How to use the primme.svds function in primme

"""
   Generate all test cases for primme.svds with csr and LinearOperator matrix types.
   """

   n = 10
   for dtype in (np.float64, np.complex64):
      A = Lauchli_like(n*2, n, dtype=dtype)
      svl, sva, svr = np.linalg.svd(A, full_matrices=False)
      sigma0 = sva[0]*.51 + sva[-1]*.49
      for op in ((lambda x : x), csr_matrix, aslinearoperator): 
         which, sigma = 'SM', 0
         prec = sqr_diagonal_prec(A, sigma)
         k = 2
         case_desc = ("A=%s(%d, %s), k=%d, M=%s, which=%s" %
                      ("Lauchli_like_vert", n, dtype, k, bool(prec), which))
         yield (svds_check, svds, op(A), k, prec, which, 1e-5, sva, dtype, case_desc, False)

def test_return_stats():
    A, _ = diagonal(100)
    evals, evecs, stats = primme.eigsh(A, 3, tol=1e-6, which='LA',
            return_stats=True, return_history=True)
    assert(stats["hist"]["numMatvecs"])

    svecs_left, svals, svecs_right, stats = primme.svds(A, 3, tol=1e-6,
            which='SM', return_stats=True, return_history=True)
    assert(stats["hist"]["numMatvecs"])

print(stats["elapsedTime"], stats["numMatvecs"])

# Compute the square diagonal preconditioner
prec = scipy.sparse.spdiags(np.reciprocal(A.multiply(A).sum(axis=0)),
          [0], 100, 100)

# Recompute the singular values but using the preconditioner
svecs_left, svals, svecs_right, stats = primme.svds(A, 3, which='SM', tol=1e-6,
                        precAHA=prec, return_stats=True)
assert_allclose(svals, A_svals, atol=1e-6*100)
print(stats["elapsedTime"], stats["numMatvecs"])

# Estimation of the smallest singular value
def convtest_sm(sval, svecl, svecr, rnorm):
   return sval > 0.1 * rnorm
svec_left, sval, svec_right, stats = primme.svds(A, 1, which='SM',
                        convtest=convtest_sm, return_stats=True)
assert_allclose(sval, [ 1.], atol=.1)

# User-defined matvec: implicit rectangular matrix with nonzero elements on the diagonal only
Bdiag = np.arange(0, 100).reshape((100,1))
Bdiagr = np.concatenate((np.arange(0, 100).reshape((100,1)).astype(np.float32), np.zeros((100,1), dtype=np.float32)), axis=None).reshape((200,1))
def Bmatmat(x):
   if len(x.shape) == 1: x = x.reshape((100,1))
   return np.vstack((Bdiag * x, np.zeros((100, x.shape[1]), dtype=np.float32)))
def Brmatmat(x):
   if len(x.shape) == 1: x = x.reshape((200,1))
   return (Bdiagr * x)[0:100,:]

B = scipy.sparse.linalg.LinearOperator((200,100), matvec=Bmatmat, matmat=Bmatmat, rmatvec=Brmatmat, dtype=np.float32)
svecs_left, svals, svecs_right = primme.svds(B, 3, which='LM', tol=1e-6)
assert_allclose(svals, [ 99.,  98.,  97.], atol=1e-6*100)

# Sparse rectangular matrix 100x10 with non-zeros on the main diagonal
A = scipy.sparse.spdiags(range(10), [0], 100, 10)

# Compute the three closest to 4.1 singular values and the left and right corresponding
# singular vectors
svecs_left, svals, svecs_right = primme.svds(A, 3, tol=1e-6, which=4.1)
assert_allclose(sorted(svals), [ 3.,  4.,  5.], atol=1e-6*10)
print(svals) # [ 4.,  5.,  3.]

# Sparse random rectangular matrix 10^5x100
A = scipy.sparse.rand(10000, 100, density=0.001, random_state=10)

# Compute the three closest singular values to 6.0 with a tolerance of 1e-6
svecs_left, svals, svecs_right, stats = primme.svds(A, 3, which='SM', tol=1e-6,
                                                    return_stats=True)
A_svals = svals
print(svals)
print(stats["elapsedTime"], stats["numMatvecs"])

# Compute the square diagonal preconditioner
prec = scipy.sparse.spdiags(np.reciprocal(A.multiply(A).sum(axis=0)),
          [0], 100, 100)

# Recompute the singular values but using the preconditioner
svecs_left, svals, svecs_right, stats = primme.svds(A, 3, which='SM', tol=1e-6,
                        precAHA=prec, return_stats=True)
assert_allclose(svals, A_svals, atol=1e-6*100)
print(stats["elapsedTime"], stats["numMatvecs"])

# Estimation of the smallest singular value

assert_allclose(evals, [ 99.,  98.,  97.], atol=1e-6*100)

# Sparse singular mass matrix
A = scipy.sparse.spdiags(np.asarray(range(100), dtype=np.float32), [0], 100, 100)
M = scipy.sparse.spdiags(np.asarray(range(99,-1,-1), dtype=np.float32), [0], 100, 100)
evals, evecs = primme.eigsh(A, 3, M=M, tol=1e-6, which='SA')
assert_allclose(evals, [ 0./99.,  1./98.,  2./97.], atol=1e-6*100)
print(evals)


# Sparse rectangular matrix 100x10 with non-zeros on the main diagonal
A = scipy.sparse.spdiags(range(10), [0], 100, 10)

# Compute the three closest to 4.1 singular values and the left and right corresponding
# singular vectors
svecs_left, svals, svecs_right = primme.svds(A, 3, tol=1e-6, which=4.1)
assert_allclose(sorted(svals), [ 3.,  4.,  5.], atol=1e-6*10)
print(svals) # [ 4.,  5.,  3.]

# Sparse random rectangular matrix 10^5x100
A = scipy.sparse.rand(10000, 100, density=0.001, random_state=10)

# Compute the three closest singular values to 6.0 with a tolerance of 1e-6
svecs_left, svals, svecs_right, stats = primme.svds(A, 3, which='SM', tol=1e-6,
                                                    return_stats=True)
A_svals = svals
print(svals)
print(stats["elapsedTime"], stats["numMatvecs"])

# Compute the square diagonal preconditioner
prec = scipy.sparse.spdiags(np.reciprocal(A.multiply(A).sum(axis=0)),
          [0], 100, 100)

# Sparse random rectangular matrix 10^5x100
A = scipy.sparse.rand(10000, 100, density=0.001, random_state=10)

# Compute the three closest singular values to 6.0 with a tolerance of 1e-6
svecs_left, svals, svecs_right, stats = primme.svds(A, 3, which='SM', tol=1e-6,
                                                    return_stats=True)
A_svals = svals
print(svals)
print(stats["elapsedTime"], stats["numMatvecs"])

# Compute the square diagonal preconditioner
prec = scipy.sparse.spdiags(np.reciprocal(A.multiply(A).sum(axis=0)),
          [0], 100, 100)

# Recompute the singular values but using the preconditioner
svecs_left, svals, svecs_right, stats = primme.svds(A, 3, which='SM', tol=1e-6,
                        precAHA=prec, return_stats=True)
assert_allclose(svals, A_svals, atol=1e-6*100)
print(stats["elapsedTime"], stats["numMatvecs"])

# Estimation of the smallest singular value
def convtest_sm(sval, svecl, svecr, rnorm):
   return sval > 0.1 * rnorm
svec_left, sval, svec_right, stats = primme.svds(A, 1, which='SM',
                        convtest=convtest_sm, return_stats=True)
assert_allclose(sval, [ 1.], atol=.1)

# User-defined matvec: implicit rectangular matrix with nonzero elements on the diagonal only
Bdiag = np.arange(0, 100).reshape((100,1))
Bdiagr = np.concatenate((np.arange(0, 100).reshape((100,1)).astype(np.float32), np.zeros((100,1), dtype=np.float32)), axis=None).reshape((200,1))
def Bmatmat(x):
   if len(x.shape) == 1: x = x.reshape((100,1))

svec_left, sval, svec_right, stats = primme.svds(A, 1, which='SM',
                        convtest=convtest_sm, return_stats=True)
assert_allclose(sval, [ 1.], atol=.1)

# User-defined matvec: implicit rectangular matrix with nonzero elements on the diagonal only
Bdiag = np.arange(0, 100).reshape((100,1))
Bdiagr = np.concatenate((np.arange(0, 100).reshape((100,1)).astype(np.float32), np.zeros((100,1), dtype=np.float32)), axis=None).reshape((200,1))
def Bmatmat(x):
   if len(x.shape) == 1: x = x.reshape((100,1))
   return np.vstack((Bdiag * x, np.zeros((100, x.shape[1]), dtype=np.float32)))
def Brmatmat(x):
   if len(x.shape) == 1: x = x.reshape((200,1))
   return (Bdiagr * x)[0:100,:]

B = scipy.sparse.linalg.LinearOperator((200,100), matvec=Bmatmat, matmat=Bmatmat, rmatvec=Brmatmat, dtype=np.float32)
svecs_left, svals, svecs_right = primme.svds(B, 3, which='LM', tol=1e-6)
assert_allclose(svals, [ 99.,  98.,  97.], atol=1e-6*100)