Arrays¶
Basic functions¶

ndims
(A) → Integer¶ Returns the number of dimensions of
A

size
(A[, dim...])¶ Returns a tuple containing the dimensions of
A
. Optionally you can specify the dimension(s) you want the length of, and get the length of that dimension, or a tuple of the lengths of dimensions you asked for.:julia> A = rand(2,3,4); julia> size(A, 2) 3 julia> size(A,3,2) (4,3)

iseltype
(A, T)¶ Tests whether
A
or its elements are of typeT
.

length
(A) → Integer¶ Returns the number of elements in
A
.

eachindex
(A...)¶ Creates an iterable object for visiting each index of an AbstractArray
A
in an efficient manner. For array types that have opted into fast linear indexing (likeArray
), this is simply the range1:length(A)
. For other array types, this returns a specialized Cartesian range to efficiently index into the array with indices specified for every dimension. For other iterables, including strings and dictionaries, this returns an iterator object supporting arbitrary index types (e.g. unevenly spaced or noninteger indices).Example for a sparse 2d array:
julia> A = sprand(2, 3, 0.5) 2x3 sparse matrix with 4 Float64 entries: [1, 1] = 0.598888 [1, 2] = 0.0230247 [1, 3] = 0.486499 [2, 3] = 0.809041 julia> for iter in eachindex(A) @show iter.I_1, iter.I_2 @show A[iter] end (iter.I_1,iter.I_2) = (1,1) A[iter] = 0.5988881393454597 (iter.I_1,iter.I_2) = (2,1) A[iter] = 0.0 (iter.I_1,iter.I_2) = (1,2) A[iter] = 0.02302469881746183 (iter.I_1,iter.I_2) = (2,2) A[iter] = 0.0 (iter.I_1,iter.I_2) = (1,3) A[iter] = 0.4864987874354343 (iter.I_1,iter.I_2) = (2,3) A[iter] = 0.8090413606455655
If you supply more than one
AbstractArray
argument,eachindex
will create an iterable object that is fast for all arguments (aUnitRange
if all inputs have fast linear indexing, a CartesianRange otherwise). If the arrays have different sizes and/or dimensionalities,eachindex
returns an iterable that spans the largest range along each dimension.

Base.
linearindexing
(A)¶ linearindexing
defines how an AbstractArray most efficiently accesses its elements. IfBase.linearindexing(A)
returnsBase.LinearFast()
, this means that linear indexing with only one index is an efficient operation. If it instead returnsBase.LinearSlow()
(by default), this means that the array intrinsically accesses its elements with indices specified for every dimension. Since converting a linear index to multiple indexing subscripts is typically very expensive, this provides a traitsbased mechanism to enable efficient generic code for all array types.An abstract array subtype
MyArray
that wishes to opt into fast linear indexing behaviors should definelinearindexing
in the typedomain:Base.linearindexing{T<:MyArray}(::Type{T}) = Base.LinearFast()

countnz
(A)¶ Counts the number of nonzero values in array
A
(dense or sparse). Note that this is not a constanttime operation. For sparse matrices, one should usually usennz
, which returns the number of stored values.

conj!
(A)¶ Convert an array to its complex conjugate inplace

stride
(A, k)¶ Returns the distance in memory (in number of elements) between adjacent elements in dimension
k
.

strides
(A)¶ Returns a tuple of the memory strides in each dimension

ind2sub
(dims, index) → subscripts¶ Returns a tuple of subscripts into an array with dimensions
dims
, corresponding to the linear indexindex
.Example:
i, j, ... = ind2sub(size(A), indmax(A))
provides the indices of the maximum element

ind2sub
(a, index) → subscripts Returns a tuple of subscripts into array
a
corresponding to the linear indexindex

sub2ind
(dims, i, j, k...) → index¶ The inverse of
ind2sub
, returns the linear index corresponding to the provided subscripts
Constructors¶

Array
(dims)¶ Array{T}(dims)
constructs an uninitialized dense array with element typeT
.dims
may be a tuple or a series of integer arguments. The syntaxArray(T, dims)
is also available, but deprecated.

getindex
(type[, elements...])¶ Construct a 1d array of the specified type. This is usually called with the syntax
Type[]
. Element values can be specified usingType[a,b,c,...]
.

cell
(dims)¶ Construct an uninitialized cell array (heterogeneous array).
dims
can be either a tuple or a series of integer arguments.

zeros
(type, dims)¶ Create an array of all zeros of specified type. The type defaults to Float64 if not specified.

zeros
(A) Create an array of all zeros with the same element type and shape as
A
.

ones
(type, dims)¶ Create an array of all ones of specified type. The type defaults to
Float64
if not specified.

ones
(A) Create an array of all ones with the same element type and shape as
A
.

trues
(dims)¶ Create a
BitArray
with all values set totrue

falses
(dims)¶ Create a
BitArray
with all values set tofalse

fill
(x, dims)¶ Create an array filled with the value
x
. For example,fill(1.0, (10,10))
returns a 10x10 array of floats, with each element initialized to1.0
.If
x
is an object reference, all elements will refer to the same object.fill(Foo(), dims)
will return an array filled with the result of evaluatingFoo()
once.

fill!
(A, x)¶ Fill array
A
with the valuex
. Ifx
is an object reference, all elements will refer to the same object.fill!(A, Foo())
will returnA
filled with the result of evaluatingFoo()
once.

reshape
(A, dims)¶ Create an array with the same data as the given array, but with different dimensions. An implementation for a particular type of array may choose whether the data is copied or shared.

similar
(array[, element_type=eltype(array)][, dims=size(array)])¶ Create an uninitialized mutable array with the given element type and size, based upon the given source array. The second and third arguments are both optional, defaulting to the given array’s
eltype
andsize
. The dimensions may be specified either as a single tuple argument or as a series of integer arguments.Custom AbstractArray subtypes may choose which specific array type is bestsuited to return for the given element type and dimensionality. If they do not specialize this method, the default is an
Array(element_type, dims...)
.For example,
similar(1:10, 1, 4)
returns an uninitializedArray{Int,2}
since ranges are neither mutable nor support 2 dimensions:julia> similar(1:10, 1, 4) 1x4 Array{Int64,2}: 4419743872 4374413872 4419743888 0
Conversely,
similar(trues(10,10), 2)
returns an uninitializedBitVector
with two elements sinceBitArray
s are both mutable and can support 1dimensional arrays:julia> similar(trues(10,10), 2) 2element BitArray{1}: false false
Since
BitArray
s can only store elements of typeBool
, however, if you request a different element type it will create a regularArray
instead:julia> similar(falses(10), Float64, 2, 4) 2x4 Array{Float64,2}: 2.18425e314 2.18425e314 2.18425e314 2.18425e314 2.18425e314 2.18425e314 2.18425e314 2.18425e314

reinterpret
(type, A)¶ Change the typeinterpretation of a block of memory. For example,
reinterpret(Float32, UInt32(7))
interprets the 4 bytes corresponding toUInt32(7)
as aFloat32
. For arrays, this constructs an array with the same binary data as the given array, but with the specified element type.

eye
(n)¶ n
byn
identity matrix

eye
(m, n) m
byn
identity matrix

eye
(A) Constructs an identity matrix of the same dimensions and type as
A
.

linspace
(start, stop, n=100)¶ Construct a range of
n
linearly spaced elements fromstart
tostop
.

logspace
(start, stop, n=50)¶ Construct a vector of
n
logarithmically spaced numbers from10^start
to10^stop
.
Mathematical operators and functions¶
All mathematical operations and functions are supported for arrays

broadcast
(f, As...)¶ Broadcasts the arrays
As
to a common size by expanding singleton dimensions, and returns an array of the resultsf(as...)
for each position.

broadcast!
(f, dest, As...)¶ Like
broadcast
, but store the result ofbroadcast(f, As...)
in thedest
array. Note thatdest
is only used to store the result, and does not supply arguments tof
unless it is also listed in theAs
, as inbroadcast!(f, A, A, B)
to performA[:] = broadcast(f, A, B)
.

bitbroadcast
(f, As...)¶ Like
broadcast
, but allocates aBitArray
to store the result, rather then anArray
.

broadcast_function
(f)¶ Returns a function
broadcast_f
such thatbroadcast_function(f)(As...) === broadcast(f, As...)
. Most useful in the formconst broadcast_f = broadcast_function(f)
.

broadcast!_function
(f)¶ Like
broadcast_function
, but forbroadcast!
.
Indexing, Assignment, and Concatenation¶

getindex
(A, inds...) Returns a subset of array
A
as specified byinds
, where eachind
may be anInt
, aRange
, or aVector
. See the manual section on array indexing for details.

sub
(A, inds...)¶ Like
getindex()
, but returns a view into the parent arrayA
with the given indices instead of making a copy. Callinggetindex()
orsetindex!()
on the returnedSubArray
computes the indices to the parent array on the fly without checking bounds.

parent
(A)¶ Returns the “parent array” of an array view type (e.g.,
SubArray
), or the array itself if it is not a view

parentindexes
(A)¶ From an array view
A
, returns the corresponding indexes in the parent

slicedim
(A, d, i)¶ Return all the data of
A
where the index for dimensiond
equalsi
. Equivalent toA[:,:,...,i,:,:,...]
wherei
is in positiond
.

slice
(A, inds...)¶ Returns a view of array
A
with the given indices likesub()
, but drops all dimensions indexed with scalars.

setindex!
(A, X, inds...)¶ Store values from array
X
within some subset ofA
as specified byinds
.

broadcast_getindex
(A, inds...)¶ Broadcasts the
inds
arrays to a common size likebroadcast
, and returns an array of the resultsA[ks...]
, whereks
goes over the positions in the broadcast.

broadcast_setindex!
(A, X, inds...)¶ Broadcasts the
X
andinds
arrays to a common size and stores the value from each position inX
at the indices given by the same positions ininds
.

cat
(dims, A...)¶ Concatenate the input arrays along the specified dimensions in the iterable
dims
. For dimensions not indims
, all input arrays should have the same size, which will also be the size of the output array along that dimension. For dimensions indims
, the size of the output array is the sum of the sizes of the input arrays along that dimension. Ifdims
is a single number, the different arrays are tightly stacked along that dimension. Ifdims
is an iterable containing several dimensions, this allows one to construct block diagonal matrices and their higherdimensional analogues by simultaneously increasing several dimensions for every new input array and putting zero blocks elsewhere. For example,cat([1,2], matrices...)
builds a block diagonal matrix, i.e. a block matrix withmatrices[1]
,matrices[2]
, ... as diagonal blocks and matching zero blocks away from the diagonal.

vcat
(A...)¶ Concatenate along dimension 1

hcat
(A...)¶ Concatenate along dimension 2

hvcat
(rows::Tuple{Vararg{Int}}, values...)¶ Horizontal and vertical concatenation in one call. This function is called for block matrix syntax. The first argument specifies the number of arguments to concatenate in each block row.
julia> a, b, c, d, e, f = 1, 2, 3, 4, 5, 6 (1,2,3,4,5,6) julia> [a b c; d e f] 2x3 Array{Int64,2}: 1 2 3 4 5 6 julia> hvcat((3,3), a,b,c,d,e,f) 2x3 Array{Int64,2}: 1 2 3 4 5 6 julia> [a b;c d; e f] 3x2 Array{Int64,2}: 1 2 3 4 5 6 julia> hvcat((2,2,2), a,b,c,d,e,f) 3x2 Array{Int64,2}: 1 2 3 4 5 6
If the first argument is a single integer
n
, then all block rows are assumed to haven
block columns.

flipdim
(A, d)¶ Reverse
A
in dimensiond
.

circshift
(A, shifts)¶ Circularly shift the data in an array. The second argument is a vector giving the amount to shift in each dimension.

find
(A)¶ Return a vector of the linear indexes of the nonzeros in
A
(determined byA[i]!=0
). A common use of this is to convert a boolean array to an array of indexes of thetrue
elements.

find
(f, A) Return a vector of the linear indexes of
A
wheref
returnstrue
.

findn
(A)¶ Return a vector of indexes for each dimension giving the locations of the nonzeros in
A
(determined byA[i]!=0
).

findnz
(A)¶ Return a tuple
(I, J, V)
whereI
andJ
are the row and column indexes of the nonzero values in matrixA
, andV
is a vector of the nonzero values.

findfirst
(A)¶ Return the index of the first nonzero value in
A
(determined byA[i]!=0
).

findfirst
(A, v) Return the index of the first element equal to
v
inA
.

findfirst
(predicate, A) Return the index of the first element of
A
for whichpredicate
returnstrue
.

findlast
(A)¶ Return the index of the last nonzero value in
A
(determined byA[i]!=0
).

findlast
(A, v) Return the index of the last element equal to
v
inA
.

findlast
(predicate, A) Return the index of the last element of
A
for whichpredicate
returnstrue
.

findnext
(A, i)¶ Find the next index >=
i
of a nonzero element ofA
, or0
if not found.

findnext
(predicate, A, i) Find the next index >=
i
of an element ofA
for whichpredicate
returnstrue
, or0
if not found.

findnext
(A, v, i) Find the next index >=
i
of an element ofA
equal tov
(using==
), or0
if not found.

findprev
(A, i)¶ Find the previous index <=
i
of a nonzero element ofA
, or0
if not found.

findprev
(predicate, A, i) Find the previous index <=
i
of an element ofA
for whichpredicate
returnstrue
, or0
if not found.

findprev
(A, v, i) Find the previous index <=
i
of an element ofA
equal tov
(using==
), or0
if not found.

permutedims
(A, perm)¶ Permute the dimensions of array
A
.perm
is a vector specifying a permutation of lengthndims(A)
. This is a generalization of transpose for multidimensional arrays. Transpose is equivalent topermutedims(A, [2,1])
.

ipermutedims
(A, perm)¶ Like
permutedims()
, except the inverse of the given permutation is applied.

permutedims!
(dest, src, perm)¶ Permute the dimensions of array
src
and store the result in the arraydest
.perm
is a vector specifying a permutation of lengthndims(src)
. The preallocated arraydest
should havesize(dest) == size(src)[perm]
and is completely overwritten. No inplace permutation is supported and unexpected results will happen ifsrc
anddest
have overlapping memory regions.

squeeze
(A, dims)¶ Remove the dimensions specified by
dims
from arrayA
. Elements ofdims
must be unique and within the range1:ndims(A)
.

vec
(Array) → Vector¶ Vectorize an array using columnmajor convention.

promote_shape
(s1, s2)¶ Check two array shapes for compatibility, allowing trailing singleton dimensions, and return whichever shape has more dimensions.

checkbounds
(array, indexes...)¶ Throw an error if the specified indexes are not in bounds for the given array. Subtypes of
AbstractArray
should specialize this method if they need to provide custom bounds checking behaviors.

checkbounds
(::Type{Bool}, dimlength::Integer, index) Return a
Bool
describing if the given index is within the bounds of the given dimension length. Custom types that would like to behave as indices for all arrays can extend this method in order to provide a specialized bounds checking implementation.

randsubseq
(A, p) → Vector¶ Return a vector consisting of a random subsequence of the given array
A
, where each element ofA
is included (in order) with independent probabilityp
. (Complexity is linear inp*length(A)
, so this function is efficient even ifp
is small andA
is large.) Technically, this process is known as “Bernoulli sampling” ofA
.

randsubseq!
(S, A, p)¶ Like
randsubseq
, but the results are stored inS
(which is resized as needed).
Array functions¶

cumprod
(A[, dim])¶ Cumulative product along a dimension
dim
(defaults to 1). See alsocumprod!()
to use a preallocated output array, both for performance and to control the precision of the output (e.g. to avoid overflow).

cumprod!
(B, A[, dim])¶ Cumulative product of
A
along a dimension, storing the result inB
. The dimension defaults to 1.

cumsum
(A[, dim])¶ Cumulative sum along a dimension
dim
(defaults to 1). See alsocumsum!()
to use a preallocated output array, both for performance and to control the precision of the output (e.g. to avoid overflow).

cumsum!
(B, A[, dim])¶ Cumulative sum of
A
along a dimension, storing the result inB
. The dimension defaults to 1.

cumsum_kbn
(A[, dim])¶ Cumulative sum along a dimension, using the KahanBabuskaNeumaier compensated summation algorithm for additional accuracy. The dimension defaults to 1.

cummin
(A[, dim])¶ Cumulative minimum along a dimension. The dimension defaults to 1.

cummax
(A[, dim])¶ Cumulative maximum along a dimension. The dimension defaults to 1.

diff
(A[, dim])¶ Finite difference operator of matrix or vector.

gradient
(F[, h])¶ Compute differences along vector
F
, usingh
as the spacing between points. The default spacing is one.

rot180
(A)¶ Rotate matrix
A
180 degrees.

rot180
(A, k) Rotate matrix
A
180 degrees an integerk
number of times. Ifk
is even, this is equivalent to acopy
.

rotl90
(A)¶ Rotate matrix
A
left 90 degrees.

rotl90
(A, k) Rotate matrix
A
left 90 degrees an integerk
number of times. Ifk
is zero or a multiple of four, this is equivalent to acopy
.

rotr90
(A)¶ Rotate matrix
A
right 90 degrees.

rotr90
(A, k) Rotate matrix
A
right 90 degrees an integerk
number of times. Ifk
is zero or a multiple of four, this is equivalent to acopy
.

reducedim
(f, A, dims[, initial])¶ Reduce 2argument function
f
along dimensions ofA
.dims
is a vector specifying the dimensions to reduce, andinitial
is the initial value to use in the reductions. For+
,*
,max
andmin
theinitial
argument is optional.The associativity of the reduction is implementationdependent; if you need a particular associativity, e.g. lefttoright, you should write your own loop. See documentation for
reduce
.

mapreducedim
(f, op, A, dims[, initial])¶ Evaluates to the same as
reducedim(op, map(f, A), dims, f(initial))
, but is generally faster because the intermediate array is avoided.

mapslices
(f, A, dims)¶ Transform the given dimensions of array
A
using functionf
.f
is called on each slice ofA
of the formA[...,:,...,:,...]
.dims
is an integer vector specifying where the colons go in this expression. The results are concatenated along the remaining dimensions. For example, ifdims
is[1,2]
andA
is 4dimensional,f
is called onA[:,:,i,j]
for alli
andj
.

sum_kbn
(A)¶ Returns the sum of all array elements, using the KahanBabuskaNeumaier compensated summation algorithm for additional accuracy.
Combinatorics¶

nthperm
(v, k)¶ Compute the kth lexicographic permutation of a vector.

nthperm
(p) Return the
k
that generated permutationp
. Note thatnthperm(nthperm([1:n], k)) == k
for1 <= k <= factorial(n)
.

nthperm!
(v, k)¶ Inplace version of
nthperm()
.

randperm
([rng, ]n)¶ Construct a random permutation of length
n
. The optionalrng
argument specifies a random number generator, see Random Numbers.

invperm
(v)¶ Return the inverse permutation of v.

isperm
(v) → Bool¶ Returns
true
ifv
is a valid permutation.

permute!
(v, p)¶ Permute vector
v
inplace, according to permutationp
. No checking is done to verify thatp
is a permutation.To return a new permutation, use
v[p]
. Note that this is generally faster thanpermute!(v,p)
for large vectors.

ipermute!
(v, p)¶ Like permute!, but the inverse of the given permutation is applied.

randcycle
([rng, ]n)¶ Construct a random cyclic permutation of length
n
. The optionalrng
argument specifies a random number generator, see Random Numbers.

shuffle
([rng, ]v)¶ Return a randomly permuted copy of
v
. The optionalrng
argument specifies a random number generator, see Random Numbers.

shuffle!
([rng, ]v)¶ Inplace version of
shuffle()
.

reverse
(v[, start=1[, stop=length(v)]])¶ Return a copy of
v
reversed from start to stop.

reverseind
(v, i)¶ Given an index
i
inreverse(v)
, return the corresponding index inv
so thatv[reverseind(v,i)] == reverse(v)[i]
. (This can be nontrivial in the case wherev
is a Unicode string.)

reverse!
(v[, start=1[, stop=length(v)]]) → v¶ Inplace version of
reverse()
.

combinations
(array, n)¶ Generate all combinations of
n
elements from an indexable object. Because the number of combinations can be very large, this function returns an iterator object. Usecollect(combinations(array,n))
to get an array of all combinations.

permutations
(array)¶ Generate all permutations of an indexable object. Because the number of permutations can be very large, this function returns an iterator object. Use
collect(permutations(array))
to get an array of all permutations.

partitions
(n)¶ Generate all integer arrays that sum to
n
. Because the number of partitions can be very large, this function returns an iterator object. Usecollect(partitions(n))
to get an array of all partitions. The number of partitions to generate can be efficiently computed usinglength(partitions(n))
.

partitions
(n, m) Generate all arrays of
m
integers that sum ton
. Because the number of partitions can be very large, this function returns an iterator object. Usecollect(partitions(n,m))
to get an array of all partitions. The number of partitions to generate can be efficiently computed usinglength(partitions(n,m))
.

partitions
(array) Generate all set partitions of the elements of an array, represented as arrays of arrays. Because the number of partitions can be very large, this function returns an iterator object. Use
collect(partitions(array))
to get an array of all partitions. The number of partitions to generate can be efficiently computed usinglength(partitions(array))
.

partitions
(array, m) Generate all set partitions of the elements of an array into exactly m subsets, represented as arrays of arrays. Because the number of partitions can be very large, this function returns an iterator object. Use
collect(partitions(array,m))
to get an array of all partitions. The number of partitions into m subsets is equal to the Stirling number of the second kind and can be efficiently computed usinglength(partitions(array,m))
.
BitArrays¶

bitpack
(A::AbstractArray{T, N}) → BitArray¶ Converts a numeric array to a packed boolean array

bitunpack
(B::BitArray{N}) → Array{Bool,N}¶ Converts a packed boolean array to an array of booleans

flipbits!
(B::BitArray{N}) → BitArray{N}¶ Performs a bitwise not operation on
B
. See ~ operator.

rol!
(dest::BitArray{1}, src::BitArray{1}, i::Integer) → BitArray{1}¶ Performs a left rotation operation on
src
and put the result intodest
.

rol!
(B::BitArray{1}, i::Integer) → BitArray{1} Performs a left rotation operation on
B
.

rol
(B::BitArray{1}, i::Integer) → BitArray{1}¶ Performs a left rotation operation.

ror!
(dest::BitArray{1}, src::BitArray{1}, i::Integer) → BitArray{1}¶ Performs a right rotation operation on
src
and put the result intodest
.

ror!
(B::BitArray{1}, i::Integer) → BitArray{1} Performs a right rotation operation on
B
.

ror
(B::BitArray{1}, i::Integer) → BitArray{1}¶ Performs a right rotation operation.
Sparse Matrices¶
Sparse matrices support much of the same set of operations as dense matrices. The following functions are specific to sparse matrices.

sparse
(I, J, V[, m, n, combine])¶ Create a sparse matrix
S
of dimensionsm x n
such thatS[I[k], J[k]] = V[k]
. Thecombine
function is used to combine duplicates. Ifm
andn
are not specified, they are set tomaximum(I)
andmaximum(J)
respectively. If thecombine
function is not supplied, duplicates are added by default. All elements ofI
must satisfy1 <= I[k] <= m
, and all elements ofJ
must satisfy1 <= J[k] <= n
.

sparsevec
(I, V[, m, combine])¶ Create a sparse matrix
S
of sizem x 1
such thatS[I[k]] = V[k]
. Duplicates are combined using thecombine
function, which defaults to+
if it is not provided. In julia, sparse vectors are really just sparse matrices with one column. Given Julia’s Compressed Sparse Columns (CSC) storage format, a sparse column matrix with one column is sparse, whereas a sparse row matrix with one row ends up being dense.

sparsevec
(D::Dict[, m]) Create a sparse matrix of size
m x 1
where the row values are keys from the dictionary, and the nonzero values are the values from the dictionary.

issparse
(S)¶ Returns
true
ifS
is sparse, andfalse
otherwise.

sparse
(A) Convert an AbstractMatrix
A
into a sparse matrix.

sparsevec
(A) Convert a dense vector
A
into a sparse matrix of sizem x 1
. In julia, sparse vectors are really just sparse matrices with one column.

full
(S)¶ Convert a sparse matrix
S
into a dense matrix.

nnz
(A)¶ Returns the number of stored (filled) elements in a sparse matrix.

spzeros
(m, n)¶ Create a sparse matrix of size
m x n
. This sparse matrix will not contain any nonzero values. No storage will be allocated for nonzero values during construction.

spones
(S)¶ Create a sparse matrix with the same structure as that of
S
, but with every nonzero element having the value1.0
.

speye
(type, m[, n])¶ Create a sparse identity matrix of specified type of size
m x m
. In casen
is supplied, create a sparse identity matrix of sizem x n
.

spdiagm
(B, d[, m, n])¶ Construct a sparse diagonal matrix.
B
is a tuple of vectors containing the diagonals andd
is a tuple containing the positions of the diagonals. In the case the input contains only one diagonal,B
can be a vector (instead of a tuple) andd
can be the diagonal position (instead of a tuple), defaulting to 0 (diagonal). Optionally,m
andn
specify the size of the resulting sparse matrix.

sprand
([rng, ]m, n, p[, rfn])¶ Create a random
m
byn
sparse matrix, in which the probability of any element being nonzero is independently given byp
(and hence the mean density of nonzeros is also exactlyp
). Nonzero values are sampled from the distribution specified byrfn
. The uniform distribution is used in caserfn
is not specified. The optionalrng
argument specifies a random number generator, see Random Numbers.

sprandn
(m, n, p)¶ Create a random
m
byn
sparse matrix with the specified (independent) probabilityp
of any entry being nonzero, where nonzero values are sampled from the normal distribution.

sprandbool
(m, n, p)¶ Create a random
m
byn
sparse boolean matrix with the specified (independent) probabilityp
of any entry beingtrue
.

etree
(A[, post])¶ Compute the elimination tree of a symmetric sparse matrix
A
fromtriu(A)
and, optionally, its postordering permutation.

symperm
(A, p)¶ Return the symmetric permutation of
A
, which isA[p,p]
.A
should be symmetric and sparse, where only the upper triangular part of the matrix is stored. This algorithm ignores the lower triangular part of the matrix. Only the upper triangular part of the result is returned as well.

nonzeros
(A)¶ Return a vector of the structural nonzero values in sparse matrix
A
. This includes zeros that are explicitly stored in the sparse matrix. The returned vector points directly to the internal nonzero storage ofA
, and any modifications to the returned vector will mutateA
as well. Seerowvals(A)
andnzrange(A, col)
.

rowvals
(A)¶ Return a vector of the row indices of
A
, and any modifications to the returned vector will mutateA
as well. Given the internal storage format of sparse matrices, providing access to how the row indices are stored internally can be useful in conjunction with iterating over structural nonzero values. Seenonzeros(A)
andnzrange(A, col)
.

nzrange
(A, col)¶ Return the range of indices to the structural nonzero values of a sparse matrix column. In conjunction with
nonzeros(A)
androwvals(A)
, this allows for convenient iterating over a sparse matrix :A = sparse(I,J,V) rows = rowvals(A) vals = nonzeros(A) m, n = size(A) for i = 1:n for j in nzrange(A, i) row = rows[j] val = vals[j] # perform sparse wizardry... end end