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Instantiating and setting up a vector is very easy and intuitive. However, there are a few rules to take care of:
StaticVector
or HybridVector
are default initialized (i.e. built-in data types are initialized to 0, class types are initialized via the default constructor).DynamicVector
or CompressedVector
remain uninitialized if they are of built-in type and are default constructed if they are of class type.
The DynamicVector
, HybridVector
and CompressedVector
classes offer a constructor that allows to immediately give the vector the required size. Whereas both dense vectors (i.e. DynamicVector
and HybridVector
) use this information to allocate memory for all vector elements, CompressedVector
merely acquires the size but remains empty.
All dense vector classes offer a constructor that allows for a direct, homogeneous initialization of all vector elements. In contrast, for sparse vectors the predicted number of non-zero elements can be specified
Alternatively, all dense vector classes offer a constructor for an initialization with a dynamic or static array. If the vector is initialized from a dynamic array, the constructor expects the actual size of the array as first argument, the array as second argument. In case of a static array, the fixed size of the array is used:
In addition, all dense vector classes can be directly initialized by means of an initializer list:
All dense and sparse vectors can be created as the copy of any other dense or sparse vector with the same transpose flag (i.e. blaze::rowVector or blaze::columnVector).
Note that it is not possible to create a StaticVector
as a copy of a vector with a different size:
There are several types of assignment to dense and sparse vectors: Homogeneous Assignment, Array Assignment, Copy Assignment, and Compound Assignment.
Sometimes it may be necessary to assign the same value to all elements of a dense vector. For this purpose, the assignment operator can be used:
Dense vectors can also be assigned a static array:
Alternatively, it is possible to directly assign an initializer list to a dense vector:
For all vector types it is generally possible to assign another vector with the same transpose flag (i.e. blaze::columnVector or blaze::rowVector). Note that in case of StaticVectors
, the assigned vector is required to have the same size as the StaticVector
since the size of a StaticVector
cannot be adapted!
Next to plain assignment, it is also possible to use addition assignment, subtraction assignment, and multiplication assignment. Note however, that in contrast to plain assignment the size and the transpose flag of the vectors has be to equal in order to able to perform a compound assignment.
The easiest and most intuitive way to access a dense or sparse vector is via the subscript operator. The indices to access a vector are zero-based:
Whereas using the subscript operator on a dense vector only accesses the already existing element, accessing an element of a sparse vector via the subscript operator potentially inserts the element into the vector and may therefore be more expensive. Consider the following example:
Although the compressed vector is only used for read access within the for loop, using the subscript operator temporarily inserts 10 non-zero elements into the vector. Therefore, all vectors (sparse as well as dense) offer an alternate way via the begin()
, cbegin()
, end()
, and cend()
functions to traverse the currently contained elements by iterators. In case of non-const vectors, begin()
and end()
return an Iterator
, which allows a manipulation of the non-zero value, in case of a constant vector or in case cbegin()
or cend()
are used a ConstIterator
is returned:
Note that begin()
, cbegin()
, end()
, and cend()
are also available as free functions:
In contrast to dense vectors, that store all elements independent of their value and that offer direct access to all elements, spares vectors only store the non-zero elements contained in the vector. Therefore it is necessary to explicitly add elements to the vector. The first option to add elements to a sparse vector is the subscript operator:
In case the element at the given index is not yet contained in the vector, it is automatically inserted. Otherwise the old value is replaced by the new value 2. The operator returns a reference to the sparse vector element.
An alternative is the set()
function: In case the element is not yet contained in the vector the element is inserted, else the element's value is modified:
However, insertion of elements can be better controlled via the insert()
function. In contrast to the subscript operator and the set()
function it emits an exception in case the element is already contained in the vector. In order to check for this case, the find()
function can be used:
Although the insert()
function is very flexible, due to performance reasons it is not suited for the setup of large sparse vectors. A very efficient, yet also very low-level way to fill a sparse vector is the append()
function. It requires the sparse vector to provide enough capacity to insert a new element. Additionally, the index of the new element must be larger than the index of the previous element. Violating these conditions results in undefined behavior!
Via the size()
member function, the current size of a dense or sparse vector can be queried:
Alternatively, the free function size()
can be used to query to current size of a vector. In contrast to the member function, the free function can also be used to query the size of vector expressions:
Via the capacity()
(member) function the internal capacity of a dense or sparse vector can be queried. Note that the capacity of a vector doesn't have to be equal to the size of a vector. In case of a dense vector the capacity will always be greater or equal than the size of the vector, in case of a sparse vector the capacity may even be less than the size.
For symmetry reasons, there is also a free function /c capacity() available that can be used to query the capacity:
Note, however, that it is not possible to query the capacity of a vector expression:
For both dense and sparse vectors the number of non-zero elements can be determined via the nonZeros()
member function. Sparse vectors directly return their number of non-zero elements, dense vectors traverse their elements and count the number of non-zero elements.
There is also a free function nonZeros()
available to query the current number of non-zero elements:
The free nonZeros()
function can also be used to query the number of non-zero elements in a vector expression. However, the result is not the exact number of non-zero elements, but may be a rough estimation:
The size of a StaticVector
is fixed by the second template parameter and a CustomVector
cannot be resized. In contrast, the size of DynamicVectors
, HybridVectors
as well as CompressedVectors
can be changed via the resize()
function:
Note that resizing a vector invalidates all existing views (see e.g. Subvectors) on the vector:
When the internal capacity of a vector is no longer sufficient, the allocation of a larger junk of memory is triggered. In order to avoid frequent reallocations, the reserve()
function can be used up front to set the internal capacity:
Note that the size of the vector remains unchanged, but only the internal capacity is set according to the specified value!
In order to reset all elements of a vector, the reset()
function can be used:
In order to return a vector to its default state (i.e. the state of a default constructed vector), the clear()
function can be used:
Note that resetting or clearing both dense and sparse vectors does not change the capacity of the vectors.
The isnan()
function provides the means to check a dense or sparse vector for non-a-number elements:
If at least one element of the vector is not-a-number, the function returns true
, otherwise it returns false
. Please note that this function only works for vectors with floating point elements. The attempt to use it for a vector with a non-floating point element type results in a compile time error.
The isDefault()
function returns whether the given dense or sparse vector is in default state:
A vector is in default state if it appears to just have been default constructed. All resizable vectors (HybridVector
, DynamicVector
, or CompressedVector
) and CustomVector
are in default state if its size is equal to zero. A non-resizable vector (StaticVector
, all subvectors, rows, and columns) is in default state if all its elements are in default state. For instance, in case the vector is instantiated for a built-in integral or floating point data type, the function returns true
in case all vector elements are 0 and false
in case any vector element is not 0.
In order to check if all vector elements are identical, the isUniform
function can be used:
Note that in case of sparse vectors also the zero elements are also taken into account!
The min()
and the max()
functions return the smallest and largest element of the given dense or sparse vector, respectively:
In case the vector currently has a size of 0, both functions return 0. Additionally, in case a given sparse vector is not completely filled, the zero elements are taken into account. For example: the following compressed vector has only 2 non-zero elements. However, the minimum of this vector is 0:
Also note that the min()
and max()
functions can be used to compute the smallest and largest element of a vector expression:
The abs()
function can be used to compute the absolute values of each element of a vector. For instance, the following computation
results in the vector
The floor()
and ceil()
functions can be used to round down/up each element of a vector, respectively:
The conj()
function can be applied on a dense or sparse vector to compute the complex conjugate of each element of the vector:
Additionally, vectors can be conjugated in-place via the conjugate()
function:
The real()
function can be used on a dense or sparse vector to extract the real part of each element of the vector:
The imag()
function can be used on a dense or sparse vector to extract the imaginary part of each element of the vector:
Via the sqrt()
and invsqrt()
functions the (inverse) square root of each element of a vector can be computed:
Note that in case of sparse vectors only the non-zero elements are taken into account!
The cbrt()
and invcbrt()
functions can be used to compute the the (inverse) cubic root of each element of a vector:
Note that in case of sparse vectors only the non-zero elements are taken into account!
The clip()
function can be used to restrict all elements of a vector to a specific range:
Note that in case of sparse vectors only the non-zero elements are taken into account!
The pow()
function can be used to compute the exponential value of each element of a vector:
exp()
computes the base e exponential of each element of a vector:
Note that in case of sparse vectors only the non-zero elements are taken into account!
The log()
and log10()
functions can be used to compute the natural and common logarithm of each element of a vector:
The following trigonometric functions are available for both dense and sparse vectors:
Note that in case of sparse vectors only the non-zero elements are taken into account!
The following hyperbolic functions are available for both dense and sparse vectors:
Note that in case of sparse vectors only the non-zero elements are taken into account!
The erf()
and erfc()
functions compute the (complementary) error function of each element of a vector:
Note that in case of sparse vectors only the non-zero elements are taken into account!
Via the forEach()
function it is possible to execute custom operations on dense and sparse vectors. For instance, the following example demonstrates a custom square root computation via a lambda:
Although the computation can be parallelized it is not vectorized and thus cannot perform at peak performance. However, it is also possible to create vectorized custom operations. See Custom Operations for a detailed overview of the possibilities of custom operations.
In order to calculate the length of a vector, both the length()
and sqrLength()
function can be used:
Note that both functions can only be used for vectors with built-in or complex element type!
As already mentioned, vectors can either be column vectors (blaze::columnVector) or row vectors (blaze::rowVector). A column vector cannot be assigned to a row vector and vice versa. However, vectors can be transposed via the trans()
function:
It is also possible to compute the conjugate transpose of a vector. This operation is available via the ctrans()
function:
Note that the ctrans()
function has the same effect as manually applying the conj()
and trans()
function in any order:
The normalize()
function can be used to scale any non-zero vector to a length of 1. In case the vector does not contain a single non-zero element (i.e. is a zero vector), the normalize()
function returns a zero vector.
Note that the normalize()
function only works for floating point vectors. The attempt to use it for an integral vector results in a compile time error.
Via the swap()
function it is possible to completely swap the contents of two vectors of the same type:
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