package slap

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Module Slap_common

Slap.Common contains definitions independent of the precision.

Flags

Diagonal-element flags

type diag

The type of diagonal-element flags

val unit : diag

A matrix is unit triagular.

val non_unit : diag

A matrix is not unit triagular.

val char_of_diag : diag -> char

Return a character of a flag (for BLAS/LAPACK).

Uppper/lower (triangular matrix) flags

type +'a uplo constraint 'a = [< `U | `L | `A ]

The type of upper/lower flags.

val upper : [> `U ] uplo

Using the upper triangular (or trapezoidal) part of a matrix.

val lower : [> `L ] uplo

Using the lower triangular (or trapezoidal) part of a matrix.

val upper_lower : [> `A ] uplo

Using both of the upper and lower triangular parts (i.e., all elements) of a matrix.

val char_of_uplo : _ uplo -> char

Return a character of a flag (for BLAS/LAPACK).

Transpose flags

type (+'indim, +'outdim, +'tag) trans constraint 'tag = [< `N | `T | `C ]

The type of transpose flags.

  • 'indim and 'outdim respectively mean pairs of dimensions of an input matrix and an output matrix:
  • Not transposing: 'indim = 'outdim = 'm * 'n, and
  • Transposing: 'indim = 'm * 'n, 'outdim = 'n * 'm (swapped from 'indim).
  • 'tag is `N (normal, i.e. not transposing), `T (transpose), or `C (conjugate transpose).
type (+'indim, +'outdim, +'tag) trans2 = ('indim, 'outdim, 'tag) trans constraint 'tag = [< `N | `T ]

Types of transpose flags for real vectors or matrices. Values of this type are

type (+'indim, +'outdim, +'tag) trans3 = ('indim, 'outdim, 'tag) trans

Types of transpose flags for complex vectors or matrices. Values of this type are

val normal : ('m * 'n, 'm * 'n, [> `N ]) trans

Non-transposed matrix.

val trans : ('m * 'n, 'n * 'm, [> `T ]) trans

Transpose of a matrix.

val conjtr : ('m * 'n, 'n * 'm, [> `C ]) trans3

Conjugate transpose of a matrix.

val get_transposed_dim : ('m * 'n, 'k * 'l, _) trans -> 'm Slap_size.t -> 'n Slap_size.t -> 'k Slap_size.t * 'l Slap_size.t

get_transposed_dim trans m n returns

val char_of_trans : ('indim, 'outdim, 'tag) trans -> char

Return a character of a flag (for BLAS/LAPACK).

Direction of matrix multiplication

type (+'k, +'m, +'n) side

('k, 'm, 'n) side is the type of left- and right-multiplication flags. The type parameters 'k, 'm and 'n correspond to dimensions of two multiplied matrices: Let A be a 'k-by-'k square matrix and B be a 'm-by-'n general matrix.

  • When A is multiplied from the left by B (i.e., A*B), 'k is equal to 'm; therefore the type of Slap_common.left is ('m, 'm, 'n) side.
  • Conversely, if A is right-multiplied by B (i.e., B*A), 'k is equal to 'n. Thus, the flag Slap_common.right is given the type ('n, 'm, 'n) side.
val left : ('m, 'm, 'n) side

Left multiplication

val right : ('n, 'm, 'n) side

Right multiplication

val check_side_dim : 'k Slap_size.t -> 'm Slap_size.t -> 'n Slap_size.t -> ('k, 'm, 'n) side -> bool

Auxiliary function (used internally)

val char_of_side : ('k, 'm, 'n) side -> char

Return a character of a flag (for BLAS/LAPACK).

Matrix norms

type +'a norm constraint 'a = [< `O | `I | `M | `F ]

The type of matrix norms.

type +'a norm2 = 'a norm constraint 'a = [< `O | `I ]

Values of this type are Slap_common.norm_1 and Slap_common.norm_inf.

type +'a norm4 = 'a norm

Values of this type are

val norm_1 : [> `O ] norm

1-norm of a matrix (maximum column sum).

val norm_inf : [> `I ] norm

Infinity-norm of a matrix (maximum row sum).

val norm_amax : [> `M ] norm

Largest absolute value of a matrix. (not a matrix norm)

val norm_frob : [> `F ] norm

Frobenius norm of a matrix.

val char_of_norm : _ norm -> char

Return a character of a flag (for BLAS/LAPACK).

SVD computation flags

type (+'a, +'b, +'c, +'d, +'e) svd_job
val svd_all : ('a, 'a, 'b, 'c, 'd) svd_job
val svd_top : ('b, 'a, 'b, 'c, 'd) svd_job
val svd_overwrite : ('c, 'a, 'b, 'c, 'd) svd_job
val svd_no : ('d, 'a, 'b, 'c, 'd) svd_job
val char_of_svd_job : (_, _, _, _, _) svd_job -> char

Return a character of a flag (for BLAS/LAPACK).

Integer vectors

type (+'n, +'cnt_or_dsc) int_vec = ('n, int, Bigarray.int_elt, 'cnt_or_dsc) Slap_vec.t
val create_int_vec : 'n Slap_size.t -> ('n, 'cnt) int_vec
type (+'n, +'cnt_or_dsc) int32_vec = ('n, int32, Bigarray.int32_elt, 'cnt_or_dsc) Slap_vec.t
val create_int32_vec : 'n Slap_size.t -> ('n, 'cnt) int32_vec

Utilities

val lacaml_trans2 : (_, _, _) trans -> Lacaml.Common.trans2
val lacaml_trans3 : (_, _, _) trans -> [ `N | `T | `C ]
val lacaml_svd_job : (_, _, _, _, _) svd_job -> Lacaml.Common.svd_job