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Matrix operations
Creation of matrices
Unary matrix operations
Binary matrix operations
Miscellaneous functions
Ternary matrix operations
Creation of matrices and accessors
Matrix transformations
Operations on one matrix
Operations on two matrices
Iterators over matrices

package lacaml

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Module `D.Mat`Source

Sourcetype t = mat

Matrix operations

Sourcetype patt = [

| `Full
| `Utr
| `Ltr
| `Upent of int
| `Lpent of int

]

Source

type unop =
  ?patt:patt ->
  ?m:int ->
  ?n:int ->
  ?br:int ->
  ?bc:int ->
  ?b:mat ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  mat

Source

type binop =
  ?patt:patt ->
  ?m:int ->
  ?n:int ->
  ?cr:int ->
  ?cc:int ->
  ?c:mat ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  ?br:int ->
  ?bc:int ->
  mat ->
  mat

Creation of matrices

Sourceval hilbert : int -> mat

hilbert n

returns
an nxn Hilbert matrix.

Sourceval hankel : int -> mat

hankel n

returns
an nxn Hankel matrix.

Sourceval pascal : int -> mat

pascal n

returns
an nxn Pascal matrix.

Sourceval rosser : unit -> mat

rosser n

returns
8x8 Rosser matrix.

Sourceval toeplitz : vec -> mat

toeplitz v

returns
the Toeplitz matrix associated with v. The constant diagonals are read from left to right from v.

raises Invalid_argument
if the length of v is not an odd number.

Sourceval vandermonde : vec -> mat

vandermonde v

returns
the Vandermonde matrix associated with v.

Sourceval wilkinson : int -> mat

wilkinson n

returns
the nxn Wilkinson matrix.

raises Invalid_argument
if n is not an odd number >= 3.

Source

val random : 
  ?rnd_state:Random.State.t ->
  ?from:float ->
  ?range:float ->
  int ->
  int ->
  mat

random ?rnd_state ?from ?range m n

returns
an mxn matrix initialized with random elements sampled uniformly from range starting at from. A random state rnd_state can be passed.

parameter rnd_state
default = Random.get_state ()

parameter from
default = -1.0

parameter range
default = 2.0

Unary matrix operations

Sourceval abs : unop

abs ?patt ?m ?n ?br ?bc ?b ?ar ?ac a computes the absolute value of the elements in the m by n sub-matrix of the matrix a starting in row ar and column ac and pattern patt. If b is given, the result will be stored in there using offsets br and bc, otherwise a fresh matrix will be used. The resulting matrix is returned.

parameter patt
default = `Full

parameter m
default = greater n s.t. ar + m - 1 <= dim1 a

parameter n
default = greater n s.t. ac + n - 1 <= dim2 a

parameter br
default = 1

parameter bc
default = 1

parameter b
default = fresh matrix with br + m - 1 rows and bc + n - 1 columns

parameter ar
default = 1

parameter ac
default = 1

Sourceval signum : unop

signum ?patt ?m ?n ?br ?bc ?b ?ar ?ac a computes the sign value (-1 for negative numbers, 0 (or -0) for zero, 1 for positive numbers, nan for nan) of the elements in the m by n sub-matrix of the matrix a starting in row ar and column ac and pattern patt. If b is given, the result will be stored in there using offsets br and bc, otherwise a fresh matrix will be used. The resulting matrix is returned.

parameter patt
default = `Full

parameter m
default = greater n s.t. ar + m - 1 <= dim1 a

parameter n
default = greater n s.t. ac + n - 1 <= dim2 a

parameter br
default = 1

parameter bc
default = 1

parameter b
default = fresh matrix with br + m - 1 rows and bc + n - 1 columns

parameter ar
default = 1

parameter ac
default = 1

Sourceval sqr : unop

sqr ?patt ?m ?n ?br ?bc ?b ?ar ?ac a computes the square of the elements in the m by n sub-matrix of the matrix a starting in row ar and column ac and pattern patt. If b is given, the result will be stored in there using offsets br and bc, otherwise a fresh matrix will be used. The resulting matrix is returned.

parameter patt
default = `Full

parameter m
default = greater n s.t. ar + m - 1 <= dim1 a

parameter n
default = greater n s.t. ac + n - 1 <= dim2 a

parameter br
default = 1

parameter bc
default = 1

parameter b
default = fresh matrix with br + m - 1 rows and bc + n - 1 columns

parameter ar
default = 1

parameter ac
default = 1

Sourceval sqrt : unop

sqrt ?patt ?m ?n ?br ?bc ?b ?ar ?ac a computes the square root of the elements in the m by n sub-matrix of the matrix a starting in row ar and column ac and pattern patt. If b is given, the result will be stored in there using offsets br and bc, otherwise a fresh matrix will be used. The resulting matrix is returned.

parameter patt
default = `Full

parameter m
default = greater n s.t. ar + m - 1 <= dim1 a

parameter n
default = greater n s.t. ac + n - 1 <= dim2 a

parameter br
default = 1

parameter bc
default = 1

parameter b
default = fresh matrix with br + m - 1 rows and bc + n - 1 columns

parameter ar
default = 1

parameter ac
default = 1

Sourceval cbrt : unop

cbrt ?patt ?m ?n ?br ?bc ?b ?ar ?ac a computes the cubic root of the elements in the m by n sub-matrix of the matrix a starting in row ar and column ac and pattern patt. If b is given, the result will be stored in there using offsets br and bc, otherwise a fresh matrix will be used. The resulting matrix is returned.

parameter patt
default = `Full

parameter m
default = greater n s.t. ar + m - 1 <= dim1 a

parameter n
default = greater n s.t. ac + n - 1 <= dim2 a

parameter br
default = 1

parameter bc
default = 1

parameter b
default = fresh matrix with br + m - 1 rows and bc + n - 1 columns

parameter ar
default = 1

parameter ac
default = 1

Sourceval exp : unop

exp ?patt ?m ?n ?br ?bc ?b ?ar ?ac a computes the exponential of the elements in the m by n sub-matrix of the matrix a starting in row ar and column ac and pattern patt. If b is given, the result will be stored in there using offsets br and bc, otherwise a fresh matrix will be used. The resulting matrix is returned.

parameter patt
default = `Full

parameter m
default = greater n s.t. ar + m - 1 <= dim1 a

parameter n
default = greater n s.t. ac + n - 1 <= dim2 a

parameter br
default = 1

parameter bc
default = 1

parameter b
default = fresh matrix with br + m - 1 rows and bc + n - 1 columns

parameter ar
default = 1

parameter ac
default = 1

Sourceval exp2 : unop

exp2 ?patt ?m ?n ?br ?bc ?b ?ar ?ac a computes the base-2 exponential of the elements in the m by n sub-matrix of the matrix a starting in row ar and column ac and pattern patt. If b is given, the result will be stored in there using offsets br and bc, otherwise a fresh matrix will be used. The resulting matrix is returned.

parameter patt
default = `Full

parameter m
default = greater n s.t. ar + m - 1 <= dim1 a

parameter n
default = greater n s.t. ac + n - 1 <= dim2 a

parameter br
default = 1

parameter bc
default = 1

parameter b
default = fresh matrix with br + m - 1 rows and bc + n - 1 columns

parameter ar
default = 1

parameter ac
default = 1

Sourceval expm1 : unop

expm1 ?patt ?m ?n ?br ?bc ?b ?ar ?ac a computes exp a -. 1. of the elements in the m by n sub-matrix of the matrix a starting in row ar and column ac and pattern patt. If b is given, the result will be stored in there using offsets br and bc, otherwise a fresh matrix will be used. The resulting matrix is returned.

parameter patt
default = `Full

parameter m
default = greater n s.t. ar + m - 1 <= dim1 a

parameter n
default = greater n s.t. ac + n - 1 <= dim2 a

parameter br
default = 1

parameter bc
default = 1

parameter b
default = fresh matrix with br + m - 1 rows and bc + n - 1 columns

parameter ar
default = 1

parameter ac
default = 1

Sourceval log : unop

log ?patt ?m ?n ?br ?bc ?b ?ar ?ac a computes the logarithm of the elements in the m by n sub-matrix of the matrix a starting in row ar and column ac and pattern patt. If b is given, the result will be stored in there using offsets br and bc, otherwise a fresh matrix will be used. The resulting matrix is returned.

parameter m
default = greater n s.t. ar + m - 1 <= dim1 a

parameter n
default = greater n s.t. ac + n - 1 <= dim2 a

parameter br
default = 1

parameter bc
default = 1

parameter b
default = fresh matrix with br + m - 1 rows and bc + n - 1 columns

parameter ar
default = 1

parameter ac
default = 1

Sourceval log10 : unop

log10 ?patt ?m ?n ?br ?bc ?b ?ar ?ac a computes the base-10 logarithm of the elements in the m by n sub-matrix of the matrix a starting in row ar and column ac and pattern patt. If b is given, the result will be stored in there using offsets br and bc, otherwise a fresh matrix will be used. The resulting matrix is returned.

parameter patt
default = `Full

parameter m
default = greater n s.t. ar + m - 1 <= dim1 a

parameter n
default = greater n s.t. ac + n - 1 <= dim2 a

parameter br
default = 1

parameter bc
default = 1

parameter b
default = fresh matrix with br + m - 1 rows and bc + n - 1 columns

parameter ar
default = 1

parameter ac
default = 1

Sourceval log2 : unop

log2 ?patt ?m ?n ?br ?bc ?b ?ar ?ac a computes base-2 logarithm of the elements in the m by n sub-matrix of the matrix a starting in row ar and column ac and pattern patt. If b is given, the result will be stored in there using offsets br and bc, otherwise a fresh matrix will be used. The resulting matrix is returned.

parameter patt
default = `Full

parameter m
default = greater n s.t. ar + m - 1 <= dim1 a

parameter n
default = greater n s.t. ac + n - 1 <= dim2 a

parameter br
default = 1

parameter bc
default = 1

parameter b
default = fresh matrix with br + m - 1 rows and bc + n - 1 columns

parameter ar
default = 1

parameter ac
default = 1

Sourceval log1p : unop

log1p ?patt ?m ?n ?br ?bc ?b ?ar ?ac a computes log (1 + a) of the elements in the m by n sub-matrix of the matrix a starting in row ar and column ac and pattern patt. If b is given, the result will be stored in there using offsets br and bc, otherwise a fresh matrix will be used. The resulting matrix is returned.

parameter patt
default = `Full

parameter m
default = greater n s.t. ar + m - 1 <= dim1 a

parameter n
default = greater n s.t. ac + n - 1 <= dim2 a

parameter br
default = 1

parameter bc
default = 1

parameter b
default = fresh matrix with br + m - 1 rows and bc + n - 1 columns

parameter ar
default = 1

parameter ac
default = 1

Sourceval sin : unop

sin ?patt ?m ?n ?br ?bc ?b ?ar ?ac a computes the sine of the elements in the m by n sub-matrix of the matrix a starting in row ar and column ac and pattern patt. If b is given, the result will be stored in there using offsets br and bc, otherwise a fresh matrix will be used. The resulting matrix is returned.

parameter patt
default = `Full

parameter m
default = greater n s.t. ar + m - 1 <= dim1 a

parameter n
default = greater n s.t. ac + n - 1 <= dim2 a

parameter br
default = 1

parameter bc
default = 1

parameter b
default = fresh matrix with br + m - 1 rows and bc + n - 1 columns

parameter ar
default = 1

parameter ac
default = 1

Sourceval cos : unop

cos ?patt ?m ?n ?br ?bc ?b ?ar ?ac a computes the cosine of the elements in the m by n sub-matrix of the matrix a starting in row ar and column ac and pattern patt. If b is given, the result will be stored in there using offsets br and bc, otherwise a fresh matrix will be used. The resulting matrix is returned.

parameter patt
default = `Full

parameter m
default = greater n s.t. ar + m - 1 <= dim1 a

parameter n
default = greater n s.t. ac + n - 1 <= dim2 a

parameter br
default = 1

parameter bc
default = 1

parameter b
default = fresh matrix with br + m - 1 rows and bc + n - 1 columns

parameter ar
default = 1

parameter ac
default = 1

Sourceval tan : unop

tan ?patt ?m ?n ?br ?bc ?b ?ar ?ac a computes the tangent of the elements in the m by n sub-matrix of the matrix a starting in row ar and column ac and pattern patt. If b is given, the result will be stored in there using offsets br and bc, otherwise a fresh matrix will be used. The resulting matrix is returned.

parameter patt
default = `Full

parameter m
default = greater n s.t. ar + m - 1 <= dim1 a

parameter n
default = greater n s.t. ac + n - 1 <= dim2 a

parameter br
default = 1

parameter bc
default = 1

parameter b
default = fresh matrix with br + m - 1 rows and bc + n - 1 columns

parameter ar
default = 1

parameter ac
default = 1

Sourceval asin : unop

asin ?patt ?m ?n ?br ?bc ?b ?ar ?ac a computes the arc sine of the elements in the m by n sub-matrix of the matrix a starting in row ar and column ac and pattern patt. If b is given, the result will be stored in there using offsets br and bc, otherwise a fresh matrix will be used. The resulting matrix is returned.

parameter patt
default = `Full

parameter m
default = greater n s.t. ar + m - 1 <= dim1 a

parameter n
default = greater n s.t. ac + n - 1 <= dim2 a

parameter br
default = 1

parameter bc
default = 1

parameter b
default = fresh matrix with br + m - 1 rows and bc + n - 1 columns

parameter ar
default = 1

parameter ac
default = 1

Sourceval acos : unop

acos ?patt ?m ?n ?br ?bc ?b ?ar ?ac a computes the arc cosine of the elements in the m by n sub-matrix of the matrix a starting in row ar and column ac and pattern patt. If b is given, the result will be stored in there using offsets br and bc, otherwise a fresh matrix will be used. The resulting matrix is returned.

parameter patt
default = `Full

parameter m
default = greater n s.t. ar + m - 1 <= dim1 a

parameter n
default = greater n s.t. ac + n - 1 <= dim2 a

parameter br
default = 1

parameter bc
default = 1

parameter b
default = fresh matrix with br + m - 1 rows and bc + n - 1 columns

parameter ar
default = 1

parameter ac
default = 1

Sourceval atan : unop

atan ?patt ?m ?n ?br ?bc ?b ?ar ?ac a computes the arc tangent of the elements in the m by n sub-matrix of the matrix a starting in row ar and column ac and pattern patt. If b is given, the result will be stored in there using offsets br and bc, otherwise a fresh matrix will be used. The resulting matrix is returned.

parameter patt
default = `Full

parameter m
default = greater n s.t. ar + m - 1 <= dim1 a

parameter n
default = greater n s.t. ac + n - 1 <= dim2 a

parameter br
default = 1

parameter bc
default = 1

parameter b
default = fresh matrix with br + m - 1 rows and bc + n - 1 columns

parameter ar
default = 1

parameter ac
default = 1

Sourceval sinh : unop

sinh ?patt ?m ?n ?br ?bc ?b ?ar ?ac a computes the hyperbolic sine of the elements in the m by n sub-matrix of the matrix a starting in row ar and column ac and pattern patt. If b is given, the result will be stored in there using offsets br and bc, otherwise a fresh matrix will be used. The resulting matrix is returned.

parameter patt
default = `Full

parameter m
default = greater n s.t. ar + m - 1 <= dim1 a

parameter n
default = greater n s.t. ac + n - 1 <= dim2 a

parameter br
default = 1

parameter bc
default = 1

parameter b
default = fresh matrix with br + m - 1 rows and bc + n - 1 columns

parameter ar
default = 1

parameter ac
default = 1

Sourceval cosh : unop

cosh ?patt ?m ?n ?br ?bc ?b ?ar ?ac a computes the hyperbolic cosine of the elements in the m by n sub-matrix of the matrix a starting in row ar and column ac and pattern patt. If b is given, the result will be stored in there using offsets br and bc, otherwise a fresh matrix will be used. The resulting matrix is returned.

parameter patt
default = `Full

parameter m
default = greater n s.t. ar + m - 1 <= dim1 a

parameter n
default = greater n s.t. ac + n - 1 <= dim2 a

parameter br
default = 1

parameter bc
default = 1

parameter b
default = fresh matrix with br + m - 1 rows and bc + n - 1 columns

parameter ar
default = 1

parameter ac
default = 1

Sourceval tanh : unop

tanh ?patt ?m ?n ?br ?bc ?b ?ar ?ac a computes the hyperbolic tangent of the elements in the m by n sub-matrix of the matrix a starting in row ar and column ac and pattern patt. If b is given, the result will be stored in there using offsets br and bc, otherwise a fresh matrix will be used. The resulting matrix is returned.

parameter patt
default = `Full

parameter m
default = greater n s.t. ar + m - 1 <= dim1 a

parameter n
default = greater n s.t. ac + n - 1 <= dim2 a

parameter br
default = 1

parameter bc
default = 1

parameter b
default = fresh matrix with br + m - 1 rows and bc + n - 1 columns

parameter ar
default = 1

parameter ac
default = 1

Sourceval asinh : unop

asinh ?patt ?m ?n ?br ?bc ?b ?ar ?ac a computes the hyperbolic arc sine of the elements in the m by n sub-matrix of the matrix a starting in row ar and column ac and pattern patt. If b is given, the result will be stored in there using offsets br and bc, otherwise a fresh matrix will be used. The resulting matrix is returned.

parameter patt
default = `Full

parameter m
default = greater n s.t. ar + m - 1 <= dim1 a

parameter n
default = greater n s.t. ac + n - 1 <= dim2 a

parameter br
default = 1

parameter bc
default = 1

parameter b
default = fresh matrix with br + m - 1 rows and bc + n - 1 columns

parameter ar
default = 1

parameter ac
default = 1

Sourceval acosh : unop

acosh ?patt ?m ?n ?br ?bc ?b ?ar ?ac a computes the hyperbolic arc cosine of the elements in the m by n sub-matrix of the matrix a starting in row ar and column ac and pattern patt. If b is given, the result will be stored in there using offsets br and bc, otherwise a fresh matrix will be used. The resulting matrix is returned.

parameter patt
default = `Full

parameter m
default = greater n s.t. ar + m - 1 <= dim1 a

parameter n
default = greater n s.t. ac + n - 1 <= dim2 a

parameter br
default = 1

parameter bc
default = 1

parameter b
default = fresh matrix with br + m - 1 rows and bc + n - 1 columns

parameter ar
default = 1

parameter ac
default = 1

Sourceval atanh : unop

atanh ?patt ?m ?n ?br ?bc ?b ?ar ?ac a computes the hyperbolic arc tangent of the elements in the m by n sub-matrix of the matrix a starting in row ar and column ac and pattern patt. If b is given, the result will be stored in there using offsets br and bc, otherwise a fresh matrix will be used. The resulting matrix is returned.

parameter patt
default = `Full

parameter m
default = greater n s.t. ar + m - 1 <= dim1 a

parameter n
default = greater n s.t. ac + n - 1 <= dim2 a

parameter br
default = 1

parameter bc
default = 1

parameter b
default = fresh matrix with br + m - 1 rows and bc + n - 1 columns

parameter ar
default = 1

parameter ac
default = 1

Sourceval floor : unop

floor ?patt ?m ?n ?br ?bc ?b ?ar ?ac a computes the floor of the elements in the m by n sub-matrix of the matrix a starting in row ar and column ac and pattern patt. If b is given, the result will be stored in there using offsets br and bc, otherwise a fresh matrix will be used. The resulting matrix is returned.

parameter patt
default = `Full

parameter m
default = greater n s.t. ar + m - 1 <= dim1 a

parameter n
default = greater n s.t. ac + n - 1 <= dim2 a

parameter br
default = 1

parameter bc
default = 1

parameter b
default = fresh matrix with br + m - 1 rows and bc + n - 1 columns

parameter ar
default = 1

parameter ac
default = 1

Sourceval ceil : unop

ceil ?patt ?m ?n ?br ?bc ?b ?ar ?ac a computes the ceiling of the elements in the m by n sub-matrix of the matrix a starting in row ar and column ac and pattern patt. If b is given, the result will be stored in there using offsets br and bc, otherwise a fresh matrix will be used. The resulting matrix is returned.

parameter patt
default = `Full

parameter m
default = greater n s.t. ar + m - 1 <= dim1 a

parameter n
default = greater n s.t. ac + n - 1 <= dim2 a

parameter br
default = 1

parameter bc
default = 1

parameter b
default = fresh matrix with br + m - 1 rows and bc + n - 1 columns

parameter ar
default = 1

parameter ac
default = 1

Sourceval round : unop

round ?patt ?m ?n ?br ?bc ?b ?ar ?ac a rounds the elements in the m by n sub-matrix of the matrix a starting in row ar and column ac and pattern patt. If b is given, the result will be stored in there using offsets br and bc, otherwise a fresh matrix will be used. The resulting matrix is returned.

parameter patt
default = `Full

parameter m
default = greater n s.t. ar + m - 1 <= dim1 a

parameter n
default = greater n s.t. ac + n - 1 <= dim2 a

parameter br
default = 1

parameter bc
default = 1

parameter b
default = fresh matrix with br + m - 1 rows and bc + n - 1 columns

parameter ar
default = 1

parameter ac
default = 1

Sourceval trunc : unop

trunc ?patt ?m ?n ?br ?bc ?b ?ar ?ac a computes the truncation of the elements in the m by n sub-matrix of the matrix a starting in row ar and column ac and pattern patt. If b is given, the result will be stored in there using offsets br and bc, otherwise a fresh matrix will be used. The resulting matrix is returned.

parameter patt
default = `Full

parameter m
default = greater n s.t. ar + m - 1 <= dim1 a

parameter n
default = greater n s.t. ac + n - 1 <= dim2 a

parameter br
default = 1

parameter bc
default = 1

parameter b
default = fresh matrix with br + m - 1 rows and bc + n - 1 columns

parameter ar
default = 1

parameter ac
default = 1

Sourceval erf : unop

erf ?patt ?m ?n ?br ?bc ?b ?ar ?ac a computes the error function of the elements in the m by n sub-matrix of the matrix a starting in row ar and column ac and pattern patt. If b is given, the result will be stored in there using offsets br and bc, otherwise a fresh matrix will be used. The resulting matrix is returned.

parameter patt
default = `Full

parameter m
default = greater n s.t. ar + m - 1 <= dim1 a

parameter n
default = greater n s.t. ac + n - 1 <= dim2 a

parameter br
default = 1

parameter bc
default = 1

parameter b
default = fresh matrix with br + m - 1 rows and bc + n - 1 columns

parameter ar
default = 1

parameter ac
default = 1

Sourceval erfc : unop

erfc ?patt ?m ?n ?br ?bc ?b ?ar ?ac a computes the complementary error function of the elements in the m by n sub-matrix of the matrix a starting in row ar and column ac and pattern patt. If b is given, the result will be stored in there using offsets br and bc, otherwise a fresh matrix will be used. The resulting matrix is returned.

parameter patt
default = `Full

parameter m
default = greater n s.t. ar + m - 1 <= dim1 a

parameter n
default = greater n s.t. ac + n - 1 <= dim2 a

parameter br
default = 1

parameter bc
default = 1

parameter b
default = fresh matrix with br + m - 1 rows and bc + n - 1 columns

parameter ar
default = 1

parameter ac
default = 1

Sourceval logistic : unop

logistic ?patt ?m ?n ?br ?bc ?b ?ar ?ac a computes the logistic function 1/(1 + exp(-a) of the elements in the m by n sub-matrix of the matrix a starting in row ar and column ac and pattern patt. If b is given, the result will be stored in there using offsets br and bc, otherwise a fresh matrix will be used. The resulting matrix is returned.

parameter patt
default = `Full

parameter m
default = greater n s.t. ar + m - 1 <= dim1 a

parameter n
default = greater n s.t. ac + n - 1 <= dim2 a

parameter br
default = 1

parameter bc
default = 1

parameter b
default = fresh matrix with br + m - 1 rows and bc + n - 1 columns

parameter ar
default = 1

parameter ac
default = 1

Sourceval relu : unop

relu ?patt ?m ?n ?br ?bc ?b ?ar ?ac a computes the rectified linear unit function max(a, 0) of the elements in the m by n sub-matrix of the matrix a starting in row ar and column ac and pattern patt. If b is given, the result will be stored in there using offsets br and bc, otherwise a fresh matrix will be used. The resulting matrix is returned.

parameter patt
default = `Full

parameter m
default = greater n s.t. ar + m - 1 <= dim1 a

parameter n
default = greater n s.t. ac + n - 1 <= dim2 a

parameter br
default = 1

parameter bc
default = 1

parameter b
default = fresh matrix with br + m - 1 rows and bc + n - 1 columns

parameter ar
default = 1

parameter ac
default = 1

Sourceval softplus : unop

softplus ?patt ?m ?n ?br ?bc ?b ?ar ?ac a computes the softplus function log(1 + exp(x) of the elements in the m by n sub-matrix of the matrix a starting in row ar and column ac and pattern patt. If b is given, the result will be stored in there using offsets br and bc, otherwise a fresh matrix will be used. The resulting matrix is returned.

parameter patt
default = `Full

parameter m
default = greater n s.t. ar + m - 1 <= dim1 a

parameter n
default = greater n s.t. ac + n - 1 <= dim2 a

parameter br
default = 1

parameter bc
default = 1

parameter b
default = fresh matrix with br + m - 1 rows and bc + n - 1 columns

parameter ar
default = 1

parameter ac
default = 1

Sourceval softsign : unop

softsign ?patt ?m ?n ?br ?bc ?b ?ar ?ac a computes the softsign function x / (1 + abs(x)) of the elements in the m by n sub-matrix of the matrix a starting in row ar and column ac and pattern patt. If b is given, the result will be stored in there using offsets br and bc, otherwise a fresh matrix will be used. The resulting matrix is returned.

parameter patt
default = `Full

parameter m
default = greater n s.t. ar + m - 1 <= dim1 a

parameter n
default = greater n s.t. ac + n - 1 <= dim2 a

parameter br
default = 1

parameter bc
default = 1

parameter b
default = fresh matrix with br + m - 1 rows and bc + n - 1 columns

parameter ar
default = 1

parameter ac
default = 1

Binary matrix operations

Sourceval pow : binop

pow ?patt ?m ?n ?cr ?cc ?c ?ar ?ac a ?br ?bc b computes pow(a, b) for the m by n sub-matrix of the matrix a starting in row ar and column ac and pattern patt with the corresponding sub-matrix of the matrix b starting in row br and column bc. If c is given, the result will be stored in there starting in row cr and column cc, otherwise a fresh matrix will be used. The resulting matrix is returned.

parameter patt
default = `Full

parameter m
default = greater n s.t. ar + m - 1 <= dim1 a

parameter n
default = greater n s.t. ac + n - 1 <= dim2 a

parameter cr
default = 1

parameter cc
default = 1

parameter c
default = fresh matrix with cr + m - 1 rows and cc + n - 1 columns

parameter br
default = 1

parameter bc
default = 1

parameter ar
default = 1

parameter ac
default = 1

Sourceval atan2 : binop

atan2 ?patt ?m ?n ?cr ?cc ?c ?ar ?ac a ?br ?bc b computes atan2(a, b) for the m by n sub-matrix of the matrix a starting in row ar and column ac and pattern patt with the corresponding sub-matrix of the matrix b starting in row br and column bc. If c is given, the result will be stored in there starting in row cr and column cc, otherwise a fresh matrix will be used. The resulting matrix is returned.

NOTE: WARNING! From a geometric point of view, the atan2 function takes the y-coordinate in a and the x-coordinate in b. This confusion is a sad consequence of the C99-standard reversing the argument order for atan2 for no good reason.

parameter patt
default = `Full

parameter m
default = greater n s.t. ar + m - 1 <= dim1 a

parameter n
default = greater n s.t. ac + n - 1 <= dim2 a

parameter cr
default = 1

parameter cc
default = 1

parameter c
default = fresh matrix with cr + m - 1 rows and cc + n - 1 columns

parameter br
default = 1

parameter bc
default = 1

parameter ar
default = 1

parameter ac
default = 1

Sourceval hypot : binop

hypot ?patt ?m ?n ?cr ?cc ?c ?ar ?ac a ?br ?bc b computes sqrt(a*a+b*b) for the m by n sub-matrix of the matrix a starting in row ar and column ac and pattern patt with the corresponding sub-matrix of the matrix b starting in row br and column bc. If c is given, the result will be stored in there starting in row cr and column cc, otherwise a fresh matrix will be used. The resulting matrix is returned.

parameter patt
default = `Full

parameter m
default = greater n s.t. ar + m - 1 <= dim1 a

parameter n
default = greater n s.t. ac + n - 1 <= dim2 a

parameter cr
default = 1

parameter cc
default = 1

parameter c
default = fresh matrix with cr + m - 1 rows and cc + n - 1 columns

parameter br
default = 1

parameter bc
default = 1

parameter ar
default = 1

parameter ac
default = 1

Sourceval min2 : binop

min2 ?patt ?m ?n ?cr ?cc ?c ?ar ?ac a ?br ?bc b computes the elementwise minimum of the m by n sub-matrix of the matrix a starting in row ar and column ac and pattern patt with the corresponding sub-matrix of the matrix b starting in row br and column bc. If c is given, the result will be stored in there starting in row cr and column cc, otherwise a fresh matrix will be used. The resulting matrix is returned.

parameter patt
default = `Full

parameter m
default = greater n s.t. ar + m - 1 <= dim1 a

parameter n
default = greater n s.t. ac + n - 1 <= dim2 a

parameter cr
default = 1

parameter cc
default = 1

parameter c
default = fresh matrix with cr + m - 1 rows and cc + n - 1 columns

parameter br
default = 1

parameter bc
default = 1

parameter ar
default = 1

parameter ac
default = 1

Sourceval max2 : binop

max2 ?patt ?m ?n ?cr ?cc ?c ?ar ?ac a ?br ?bc b computes the elementwise maximum of the m by n sub-matrix of the matrix a starting in row ar and column ac and pattern patt with the corresponding sub-matrix of the matrix b starting in row br and column bc. If c is given, the result will be stored in there starting in row cr and column cc, otherwise a fresh matrix will be used. The resulting matrix is returned.

parameter patt
default = `Full

parameter m
default = greater n s.t. ar + m - 1 <= dim1 a

parameter n
default = greater n s.t. ac + n - 1 <= dim2 a

parameter cr
default = 1

parameter cc
default = 1

parameter c
default = fresh matrix with cr + m - 1 rows and cc + n - 1 columns

parameter br
default = 1

parameter bc
default = 1

parameter ar
default = 1

parameter ac
default = 1

Source

val sum_prod : 
  ?patt:patt ->
  ?m:int ->
  ?n:int ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  ?br:int ->
  ?bc:int ->
  mat ->
  float

sum_prod ?patt ?m ?n ?ar ?ac a ?br ?bc b

returns
the sum of elementwise products between the m by n sub-matrix of the matrix a starting in row ar and column ac with the corresponding sub-matrix of the matrix b starting in row br and column bc.

parameter patt
default = `Full

parameter m
default = greater n s.t. ar + m - 1 <= dim1 a

parameter n
default = greater n s.t. ac + n - 1 <= dim2 a

parameter ar
default = 1

parameter ac
default = 1

parameter br
default = 1

parameter bc
default = 1

Miscellaneous functions

Source

val log_sum_exp : 
  ?patt:patt ->
  ?m:int ->
  ?n:int ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  float

log_sum_exp ?patt ?m ?n ?ar ?ac a computes the logarithm of the sum of exponentials of all elements in the m-by-n submatrix using pattern patt, starting at row ar and column ac.

parameter patt
default = `Full

parameter m
default = number of rows of a

parameter n
default = number of columns of a

Ternary matrix operations

Source

val cpab : 
  ?patt:patt ->
  ?m:int ->
  ?n:int ->
  ?cr:int ->
  ?cc:int ->
  mat ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  ?br:int ->
  ?bc:int ->
  mat ->
  unit

cpab ?patt ?m ?n ?cr ?cc c ?ar ?ac a ?br ?bc b multiplies designated m-by-n range of elements of matrices a and b using pattern patt elementwise and adds the result to and stores it in the specified range in c. This function is useful for convolutions. Similar to Vec.zpxy.

parameter patt
default = `Full

parameter m
default = number of rows of a

parameter n
default = number of columns of a

parameter cr
default = 1

parameter cc
default = 1

parameter ar
default = 1

parameter ac
default = 1

parameter br
default = 1

parameter bc
default = 1

Source

val cmab : 
  ?patt:patt ->
  ?m:int ->
  ?n:int ->
  ?cr:int ->
  ?cc:int ->
  mat ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  ?br:int ->
  ?bc:int ->
  mat ->
  unit

cmab ?patt ?m ?n ?cr ?cc c ?ar ?ac a ?br ?bc b multiplies designated m-by-n range of elements of matrices a and b elementwise using pattern patt and subtracts the result from and stores it in the specified range in c. This function is useful for convolutions. Similar to Vec.zmxy.

parameter patt
default = `Full

parameter m
default = number of rows of a

parameter n
default = number of columns of a

parameter cr
default = 1

parameter cc
default = 1

parameter ar
default = 1

parameter ac
default = 1

parameter br
default = 1

parameter bc
default = 1

Creation of matrices and accessors

Sourceval create : int -> int -> mat

create m n

returns
a matrix containing m rows and n columns.

Sourceval make : int -> int -> float -> mat

make m n x

returns
a matrix containing m rows and n columns initialized with value x.

Sourceval make0 : int -> int -> mat

make0 m n x

returns
a matrix containing m rows and n columns initialized with the zero element.

Sourceval of_array : float array array -> mat

of_array ar

returns
a matrix initialized from the array of arrays ar. It is assumed that the OCaml matrix is in row major order (standard).

Sourceval to_array : mat -> float array array

to_array mat

returns
an array of arrays initialized from matrix mat.

Sourceval of_list : float list list -> mat

of_list ls

returns
a matrix initialized from the list of lists ls. Each sublist of ls represents a row of the desired matrix, and must be of the same length.

Sourceval to_list : mat -> float list list

to_array mat

returns
mat in row major order as lists.

Sourceval of_col_vecs : vec array -> mat

of_col_vecs ar

returns
a matrix whose columns are initialized from the array of vectors ar. The vectors must be of same length.

Sourceval to_col_vecs : mat -> vec array

to_col_vecs mat

returns
an array of column vectors initialized from matrix mat.

Sourceval of_col_vecs_list : vec list -> mat

of_col_vecs_list ar

returns
a matrix whose columns are initialized from the list of vectors ar. The vectors must be of same length.

Sourceval to_col_vecs_list : mat -> vec list

to_col_vecs_list mat

returns
a list of column vectors initialized from matrix mat.

Sourceval as_vec : mat -> vec

as_vec mat

returns
a vector containing all elements of the matrix in column-major order. The data is shared.

Sourceval init_rows : int -> int -> (int -> int -> float) -> mat

init_cols m n f

returns
a matrix containing m rows and n columns, where each element at row and col is initialized by the result of calling f row col. The elements are passed row-wise.

Sourceval init_cols : int -> int -> (int -> int -> float) -> mat

init_cols m n f

returns
a matrix containing m rows and n columns, where each element at row and col is initialized by the result of calling f row col. The elements are passed column-wise.

Sourceval create_mvec : int -> mat

create_mvec m

returns
a matrix with one column containing m rows.

Sourceval make_mvec : int -> float -> mat

make_mvec m x

returns
a matrix with one column containing m rows initialized with value x.

Sourceval mvec_of_array : float array -> mat

mvec_of_array ar

returns
a matrix with one column initialized with values from array ar.

Sourceval mvec_to_array : mat -> float array

mvec_to_array mat

returns
an array initialized with values from the first (not necessarily only) column vector of matrix mat.

Sourceval from_col_vec : vec -> mat

from_col_vec v

returns
a matrix with one column representing vector v. The data is shared.

Sourceval from_row_vec : vec -> mat

from_row_vec v

returns
a matrix with one row representing vector v. The data is shared.

Sourceval empty : mat

empty, the empty matrix.

Sourceval identity : int -> mat

identity n

returns
the nxn identity matrix.

Source

val of_diag : 
  ?n:int ->
  ?br:int ->
  ?bc:int ->
  ?b:mat ->
  ?ofsx:int ->
  ?incx:int ->
  vec ->
  mat

of_diag ?n ?br ?bc ?b ?ofsx ?incx x

returns
matrix b with diagonal elements in the designated sub-matrix coming from the designated sub-vector in x.

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

parameter br
default = 1

parameter bc
default = 1

parameter b
default = minimal fresh matrix consistent with n, br, and bc

parameter ofsx
default = 1

parameter incx
default = 1

Sourceval dim1 : mat -> int

dim1 m

returns
the first dimension of matrix m (number of rows).

Sourceval dim2 : mat -> int

dim2 m

returns
the second dimension of matrix m (number of columns).

Sourceval has_zero_dim : mat -> bool

has_zero_dim mat checks whether matrix mat has a dimension of size zero. In this case it cannot contain data.

Sourceval col : mat -> int -> vec

col m n

returns
the nth column of matrix m as a vector. The data is shared.

Sourceval copy_row : ?vec:vec -> mat -> int -> vec

copy_row ?vec mat int

returns
a copy of the nth row of matrix m in vector vec.

parameter vec
default = fresh vector of length dim2 mat

Matrix transformations

Source

val swap : 
  ?patt:patt ->
  ?m:int ->
  ?n:int ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  ?br:int ->
  ?bc:int ->
  mat ->
  unit

swap ?patt ?m ?n ?ar ?ac a ?br ?bc b swaps the contents of (sub-matrices) a and b.

parameter patt
default = `Full

parameter m
default = greater n s.t. ar + m - 1 <= dim1 a

parameter n
default = greater n s.t. ac + n - 1 <= dim2 a

parameter ar
default = 1

parameter ac
default = 1

parameter br
default = 1

parameter bc
default = 1

Source

val transpose_copy : 
  ?m:int ->
  ?n:int ->
  ?br:int ->
  ?bc:int ->
  ?b:mat ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  mat

transpose_copy ?m ?n ?br ?bc ?b ?ar ?ac a

returns
the transpose of (sub-)matrix a. If b is given, the result will be stored in there using offsets br and bc, otherwise a fresh matrix will be used. NOTE: this operations does _not_ support in-place transposes!

parameter m
default = greater n s.t. ar + m - 1 <= dim1 a

parameter n
default = greater n s.t. ac + n - 1 <= dim2 a

parameter br
default = 1

parameter bc
default = 1

parameter b
default = fresh matrix with br + n - 1 rows and bc + m - 1 columns

parameter ar
default = 1

parameter ac
default = 1

Sourceval detri : ?up:bool -> ?n:int -> ?ar:int -> ?ac:int -> mat -> unit

detri ?up ?n ?ar ?ac a takes a triangular (sub-)matrix a, i.e. one where only the upper (iff up is true) or lower triangle is defined, and makes it a symmetric matrix by mirroring the defined triangle along the diagonal.

parameter up
default = true

parameter n
default = Mat.dim2 a

parameter ar
default = 1

parameter ac
default = 1

Sourceval packed : ?up:bool -> ?n:int -> ?ar:int -> ?ac:int -> mat -> vec

packed ?up ?n ?ar ?ac a

returns
(sub-)matrix a in packed storage format.

parameter up
default = true

parameter n
default = Mat.dim2 a

parameter ar
default = 1

parameter ac
default = 1

Sourceval unpacked : ?up:bool -> ?n:int -> vec -> mat

unpacked ?up x

returns
an upper or lower (depending on up) triangular matrix from packed representation vec. The other triangle of the matrix will be filled with zeros.

parameter up
default = true

parameter n
default = Vec.dim x

Operations on one matrix

Source

val fill : 
  ?patt:patt ->
  ?m:int ->
  ?n:int ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  float ->
  unit

fill ?patt ?m ?n ?ar ?ac a x fills the specified sub-matrix in a with value x.

Sourceval sum : ?patt:patt -> ?m:int -> ?n:int -> ?ar:int -> ?ac:int -> mat -> float

sum ?patt ?m ?n ?ar ?ac a computes the sum of all elements in the m-by-n submatrix using pattern patt, starting at row ar and column ac.

Sourceval add_const : float -> unop

add_const c ?patt ?m ?n ?br ?bc ?b ?ar ?ac a adds constant c to the designated m by n submatrix in a using pattern patt and stores the result in the designated submatrix in b.

parameter patt
default = `Full

parameter m
default = Mat.dim1 a

parameter n
default = Mat.dim2 a

parameter ar
default = 1

parameter ac
default = 1

parameter br
default = 1

parameter bc
default = 1

parameter b
default = fresh matrix of size m by n

Sourceval add_const_diag : float -> ?n:int -> ?ar:int -> ?ac:int -> mat -> unit

add_const c ?n ?ar ?ac a adds constant c to the diagonal of the designated n by n submatrix in a.

parameter n
default = Mat.dim2 a

parameter ar
default = 1

parameter ac
default = 1

Sourceval neg : unop

neg ?m ?n ?br ?bc ?b ?ar ?ac a computes the negative of the elements in the m by n (sub-)matrix of the matrix a starting in row ar and column ac. If b is given, the result will be stored in there using offsets br and bc, otherwise a fresh matrix will be used. The resulting matrix is returned.

parameter m
default = greater n s.t. ar + m - 1 <= dim1 a

parameter n
default = greater n s.t. ac + n - 1 <= dim2 a

parameter br
default = 1

parameter bc
default = 1

parameter b
default = fresh matrix with br + m - 1 rows and bc + n - 1 columns

parameter ar
default = 1

parameter ac
default = 1

Sourceval reci : unop

reci ?m ?n ?br ?bc ?b ?ar ?ac a computes the reciprocal of the elements in the m by n (sub-)matrix of the matrix a starting in row ar and column ac. If b is given, the result will be stored in there using offsets br and bc, otherwise a fresh matrix will be used. The resulting matrix is returned.

parameter m
default = greater n s.t. ar + m - 1 <= dim1 a

parameter n
default = greater n s.t. ac + n - 1 <= dim2 a

parameter br
default = 1

parameter bc
default = 1

parameter b
default = fresh matrix with br + m - 1 rows and bc + n - 1 columns

parameter ar
default = 1

parameter ac
default = 1

Source

val copy_diag : 
  ?n:int ->
  ?ofsy:int ->
  ?incy:int ->
  ?y:vec ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  vec

copy_diag ?n ?ofsy ?incy ?y ?ar ?ac a

returns
the diagonal of the (sub-)matrix a in a (sub-)vector.

parameter n
default = greatest n that does not exceed matrix dimensions

parameter ofsy
default = 1

parameter incy
default = 1

parameter y
default = fresh vector of length n

parameter ar
default = 1

parameter ac
default = 1

Sourceval trace : mat -> float

trace m

returns
the trace of matrix m. If m is not a square matrix, the sum of the longest possible sequence of diagonal elements will be returned.

Source

val scal : 
  ?patt:patt ->
  ?m:int ->
  ?n:int ->
  float ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  unit

scal ?patt ?m ?n alpha ?ar ?ac a BLAS scal function for (sub-)matrices.

Source

val scal_cols : 
  ?patt:patt ->
  ?m:int ->
  ?n:int ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  ?ofs:int ->
  vec ->
  unit

scal_cols ?patt ?m ?n ?ar ?ac a ?ofs alphas column-wise scal function for matrices.

Source

val scal_rows : 
  ?patt:patt ->
  ?m:int ->
  ?n:int ->
  ?ofs:int ->
  vec ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  unit

scal_rows ?patt ?m ?n ?ofs alphas ?ar ?ac a row-wise scal function for matrices.

Sourceval syrk_trace : ?n:int -> ?k:int -> ?ar:int -> ?ac:int -> mat -> float

syrk_trace ?n ?k ?ar ?ac a computes the trace of either a' * a or a * a', whichever is more efficient (results are identical), of the (sub-)matrix a multiplied by its own transpose. This is the same as the square of the Frobenius norm of a matrix. n is the number of rows to consider in a, and k the number of columns to consider.

parameter n
default = number of rows of a

parameter k
default = number of columns of a

parameter ar
default = 1

parameter ac
default = 1

Source

val syrk_diag : 
  ?n:int ->
  ?k:int ->
  ?beta:float ->
  ?ofsy:int ->
  ?y:vec ->
  ?trans:Common.trans2 ->
  ?alpha:float ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  vec

syrk_diag ?n ?k ?beta ?ofsy ?y ?trans ?alpha ?ar ?ac a computes the diagonal of the symmetric rank-k product of the (sub-)matrix a, multiplying it with alpha and adding beta times y, storing the result in y starting at the specified offset. n elements of the diagonal will be computed, and k elements of the matrix will be part of the dot product associated with each diagonal element.

parameter n
default = number of rows of a (or tra)

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

parameter beta
default = 0

parameter ofsy
default = 1

parameter y
default = fresh vector of size n + ofsy - 1

parameter trans
default = `N

parameter alpha
default = 1

parameter ar
default = 1

parameter ac
default = 1

Operations on two matrices

Sourceval add : binop

add ?m ?n ?cr ?cc ?c ?ar ?ac a ?br ?bc b computes the sum of the m by n sub-matrix of the matrix a starting in row ar and column ac with the corresponding sub-matrix of the matrix b starting in row br and column bc. If c is given, the result will be stored in there starting in row cr and column cc, otherwise a fresh matrix will be used. The resulting matrix is returned.

parameter m
default = greater n s.t. ar + m - 1 <= dim1 a

parameter n
default = greater n s.t. ac + n - 1 <= dim2 a

parameter cr
default = 1

parameter cc
default = 1

parameter c
default = fresh matrix with cr + m - 1 rows and cc + n - 1 columns

parameter br
default = 1

parameter bc
default = 1

parameter ar
default = 1

parameter ac
default = 1

Sourceval sub : binop

sub ?m ?n ?cr ?cc ?c ?ar ?ac a ?br ?bc b computes the difference of the m by n sub-matrix of the matrix a starting in row ar and column ac with the corresponding sub-matrix of the matrix b starting in row br and column bc. If c is given, the result will be stored in there starting in row cr and column cc, otherwise a fresh matrix will be used. The resulting matrix is returned.

parameter m
default = greater n s.t. ar + m - 1 <= dim1 a

parameter n
default = greater n s.t. ac + n - 1 <= dim2 a

parameter cr
default = 1

parameter cc
default = 1

parameter c
default = fresh matrix with cr + m - 1 rows and cc + n - 1 columns

parameter br
default = 1

parameter bc
default = 1

parameter ar
default = 1

parameter ac
default = 1

Sourceval mul : binop

mul ?m ?n ?cr ?cc ?c ?ar ?ac a ?br ?bc b computes the element-wise product of the m by n sub-matrix of the matrix a starting in row ar and column ac with the corresponding sub-matrix of the matrix b starting in row br and column bc. If c is given, the result will be stored in there starting in row cr and column cc, otherwise a fresh matrix will be used. The resulting matrix is returned.

NOTE: please do not confuse this function with matrix multiplication! The LAPACK-function for matrix multiplication is called gemm, e.g. Lacaml.D.gemm.

parameter m
default = greater n s.t. ar + m - 1 <= dim1 a

parameter n
default = greater n s.t. ac + n - 1 <= dim2 a

parameter cr
default = 1

parameter cc
default = 1

parameter c
default = fresh matrix with cr + m - 1 rows and cc + n - 1 columns

parameter br
default = 1

parameter bc
default = 1

parameter ar
default = 1

parameter ac
default = 1

Sourceval div : binop

div ?m ?n ?cr ?cc ?c ?ar ?ac a ?br ?bc b computes the division of the m by n sub-matrix of the matrix a starting in row ar and column ac with the corresponding sub-matrix of the matrix b starting in row br and column bc. If c is given, the result will be stored in there starting in row cr and column cc, otherwise a fresh matrix will be used. The resulting matrix is returned.

parameter m
default = greater n s.t. ar + m - 1 <= dim1 a

parameter n
default = greater n s.t. ac + n - 1 <= dim2 a

parameter cr
default = 1

parameter cc
default = 1

parameter c
default = fresh matrix with cr + m - 1 rows and cc + n - 1 columns

parameter br
default = 1

parameter bc
default = 1

parameter ar
default = 1

parameter ac
default = 1

Source

val axpy : 
  ?alpha:float ->
  ?patt:patt ->
  ?m:int ->
  ?n:int ->
  ?xr:int ->
  ?xc:int ->
  mat ->
  ?yr:int ->
  ?yc:int ->
  mat ->
  unit

axpy ?alpha ?patt ?m ?n ?xr ?xc x ?yr ?yc y BLAS axpy function for matrices.

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

parameter patt
default = `Full

parameter m
default = greater n s.t. xr + m - 1 <= dim1 x

parameter n
default = greater n s.t. xc + n - 1 <= dim2 x

parameter xr
default = 1

parameter xc
default = 1

parameter yr
default = 1

parameter yc
default = 1

Source

val gemm_diag : 
  ?n:int ->
  ?k:int ->
  ?beta:float ->
  ?ofsy:int ->
  ?y:vec ->
  ?transa:trans3 ->
  ?alpha:float ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  ?transb:trans3 ->
  ?br:int ->
  ?bc:int ->
  mat ->
  vec

gemm_diag ?n ?k ?beta ?ofsy ?y ?transa ?transb ?alpha ?ar ?ac a ?br ?bc b computes the diagonal of the product of the (sub-)matrices a and b (taking into account potential transposing), multiplying it with alpha and adding beta times y, storing the result in y starting at the specified offset. n elements of the diagonal will be computed, and k elements of the matrices will be part of the dot product associated with each diagonal element.

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

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

parameter beta
default = 0

parameter ofsy
default = 1

parameter y
default = fresh vector of size n + ofsy - 1

parameter transa
default = `N

parameter alpha
default = 1

parameter ar
default = 1

parameter ac
default = 1

parameter transb
default = `N

parameter br
default = 1

parameter bc
default = 1

Source

val gemm_trace : 
  ?n:int ->
  ?k:int ->
  ?transa:trans3 ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  ?transb:trans3 ->
  ?br:int ->
  ?bc:int ->
  mat ->
  float

gemm_trace ?n ?k ?transa ?ar ?ac a ?transb ?br ?bc b computes the trace of the product of the (sub-)matrices a and b (taking into account potential transposing). When transposing a, this yields the so-called Frobenius product of a and b. n is the number of rows (columns) to consider in a and the number of columns (rows) in b. k is the inner dimension to use for the product.

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

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

parameter transa
default = `N

parameter ar
default = 1

parameter ac
default = 1

parameter transb
default = `N

parameter br
default = 1

parameter bc
default = 1

Source

val symm2_trace : 
  ?n:int ->
  ?upa:bool ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  ?upb:bool ->
  ?br:int ->
  ?bc:int ->
  mat ->
  float

symm2_trace ?n ?upa ?ar ?ac a ?upb ?br ?bc b computes the trace of the product of the symmetric (sub-)matrices a and b. n is the number of rows and columns to consider in a and b.

parameter n
default = dimensions of a and b

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

parameter ar
default = 1

parameter ac
default = 1

parameter upb
default = true (upper triangular portion of b is accessed)

parameter br
default = 1

parameter bc
default = 1

Source

val ssqr_diff : 
  ?patt:patt ->
  ?m:int ->
  ?n:int ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  ?br:int ->
  ?bc:int ->
  mat ->
  float

ssqr_diff ?patt ?m ?n ?ar ?ac a ?br ?bc b

returns
the sum of squared differences between the m by n sub-matrix of the matrix a starting in row ar and column ac with the corresponding sub-matrix of the matrix b starting in row br and column bc.

parameter patt
default = `Full

parameter m
default = greater n s.t. ar + m - 1 <= dim1 a

parameter n
default = greater n s.t. ac + n - 1 <= dim2 a

parameter ar
default = 1

parameter ac
default = 1

parameter br
default = 1

parameter bc
default = 1

Iterators over matrices

Source

val map : 
  (float -> float) ->
  ?m:int ->
  ?n:int ->
  ?br:int ->
  ?bc:int ->
  ?b:mat ->
  ?ar:int ->
  ?ac:int ->
  mat ->
  mat

map f ?m ?n ?br ?bc ?b ?ar ?ac a

returns
matrix with f applied to each element of a.

parameter m
default = number of rows of a

parameter n
default = number of columns of a

parameter b
default = fresh matrix of size m by n

Sourceval fold_cols : ('a -> vec -> 'a) -> ?n:int -> ?ac:int -> 'a -> mat -> 'a

fold_cols f ?n ?ac acc a

returns
accumulator resulting from folding over each column vector.

parameter ac
default = 1

parameter n
default = number of columns of a

package lacaml

Module D.MatSource

Matrix operations

Creation of matrices

Unary matrix operations

Binary matrix operations

Miscellaneous functions

Ternary matrix operations

Creation of matrices and accessors

Matrix transformations

Operations on one matrix

Operations on two matrices

Iterators over matrices

Module `D.Mat`Source