Template Numerical Library version\ main:9e207324
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This tutorial introduces vectors in TNL. Vector
, in addition to Array
, offers also basic operations from linear algebra. The reader will mainly learn how to do Blas level 1 operations in TNL. Thanks to the design of TNL, it is easier to implement, hardware architecture transparent and in some cases even faster then Blas or cuBlas implementation.
Vector
is, similar to Array
, templated class defined in namespace TNL::Containers
having three template parameters:
Real
is type of data to be stored in the vectorDevice
is the device where the vector is allocated. Currently it can be either Devices::Host
for CPU or Devices::Cuda
for GPU supporting CUDA.Index
is the type to be used for indexing the vector elements.Vector
, unlike Array
, requires that the Real
type is numeric or a type for which basic algebraic operations are defined. What kind of algebraic operations is required depends on what vector operations the user will call. Vector
is derived from Array
so it inherits all its methods. In the same way the Array
has its counterpart ArraView
, Vector
has VectorView
which is derived from ArrayView
. We refer to to Arrays tutorial for more details.
By horizontal operations we mean vector expressions where we have one or more vectors as an input and a vector as an output. In TNL, this kind of operations is performed by the Expression Templates. It makes algebraic operations with vectors easy to do and very efficient at the same time. In some cases, one get even more efficient code compared to Blas and cuBlas. See the following example.
Output is:
The expression is evaluated on the same device where the vectors are allocated, this is done automatically. One cannot, however, mix vectors from different devices in one expression. Vector expression may contain any common function like the following:
Expression | Meaning |
---|---|
v = TNL::min( expr1, expr2 ) | v[ i ] = min( expr1[ i ], expr2[ i ] ) |
v = TNL::max( expr1, expr2 ) | v[ i ] = max( expr1[ i ], expr2[ i ] ) |
v = TNL::abs( expr ) | v[ i ] = abs( expr[ i ] ) |
v = TNL::sin( expr ) | v[ i ] = sin( expr[ i ] ) |
v = TNL::cos( expr ) | v[ i ] = cos( expr[ i ] ) |
v = TNL::tan( expr ) | v[ i ] = tan( expr[ i ] ) |
v = TNL::asin( expr ) | v[ i ] = asin( expr[ i ] ) |
v = TNL::acos( expr ) | v[ i ] = acos( expr[ i ] ) |
v = TNL::atan( expr ) | v[ i ] = atan( expr[ i ] ) |
v = TNL::sinh( expr ) | v[ i ] = sinh( expr[ i ] ) |
v = TNL::cosh( expr ) | v[ i ] = cosh( expr[ i ] ) |
v = TNL::tanh( expr ) | v[ i ] = tanh( expr[ i ] ) |
v = TNL::asinh( expr ) | v[ i ] = asinh( expr[ i ] ) |
v = TNL::acosh( expr ) | v[ i ] = acosh( expr[ i ] ) |
v = TNL::atanh( expr ) | v[ i ] = atanh( expr[ i ] ) |
v = TNL::exp( expr ) | v[ i ] = exp( expr[ i ] ) |
v = TNL::log( expr ) | v[ i ] = log( expr[ i ] ) |
v = TNL::log10( expr ) | v[ i ] = log10( expr[ i ] ) |
v = TNL::log2( expr ) | v[ i ] = log2( expr[ i ] ) |
v = TNL::sqrt( expr ) | v[ i ] = sqrt( expr[ i ] ) |
v = TNL::cbrt( expr ) | v[ i ] = cbrt( expr[ i ] ) |
v = TNL::pow( expr ) | v[ i ] = pow( expr[ i ] ) |
v = TNL::floor( expr ) | v[ i ] = floor( expr[ i ] ) |
v = TNL::ceil( expr ) | v[ i ] = ceil( expr[ i ] ) |
v = TNL::sign( expr ) | v[ i ] = sign( expr[ i ] ) |
Where v
is a result vector and expr
, expr1
and expr2
are vector expressions. Vector expressions can be combined with vector views (TNL::Containers::VectorView) as well.
By vertical operations we mean (parallel) reduction based operations where we have one vector expressions as an input and one value as an output. For example computing scalar product, vector norm or finding minimum or maximum of vector elements is based on reduction. See the following example.
Output is:
The following table shows vertical operations that can be used on vector expressions:
Expression | Meaning |
---|---|
v = TNL::min( expr ) | v is minimum of expr[ 0 ], expr[ 1 ] , .... expr[ n-1 ] . |
std::pair( v, i ) = TNL::argMin( expr ) | v is minimum of expr[ 0 ], expr[ 1 ] , .... expr[ n-1 ] , i is index of the smallest element. |
v = TNL::max( expr ) | v is maximum of expr[ 0 ], expr[ 1 ] , .... expr[ n-1 ] . |
std::pair( v, i ) = TNL::argMax( expr ) | v is maximum of expr[ 0 ], expr[ 1 ] , .... expr[ n-1 ] , i is index of the largest element. |
v = TNL::sum( expr ) | v is sum of expr[ 0 ], expr[ 1 ] , .... expr[ n-1 ] . |
v = TNL::maxNorm( expr ) | v is maximal norm of expr[ 0 ], expr[ 1 ] , .... expr[ n-1 ] . |
v = TNL::l1Norm( expr ) | v is l1 norm of expr[ 0 ], expr[ 1 ] , .... expr[ n-1 ] . |
v = TNL::l2Norm( expr ) | v is l2 norm of expr[ 0 ], expr[ 1 ] , .... expr[ n-1 ] . |
v = TNL::lpNorm( expr, p ) | v is lp norm of expr[ 0 ], expr[ 1 ] , .... expr[ n-1 ] . |
v = TNL::product( expr ) | v is product of expr[ 0 ], expr[ 1 ] , .... expr[ n-1 ] . |
v = TNL::logicalAnd( expr ) | v is logical AND of expr[ 0 ], expr[ 1 ] , .... expr[ n-1 ] . |
v = TNL::logicalOr( expr ) | v is logical OR of expr[ 0 ], expr[ 1 ] , .... expr[ n-1 ] . |
v = TNL::binaryAnd( expr ) | v is binary AND of expr[ 0 ], expr[ 1 ] , .... expr[ n-1 ] . |
v = TNL::binaryOr( expr ) | v is binary OR of expr[ 0 ], expr[ 1 ] , .... expr[ n-1 ] . |
Static vectors are derived from static arrays and so they are allocated on the stack and can be created in CUDA kernels as well. Their size is fixed as well and it is given by a template parameter. Static vector is a templated class defined in namespace TNL::Containers
having two template parameters:
Size
is the array size.Real
is type of numbers stored in the array.The interface of StaticVectors is smillar to Vector. Probably the most important methods are those related with static vector expressions which are handled by expression templates. They make the use of static vectors simpel and efficient at the same time. See the following simple demonstration:
The output looks as:
DistributedVector extends DistributedArray with algebraic operations. The functionality is similar to how Vector extends Array. DistributedVector also supports expression templates and other operations present in Vector.
Example:
The output looks as: