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local bit = require 'bit'
local gsl = require 'gsl'
local check = require 'check'
local band, rshift = bit.band, bit.rshift
local is_integer = check.is_integer
local tonumber = tonumber
local NT = gsl.CblasNoTrans
local function power_raw(r, m, n, e)
local aux = gsl.gsl_matrix_alloc(n, n)
local m2 = aux
local r_init = false
while e > 0 do
if band(e, 1) ~= 0 then
if r_init then
-- The content of m2 is not needed here.
-- We compute r <- r * m using m2 as a temporary store
gsl.gsl_matrix_memcpy(m2, r)
gsl.gsl_blas_dgemm(NT, NT, 1, m, m2, 0, r)
else
gsl.gsl_matrix_memcpy(r, m)
end
r_init = true
end
e = rshift(e, 1)
if e > 0 then
-- compute m2 <- m * m
gsl.gsl_blas_dgemm(NT, NT, 1, m, m, 0, m2)
m, m2 = m2, m
end
end
if aux then gsl.gsl_matrix_free(aux) end
end
local function power_complex_raw(r, m, n, e)
local aux = gsl.gsl_matrix_complex_alloc(n, n)
local m2 = aux
local r_init = false
while e > 0 do
if band(e, 1) ~= 0 then
if r_init then
-- The content of m2 is not needed here.
-- We compute r <- r * m using m2 as a temporary store
gsl.gsl_matrix_complex_memcpy(m2, r)
gsl.gsl_blas_zgemm(NT, NT, 1, m, m2, 0, r)
else
gsl.gsl_matrix_complex_memcpy(r, m)
end
r_init = true
end
e = rshift(e, 1)
if e > 0 then
-- compute m2 <- m * m
gsl.gsl_blas_zgemm(NT, NT, 1, m, m, 0, m2)
m, m2 = m2, m
end
end
if aux then gsl.gsl_matrix_complex_free(aux) end
end
local function power_check_input(m, e)
if not is_integer(e) then
error("exponent should be an integer", 3)
end
if m.size1 ~= m.size2 then
error("cannot compute powers of a non-square matrix", 3)
end
end
local function matrix_power(m, e)
power_check_input(m, e)
local n = tonumber(m.size1)
local r = matrix.alloc(n, n)
if e > 0 then
local aux = gsl.gsl_matrix_alloc(n, n)
gsl.gsl_matrix_memcpy(aux, m)
power_raw(r, aux, n, e)
gsl.gsl_matrix_free(aux)
elseif e == 0 then
gsl.gsl_matrix_set_identity(r)
else
local mi = matrix.inv(m)
power_raw(r, mi, n, -e)
end
return r
end
local function matrix_complex_power(m, e)
power_check_input(m, e)
local n = tonumber(m.size1)
local r = matrix.calloc(n, n)
if e > 0 then
local aux = gsl.gsl_matrix_complex_alloc(n, n)
gsl.gsl_matrix_complex_memcpy(aux, m)
power_complex_raw(r, aux, n, e)
gsl.gsl_matrix_complex_free(aux)
elseif e == 0 then
gsl.gsl_matrix_complex_set_identity(r)
else
local mi = matrix.inv(m)
power_complex_raw(r, mi, n, -e)
end
return r
end
return {power = matrix_power, cpower = matrix_complex_power}
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