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require 'test_helper'
class LinalgTest < GSL::TestCase
def _check(x, actual, eps, desc)
if x == actual
assert true
elsif actual.zero?
refute x.abs > eps, desc
else
refute((x - actual).abs / actual.abs > eps, desc)
end
end
def _create_general_matrix(size1, size2)
m = GSL::Matrix.alloc(size1, size2)
size1.times { |i|
size2.times { |j|
m.set(i, j, 1.0 / (i + j + 1.0))
}
}
m
end
def _create_hilbert_matrix(size)
_create_general_matrix(size, size)
end
def _create_vandermonde_matrix(size)
m = GSL::Matrix.alloc(size, size)
size.times { |i|
size.times { |j|
m.set(i, j, GSL.pow(i + 1.0, size - j - 1.0))
}
}
m
end
def setup
@hilb2 = _create_hilbert_matrix(2)
@hilb3 = _create_hilbert_matrix(3)
@hilb4 = _create_hilbert_matrix(4)
@hilb12 = _create_hilbert_matrix(12)
@vander2 = _create_vandermonde_matrix(2)
@vander3 = _create_vandermonde_matrix(3)
@vander4 = _create_vandermonde_matrix(4)
@vander12 = _create_vandermonde_matrix(12)
@hilb2_solution = GSL::Vector.alloc(-8.0, 18.0)
@hilb3_solution = GSL::Vector.alloc(27.0, -192.0, 210.0)
@hilb4_solution = GSL::Vector.alloc(-64.0, 900.0, -2520.0, 1820.0)
@hilb12_solution = GSL::Vector.alloc(
-1728.0, 245388.0, -8528520.0,
127026900.0, -1009008000.0, 4768571808.0,
-14202796608.0, 27336497760.0, -33921201600.0,
26189163000.0, -11437874448.0, 2157916488.0
)
@vander2_solution = GSL::Vector.alloc(1.0, 0.0)
@vander3_solution = GSL::Vector.alloc(0.0, 1.0, 0.0)
@vander4_solution = GSL::Vector.alloc(0.0, 0.0, 1.0, 0.0)
@vander12_solution = GSL::Vector.alloc(0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 1.0, 0.0)
end
def test_matmult
a = GSL::Matrix.alloc([10.0, 5.0, 1.0, 20.0], 2, 2)
b = GSL::Matrix.alloc([10.0, 5.0, 2.0, 1.0, 3.0, 2.0], 2, 3)
c = a * b
refute((c[0, 0] - 105.0).abs > GSL::DBL_EPSILON)
refute((c[0, 1] - 65.0).abs > GSL::DBL_EPSILON)
refute((c[0, 2] - 30.0).abs > GSL::DBL_EPSILON)
refute((c[1, 0] - 30.0).abs > GSL::DBL_EPSILON)
refute((c[1, 1] - 65.0).abs > GSL::DBL_EPSILON)
refute((c[1, 2] - 42.0).abs > GSL::DBL_EPSILON)
end
def _test_bidiag_decomp_dim(m, eps, desc)
eps *= 2 * GSL::DBL_EPSILON
mm = m.size1
nn = m.size2
a = m.duplicate
b = GSL::Matrix.calloc(nn, nn)
u, v, d, sd = GSL::Linalg::Bidiag.unpack(*GSL::Linalg::Bidiag.decomp(a))
b.set_diagonal(d)
(nn - 1).times { |i| b[i, i + 1] = sd[i] }
a = u * b * v.trans
mm.times { |i|
nn.times { |j|
_check(aij = a[i, j], mij = m[i, j], eps,
'%s: (%d,%d)[%d,%d]: %22.18g %22.18g' % [desc, mm, nn, i, j, aij, mij])
}
}
end
def test_bidiag_decomp
m53 = _create_general_matrix(5, 3)
m97 = _create_general_matrix(9, 7)
_test_bidiag_decomp_dim(m53, 64.0, 'bidiag_decomp m(5,3)')
_test_bidiag_decomp_dim(m97, 64.0, 'bidiag_decomp m(9,7)')
_test_bidiag_decomp_dim(@hilb2, 8.0, 'bidiag_decomp hilbert(2)')
_test_bidiag_decomp_dim(@hilb3, 64.0, 'bidiag_decomp hilbert(3)')
_test_bidiag_decomp_dim(@hilb4, 1024.0, 'bidiag_decomp hilbert(4)')
_test_bidiag_decomp_dim(@hilb12, 1024.0, 'bidiag_decomp hilbert(12)')
end
def test_cholesky
m = GSL::Matrix.pascal(6)
c_exp = GSL::Matrix[[1, 0, 0, 0, 0, 0],
[1, 1, 0, 0, 0, 0],
[1, 2, 1, 0, 0, 0],
[1, 3, 3, 1, 0, 0],
[1, 4, 6, 4, 1, 0],
[1, 5, 10, 10, 5, 1]]
c = m.cholesky_decomp
a = c.lower
assert a == c_exp, "#{m.class}#cholesky_decomp"
assert a * a.trans == m, "#{m.class}#cholesky_decomp"
end
def _test_HH_solve_dim(m, actual, eps, desc)
eps *= GSL::DBL_EPSILON if eps > 1
dim = m.size1
x = GSL::Vector.indgen(dim) + 1
GSL::Linalg::HH.svx(m.duplicate, x)
dim.times { |i|
_check(si = x[i], ai = actual[i], eps,
'%s: %d[%d]: %22.18g %22.18g' % [desc, dim, i, si, ai])
}
end
def test_HH_solve
_test_HH_solve_dim(@hilb2, @hilb2_solution, 8.0, 'HH_solve Hilbert(2)')
_test_HH_solve_dim(@hilb3, @hilb3_solution, 128.0, 'HH_solve Hilbert(3)')
_test_HH_solve_dim(@hilb4, @hilb4_solution, 2048.0, 'HH_solve Hilbert(4)')
_test_HH_solve_dim(@hilb12, @hilb12_solution, 0.5, 'HH_solve Hilbert(12)')
_test_HH_solve_dim(@vander2, @vander2_solution, 8.0, 'HH_solve Vander(2)')
_test_HH_solve_dim(@vander3, @vander3_solution, 64.0, 'HH_solve Vander(3)')
_test_HH_solve_dim(@vander4, @vander4_solution, 1024.0, 'HH_solve Vander(4)')
_test_HH_solve_dim(@vander12, @vander12_solution, 0.05, 'HH_solve Vander(12)')
end
def test_LU
m = GSL::Matrix.alloc([0.18, 0.60, 0.57, 0.96], [0.41, 0.24, 0.99, 0.58],
[0.14, 0.30, 0.97, 0.66], [0.51, 0.13, 0.19, 0.85])
a = m.clone
assert m == a, "#{a.class}#LU_decomp: matrix not destroyed"
lu_exp = GSL::Matrix.alloc([0.51, 0.13, 0.19, 0.85],
[0.352941176470588, 0.554117647058823, 0.502941176470588, 0.66],
[0.803921568627451, 0.244515215852796, 0.71427813163482, -0.264713375796178],
[0.274509803921569, 0.476999292285916, 0.949126848480345, 0.363093705877982])
x_exp = GSL::Vector[-4.05205022957397, -12.6056113959069, 1.66091162670884, 8.69376692879523]
lu, perm, _sign = m.LU_decomp
assert lu == lu_exp, "#{a.class}#LU_decomp"
b = GSL::Vector[1, 2, 3, 4]
x = GSL::Linalg::LU.solve(lu, perm, b)
assert x == x_exp, "#{a.class}.LU_solve"
x = lu.solve(perm, b)
assert x == x_exp, "#{lu.class}#solve"
perm, _sign = m.LU_decomp!
assert m == lu_exp, "#{a.class}#LU_decomp!"
m = a.clone
x = GSL::Linalg::LU.solve(m, perm, b)
assert x == x_exp, "#{a.class}.LU_solve"
x = m.LU_solve(perm, b)
assert x == x_exp, "#{a.class}#LU_solve"
assert m == a, "#{a.class}#LU_solve: matrix not destroyed"
h = GSL::Matrix.hilbert(5)
invh = GSL::Matrix.invhilbert(5)
lu, perm, _sign = h.LU_decomp
a = GSL::Linalg::LU.invert(lu, perm)
assert a.equal?(invh, 1e-6), "#{h.class}#LU_invert, Hilbert matrix of order 5"
a = lu.invert(perm)
assert a.equal?(invh, 1e-6), "#{h.class}#LU_invert, Hilbert matrix of order 5"
a = h.inv
assert a.equal?(invh, 1e-6), "#{h.class}#LU_invert, Hilbert matrix of order 5"
end
def test_QR
m = GSL::Matrix.alloc([0.18, 0.60, 0.57, 0.96], [0.41, 0.24, 0.99, 0.58],
[0.14, 0.30, 0.97, 0.66], [0.51, 0.13, 0.19, 0.85])
a = m.clone
assert m == a, "#{m.class}#QR_decomp: matrix not destroyed"
x_exp = GSL::Vector[-4.05205022957397, -12.6056113959069, 1.66091162670884, 8.69376692879523]
b = GSL::Vector[1, 2, 3, 4]
qr, tau = m.QR_decomp
x = m.QR_solve(b)
assert x == x_exp, "#{m.class}#QR_solve(b)"
x = GSL::Linalg::QR.solve(m, b)
assert x == x_exp, 'GSL::Linalg::QR::solve(b)'
tau = m.QR_decomp!
assert m != a, "#{m.class}#QR_decomp: matrix destroyed"
x = m.QR_solve(tau, b)
assert x == x_exp, "#{m.class}#QR_solve(tau, b)"
x = qr.solve(tau, b)
assert x == x_exp, "#{qr.class}#solve(tau, b)"
assert_raises(ArgumentError) { m.QR_solve(b) }
assert_raises(ArgumentError) { m.solve(b) }
x = m.solve(tau, b)
assert x == x_exp, "#{m.class}#solve(tau, b)"
m = a.clone
bb = b.clone
m.QR_svx(bb)
assert bb == x_exp, "#{m.class}#QR_svx(b)"
tau = GSL::Linalg::QR.decomp!(m)
bb = b.clone
m.QR_svx(tau, bb)
assert bb == x_exp, "#{m.class}#QR_svx(tau, b)"
assert_raises(ArgumentError) { m.QR_svx(bb) }
m = a.clone
qr, tau = m.QR_decomp
assert m == a, "#{m.class}#QR_decomp: matrix not destroyed"
x, r = m.QR_lssolve(b)
assert x == x_exp, "#{m.class}#QR_lssolve(b)"
r = m.QR_lssolve(b, x)
assert x == x_exp, "#{qr.class}#QR_lssolve(b, x)"
m.QR_lssolve(b, x, r)
assert x == x_exp, "#{qr.class}#QR_lssolve(b, x, r)"
x, r = qr.QR_lssolve(tau, b)
assert x == x_exp, "#{qr.class}#QR_lssolve(tau, b)"
r = qr.QR_lssolve(tau, b, x)
assert x == x_exp, "#{qr.class}#QR_lssolve(tau, b, x)"
qr.QR_lssolve(tau, b, x, r)
assert x == x_exp, "#{qr.class}#QR_lssolve(tau, b, x, r)"
assert_raises(ArgumentError) { qr.QR_lssolve(bb) }
end
def test_SV
a = GSL::Matrix.alloc([1, 2, 3, 4], 2, 2)
i = GSL::Matrix.identity(2)
ainv = a.inv
u, v, s = a.SV_decomp
sm = s.to_m_diagonal
sinv = s.map { |x| 1.0 / x }.to_m_diagonal
assert u * sm * v.trans == a, "#{a.class}#SV_decomp"
assert v * sinv * u.trans == ainv, "#{a.class}#SV_decomp"
assert u.trans * u == i, "#{a.class}#SV_decomp"
assert v.trans * v == i, "#{a.class}#SV_decomp"
assert a * v == u * sm, "#{a.class}#SV_decomp"
assert a.trans * u == v * sm, "#{a.class}#SV_decomp"
end
def _test_TDN_solve_dim(dim, d, a, b, actual, eps, desc)
eps *= GSL::DBL_EPSILON
abovediag = GSL::Vector.alloc(dim - 1)
belowdiag = GSL::Vector.alloc(dim - 1)
diag = GSL::Vector.alloc(dim)
diag.set_all(d)
rhs = GSL::Vector.indgen(dim) + 1
abovediag.set_all(a)
belowdiag.set_all(b)
x = GSL::Linalg.solve_tridiag(diag, abovediag, belowdiag, rhs)
dim.times { |i|
_check(si = x[i], ai = actual[i], eps,
'%s: %d[%d]: %22.18g %22.18g' % [desc, dim, i, si, ai])
}
end
def test_TDN_solve
actual = GSL::Vector.alloc(5)
actual[0] = -7.0 / 3.0
actual[1] = 5.0 / 3.0
actual[2] = 4.0 / 3.0
_test_TDN_solve_dim(3, 1.0, 2.0, 1.0, actual, 2.0, 'solve_TDN dim=2 A')
actual[0] = 0.75
actual[1] = 0.75
actual[2] = 2.625
_test_TDN_solve_dim(3, 1.0, 1.0 / 3.0, 1.0 / 2.0, actual, 2.0, 'solve_TDN dim=2 B')
actual[0] = 99.0 / 140.0
actual[1] = 41.0 / 35.0
actual[2] = 19.0 / 10.0
actual[3] = 72.0 / 35.0
actual[4] = 139.0 / 35.0
_test_TDN_solve_dim(5, 1.0, 1.0 / 4.0, 1.0 / 2.0, actual, 35.0 / 8.0, 'solve_TDN dim=5')
end
def _test_TDN_cyc_solve_dim(dim, d, a, b, actual, eps, desc)
eps *= GSL::DBL_EPSILON
abovediag = GSL::Vector.alloc(dim)
belowdiag = GSL::Vector.alloc(dim)
diag = GSL::Vector.alloc(dim)
rhs = GSL::Vector.indgen(dim) + 1
abovediag.set_all(a)
belowdiag.set_all(b)
diag.set_all(d)
x = GSL::Linalg.solve_cyc_tridiag(diag, abovediag, belowdiag, rhs)
dim.times { |i|
_check(si = x[i], ai = actual[i], eps,
'%s: %d[%d]: %22.18g %22.18g' % [desc, dim, i, si, ai])
}
end
def test_TDN_cyc_solve
actual = GSL::Vector.alloc(5)
actual[0] = 3.0 / 2.0
actual[1] = -1.0 / 2.0
actual[2] = 1.0 / 2.0
_test_TDN_cyc_solve_dim(3, 1.0, 2.0, 1.0, actual, 32.0, 'solve_TDN_cyc dim=2')
actual[0] = -5.0 / 22.0
actual[1] = -3.0 / 22.0
actual[2] = 29.0 / 22.0
actual[3] = -9.0 / 22.0
actual[4] = 43.0 / 22.0
_test_TDN_cyc_solve_dim(5, 3.0, 2.0, 1.0, actual, 66.0, 'solve_TDN_cyc dim=5')
end
def _test_TDS_solve_dim(dim, d, od, actual, eps, desc)
eps *= GSL::DBL_EPSILON
diag = GSL::Vector.alloc(dim)
diag.set_all(d)
rhs = GSL::Vector.indgen(dim) + 1
offdiag = GSL::Vector.alloc(dim - 1)
offdiag.set_all(od)
x = GSL::Linalg.solve_symm_tridiag(diag, offdiag, rhs)
dim.times { |i|
_check(si = x[i], ai = actual[i], eps,
'%s: %d[%d]: %22.18g %22.18g' % [desc, dim, i, si, ai])
}
end
def test_TDS_solve
actual = GSL::Vector[0.0, 2.0]
_test_TDS_solve_dim(2, 1.0, 0.5, actual, 8.0, 'solve_TDS dim=2 A')
actual = GSL::Vector[3.0 / 8.0, 15.0 / 8.0]
_test_TDS_solve_dim(2, 1.0, 1.0 / 3.0, actual, 8.0, 'solve_TDS dim=2 B')
actual = GSL::Vector[5.0 / 8.0, 9.0 / 8.0, 2.0, 15.0 / 8.0, 35.0 / 8.0]
_test_TDS_solve_dim(5, 1.0, 1.0 / 3.0, actual, 8.0, 'solve_TDS dim=5')
end
def _test_TDS_cyc_solve_one(dim, d, od, r, actual, eps, desc)
eps *= GSL::DBL_EPSILON
diag = d.duplicate
offdiag = od.duplicate
rhs = r.duplicate
x = GSL::Linalg.solve_symm_cyc_tridiag(diag, offdiag, rhs)
dim.times { |i|
_check(si = x[i], ai = actual[i], eps,
'%s: %d[%d]: %22.18g %22.18g' % [desc, dim, i, si, ai])
}
end
def test_TDS_cyc_solve
diag = GSL::Vector.alloc(1)
diag[0] = 2
offdiag = GSL::Vector.alloc(1)
offdiag[0] = 3
rhs = GSL::Vector.alloc(1)
rhs[0] = 7
actual = GSL::Vector.alloc(1)
actual[0] = 3.5
# XXX GSL::ERROR::EBADLEN: Ruby/GSL error code 19, size of cyclic system must be
# 3 or more (file tridiag.c, line 531), matrix/vector sizes are not conformant
#_test_TDS_cyc_solve_one(1, diag, offdiag, rhs, actual, 28.0, 'solve_TDS_cyc dim=1')
diag = GSL::Vector[1, 2]
offdiag = GSL::Vector[3, 4]
rhs = GSL::Vector[7, -7]
actual = GSL::Vector[-5, 4]
# XXX GSL::ERROR::EBADLEN: Ruby/GSL error code 19, size of cyclic system must be
# 3 or more (file tridiag.c, line 531), matrix/vector sizes are not conformant
#_test_TDS_cyc_solve_one(2, diag, offdiag, rhs, actual, 28.0, 'solve_TDS_cyc dim=2')
diag = GSL::Vector[1, 1, 1]
offdiag = GSL::Vector[3, 3, 3]
rhs = GSL::Vector[7, -7, 7]
actual = GSL::Vector[-2, 5, -2]
_test_TDS_cyc_solve_one(3, diag, offdiag, rhs, actual, 28.0, 'solve_TDS_cyc dim=3')
diag = GSL::Vector[4, 2, 1, 2, 4]
offdiag = GSL::Vector[1, 1, 1, 1, 1]
rhs = GSL::Vector[30, -24, 3, 21, -30]
actual = GSL::Vector[12, 3, -42, 42, -21]
_test_TDS_cyc_solve_one(5, diag, offdiag, rhs, actual, 35.0, 'solve_TDS_cyc dim=5')
end
end
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