Reference documentation for deal.II version 9.0.0

#include <deal.II/lac/vector.h>
Public Types  
typedef Number  value_type 
typedef numbers::NumberTraits< Number >::real_type  real_type 
Public Member Functions  
Basic object handling  
Vector ()  
Vector (const Vector< Number > &v)  
Vector (Vector< Number > &&v) noexcept  
template<typename OtherNumber >  
Vector (const Vector< OtherNumber > &v)  
Vector (const PETScWrappers::VectorBase &v)  
Vector (const TrilinosWrappers::MPI::Vector &v)  
Vector (const size_type n)  
template<typename InputIterator >  
Vector (const InputIterator first, const InputIterator last)  
virtual  ~Vector ()=default 
void  compress (::VectorOperation::values operation=::VectorOperation::unknown) const 
virtual void  reinit (const size_type N, const bool omit_zeroing_entries=false) 
void  grow_or_shrink (const size_type N) 
template<typename Number2 >  
void  reinit (const Vector< Number2 > &V, const bool omit_zeroing_entries=false) 
virtual void  swap (Vector< Number > &v) 
Vector< Number > &  operator= (const Number s) 
Vector< Number > &  operator= (const Vector< Number > &v) 
Vector< Number > &  operator= (Vector< Number > &&v) noexcept 
template<typename Number2 >  
Vector< Number > &  operator= (const Vector< Number2 > &v) 
Vector< Number > &  operator= (const BlockVector< Number > &v) 
Vector< Number > &  operator= (const PETScWrappers::VectorBase &v) 
Vector< Number > &  operator= (const TrilinosWrappers::MPI::Vector &v) 
template<typename Number2 >  
bool  operator== (const Vector< Number2 > &v) const 
template<typename Number2 >  
bool  operator!= (const Vector< Number2 > &v) const 
Scalar products, norms and related operations  
template<typename Number2 >  
Number  operator* (const Vector< Number2 > &V) const 
real_type  norm_sqr () const 
Number  mean_value () const 
real_type  l1_norm () const 
real_type  l2_norm () const 
real_type  lp_norm (const real_type p) const 
real_type  linfty_norm () const 
Number  add_and_dot (const Number a, const Vector< Number > &V, const Vector< Number > &W) 
Data access  
iterator  begin () 
const_iterator  begin () const 
iterator  end () 
const_iterator  end () const 
Number  operator() (const size_type i) const 
Number &  operator() (const size_type i) 
Number  operator[] (const size_type i) const 
Number &  operator[] (const size_type i) 
template<typename OtherNumber >  
void  extract_subvector_to (const std::vector< size_type > &indices, std::vector< OtherNumber > &values) const 
template<typename ForwardIterator , typename OutputIterator >  
void  extract_subvector_to (ForwardIterator indices_begin, const ForwardIterator indices_end, OutputIterator values_begin) const 
Modification of vectors  
Vector< Number > &  operator+= (const Vector< Number > &V) 
Vector< Number > &  operator= (const Vector< Number > &V) 
template<typename OtherNumber >  
void  add (const std::vector< size_type > &indices, const std::vector< OtherNumber > &values) 
template<typename OtherNumber >  
void  add (const std::vector< size_type > &indices, const Vector< OtherNumber > &values) 
template<typename OtherNumber >  
void  add (const size_type n_elements, const size_type *indices, const OtherNumber *values) 
void  add (const Number s) 
void  add (const Number a, const Vector< Number > &V, const Number b, const Vector< Number > &W) 
void  add (const Number a, const Vector< Number > &V) 
void  sadd (const Number s, const Vector< Number > &V) 
void  sadd (const Number s, const Number a, const Vector< Number > &V) 
Vector< Number > &  operator*= (const Number factor) 
Vector< Number > &  operator/= (const Number factor) 
void  scale (const Vector< Number > &scaling_factors) 
template<typename Number2 >  
void  scale (const Vector< Number2 > &scaling_factors) 
void  equ (const Number a, const Vector< Number > &u) 
template<typename Number2 >  
void  equ (const Number a, const Vector< Number2 > &u) 
void  ratio (const Vector< Number > &a, const Vector< Number > &b) 
void  update_ghost_values () const 
Input and output  
void  print (const char *format=nullptr) const 
void  print (std::ostream &out, const unsigned int precision=3, const bool scientific=true, const bool across=true) const 
void  print (LogStream &out, const unsigned int width=6, const bool across=true) const 
void  block_write (std::ostream &out) const 
void  block_read (std::istream &in) 
template<class Archive >  
void  save (Archive &ar, const unsigned int version) const 
template<class Archive >  
void  load (Archive &ar, const unsigned int version) 
Information about the object  
bool  in_local_range (const size_type global_index) const 
IndexSet  locally_owned_elements () const 
size_type  size () const 
bool  all_zero () const 
bool  is_non_negative () const 
std::size_t  memory_consumption () const 
Public Member Functions inherited from Subscriptor  
Subscriptor ()  
Subscriptor (const Subscriptor &)  
Subscriptor (Subscriptor &&) noexcept  
virtual  ~Subscriptor () 
Subscriptor &  operator= (const Subscriptor &) 
Subscriptor &  operator= (Subscriptor &&) noexcept 
void  subscribe (const char *identifier=nullptr) const 
void  unsubscribe (const char *identifier=nullptr) const 
unsigned int  n_subscriptions () const 
void  list_subscribers () const 
template<class Archive >  
void  serialize (Archive &ar, const unsigned int version) 
Protected Attributes  
size_type  vec_size 
size_type  max_vec_size 
std::unique_ptr< Number[], decltype(&free)>  values 
std::shared_ptr< parallel::internal::TBBPartitioner >  thread_loop_partitioner 
Private Member Functions  
void  allocate (const size_type copy_n_el=0) 
Friends  
template<typename Number2 >  
class  Vector 
template<typename Number2 >  
class  LAPACKFullMatrix 
class  VectorView< Number > 
Related Functions  
(Note that these are not member functions.)  
template<typename Number >  
void  swap (LinearAlgebra::distributed::Vector< Number > &u, LinearAlgebra::distributed::Vector< Number > &v) 
template<typename Number >  
void  swap (LinearAlgebra::ReadWriteVector< Number > &u, LinearAlgebra::ReadWriteVector< Number > &v) 
template<typename Number >  
void  swap (Vector< Number > &u, Vector< Number > &v) 
Additional Inherited Members  
Static Public Member Functions inherited from Subscriptor  
static::ExceptionBase &  ExcInUse (int arg1, std::string arg2, std::string arg3) 
static::ExceptionBase &  ExcNoSubscriber (std::string arg1, std::string arg2) 
Numerical vector of data. For this class there are different types of functions available. The first type of function initializes the vector, changes its size, or computes the norm of the vector in order to measure its length in a suitable norm. The second type helps us to manipulate the components of the vector. The third type defines the algebraic operations for vectors, while the last type defines a few input and output functions. As opposed to the array of the C++ standard library called vector
(with a lowercase "v"), this class implements an element of a vector space suitable for numerical computations.
<float>, <double>, <std::complex<float>>, <std::complex<double>>
; others can be generated in application programs (see the section on Template instantiations in the manual).Definition at line 34 of file function.h.
typedef Number Vector< Number >::value_type 
typedef numbers::NumberTraits<Number>::real_type Vector< Number >::real_type 
Declare a type that has holds realvalued numbers with the same precision as the template argument to this class. If the template argument of this class is a real data type, then real_type equals the template argument. If the template argument is a std::complex type then real_type equals the type underlying the complex numbers.
This typedef is used to represent the return type of norms.
Constructor. Create a vector of dimension zero.
Copy constructor. Sets the dimension to that of the given vector, and copies all elements.
We would like to make this constructor explicit, but standard containers insist on using it implicitly.
Move constructor. Creates a new vector by stealing the internal data of the vector v
.

explicit 
Copy constructor taking a vector of another data type. This will fail if there is no conversion path from OtherNumber
to Number
. Note that you may lose accuracy when copying to a vector with data elements with less accuracy.
Older versions of gcc did not honor the explicit
keyword on template constructors. In such cases, it is easy to accidentally write code that can be very inefficient, since the compiler starts performing hidden conversions. To avoid this, this function is disabled if we have detected a broken compiler during configuration.

explicit 
Another copy constructor: copy the values from a PETSc vector class. This copy constructor is only available if PETSc was detected during configuration time.
Note that due to the communication model used in MPI, this operation can only succeed if all processes do it at the same time when v
is a distributed vector: It is not possible for only one process to obtain a copy of a parallel vector while the other jobs do something else.

explicit 
Another copy constructor: copy the values from a Trilinos wrapper vector. This copy constructor is only available if Trilinos was detected during configuration time.
v
(i.e. those given by v.get_mpi_communicator()
) do it at the same time. This means that unless you use a split MPI communicator then it is not normally possible for only one or a subset of processes to obtain a copy of a parallel vector while the other jobs do something else. In other words, calling this function is a 'collective operation' that needs to be executed by all MPI processes that jointly share v
. Constructor. Set dimension to n
and initialize all elements with zero.
The constructor is made explicit to avoid accidents like this: v=0;
. Presumably, the user wants to set every element of the vector to zero, but instead, what happens is this call: v=Vector<number>(0);
, i.e. the vector is replaced by one of length zero.
Vector< Number >::Vector  (  const InputIterator  first, 
const InputIterator  last  
) 
Initialize the vector with a given range of values pointed to by the iterators. This function is there in analogy to the std::vector
class.
Destructor, deallocates memory. Made virtual to allow for derived classes to behave properly.
void Vector< Number >::compress  (  ::VectorOperation::values  operation = ::VectorOperation::unknown  )  const 
This function does nothing but exists for compatibility with the parallel vector classes.
For the parallel vector wrapper class, this function compresses the underlying representation of the vector, i.e. flushes the buffers of the vector object if it has any. This function is necessary after writing into a vector elementbyelement and before anything else can be done on it.
However, for the implementation of this class, it is immaterial and thus an empty function.

virtual 
Change the dimension of the vector to N
. The reserved memory for this vector remains unchanged if possible, to make things faster; this may waste some memory, so keep this in mind. However, if N==0
all memory is freed, i.e. if you want to resize the vector and release the memory not needed, you have to first call reinit(0)
and then reinit(N)
. This cited behaviour is analogous to that of the standard library containers.
If omit_zeroing_entries
is false, the vector is filled by zeros. Otherwise, the elements are left an unspecified state.
This function is virtual in order to allow for derived classes to handle memory separately.
Reimplemented in VectorView< Number >.
void Vector< Number >::grow_or_shrink  (  const size_type  N  ) 
Same as above, but will preserve the values of vector upon resizing. If we new size is bigger, we will have
\[ \mathbf V \rightarrow \left( \begin{array}{c} \mathbf V \\ \mathbf 0 \end{array} \right) \]
whereas if the desired size is smaller, then
\[ \left( \begin{array}{c} \mathbf V_1 \\ \mathbf V_2 \end{array} \right) \rightarrow \mathbf V_1 \]
void Vector< Number >::reinit  (  const Vector< Number2 > &  V, 
const bool  omit_zeroing_entries = false 

) 
Change the dimension to that of the vector V
. The same applies as for the other reinit
function.
The elements of V
are not copied, i.e. this function is the same as calling reinit (V.size(), omit_zeroing_entries)
.
Swap the contents of this vector and the other vector v
. One could do this operation with a temporary variable and copying over the data elements, but this function is significantly more efficient since it only swaps the pointers to the data of the two vectors and therefore does not need to allocate temporary storage and move data around.
This function is analogous to the swap
function of all C++ standard containers. Also, there is a global function swap(u,v)
that simply calls u.swap(v)
, again in analogy to standard functions.
This function is virtual in order to allow for derived classes to handle memory separately.
Reimplemented in VectorView< Number >.
Set all components of the vector to the given number s
. Simply pass this down to the individual block objects, but we still need to declare this function to make the example given in the discussion about making the constructor explicit work.
Since the semantics of assigning a scalar to a vector are not immediately clear, this operator should really only be used if you want to set the entire vector to zero. This allows the intuitive notation v=0
. Assigning other values is deprecated and may be disallowed in the future.
Copy the given vector. Resize the present vector if necessary.

noexcept 
Move the given vector. This operator replaces the present vector with the internal data of the vector v
and resets v
to the state it would have after being newly defaultconstructed.
Vector<Number>& Vector< Number >::operator=  (  const Vector< Number2 > &  v  ) 
Copy the given vector. Resize the present vector if necessary.
Vector<Number>& Vector< Number >::operator=  (  const BlockVector< Number > &  v  ) 
Copy operator for assigning a block vector to a regular vector.
Vector<Number>& Vector< Number >::operator=  (  const PETScWrappers::VectorBase &  v  ) 
Another copy operator: copy the values from a PETSc wrapper vector class. This operator is only available if PETSc was detected during configuration time.
Note that due to the communication model used in MPI, this operation can only succeed if all processes do it at the same time when v
is a distributed vector: It is not possible for only one process to obtain a copy of a parallel vector while the other jobs do something else.
Vector<Number>& Vector< Number >::operator=  (  const TrilinosWrappers::MPI::Vector< Number > &  v  ) 
Another copy operator: copy the values from a (sequential or parallel, depending on the underlying compiler) Trilinos wrapper vector class. This operator is only available if Trilinos was detected during configuration time.
v
(i.e. those given by v.get_mpi_communicator()
) do it at the same time. This means that unless you use a split MPI communicator then it is not normally possible for only one or a subset of processes to obtain a copy of a parallel vector while the other jobs do something else. In other words, calling this function is a 'collective operation' that needs to be executed by all MPI processes that jointly share v
. bool Vector< Number >::operator==  (  const Vector< Number2 > &  v  )  const 
Test for equality. This function assumes that the present vector and the one to compare with have the same size already, since comparing vectors of different sizes makes not much sense anyway.
bool Vector< Number >::operator!=  (  const Vector< Number2 > &  v  )  const 
Test for inequality. This function assumes that the present vector and the one to compare with have the same size already, since comparing vectors of different sizes makes not much sense anyway.
Number Vector< Number >::operator*  (  const Vector< Number2 > &  V  )  const 
Return the scalar product of two vectors. The return type is the underlying type of this
vector, so the return type and the accuracy with which it the result is computed depend on the order of the arguments of this vector.
For complex vectors, the scalar product is implemented as \(\left<v,w\right>=\sum_i v_i \bar{w_i}\).
Return the square of the \(l_2\)norm.
Number Vector< Number >::mean_value  (  )  const 
Mean value of the elements of this vector.
\(l_1\)norm of the vector. The sum of the absolute values.
\(l_2\)norm of the vector. The square root of the sum of the squares of the elements.
\(l_p\)norm of the vector. The pth root of the sum of the pth powers of the absolute values of the elements.
Maximum absolute value of the elements.
Number Vector< Number >::add_and_dot  (  const Number  a, 
const Vector< Number > &  V,  
const Vector< Number > &  W  
) 
Performs a combined operation of a vector addition and a subsequent inner product, returning the value of the inner product. In other words, the result of this function is the same as if the user called
The reason this function exists is that this operation involves less memory transfer than calling the two functions separately. This method only needs to load three vectors, this
, V
, W
, whereas calling separate methods means to load the calling vector this
twice. Since most vector operations are memory transfer limited, this reduces the time by 25% (or 50% if W
equals this
).
For complexvalued vectors, the scalar product in the second step is implemented as \(\left<v,w\right>=\sum_i v_i \bar{w_i}\).
iterator Vector< Number >::begin  (  ) 
Make the Vector
class a bit like the vector<>
class of the C++ standard library by returning iterators to the start and end of the elements of this vector.
const_iterator Vector< Number >::begin  (  )  const 
Return constant iterator to the start of the vectors.
iterator Vector< Number >::end  (  ) 
Return an iterator pointing to the element past the end of the array.
const_iterator Vector< Number >::end  (  )  const 
Return a constant iterator pointing to the element past the end of the array.
Number Vector< Number >::operator()  (  const size_type  i  )  const 
Access the value of the ith
component.
Number& Vector< Number >::operator()  (  const size_type  i  ) 
Access the ith
component as a writeable reference.
Number Vector< Number >::operator[]  (  const size_type  i  )  const 
Access the value of the ith
component.
Exactly the same as operator().
Number& Vector< Number >::operator[]  (  const size_type  i  ) 
Access the ith
component as a writeable reference.
Exactly the same as operator().
void Vector< Number >::extract_subvector_to  (  const std::vector< size_type > &  indices, 
std::vector< OtherNumber > &  values  
)  const 
Instead of getting individual elements of a vector via operator(), this function allows getting a whole set of elements at once. The indices of the elements to be read are stated in the first argument, the corresponding values are returned in the second.
If the current vector is called v
, then this function is the equivalent to the code
indices
and values
arrays must be identical. void Vector< Number >::extract_subvector_to  (  ForwardIterator  indices_begin, 
const ForwardIterator  indices_end,  
OutputIterator  values_begin  
)  const 
Instead of getting individual elements of a vector via operator(), this function allows getting a whole set of elements at once. In contrast to the previous function, this function obtains the indices of the elements by dereferencing all elements of the iterator range provided by the first two arguments, and puts the vector values into memory locations obtained by dereferencing a range of iterators starting at the location pointed to by the third argument.
If the current vector is called v
, then this function is the equivalent to the code
values_begin
as there are iterators between indices_begin
and indices_end
. Vector<Number>& Vector< Number >::operator+=  (  const Vector< Number > &  V  ) 
Add the given vector to the present one.
Vector<Number>& Vector< Number >::operator=  (  const Vector< Number > &  V  ) 
Subtract the given vector from the present one.
void Vector< Number >::add  (  const std::vector< size_type > &  indices, 
const std::vector< OtherNumber > &  values  
) 
A collective add operation: This function adds a whole set of values stored in values
to the vector components specified by indices
.
void Vector< Number >::add  (  const std::vector< size_type > &  indices, 
const Vector< OtherNumber > &  values  
) 
This is a second collective add operation. As a difference, this function takes a deal.II vector of values.
void Vector< Number >::add  (  const size_type  n_elements, 
const size_type *  indices,  
const OtherNumber *  values  
) 
Take an address where n_elements
are stored contiguously and add them into the vector. Handles all cases which are not covered by the other two add()
functions above.
void Vector< Number >::add  (  const Number  s  ) 
Addition of s
to all components. Note that s
is a scalar and not a vector.
void Vector< Number >::add  (  const Number  a, 
const Vector< Number > &  V,  
const Number  b,  
const Vector< Number > &  W  
) 
Multiple addition of scaled vectors, i.e. *this += a*V+b*W
.
Simple addition of a multiple of a vector, i.e. *this += a*V
.
void Vector< Number >::sadd  (  const Number  s, 
const Vector< Number > &  V  
) 
Scaling and simple vector addition, i.e. *this = s*(*this)+V
.
void Vector< Number >::sadd  (  const Number  s, 
const Number  a,  
const Vector< Number > &  V  
) 
Scaling and simple addition, i.e. *this = s*(*this)+a*V
.
Scale each element of the vector by a constant value.
Scale each element of the vector by the inverse of the given value.
Scale each element of this vector by the corresponding element in the argument. This function is mostly meant to simulate multiplication (and immediate reassignment) by a diagonal scaling matrix.
void Vector< Number >::scale  (  const Vector< Number2 > &  scaling_factors  ) 
Scale each element of this vector by the corresponding element in the argument. This function is mostly meant to simulate multiplication (and immediate reassignment) by a diagonal scaling matrix.
Assignment *this = a*u
.
void Vector< Number >::equ  (  const Number  a, 
const Vector< Number2 > &  u  
) 
Assignment *this = a*u
.
void Vector< Number >::ratio  (  const Vector< Number > &  a, 
const Vector< Number > &  b  
) 
Compute the elementwise ratio of the two given vectors, that is let this[i] = a[i]/b[i]
. This is useful for example if you want to compute the cellwise ratio of true to estimated error.
This vector is appropriately scaled to hold the result.
If any of the b[i]
is zero, the result is undefined. No attempt is made to catch such situations.
void Vector< Number >::update_ghost_values  (  )  const 
This function does nothing but exists for compatibility with the parallel
vector classes (e.g., LinearAlgebra::distributed::Vector class).
void Vector< Number >::print  (  const char *  format = nullptr  )  const 
Output of vector in userdefined format. For complexvalued vectors, the format should include specifiers for both the real and imaginary parts.
This function is deprecated.
void Vector< Number >::print  (  std::ostream &  out, 
const unsigned int  precision = 3 , 

const bool  scientific = true , 

const bool  across = true 

)  const 
Print to a stream. precision
denotes the desired precision with which values shall be printed, scientific
whether scientific notation shall be used. If across
is true
then the vector is printed in a line, while if false
then the elements are printed on a separate line each.
void Vector< Number >::print  (  LogStream &  out, 
const unsigned int  width = 6 , 

const bool  across = true 

)  const 
Print to a LogStream. width
is used as argument to the std::setw manipulator, if printing across. If across
is true
then the vector is printed in a line, while if false
then the elements are printed on a separate line each.
This function is deprecated.
void Vector< Number >::block_write  (  std::ostream &  out  )  const 
Write the vector en bloc to a file. This is done in a binary mode, so the output is neither readable by humans nor (probably) by other computers using a different operating system or number format.
void Vector< Number >::block_read  (  std::istream &  in  ) 
Read a vector en block from a file. This is done using the inverse operations to the above function, so it is reasonably fast because the bitstream is not interpreted.
The vector is resized if necessary.
A primitive form of error checking is performed which will recognize the bluntest attempts to interpret some data as a vector stored bitwise to a file, but not more.
void Vector< Number >::save  (  Archive &  ar, 
const unsigned int  version  
)  const 
Write the data of this object to a stream for the purpose of serialization.
void Vector< Number >::load  (  Archive &  ar, 
const unsigned int  version  
) 
Read the data of this object from a stream for the purpose of serialization.
bool Vector< Number >::in_local_range  (  const size_type  global_index  )  const 
Return true if the given global index is in the local range of this processor. Since this is not a distributed vector the method always returns true.
Return an index set that describes which elements of this vector are owned by the current processor. Note that this index set does not include elements this vector may store locally as ghost elements but that are in fact owned by another processor. As a consequence, the index sets returned on different processors if this is a distributed vector will form disjoint sets that add up to the complete index set. Obviously, if a vector is created on only one processor, then the result would satisfy
Since the current data type does not support parallel data storage across different processors, the returned index set is the complete index set.
size_type Vector< Number >::size  (  )  const 
Return dimension of the vector.
bool Vector< Number >::all_zero  (  )  const 
Return whether the vector contains only elements with value zero. This function is mainly for internal consistency checks and should seldom be used when not in debug mode since it uses quite some time.
bool Vector< Number >::is_non_negative  (  )  const 
Return true
if the vector has no negative entries, i.e. all entries are zero or positive. This function is used, for example, to check whether refinement indicators are really all positive (or zero).
The function obviously only makes sense if the template argument of this class is a real type. If it is a complex type, then an exception is thrown.
std::size_t Vector< Number >::memory_consumption  (  )  const 
Determine an estimate for the memory consumption (in bytes) of this object.

private 
Allocate and align values
along 64byte boundaries. The size of the allocated memory is determined by max_vec_size
. Copy first copy_n_el
from the old values.

friend 
VectorView will access the pointer.

related 
Global function swap
which overloads the default implementation of the C++ standard library which uses a temporary object. The function simply exchanges the data of the two vectors.
Definition at line 1545 of file la_parallel_vector.h.

related 
Global function swap
which overloads the default implementation of the C++ standard library which uses a temporary object. The function simply exchanges the data of the two vectors.
Definition at line 977 of file read_write_vector.h.

protected 

protected 
Amount of memory actually reserved for this vector. This number may be greater than vec_size
if a reinit
was called with less memory requirements than the vector needed last time. At present reinit
does not free memory when the number of needed elements is reduced.

protected 
Pointer to the array of elements of this vector.
Because we allocate these arrays via Utilities::System::posix_memalign, we need to use a custom deleter for this object that does not call delete[]
, but instead calls free()
.

mutableprotected 