 

type of the returned matrix values. 

random_state : {numpy.random.RandomState, int}, optional 

Random number generator or random seed. If not given, the singleton 

numpy.random will be used. 

 

Returns 

------- 

res : sparse matrix 

 

Notes 

----- 

Only float types are supported for now. 

 

See Also 

-------- 

scipy.sparse.random : Similar function that allows a user-specified random 

data source. 

 

Examples 

-------- 

>>> from scipy.sparse import rand 

>>> matrix = rand(3, 4, density=0.25, format="csr", random_state=42) 

>>> matrix 

<3x4 sparse matrix of type '<class 'numpy.float64'>' 

with 3 stored elements in Compressed Sparse Row format> 

>>> matrix.todense() 

matrix([[ 0. , 0.59685016, 0.779691 , 0. ], 

[ 0. , 0. , 0. , 0.44583275], 

[ 0. , 0. , 0. , 0. ]]) 

""" 

return random(m, n, density, format, dtype, random_state)