Source file owl_base_linalg_generic.ml
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# 1 "src/base/linalg/owl_base_linalg_generic.ml"
type ('a, 'b) t = ('a, 'b) Owl_base_dense_ndarray_generic.t
module M = Owl_base_dense_ndarray_generic
let is_triu x =
let shp = M.shape x in
let m, n = shp.(0), shp.(1) in
let k = Stdlib.min m n in
let _a0 = Owl_const.zero (M.kind x) in
try
for i = 0 to k - 1 do
for j = 0 to i - 1 do
assert (M.get x [|i; j|] = _a0)
done
done;
true
with _exn -> false
let is_tril x =
let shp = M.shape x in
let m, n = shp.(0), shp.(1) in
let k = Stdlib.min m n in
let _a0 = Owl_const.zero (M.kind x) in
try
for i = 0 to k - 1 do
for j = i + 1 to k - 1 do
assert (M.get x [|i; j|] = _a0)
done
done;
true
with _exn -> false
let is_symmetric x =
let shp = M.shape x in
let m, n = shp.(0), shp.(1) in
if m <> n then false
else (
try
for i = 0 to n - 1 do
for j = i + 1 to n - 1 do
let a = M.get x [|j; i|] in
let b = M.get x [|i; j|] in
assert (a = b)
done
done;
true
with _exn -> false
)
let is_hermitian x =
let shp = M.shape x in
let m, n = shp.(0), shp.(1) in
if m <> n then false
else (
try
for i = 0 to n - 1 do
for j = i to n - 1 do
let a = M.get x [|j; i|] in
let b = Complex.conj (M.get x [|i; j|]) in
assert (a = b)
done
done;
true
with _exn -> false
)
let is_diag x = is_triu x && is_tril x
let _check_is_matrix dims =
if (Array.length dims) <> 2
then raise (Invalid_argument "The given NDarray is not a matrix!")
else ()
let linsolve_gauss a b =
let (dims_a, dims_b) = (M.shape a, M.shape b) in
let (_, _) = (_check_is_matrix dims_a, _check_is_matrix dims_b) in
let a = M.copy a in
let b = M.copy b in
let n = dims_a.(0) in
let m = dims_b.(1) in
let icol = ref 0 in
let irow = ref 0 in
let dum = ref 0.0 in
let pivinv = ref 0.0 in
let indxc = Array.make n 0 in
let indxr = Array.make n 0 in
let ipiv = Array.make n 0 in
for i = 0 to n - 1 do
let big = ref 0.0 in
for j = 0 to n - 1 do
if ipiv.(j) <> 1 then (
for k = 0 to n - 1 do
if ipiv.(k) == 0 then (
let v = M.get a [|j; k|] |> abs_float in
if (v >= !big) then (
big := v;
irow := j; icol := k;
)
)
done
)
done;
ipiv.(!icol) <- ipiv.(!icol) + 1;
if (!irow <> !icol) then (
for l = 0 to n - 1 do
let u = M.get a [|!irow; l|] in
let v = M.get a [|!icol; l|] in
M.set a [|!icol; l|] u;
M.set a [|!irow; l|] v
done;
for l = 0 to m - 1 do
let u = M.get b [|!irow; l|] in
let v = M.get b [|!icol; l|] in
M.set b [|!icol; l|] u;
M.set b [|!irow; l|] v
done
);
indxr.(i) <- !irow;
indxc.(i) <- !icol;
let p = M.get a [|!icol; !icol|] in
if (p = 0.0) then raise Owl_exception.SINGULAR;
pivinv := 1.0 /. p;
M.set a [|!icol; !icol|] 1.0;
for l = 0 to n - 1 do
let prev = M.get a [|!icol; l|] in
M.set a [|!icol; l|] (prev *. !pivinv)
done;
for l = 0 to m - 1 do
let prev = M.get b [|!icol; l|] in
M.set b [|!icol; l|] (prev *. !pivinv)
done;
for ll = 0 to n - 1 do
if (ll <> !icol) then (
dum := M.get a [|ll; !icol|];
M.set a [|ll; !icol|] 0.0;
for l = 0 to n - 1 do
let p = M.get a [|!icol; l|] in
let prev = M.get a [|ll; l|] in
M.set a [|ll; l|] (prev -. p *. !dum)
done;
for l = 0 to m - 1 do
let p = M.get b [|!icol; l|] in
let prev = M.get b [|ll; l|] in
M.set b [|ll; l|] (prev -. p *. !dum)
done
)
done
done;
for l = n - 1 downto 0 do
if (indxr.(l) <> indxc.(l)) then (
for k = 0 to n - 1 do
let u = M.get a [|k; indxr.(l)|] in
let v = M.get a [|k; indxc.(l)|] in
M.set a [|k; indxc.(l)|] u;
M.set a [|k; indxr.(l)|] v
done
)
done;
a, b
let _lu_base a =
let lu = M.copy a in
let n = (M.shape a).(0) in
let m = (M.shape a).(1) in
assert (n = m);
let indx = Array.make n 0 in
let vv = Array.make n 0. in
let tiny = 1.0e-40 in
let big = ref 0. in
let temp = ref 0. in
let d = ref 1.0 in
let imax = ref 0 in
for i = 0 to n - 1 do
big := 0.;
for j = 0 to n - 1 do
temp := M.get lu [| i; j |] |> abs_float;
if !temp > !big then big := !temp
done;
if !big = 0. then raise Owl_exception.SINGULAR;
vv.(i) <- 1.0 /. !big
done;
for k = 0 to n - 1 do
big := 0.;
for i = k to n - 1 do
temp := (M.get lu [| i; k |] |> abs_float) *. vv.(i);
if !temp > !big
then (
big := !temp;
imax := i)
done;
if k <> !imax
then (
for j = 0 to n - 1 do
temp := M.get lu [| !imax; j |];
let tmp = M.get lu [| k; j |] in
M.set lu [| !imax; j |] tmp;
M.set lu [| k; j |] !temp
done;
d := !d *. -1.;
vv.(!imax) <- vv.(k));
indx.(k) <- !imax;
if M.get lu [| k; k |] = 0. then M.set lu [| k; k |] tiny;
for i = k + 1 to n - 1 do
let tmp0 = M.get lu [| i; k |] in
let tmp1 = M.get lu [| k; k |] in
temp := tmp0 /. tmp1;
M.set lu [| i; k |] !temp;
for j = k + 1 to n - 1 do
let prev = M.get lu [| i; j |] in
M.set lu [| i; j |] (prev -. (!temp *. M.get lu [| k; j |]))
done
done
done;
lu, indx, !d
let lu a =
let k = M.kind a in
let lu, indx, _ = _lu_base a in
let n = (M.shape lu).(0) in
let m = (M.shape lu).(1) in
assert (n = m && n >= 2);
let l = M.eye k n in
for r = 1 to n - 1 do
for c = 0 to r - 1 do
let v = M.get lu [| r; c |] in
M.set l [| r; c |] v;
M.set lu [| r; c |] 0.
done
done;
l, lu, indx
let _lu_solve_vec a b =
assert (Array.length (M.shape b) = 1);
let n = (M.shape a).(0) in
if (M.shape b).(0) <> n then failwith "LUdcmp::solve bad sizes";
let ii = ref 0 in
let sum = ref 0. in
let x = M.copy b in
let lu, indx, _ = _lu_base a in
for i = 0 to n - 1 do
let ip = indx.(i) in
sum := M.get x [| ip |];
M.set x [| ip |] (M.get x [| i |]);
if !ii <> 0
then
for j = !ii - 1 to i - 1 do
sum := !sum -. (M.get lu [| i; j |] *. M.get x [| j |])
done
else if !sum <> 0.
then ii := !ii + 1;
M.set x [| i |] !sum
done;
for i = n - 1 downto 0 do
sum := M.get x [| i |];
for j = i + 1 to n - 1 do
sum := !sum -. (M.get lu [| i; j |] *. M.get x [| j |])
done;
M.set x [| i |] (!sum /. M.get lu [| i; i |])
done;
x
let linsolve_lu a b =
let dims_a, dims_b = M.shape a, M.shape b in
let _, _ = _check_is_matrix dims_a, _check_is_matrix dims_b in
assert (dims_a.(0) = dims_a.(1));
let m = dims_b.(1) in
let b = M.copy b in
for j = 0 to m - 1 do
let vec = M.get_slice [ []; [ j ] ] b |> M.flatten in
let x = _lu_solve_vec a vec in
M.set_slice [ []; [ j ] ] b x
done;
b
let inv a =
let dims_a = M.shape a in
_check_is_matrix dims_a |> ignore;
assert (dims_a.(0) = dims_a.(1));
let n = dims_a.(0) in
let b = M.eye (M.kind a) n in
linsolve_lu a b
let det a =
let dims_a = M.shape a in
_check_is_matrix dims_a |> ignore;
assert (dims_a.(0) = dims_a.(1));
let n = dims_a.(0) in
let lu, _, sign = _lu_base a in
let big = ref sign in
for i = 0 to n - 1 do
big := !big *. M.get lu [| i; i |]
done;
!big
let tridiag_solve_vec a b c r =
let n = Array.length a in
let n1 = Array.length b in
let n2 = Array.length c in
assert (n = n1 && n = n2);
if b.(0) = 0.
then raise (Invalid_argument
"tridiag_solve_vec: 0 at the beginning of diagonal vector");
let bet = ref b.(0) in
let gam = Array.make n 0. in
let x = Array.make n 0. in
x.(0) <- r.(0) /. !bet;
for j = 1 to n - 1 do
gam.(j) <- c.(j - 1) /. !bet;
bet := b.(j) -. (a.(j) *. gam.(j));
if !bet = 0.
then raise (Invalid_argument "tridiag_solve_vec: algorithm fails");
x.(j) <- (r.(j) -. (a.(j) *. x.(j - 1))) /. !bet
done;
for j = n - 2 downto 0 do
x.(j) <- x.(j) -. (gam.(j + 1) *. x.(j + 1))
done;
x