Index of values

(a $=> (sr<->lr,sc<->lc)) b will replace the contents of b $ (sr<->lc,sc<->lc) with that of a.

a $@ (i,j) returns the (i,j)-th entry of the matrix a.

a *$ b will create a new matrix with the contents of a * b.

a *$~ b will create a new matrix with the contents of a *$ transp b.

a *@ q applies the transform q to the matrix a from the right, changing its contents.

a *~$ b will create a new matrix with the contents of transp a *$ b.

a *~@ q applies the conjugate-transpose of the transform q to the matrix a from the right, changing its contents.

a +$ b returns a new matrix whose entries are those of a + b.

a -$ b returns a new matrix whose entries are those of a - b.

a /$ b returns a new matrix obtained by applying the pseudo-inverse of a to b.

a /~$ b returns a new matrix obtained by applying the pseudo-inverse of the conjugate-transpose of a to b.

People who do not like to write (a $=> (sr<->lr,All)) b can now write (b $ (sr<->lr,All)) <-$ a instead.

Equivalent to Matlab's colon operator.

People who do not like to write the destination storage on the right-hand side, need this operator <-|.

The weird syntax (x => (i,j)) a has the effect of making a $@ (i,j) be equal to x.

q @* a applies a transform q to the matrix a changing its contents.

q @~* a applies the conjugate-transpose of the transform q to the matrix a, changing its contents.

(a |*++| b) c will replace the contents of c with that of c + a * b.

(a |*--| b) c will replace the contents of c with that of c - a * b.

(a |*| b) c will replace the contents of c with that of a * b.

(a |*~++| b) c will replace the contents of c with that of c + a * transp b.

(a |*~--| b) c will replace the contents of c with that of a * b.

(a |*~| b) c will replace the contents of c with that of a *$ transp b.

a |++| b will replace the contents of b with that of a + b.

(a |+| b) c will replace the contents of c with that of a + b.

a |--| b will replace the contents of b with that of b - a.

(a |-| b) c will replace the contents of c with that of a - b.

a |/| b replaces the contents of the matrix b by the contents of the minimum-norm least-squares solution of the system of linear equations ax = b.

(a |~*++| b) c will replace the contents of c with that of c + transp a * b.

(a |~*--| b) c will replace the contents of c with that of c - transp a * b.

(a |~*| b) c will replace the contents of c with that of transp a *$ b.

The same semantics and restrictions as |/|, except that the system being solved now is (transp a)x=b.

Adds two possibly complex numbers.

colScale' a x scales every column of a in place by the corresponding entry in x.

Same as colScale' except that the second argument must be a real array.

(col_partitions sp).(j) is the size of the j-th colun partition of sp.

cond a returns the 2-norm condition number of the matrix a.

conjg' a replaces the entries of a by their conjugates.

conjugate z returns the complex conjugate of the (possibly) complex number z.

const x a sets every entry of the matrix a to x.

consts x m n creates an m by n matrix with every entry set to x.

copy sp returns a new sparse matrix that does not share its spine or its blocks with sp.

Since the $ operator produces sub-matrices that share storage with the parent matrix, we need a way to make copies of matrices.

Given an L factor l computed from ql' or lq', copyL l returns a lower-triangular (or lower-trapezoidal) matrix that is equivalent to l.

empty m n returns a zero sparse matrix with m row partitions and n column partitions.

eye m n returns the top-left m by n submatrix of the max m n by max m n identity matrix.

fSubs' l b applies the inverse of the sparse block lower-triangular l (usually computed by ql_factorize') to the matrix b.

Converts a floating point number to floating point number or Complex.t as the case may be.

fromInt n returns either the floating-point version of n or the Complex.t version of n.

fun2mat fn m n creates an m by n matrix whose (i,j)-th entry is fn i j.

fun2mat' fn a modifies all the entries of the matrix a such that the (i,j)-th entry becomes fn i j.

get sp i j returns the (i,j)-th block from the sparse matrix sp.

iD a b replaces the contents of the matrix b with that of a.

Given an l factor computed using ql' or lq', iDL l a copies the lower-trianglar (or lower-trapezoidal) part of l into a.

im z returns the imaginary part of the (possibly) complex number z.

linear_solve' sp b applies the inverse of sp to b.

lq' a computes the LQ factorization of a.

The machine precision.

Efficiently converts a standard two-dimensional OCaml array into a matrix.

matrix1x2 n1 n2 a1 a2 a modifies the entries of a by applying the two transformers a1 and a2 to the two block column partitions of a.

matrix1x3 n1 n2 n3 a1 a2 a3 a modifies the entries of the matrix a by applying the transformers a1, a2 and a3 to the corresponding block column partitions of a.

matrix2x1 m1 a1 m2 a2 a modifies the entries of the matrix a, by applying the function (transformer) a1 to a $ (1<-> m1, All) and the transformer a2 to a $ (m1+1 <-> m1+m1, All).

matrix2x2 n1 n2 m1 a11 a12 m2 a21 a22 a modifies the entries of the matrix a by applying the transformers a11, a12, a21 and a22 to the corresponding sub-matrices of a obtained by a block 2 by 2 partitioning.

matrix2x3 n1 n2 n3 m1 a11 a12 a13 m2 a21 a22 a23 a modifies the entries of the matrix a by applying the transformers a11, a12, a13, a21, a22 and a23 to the corresponding sub-matrices of a obtained by a block 2 by 3 partitioning.

matrix3x1 m1 a1 m2 a2 m3 a3 a modifies the entries of a by first applying the transformer a1 to the first block row of the 3 by 1 block row partitioning of a, then applying the transformer a2 to the second block row partition of a, and so on.

matrix4x2 n1 n2 m1 a11 a12 m2 a21 a22 m3 a31 a32 m4 a41 a42 a modifies the entries of the matrix a by applying the transformers aij to the corresponding sub-matrices of a obtained by a block 4 by 2 partitioning.

matrixInfx1 ms ais a applies the transformers in the list ais to the corresponding row partitions of a as determined by the block sizes in the list ms.

Either the real or complex minus one.

mul sp b c replaces the contents of the matrix c with the product of the sparse matrix sp and the matrix b.

mul_transform q_sp b will apply the sparse unitary transform q_sp computed by ql_factorize' to the matrix b.

Multiplies two possibly complex numbers.

mulr r z multiplies the possibly complex number z by the real number r.

Returns the number of columns in the matrix.

Returns the number of rows in the matrix.

no_of_col_partitions (empty m n) returns n.

no_of_cols sp returns the actual number of columns that sp has.

no_of_row_partitions (empty m n) returns m.

no_of_rows sp returns the actual number of rows that sp has.

norm1 a returns the 1-norm of a.

normF a returns the Frobenius-norm of a.

normInf a returns the infinity-norm of a.

normMax a returns the largest entry of a in magnitude.

Either the real or complex one.

ones m n creates a m by n matrix of ones.

The function ooo is a nop.

partition1x2 n1 n2 a returns the tuple (a1,a2) obtained by column partitioning a, with first block column a1 having the first n1 columns, and the second block column a2 having the last n2 columns.

partition1x3 n1 n2 n3 a returns (a1,a2,a3) obtained by doing a 1 by 3 block column partition of a.

partition1xInf ns a returns a list of block column partitions of a, where the number of columns in the j-th partition is determined by the number in the j-th position in the list ns.

partition1xN ns a is identical to partition1xInf ns a, except that ns must be an array now.

In CamlFloat I strongly discourage you from programming as if you were in Matlab.

partition2x2 n1 n2 m1 m2 a returns the tuple (a11, a12, a21, a22) obtained by block partitioning a into a 2 by 2 matrix, with n1 columns in the first column partition and m1 rows in the first row partition.

partition3x1 m1 m2 m3 a returns (a1,a2,a3) obtained by doing a 3 by 1 block row partition of a.

partition3x3 n1 n2 n3 m1 m2 m3 a returns (a11,a12,a13,a21,a22,a23,a31,a32,a33) obtained by doing a 3 by 3 block partitioning of a.

partitionInfx1 ms a returns a list of block row partitions of a, where the number of rows in the i-th partition is determined by the number in the i-th position in the list ms.

partitionNx1 ms a is identical to partitionInfx1 ms a, except tha ms must be an array now.

The mechanism for specifying the type of array you want from Bigarray.

Same as above except when you need a real array even inside a complex module.

Prints a matrix to stdout.

Determine the number of rows in a matrix that will be printed by printMatrix.

Determines the number of columns of a matrix that will be printed by printMatrix.

Prints a possibly complex number to stdout.

ql' a computes the QL factorization of a.

ql_factorize' sp computes the QL factorization of the sparse matrix sp.

randn () returns a random possibly complex number.

randomMatrix m n creates a m by n random matrix whose entries (real and imaginary parts) are uniformly distributed between -1.0 and 1.0.

rawMatrix m n creates an m by n matrix whose entries are uninitialized.

re z returns the real part of the (possibly) complex number z.

rowScale' x a scales every row of a in place by the corresponding entry in x.

Same as rowScale' except that the first argument must be a real array.

(row_partitions sp).(i) is the size of the i-th row partition of sp.

scale' x a multiplies every entry of a in place by x.

Same as scale' except that first argument must be a real number.

set sp i j (Some a) will set the (i,j)-th block of the sparse matrix sp to the matrix a.

shallow_copy sp returns a new sparse matrix that shares its blocks with sp but not its spine.

singValues' a is identical to svd' a except that the none of the singular vectors are computed.

Subtracts two possibly complex numebrs.

subs' l b replaces the contents of the matrix b by l^-1b.

subsT' l b replaces the contents of the matrix b with that of (transpose l)^-1b.

svd' a returns the economy SVD of a, destroying its contents in the process.

svdL' a is identical svd' a except that the right singular vectors are not calculated.

svdR' a is identical to svd' a except that the left singular vectors are not calculated.

toInt z returns the integer part of the real part of (possibly) complex number z.

transp a returns a new matrix formed by conjugate-transposing a.

transp' a b replaces the contents of b with the conjugate-transpose of a.

Either the real or complex zero.

zeros m n creates a m by n zero matrix.