text: #
  # Created by: Pearu Peterson, April 2002
  #
  from __future__ import division, print_function, absolute_import
  
  
  __usage__ = """
  Build linalg:
    python setup.py build
  Run tests if scipy is installed:
    python -c 'import scipy;scipy.linalg.test()'
  """
  
  import math
  
  import numpy as np
  from numpy.testing import (assert_equal, assert_almost_equal, assert_,
                             assert_array_almost_equal, assert_allclose)
  from pytest import raises as assert_raises
  
  from numpy import float32, float64, complex64, complex128, arange, triu, \
                    tril, zeros, tril_indices, ones, mod, diag, append, eye, \
                    nonzero
  
  from numpy.random import rand, seed
  from scipy.linalg import _fblas as fblas, get_blas_funcs, toeplitz, solve, \
                                            solve_triangular
  
  try:
      from scipy.linalg import _cblas as cblas
  except ImportError:
      cblas = None
  
  REAL_DTYPES = [float32, float64]
  COMPLEX_DTYPES = [complex64, complex128]
  DTYPES = REAL_DTYPES + COMPLEX_DTYPES
  
  
  def test_get_blas_funcs():
      # check that it returns Fortran code for arrays that are
      # fortran-ordered
      f1, f2, f3 = get_blas_funcs(
          ('axpy', 'axpy', 'axpy'),
          (np.empty((2, 2), dtype=np.complex64, order='F'),
           np.empty((2, 2), dtype=np.complex128, order='C'))
          )
  
      # get_blas_funcs will choose libraries depending on most generic
      # array
      assert_equal(f1.typecode, 'z')
      assert_equal(f2.typecode, 'z')
      if cblas is not None:
          assert_equal(f1.module_name, 'cblas')
          assert_equal(f2.module_name, 'cblas')
  
      # check defaults.
      f1 = get_blas_funcs('rotg')
      assert_equal(f1.typecode, 'd')
  
      # check also dtype interface
      f1 = get_blas_funcs('gemm', dtype=np.complex64)
      assert_equal(f1.typecode, 'c')
      f1 = get_blas_funcs('gemm', dtype='F')
      assert_equal(f1.typecode, 'c')
  
      # extended precision complex
      f1 = get_blas_funcs('gemm', dtype=np.longcomplex)
      assert_equal(f1.typecode, 'z')
  
      # check safe complex upcasting
      f1 = get_blas_funcs('axpy',
                          (np.empty((2, 2), dtype=np.float64),
                           np.empty((2, 2), dtype=np.complex64))
                          )
      assert_equal(f1.typecode, 'z')
  
  
  def test_get_blas_funcs_alias():
      # check alias for get_blas_funcs
      f, g = get_blas_funcs(('nrm2', 'dot'), dtype=np.complex64)
      assert f.typecode == 'c'
      assert g.typecode == 'c'
  
      f, g, h = get_blas_funcs(('dot', 'dotc', 'dotu'), dtype=np.float64)
      assert f is g
      assert f is h
  
  
  class TestCBLAS1Simple(object):
  
      def test_axpy(self):
          for p in 'sd':
              f = getattr(cblas, p+'axpy', None)
              if f is None:
                  continue
              assert_array_almost_equal(f([1, 2, 3], [2, -1, 3], a=5),
                                        [7, 9, 18])
          for p in 'cz':
              f = getattr(cblas, p+'axpy', None)
              if f is None:
                  continue
              assert_array_almost_equal(f([1, 2j, 3], [2, -1, 3], a=5),
                                        [7, 10j-1, 18])
  
  
  class TestFBLAS1Simple(object):
  
      def test_axpy(self):
          for p in 'sd':
              f = getattr(fblas, p+'axpy', None)
              if f is None:
                  continue
              assert_array_almost_equal(f([1, 2, 3], [2, -1, 3], a=5),
                                        [7, 9, 18])
          for p in 'cz':
              f = getattr(fblas, p+'axpy', None)
              if f is None:
                  continue
              assert_array_almost_equal(f([1, 2j, 3], [2, -1, 3], a=5),
                                        [7, 10j-1, 18])
  
      def test_copy(self):
          for p in 'sd':
              f = getattr(fblas, p+'copy', None)
              if f is None:
                  continue
              assert_array_almost_equal(f([3, 4, 5], [8]*3), [3, 4, 5])
          for p in 'cz':
              f = getattr(fblas, p+'copy', None)
              if f is None:
                  continue
              assert_array_almost_equal(f([3, 4j, 5+3j], [8]*3), [3, 4j, 5+3j])
  
      def test_asum(self):
          for p in 'sd':
              f = getattr(fblas, p+'asum', None)
              if f is None:
                  continue
              assert_almost_equal(f([3, -4, 5]), 12)
          for p in ['sc', 'dz']:
              f = getattr(fblas, p+'asum', None)
              if f is None:
                  continue
              assert_almost_equal(f([3j, -4, 3-4j]), 14)
  
      def test_dot(self):
          for p in 'sd':
              f = getattr(fblas, p+'dot', None)
              if f is None:
                  continue
              assert_almost_equal(f([3, -4, 5], [2, 5, 1]), -9)
  
      def test_complex_dotu(self):
          for p in 'cz':
              f = getattr(fblas, p+'dotu', None)
              if f is None:
                  continue
              assert_almost_equal(f([3j, -4, 3-4j], [2, 3, 1]), -9+2j)
  
      def test_complex_dotc(self):
          for p in 'cz':
              f = getattr(fblas, p+'dotc', None)
              if f is None:
                  continue
              assert_almost_equal(f([3j, -4, 3-4j], [2, 3j, 1]), 3-14j)
  
      def test_nrm2(self):
          for p in 'sd':
              f = getattr(fblas, p+'nrm2', None)
              if f is None:
                  continue
              assert_almost_equal(f([3, -4, 5]), math.sqrt(50))
          for p in ['c', 'z', 'sc', 'dz']:
              f = getattr(fblas, p+'nrm2', None)
              if f is None:
                  continue
              assert_almost_equal(f([3j, -4, 3-4j]), math.sqrt(50))
  
      def test_scal(self):
          for p in 'sd':
              f = getattr(fblas, p+'scal', None)
              if f is None:
                  continue
              assert_array_almost_equal(f(2, [3, -4, 5]), [6, -8, 10])
          for p in 'cz':
              f = getattr(fblas, p+'scal', None)
              if f is None:
                  continue
              assert_array_almost_equal(f(3j, [3j, -4, 3-4j]), [-9, -12j, 12+9j])
          for p in ['cs', 'zd']:
              f = getattr(fblas, p+'scal', None)
              if f is None:
                  continue
              assert_array_almost_equal(f(3, [3j, -4, 3-4j]), [9j, -12, 9-12j])
  
      def test_swap(self):
          for p in 'sd':
              f = getattr(fblas, p+'swap', None)
              if f is None:
                  continue
              x, y = [2, 3, 1], [-2, 3, 7]
              x1, y1 = f(x, y)
              assert_array_almost_equal(x1, y)
              assert_array_almost_equal(y1, x)
          for p in 'cz':
              f = getattr(fblas, p+'swap', None)
              if f is None:
                  continue
              x, y = [2, 3j, 1], [-2, 3, 7-3j]
              x1, y1 = f(x, y)
              assert_array_almost_equal(x1, y)
              assert_array_almost_equal(y1, x)
  
      def test_amax(self):
          for p in 'sd':
              f = getattr(fblas, 'i'+p+'amax')
              assert_equal(f([-2, 4, 3]), 1)
          for p in 'cz':
              f = getattr(fblas, 'i'+p+'amax')
              assert_equal(f([-5, 4+3j, 6]), 1)
      # XXX: need tests for rot,rotm,rotg,rotmg
  
  
  class TestFBLAS2Simple(object):
  
      def test_gemv(self):
          for p in 'sd':
              f = getattr(fblas, p+'gemv', None)
              if f is None:
                  continue
              assert_array_almost_equal(f(3, [[3]], [-4]), [-36])
              assert_array_almost_equal(f(3, [[3]], [-4], 3, [5]), [-21])
          for p in 'cz':
              f = getattr(fblas, p+'gemv', None)
              if f is None:
                  continue
              assert_array_almost_equal(f(3j, [[3-4j]], [-4]), [-48-36j])
              assert_array_almost_equal(f(3j, [[3-4j]], [-4], 3, [5j]),
                                        [-48-21j])
  
      def test_ger(self):
  
          for p in 'sd':
              f = getattr(fblas, p+'ger', None)
              if f is None:
                  continue
              assert_array_almost_equal(f(1, [1, 2], [3, 4]), [[3, 4], [6, 8]])
              assert_array_almost_equal(f(2, [1, 2, 3], [3, 4]),
                                        [[6, 8], [12, 16], [18, 24]])
  
              assert_array_almost_equal(f(1, [1, 2], [3, 4],
                                          a=[[1, 2], [3, 4]]), [[4, 6], [9, 12]])
  
          for p in 'cz':
              f = getattr(fblas, p+'geru', None)
              if f is None:
                  continue
              assert_array_almost_equal(f(1, [1j, 2], [3, 4]),
                                        [[3j, 4j], [6, 8]])
              assert_array_almost_equal(f(-2, [1j, 2j, 3j], [3j, 4j]),
                                        [[6, 8], [12, 16], [18, 24]])
  
          for p in 'cz':
              for name in ('ger', 'gerc'):
                  f = getattr(fblas, p+name, None)
                  if f is None:
                      continue
                  assert_array_almost_equal(f(1, [1j, 2], [3, 4]),
                                            [[3j, 4j], [6, 8]])
                  assert_array_almost_equal(f(2, [1j, 2j, 3j], [3j, 4j]),
                                            [[6, 8], [12, 16], [18, 24]])
  
      def test_syr_her(self):
          x = np.arange(1, 5, dtype='d')
          resx = np.triu(x[:, np.newaxis] * x)
          resx_reverse = np.triu(x[::-1, np.newaxis] * x[::-1])
  
          y = np.linspace(0, 8.5, 17, endpoint=False)
  
          z = np.arange(1, 9, dtype='d').view('D')
          resz = np.triu(z[:, np.newaxis] * z)
          resz_reverse = np.triu(z[::-1, np.newaxis] * z[::-1])
          rehz = np.triu(z[:, np.newaxis] * z.conj())
          rehz_reverse = np.triu(z[::-1, np.newaxis] * z[::-1].conj())
  
          w = np.c_[np.zeros(4), z, np.zeros(4)].ravel()
  
          for p, rtol in zip('sd', [1e-7, 1e-14]):
              f = getattr(fblas, p+'syr', None)
              if f is None:
                  continue
              assert_allclose(f(1.0, x), resx, rtol=rtol)
              assert_allclose(f(1.0, x, lower=True), resx.T, rtol=rtol)
              assert_allclose(f(1.0, y, incx=2, offx=2, n=4), resx, rtol=rtol)
              # negative increments imply reversed vectors in blas
              assert_allclose(f(1.0, y, incx=-2, offx=2, n=4),
                              resx_reverse, rtol=rtol)
  
              a = np.zeros((4, 4), 'f' if p == 's' else 'd', 'F')
              b = f(1.0, x, a=a, overwrite_a=True)
              assert_allclose(a, resx, rtol=rtol)
  
              b = f(2.0, x, a=a)
              assert_(a is not b)
              assert_allclose(b, 3*resx, rtol=rtol)
  
              assert_raises(Exception, f, 1.0, x, incx=0)
              assert_raises(Exception, f, 1.0, x, offx=5)
              assert_raises(Exception, f, 1.0, x, offx=-2)
              assert_raises(Exception, f, 1.0, x, n=-2)
              assert_raises(Exception, f, 1.0, x, n=5)
              assert_raises(Exception, f, 1.0, x, lower=2)
              assert_raises(Exception, f, 1.0, x, a=np.zeros((2, 2), 'd', 'F'))
  
          for p, rtol in zip('cz', [1e-7, 1e-14]):
              f = getattr(fblas, p+'syr', None)
              if f is None:
                  continue
              assert_allclose(f(1.0, z), resz, rtol=rtol)
              assert_allclose(f(1.0, z, lower=True), resz.T, rtol=rtol)
              assert_allclose(f(1.0, w, incx=3, offx=1, n=4), resz, rtol=rtol)
              # negative increments imply reversed vectors in blas
              assert_allclose(f(1.0, w, incx=-3, offx=1, n=4),
                              resz_reverse, rtol=rtol)
  
              a = np.zeros((4, 4), 'F' if p == 'c' else 'D', 'F')
              b = f(1.0, z, a=a, overwrite_a=True)
              assert_allclose(a, resz, rtol=rtol)
  
              b = f(2.0, z, a=a)
              assert_(a is not b)
              assert_allclose(b, 3*resz, rtol=rtol)
  
              assert_raises(Exception, f, 1.0, x, incx=0)
              assert_raises(Exception, f, 1.0, x, offx=5)
              assert_raises(Exception, f, 1.0, x, offx=-2)
              assert_raises(Exception, f, 1.0, x, n=-2)
              assert_raises(Exception, f, 1.0, x, n=5)
              assert_raises(Exception, f, 1.0, x, lower=2)
              assert_raises(Exception, f, 1.0, x, a=np.zeros((2, 2), 'd', 'F'))
  
          for p, rtol in zip('cz', [1e-7, 1e-14]):
              f = getattr(fblas, p+'her', None)
              if f is None:
                  continue
              assert_allclose(f(1.0, z), rehz, rtol=rtol)
              assert_allclose(f(1.0, z, lower=True), rehz.T.conj(), rtol=rtol)
              assert_allclose(f(1.0, w, incx=3, offx=1, n=4), rehz, rtol=rtol)
              # negative increments imply reversed vectors in blas
              assert_allclose(f(1.0, w, incx=-3, offx=1, n=4),
                              rehz_reverse, rtol=rtol)
  
              a = np.zeros((4, 4), 'F' if p == 'c' else 'D', 'F')
              b = f(1.0, z, a=a, overwrite_a=True)
              assert_allclose(a, rehz, rtol=rtol)
  
              b = f(2.0, z, a=a)
              assert_(a is not b)
              assert_allclose(b, 3*rehz, rtol=rtol)
  
              assert_raises(Exception, f, 1.0, x, incx=0)
              assert_raises(Exception, f, 1.0, x, offx=5)
              assert_raises(Exception, f, 1.0, x, offx=-2)
              assert_raises(Exception, f, 1.0, x, n=-2)
              assert_raises(Exception, f, 1.0, x, n=5)
              assert_raises(Exception, f, 1.0, x, lower=2)
              assert_raises(Exception, f, 1.0, x, a=np.zeros((2, 2), 'd', 'F'))
  
      def test_syr2(self):
          x = np.arange(1, 5, dtype='d')
          y = np.arange(5, 9, dtype='d')
          resxy = np.triu(x[:, np.newaxis] * y + y[:, np.newaxis] * x)
          resxy_reverse = np.triu(x[::-1, np.newaxis] * y[::-1]
                                  + y[::-1, np.newaxis] * x[::-1])
  
          q = np.linspace(0, 8.5, 17, endpoint=False)
  
          for p, rtol in zip('sd', [1e-7, 1e-14]):
              f = getattr(fblas, p+'syr2', None)
              if f is None:
                  continue
              assert_allclose(f(1.0, x, y), resxy, rtol=rtol)
              assert_allclose(f(1.0, x, y, n=3), resxy[:3, :3], rtol=rtol)
              assert_allclose(f(1.0, x, y, lower=True), resxy.T, rtol=rtol)
  
              assert_allclose(f(1.0, q, q, incx=2, offx=2, incy=2, offy=10),
                              resxy, rtol=rtol)
              assert_allclose(f(1.0, q, q, incx=2, offx=2, incy=2, offy=10, n=3),
                              resxy[:3, :3], rtol=rtol)
              # negative increments imply reversed vectors in blas
              assert_allclose(f(1.0, q, q, incx=-2, offx=2, incy=-2, offy=10),
                              resxy_reverse, rtol=rtol)
  
              a = np.zeros((4, 4), 'f' if p == 's' else 'd', 'F')
              b = f(1.0, x, y, a=a, overwrite_a=True)
              assert_allclose(a, resxy, rtol=rtol)
  
              b = f(2.0, x, y, a=a)
              assert_(a is not b)
              assert_allclose(b, 3*resxy, rtol=rtol)
  
              assert_raises(Exception, f, 1.0, x, y, incx=0)
              assert_raises(Exception, f, 1.0, x, y, offx=5)
              assert_raises(Exception, f, 1.0, x, y, offx=-2)
              assert_raises(Exception, f, 1.0, x, y, incy=0)
              assert_raises(Exception, f, 1.0, x, y, offy=5)
              assert_raises(Exception, f, 1.0, x, y, offy=-2)
              assert_raises(Exception, f, 1.0, x, y, n=-2)
              assert_raises(Exception, f, 1.0, x, y, n=5)
              assert_raises(Exception, f, 1.0, x, y, lower=2)
              assert_raises(Exception, f, 1.0, x, y,
                            a=np.zeros((2, 2), 'd', 'F'))
  
      def test_her2(self):
          x = np.arange(1, 9, dtype='d').view('D')
          y = np.arange(9, 17, dtype='d').view('D')
          resxy = x[:, np.newaxis] * y.conj() + y[:, np.newaxis] * x.conj()
          resxy = np.triu(resxy)
  
          resxy_reverse = x[::-1, np.newaxis] * y[::-1].conj()
          resxy_reverse += y[::-1, np.newaxis] * x[::-1].conj()
          resxy_reverse = np.triu(resxy_reverse)
  
          u = np.c_[np.zeros(4), x, np.zeros(4)].ravel()
          v = np.c_[np.zeros(4), y, np.zeros(4)].ravel()
  
          for p, rtol in zip('cz', [1e-7, 1e-14]):
              f = getattr(fblas, p+'her2', None)
              if f is None:
                  continue
              assert_allclose(f(1.0, x, y), resxy, rtol=rtol)
              assert_allclose(f(1.0, x, y, n=3), resxy[:3, :3], rtol=rtol)
              assert_allclose(f(1.0, x, y, lower=True), resxy.T.conj(),
                              rtol=rtol)
  
              assert_allclose(f(1.0, u, v, incx=3, offx=1, incy=3, offy=1),
                              resxy, rtol=rtol)
              assert_allclose(f(1.0, u, v, incx=3, offx=1, incy=3, offy=1, n=3),
                              resxy[:3, :3], rtol=rtol)
              # negative increments imply reversed vectors in blas
              assert_allclose(f(1.0, u, v, incx=-3, offx=1, incy=-3, offy=1),
                              resxy_reverse, rtol=rtol)
  
              a = np.zeros((4, 4), 'F' if p == 'c' else 'D', 'F')
              b = f(1.0, x, y, a=a, overwrite_a=True)
              assert_allclose(a, resxy, rtol=rtol)
  
              b = f(2.0, x, y, a=a)
              assert_(a is not b)
              assert_allclose(b, 3*resxy, rtol=rtol)
  
              assert_raises(Exception, f, 1.0, x, y, incx=0)
              assert_raises(Exception, f, 1.0, x, y, offx=5)
              assert_raises(Exception, f, 1.0, x, y, offx=-2)
              assert_raises(Exception, f, 1.0, x, y, incy=0)
              assert_raises(Exception, f, 1.0, x, y, offy=5)
              assert_raises(Exception, f, 1.0, x, y, offy=-2)
              assert_raises(Exception, f, 1.0, x, y, n=-2)
              assert_raises(Exception, f, 1.0, x, y, n=5)
              assert_raises(Exception, f, 1.0, x, y, lower=2)
              assert_raises(Exception, f, 1.0, x, y,
                            a=np.zeros((2, 2), 'd', 'F'))
  
      def test_gbmv(self):
          seed(1234)
          for ind, dtype in enumerate(DTYPES):
              n = 7
              m = 5
              kl = 1
              ku = 2
              # fake a banded matrix via toeplitz
              A = toeplitz(append(rand(kl+1), zeros(m-kl-1)),
                           append(rand(ku+1), zeros(n-ku-1)))
              A = A.astype(dtype)
              Ab = zeros((kl+ku+1, n), dtype=dtype)
  
              # Form the banded storage
              Ab[2, :5] = A[0, 0]  # diag
              Ab[1, 1:6] = A[0, 1]  # sup1
              Ab[0, 2:7] = A[0, 2]  # sup2
              Ab[3, :4] = A[1, 0]  # sub1
  
              x = rand(n).astype(dtype)
              y = rand(m).astype(dtype)
              alpha, beta = dtype(3), dtype(-5)
  
              func, = get_blas_funcs(('gbmv',), dtype=dtype)
              y1 = func(m=m, n=n, ku=ku, kl=kl, alpha=alpha, a=Ab,
                        x=x, y=y, beta=beta)
              y2 = alpha * A.dot(x) + beta * y
              assert_array_almost_equal(y1, y2)
  
      def test_sbmv_hbmv(self):
          seed(1234)
          for ind, dtype in enumerate(DTYPES):
              n = 6
              k = 2
              A = zeros((n, n), dtype=dtype)
              Ab = zeros((k+1, n), dtype=dtype)
  
              # Form the array and its packed banded storage
              A[arange(n), arange(n)] = rand(n)
              for ind2 in range(1, k+1):
                  temp = rand(n-ind2)
                  A[arange(n-ind2), arange(ind2, n)] = temp
                  Ab[-1-ind2, ind2:] = temp
              A = A.astype(dtype)
              A = A + A.T if ind < 2 else A + A.conj().T
              Ab[-1, :] = diag(A)
              x = rand(n).astype(dtype)
              y = rand(n).astype(dtype)
              alpha, beta = dtype(1.25), dtype(3)
  
              if ind > 1:
                  func, = get_blas_funcs(('hbmv',), dtype=dtype)
              else:
                  func, = get_blas_funcs(('sbmv',), dtype=dtype)
              y1 = func(k=k, alpha=alpha, a=Ab, x=x, y=y, beta=beta)
              y2 = alpha * A.dot(x) + beta * y
              assert_array_almost_equal(y1, y2)
  
      def test_spmv_hpmv(self):
          seed(1234)
          for ind, dtype in enumerate(DTYPES+COMPLEX_DTYPES):
              n = 3
              A = rand(n, n).astype(dtype)
              if ind > 1:
                  A += rand(n, n)*1j
              A = A.astype(dtype)
              A = A + A.T if ind < 4 else A + A.conj().T
              c, r = tril_indices(n)
              Ap = A[r, c]
              x = rand(n).astype(dtype)
              y = rand(n).astype(dtype)
              xlong = arange(2*n).astype(dtype)
              ylong = ones(2*n).astype(dtype)
              alpha, beta = dtype(1.25), dtype(2)
  
              if ind > 3:
                  func, = get_blas_funcs(('hpmv',), dtype=dtype)
              else:
                  func, = get_blas_funcs(('spmv',), dtype=dtype)
              y1 = func(n=n, alpha=alpha, ap=Ap, x=x, y=y, beta=beta)
              y2 = alpha * A.dot(x) + beta * y
              assert_array_almost_equal(y1, y2)
  
              # Test inc and offsets
              y1 = func(n=n-1, alpha=alpha, beta=beta, x=xlong, y=ylong, ap=Ap,
                        incx=2, incy=2, offx=n, offy=n)
              y2 = (alpha * A[:-1, :-1]).dot(xlong[3::2]) + beta * ylong[3::2]
              assert_array_almost_equal(y1[3::2], y2)
              assert_almost_equal(y1[4], ylong[4])
  
      def test_spr_hpr(self):
          seed(1234)
          for ind, dtype in enumerate(DTYPES+COMPLEX_DTYPES):
              n = 3
              A = rand(n, n).astype(dtype)
              if ind > 1:
                  A += rand(n, n)*1j
              A = A.astype(dtype)
              A = A + A.T if ind < 4 else A + A.conj().T
              c, r = tril_indices(n)
              Ap = A[r, c]
              x = rand(n).astype(dtype)
              alpha = (DTYPES+COMPLEX_DTYPES)[mod(ind, 4)](2.5)
  
              if ind > 3:
                  func, = get_blas_funcs(('hpr',), dtype=dtype)
                  y2 = alpha * x[:, None].dot(x[None, :].conj()) + A
              else:
                  func, = get_blas_funcs(('spr',), dtype=dtype)
                  y2 = alpha * x[:, None].dot(x[None, :]) + A
  
              y1 = func(n=n, alpha=alpha, ap=Ap, x=x)
              y1f = zeros((3, 3), dtype=dtype)
              y1f[r, c] = y1
              y1f[c, r] = y1.conj() if ind > 3 else y1
              assert_array_almost_equal(y1f, y2)
  
      def test_spr2_hpr2(self):
          seed(1234)
          for ind, dtype in enumerate(DTYPES):
              n = 3
              A = rand(n, n).astype(dtype)
              if ind > 1:
                  A += rand(n, n)*1j
              A = A.astype(dtype)
              A = A + A.T if ind < 2 else A + A.conj().T
              c, r = tril_indices(n)
              Ap = A[r, c]
              x = rand(n).astype(dtype)
              y = rand(n).astype(dtype)
              alpha = dtype(2)
  
              if ind > 1:
                  func, = get_blas_funcs(('hpr2',), dtype=dtype)
              else:
                  func, = get_blas_funcs(('spr2',), dtype=dtype)
  
              u = alpha.conj() * x[:, None].dot(y[None, :].conj())
              y2 = A + u + u.conj().T
              y1 = func(n=n, alpha=alpha, x=x, y=y, ap=Ap)
              y1f = zeros((3, 3), dtype=dtype)
              y1f[r, c] = y1
              y1f[[1, 2, 2], [0, 0, 1]] = y1[[1, 3, 4]].conj()
              assert_array_almost_equal(y1f, y2)
  
      def test_tbmv(self):
          seed(1234)
          for ind, dtype in enumerate(DTYPES):
              n = 10
              k = 3
              x = rand(n).astype(dtype)
              A = zeros((n, n), dtype=dtype)
              # Banded upper triangular array
              for sup in range(k+1):
                  A[arange(n-sup), arange(sup, n)] = rand(n-sup)
  
              # Add complex parts for c,z
              if ind > 1:
                  A[nonzero(A)] += 1j * rand((k+1)*n-(k*(k+1)//2)).astype(dtype)
  
              # Form the banded storage
              Ab = zeros((k+1, n), dtype=dtype)
              for row in range(k+1):
                  Ab[-row-1, row:] = diag(A, k=row)
              func, = get_blas_funcs(('tbmv',), dtype=dtype)
  
              y1 = func(k=k, a=Ab, x=x)
              y2 = A.dot(x)
              assert_array_almost_equal(y1, y2)
  
              y1 = func(k=k, a=Ab, x=x, diag=1)
              A[arange(n), arange(n)] = dtype(1)
              y2 = A.dot(x)
              assert_array_almost_equal(y1, y2)
  
              y1 = func(k=k, a=Ab, x=x, diag=1, trans=1)
              y2 = A.T.dot(x)
              assert_array_almost_equal(y1, y2)
  
              y1 = func(k=k, a=Ab, x=x, diag=1, trans=2)
              y2 = A.conj().T.dot(x)
              assert_array_almost_equal(y1, y2)
  
      def test_tbsv(self):
          seed(1234)
          for ind, dtype in enumerate(DTYPES):
              n = 6
              k = 3
              x = rand(n).astype(dtype)
              A = zeros((n, n), dtype=dtype)
              # Banded upper triangular array
              for sup in range(k+1):
                  A[arange(n-sup), arange(sup, n)] = rand(n-sup)
  
              # Add complex parts for c,z
              if ind > 1:
                  A[nonzero(A)] += 1j * rand((k+1)*n-(k*(k+1)//2)).astype(dtype)
  
              # Form the banded storage
              Ab = zeros((k+1, n), dtype=dtype)
              for row in range(k+1):
                  Ab[-row-1, row:] = diag(A, k=row)
              func, = get_blas_funcs(('tbsv',), dtype=dtype)
  
              y1 = func(k=k, a=Ab, x=x)
              y2 = solve(A, x)
              assert_array_almost_equal(y1, y2)
  
              y1 = func(k=k, a=Ab, x=x, diag=1)
              A[arange(n), arange(n)] = dtype(1)
              y2 = solve(A, x)
              assert_array_almost_equal(y1, y2)
  
              y1 = func(k=k, a=Ab, x=x, diag=1, trans=1)
              y2 = solve(A.T, x)
              assert_array_almost_equal(y1, y2)
  
              y1 = func(k=k, a=Ab, x=x, diag=1, trans=2)
              y2 = solve(A.conj().T, x)
              assert_array_almost_equal(y1, y2)
  
      def test_tpmv(self):
          seed(1234)
          for ind, dtype in enumerate(DTYPES):
              n = 10
              x = rand(n).astype(dtype)
              # Upper triangular array
              A = triu(rand(n, n)) if ind < 2 else triu(rand(n, n)+rand(n, n)*1j)
              # Form the packed storage
              c, r = tril_indices(n)
              Ap = A[r, c]
              func, = get_blas_funcs(('tpmv',), dtype=dtype)
  
              y1 = func(n=n, ap=Ap, x=x)
              y2 = A.dot(x)
              assert_array_almost_equal(y1, y2)
  
              y1 = func(n=n, ap=Ap, x=x, diag=1)
              A[arange(n), arange(n)] = dtype(1)
              y2 = A.dot(x)
              assert_array_almost_equal(y1, y2)
  
              y1 = func(n=n, ap=Ap, x=x, diag=1, trans=1)
              y2 = A.T.dot(x)
              assert_array_almost_equal(y1, y2)
  
              y1 = func(n=n, ap=Ap, x=x, diag=1, trans=2)
              y2 = A.conj().T.dot(x)
              assert_array_almost_equal(y1, y2)
  
      def test_tpsv(self):
          seed(1234)
          for ind, dtype in enumerate(DTYPES):
              n = 10
              x = rand(n).astype(dtype)
              # Upper triangular array
              A = triu(rand(n, n)) if ind < 2 else triu(rand(n, n)+rand(n, n)*1j)
              A += eye(n)
              # Form the packed storage
              c, r = tril_indices(n)
              Ap = A[r, c]
              func, = get_blas_funcs(('tpsv',), dtype=dtype)
  
              y1 = func(n=n, ap=Ap, x=x)
              y2 = solve(A, x)
              assert_array_almost_equal(y1, y2)
  
              y1 = func(n=n, ap=Ap, x=x, diag=1)
              A[arange(n), arange(n)] = dtype(1)
              y2 = solve(A, x)
              assert_array_almost_equal(y1, y2)
  
              y1 = func(n=n, ap=Ap, x=x, diag=1, trans=1)
              y2 = solve(A.T, x)
              assert_array_almost_equal(y1, y2)
  
              y1 = func(n=n, ap=Ap, x=x, diag=1, trans=2)
              y2 = solve(A.conj().T, x)
              assert_array_almost_equal(y1, y2)
  
      def test_trmv(self):
          seed(1234)
          for ind, dtype in enumerate(DTYPES):
              n = 3
              A = (rand(n, n)+eye(n)).astype(dtype)
              x = rand(3).astype(dtype)
              func, = get_blas_funcs(('trmv',), dtype=dtype)
  
              y1 = func(a=A, x=x)
              y2 = triu(A).dot(x)
              assert_array_almost_equal(y1, y2)
  
              y1 = func(a=A, x=x, diag=1)
              A[arange(n), arange(n)] = dtype(1)
              y2 = triu(A).dot(x)
              assert_array_almost_equal(y1, y2)
  
              y1 = func(a=A, x=x, diag=1, trans=1)
              y2 = triu(A).T.dot(x)
              assert_array_almost_equal(y1, y2)
  
              y1 = func(a=A, x=x, diag=1, trans=2)
              y2 = triu(A).conj().T.dot(x)
              assert_array_almost_equal(y1, y2)
  
      def test_trsv(self):
          seed(1234)
          for ind, dtype in enumerate(DTYPES):
              n = 15
              A = (rand(n, n)+eye(n)).astype(dtype)
              x = rand(n).astype(dtype)
              func, = get_blas_funcs(('trsv',), dtype=dtype)
  
              y1 = func(a=A, x=x)
              y2 = solve(triu(A), x)
              assert_array_almost_equal(y1, y2)
  
              y1 = func(a=A, x=x, lower=1)
              y2 = solve(tril(A), x)
              assert_array_almost_equal(y1, y2)
  
              y1 = func(a=A, x=x, diag=1)
              A[arange(n), arange(n)] = dtype(1)
              y2 = solve(triu(A), x)
              assert_array_almost_equal(y1, y2)
  
              y1 = func(a=A, x=x, diag=1, trans=1)
              y2 = solve(triu(A).T, x)
              assert_array_almost_equal(y1, y2)
  
              y1 = func(a=A, x=x, diag=1, trans=2)
              y2 = solve(triu(A).conj().T, x)
              assert_array_almost_equal(y1, y2)
  
  
  class TestFBLAS3Simple(object):
  
      def test_gemm(self):
          for p in 'sd':
              f = getattr(fblas, p+'gemm', None)
              if f is None:
                  continue
              assert_array_almost_equal(f(3, [3], [-4]), [[-36]])
              assert_array_almost_equal(f(3, [3], [-4], 3, [5]), [-21])
          for p in 'cz':
              f = getattr(fblas, p+'gemm', None)
              if f is None:
                  continue
              assert_array_almost_equal(f(3j, [3-4j], [-4]), [[-48-36j]])
              assert_array_almost_equal(f(3j, [3-4j], [-4], 3, [5j]), [-48-21j])
  
  
  def _get_func(func, ps='sdzc'):
      """Just a helper: return a specified BLAS function w/typecode."""
      for p in ps:
          f = getattr(fblas, p+func, None)
          if f is None:
              continue
          yield f
  
  
  class TestBLAS3Symm(object):
  
      def setup_method(self):
          self.a = np.array([[1., 2.],
                             [0., 1.]])
          self.b = np.array([[1., 0., 3.],
                             [0., -1., 2.]])
          self.c = np.ones((2, 3))
          self.t = np.array([[2., -1., 8.],
                             [3., 0., 9.]])
  
      def test_symm(self):
          for f in _get_func('symm'):
              res = f(a=self.a, b=self.b, c=self.c, alpha=1., beta=1.)
              assert_array_almost_equal(res, self.t)
  
              res = f(a=self.a.T, b=self.b, lower=1, c=self.c, alpha=1., beta=1.)
              assert_array_almost_equal(res, self.t)
  
              res = f(a=self.a, b=self.b.T, side=1, c=self.c.T,
                      alpha=1., beta=1.)
              assert_array_almost_equal(res, self.t.T)
  
      def test_summ_wrong_side(self):
          f = getattr(fblas, 'dsymm', None)
          if f is not None:
              assert_raises(Exception, f, **{'a': self.a, 'b': self.b,
                                             'alpha': 1, 'side': 1})
              # `side=1` means C <- B*A, hence shapes of A and B are to be
              #  compatible. Otherwise, f2py exception is raised
  
      def test_symm_wrong_uplo(self):
          """SYMM only considers the upper/lower part of A. Hence setting
          wrong value for `lower` (default is lower=0, meaning upper triangle)
          gives a wrong result.
          """
          f = getattr(fblas, 'dsymm', None)
          if f is not None:
              res = f(a=self.a, b=self.b, c=self.c, alpha=1., beta=1.)
              assert np.allclose(res, self.t)
  
              res = f(a=self.a, b=self.b, lower=1, c=self.c, alpha=1., beta=1.)
              assert not np.allclose(res, self.t)
  
  
  class TestBLAS3Syrk(object):
      def setup_method(self):
          self.a = np.array([[1., 0.],
                             [0., -2.],
                             [2., 3.]])
          self.t = np.array([[1., 0., 2.],
                             [0., 4., -6.],
                             [2., -6., 13.]])
          self.tt = np.array([[5., 6.],
                              [6., 13.]])
  
      def test_syrk(self):
          for f in _get_func('syrk'):
              c = f(a=self.a, alpha=1.)
              assert_array_almost_equal(np.triu(c), np.triu(self.t))
  
              c = f(a=self.a, alpha=1., lower=1)
              assert_array_almost_equal(np.tril(c), np.tril(self.t))
  
              c0 = np.ones(self.t.shape)
              c = f(a=self.a, alpha=1., beta=1., c=c0)
              assert_array_almost_equal(np.triu(c), np.triu(self.t+c0))
  
              c = f(a=self.a, alpha=1., trans=1)
              assert_array_almost_equal(np.triu(c), np.triu(self.tt))
  
      # prints '0-th dimension must be fixed to 3 but got 5',
      # FIXME: suppress?
      # FIXME: how to catch the _fblas.error?
      def test_syrk_wrong_c(self):
          f = getattr(fblas, 'dsyrk', None)
          if f is not None:
              assert_raises(Exception, f, **{'a': self.a, 'alpha': 1.,
                                             'c': np.ones((5, 8))})
          # if C is supplied, it must have compatible dimensions
  
  
  class TestBLAS3Syr2k(object):
      def setup_method(self):
          self.a = np.array([[1., 0.],
                             [0., -2.],
                             [2., 3.]])
          self.b = np.array([[0., 1.],
                             [1., 0.],
                             [0, 1.]])
          self.t = np.array([[0., -1., 3.],
                             [-1., 0., 0.],
                             [3., 0., 6.]])
          self.tt = np.array([[0., 1.],
                              [1., 6]])
  
      def test_syr2k(self):
          for f in _get_func('syr2k'):
              c = f(a=self.a, b=self.b, alpha=1.)
              assert_array_almost_equal(np.triu(c), np.triu(self.t))
  
              c = f(a=self.a, b=self.b, alpha=1., lower=1)
              assert_array_almost_equal(np.tril(c), np.tril(self.t))
  
              c0 = np.ones(self.t.shape)
              c = f(a=self.a, b=self.b, alpha=1., beta=1., c=c0)
              assert_array_almost_equal(np.triu(c), np.triu(self.t+c0))
  
              c = f(a=self.a, b=self.b, alpha=1., trans=1)
              assert_array_almost_equal(np.triu(c), np.triu(self.tt))
  
      # prints '0-th dimension must be fixed to 3 but got 5', FIXME: suppress?
      def test_syr2k_wrong_c(self):
          f = getattr(fblas, 'dsyr2k', None)
          if f is not None:
              assert_raises(Exception, f, **{'a': self.a,
                                             'b': self.b,
                                             'alpha': 1.,
                                             'c': np.zeros((15, 8))})
          # if C is supplied, it must have compatible dimensions
  
  
  class TestSyHe(object):
      """Quick and simple tests for (zc)-symm, syrk, syr2k."""
      def setup_method(self):
          self.sigma_y = np.array([[0., -1.j],
                                   [1.j, 0.]])
  
      def test_symm_zc(self):
          for f in _get_func('symm', 'zc'):
              # NB: a is symmetric w/upper diag of ONLY
              res = f(a=self.sigma_y, b=self.sigma_y, alpha=1.)
              assert_array_almost_equal(np.triu(res), np.diag([1, -1]))
  
      def test_hemm_zc(self):
          for f in _get_func('hemm', 'zc'):
              # NB: a is hermitian w/upper diag of ONLY
              res = f(a=self.sigma_y, b=self.sigma_y, alpha=1.)
              assert_array_almost_equal(np.triu(res), np.diag([1, 1]))
  
      def test_syrk_zr(self):
          for f in _get_func('syrk', 'zc'):
              res = f(a=self.sigma_y, alpha=1.)
              assert_array_almost_equal(np.triu(res), np.diag([-1, -1]))
  
      def test_herk_zr(self):
          for f in _get_func('herk', 'zc'):
              res = f(a=self.sigma_y, alpha=1.)
              assert_array_almost_equal(np.triu(res), np.diag([1, 1]))
  
      def test_syr2k_zr(self):
          for f in _get_func('syr2k', 'zc'):
              res = f(a=self.sigma_y, b=self.sigma_y, alpha=1.)
              assert_array_almost_equal(np.triu(res), 2.*np.diag([-1, -1]))
  
      def test_her2k_zr(self):
          for f in _get_func('her2k', 'zc'):
              res = f(a=self.sigma_y, b=self.sigma_y, alpha=1.)
              assert_array_almost_equal(np.triu(res), 2.*np.diag([1, 1]))
  
  
  class TestTRMM(object):
      """Quick and simple tests for dtrmm."""
      def setup_method(self):
          self.a = np.array([[1., 2., ],
                             [-2., 1.]])
          self.b = np.array([[3., 4., -1.],
                             [5., 6., -2.]])
  
      def test_ab(self):
          f = getattr(fblas, 'dtrmm', None)
          if f is not None:
              result = f(1., self.a, self.b)
              # default a is upper triangular
              expected = np.array([[13., 16., -5.],
                                   [5., 6., -2.]])
              assert_array_almost_equal(result, expected)
  
      def test_ab_lower(self):
          f = getattr(fblas, 'dtrmm', None)
          if f is not None:
              result = f(1., self.a, self.b, lower=True)
              expected = np.array([[3., 4., -1.],
                                   [-1., -2., 0.]])  # now a is lower triangular
              assert_array_almost_equal(result, expected)
  
      def test_b_overwrites(self):
          # BLAS dtrmm modifies B argument in-place.
          # Here the default is to copy, but this can be overridden
          f = getattr(fblas, 'dtrmm', None)
          if f is not None:
              for overwr in [True, False]:
                  bcopy = self.b.copy()
                  result = f(1., self.a, bcopy, overwrite_b=overwr)
                  # C-contiguous arrays are copied
                  assert_(bcopy.flags.f_contiguous is False and
                          np.may_share_memory(bcopy, result) is False)
                  assert_equal(bcopy, self.b)
  
              bcopy = np.asfortranarray(self.b.copy())  # or just transpose it
              result = f(1., self.a, bcopy, overwrite_b=True)
              assert_(bcopy.flags.f_contiguous is True and
                      np.may_share_memory(bcopy, result) is True)
              assert_array_almost_equal(bcopy, result)
  
  
  def test_trsm():
      seed(1234)
      for ind, dtype in enumerate(DTYPES):
          tol = np.finfo(dtype).eps*1000
          func, = get_blas_funcs(('trsm',), dtype=dtype)
  
          # Test protection against size mismatches
          A = rand(4, 5).astype(dtype)
          B = rand(4, 4).astype(dtype)
          alpha = dtype(1)
          assert_raises(Exception, func, alpha, A, B)
          assert_raises(Exception, func, alpha, A.T, B)
  
          n = 8
          m = 7
          alpha = dtype(-2.5)
          A = (rand(m, m) if ind < 2 else rand(m, m) + rand(m, m)*1j) + eye(m)
          A = A.astype(dtype)
          Au = triu(A)
          Al = tril(A)
          B1 = rand(m, n).astype(dtype)
          B2 = rand(n, m).astype(dtype)
  
          x1 = func(alpha=alpha, a=A, b=B1)
          assert_equal(B1.shape, x1.shape)
          x2 = solve(Au, alpha*B1)
          assert_allclose(x1, x2, atol=tol)
  
          x1 = func(alpha=alpha, a=A, b=B1, trans_a=1)
          x2 = solve(Au.T, alpha*B1)
          assert_allclose(x1, x2, atol=tol)
  
          x1 = func(alpha=alpha, a=A, b=B1, trans_a=2)
          x2 = solve(Au.conj().T, alpha*B1)
          assert_allclose(x1, x2, atol=tol)
  
          x1 = func(alpha=alpha, a=A, b=B1, diag=1)
          Au[arange(m), arange(m)] = dtype(1)
          x2 = solve(Au, alpha*B1)
          assert_allclose(x1, x2, atol=tol)
  
          x1 = func(alpha=alpha, a=A, b=B2, diag=1, side=1)
          x2 = solve(Au.conj().T, alpha*B2.conj().T)
          assert_allclose(x1, x2.conj().T, atol=tol)
  
          x1 = func(alpha=alpha, a=A, b=B2, diag=1, side=1, lower=1)
          Al[arange(m), arange(m)] = dtype(1)
          x2 = solve(Al.conj().T, alpha*B2.conj().T)
          assert_allclose(x1, x2.conj().T, atol=tol)
  