package lacaml

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BLAS-1 interface
BLAS-2 interface
LAPACK interface
Auxiliary routines
Linear equations (computational routines)
Least squares (expert drivers)
General Schur factorization
General SVD routines
General eigenvalue problem (simple drivers)
Symmetric-matrix eigenvalue and singular value problems (simple drivers)
Symmetric-matrix eigenvalue and singular value problems (expert & RRR drivers)
BLAS-1 interface
BLAS-2 interface
BLAS-3 interface
LAPACK interface
Auxiliary routines
Linear equations (computational routines)
Linear equations (simple drivers)
Least squares (simple drivers)

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Double precision real BLAS and LAPACK functions.

This module Lacaml.D contains linear algebra routines for real numbers (precision: float64). It is recommended to use this module by writing

open Lacaml.D

at the top of your file.

type prec = Bigarray.float64_elt

type num_type = float

type vec =
  (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Array1.t

Vectors (precision: float64).

type rvec = vec

type mat =
  (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Array2.t

Matrices (precision: float64).

type trans3 = [

| `N
| `T

]

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

val prec : (float, Bigarray.float64_elt) Bigarray.kind

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

module Vec : sig ... end

module Mat : sig ... end

val pp_num : Format.formatter -> float -> unit

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

val pp_vec : 
  Format.formatter ->
  (float, 'a, Bigarray.fortran_layout) Bigarray.Array1.t ->
  unit

Pretty-printer for column vectors.

val pp_mat : 
  Format.formatter ->
  (float, 'a, Bigarray.fortran_layout) Bigarray.Array2.t ->
  unit

Pretty-printer for matrices.

BLAS-1 interface

val dot : 
  ?n:int ->
  ?ofsx:int ->
  ?incx:int ->
  vec ->
  ?ofsy:int ->
  ?incy:int ->
  vec ->
  float

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

parameter n
default = greater n s.t. ofsx+(n-1)(abs incx) <= dim x

parameter ofsx
default = 1

parameter incx
default = 1

parameter ofsy
default = 1

parameter incy
default = 1

val asum : ?n:int -> ?ofsx:int -> ?incx:int -> vec -> float

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

parameter n
default = greater n s.t. ofsx+(n-1)(abs incx) <= dim x

parameter ofsx
default = 1

parameter incx
default = 1

BLAS-2 interface

val sbmv : 
  ?n:int ->
  ?k:int ->
  ?ofsy:int ->
  ?incy:int ->
  ?y:vec ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  ?up:bool ->
  ?alpha:float ->
  ?beta:float ->
  ?ofsx:int ->
  ?incx:int ->
  vec ->
  vec

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

returns
vector y, which is overwritten.

parameter n
default = number of available columns to the right of ac.

parameter k
default = number of available rows in matrix a - 1

parameter ofsy
default = 1

parameter incy
default = 1

parameter ar
default = 1

parameter ac
default = 1

parameter y
default = uninitialized vector of minimal length (see BLAS)

parameter up
default = true i.e., upper band of a is supplied

parameter alpha
default = 1.0

parameter beta
default = 0.0

parameter ofsx
default = 1

parameter incx
default = 1

val ger : 
  ?m:int ->
  ?n:int ->
  ?alpha:float ->
  ?ofsx:int ->
  ?incx:int ->
  vec ->
  ?ofsy:int ->
  ?incy:int ->
  vec ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  unit

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

parameter m
default = number of rows of a

parameter n
default = number of columns of a

parameter alpha
default = 1.0

parameter ofsx
default = 1

parameter incx
default = 1

parameter ofsy
default = 1

parameter incy
default = 1

parameter ar
default = 1

parameter ac
default = 1

val syr : 
  ?n:int ->
  ?alpha:float ->
  ?up:bool ->
  ?ofsx:int ->
  ?incx:int ->
  vec ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  unit

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

parameter n
default = number of rows of a

parameter alpha
default = 1.0

parameter up
default = true i.e., upper triangle of a is supplied

parameter ofsx
default = 1

parameter incx
default = 1

parameter ar
default = 1

parameter ac
default = 1

LAPACK interface

Auxiliary routines

val lansy_min_lwork : int -> [ Lacaml__common.norm2 | `M | `F ] -> int

lansy_min_lwork m norm

returns
the minimum length of the work array used by the lansy-function.

parameter norm
type of norm that will be computed by lansy

parameter n
the number of columns (and rows) in the matrix

val lansy : 
  ?n:int ->
  ?up:bool ->
  ?norm:[ Lacaml__common.norm2 | `M | `F ] ->
  ?work:vec ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  float

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

parameter norm
default = `O

parameter up
default = true (reference upper triangular part of a)

parameter n
default = number of columns of matrix a

parameter work
default = allocated work space for norm `I

val lamch : [ `E | `S | `B | `P | `N | `R | `M | `U | `L | `O ] -> float

lamch cmach see LAPACK documentation!

Linear equations (computational routines)

val orgqr_min_lwork : n:int -> int

orgqr_min_lwork ~n

returns
the minimum length of the work-array used by the orgqr-function if the matrix has n columns.

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

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

returns
the optimum length of the work-array used by the orgqr-function given matrix a, optionally its logical dimensions m and n, and the number of reflectors k.

parameter m
default = available number of rows in matrix a

parameter n
default = available number of columns in matrix a

parameter k
default = available number of elements in vector tau

val orgqr : 
  ?m:int ->
  ?n:int ->
  ?k:int ->
  ?work:vec ->
  tau:vec ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  unit

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

parameter m
default = available number of rows in matrix a

parameter n
default = available number of columns in matrix a

parameter k
default = available number of elements in vector tau

val ormqr_opt_lwork : 
  ?side:[ `L | `R ] ->
  ?trans:[ `N | `T ] ->
  ?m:int ->
  ?n:int ->
  ?k:int ->
  tau:vec ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  ?cr:int ->
  ?cc:int ->
  mat ->
  int

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

returns
the optimum length of the work-array used by the ormqr-function given matrix a and b, optionally its logical dimensions m and n, and the number of reflectors k.

parameter m
default = available number of rows in matrix a

parameter n
default = available number of columns in matrix a

parameter k
default = available number of elements in vector tau

val ormqr : 
  ?side:[ `L | `R ] ->
  ?trans:[ `N | `T ] ->
  ?m:int ->
  ?n:int ->
  ?k:int ->
  ?work:vec ->
  tau:vec ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  ?cr:int ->
  ?cc:int ->
  mat ->
  unit

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

parameter side
default = `L

parameter trans
default = `N

parameter m
default = available number of rows in matrix a

parameter n
default = available number of columns in matrix a

parameter k
default = available number of elements in vector tau

val gecon_min_lwork : int -> int

gecon_min_lwork n

returns
the minimum length of the work array used by the gecon-function.

parameter n
the logical dimensions of the matrix given to the gecon-function

val gecon_min_liwork : int -> int

gecon_min_liwork n

returns
the minimum length of the iwork array used by the gecon-function.

parameter n
the logical dimensions of the matrix given to gecon-function

val gecon : 
  ?n:int ->
  ?norm:[ `O | `I ] ->
  ?anorm:float ->
  ?work:vec ->
  ?iwork:(int32, Bigarray.int32_elt, Bigarray.fortran_layout) Bigarray.Array1.t ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  float

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

returns
estimate of the reciprocal of the condition number of matrix a

parameter n
default = available number of columns of matrix a

parameter norm
default = 1-norm

parameter anorm
default = norm of the matrix a as returned by lange

parameter work
default = automatically allocated workspace

parameter iwork
default = automatically allocated workspace

parameter ar
default = 1

parameter ac
default = 1

val sycon_min_lwork : int -> int

sycon_min_lwork n

returns
the minimum length of the work array used by the sycon-function.

parameter n
the logical dimensions of the matrix given to the sycon-function

val sycon_min_liwork : int -> int

sycon_min_liwork n

returns
the minimum length of the iwork array used by the sycon-function.

parameter n
the logical dimensions of the matrix given to sycon-function

val sycon : 
  ?n:int ->
  ?up:bool ->
  ?ipiv:(int32, Bigarray.int32_elt, Bigarray.fortran_layout) Bigarray.Array1.t ->
  ?anorm:float ->
  ?work:vec ->
  ?iwork:(int32, Bigarray.int32_elt, Bigarray.fortran_layout) Bigarray.Array1.t ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  float

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

returns
estimate of the reciprocal of the condition number of symmetric matrix a

parameter n
default = available number of columns of matrix a

parameter up
default = upper triangle of the factorization of a is stored

parameter ipiv
default = vec of length n

parameter anorm
default = 1-norm of the matrix a as returned by lange

parameter work
default = automatically allocated workspace

parameter iwork
default = automatically allocated workspace

val pocon_min_lwork : int -> int

pocon_min_lwork n

returns
the minimum length of the work array used by the pocon-function.

parameter n
the logical dimensions of the matrix given to the pocon-function

val pocon_min_liwork : int -> int

pocon_min_liwork n

returns
the minimum length of the iwork array used by the pocon-function.

parameter n
the logical dimensions of the matrix given to pocon-function

val pocon : 
  ?n:int ->
  ?up:bool ->
  ?anorm:float ->
  ?work:vec ->
  ?iwork:(int32, Bigarray.int32_elt, Bigarray.fortran_layout) Bigarray.Array1.t ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  float

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

returns
estimate of the reciprocal of the condition number of symmetric positive definite matrix a

parameter n
default = available number of columns of matrix a

parameter up
default = upper triangle of Cholesky factorization of a is stored

parameter work
default = automatically allocated workspace

parameter iwork
default = automatically allocated workspace

parameter anorm
default = 1-norm of the matrix a as returned by lange

Least squares (expert drivers)

val gelsy_min_lwork : m:int -> n:int -> nrhs:int -> int

gelsy_min_lwork ~m ~n ~nrhs

returns
the minimum length of the work-array used by the gelsy-function if the logical dimensions of the matrix are m rows and n columns and if there are nrhs right hand side vectors.

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

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

returns
the optimum length of the work-array used by the gelsy-function given matrix a, optionally its logical dimensions m and n and given right hand side matrix b with an optional number nrhs of vectors.

parameter m
default = available number of rows in matrix a

parameter n
default = available number of columns in matrix a

parameter nrhs
default = available number of columns in matrix b

val gelsy : 
  ?m:int ->
  ?n:int ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  ?rcond:float ->
  ?jpvt:(int32, Bigarray.int32_elt, Bigarray.fortran_layout) Bigarray.Array1.t ->
  ?work:vec ->
  ?nrhs:int ->
  ?br:int ->
  ?bc:int ->
  mat ->
  int

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

returns
the effective rank of a.

parameter m
default = available number of rows in matrix a

parameter n
default = available number of columns of matrix a

parameter rcond
default = (-1) => machine precision

parameter jpvt
default = vec of length n

parameter work
default = vec of optimum length (-> gelsy_opt_lwork)

parameter 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

returns
the minimum length of the work-array used by the gelsd-function if the logical dimensions of the matrix are m and n and if there are nrhs right hand side vectors.

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

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

returns
the optimum length of the work-array used by the gelsd-function given matrix a, optionally its logical dimensions m and n and given right hand side matrix b with an optional number nrhs of vectors.

parameter m
default = available number of rows in matrix a

parameter n
default = available number of columns in matrix a

parameter nrhs
default = available number of columns in matrix b

val gelsd_min_iwork : int -> int -> int

gelsd_min_iwork m n

returns
the minimum (= optimum) length of the iwork-array used by the gelsd-function if the logical dimensions of the matrix are m and n.

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

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

returns
the effective rank of a.

raises Failure
if the function fails to converge.

parameter m
default = available number of rows in matrix a

parameter n
default = available number of columns of matrix a

parameter rcond
default = (-1) => machine precision

parameter ofss
default = 1 or ignored if s is not given

parameter s
default = vec of length min rows cols

parameter work
default = vec of optimum length (-> gelsd_opt_lwork)

parameter iwork
default = vec of optimum (= minimum) length

parameter 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

returns
the minimum length of the work-array used by the gelss-function if the logical dimensions of the matrix are m rows and n columns and if there are nrhs right hand side vectors.

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

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

returns
the optimum length of the work-array used by the gelss-function given matrix a, optionally its logical dimensions m and n and given right hand side matrix b with an optional number nrhs of vectors.

parameter m
default = available number of rows in matrix a

parameter n
default = available number of columns in matrix a

parameter nrhs
default = available number of columns in matrix b

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

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

returns
the effective rank of a.

raises Failure
if the function fails to converge.

parameter m
default = available number of rows in matrix a

parameter n
default = available number of columns of matrix a

parameter rcond
default = (-1) => machine precision

parameter ofss
default = 1 or ignored if s is not given

parameter s
default = vec of length min m n

parameter work
default = vec of optimum length (-> gelss_opt_lwork)

parameter nrhs
default = available number of columns in matrix b

General Schur factorization

val gees : 
  ?n:int ->
  ?jobvs:[ `No_Schur_vectors | `Compute_Schur_vectors ] ->
  ?sort:
    [ `No_sort
    | `Select_left_plane
    | `Select_right_plane
    | `Select_interior_disk
    | `Select_exterior_disk
    | `Select_custom of Complex.t -> bool ] ->
  ?wr:vec ->
  ?wi:vec ->
  ?vsr:int ->
  ?vsc:int ->
  ?vs:mat ->
  ?work:vec ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  int * vec * vec * mat

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

returns
(sdim, wr, wi, vs)

General SVD routines

val gesvd_min_lwork : m:int -> n:int -> int

gesvd_min_lwork ~m ~n

returns
the minimum length of the work array used by the gesvd-function for matrices with m rows and n columns.

val gesvd_opt_lwork : 
  ?m:int ->
  ?n:int ->
  ?jobu:[ `A | `S | `O | `N ] ->
  ?jobvt:[ `A | `S | `O | `N ] ->
  ?s:vec ->
  ?ur:int ->
  ?uc:int ->
  ?u:mat ->
  ?vtr:int ->
  ?vtc:int ->
  ?vt:mat ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  int

val gesvd : 
  ?m:int ->
  ?n:int ->
  ?jobu:[ `A | `S | `O | `N ] ->
  ?jobvt:[ `A | `S | `O | `N ] ->
  ?s:vec ->
  ?ur:int ->
  ?uc:int ->
  ?u:mat ->
  ?vtr:int ->
  ?vtc:int ->
  ?vt:mat ->
  ?work:vec ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  vec * mat * mat

val gesdd_liwork : m:int -> n:int -> int

val gesdd_min_lwork : 
  ?jobz:[ `A | `S | `O | `N ] ->
  m:int ->
  n:int ->
  unit ->
  int

gesdd_min_lwork ?jobz ~m ~n

returns
the minimum length of the work array used by the gesdd-function for matrices with m rows and n columns for SVD-job jobz.

val gesdd_opt_lwork : 
  ?m:int ->
  ?n:int ->
  ?jobz:[ `A | `S | `O | `N ] ->
  ?s:vec ->
  ?ur:int ->
  ?uc:int ->
  ?u:mat ->
  ?vtr:int ->
  ?vtc:int ->
  ?vt:mat ->
  ?iwork:(int32, Bigarray.int32_elt, Bigarray.fortran_layout) Bigarray.Array1.t ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  int

val gesdd : 
  ?m:int ->
  ?n:int ->
  ?jobz:[ `A | `S | `O | `N ] ->
  ?s:vec ->
  ?ur:int ->
  ?uc:int ->
  ?u:mat ->
  ?vtr:int ->
  ?vtc:int ->
  ?vt:mat ->
  ?work:vec ->
  ?iwork:(int32, Bigarray.int32_elt, Bigarray.fortran_layout) Bigarray.Array1.t ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  vec * mat * mat

General eigenvalue problem (simple drivers)

val geev_min_lwork : ?vectors:bool -> int -> int

geev_min_lwork vectors n

returns
the minimum length of the work array used by the geev-function. vectors indicates whether eigenvectors are supposed to be computed.

parameter n
the logical dimensions of the matrix given to geev-function

parameter vectors
default = true

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

returns
"optimal" size of work array.

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

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

returns
(lv, wr, wi, rv), where wr and wv are the real and imaginary components of the eigenvalues, and lv and rv are the left and right eigenvectors. lv (rv) is the empty matrix if vl (vr) is set to None.

raises Failure
if the function fails to converge

parameter n
default = available number of columns of matrix a

parameter work
default = automatically allocated workspace

parameter 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)

parameter 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.

parameter wr
default = vector of size n; real components of the eigenvalues

parameter wi
default = vector of size n; imaginary components of the eigenvalues

parameter a
the matrix whose eigensystem is computed

Symmetric-matrix eigenvalue and singular value problems (simple drivers)

val syev_min_lwork : int -> int

syev_min_lwork n

returns
the minimum length of the work-array used by the syev-function if the logical dimensions of the matrix are n.

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

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

returns
the optimum length of the work-array used by the syev-function given matrix a, optionally its logical dimension n and whether the eigenvectors must be computed (vectors).

parameter n
default = available number of columns of matrix a

parameter vectors
default = false, i.e. eigenvectors are not computed

parameter up
default = true, i.e. upper triangle of a is stored

val syev : 
  ?n:int ->
  ?vectors:bool ->
  ?up:bool ->
  ?work:vec ->
  ?ofsw:int ->
  ?w:vec ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  vec

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

returns
the vector w of eigenvalues in ascending order.

raises Failure
if the function fails to converge.

parameter n
default = available number of columns of matrix a

parameter vectors
default = false i.e, eigenvectors are not computed

parameter up
default = true i.e., upper triangle of a is stored

parameter work
default = vec of optimum length (-> syev_opt_lwork)

parameter ofsw
default = 1 or ignored if w is not given

parameter w
default = vec of length n

val syevd_min_lwork : vectors:bool -> int -> int

syevd_min_lwork vectors n

returns
the minimum length of the work-array used by the syevd-function if the logical dimensions of the matrix are n and given whether eigenvectors should be computed (vectors).

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

syevd_min_liwork vectors n

returns
the minimum length of the iwork-array used by the syevd-function if the logical dimensions of the matrix are n and given whether eigenvectors should be computed (vectors).

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

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

returns
the optimum length of the work-array used by the syevd-function given matrix a, optionally its logical dimension n and whether the eigenvectors must be computed (vectors).

parameter n
default = available number of columns of matrix a

parameter vectors
default = false, i.e. eigenvectors are not computed

parameter 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 ->
  mat ->
  int

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

returns
the optimum length of the iwork-array used by the syevd-function given matrix a, optionally its logical dimension n and whether the eigenvectors must be computed (vectors).

parameter n
default = available number of columns of matrix a

parameter vectors
default = false, i.e. eigenvectors are not computed

parameter 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 ->
  mat ->
  int * int

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

returns
the tuple of optimum lengths of the work- and iwork-arrays respectively, used by the syevd-function given matrix a, optionally its logical dimension n and whether the eigenvectors must be computed (vectors).

parameter n
default = available number of columns of matrix a

parameter vectors
default = false, i.e. eigenvectors are not computed

parameter up
default = true, i.e. upper triangle of a is stored

val syevd : 
  ?n:int ->
  ?vectors:bool ->
  ?up:bool ->
  ?work:vec ->
  ?iwork:(int32, Bigarray.int32_elt, Bigarray.fortran_layout) Bigarray.Array1.t ->
  ?ofsw:int ->
  ?w:vec ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  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.

returns
the vector w of eigenvalues in ascending order.

raises Failure
if the function fails to converge.

parameter n
default = available number of columns of matrix a

parameter vectors
default = false i.e, eigenvectors are not computed

parameter up
default = true i.e., upper triangle of a is stored

parameter work
default = vec of optimum length (-> syev_opt_lwork)

parameter iwork
default = int32_vec of optimum length (-> syevd_opt_liwork)

parameter ofsw
default = 1 or ignored if w is not given

parameter w
default = vec of length n

val sbev_min_lwork : int -> int

sbev_min_lwork n

returns
the minimum length of the work-array used by the sbev-function if the logical dimensions of the matrix are n.

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

raises Failure
if the function fails to converge.

returns
the vector w of eigenvalues in ascending order.

raises Failure
if the function fails to converge.

parameter n
default = available number of columns of matrix ab

parameter 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

parameter kd
default = number of rows in matrix ab - 1

parameter up
default = true i.e., upper triangle of the matrix is stored

parameter work
default = vec of minimal length (-> sbev_min_lwork)

parameter ofsw
default = 1 or ignored if w is not given

parameter w
default = vec of length n

parameter abr
default = 1

parameter abc
default = 1

Symmetric-matrix eigenvalue and singular value problems (expert & RRR drivers)

val syevr_min_lwork : int -> int

syevr_min_lwork n

returns
the minimum length of the work-array used by the syevr-function if the logical dimensions of the matrix are n.

val syevr_min_liwork : int -> int

syevr_min_liwork n

returns
the minimum length of the iwork-array used by the syevr-function if the logical dimensions of the matrix are n.

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

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

returns
the optimum length of the work-array used by the syevr-function given matrix a, optionally its logical dimension n and whether the eigenvectors must be computed (vectors).

parameter n
default = available number of columns of matrix a

parameter vectors
default = false, i.e. eigenvectors are not computed

parameter up
default = true, i.e. upper triangle of a is stored

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

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

returns
the optimum length of the iwork-array used by the syevr-function given matrix a, optionally its logical dimension n and whether the eigenvectors must be computed (vectors).

parameter n
default = available number of columns of matrix a

parameter vectors
default = false, i.e. eigenvectors are not computed

parameter up
default = true, i.e. upper triangle of a is stored

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

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

returns
the tuple of optimum lengths of the work- and iwork-arrays respectively, used by the syevr-function given matrix a, optionally its logical dimension n and whether the eigenvectors must be computed (vectors).

parameter n
default = available number of columns of matrix a

parameter vectors
default = false, i.e. eigenvectors are not computed

parameter up
default = true, i.e. upper triangle of a is stored

val syevr : 
  ?n:int ->
  ?vectors:bool ->
  ?range:[ `A | `V of float * float | `I of int * int ] ->
  ?up:bool ->
  ?abstol:float ->
  ?work:vec ->
  ?iwork:(int32, Bigarray.int32_elt, Bigarray.fortran_layout) Bigarray.Array1.t ->
  ?ofsw:int ->
  ?w:vec ->
  ?zr:int ->
  ?zc:int ->
  ?z:mat ->
  ?isuppz:
    (int32, Bigarray.int32_elt, Bigarray.fortran_layout) Bigarray.Array1.t ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  int
  * vec
  * mat
  * (int32, Bigarray.int32_elt, Bigarray.fortran_layout) Bigarray.Array1.t

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.

returns
the tuple (m, w, z, isuppz), where m is the number of computed eigenpairs, vector w contains the computed eigenvalues in ascending order, z contains the computed eigenvectors in same order, and isuppz indicates the nonzero elements in z.

parameter n
default = available number of columns of matrix a

parameter vectors
default = false i.e, eigenvectors are not computed

parameter range
default = `A

parameter up
default = true i.e., upper triangle of a is stored

parameter abstol
default = result of calling lamch `S

parameter work
default = vec of optimum length (-> syev_opt_lwork)

parameter iwork
default = int32_vec of optimum length (-> syevr_opt_liwork)

parameter ofsw
default = 1 or ignored if w is not given

parameter w
default = vec of length n

parameter zr
default = 1

parameter zc
default = 1

parameter z
default = matrix with minimal required dimension

parameter isuppz
default = int32_vec with minimal required dimension

parameter ar
default = 1

parameter ac
default = 1

val sygv_opt_lwork : 
  ?n:int ->
  ?vectors:bool ->
  ?up:bool ->
  ?itype:[ `A_B | `AB | `BA ] ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  ?br:int ->
  ?bc:int ->
  mat ->
  int

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

returns
the optimum length of the work-array used by the sygv-function for the given matrices a and b, optionally their logical dimension n and whether the eigenvectors must be computed (vectors).

parameter n
default = available number of columns of matrix a

parameter vectors
default = false, i.e. eigenvectors are not computed

parameter up
default = true, i.e. upper triangle of a is stored

parameter itype
specifies the problem type to be solved:
- `A_B (default): a*x = (lambda)*a*x
- `AB: a*b*x = (lambda)*x
- `BA: b*a*x = (lambda)*x

val sygv : 
  ?n:int ->
  ?vectors:bool ->
  ?up:bool ->
  ?work:vec ->
  ?ofsw:int ->
  ?w:vec ->
  ?itype:[ `A_B | `AB | `BA ] ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  ?br:int ->
  ?bc:int ->
  mat ->
  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.

returns
the vector w of eigenvalues in ascending order.

raises Failure
if the function fails to converge.

parameter n
default = available number of columns of matrix a

parameter vectors
default = false i.e, eigenvectors are not computed

parameter up
default = true i.e., upper triangle of a is stored

parameter work
default = vec of optimum length (-> sygv_opt_lwork)

parameter ofsw
default = 1 or ignored if w is not given

parameter w
default = vec of length n

parameter itype
specifies the problem type to be solved:
- `A_B (default): a*x = (lambda)*a*x
- `AB: a*b*x = (lambda)*x
- `BA: b*a*x = (lambda)*x

val sbgv : 
  ?n:int ->
  ?ka:int ->
  ?kb:int ->
  ?zr:int ->
  ?zc:int ->
  ?z:mat ->
  ?up:bool ->
  ?work:vec ->
  ?ofsw:int ->
  ?w:vec ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  ?br:int ->
  ?bc:int ->
  mat ->
  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.

returns
the vector w of eigenvalues in ascending order.

raises Failure
if the function fails to converge.

parameter n
default = available number of columns of matrix a

parameter ka
the number of superdiagonals (or subdiagonals if up = false) of the matrix a. Default = dim1 a - ar.

parameter kb
same as ka but for the matrix b.

parameter z
default = None i.e, eigenvectors are not computed

parameter up
default = true i.e., upper triangle of a is stored

parameter work
default = vec of optimum length (3 * n)

parameter ofsw
default = 1 or ignored if w is not given

parameter w
default = vec of length n

BLAS-1 interface

val swap : 
  ?n:int ->
  ?ofsx:int ->
  ?incx:int ->
  vec ->
  ?ofsy:int ->
  ?incy:int ->
  vec ->
  unit

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

parameter n
default = greater n s.t. ofsx+(n-1)(abs incx) <= dim x

parameter ofsx
default = 1

parameter incx
default = 1

parameter ofsy
default = 1

parameter incy
default = 1

val scal : ?n:int -> float -> ?ofsx:int -> ?incx:int -> vec -> unit

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

parameter n
default = greater n s.t. ofsx+(n-1)(abs incx) <= dim x

parameter ofsx
default = 1

parameter incx
default = 1

val copy : 
  ?n:int ->
  ?ofsy:int ->
  ?incy:int ->
  ?y:vec ->
  ?ofsx:int ->
  ?incx:int ->
  vec ->
  vec

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

returns
vector y, which is overwritten.

parameter n
default = greater n s.t. ofsx+(n-1)(abs incx) <= dim x

parameter ofsy
default = 1

parameter incy
default = 1

parameter y
default = new vector with ofsy+(n-1)(abs incy) rows

parameter ofsx
default = 1

parameter incx
default = 1

val nrm2 : ?n:int -> ?ofsx:int -> ?incx:int -> vec -> float

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

parameter n
default = greater n s.t. ofsx+(n-1)(abs incx) <= dim x

parameter ofsx
default = 1

parameter incx
default = 1

val axpy : 
  ?alpha:float ->
  ?n:int ->
  ?ofsx:int ->
  ?incx:int ->
  vec ->
  ?ofsy:int ->
  ?incy:int ->
  vec ->
  unit

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

parameter alpha
default = { re = 1.; im = 0. }

parameter n
default = greater n s.t. ofsx+(n-1)(abs incx) <= dim x

parameter ofsx
default = 1

parameter incx
default = 1

parameter ofsy
default = 1

parameter incy
default = 1

val iamax : ?n:int -> ?ofsx:int -> ?incx:int -> vec -> int

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

parameter n
default = greater n s.t. ofsx+(n-1)(abs incx) <= dim x

parameter ofsx
default = 1

parameter incx
default = 1

val amax : ?n:int -> ?ofsx:int -> ?incx:int -> vec -> float

amax ?n ?ofsx ?incx x

returns
the greater of the absolute values of the elements of the vector x.

parameter n
default = greater n s.t. ofsx+(n-1)(abs incx) <= dim x

parameter ofsx
default = 1

parameter incx
default = 1

BLAS-2 interface

val gemv : 
  ?m:int ->
  ?n:int ->
  ?beta:float ->
  ?ofsy:int ->
  ?incy:int ->
  ?y:vec ->
  ?trans:trans3 ->
  ?alpha:float ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  ?ofsx:int ->
  ?incx:int ->
  vec ->
  vec

gemv ?m ?n ?beta ?ofsy ?incy ?y ?trans ?alpha ?ar ?ac a ?ofsx ?incx x performs the operation y := alpha * op(a) * x + beta * y where op(a) = a or aᵀ according to the value of trans. See BLAS documentation for more information. BEWARE that the 1988 BLAS-2 specification mandates that this function has no effect when n=0 while the mathematically expected behavior is y ← beta * y.

returns
vector y, which is overwritten.

parameter m
default = number of available rows in matrix a

parameter n
default = available columns in matrix a

parameter beta
default = { re = 0.; im = 0. }

parameter ofsy
default = 1

parameter incy
default = 1

parameter y
default = vector with minimal required length (see BLAS)

parameter trans
default = `N

parameter alpha
default = { re = 1.; im = 0. }

parameter ar
default = 1

parameter ac
default = 1

parameter ofsx
default = 1

parameter incx
default = 1

val gbmv : 
  ?m:int ->
  ?n:int ->
  ?beta:float ->
  ?ofsy:int ->
  ?incy:int ->
  ?y:vec ->
  ?trans:trans3 ->
  ?alpha:float ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  int ->
  int ->
  ?ofsx:int ->
  ?incx:int ->
  vec ->
  vec

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

returns
vector y, which is overwritten.

parameter m
default = same as n (i.e., a is a square matrix)

parameter n
default = available number of columns in matrix a

parameter beta
default = { re = 0.; im = 0. }

parameter ofsy
default = 1

parameter incy
default = 1

parameter y
default = vector with minimal required length (see BLAS)

parameter trans
default = `N

parameter alpha
default = { re = 1.; im = 0. }

parameter ar
default = 1

parameter ac
default = 1

parameter ofsx
default = 1

parameter incx
default = 1

val symv : 
  ?n:int ->
  ?beta:float ->
  ?ofsy:int ->
  ?incy:int ->
  ?y:vec ->
  ?up:bool ->
  ?alpha:float ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  ?ofsx:int ->
  ?incx:int ->
  vec ->
  vec

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

returns
vector y, which is overwritten.

parameter n
default = dimension of symmetric matrix a

parameter beta
default = { re = 0.; im = 0. }

parameter ofsy
default = 1

parameter incy
default = 1

parameter y
default = vector with minimal required length (see BLAS)

parameter up
default = true (upper triangular portion of a is accessed)

parameter alpha
default = { re = 1.; im = 0. }

parameter ar
default = 1

parameter ac
default = 1

parameter ofsx
default = 1

parameter incx
default = 1

val trmv : 
  ?n:int ->
  ?trans:trans3 ->
  ?diag:[ `U | `N ] ->
  ?up:bool ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  ?ofsx:int ->
  ?incx:int ->
  vec ->
  unit

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

parameter n
default = dimension of triangular matrix a

parameter trans
default = `N

parameter diag
default = false (not a unit triangular matrix)

parameter up
default = true (upper triangular portion of a is accessed)

parameter ar
default = 1

parameter ac
default = 1

parameter ofsx
default = 1

parameter incx
default = 1

val trsv : 
  ?n:int ->
  ?trans:trans3 ->
  ?diag:[ `U | `N ] ->
  ?up:bool ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  ?ofsx:int ->
  ?incx:int ->
  vec ->
  unit

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

parameter n
default = dimension of triangular matrix a

parameter trans
default = `N

parameter diag
default = false (not a unit triangular matrix)

parameter up
default = true (upper triangular portion of a is accessed)

parameter ar
default = 1

parameter ac
default = 1

parameter ofsx
default = 1

parameter incx
default = 1

val tpmv : 
  ?n:int ->
  ?trans:trans3 ->
  ?diag:[ `U | `N ] ->
  ?up:bool ->
  ?ofsap:int ->
  vec ->
  ?ofsx:int ->
  ?incx:int ->
  vec ->
  unit

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

parameter n
default = dimension of packed triangular matrix ap

parameter trans
default = `N

parameter diag
default = false (not a unit triangular matrix)

parameter up
default = true (upper triangular portion of ap is accessed)

parameter ofsap
default = 1

parameter ofsx
default = 1

parameter incx
default = 1

val tpsv : 
  ?n:int ->
  ?trans:trans3 ->
  ?diag:[ `U | `N ] ->
  ?up:bool ->
  ?ofsap:int ->
  vec ->
  ?ofsx:int ->
  ?incx:int ->
  vec ->
  unit

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

parameter n
default = dimension of packed triangular matrix ap

parameter trans
default = `N

parameter diag
default = false (not a unit triangular matrix)

parameter up
default = true (upper triangular portion of ap is accessed)

parameter ofsap
default = 1

parameter ofsx
default = 1

parameter incx
default = 1

BLAS-3 interface

val gemm : 
  ?m:int ->
  ?n:int ->
  ?k:int ->
  ?beta:float ->
  ?cr:int ->
  ?cc:int ->
  ?c:mat ->
  ?transa:trans3 ->
  ?alpha:float ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  ?transb:trans3 ->
  ?br:int ->
  ?bc:int ->
  mat ->
  mat

gemm ?m ?n ?k ?beta ?cr ?cc ?c ?transa ?alpha ?ar ?ac a ?transb ?br ?bc b performs the operation c := alpha * op(a) * op(b) + beta * c where op(x) = x or xᵀ depending on transx. See BLAS documentation for more information.

returns
matrix c, which is overwritten.

parameter m
default = number of rows of a (or tr a) and c

parameter n
default = number of columns of b (or tr b) and c

parameter k
default = number of columns of a (or tr a) and number of rows of b (or tr b)

parameter beta
default = { re = 0.; im = 0. }

parameter cr
default = 1

parameter cc
default = 1

parameter c
default = matrix with minimal required dimension

parameter transa
default = `N

parameter alpha
default = { re = 1.; im = 0. }

parameter ar
default = 1

parameter ac
default = 1

parameter transb
default = `N

parameter br
default = 1

parameter bc
default = 1

val symm : 
  ?m:int ->
  ?n:int ->
  ?side:[ `L | `R ] ->
  ?up:bool ->
  ?beta:float ->
  ?cr:int ->
  ?cc:int ->
  ?c:mat ->
  ?alpha:float ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  ?br:int ->
  ?bc:int ->
  mat ->
  mat

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

returns
matrix c, which is overwritten.

parameter m
default = number of rows of c

parameter n
default = number of columns of c

parameter side
default = `L (left - multiplication is ab)

parameter up
default = true (upper triangular portion of a is accessed)

parameter beta
default = { re = 0.; im = 0. }

parameter cr
default = 1

parameter cc
default = 1

parameter c
default = matrix with minimal required dimension

parameter alpha
default = { re = 1.; im = 0. }

parameter ar
default = 1

parameter ac
default = 1

parameter br
default = 1

parameter bc
default = 1

val trmm : 
  ?m:int ->
  ?n:int ->
  ?side:[ `L | `R ] ->
  ?up:bool ->
  ?transa:trans3 ->
  ?diag:[ `U | `N ] ->
  ?alpha:float ->
  ?ar:int ->
  ?ac:int ->
  a:mat ->
  ?br:int ->
  ?bc:int ->
  mat ->
  unit

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

parameter m
default = number of rows of b

parameter n
default = number of columns of b

parameter side
default = `L (left - multiplication is ab)

parameter up
default = true (upper triangular portion of a is accessed)

parameter transa
default = `N

parameter diag
default = `N (non-unit)

parameter alpha
default = { re = 1.; im = 0. }

parameter ar
default = 1

parameter ac
default = 1

parameter br
default = 1

parameter bc
default = 1

val trsm : 
  ?m:int ->
  ?n:int ->
  ?side:[ `L | `R ] ->
  ?up:bool ->
  ?transa:trans3 ->
  ?diag:[ `U | `N ] ->
  ?alpha:float ->
  ?ar:int ->
  ?ac:int ->
  a:mat ->
  ?br:int ->
  ?bc:int ->
  mat ->
  unit

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

returns
matrix b, which is overwritten.

parameter m
default = number of rows of b

parameter n
default = number of columns of b

parameter side
default = `L (left - multiplication is ab)

parameter up
default = true (upper triangular portion of a is accessed)

parameter transa
default = `N

parameter diag
default = `N (non-unit)

parameter alpha
default = { re = 1.; im = 0. }

parameter ar
default = 1

parameter ac
default = 1

parameter br
default = 1

parameter bc
default = 1

val syrk : 
  ?n:int ->
  ?k:int ->
  ?up:bool ->
  ?beta:float ->
  ?cr:int ->
  ?cc:int ->
  ?c:mat ->
  ?trans:[ `N | `T ] ->
  ?alpha:float ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  mat

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

returns
matrix c, which is overwritten.

parameter n
default = number of rows of a (or a'), c

parameter k
default = number of columns of a (or a')

parameter up
default = true (upper triangular portion of c is accessed)

parameter beta
default = { re = 0.; im = 0. }

parameter cr
default = 1

parameter cc
default = 1

parameter c
default = matrix with minimal required dimension

parameter trans
default = `N

parameter alpha
default = { re = 1.; im = 0. }

parameter ar
default = 1

parameter ac
default = 1

val syr2k : 
  ?n:int ->
  ?k:int ->
  ?up:bool ->
  ?beta:float ->
  ?cr:int ->
  ?cc:int ->
  ?c:mat ->
  ?trans:[ `N | `T ] ->
  ?alpha:float ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  ?br:int ->
  ?bc:int ->
  mat ->
  mat

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

returns
matrix c, which is overwritten.

parameter n
default = number of rows of a (or a'), c

parameter k
default = number of columns of a (or a')

parameter up
default = true (upper triangular portion of c is accessed)

parameter beta
default = { re = 0.; im = 0. }

parameter cr
default = 1

parameter cc
default = 1

parameter c
default = matrix with minimal required dimension

parameter trans
default = `N

parameter alpha
default = { re = 1.; im = 0. }

parameter ar
default = 1

parameter ac
default = 1

parameter br
default = 1

parameter bc
default = 1

LAPACK interface

Auxiliary routines

val lacpy : 
  ?uplo:[ `U | `L ] ->
  ?m:int ->
  ?n:int ->
  ?br:int ->
  ?bc:int ->
  ?b:mat ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  mat

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

parameter uplo
default = whole matrix

parameter b
The target matrix. By default a fresh matrix to accommodate the sizes m and n and the offsets br and bc is created.

val laswp : 
  ?n:int ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  ?k1:int ->
  ?k2:int ->
  ?incx:int ->
  (int32, Bigarray.int32_elt, Bigarray.fortran_layout) Bigarray.Array1.t ->
  unit

laswp ?n ?ar ?ac a ?k1 ?k2 ?incx ipiv swap rows of a according to ipiv. See LAPACK-documentation for details!

parameter n
default = number of columns of matrix

parameter ar
default = 1

parameter ac
default = 1

parameter k1
default = 1

parameter k2
default = dimension of ipiv

parameter incx
default = 1

parameter ipiv
is a vector of sequential row interchanges.

val lapmt : 
  ?forward:bool ->
  ?m:int ->
  ?n:int ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  (int32, Bigarray.int32_elt, Bigarray.fortran_layout) Bigarray.Array1.t ->
  unit

lapmt ?forward ?n ?m ?ar ?ac a k swap columns of a according to the permutations in k. See LAPACK-documentation for details!

parameter forward
default = true

parameter m
default = number of rows of matrix

parameter n
default = number of columns of matrix

parameter ar
default = 1

parameter ac
default = 1

parameter k
is vector of column permutations and must be of length n. Note that checking for duplicates in k is not performed and this could lead to undefined behavior. Furthermore, LAPACK uses k as a workspace and restore it upon completion, sharing this permutation array is not thread safe.

val lassq : 
  ?n:int ->
  ?scale:float ->
  ?sumsq:float ->
  ?ofsx:int ->
  ?incx:int ->
  vec ->
  float * float

lassq ?n ?ofsx ?incx ?scale ?sumsq

returns
(scl, ssq), where scl is a scaling factor and ssq the sum of squares of vector x starting at ofs and using increment incx and initial scale and sumsq. The following equality holds: scl**2. *. ssq = x.{1}**2. +. ... +. x.{n}**2. +. scale**2. *. sumsq. See LAPACK-documentation for details!

parameter n
default = greater n s.t. ofsx+(n-1)(abs incx) <= dim x

parameter ofsx
default = 1

parameter incx
default = 1

parameter scale
default = 0.

parameter sumsq
default = 1.

val larnv : 
  ?idist:[ `Uniform0 | `Uniform1 | `Normal ] ->
  ?iseed:(int32, Bigarray.int32_elt, Bigarray.fortran_layout) Bigarray.Array1.t ->
  ?n:int ->
  ?ofsx:int ->
  ?x:vec ->
  unit ->
  vec

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

returns
a random vector with random distribution as specifified by idist, random seed iseed, vector offset ofsx and optional vector x.

parameter idist
default = `Normal

parameter iseed
default = integer vector of size 4 with all ones.

parameter n
default = dim x - ofsx + 1 if x is provided, 1 otherwise.

parameter ofsx
default = 1

parameter x
default = vector of length ofsx - 1 + n if n is provided.

val lange_min_lwork : int -> [ Lacaml__common.norm2 | `M | `F ] -> int

lange_min_lwork m norm

returns
the minimum length of the work array used by the lange-function.

parameter m
the number of rows in the matrix

parameter norm
type of norm that will be computed by lange

val lange : 
  ?m:int ->
  ?n:int ->
  ?norm:[ Lacaml__common.norm2 | `M | `F ] ->
  ?work:rvec ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  float

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

returns
the value of the one norm (norm = `O), or the Frobenius norm (norm = `F), or the infinity norm (norm = `I), or the element of largest absolute value (norm = `M) of a real matrix a.

parameter m
default = number of rows of matrix a

parameter n
default = number of columns of matrix a

parameter norm
default = `O

parameter work
default = allocated work space for norm `I

parameter ar
default = 1

parameter ac
default = 1

val lauum : ?up:bool -> ?n:int -> ?ar:int -> ?ac:int -> 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.

parameter up
default = true

parameter n
default = minimum of available number of rows/columns in matrix a

parameter ar
default = 1

parameter ac
default = 1

Linear equations (computational routines)

val getrf : 
  ?m:int ->
  ?n:int ->
  ?ipiv:(int32, Bigarray.int32_elt, Bigarray.fortran_layout) Bigarray.Array1.t ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  (int32, Bigarray.int32_elt, Bigarray.fortran_layout) Bigarray.Array1.t

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.

returns
ipiv, the pivot indices.

raises Failure
if the matrix is singular.

parameter m
default = number of rows in matrix a

parameter n
default = number of columns in matrix a

parameter ipiv
= vec of length min(m, n)

parameter ar
default = 1

parameter ac
default = 1

val getrs : 
  ?n:int ->
  ?ipiv:(int32, Bigarray.int32_elt, Bigarray.fortran_layout) Bigarray.Array1.t ->
  ?trans:trans3 ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  ?nrhs:int ->
  ?br:int ->
  ?bc:int ->
  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 getrf. Note that matrix a will be passed to getrf if ipiv was not provided.

raises Failure
if the matrix is singular.

parameter n
default = number of columns in matrix a

parameter ipiv
default = result from getrf applied to a

parameter trans
default = `N

parameter ar
default = 1

parameter ac
default = 1

parameter nrhs
default = available number of columns in matrix b

parameter br
default = 1

parameter bc
default = 1

val getri_min_lwork : int -> int

getri_min_lwork n

returns
the minimum length of the work array used by the getri-function if the matrix has n columns.

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

getri_opt_lwork ?n ?ar ?ac a

returns
the optimal size of the work array used by the getri-function.

parameter n
default = number of columns of matrix a

parameter ar
default = 1

parameter ac
default = 1

val getri : 
  ?n:int ->
  ?ipiv:(int32, Bigarray.int32_elt, Bigarray.fortran_layout) Bigarray.Array1.t ->
  ?work:vec ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  unit

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

raises Failure
if the matrix is singular.

parameter n
default = number of columns in matrix a

parameter ipiv
default = vec of length m from getri

parameter work
default = vec of optimum length

parameter ar
default = 1

parameter ac
default = 1

val sytrf_min_lwork : unit -> int

sytrf_min_lwork ()

returns
the minimum length of the work array used by the sytrf-function.

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

sytrf_opt_lwork ?n ?up ?ar ?ac a

returns
the optimal size of the work array used by the sytrf-function.

parameter n
default = number of columns of matrix a

parameter up
default = true (store upper triangle in a)

parameter a
the matrix a

parameter ar
default = 1

parameter ac
default = 1

val sytrf : 
  ?n:int ->
  ?up:bool ->
  ?ipiv:(int32, Bigarray.int32_elt, Bigarray.fortran_layout) Bigarray.Array1.t ->
  ?work:vec ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  (int32, Bigarray.int32_elt, Bigarray.fortran_layout) Bigarray.Array1.t

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

raises Failure
if D in a = U*D*U' or L*D*L' is singular.

parameter n
default = number of columns in matrix a

parameter up
default = true (store upper triangle in a)

parameter ipiv
= vec of length n

parameter work
default = vec of optimum length

parameter ar
default = 1

parameter ac
default = 1

val sytrs : 
  ?n:int ->
  ?up:bool ->
  ?ipiv:(int32, Bigarray.int32_elt, Bigarray.fortran_layout) Bigarray.Array1.t ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  ?nrhs:int ->
  ?br:int ->
  ?bc:int ->
  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 sytrf. Note that matrix a will be passed to sytrf if ipiv was not provided.

raises Failure
if the matrix is singular.

parameter n
default = number of columns in matrix a

parameter up
default = true (store upper triangle in a)

parameter ipiv
default = vec of length n

parameter ar
default = 1

parameter ac
default = 1

parameter nrhs
default = available number of columns in matrix b

parameter br
default = 1

parameter bc
default = 1

val sytri_min_lwork : int -> int

sytri_min_lwork n

returns
the minimum length of the work array used by the sytri-function if the matrix has n columns.

val sytri : 
  ?n:int ->
  ?up:bool ->
  ?ipiv:(int32, Bigarray.int32_elt, Bigarray.fortran_layout) Bigarray.Array1.t ->
  ?work:vec ->
  ?ar:int ->
  ?ac:int ->
  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 sytrf. Note that matrix a will be passed to sytrf if ipiv was not provided.

raises Failure
if the matrix is singular.

parameter n
default = number of columns in matrix a

parameter up
default = true (store upper triangle in a)

parameter ipiv
default = vec of length n from sytrf

parameter work
default = vec of optimum length

parameter ar
default = 1

parameter ac
default = 1

val potrf : 
  ?n:int ->
  ?up:bool ->
  ?ar:int ->
  ?ac:int ->
  ?jitter:float ->
  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.

raises Failure
if the matrix is singular.

parameter n
default = number of columns in matrix a

parameter up
default = true (store upper triangle in a)

parameter ar
default = 1

parameter ac
default = 1

parameter jitter
default = nothing

val potrs : 
  ?n:int ->
  ?up:bool ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  ?nrhs:int ->
  ?br:int ->
  ?bc:int ->
  ?factorize:bool ->
  ?jitter:float ->
  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 potrf.

raises Failure
if the matrix is singular.

parameter n
default = number of columns in matrix a

parameter up
default = true

parameter ar
default = 1

parameter ac
default = 1

parameter nrhs
default = available number of columns in matrix b

parameter br
default = 1

parameter bc
default = 1

parameter factorize
default = true (calls potrf implicitly)

parameter jitter
default = nothing

val potri : 
  ?n:int ->
  ?up:bool ->
  ?ar:int ->
  ?ac:int ->
  ?factorize:bool ->
  ?jitter:float ->
  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 potrf.

raises Failure
if the matrix is singular.

parameter n
default = number of columns in matrix a

parameter up
default = true (upper triangle stored in a)

parameter ar
default = 1

parameter ac
default = 1

parameter factorize
default = true (calls potrf implicitly)

parameter jitter
default = nothing

val trtrs : 
  ?n:int ->
  ?up:bool ->
  ?trans:trans3 ->
  ?diag:[ `U | `N ] ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  ?nrhs:int ->
  ?br:int ->
  ?bc:int ->
  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.

raises Failure
if the matrix a is singular.

parameter n
default = number of columns in matrix a

parameter up
default = true

parameter trans
default = `N

parameter diag
default = `N

parameter ar
default = 1

parameter ac
default = 1

parameter nrhs
default = available number of columns in matrix b

parameter br
default = 1

parameter bc
default = 1

val tbtrs : 
  ?n:int ->
  ?kd:int ->
  ?up:bool ->
  ?trans:trans3 ->
  ?diag:[ `U | `N ] ->
  ?abr:int ->
  ?abc:int ->
  mat ->
  ?nrhs:int ->
  ?br:int ->
  ?bc:int ->
  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.

raises Failure
if the matrix a is singular.

parameter n
default = number of columns in matrix ab

parameter kd
default = number of rows in matrix ab - 1

parameter up
default = true

parameter trans
default = `N

parameter diag
default = `N

parameter abr
default = 1

parameter abc
default = 1

parameter nrhs
default = available number of columns in matrix b

parameter br
default = 1

parameter bc
default = 1

val trtri : 
  ?n:int ->
  ?up:bool ->
  ?diag:[ `U | `N ] ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  unit

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

raises Failure
if the matrix a is singular.

parameter n
default = number of columns in matrix a

parameter up
default = true (upper triangle stored in a)

parameter diag
default = `N

parameter ar
default = 1

parameter ac
default = 1

val geqrf_opt_lwork : ?m:int -> ?n:int -> ?ar:int -> ?ac:int -> mat -> int

geqrf_opt_lwork ?m ?n ?ar ?ac a

returns
the optimum length of the work-array used by the geqrf-function given matrix a and optionally its logical dimensions m and n.

parameter m
default = number of rows in matrix a

parameter n
default = number of columns in matrix a

parameter ar
default = 1

parameter ac
default = 1

val geqrf_min_lwork : n:int -> int

geqrf_min_lwork ~n

returns
the minimum length of the work-array used by the geqrf-function if the matrix has n columns.

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

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

returns
tau, the scalar factors of the elementary reflectors.

parameter m
default = number of rows in matrix a

parameter n
default = number of columns in matrix a

parameter work
default = vec of optimum length

parameter tau
default = vec of required length

parameter ar
default = 1

parameter ac
default = 1

Linear equations (simple drivers)

val gesv : 
  ?n:int ->
  ?ipiv:(int32, Bigarray.int32_elt, Bigarray.fortran_layout) Bigarray.Array1.t ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  ?nrhs:int ->
  ?br:int ->
  ?bc:int ->
  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.

raises Failure
if the matrix a is singular.

parameter n
default = available number of columns in matrix a

parameter ipiv
default = vec of length n

parameter ar
default = 1

parameter ac
default = 1

parameter nrhs
default = available number of columns in matrix b

parameter br
default = 1

parameter bc
default = 1

val gbsv : 
  ?n:int ->
  ?ipiv:(int32, Bigarray.int32_elt, Bigarray.fortran_layout) Bigarray.Array1.t ->
  ?abr:int ->
  ?abc:int ->
  mat ->
  int ->
  int ->
  ?nrhs:int ->
  ?br:int ->
  ?bc:int ->
  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.

raises Failure
if the matrix a is singular.

parameter n
default = available number of columns in matrix ab

parameter ipiv
default = vec of length n

parameter abr
default = 1

parameter abc
default = 1

parameter nrhs
default = available number of columns in matrix b

parameter br
default = 1

parameter bc
default = 1

val gtsv : 
  ?n:int ->
  ?ofsdl:int ->
  vec ->
  ?ofsd:int ->
  vec ->
  ?ofsdu:int ->
  vec ->
  ?nrhs:int ->
  ?br:int ->
  ?bc:int ->
  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.

raises Failure
if the matrix is singular.

parameter n
default = available length of vector d

parameter ofsdl
default = 1

parameter ofsd
default = 1

parameter ofsdu
default = 1

parameter nrhs
default = available number of columns in matrix b

parameter br
default = 1

parameter bc
default = 1

val posv : 
  ?n:int ->
  ?up:bool ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  ?nrhs:int ->
  ?br:int ->
  ?bc:int ->
  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.

raises Failure
if the matrix is singular.

parameter n
default = available number of columns in matrix a

parameter up
default = true i.e., upper triangle of a is stored

parameter ar
default = 1

parameter ac
default = 1

parameter nrhs
default = available number of columns in matrix b

parameter br
default = 1

parameter bc
default = 1

val ppsv : 
  ?n:int ->
  ?up:bool ->
  ?ofsap:int ->
  vec ->
  ?nrhs:int ->
  ?br:int ->
  ?bc:int ->
  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.

raises Failure
if the matrix is singular.

parameter n
default = the greater n s.t. n(n+1)/2 <= Vec.dim ap

parameter up
default = true i.e., upper triangle of ap is stored

parameter ofsap
default = 1

parameter nrhs
default = available number of columns in matrix b

parameter br
default = 1

parameter bc
default = 1

val pbsv : 
  ?n:int ->
  ?up:bool ->
  ?kd:int ->
  ?abr:int ->
  ?abc:int ->
  mat ->
  ?nrhs:int ->
  ?br:int ->
  ?bc:int ->
  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.

raises Failure
if the matrix is singular.

parameter n
default = available number of columns in matrix ab

parameter up
default = true i.e., upper triangle of ab is stored

parameter kd
default = available number of rows in matrix ab - 1

parameter abr
default = 1

parameter abc
default = 1

parameter nrhs
default = available number of columns in matrix b

parameter br
default = 1

parameter bc
default = 1

val ptsv : 
  ?n:int ->
  ?ofsd:int ->
  vec ->
  ?ofse:int ->
  vec ->
  ?nrhs:int ->
  ?br:int ->
  ?bc:int ->
  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.

raises Failure
if the matrix is singular.

parameter n
default = available length of vector d

parameter ofsd
default = 1

parameter ofse
default = 1

parameter nrhs
default = available number of columns in matrix b

parameter br
default = 1

parameter bc
default = 1

val sysv_opt_lwork : 
  ?n:int ->
  ?up:bool ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  ?nrhs:int ->
  ?br:int ->
  ?bc:int ->
  mat ->
  int

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

returns
the optimum length of the work-array used by the sysv-function given matrix a, optionally its logical dimension n and given right hand side matrix b with an optional number nrhs of vectors.

parameter n
default = available number of columns in matrix a

parameter up
default = true i.e., upper triangle of a is stored

parameter ar
default = 1

parameter ac
default = 1

parameter nrhs
default = available number of columns in matrix b

parameter br
default = 1

parameter bc
default = 1

val sysv : 
  ?n:int ->
  ?up:bool ->
  ?ipiv:(int32, Bigarray.int32_elt, Bigarray.fortran_layout) Bigarray.Array1.t ->
  ?work:vec ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  ?nrhs:int ->
  ?br:int ->
  ?bc:int ->
  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.

raises Failure
if the matrix is singular.

parameter n
default = available number of columns in matrix a

parameter up
default = true i.e., upper triangle of a is stored

parameter ipiv
default = vec of length n

parameter work
default = vec of optimum length (-> sysv_opt_lwork)

parameter ar
default = 1

parameter ac
default = 1

parameter nrhs
default = available number of columns in matrix b

parameter br
default = 1

parameter bc
default = 1

val spsv : 
  ?n:int ->
  ?up:bool ->
  ?ipiv:(int32, Bigarray.int32_elt, Bigarray.fortran_layout) Bigarray.Array1.t ->
  ?ofsap:int ->
  vec ->
  ?nrhs:int ->
  ?br:int ->
  ?bc:int ->
  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.

raises Failure
if the matrix is singular.

parameter n
default = the greater n s.t. n(n+1)/2 <= Vec.dim ap

parameter up
default = true i.e., upper triangle of ap is stored

parameter ipiv
default = vec of length n

parameter ofsap
default = 1

parameter nrhs
default = available number of columns in matrix b

parameter br
default = 1

parameter bc
default = 1

Least squares (simple drivers)

val gels_min_lwork : m:int -> n:int -> nrhs:int -> int

gels_min_lwork ~m ~n ~nrhs

returns
the minimum length of the work-array used by the gels-function if the logical dimensions of the matrix are m rows and n columns and if there are nrhs right hand side vectors.

val gels_opt_lwork : 
  ?m:int ->
  ?n:int ->
  ?trans:[ `N | `T ] ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  ?nrhs:int ->
  ?br:int ->
  ?bc:int ->
  mat ->
  int

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

returns
the optimum length of the work-array used by the gels-function given matrix a, optionally its logical dimensions m and n and given right hand side matrix b with an optional number nrhs of vectors.

parameter m
default = available number of rows in matrix a

parameter n
default = available number of columns in matrix a

parameter trans
default = `N

parameter ar
default = 1

parameter ac
default = 1

parameter nrhs
default = available number of columns in matrix b

parameter br
default = 1

parameter bc
default = 1

val gels : 
  ?m:int ->
  ?n:int ->
  ?work:vec ->
  ?trans:[ `N | `T ] ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  ?nrhs:int ->
  ?br:int ->
  ?bc:int ->
  mat ->
  unit

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

parameter m
default = available number of rows in matrix a

parameter n
default = available number of columns of matrix a

parameter work
default = vec of optimum length (-> gels_opt_lwork)

parameter trans
default = `N

parameter ar
default = 1

parameter ac
default = 1

parameter nrhs
default = available number of columns in matrix b

parameter br
default = 1

parameter bc
default = 1