Module Lacaml.S

module S: Lacaml_S

Single precision real BLAS and LAPACK functions.


type prec = Bigarray.float32_elt 
type num_type = float 
type vec = (float, Bigarray.float32_elt, Bigarray.fortran_layout) Bigarray.Array1.t 

Vectors (precision: float32).

type rvec = vec 
type mat = (float, Bigarray.float32_elt, Bigarray.fortran_layout) Bigarray.Array2.t 

Matrices (precision: float32).

type trans3 = [ `N | `T ] 

Transpose parameter (normal or transposed). For complex matrices, conjugate transpose is also offered, hence the name.

val prec : (float, Bigarray.float32_elt) Bigarray.kind

Precision for this submodule S. Allows to write precision independent code.

module Vec: sig .. end
module Mat: sig .. end
val pp_num : Stdlib.Format.formatter -> float -> unit

pp_num ppf el is equivalent to fprintf ppf "%G" el.

val pp_vec : (float, 'a) Lacaml_io.pp_vec

Pretty-printer for column vectors.

val pp_mat : (float, 'a) Lacaml_io.pp_mat

Pretty-printer for matrices.

BLAS-1 interface
val dot : ?n:int ->
?ofsx:int ->
?incx:int ->
Lacaml_float32.vec -> ?ofsy:int -> ?incy:int -> Lacaml_float32.vec -> float

dot ?n ?ofsx ?incx x ?ofsy ?incy y see BLAS documentation!

n : default = greater n s.t. ofsx+(n-1)(abs incx) <= dim x
ofsx : default = 1
incx : default = 1
ofsy : default = 1
incy : default = 1
val asum : ?n:int -> ?ofsx:int -> ?incx:int -> Lacaml_float32.vec -> float

asum ?n ?ofsx ?incx x see BLAS documentation!

n : default = greater n s.t. ofsx+(n-1)(abs incx) <= dim x
ofsx : default = 1
incx : default = 1
BLAS-2 interface
val sbmv : ?n:int ->
?k:int ->
?ofsy:int ->
?incy:int ->
?y:Lacaml_float32.vec ->
?ar:int ->
?ac:int ->
Lacaml_float32.mat ->
?up:bool ->
?alpha:float ->
?beta:float ->
?ofsx:int -> ?incx:int -> Lacaml_float32.vec -> Lacaml_float32.vec

sbmv ?n ?k ?ofsy ?incy ?y ?ar ?ac a ?up ?alpha ?beta ?ofsx ?incx x see BLAS documentation!

n : default = number of available columns to the right of ac.
k : default = number of available rows in matrix a - 1
ofsy : default = 1
incy : default = 1
y : default = uninitialized vector of minimal length (see BLAS)
ar : default = 1
ac : default = 1
up : default = true i.e., upper band of a is supplied
alpha : default = 1.0
beta : default = 0.0
ofsx : default = 1
incx : default = 1
val ger : ?m:int ->
?n:int ->
?alpha:float ->
?ofsx:int ->
?incx:int ->
Lacaml_float32.vec ->
?ofsy:int ->
?incy:int ->
Lacaml_float32.vec ->
?ar:int -> ?ac:int -> Lacaml_float32.mat -> Lacaml_float32.mat

ger ?m ?n ?alpha ?ofsx ?incx x ?ofsy ?incy y n ?ar ?ac a see BLAS documentation!

m : default = number of rows of a
n : default = number of columns of a
alpha : default = 1.0
ofsx : default = 1
incx : default = 1
ofsy : default = 1
incy : default = 1
ar : default = 1
ac : default = 1
val syr : ?n:int ->
?alpha:float ->
?up:bool ->
?ofsx:int ->
?incx:int ->
Lacaml_float32.vec ->
?ar:int -> ?ac:int -> Lacaml_float32.mat -> Lacaml_float32.mat

syr ?n ?alpha ?up ?ofsx ?incx x ?ar ?ac a see BLAS documentation!

n : default = number of rows of a
alpha : default = 1.0
up : default = true i.e., upper triangle of a is supplied
ofsx : default = 1
incx : default = 1
ar : default = 1
ac : default = 1
LAPACK interface
Auxiliary routines
val lansy_min_lwork : int -> Lacaml_common.norm4 -> int

lansy_min_lwork m norm

val lansy : ?n:int ->
?up:bool ->
?norm:Lacaml_common.norm4 ->
?work:Lacaml_float32.vec -> ?ar:int -> ?ac:int -> Lacaml_float32.mat -> float

lansy ?norm ?up ?n ?ar ?ac ?work a see LAPACK documentation!

n : default = number of columns of matrix a
up : default = true (reference upper triangular part of a)
norm : default = `O
work : default = allocated work space for norm `I
val lamch : [ `B | `E | `L | `M | `N | `O | `P | `R | `S | `U ] -> float

lamch cmach see LAPACK documentation!

Linear equations (computational routines)
val orgqr_min_lwork : n:int -> int

orgqr_min_lwork ~n

val orgqr_opt_lwork : ?m:int ->
?n:int ->
?k:int ->
tau:Lacaml_float32.vec -> ?ar:int -> ?ac:int -> Lacaml_float32.mat -> int

orgqr_opt_lwork ?m ?n ?k ~tau ?ar ?ac a

m : default = available number of rows in matrix a
n : default = available number of columns in matrix a
k : default = available number of elements in vector tau
val orgqr : ?m:int ->
?n:int ->
?k:int ->
?work:Lacaml_float32.vec ->
tau:Lacaml_float32.vec -> ?ar:int -> ?ac:int -> Lacaml_float32.mat -> unit

orgqr ?m ?n ?k ?work ~tau ?ar ?ac a see LAPACK documentation!

m : default = available number of rows in matrix a
n : default = available number of columns in matrix a
k : default = available number of elements in vector tau
val ormqr_opt_lwork : ?side:Lacaml_common.side ->
?trans:Lacaml_common.trans2 ->
?m:int ->
?n:int ->
?k:int ->
tau:Lacaml_float32.vec ->
?ar:int ->
?ac:int ->
Lacaml_float32.mat -> ?cr:int -> ?cc:int -> Lacaml_float32.mat -> int

ormqr_opt_lwork ?side ?trans ?m ?n ?k ~tau ?ar ?ac a ?cr ?cc c

m : default = available number of rows in matrix a
n : default = available number of columns in matrix a
k : default = available number of elements in vector tau
val ormqr : ?side:Lacaml_common.side ->
?trans:Lacaml_common.trans2 ->
?m:int ->
?n:int ->
?k:int ->
?work:Lacaml_float32.vec ->
tau:Lacaml_float32.vec ->
?ar:int ->
?ac:int ->
Lacaml_float32.mat -> ?cr:int -> ?cc:int -> Lacaml_float32.mat -> unit

ormqr ?side ?trans ?m ?n ?k ?work ~tau ?ar ?ac a ?cr ?cc c see LAPACK documentation!

side : default = `L
trans : default = `N
m : default = available number of rows in matrix a
n : default = available number of columns in matrix a
k : default = available number of elements in vector tau
val gecon_min_lwork : int -> int

gecon_min_lwork n

val gecon_min_liwork : int -> int

gecon_min_liwork n

val gecon : ?n:int ->
?norm:Lacaml_common.norm2 ->
?anorm:float ->
?work:Lacaml_float32.vec ->
?iwork:Lacaml_common.int32_vec ->
?ar:int -> ?ac:int -> Lacaml_float32.mat -> float

gecon ?n ?norm ?anorm ?work ?rwork ?ar ?ac a

n : default = available number of columns of matrix a
norm : default = 1-norm
anorm : default = norm of the matrix a as returned by lange
work : default = automatically allocated workspace
iwork : default = automatically allocated workspace
ar : default = 1
ac : default = 1
val sycon_min_lwork : int -> int

sycon_min_lwork n

val sycon_min_liwork : int -> int

sycon_min_liwork n

val sycon : ?n:int ->
?up:bool ->
?ipiv:Lacaml_common.int32_vec ->
?anorm:float ->
?work:Lacaml_float32.vec ->
?iwork:Lacaml_common.int32_vec ->
?ar:int -> ?ac:int -> Lacaml_float32.mat -> float

sycon ?n ?up ?ipiv ?anorm ?work ?iwork ?ar ?ac a

n : default = available number of columns of matrix a
up : default = upper triangle of the factorization of a is stored
ipiv : default = vec of length n
anorm : default = 1-norm of the matrix a as returned by lange
work : default = automatically allocated workspace
iwork : default = automatically allocated workspace
val pocon_min_lwork : int -> int

pocon_min_lwork n

val pocon_min_liwork : int -> int

pocon_min_liwork n

val pocon : ?n:int ->
?up:bool ->
?anorm:float ->
?work:Lacaml_float32.vec ->
?iwork:Lacaml_common.int32_vec ->
?ar:int -> ?ac:int -> Lacaml_float32.mat -> float

pocon ?n ?up ?anorm ?work ?iwork ?ar ?ac a

n : default = available number of columns of matrix a
up : default = upper triangle of Cholesky factorization of a is stored
anorm : default = 1-norm of the matrix a as returned by lange
work : default = automatically allocated workspace
iwork : default = automatically allocated workspace
Least squares (expert drivers)
val gelsy_min_lwork : m:int -> n:int -> nrhs:int -> int

gelsy_min_lwork ~m ~n ~nrhs

val gelsy_opt_lwork : ?m:int ->
?n:int ->
?ar:int ->
?ac:int ->
Lacaml_float32.mat ->
?nrhs:int -> ?br:int -> ?bc:int -> Lacaml_float32.mat -> int

gelsy_opt_lwork ?m ?n ?ar ?ac a ?nrhs ?br ?bc b

m : default = available number of rows in matrix a
n : default = available number of columns in matrix a
nrhs : default = available number of columns in matrix b
val gelsy : ?m:int ->
?n:int ->
?ar:int ->
?ac:int ->
Lacaml_float32.mat ->
?rcond:float ->
?jpvt:Lacaml_common.int32_vec ->
?work:Lacaml_float32.vec ->
?nrhs:int -> ?br:int -> ?bc:int -> Lacaml_float32.mat -> int

gelsy ?m ?n ?ar ?ac a ?rcond ?jpvt ?ofswork ?work ?nrhs b see LAPACK documentation!

m : default = available number of rows in matrix a
n : default = available number of columns of matrix a
rcond : default = (-1) => machine precision
jpvt : default = vec of length n
work : default = vec of optimum length (-> gelsy_opt_lwork)
nrhs : default = available number of columns in matrix b
val gelsd_min_lwork : m:int -> n:int -> nrhs:int -> int

gelsd_min_lwork ~m ~n ~nrhs

val gelsd_opt_lwork : ?m:int ->
?n:int ->
?ar:int ->
?ac:int ->
Lacaml_float32.mat ->
?nrhs:int -> ?br:int -> ?bc:int -> Lacaml_float32.mat -> int

gelsd_opt_lwork ?m ?n ?ar ?ac a ?nrhs b

m : default = available number of rows in matrix a
n : default = available number of columns in matrix a
nrhs : default = available number of columns in matrix b
val gelsd_min_iwork : int -> int -> int

gelsd_min_iwork m n

val gelsd : ?m:int ->
?n:int ->
?rcond:float ->
?ofss:int ->
?s:Lacaml_float32.vec ->
?work:Lacaml_float32.vec ->
?iwork:Lacaml_float32.vec ->
?ar:int ->
?ac:int ->
Lacaml_float32.mat ->
?nrhs:int -> ?br:int -> ?bc:int -> Lacaml_float32.mat -> int

gelsd ?m ?n ?rcond ?ofss ?s ?ofswork ?work ?ar ?ac a ?nrhs b see LAPACK documentation!

m : default = available number of rows in matrix a
n : default = available number of columns of matrix a
rcond : default = (-1) => machine precision
ofss : default = 1 or ignored if s is not given
s : default = vec of length min rows cols
work : default = vec of optimum length (-> gelsd_opt_lwork)
iwork : default = vec of optimum (= minimum) length
nrhs : default = available number of columns in matrix b
val gelss_min_lwork : m:int -> n:int -> nrhs:int -> int

gelss_min_lwork ~m ~n ~nrhs

val gelss_opt_lwork : ?ar:int ->
?ac:int ->
Lacaml_float32.mat ->
?m:int ->
?n:int -> ?nrhs:int -> ?br:int -> ?bc:int -> Lacaml_float32.mat -> int

gelss_opt_lwork ?ar ?ac a ?m ?n ?nrhs ?br ?bc b

m : default = available number of rows in matrix a
n : default = available number of columns in matrix a
nrhs : default = available number of columns in matrix b
val gelss : ?m:int ->
?n:int ->
?rcond:float ->
?ofss:int ->
?s:Lacaml_float32.vec ->
?work:Lacaml_float32.vec ->
?ar:int ->
?ac:int ->
Lacaml_float32.mat ->
?nrhs:int -> ?br:int -> ?bc:int -> Lacaml_float32.mat -> int

gelss ?m ?n ?rcond ?ofss ?s ?ofswork ?work ?ar ?ac a ?nrhs ?br ?bc b see LAPACK documentation!

m : default = available number of rows in matrix a
n : default = available number of columns of matrix a
rcond : default = (-1) => machine precision
ofss : default = 1 or ignored if s is not given
s : default = vec of length min m n
work : default = vec of optimum length (-> gelss_opt_lwork)
nrhs : default = available number of columns in matrix b
General Schur factorization
val gees : ?n:int ->
?jobvs:Lacaml_common.schur_vectors ->
?sort:Lacaml_common.eigen_value_sort ->
?wr:Lacaml_float32.vec ->
?wi:Lacaml_float32.vec ->
?vsr:int ->
?vsc:int ->
?vs:Lacaml_float32.mat ->
?work:Lacaml_float32.vec ->
?ar:int ->
?ac:int ->
Lacaml_float32.mat ->
int * Lacaml_float32.vec * Lacaml_float32.vec * Lacaml_float32.mat

gees ?n ?jobvs ?sort ?w ?vsr ?vsc ?vs ?work ?ar ?ac a See gees-function for details about arguments.

General SVD routines
val gesvd_min_lwork : m:int -> n:int -> int

gesvd_min_lwork ~m ~n

val gesvd_opt_lwork : ?m:int ->
?n:int ->
?jobu:Lacaml_common.svd_job ->
?jobvt:Lacaml_common.svd_job ->
?s:Lacaml_float32.vec ->
?ur:int ->
?uc:int ->
?u:Lacaml_float32.mat ->
?vtr:int ->
?vtc:int ->
?vt:Lacaml_float32.mat -> ?ar:int -> ?ac:int -> Lacaml_float32.mat -> int
val gesvd : ?m:int ->
?n:int ->
?jobu:Lacaml_common.svd_job ->
?jobvt:Lacaml_common.svd_job ->
?s:Lacaml_float32.vec ->
?ur:int ->
?uc:int ->
?u:Lacaml_float32.mat ->
?vtr:int ->
?vtc:int ->
?vt:Lacaml_float32.mat ->
?work:Lacaml_float32.vec ->
?ar:int ->
?ac:int ->
Lacaml_float32.mat ->
Lacaml_float32.vec * Lacaml_float32.mat * Lacaml_float32.mat
val gesdd_liwork : m:int -> n:int -> int
val gesdd_min_lwork : ?jobz:Lacaml_common.svd_job -> m:int -> n:int -> unit -> int

gesdd_min_lwork ?jobz ~m ~n

val gesdd_opt_lwork : ?m:int ->
?n:int ->
?jobz:Lacaml_common.svd_job ->
?s:Lacaml_float32.vec ->
?ur:int ->
?uc:int ->
?u:Lacaml_float32.mat ->
?vtr:int ->
?vtc:int ->
?vt:Lacaml_float32.mat ->
?iwork:Lacaml_common.int32_vec ->
?ar:int -> ?ac:int -> Lacaml_float32.mat -> int
val gesdd : ?m:int ->
?n:int ->
?jobz:Lacaml_common.svd_job ->
?s:Lacaml_float32.vec ->
?ur:int ->
?uc:int ->
?u:Lacaml_float32.mat ->
?vtr:int ->
?vtc:int ->
?vt:Lacaml_float32.mat ->
?work:Lacaml_float32.vec ->
?iwork:Lacaml_common.int32_vec ->
?ar:int ->
?ac:int ->
Lacaml_float32.mat ->
Lacaml_float32.vec * Lacaml_float32.mat * Lacaml_float32.mat
General eigenvalue problem (simple drivers)
val geev_min_lwork : ?vectors:bool -> int -> int

geev_min_lwork vectors n

vectors : default = true
val geev_opt_lwork : ?n:int ->
?vlr:int ->
?vlc:int ->
?vl:Lacaml_float32.mat option ->
?vrr:int ->
?vrc:int ->
?vr:Lacaml_float32.mat option ->
?ofswr:int ->
?wr:Lacaml_float32.vec ->
?ofswi:int ->
?wi:Lacaml_float32.vec -> ?ar:int -> ?ac:int -> Lacaml_float32.mat -> int

geev_opt_lwork ?n ?vlr ?vlc ?vl ?vrr ?vrc ?vr ?ofswr wr ?ofswi wi ?ar ?ac a See geev-function for details about arguments.

val geev : ?n:int ->
?work:Lacaml_float32.vec ->
?vlr:int ->
?vlc:int ->
?vl:Lacaml_float32.mat option ->
?vrr:int ->
?vrc:int ->
?vr:Lacaml_float32.mat option ->
?ofswr:int ->
?wr:Lacaml_float32.vec ->
?ofswi:int ->
?wi:Lacaml_float32.vec ->
?ar:int ->
?ac:int ->
Lacaml_float32.mat ->
Lacaml_float32.mat * Lacaml_float32.vec * Lacaml_float32.vec *
Lacaml_float32.mat

geev ?work ?n ?vlr ?vlc ?vl ?vrr ?vrc ?vr ?ofswr wr ?ofswi wi ?ar ?ac a

n : default = available number of columns of matrix a
work : default = automatically allocated workspace
vl : default = Automatically allocated left eigenvectors. Pass None if you do not want to compute them, Some lv if you want to provide the storage. You can set vlr, vlc in the last case. (See LAPACK GEEV docs for details about storage of complex eigenvectors)
vr : default = Automatically allocated right eigenvectors. Pass None if you do not want to compute them, Some rv if you want to provide the storage. You can set vrr, vrc in the last case.
wr : default = vector of size n; real components of the eigenvalues
wi : default = vector of size n; imaginary components of the eigenvalues
Symmetric-matrix eigenvalue and singular value problems (simple drivers)
val syev_min_lwork : int -> int

syev_min_lwork n

val syev_opt_lwork : ?n:int ->
?vectors:bool -> ?up:bool -> ?ar:int -> ?ac:int -> Lacaml_float32.mat -> int

syev_opt_lwork ?n ?vectors ?up ?ar ?ac a

n : default = available number of columns of matrix a
vectors : default = false, i.e. eigenvectors are not computed
up : default = true, i.e. upper triangle of a is stored
val syev : ?n:int ->
?vectors:bool ->
?up:bool ->
?work:Lacaml_float32.vec ->
?ofsw:int ->
?w:Lacaml_float32.vec ->
?ar:int -> ?ac:int -> Lacaml_float32.mat -> Lacaml_float32.vec

syev ?n ?vectors ?up ?ofswork ?work ?ofsw ?w ?ar ?ac a computes all eigenvalues and, optionally, eigenvectors of the real symmetric matrix a.

n : default = available number of columns of matrix a
vectors : default = false i.e, eigenvectors are not computed
up : default = true i.e., upper triangle of a is stored
work : default = vec of optimum length (-> Lacaml_S.syev_opt_lwork)
ofsw : default = 1 or ignored if w is not given
w : default = vec of length n
val syevd_min_lwork : vectors:bool -> int -> int

syevd_min_lwork vectors n

val syevd_min_liwork : vectors:bool -> int -> int

syevd_min_liwork vectors n

val syevd_opt_lwork : ?n:int ->
?vectors:bool -> ?up:bool -> ?ar:int -> ?ac:int -> Lacaml_float32.mat -> int

syevd_opt_lwork ?n ?vectors ?up ?ar ?ac a

n : default = available number of columns of matrix a
vectors : default = false, i.e. eigenvectors are not computed
up : default = true, i.e. upper triangle of a is stored
val syevd_opt_liwork : ?n:int ->
?vectors:bool -> ?up:bool -> ?ar:int -> ?ac:int -> Lacaml_float32.mat -> int

syevd_opt_liwork ?n ?vectors ?up ?ar ?ac a

n : default = available number of columns of matrix a
vectors : default = false, i.e. eigenvectors are not computed
up : default = true, i.e. upper triangle of a is stored
val syevd_opt_l_li_work : ?n:int ->
?vectors:bool ->
?up:bool -> ?ar:int -> ?ac:int -> Lacaml_float32.mat -> int * int

syevd_opt_l_li_iwork ?n ?vectors ?up ?ar ?ac a

n : default = available number of columns of matrix a
vectors : default = false, i.e. eigenvectors are not computed
up : default = true, i.e. upper triangle of a is stored
val syevd : ?n:int ->
?vectors:bool ->
?up:bool ->
?work:Lacaml_float32.vec ->
?iwork:Lacaml_common.int32_vec ->
?ofsw:int ->
?w:Lacaml_float32.vec ->
?ar:int -> ?ac:int -> Lacaml_float32.mat -> Lacaml_float32.vec

syevd ?n ?vectors ?up ?ofswork ?work ?iwork ?ofsw ?w ?ar ?ac a computes all eigenvalues and, optionally, eigenvectors of the real symmetric matrix a. If eigenvectors are desired, it uses a divide and conquer algorithm.

n : default = available number of columns of matrix a
vectors : default = false i.e, eigenvectors are not computed
up : default = true i.e., upper triangle of a is stored
work : default = vec of optimum length (-> Lacaml_S.syev_opt_lwork)
iwork : default = int32_vec of optimum length (-> Lacaml_S.syevd_opt_liwork)
ofsw : default = 1 or ignored if w is not given
w : default = vec of length n
val sbev_min_lwork : int -> int

sbev_min_lwork n

val sbev : ?n:int ->
?kd:int ->
?zr:int ->
?zc:int ->
?z:Lacaml_float32.mat ->
?up:bool ->
?work:Lacaml_float32.vec ->
?ofsw:int ->
?w:Lacaml_float32.vec ->
?abr:int -> ?abc:int -> Lacaml_float32.mat -> Lacaml_float32.vec

sbev ?n ?vectors ?zr ?zc ?z ?up ?ofswork ?work ?ofsw ?w ?abr ?abc ab computes all the eigenvalues and, optionally, eigenvectors of the real symmetric band matrix ab.

n : default = available number of columns of matrix ab
kd : default = number of rows in matrix ab - 1
z : matrix to contain the orthonormal eigenvectors of ab, the i-th column of z holding the eigenvector associated with w.{i}. default = None i.e, eigenvectors are not computed
up : default = true i.e., upper triangle of the matrix is stored
work : default = vec of minimal length (-> Lacaml_S.sbev_min_lwork)
ofsw : default = 1 or ignored if w is not given
w : default = vec of length n
abr : default = 1
abc : default = 1
Symmetric-matrix eigenvalue and singular value problems (expert & RRR drivers)
val syevr_min_lwork : int -> int

syevr_min_lwork n

val syevr_min_liwork : int -> int

syevr_min_liwork n

val syevr_opt_lwork : ?n:int ->
?vectors:bool ->
?range:[ `A | `I of int * int | `V of float * float ] ->
?up:bool -> ?abstol:float -> ?ar:int -> ?ac:int -> Lacaml_float32.mat -> int

syevr_opt_lwork ?n ?vectors ?range ?up ?abstol ?ar ?ac a

n : default = available number of columns of matrix a
vectors : default = false, i.e. eigenvectors are not computed
up : default = true, i.e. upper triangle of a is stored
val syevr_opt_liwork : ?n:int ->
?vectors:bool ->
?range:[ `A | `I of int * int | `V of float * float ] ->
?up:bool -> ?abstol:float -> ?ar:int -> ?ac:int -> Lacaml_float32.mat -> int

syevr_opt_liwork ?n ?vectors ?range ?up ?abstol ?ar ?ac a

n : default = available number of columns of matrix a
vectors : default = false, i.e. eigenvectors are not computed
up : default = true, i.e. upper triangle of a is stored
val syevr_opt_l_li_work : ?n:int ->
?vectors:bool ->
?range:[ `A | `I of int * int | `V of float * float ] ->
?up:bool ->
?abstol:float -> ?ar:int -> ?ac:int -> Lacaml_float32.mat -> int * int

syevr_opt_l_li_iwork ?n ?vectors ?range ?up ?abstol ?ar ?ac a

n : default = available number of columns of matrix a
vectors : default = false, i.e. eigenvectors are not computed
up : default = true, i.e. upper triangle of a is stored
val syevr : ?n:int ->
?vectors:bool ->
?range:[ `A | `I of int * int | `V of float * float ] ->
?up:bool ->
?abstol:float ->
?work:Lacaml_float32.vec ->
?iwork:Lacaml_common.int32_vec ->
?ofsw:int ->
?w:Lacaml_float32.vec ->
?zr:int ->
?zc:int ->
?z:Lacaml_float32.mat ->
?isuppz:Lacaml_common.int32_vec ->
?ar:int ->
?ac:int ->
Lacaml_float32.mat ->
int * Lacaml_float32.vec * Lacaml_float32.mat * Lacaml_common.int32_vec

syevr ?n ?vectors ?range ?up ?abstol ?work ?iwork ?ofsw ?w ?zr ?zc ?z ?isuppz ?ar ?ac a range is either `A for computing all eigenpairs, `V (vl, vu) defines the lower and upper range of computed eigenvalues, `I (il, iu) defines the indexes of the computed eigenpairs, which are sorted in ascending order.

n : default = available number of columns of matrix a
vectors : default = false i.e, eigenvectors are not computed
range : default = `A
up : default = true i.e., upper triangle of a is stored
abstol : default = result of calling lamch `S
work : default = vec of optimum length (-> Lacaml_S.syev_opt_lwork)
iwork : default = int32_vec of optimum length (-> Lacaml_S.syevr_opt_liwork)
ofsw : default = 1 or ignored if w is not given
w : default = vec of length n
zr : default = 1
zc : default = 1
z : default = matrix with minimal required dimension
isuppz : default = int32_vec with minimal required dimension
ar : default = 1
ac : default = 1
val sygv_opt_lwork : ?n:int ->
?vectors:bool ->
?up:bool ->
?itype:[ `AB | `A_B | `BA ] ->
?ar:int ->
?ac:int ->
Lacaml_float32.mat -> ?br:int -> ?bc:int -> Lacaml_float32.mat -> int

sygv_opt_lwork ?n ?vectors ?up ?ar ?ac a ?br ?bc b

n : default = available number of columns of matrix a
vectors : default = false, i.e. eigenvectors are not computed
up : default = true, i.e. upper triangle of a is stored
itype : specifies the problem type to be solved:
val sygv : ?n:int ->
?vectors:bool ->
?up:bool ->
?work:Lacaml_float32.vec ->
?ofsw:int ->
?w:Lacaml_float32.vec ->
?itype:[ `AB | `A_B | `BA ] ->
?ar:int ->
?ac:int ->
Lacaml_float32.mat ->
?br:int -> ?bc:int -> Lacaml_float32.mat -> Lacaml_float32.vec

sygv ?n ?vectors ?up ?ofswork ?work ?ofsw ?w ?ar ?ac a computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, of the form a*x=(lambda)*b*x, a*b*x=(lambda)*x, or b*a*x=(lambda)*x. Here a and b are assumed to be symmetric and b is also positive definite.

n : default = available number of columns of matrix a
vectors : default = false i.e, eigenvectors are not computed
up : default = true i.e., upper triangle of a is stored
work : default = vec of optimum length (-> Lacaml_S.sygv_opt_lwork)
ofsw : default = 1 or ignored if w is not given
w : default = vec of length n
itype : specifies the problem type to be solved:
val sbgv : ?n:int ->
?ka:int ->
?kb:int ->
?zr:int ->
?zc:int ->
?z:Lacaml_float32.mat ->
?up:bool ->
?work:Lacaml_float32.vec ->
?ofsw:int ->
?w:Lacaml_float32.vec ->
?ar:int ->
?ac:int ->
Lacaml_float32.mat ->
?br:int -> ?bc:int -> Lacaml_float32.mat -> Lacaml_float32.vec

sbgv ?n ?ka ?kb ?zr ?zc ?z ?up ?work ?ofsw ?w ?ar ?ac a ?br ?bc b computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite banded eigenproblem, of the form a*x=(lambda)*b*x. Here a and b are assumed to be symmetric and banded, and b is also positive definite.

n : default = available number of columns of matrix a
ka : the number of superdiagonals (or subdiagonals if up = false) of the matrix a. Default = dim1 a - ar.
kb : same as ka but for the matrix b.
z : default = None i.e, eigenvectors are not computed
up : default = true i.e., upper triangle of a is stored
work : default = vec of optimum length (3 * n)
ofsw : default = 1 or ignored if w is not given
w : default = vec of length n
BLAS-1 interface
val swap : ?n:int ->
?ofsx:int ->
?incx:int ->
x:Lacaml_float32.vec -> ?ofsy:int -> ?incy:int -> Lacaml_float32.vec -> unit

swap ?n ?ofsx ?incx ~x ?ofsy ?incy y see BLAS documentation!

n : default = greater n s.t. ofsx+(n-1)(abs incx) <= dim x
ofsx : default = 1
incx : default = 1
ofsy : default = 1
incy : default = 1
val scal : ?n:int ->
Lacaml_float32.num_type ->
?ofsx:int -> ?incx:int -> Lacaml_float32.vec -> unit

scal ?n alpha ?ofsx ?incx x see BLAS documentation!

n : default = greater n s.t. ofsx+(n-1)(abs incx) <= dim x
ofsx : default = 1
incx : default = 1
val copy : ?n:int ->
?ofsy:int ->
?incy:int ->
?y:Lacaml_float32.vec ->
?ofsx:int -> ?incx:int -> Lacaml_float32.vec -> Lacaml_float32.vec

copy ?n ?ofsy ?incy ?y ?ofsx ?incx x see BLAS documentation!

n : default = greater n s.t. ofsx+(n-1)(abs incx) <= dim x
ofsy : default = 1
incy : default = 1
y : default = new vector with ofsy+(n-1)(abs incy) rows
ofsx : default = 1
incx : default = 1
val nrm2 : ?n:int -> ?ofsx:int -> ?incx:int -> Lacaml_float32.vec -> float

nrm2 ?n ?ofsx ?incx x see BLAS documentation!

n : default = greater n s.t. ofsx+(n-1)(abs incx) <= dim x
ofsx : default = 1
incx : default = 1
val axpy : ?alpha:Lacaml_float32.num_type ->
?n:int ->
?ofsx:int ->
?incx:int ->
Lacaml_float32.vec -> ?ofsy:int -> ?incy:int -> Lacaml_float32.vec -> unit

axpy ?alpha ?n ?ofsx ?incx x ?ofsy ?incy y see BLAS documentation!

alpha : default = { re = 1.; im = 0. }
n : default = greater n s.t. ofsx+(n-1)(abs incx) <= dim x
ofsx : default = 1
incx : default = 1
ofsy : default = 1
incy : default = 1
val iamax : ?n:int -> ?ofsx:int -> ?incx:int -> Lacaml_float32.vec -> int

iamax ?n ?ofsx ?incx x see BLAS documentation!

n : default = greater n s.t. ofsx+(n-1)(abs incx) <= dim x
ofsx : default = 1
incx : default = 1
val amax : ?n:int ->
?ofsx:int -> ?incx:int -> Lacaml_float32.vec -> Lacaml_float32.num_type

amax ?n ?ofsx ?incx x

n : default = greater n s.t. ofsx+(n-1)(abs incx) <= dim x
ofsx : default = 1
incx : default = 1
BLAS-2 interface
val gemv : ?m:int ->
?n:int ->
?beta:Lacaml_float32.num_type ->
?ofsy:int ->
?incy:int ->
?y:Lacaml_float32.vec ->
?trans:Lacaml_float32.trans3 ->
?alpha:Lacaml_float32.num_type ->
?ar:int ->
?ac:int ->
Lacaml_float32.mat ->
?ofsx:int -> ?incx:int -> Lacaml_float32.vec -> Lacaml_float32.vec

gemv ?m ?n ?beta ?ofsy ?incy ?y ?trans ?alpha ?ar ?ac a ?ofsx ?incx x see BLAS documentation! BEWARE that the 1988 BLAS-2 specification mandates that this function has no effect when n=0 while the mathematically expected behabior is y ← beta * y.

m : default = number of available rows in matrix a
n : default = available columns in matrix a
beta : default = { re = 0.; im = 0. }
ofsy : default = 1
incy : default = 1
y : default = vector with minimal required length (see BLAS)
trans : default = `N
alpha : default = { re = 1.; im = 0. }
ar : default = 1
ac : default = 1
ofsx : default = 1
incx : default = 1
val gbmv : ?m:int ->
?n:int ->
?beta:Lacaml_float32.num_type ->
?ofsy:int ->
?incy:int ->
?y:Lacaml_float32.vec ->
?trans:Lacaml_float32.trans3 ->
?alpha:Lacaml_float32.num_type ->
?ar:int ->
?ac:int ->
Lacaml_float32.mat ->
int ->
int -> ?ofsx:int -> ?incx:int -> Lacaml_float32.vec -> Lacaml_float32.vec

gbmv ?m ?n ?beta ?ofsy ?incy ?y ?trans ?alpha ?ar ?ac a kl ku ?ofsx ?incx x see BLAS documentation!

m : default = same as n (i.e., a is a square matrix)
n : default = available number of columns in matrix a
beta : default = { re = 0.; im = 0. }
ofsy : default = 1
incy : default = 1
y : default = vector with minimal required length (see BLAS)
trans : default = `N
alpha : default = { re = 1.; im = 0. }
ar : default = 1
ac : default = 1
ofsx : default = 1
incx : default = 1
val symv : ?n:int ->
?beta:Lacaml_float32.num_type ->
?ofsy:int ->
?incy:int ->
?y:Lacaml_float32.vec ->
?up:bool ->
?alpha:Lacaml_float32.num_type ->
?ar:int ->
?ac:int ->
Lacaml_float32.mat ->
?ofsx:int -> ?incx:int -> Lacaml_float32.vec -> Lacaml_float32.vec

symv ?n ?beta ?ofsy ?incy ?y ?up ?alpha ?ar ?ac a ?ofsx ?incx x see BLAS documentation!

n : default = dimension of symmetric matrix a
beta : default = { re = 0.; im = 0. }
ofsy : default = 1
incy : default = 1
y : default = vector with minimal required length (see BLAS)
up : default = true (upper triangular portion of a is accessed)
alpha : default = { re = 1.; im = 0. }
ar : default = 1
ac : default = 1
ofsx : default = 1
incx : default = 1
val trmv : ?n:int ->
?trans:Lacaml_float32.trans3 ->
?diag:Lacaml_common.diag ->
?up:bool ->
?ar:int ->
?ac:int ->
Lacaml_float32.mat -> ?ofsx:int -> ?incx:int -> Lacaml_float32.vec -> unit

trmv ?n ?trans ?diag ?up ?ar ?ac a ?ofsx ?incx x see BLAS documentation!

n : default = dimension of triangular matrix a
trans : default = `N
diag : default = false (not a unit triangular matrix)
up : default = true (upper triangular portion of a is accessed)
ar : default = 1
ac : default = 1
ofsx : default = 1
incx : default = 1
val trsv : ?n:int ->
?trans:Lacaml_float32.trans3 ->
?diag:Lacaml_common.diag ->
?up:bool ->
?ar:int ->
?ac:int ->
Lacaml_float32.mat -> ?ofsx:int -> ?incx:int -> Lacaml_float32.vec -> unit

trsv ?n ?trans ?diag ?up ?ar ?ac a ?ofsx ?incx x see BLAS documentation!

n : default = dimension of triangular matrix a
trans : default = `N
diag : default = false (not a unit triangular matrix)
up : default = true (upper triangular portion of a is accessed)
ar : default = 1
ac : default = 1
ofsx : default = 1
incx : default = 1
val tpmv : ?n:int ->
?trans:Lacaml_float32.trans3 ->
?diag:Lacaml_common.diag ->
?up:bool ->
?ofsap:int ->
Lacaml_float32.vec -> ?ofsx:int -> ?incx:int -> Lacaml_float32.vec -> unit

tpmv ?n ?trans ?diag ?up ?ofsap ap ?ofsx ?incx x see BLAS documentation!

n : default = dimension of packed triangular matrix ap
trans : default = `N
diag : default = false (not a unit triangular matrix)
up : default = true (upper triangular portion of ap is accessed)
ofsap : default = 1
ofsx : default = 1
incx : default = 1
val tpsv : ?n:int ->
?trans:Lacaml_float32.trans3 ->
?diag:Lacaml_common.diag ->
?up:bool ->
?ofsap:int ->
Lacaml_float32.vec -> ?ofsx:int -> ?incx:int -> Lacaml_float32.vec -> unit

tpsv ?n ?trans ?diag ?up ?ofsap ap ?ofsx ?incx x see BLAS documentation!

n : default = dimension of packed triangular matrix ap
trans : default = `N
diag : default = false (not a unit triangular matrix)
up : default = true (upper triangular portion of ap is accessed)
ofsap : default = 1
ofsx : default = 1
incx : default = 1
BLAS-3 interface
val gemm : ?m:int ->
?n:int ->
?k:int ->
?beta:Lacaml_float32.num_type ->
?cr:int ->
?cc:int ->
?c:Lacaml_float32.mat ->
?transa:Lacaml_float32.trans3 ->
?alpha:Lacaml_float32.num_type ->
?ar:int ->
?ac:int ->
Lacaml_float32.mat ->
?transb:Lacaml_float32.trans3 ->
?br:int -> ?bc:int -> Lacaml_float32.mat -> Lacaml_float32.mat

gemm ?m ?n ?k ?beta ?cr ?cc ?c ?transa ?alpha ?ar ?ac a ?transb ?br ?bc b see BLAS documentation!

m : default = number of rows of a (or tr a) and c
n : default = number of columns of b (or tr b) and c
k : default = number of columns of a (or tr a) and number of rows of b (or tr b)
beta : default = { re = 0.; im = 0. }
cr : default = 1
cc : default = 1
c : default = matrix with minimal required dimension
transa : default = `N
alpha : default = { re = 1.; im = 0. }
ar : default = 1
ac : default = 1
transb : default = `N
br : default = 1
bc : default = 1
val symm : ?m:int ->
?n:int ->
?side:Lacaml_common.side ->
?up:bool ->
?beta:Lacaml_float32.num_type ->
?cr:int ->
?cc:int ->
?c:Lacaml_float32.mat ->
?alpha:Lacaml_float32.num_type ->
?ar:int ->
?ac:int ->
Lacaml_float32.mat ->
?br:int -> ?bc:int -> Lacaml_float32.mat -> Lacaml_float32.mat

symm ?m ?n ?side ?up ?beta ?cr ?cc ?c ?alpha ?ar ?ac a ?br ?bc b see BLAS documentation!

m : default = number of rows of c
n : default = number of columns of c
side : default = `L (left - multiplication is ab)
up : default = true (upper triangular portion of a is accessed)
beta : default = { re = 0.; im = 0. }
cr : default = 1
cc : default = 1
c : default = matrix with minimal required dimension
alpha : default = { re = 1.; im = 0. }
ar : default = 1
ac : default = 1
br : default = 1
bc : default = 1
val trmm : ?m:int ->
?n:int ->
?side:Lacaml_common.side ->
?up:bool ->
?transa:Lacaml_float32.trans3 ->
?diag:Lacaml_common.diag ->
?alpha:Lacaml_float32.num_type ->
?ar:int ->
?ac:int ->
a:Lacaml_float32.mat -> ?br:int -> ?bc:int -> Lacaml_float32.mat -> unit

trmm ?m ?n ?side ?up ?transa ?diag ?alpha ?ar ?ac ~a ?br ?bc b see BLAS documentation!

m : default = number of rows of b
n : default = number of columns of b
side : default = `L (left - multiplication is ab)
up : default = true (upper triangular portion of a is accessed)
transa : default = `N
diag : default = `N (non-unit)
alpha : default = { re = 1.; im = 0. }
ar : default = 1
ac : default = 1
br : default = 1
bc : default = 1
val trsm : ?m:int ->
?n:int ->
?side:Lacaml_common.side ->
?up:bool ->
?transa:Lacaml_float32.trans3 ->
?diag:Lacaml_common.diag ->
?alpha:Lacaml_float32.num_type ->
?ar:int ->
?ac:int ->
a:Lacaml_float32.mat -> ?br:int -> ?bc:int -> Lacaml_float32.mat -> unit

trsm ?m ?n ?side ?up ?transa ?diag ?alpha ?ar ?ac ~a ?br ?bc b see BLAS documentation!

m : default = number of rows of b
n : default = number of columns of b
side : default = `L (left - multiplication is ab)
up : default = true (upper triangular portion of a is accessed)
transa : default = `N
diag : default = `N (non-unit)
alpha : default = { re = 1.; im = 0. }
ar : default = 1
ac : default = 1
br : default = 1
bc : default = 1
val syrk : ?n:int ->
?k:int ->
?up:bool ->
?beta:Lacaml_float32.num_type ->
?cr:int ->
?cc:int ->
?c:Lacaml_float32.mat ->
?trans:Lacaml_common.trans2 ->
?alpha:Lacaml_float32.num_type ->
?ar:int -> ?ac:int -> Lacaml_float32.mat -> Lacaml_float32.mat

syrk ?n ?k ?up ?beta ?cr ?cc ?c ?trans ?alpha ?ar ?ac a see BLAS documentation!

n : default = number of rows of a (or a'), c
k : default = number of columns of a (or a')
up : default = true (upper triangular portion of c is accessed)
beta : default = { re = 0.; im = 0. }
cr : default = 1
cc : default = 1
c : default = matrix with minimal required dimension
trans : default = `N
alpha : default = { re = 1.; im = 0. }
ar : default = 1
ac : default = 1
val syr2k : ?n:int ->
?k:int ->
?up:bool ->
?beta:Lacaml_float32.num_type ->
?cr:int ->
?cc:int ->
?c:Lacaml_float32.mat ->
?trans:Lacaml_common.trans2 ->
?alpha:Lacaml_float32.num_type ->
?ar:int ->
?ac:int ->
Lacaml_float32.mat ->
?br:int -> ?bc:int -> Lacaml_float32.mat -> Lacaml_float32.mat

syr2k ?n ?k ?up ?beta ?cr ?cc ?c ?trans ?alpha ?ar ?ac a ?br ?bc b see BLAS documentation!

n : default = number of rows of a (or a'), c
k : default = number of columns of a (or a')
up : default = true (upper triangular portion of c is accessed)
beta : default = { re = 0.; im = 0. }
cr : default = 1
cc : default = 1
c : default = matrix with minimal required dimension
trans : default = `N
alpha : default = { re = 1.; im = 0. }
ar : default = 1
ac : default = 1
br : default = 1
bc : default = 1
LAPACK interface
Auxiliary routines
val lacpy : ?uplo:[ `L | `U ] ->
?m:int ->
?n:int ->
?br:int ->
?bc:int ->
?b:Lacaml_float32.mat ->
?ar:int -> ?ac:int -> Lacaml_float32.mat -> Lacaml_float32.mat

lacpy ?uplo ?m ?n ?br ?bc ?b ?ar ?ac a copy a (triangular) (sub-)matrix a (to an optional (sub-)matrix b).

uplo : default = whole matrix
val lassq : ?n:int ->
?scale:float ->
?sumsq:float -> ?ofsx:int -> ?incx:int -> Lacaml_float32.vec -> float * float

lassq ?n ?ofsx ?incx ?scale ?sumsq

n : default = greater n s.t. ofsx+(n-1)(abs incx) <= dim x
scale : default = 0.
sumsq : default = 1.
ofsx : default = 1
incx : default = 1
val larnv : ?idist:[ `Normal | `Uniform0 | `Uniform1 ] ->
?iseed:Lacaml_common.int32_vec ->
?n:int -> ?ofsx:int -> ?x:Lacaml_float32.vec -> unit -> Lacaml_float32.vec

larnv ?idist ?iseed ?n ?ofsx ?x ()

idist : default = `Normal
iseed : default = integer vector of size 4 with all ones.
n : default = dim x - ofsx + 1 if x is provided, 1 otherwise.
ofsx : default = 1
x : default = vector of length ofsx - 1 + n if n is provided.
val lange_min_lwork : int -> Lacaml_common.norm4 -> int

lange_min_lwork m norm

val lange : ?m:int ->
?n:int ->
?norm:Lacaml_common.norm4 ->
?work:Lacaml_float32.rvec ->
?ar:int -> ?ac:int -> Lacaml_float32.mat -> float

lange ?m ?n ?norm ?work ?ar ?ac a

m : default = number of rows of matrix a
n : default = number of columns of matrix a
norm : default = `O
work : default = allocated work space for norm `I
ar : default = 1
ac : default = 1
val lauum : ?up:bool -> ?n:int -> ?ar:int -> ?ac:int -> Lacaml_float32.mat -> unit

lauum ?up ?n ?ar ?ac a computes the product U * U**T or L**T * L, where the triangular factor U or L is stored in the upper or lower triangular part of the array a. The upper or lower part of a is overwritten.

up : default = true
n : default = minimum of available number of rows/columns in matrix a
ar : default = 1
ac : default = 1
Linear equations (computational routines)
val getrf : ?m:int ->
?n:int ->
?ipiv:Lacaml_common.int32_vec ->
?ar:int -> ?ac:int -> Lacaml_float32.mat -> Lacaml_common.int32_vec

getrf ?m ?n ?ipiv ?ar ?ac a computes an LU factorization of a general m-by-n matrix a using partial pivoting with row interchanges. See LAPACK documentation.

m : default = number of rows in matrix a
n : default = number of columns in matrix a
ipiv : = vec of length min(m, n)
ar : default = 1
ac : default = 1
val getrs : ?n:int ->
?ipiv:Lacaml_common.int32_vec ->
?trans:Lacaml_float32.trans3 ->
?ar:int ->
?ac:int ->
Lacaml_float32.mat ->
?nrhs:int -> ?br:int -> ?bc:int -> Lacaml_float32.mat -> unit

getrs ?n ?ipiv ?trans ?ar ?ac a ?nrhs ?br ?bc b solves a system of linear equations a * X = b or a' * X = b with a general n-by-n matrix a using the LU factorization computed by Lacaml_S.getrf. Note that matrix a will be passed to Lacaml_S.getrf if ipiv was not provided.

n : default = number of columns in matrix a
ipiv : default = result from getrf applied to a
trans : default = `N
ar : default = 1
ac : default = 1
nrhs : default = available number of columns in matrix b
br : default = 1
bc : default = 1
val getri_min_lwork : int -> int

getri_min_lwork n

val getri_opt_lwork : ?n:int -> ?ar:int -> ?ac:int -> Lacaml_float32.mat -> int

getri_opt_lwork ?n ?ar ?ac a

n : default = number of columns of matrix a
ar : default = 1
ac : default = 1
val getri : ?n:int ->
?ipiv:Lacaml_common.int32_vec ->
?work:Lacaml_float32.vec -> ?ar:int -> ?ac:int -> Lacaml_float32.mat -> unit

getri ?n ?ipiv ?work ?ar ?ac a computes the inverse of a matrix using the LU factorization computed by Lacaml_S.getrf. Note that matrix a will be passed to Lacaml_S.getrf if ipiv was not provided.

n : default = number of columns in matrix a
ipiv : default = vec of length m from getri
work : default = vec of optimum length
ar : default = 1
ac : default = 1
val sytrf_min_lwork : unit -> int

sytrf_min_lwork ()

val sytrf_opt_lwork : ?n:int -> ?up:bool -> ?ar:int -> ?ac:int -> Lacaml_float32.mat -> int

sytrf_opt_lwork ?n ?up ?ar ?ac a

n : default = number of columns of matrix a
up : default = true (store upper triangle in a)
ar : default = 1
ac : default = 1
val sytrf : ?n:int ->
?up:bool ->
?ipiv:Lacaml_common.int32_vec ->
?work:Lacaml_float32.vec ->
?ar:int -> ?ac:int -> Lacaml_float32.mat -> Lacaml_common.int32_vec

sytrf ?n ?up ?ipiv ?work ?ar ?ac a computes the factorization of the real symmetric matrix a using the Bunch-Kaufman diagonal pivoting method.

n : default = number of columns in matrix a
up : default = true (store upper triangle in a)
ipiv : = vec of length n
work : default = vec of optimum length
ar : default = 1
ac : default = 1
val sytrs : ?n:int ->
?up:bool ->
?ipiv:Lacaml_common.int32_vec ->
?ar:int ->
?ac:int ->
Lacaml_float32.mat ->
?nrhs:int -> ?br:int -> ?bc:int -> Lacaml_float32.mat -> unit

sytrs ?n ?up ?ipiv ?ar ?ac a ?nrhs ?br ?bc b solves a system of linear equations a*X = b with a real symmetric matrix a using the factorization a = U*D*U**T or a = L*D*L**T computed by Lacaml_S.sytrf. Note that matrix a will be passed to Lacaml_S.sytrf if ipiv was not provided.

n : default = number of columns in matrix a
up : default = true (store upper triangle in a)
ipiv : default = vec of length n
ar : default = 1
ac : default = 1
nrhs : default = available number of columns in matrix b
br : default = 1
bc : default = 1
val sytri_min_lwork : int -> int

sytri_min_lwork n

val sytri : ?n:int ->
?up:bool ->
?ipiv:Lacaml_common.int32_vec ->
?work:Lacaml_float32.vec -> ?ar:int -> ?ac:int -> Lacaml_float32.mat -> unit

sytri ?n ?up ?ipiv ?work ?ar ?ac a computes the inverse of the real symmetric indefinite matrix a using the factorization a = U*D*U**T or a = L*D*L**T computed by Lacaml_S.sytrf. Note that matrix a will be passed to Lacaml_S.sytrf if ipiv was not provided.

n : default = number of columns in matrix a
up : default = true (store upper triangle in a)
ipiv : default = vec of length n from Lacaml_S.sytrf
work : default = vec of optimum length
ar : default = 1
ac : default = 1
val potrf : ?n:int ->
?up:bool ->
?ar:int ->
?ac:int -> ?jitter:Lacaml_float32.num_type -> Lacaml_float32.mat -> unit

potrf ?n ?up ?ar ?ac ?jitter a factorizes symmetric positive definite matrix a (or the designated submatrix) using Cholesky factorization.

Due to rounding errors ill-conditioned matrices may actually appear as if they were not positive definite, thus leading to an exception. One remedy for this problem is to add a small jitter to the diagonal of the matrix, which will usually allow Cholesky to complete successfully (though at a small bias). For extremely ill-conditioned matrices it is recommended to use (symmetric) eigenvalue decomposition instead of this function for a numerically more stable factorization.

n : default = number of columns in matrix a
up : default = true (store upper triangle in a)
ar : default = 1
ac : default = 1
jitter : default = nothing
val potrs : ?n:int ->
?up:bool ->
?ar:int ->
?ac:int ->
Lacaml_float32.mat ->
?nrhs:int ->
?br:int ->
?bc:int ->
?factorize:bool ->
?jitter:Lacaml_float32.num_type -> Lacaml_float32.mat -> unit

potrs ?n ?up ?ar ?ac a ?nrhs ?br ?bc ?factorize ?jitter b solves a system of linear equations a*X = b, where a is symmetric positive definite matrix, using the Cholesky factorization a = U**T*U or a = L*L**T computed by Lacaml_S.potrf.

n : default = number of columns in matrix a
up : default = true
ar : default = 1
ac : default = 1
nrhs : default = available number of columns in matrix b
br : default = 1
bc : default = 1
factorize : default = true (calls Lacaml_S.potrf implicitly)
jitter : default = nothing
val potri : ?n:int ->
?up:bool ->
?ar:int ->
?ac:int ->
?factorize:bool ->
?jitter:Lacaml_float32.num_type -> Lacaml_float32.mat -> unit

potri ?n ?up ?ar ?ac ?factorize ?jitter a computes the inverse of the real symmetric positive definite matrix a using the Cholesky factorization a = U**T*U or a = L*L**T computed by Lacaml_S.potrf.

n : default = number of columns in matrix a
up : default = true (upper triangle stored in a)
ar : default = 1
ac : default = 1
factorize : default = true (calls Lacaml_S.potrf implicitly)
jitter : default = nothing
val trtrs : ?n:int ->
?up:bool ->
?trans:Lacaml_float32.trans3 ->
?diag:Lacaml_common.diag ->
?ar:int ->
?ac:int ->
Lacaml_float32.mat ->
?nrhs:int -> ?br:int -> ?bc:int -> Lacaml_float32.mat -> unit

trtrs ?n ?up ?trans ?diag ?ar ?ac a ?nrhs ?br ?bc b solves a triangular system of the form a * X = b or a**T * X = n, where a is a triangular matrix of order n, and b is an n-by-nrhs matrix.

n : default = number of columns in matrix a
up : default = true
trans : default = `N
diag : default = `N
ar : default = 1
ac : default = 1
nrhs : default = available number of columns in matrix b
br : default = 1
bc : default = 1
val tbtrs : ?n:int ->
?kd:int ->
?up:bool ->
?trans:Lacaml_float32.trans3 ->
?diag:Lacaml_common.diag ->
?abr:int ->
?abc:int ->
Lacaml_float32.mat ->
?nrhs:int -> ?br:int -> ?bc:int -> Lacaml_float32.mat -> unit

tbtrs ?n ?kd ?up ?trans ?diag ?abr ?abc ab ?nrhs ?br ?bc b solves a triangular system of the form a * X = b or a**T * X = b, where a is a triangular band matrix of order n, and b is an n-by-nrhs matrix.

n : default = number of columns in matrix ab
kd : default = number of rows in matrix ab - 1
up : default = true
trans : default = `N
diag : default = `N
abr : default = 1
abc : default = 1
nrhs : default = available number of columns in matrix b
br : default = 1
bc : default = 1
val trtri : ?n:int ->
?up:bool ->
?diag:Lacaml_common.diag -> ?ar:int -> ?ac:int -> Lacaml_float32.mat -> unit

trtri ?n ?up ?diag ?ar ?ac a computes the inverse of a real upper or lower triangular matrix a.

n : default = number of columns in matrix a
up : default = true (upper triangle stored in a)
diag : default = `N
ar : default = 1
ac : default = 1
val geqrf_opt_lwork : ?m:int -> ?n:int -> ?ar:int -> ?ac:int -> Lacaml_float32.mat -> int

geqrf_opt_lwork ?m ?n ?ar ?ac a

m : default = number of rows in matrix a
n : default = number of columns in matrix a
ar : default = 1
ac : default = 1
val geqrf_min_lwork : n:int -> int

geqrf_min_lwork ~n

val geqrf : ?m:int ->
?n:int ->
?work:Lacaml_float32.vec ->
?tau:Lacaml_float32.vec ->
?ar:int -> ?ac:int -> Lacaml_float32.mat -> Lacaml_float32.vec

geqrf ?m ?n ?work ?tau ?ar ?ac a computes a QR factorization of a real m-by-n matrix a. See LAPACK documentation.

m : default = number of rows in matrix a
n : default = number of columns in matrix a
work : default = vec of optimum length
tau : default = vec of required length
ar : default = 1
ac : default = 1
Linear equations (simple drivers)
val gesv : ?n:int ->
?ipiv:Lacaml_common.int32_vec ->
?ar:int ->
?ac:int ->
Lacaml_float32.mat ->
?nrhs:int -> ?br:int -> ?bc:int -> Lacaml_float32.mat -> unit

gesv ?n ?ipiv ?ar ?ac a ?nrhs ?br ?bc b computes the solution to a real system of linear equations a * X = b, where a is an n-by-n matrix and X and b are n-by-nrhs matrices. The LU decomposition with partial pivoting and row interchanges is used to factor a as a = P * L * U, where P is a permutation matrix, L is unit lower triangular, and U is upper triangular. The factored form of a is then used to solve the system of equations a * X = b. On exit, b contains the solution matrix X.

n : default = available number of columns in matrix a
ipiv : default = vec of length n
ar : default = 1
ac : default = 1
nrhs : default = available number of columns in matrix b
br : default = 1
bc : default = 1
val gbsv : ?n:int ->
?ipiv:Lacaml_common.int32_vec ->
?abr:int ->
?abc:int ->
Lacaml_float32.mat ->
int -> int -> ?nrhs:int -> ?br:int -> ?bc:int -> Lacaml_float32.mat -> unit

gbsv ?n ?ipiv ?abr ?abc ab kl ku ?nrhs ?br ?bc b computes the solution to a real system of linear equations a * X = b, where a is a band matrix of order n with kl subdiagonals and ku superdiagonals, and X and b are n-by-nrhs matrices. The LU decomposition with partial pivoting and row interchanges is used to factor a as a = L * U, where L is a product of permutation and unit lower triangular matrices with kl subdiagonals, and U is upper triangular with kl+ku superdiagonals. The factored form of a is then used to solve the system of equations a * X = b.

n : default = available number of columns in matrix ab
ipiv : default = vec of length n
abr : default = 1
abc : default = 1
nrhs : default = available number of columns in matrix b
br : default = 1
bc : default = 1
val gtsv : ?n:int ->
?ofsdl:int ->
Lacaml_float32.vec ->
?ofsd:int ->
Lacaml_float32.vec ->
?ofsdu:int ->
Lacaml_float32.vec ->
?nrhs:int -> ?br:int -> ?bc:int -> Lacaml_float32.mat -> unit

gtsv ?n ?ofsdl dl ?ofsd d ?ofsdu du ?nrhs ?br ?bc b solves the equation a * X = b where a is an n-by-n tridiagonal matrix, by Gaussian elimination with partial pivoting. Note that the equation A'*X = b may be solved by interchanging the order of the arguments du and dl.

n : default = available length of vector d
ofsdl : default = 1
ofsd : default = 1
ofsdu : default = 1
nrhs : default = available number of columns in matrix b
br : default = 1
bc : default = 1
val posv : ?n:int ->
?up:bool ->
?ar:int ->
?ac:int ->
Lacaml_float32.mat ->
?nrhs:int -> ?br:int -> ?bc:int -> Lacaml_float32.mat -> unit

posv ?n ?up ?ar ?ac a ?nrhs ?br ?bc b computes the solution to a real system of linear equations a * X = b, where a is an n-by-n symmetric positive definite matrix and X and b are n-by-nrhs matrices. The Cholesky decomposition is used to factor a as a = U**T * U, if up = true, or a = L * L**T, if up = false, where U is an upper triangular matrix and L is a lower triangular matrix. The factored form of a is then used to solve the system of equations a * X = b.

n : default = available number of columns in matrix a
up : default = true i.e., upper triangle of a is stored
ar : default = 1
ac : default = 1
nrhs : default = available number of columns in matrix b
br : default = 1
bc : default = 1
val ppsv : ?n:int ->
?up:bool ->
?ofsap:int ->
Lacaml_float32.vec ->
?nrhs:int -> ?br:int -> ?bc:int -> Lacaml_float32.mat -> unit

ppsv ?n ?up ?ofsap ap ?nrhs ?br ?bc b computes the solution to the real system of linear equations a * X = b, where a is an n-by-n symmetric positive definite matrix stored in packed format and X and b are n-by-nrhs matrices. The Cholesky decomposition is used to factor a as a = U**T * U, if up = true, or a = L * L**T, if up = false, where U is an upper triangular matrix and L is a lower triangular matrix. The factored form of a is then used to solve the system of equations a * X = b.

n : default = the greater n s.t. n(n+1)/2 <= Vec.dim ap
up : default = true i.e., upper triangle of ap is stored
ofsap : default = 1
nrhs : default = available number of columns in matrix b
br : default = 1
bc : default = 1
val pbsv : ?n:int ->
?up:bool ->
?kd:int ->
?abr:int ->
?abc:int ->
Lacaml_float32.mat ->
?nrhs:int -> ?br:int -> ?bc:int -> Lacaml_float32.mat -> unit

pbsv ?n ?up ?kd ?abr ?abc ab ?nrhs ?br ?bc b computes the solution to a real system of linear equations a * X = b, where a is an n-by-n symmetric positive definite band matrix and X and b are n-by-nrhs matrices. The Cholesky decomposition is used to factor a as a = U**T * U, if up = true, or a = L * L**T, if up = false, where U is an upper triangular band matrix, and L is a lower triangular band matrix, with the same number of superdiagonals or subdiagonals as a. The factored form of a is then used to solve the system of equations a * X = b.

n : default = available number of columns in matrix ab
up : default = true i.e., upper triangle of ab is stored
kd : default = available number of rows in matrix ab - 1
abr : default = 1
abc : default = 1
nrhs : default = available number of columns in matrix b
br : default = 1
bc : default = 1
val ptsv : ?n:int ->
?ofsd:int ->
Lacaml_float32.vec ->
?ofse:int ->
Lacaml_float32.vec ->
?nrhs:int -> ?br:int -> ?bc:int -> Lacaml_float32.mat -> unit

ptsv ?n ?ofsd d ?ofse e ?nrhs ?br ?bc b computes the solution to the real system of linear equations a*X = b, where a is an n-by-n symmetric positive definite tridiagonal matrix, and X and b are n-by-nrhs matrices. A is factored as a = L*D*L**T, and the factored form of a is then used to solve the system of equations.

n : default = available length of vector d
ofsd : default = 1
ofse : default = 1
nrhs : default = available number of columns in matrix b
br : default = 1
bc : default = 1
val sysv_opt_lwork : ?n:int ->
?up:bool ->
?ar:int ->
?ac:int ->
Lacaml_float32.mat ->
?nrhs:int -> ?br:int -> ?bc:int -> Lacaml_float32.mat -> int

sysv_opt_lwork ?n ?up ?ar ?ac a ?nrhs ?br ?bc b

n : default = available number of columns in matrix a
up : default = true i.e., upper triangle of a is stored
ar : default = 1
ac : default = 1
nrhs : default = available number of columns in matrix b
br : default = 1
bc : default = 1
val sysv : ?n:int ->
?up:bool ->
?ipiv:Lacaml_common.int32_vec ->
?work:Lacaml_float32.vec ->
?ar:int ->
?ac:int ->
Lacaml_float32.mat ->
?nrhs:int -> ?br:int -> ?bc:int -> Lacaml_float32.mat -> unit

sysv ?n ?up ?ipiv ?work ?ar ?ac a ?nrhs ?br ?bc b computes the solution to a real system of linear equations a * X = b, where a is an N-by-N symmetric matrix and X and b are n-by-nrhs matrices. The diagonal pivoting method is used to factor a as a = U * D * U**T, if up = true, or a = L * D * L**T, if up = false, where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks. The factored form of a is then used to solve the system of equations a * X = b.

n : default = available number of columns in matrix a
up : default = true i.e., upper triangle of a is stored
ipiv : default = vec of length n
work : default = vec of optimum length (-> sysv_opt_lwork)
ar : default = 1
ac : default = 1
nrhs : default = available number of columns in matrix b
br : default = 1
bc : default = 1
val spsv : ?n:int ->
?up:bool ->
?ipiv:Lacaml_common.int32_vec ->
?ofsap:int ->
Lacaml_float32.vec ->
?nrhs:int -> ?br:int -> ?bc:int -> Lacaml_float32.mat -> unit

spsv ?n ?up ?ipiv ?ofsap ap ?nrhs ?br ?bc b computes the solution to the real system of linear equations a * X = b, where a is an n-by-n symmetric matrix stored in packed format and X and b are n-by-nrhs matrices. The diagonal pivoting method is used to factor a as a = U * D * U**T, if up = true, or a = L * D * L**T, if up = false, where U (or L) is a product of permutation and unit upper (lower) triangular matrices, D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks. The factored form of a is then used to solve the system of equations a * X = b.

n : default = the greater n s.t. n(n+1)/2 <= Vec.dim ap
up : default = true i.e., upper triangle of ap is stored
ipiv : default = vec of length n
ofsap : default = 1
nrhs : default = available number of columns in matrix b
br : default = 1
bc : default = 1
Least squares (simple drivers)
val gels_min_lwork : m:int -> n:int -> nrhs:int -> int

gels_min_lwork ~m ~n ~nrhs

val gels_opt_lwork : ?m:int ->
?n:int ->
?trans:Lacaml_common.trans2 ->
?ar:int ->
?ac:int ->
Lacaml_float32.mat ->
?nrhs:int -> ?br:int -> ?bc:int -> Lacaml_float32.mat -> int

gels_opt_lwork ?m ?n ?trans ?ar ?ac a ?nrhs ?br ?bc b

m : default = available number of rows in matrix a
n : default = available number of columns in matrix a
trans : default = `N
ar : default = 1
ac : default = 1
nrhs : default = available number of columns in matrix b
br : default = 1
bc : default = 1
val gels : ?m:int ->
?n:int ->
?work:Lacaml_float32.vec ->
?trans:Lacaml_common.trans2 ->
?ar:int ->
?ac:int ->
Lacaml_float32.mat ->
?nrhs:int -> ?br:int -> ?bc:int -> Lacaml_float32.mat -> unit

gels ?m ?n ?work ?trans ?ar ?ac a ?nrhs ?br ?bc b see LAPACK documentation!

m : default = available number of rows in matrix a
n : default = available number of columns of matrix a
work : default = vec of optimum length (-> Lacaml_S.gels_opt_lwork)
trans : default = `N
ar : default = 1
ac : default = 1
nrhs : default = available number of columns in matrix b
br : default = 1
bc : default = 1