local ffi = require 'ffi'
local gsl = require 'gsl'
local algo = require 'algorithm'
local sqrt, abs, floor = math.sqrt, math.abs, math.floor
local format = string.format
local check = require 'check'
local is_integer, is_real = check.is_integer, check.is_real
local gsl_matrix = ffi.typeof('gsl_matrix')
local gsl_matrix_complex = ffi.typeof('gsl_matrix_complex')
local gsl_complex = ffi.typeof('complex')
local gsl_check = require 'gsl-check'
local tonumber = tonumber
local function check_real(x)
 if type(x) ~= 'number' then error('expected real number', 3) end
 return x
end
local function get_typeid(a)
 if is_real(a) then return true, true
 elseif ffi.istype(gsl_complex, a) then return false, true
 elseif ffi.istype(gsl_matrix, a) then return true, false
 elseif ffi.istype(gsl_matrix_complex, a) then return false, false end
end
local function check_typeid(a)
 local isr, iss = get_typeid(a)
 if isr == nil then error('expected matrix of scalar', 2) end
 return isr, iss
end
local function cartesian(x)
 if is_real(x) then
 return x, 0
 else
 return x[0], x[1]
 end
end
local function matrix_dim(m)
 return tonumber(m.size1), tonumber(m.size2)
end
local function matrix_len(m)
 return tonumber(m.size1)
end
local function block_alloc(n)
 local b = ffi.cast('gsl_block *', ffi.C.malloc(ffi.sizeof('gsl_block')))
 local data = ffi.C.malloc(n * ffi.sizeof('double'))
 b.size, b.data, b.ref_count = n, data, 1
 return b
end
local function block_calloc(n)
 local b = ffi.cast('gsl_block_complex *', ffi.C.malloc(ffi.sizeof('gsl_block_complex')))
 local data = ffi.C.malloc(2 * n * ffi.sizeof('double'))
 b.size, b.data, b.ref_count = n, data, 1
 return b
end
local function matrix_alloc(n1, n2)
 local b = block_alloc(n1 * n2)
 local m = gsl_matrix(n1, n2, n2, b.data, b, 1)
 return m
end
local function matrix_calloc(n1, n2)
 local b = block_calloc(n1 * n2)
 local m = gsl_matrix_complex(n1, n2, n2, b.data, b, 1)
 return m
end
local function matrix_zero(m)
 gsl.gsl_matrix_set_zero(m)
end
local function matrix_complex_zero(m)
 gsl.gsl_matrix_complex_set_zero(m)
end
local function matrix_new(n1, n2, f)
 local m = matrix_alloc(n1, n2)
 if f then
 for i=0, n1-1 do
 for j=0, n2-1 do
 local x = check_real(f(i+1, j+1))
 m.data[i*n2+j] = x
 end
 end
 else
 gsl.gsl_matrix_set_zero(m)
 end
 return m
end
local function matrix_cnew(n1, n2, f)
 local m = matrix_calloc(n1, n2)
 if f then
 for i=0, n1-1 do
 for j=0, n2-1 do
 local z = f(i+1, j+1)
 local x, y = cartesian(z)
 m.data[2*i*n2+2*j ] = x
 m.data[2*i*n2+2*j+1] = y
 end
 end
 else
 gsl.gsl_matrix_complex_set_zero(m)
 end
 return m
end
local function matrix_free(m)
 if m.owner then
 local b = m.block
 b.ref_count = b.ref_count - 1
 if b.ref_count == 0 then
 ffi.C.free(b.data)
 ffi.C.free(b)
 end
 end
end
local function matrix_copy(a)
 local n1, n2 = matrix_dim(a)
 local b = matrix_alloc(n1, n2)
 gsl.gsl_matrix_memcpy(b, a)
 return b
end
local function matrix_complex_copy(a)
 local n1, n2 = matrix_dim(a)
 local b = matrix_calloc(n1, n2)
 gsl.gsl_matrix_complex_memcpy(b, a)
 return b
end
local function check_indices(m, i, j)
 local r, c = matrix_dim(m)
 if i < 1 or i> r or j < 1 or j> c then
 error('matrix index out of bounds', 3)
 end
 return i-1, j-1
end
local function check_row_index(m, i)
 if i < 1 or i> matrix_len(m) then
 error('matrix index out of bounds', 3)
 end
 return i-1
end
local function check_col_index(m, j)
 if j < 1 or j> tonumber(m.size2) then
 error('matrix index out of bounds', 3)
 end
 return j-1
end
local function matrix_get(m, i, j)
 i, j = check_indices(m, i, j)
 return gsl.gsl_matrix_get(m, i, j)
end
local function matrix_complex_get(m, i, j)
 i, j = check_indices(m, i, j)
 return gsl.gsl_matrix_complex_get(m, i, j)
end
local function matrix_set(m, i, j, v)
 i, j = check_indices(m, i, j)
 return gsl.gsl_matrix_set(m, i, j, v)
end
local function matrix_complex_set(m, i, j, v)
 i, j = check_indices(m, i, j)
 return gsl.gsl_matrix_complex_set(m, i, j, v)
end
local function complex_conj(z)
 local x, y = cartesian(z)
 return gsl_complex(x, -y)
end
local function complex_real(z)
 local x = cartesian(z)
 return x
end
local function complex_imag(z)
 local x, y = cartesian(z)
 return y
end
local function complex_norm2(z)
 local x, y = cartesian(z)
 return x*x + y*y
end
local function complex_abs(z)
 local x, y = cartesian(z)
 return sqrt(x*x + y*y)
end
local function complex_arg(z)
 local x, y = cartesian(z)
 return math.atan2(y, x)
end
local function itostr(im, eps, fmt, signed)
 local absim = abs(im)
 local sign = im + eps < 0 and '-' or (signed and '+' or '') if absim < eps then return (signed and '' or '0') else return sign .. (abs(absim-1) < eps and 'i' or format(fmt..'i', absim)) end end local function is_small_integer(x) local ax = abs(x) return (ax < 2^31 and floor(ax) == ax) end local function recttostr(x, y, eps) local x_sub, y_sub = abs(x) < eps, abs(y) < eps local fmt_x, fmt_y = '%.8g', '%.8g' if is_small_integer(x) then fmt_x = '%.0f' x_sub = false end if is_small_integer(y) then fmt_y = '%.0f' y_sub = false end if not x_sub then local sign = x+eps < 0 and '-' or '' local ax = abs(x) if y_sub then return format('%s'..fmt_x, sign, ax) else return format('%s'..fmt_x..'%s', sign, ax, itostr(y, eps, fmt_y, true)) end else return (y_sub and '0' or itostr(y, eps, fmt_y, false)) end end local function concat_pad(t, pad) local sep = ' ' local row for i, s in ipairs(t) do local x = string.rep(' ', pad - #s) .. s row = row and (row .. sep .. x) or x end return row end local function matrix_display_gen(sel) return function(m) local n1, n2 = matrix_dim(m) local sq = 0 for i=0, n1-1 do for j=0, n2-1 do local x, y = sel(m, i, j) sq = sq + abs(x) + abs(y) end end local eps = (sq / (n1*n2)) * 1e-9 eps = eps> 0 and eps or 1
 lsrow = {}
 local lmax = 0
 for i=0, n1-1 do
 local row = {}
 for j=0, n2-1 do
 local x, y = sel(m, i, j)
 local s = recttostr(x, y, eps)
 if #s> lmax then lmax = #s end
 row[j+1] = s
 end
 lsrow[i+1] = row
 end
 local ss = {}
 for i=0, n1-1 do
 ss[i+1] = '[ ' .. concat_pad(lsrow[i+1], lmax) .. ' ]'
 end
 return table.concat(ss, '\n')
 end
end
local function matrix_col(m, j)
 j = check_col_index (m, j)
 local mb = m.block
 local r = gsl_matrix(m.size1, 1, m.tda, m.data + j, mb, 1)
 mb.ref_count = mb.ref_count + 1
 return r
end
local function matrix_row(m, i)
 i = check_row_index (m, i)
 local mb = m.block
 local r = gsl_matrix(1, m.size2, 1, m.data + i*m.tda, mb, 1)
 mb.ref_count = mb.ref_count + 1
 return r
end
local function matrix_row_as_column(m, i)
 i = check_row_index (m, i)
 local mb = m.block
 local r = gsl_matrix(m.size2, 1, 1, m.data + i*m.tda, mb, 1)
 mb.ref_count = mb.ref_count + 1
 return r
end
local function matrix_slice(m, i, j, ni, nj)
 check_indices (m, i+ni-1, j+nj-1)
 i, j = check_indices (m, i, j)
 local mb = m.block
 local r = gsl_matrix(ni, nj, m.tda, m.data + i*m.tda + j, mb, 1)
 mb.ref_count = mb.ref_count + 1
 return r
end
local function matrix_complex_col(m, j)
 j = check_col_index (m, j)
 local mb = m.block
 local r = gsl_matrix_complex(m.size1, 1, m.tda, m.data + 2*j, mb, 1)
 mb.ref_count = mb.ref_count + 1
 return r
end
local function matrix_complex_row(m, i)
 i = check_row_index (m, i)
 local mb = m.block
 local r = gsl_matrix_complex(1, m.size2, 1, m.data + 2*i*m.tda, mb, 1)
 mb.ref_count = mb.ref_count + 1
 return r
end
local function matrix_complex_row_as_column(m, i)
 i = check_row_index (m, i)
 local mb = m.block
 local r = gsl_matrix_complex(m.size2, 1, 1, m.data + 2*i*m.tda, mb, 1)
 mb.ref_count = mb.ref_count + 1
 return r
end
local function matrix_complex_slice(m, i, j, ni, nj)
 check_indices (m, i+ni-1, j+nj-1)
 i, j = check_indices (m, i, j)
 local mb = m.block
 local r = gsl_matrix_complex(ni, nj, m.tda, m.data + 2*i*m.tda + 2*j, mb, 1)
 mb.ref_count = mb.ref_count + 1
 return r
end
local function matrix_vect_def(t)
 local n = #t
 local isr = true
 for i=1,n do
 if not is_real(t[i]) then
 isr = false
 break
 end
 end
 if isr then
 local m = matrix_alloc(n, 1)
 for i=0, n-1 do
 m.data[i] = t[i+1]
 end
 return m
 else
 local m = matrix_calloc(n, 1)
 for i=0, n-1 do
 local x, y = cartesian(t[i+1])
 m.data[2*i ] = x
 m.data[2*i+1] = y
 end
 return m
 end
end
local function mat_op_gen(n1, n2, opa, a, opb, b, oper)
 local c = matrix_alloc(n1, n2)
 for i = 0, n1-1 do
 for j = 0, n2-1 do
 local ar = opa(a,i,j)
 local br = opb(b,i,j)
 c.data[i*n2+j] = oper(ar, br)
 end
 end
 return c
end
local function mat_comp_op_gen(n1, n2, opa, a, opb, b, oper)
 local c = matrix_calloc(n1, n2)
 for i = 0, n1-1 do
 for j = 0, n2-1 do
 local ar, ai = opa(a,i,j)
 local br, bi = opb(b,i,j)
 local zr, zi = oper(ar, br, ai, bi)
 c.data[2*i*n2+2*j ] = zr
 c.data[2*i*n2+2*j+1] = zi
 end
 end
 return c
end
local function real_get(x) return x, 0 end
local function complex_get(z) return z[0], z[1] end
local function mat_real_get(m,i,j) return m.data[i*m.tda+j], 0 end
local function mat_complex_get(m,i,j)
 local idx = 2*i*m.tda+2*j
 return m.data[idx], m.data[idx+1]
end
local function selector(r, s)
 if s then
 return r and real_get or complex_get
 else
 return r and mat_real_get or mat_complex_get
 end
end
local function mat_complex_of_real(m)
 local n1, n2 = matrix_dim(m)
 local mc = matrix_calloc(n1, n2)
 for i=0, n1-1 do
 for j=0, n2-1 do
 mc.data[2*i*n2+2*j ] = m.data[i*n2+j]
 mc.data[2*i*n2+2*j+1] = 0
 end
 end
 return mc
end
local function opadd(ar, br, ai, bi)
 if ai then return ar+br, ai+bi else return ar+br end
end
local function opsub(ar, br, ai, bi)
 if ai then return ar-br, ai-bi else return ar-br end
end
local function opmul(ar, br, ai, bi)
 if ai then return ar*br-ai*bi, ar*bi+ai*br else return ar*br end
end
local function opdiv(ar, br, ai, bi)
 if ai then
 local d = br^2 + bi^2
 return (ar*br + ai*bi)/d, (-ar*bi + ai*br)/d
 else
 return ar/br
 end
end
local function vector_op(scalar_op, element_wise, no_inverse)
 return function(a, b)
 local ra, sa = get_typeid(a)
 local rb, sb = get_typeid(b)
 if not sb and no_inverse then
 error 'invalid operation on matrix'
 end
 if sa and sb then
 local ar, ai = cartesian(a)
 local br, bi = cartesian(b)
 local zr, zi = scalar_op(ar, br, ai, bi)
 return gsl_complex(zr, zi)
 elseif element_wise or sa or sb then
 local sela, selb = selector(ra, sa), selector(rb, sb)
 local n1 = (sa and tonumber(b.size1) or tonumber(a.size1))
 local n2 = (sa and tonumber(b.size2) or tonumber(a.size2))
 if ra and rb then
 return mat_op_gen(n1, n2, sela, a, selb, b, scalar_op)
 else
 return mat_comp_op_gen(n1, n2, sela, a, selb, b, scalar_op)
 end
 else
 if ra and rb then
 local n1, n2 = tonumber(a.size1), tonumber(b.size2)
 local c = matrix_alloc(n1, n2)
 local NT = gsl.CblasNoTrans
 gsl_check(gsl.gsl_blas_dgemm(NT, NT, 1, a, b, 0, c))
 return c
 else
 if ra then a = mat_complex_of_real(a) end
 if rb then b = mat_complex_of_real(b) end
 local n1, n2 = tonumber(a.size1), tonumber(b.size2)
 local c = matrix_calloc(n1, n2)
 local NT = gsl.CblasNoTrans
 gsl_check(gsl.gsl_blas_zgemm(NT, NT, 1, a, b, 0, c))
 return c
 end
 end
 end
end
local function complex_unm(a)
 local x, y = cartesian(a)
 return gsl_complex(-x, -y)
end
local function matrix_unm(a)
 local n1, n2 = matrix_dim(a)
 local m = matrix_alloc(n1, n2)
 for i=0, n1-1 do
 for j=0, n2-1 do
 m.data[n2*i+j] = -a.data[n2*i+j]
 end
 end
 return m
end
local function matrix_complex_unm(a)
 local n1, n2 = matrix_dim(a)
 local m = matrix_calloc(n1, n2)
 for i=0, n1-1 do
 for j=0, n2-1 do
 m.data[2*n2*i+2*j ] = -a.data[2*n2*i+2*j ]
 m.data[2*n2*i+2*j+1] = -a.data[2*n2*i+2*j+1]
 end
 end
 return m
end
local function matrix_norm2(m)
 local r, c = matrix_dim(m)
 local tda = m.tda
 local ssq, idx = 0, 0
 for i = 0, r-1 do
 for j = 0, c-1 do
 local x = m.data[idx + j]
 ssq = ssq + x*x
 end
 idx = idx + tda
 end
 return ssq
end
local function matrix_norm(m)
 return sqrt(matrix_norm2(m))
end
local function matrix_complex_norm2(m)
 local r, c = matrix_dim(m)
 local tda = m.tda
 local ssq, idx = 0, 0
 for i = 0, r-1 do
 for j = 0, c-1 do
 local x, y = m.data[idx+2*j], m.data[idx+2*j+1]
 ssq = ssq + x*x + y*y
 end
 idx = idx + 2*tda
 end
 return ssq
end
local function matrix_complex_norm(m)
 return sqrt(matrix_complex_norm2(m))
end
complex = {
 new = gsl_complex,
 conj = complex_conj,
 real = complex_real,
 imag = complex_imag,
 abs = complex_abs,
 norm = complex_abs,
 norm2 = complex_norm2,
 rect = cartesian,
 i = 1i,
 arg = complex_arg
}
local generic_add = vector_op(opadd, true)
local generic_sub = vector_op(opsub, true)
local generic_mul = vector_op(opmul, false)
local generic_div = vector_op(opdiv, true, true)
local complex_mt = {
 __add = generic_add,
 __sub = generic_sub,
 __mul = generic_mul,
 __div = generic_div,
 __unm = complex_unm,
 __eq = function(a, b)
 local ar, ai = cartesian(a)
 local br, bi = cartesian(b)
 return (ar == br) and (ai == bi)
 end,
 __pow = function(z,n)
 if is_real(n) then
 return gsl.gsl_complex_pow_real (z, n)
 else
 if is_real(z) then z = gsl_complex(z,0) end
 return gsl.gsl_complex_pow (z, n)
 end
 end,
}
ffi.metatype(gsl_complex, complex_mt)
local function matrix_new_unit(n)
 local m = matrix_alloc(n, n)
 gsl.gsl_matrix_set_identity(m)
 return m
end
local function matrix_fset(m, f)
 local n1, n2 = matrix_dim(m)
 for i=1, n1 do
 for j=1, n2 do
 m:set(i, j, f(i,j))
 end
 end
end
local function matrix_set_equal(a, b)
 local n1a, n2a = matrix_dim(a)
 local n1b, n2b = matrix_dim(b)
 if n1a ~= n1b or n2a ~= n2b then
 error('matrix dimensions does not match', 2)
 end
 for i=1, n1b do
 for j=1, n2b do
 a:set(i, j, b:get(i,j))
 end
 end
end
local function matrix_new_transpose(a)
 local n1, n2 = matrix_dim(a)
 local b = a.alloc(n2, n1)
 for i=1, n2 do
 for j=1, n1 do
 b:set(i, j, a:get(j,i))
 end
 end
 return b
end
local function matrix_new_hc(a)
 local n1, n2 = matrix_dim(a)
 local b = a.alloc(n2, n1)
 for i=1, n2 do
 for j=1, n1 do
 b:set(i, j, complex.conj(a:get(j,i)))
 end
 end
 return b
end
local function matrix_new_copy(m)
 return m:copy()
end
local function matrix_zero_tg()
 m:zero()
end
matrix = {
 new = matrix_new,
 cnew = matrix_cnew,
 alloc = matrix_alloc,
 calloc = matrix_calloc,
 zero = matrix_zero_tg,
 copy = matrix_new_copy,
 unit = matrix_new_unit,
 dim = matrix_dim,
 vec = matrix_vect_def,
 set = matrix_set_equal,
 fset = matrix_fset,
 block = block_alloc,
 transpose = matrix_new_transpose,
 hc = matrix_new_hc,
}
local function matrix_sort(m, f)
 local n = matrix_len(m)
 algo.quicksort(m.data, 0, n - 1, f)
end
local matrix_methods = {
 alloc = matrix_alloc,
 dim = matrix_dim,
 zero = matrix_zero,
 col = matrix_col,
 row = matrix_row,
 get = matrix_get,
 set = matrix_set,
 copy = matrix_copy,
 norm = matrix_norm,
 norm2 = matrix_norm2,
 slice = matrix_slice,
 sort = matrix_sort,
 show = matrix_display_gen(mat_real_get),
}
local function matrix_index(m, i)
 if is_integer(i) then
 if m.size2 == 1 then
 i = check_row_index (m, i)
 return m.data[i * m.tda]
 else
 return matrix_row_as_column(m, i)
 end
 end
 return matrix_methods[i]
end
local function matrix_newindex(m, k, v)
 if is_integer(k) then
 local nr, nc = matrix_dim(m)
 local isr, iss = check_typeid(v)
 k = check_row_index (m, k)
 if not isr then error('cannot assign element to a complex value') end
 if nc == 1 then
 if not iss then error('invalid assignment: expecting a scalar') end
 m.data[k*m.tda] = v
 else
 if iss then error('invalid assignment: expecting a row matrix') end
 if v.size1 ~= nc or v.size2 ~= 1 then
 error('incompatible matrix dimensions in assignment')
 end
 for j = 0, nc-1 do
 m.data[k*m.tda+j] = v.data[v.tda*j]
 end
 end
 else
 error 'cannot set a matrix field'
 end
end
local matrix_power = require 'matrix-power'
local matrix_mt = {
 __gc = matrix_free,
 __add = generic_add,
 __sub = generic_sub,
 __mul = generic_mul,
 __div = generic_div,
 __unm = matrix_unm,
 __pow = matrix_power.power,
 __len = matrix_len,
 __index = matrix_index,
 __newindex = matrix_newindex,
}
ffi.metatype(gsl_matrix, matrix_mt)
local matrix_complex_methods = {
 alloc = matrix_calloc,
 dim = matrix_dim,
 zero = matrix_complex_zero,
 col = matrix_complex_col,
 row = matrix_complex_row,
 get = matrix_complex_get,
 set = matrix_complex_set,
 copy = matrix_complex_copy,
 norm = matrix_complex_norm,
 norm2 = matrix_complex_norm2,
 slice = matrix_complex_slice,
 show = matrix_display_gen(mat_complex_get),
}
local function matrix_complex_index(m, i)
 if is_integer(i) then
 if m.size2 == 1 then
 i = check_row_index (m, i)
 return gsl_complex(m.data[2*i*m.tda], m.data[2*i*m.tda+1])
 else
 return matrix_complex_row_as_column(m, i)
 end
 end
 return matrix_complex_methods[i]
end
local function matrix_complex_newindex(m, k, v)
 if is_integer(k) then
 local nr, nc = matrix_dim(m)
 local isr, iss = check_typeid(v)
 k = check_row_index (m, k)
 if nc == 1 then
 if not iss then error('invalid assignment: expecting a scalar') end
 local vx, vy = cartesian(v)
 m.data[2*k*m.tda ] = vx
 m.data[2*k*m.tda+1] = vy
 else
 if iss then error('invalid assignment: expecting a row matrix') end
 if v.size1 ~= nc or v.size2 ~= 1 then
 error('incompatible matrix dimensions in assignment')
 end
 local sel = selector(isr, iss)
 for j = 0, nc-1 do
 local vx, vy = sel(v, j, 0)
 m.data[2*k*m.tda+2*j ] = vx
 m.data[2*k*m.tda+2*j+1] = vy
 end
 end
 else
 error 'cannot set a matrix field'
 end
end
local matrix_complex_mt = {
 __gc = matrix_free,
 __add = generic_add,
 __sub = generic_sub,
 __mul = generic_mul,
 __div = generic_div,
 __pow = matrix_power.cpower,
 __unm = matrix_complex_unm,
 __len = matrix_len,
 __index = matrix_complex_index,
 __newindex = matrix_complex_newindex,
}
ffi.metatype(gsl_matrix_complex, matrix_complex_mt)
local function c_function_lookup(name)
 return gsl['gsl_complex_' .. name]
end
local function c_invtrig_lookup(name)
 return gsl['gsl_complex_arc' .. name]
end
local function csqrt(x)
 return (is_real(x) and x>= 0) and sqrt(x) or gsl.gsl_complex_sqrt(x)
end
local gsl_function_list = {
 'exp', 'pow', 'log', 'log10',
 'sin', 'cos', 'sec', 'csc', 'tan', 'cot',
 'sinh', 'cosh', 'sech', 'csch', 'tanh', 'coth',
}
local gsl_inverse_trig_list = {
 'sin', 'cos', 'sec', 'csc', 'tan', 'cot',
 'sinh', 'cosh', 'sech', 'csch', 'tanh', 'coth'
}
for _, name in ipairs(gsl_function_list) do
 complex[name] = c_function_lookup(name)
end
for _, name in ipairs(gsl_inverse_trig_list) do
 complex['a' .. name] = c_invtrig_lookup(name)
end
complex.sqrt = csqrt
local function matrix_def(t)
 local r, c = #t, #t[1]
 local m = matrix_alloc(r, c)
 for i= 0, r-1 do
 local row = t[i+1]
 for j = 0, c-1 do
 local x = row[j+1]
 if not is_real(x) then error('expected real number') end
 m.data[i*c+j] = x
 end
 end
 return m
end
local function matrix_cdef(t)
 local r, c = #t, #t[1]
 local m = matrix_calloc(r, c)
 for i= 0, r-1 do
 local row = t[i+1]
 for j = 0, c-1 do
 local x, y = cartesian(row[j+1])
 m.data[2*i*c+2*j ] = x
 m.data[2*i*c+2*j+1] = y
 end
 end
 return m
end
local signum = ffi.new('int[1]')
local function matrix_inv(m)
 local n = m.size1
 local lu = matrix_copy(m)
 local p = ffi.gc(gsl.gsl_permutation_alloc(n), gsl.gsl_permutation_free)
 gsl_check(gsl.gsl_linalg_LU_decomp(lu, p, signum))
 local mi = matrix_alloc(n, n)
 gsl_check(gsl.gsl_linalg_LU_invert(lu, p, mi))
 return mi
end
local function matrix_solve(m, b)
 local n = m.size1
 local lu = matrix_copy(m)
 local p = ffi.gc(gsl.gsl_permutation_alloc(n), gsl.gsl_permutation_free)
 gsl_check(gsl.gsl_linalg_LU_decomp(lu, p, signum))
 local x = matrix_alloc(n, 1)
 local xv = gsl.gsl_matrix_column(x, 0)
 local bv = gsl.gsl_matrix_column(b, 0)
 gsl_check(gsl.gsl_linalg_LU_solve(lu, p, bv, xv))
 return x
end
local function matrix_complex_inv(m)
 local n = m.size1
 local lu = matrix_complex_copy(m)
 local p = ffi.gc(gsl.gsl_permutation_alloc(n), gsl.gsl_permutation_free)
 gsl_check(gsl.gsl_linalg_complex_LU_decomp(lu, p, signum))
 local mi = matrix_calloc(n, n)
 gsl_check(gsl.gsl_linalg_complex_LU_invert(lu, p, mi))
 return mi
end
local function matrix_complex_solve(m, b)
 local n = m.size1
 local lu = matrix_complex_copy(m)
 local p = ffi.gc(gsl.gsl_permutation_alloc(n), gsl.gsl_permutation_free)
 gsl_check(gsl.gsl_linalg_complex_LU_decomp(lu, p, signum))
 local x = matrix_calloc(n, 1)
 local xv = gsl.gsl_matrix_complex_column(x, 0)
 local bv = gsl.gsl_matrix_complex_column(b, 0)
 gsl_check(gsl.gsl_linalg_complex_LU_solve(lu, p, bv, xv))
 return x
end
function matrix.inv(m)
 if ffi.istype(gsl_matrix, m) then
 return matrix_inv(m)
 else
 return matrix_complex_inv(m)
 end
end
function matrix.solve(m, b)
 local mr = ffi.istype(gsl_matrix, m)
 local br = ffi.istype(gsl_matrix, b)
 if mr and br then
 return matrix_solve(m, b)
 else
 if mr then m = mat_complex_of_real(m) end
 if br then b = mat_complex_of_real(b) end
 return matrix_complex_solve(m, b)
 end
end
local function matrix_sv_decomp(a, v, s, w)
 local sv = gsl.gsl_matrix_column(s, 0)
 local w
 if w then
 wv = gsl.gsl_matrix_column(w, 0)
 else
 local m, n = matrix_dim(a)
 wv = ffi.gc(gsl.gsl_vector_alloc(n), gsl.gsl_vector_free)
 end
 gsl_check(gsl.gsl_linalg_SV_decomp (a, v, sv, wv))
end
function matrix.svd(a)
 local m, n = matrix_dim(a)
 local u = matrix_copy(a)
 local v = matrix_alloc(n, n)
 local s = matrix_new(n, n)
 local sv = gsl.gsl_matrix_diagonal(s)
 local wv = ffi.gc(gsl.gsl_vector_alloc(n), gsl.gsl_vector_free)
 gsl_check(gsl.gsl_linalg_SV_decomp (u, v, sv, wv))
 return u, s, v
end
matrix.diag = function(t)
 local n = #t
 local m = matrix.alloc(n, n)
 for k = 0, n*n - 1 do m.data[k] = 0 end
 for k = 0, n-1 do m.data[k*(n+1)] = t[k+1] end
 return m
 end
matrix.tr = function(a)
 local m, n = matrix_dim(a)
 local b = a.alloc(n, m)
 local bset, aget = b.set, a.get
 for i=1, n do
 for j= 1, m do
 bset(b, i, j, aget(a, j, i))
 end
 end
 return b
 end
matrix.def = matrix_def
matrix.cdef = matrix_cdef
local register_ffi_type = debug.getregistry().__gsl_reg_ffi_type
register_ffi_type(gsl_complex, "complex")
register_ffi_type(gsl_matrix, "matrix")
register_ffi_type(gsl_matrix_complex, "complex matrix")
return matrix
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