Defines operations on vectors of FunctionsThis file defines a number of operations on vectors of functions. Assume v is a vector of NDIM-D functions of a certain type. More...
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Namespaces | |
| madness | |
| Holds machinery to set up Functions/FuncImpls using various Factories and Interfaces. | |
Functions | |
| template<typename T , std::size_t NDIM> | |
| void | madness::compress (World &world, const std::vector< Function< T, NDIM > > &v, bool fence=true) |
| Compress a vector of functions. More... | |
| template<typename T , std::size_t NDIM> | |
| void | madness::reconstruct (World &world, const std::vector< Function< T, NDIM > > &v, bool fence=true) |
| Reconstruct a vector of functions. More... | |
| template<typename T , std::size_t NDIM> | |
| void | madness::nonstandard (World &world, std::vector< Function< T, NDIM > > &v, bool fence=true) |
| Generates non-standard form of a vector of functions. More... | |
| template<typename T , std::size_t NDIM> | |
| void | madness::standard (World &world, std::vector< Function< T, NDIM > > &v, bool fence=true) |
| Generates standard form of a vector of functions. More... | |
| template<typename T , std::size_t NDIM> | |
| void | madness::truncate (World &world, std::vector< Function< T, NDIM > > &v, double tol=0.0, bool fence=true) |
| Truncates a vector of functions. More... | |
| template<typename T , std::size_t NDIM> | |
| std::vector< Function< T, NDIM > > | madness::apply (World &world, const Derivative< T, NDIM > &D, const std::vector< Function< T, NDIM > > &v, bool fence=true) |
| Applies a derivative operator to a vector of functions. More... | |
| template<typename T , std::size_t NDIM> | |
| std::vector< Function< T, NDIM > > | madness::zero_functions (World &world, int n) |
| Generates a vector of zero functions. More... | |
| template<typename T , typename R , std::size_t NDIM> | |
| std::vector< Function < TENSOR_RESULT_TYPE(T, R), NDIM > > | madness::transform (World &world, const std::vector< Function< T, NDIM > > &v, const Tensor< R > &c, bool fence=true) |
| Transforms a vector of functions according to new[i] = sum[j] old[j]*c[j,i]. More... | |
| template<typename L , typename R , std::size_t NDIM> | |
| std::vector< Function < TENSOR_RESULT_TYPE(L, R), NDIM > > | madness::transform (World &world, const std::vector< Function< L, NDIM > > &v, const Tensor< R > &c, double tol, bool fence) |
| template<typename T , typename Q , std::size_t NDIM> | |
| void | madness::scale (World &world, std::vector< Function< T, NDIM > > &v, const std::vector< Q > &factors, bool fence=true) |
| Scales inplace a vector of functions by distinct values. More... | |
| template<typename T , typename Q , std::size_t NDIM> | |
| void | madness::scale (World &world, std::vector< Function< T, NDIM > > &v, const Q factor, bool fence=true) |
| Scales inplace a vector of functions by the same. More... | |
| template<typename T , std::size_t NDIM> | |
| std::vector< double > | madness::norm2s (World &world, const std::vector< Function< T, NDIM > > &v) |
| Computes the 2-norms of a vector of functions. More... | |
| template<typename T , std::size_t NDIM> | |
| double | madness::norm2 (World &world, const std::vector< Function< T, NDIM > > &v) |
| Computes the 2-norm of a vector of functions. More... | |
| double | madness::conj (double x) |
| double | madness::conj (float x) |
| template<typename T , typename R , std::size_t NDIM> | |
| Tensor< TENSOR_RESULT_TYPE(T, R) > | madness::matrix_inner (World &world, const std::vector< Function< T, NDIM > > &f, const std::vector< Function< R, NDIM > > &g, bool sym=false) |
| Computes the matrix inner product of two function vectors - q(i,j) = inner(f[i],g[j]) More... | |
| template<typename T , typename R , std::size_t NDIM> | |
| Tensor< TENSOR_RESULT_TYPE(T, R) > | madness::inner (World &world, const std::vector< Function< T, NDIM > > &f, const std::vector< Function< R, NDIM > > &g) |
| Computes the element-wise inner product of two function vectors - q(i) = inner(f[i],g[i]) More... | |
| template<typename T , typename R , std::size_t NDIM> | |
| Tensor< TENSOR_RESULT_TYPE(T, R) > | madness::inner (World &world, const Function< T, NDIM > &f, const std::vector< Function< R, NDIM > > &g) |
| Computes the inner product of a function with a function vector - q(i) = inner(f,g[i]) More... | |
| template<typename T , typename R , std::size_t NDIM> | |
| std::vector< Function < TENSOR_RESULT_TYPE(T, R), NDIM > > | madness::mul (World &world, const Function< T, NDIM > &a, const std::vector< Function< R, NDIM > > &v, bool fence=true) |
| Multiplies a function against a vector of functions — q[i] = a * v[i]. More... | |
| template<typename T , typename R , std::size_t NDIM> | |
| std::vector< Function < TENSOR_RESULT_TYPE(T, R), NDIM > > | madness::mul_sparse (World &world, const Function< T, NDIM > &a, const std::vector< Function< R, NDIM > > &v, double tol, bool fence=true) |
| Multiplies a function against a vector of functions using sparsity of a and v[i] — q[i] = a * v[i]. More... | |
| template<typename T , std::size_t NDIM> | |
| void | madness::norm_tree (World &world, const std::vector< Function< T, NDIM > > &v, bool fence=true) |
| Makes the norm tree for all functions in a vector. More... | |
| template<typename T , typename R , std::size_t NDIM> | |
| std::vector< Function < TENSOR_RESULT_TYPE(T, R), NDIM > > | madness::mul (World &world, const std::vector< Function< T, NDIM > > &a, const std::vector< Function< R, NDIM > > &b, bool fence=true) |
| Multiplies two vectors of functions q[i] = a[i] * b[i]. More... | |
| template<typename T , std::size_t NDIM> | |
| std::vector< Function< T, NDIM > > | madness::square (World &world, const std::vector< Function< T, NDIM > > &v, bool fence=true) |
| Computes the square of a vector of functions — q[i] = v[i]**2. More... | |
| template<typename T , std::size_t NDIM> | |
| void | madness::set_thresh (World &world, std::vector< Function< T, NDIM > > &v, double thresh, bool fence=true) |
| Sets the threshold in a vector of functions. More... | |
| template<typename T , std::size_t NDIM> | |
| std::vector< Function< T, NDIM > > | madness::conj (World &world, const std::vector< Function< T, NDIM > > &v, bool fence=true) |
| Returns the complex conjugate of the vector of functions. More... | |
| template<typename T , std::size_t NDIM> | |
| std::vector< Function< T, NDIM > > | madness::copy (World &world, const std::vector< Function< T, NDIM > > &v, bool fence=true) |
| Returns a deep copy of a vector of functions. More... | |
| template<typename T , std::size_t NDIM> | |
| std::vector< Function< T, NDIM > > | madness::copy (World &world, const Function< T, NDIM > &v, const unsigned int n, bool fence=true) |
| Returns a vector of deep copies of of a function. More... | |
| template<typename T , typename R , std::size_t NDIM> | |
| std::vector< Function < TENSOR_RESULT_TYPE(T, R), NDIM > > | madness::add (World &world, const std::vector< Function< T, NDIM > > &a, const std::vector< Function< R, NDIM > > &b, bool fence=true) |
| Returns new vector of functions — q[i] = a[i] + b[i]. More... | |
| template<typename T , typename R , std::size_t NDIM> | |
| std::vector< Function < TENSOR_RESULT_TYPE(T, R), NDIM > > | madness::add (World &world, const Function< T, NDIM > &a, const std::vector< Function< R, NDIM > > &b, bool fence=true) |
| Returns new vector of functions — q[i] = a + b[i]. More... | |
| template<typename T , typename R , std::size_t NDIM> | |
| std::vector< Function < TENSOR_RESULT_TYPE(T, R), NDIM > > | madness::add (World &world, const std::vector< Function< R, NDIM > > &b, const Function< T, NDIM > &a, bool fence=true) |
| template<typename T , typename R , std::size_t NDIM> | |
| std::vector< Function < TENSOR_RESULT_TYPE(T, R), NDIM > > | madness::sub (World &world, const std::vector< Function< T, NDIM > > &a, const std::vector< Function< R, NDIM > > &b, bool fence=true) |
| Returns new vector of functions — q[i] = a[i] - b[i]. More... | |
| template<typename T , typename Q , typename R , std::size_t NDIM> | |
| void | madness::gaxpy (World &world, Q alpha, std::vector< Function< T, NDIM > > &a, Q beta, const std::vector< Function< R, NDIM > > &b, bool fence=true) |
| Generalized A*X+Y for vectors of functions -— a[i] = alpha*a[i] + beta*b[i]. More... | |
| template<typename opT , typename R , std::size_t NDIM> | |
| std::vector< Function < TENSOR_RESULT_TYPE(typename opT::opT, R), NDIM > > | madness::apply (World &world, const std::vector< std::shared_ptr< opT > > &op, const std::vector< Function< R, NDIM > > f) |
| Applies a vector of operators to a vector of functions — q[i] = apply(op[i],f[i]) More... | |
| template<typename T , typename R , std::size_t NDIM> | |
| std::vector< Function < TENSOR_RESULT_TYPE(T, R), NDIM > > | madness::apply (World &world, const SeparatedConvolution< T, NDIM > &op, const std::vector< Function< R, NDIM > > f) |
| Applies an operator to a vector of functions — q[i] = apply(op,f[i]) More... | |
| template<typename T , std::size_t NDIM> | |
| void | madness::normalize (World &world, std::vector< Function< T, NDIM > > &v, bool fence=true) |
| Normalizes a vector of functions — v[i] = v[i].scale(1.0/v[i].norm2()) More... | |
| template<typename T , std::size_t NDIM> | |
| double | madness::get_size (World &world, const std::vector< Function< T, NDIM > > &v) |
Detailed Description
Defines operations on vectors of Functions
This file defines a number of operations on vectors of functions. Assume v is a vector of NDIM-D functions of a certain type.
Operations on array of functions
) copying: deep copying of vectors of functions to vector of functions
vector2 = copy(world, vector1,fence);
) compress: convert multiwavelet representation to legendre representation
compress(world, vector, fence);
) reconstruct: convert representation to multiwavelets
reconstruct(world, vector, fence);
) nonstandard: convert to non-standard form
nonstandard(world, v, fence);
) standard: convert to standard form
standard(world, v, fence);
) truncate: truncating vectors of functions to desired precision
truncate(world, v, tolerance, fence);
) zero function: create a vector of zero functions of length n
v=zero(world, n);
) transform: transform a representation from one basis to another
transform(world, vector, tensor, tolerance, fence )
Setting thresh-hold for precision
) set_thresh: setting a finite thresh-hold for a vector of functions
Arithmetic Operations on arrays of functions
) conjugation: conjugate a vector of complex functions
) add ) sub ) mul
- mul_sparse ) square ) gaxpy ) apply
Norms, inner-products, blas-1 like operations on vectors of functions
) inner ) matrix_inner ) norm_tree ) normalize ) norm2
- norm2s ) scale(world, v, alpha);
