vec_arith.h File Reference

Vector and matrix arithmetic. More...

#include <iostream>
#include <complex>
#include <o2scl/ovector_tlate.h>
#include <o2scl/omatrix_tlate.h>
#include <o2scl/uvector_tlate.h>
#include <o2scl/umatrix_tlate.h>
#include <o2scl/ovector_cx_tlate.h>
#include <o2scl/omatrix_cx_tlate.h>
#include <o2scl/uvector_cx_tlate.h>
#include <o2scl/umatrix_cx_tlate.h>

Go to the source code of this file.


Detailed Description

Vector and matrix arithmetic.

By default, the following operators are defined:

    ovector operator+(ovector_const_view &x, ovector_const_view &y);
    ovector operator+(ovector_const_view &x, uvector_const_view &y);
    ovector operator+(uvector_const_view &x, ovector_const_view &y);
    uvector operator+(uvector_const_view &x, uvector_const_view &y);

    ovector_cx operator+(ovector_cx_view &x, ovector_cx_view &y);
    ovector_cx operator+(ovector_cx_view &x, uvector_cx_view &y);
    ovector_cx operator+(uvector_cx_view &x, ovector_cx_view &y);
    uvector_cx operator+(uvector_cx_view &x, uvector_cx_view &y);
    
    ovector operator-(ovector_const_view &x, ovector_const_view &y);
    ovector operator-(ovector_const_view &x, uvector_const_view &y);
    ovector operator-(uvector_const_view &x, ovector_const_view &y);
    uvector operator-(uvector_const_view &x, uvector_const_view &y);

    ovector_cx operator-(ovector_cx_view &x, ovector_cx_view &y);
    ovector_cx operator-(ovector_cx_view &x, uvector_cx_view &y);
    ovector_cx operator-(uvector_cx_view &x, ovector_cx_view &y);
    uvector_cx operator-(uvector_cx_view &x, uvector_cx_view &y);
    
    ovector operator*(omatrix_const_view &x, ovector_const_view &y);
    ovector operator*(omatrix_const_view &x, uvector_const_view &y);
    ovector operator*(umatrix_const_view &x, ovector_const_view &y);
    uvector operator*(umatrix_const_view &x, uvector_const_view &y);

    ovector_cx operator*(omatrix_cx_view &x, ovector_cx_view &y);
    ovector_cx operator*(omatrix_cx_view &x, uvector_cx_view &y);
    ovector_cx operator*(umatrix_cx_view &x, ovector_cx_view &y);
    uvector_cx operator*(umatrix_cx_view &x, uvector_cx_view &y);

    ovector operator*(ovector_const_view &x, omatrix_const_view &y);
    ovector operator*(ovector_const_view &x, umatrix_const_view &y);
    ovector operator*(uvector_const_view &x, omatrix_const_view &y);
    uvector operator*(ovector_const_view &x, umatrix_const_view &y);

    ovector trans_mult(ovector_const_view &x, omatrix_const_view &y);
    ovector trans_mult(ovector_const_view &x, umatrix_const_view &y);
    ovector trans_mult(uvector_const_view &x, omatrix_const_view &y);
    uvector trans_mult(ovector_const_view &x, umatrix_const_view &y);

    double dot(ovector_const_view &x, ovector_const_view &y);
    double dot(ovector_const_view &x, uvector_const_view &y);
    double dot(uvector_const_view &x, ovector_const_view &y);
    double dot(uvector_const_view &x, uvector_const_view &y);

    double dot(ovector_cx_view &x, ovector_cx_view &y);
    double dot(ovector_cx_view &x, uvector_cx_view &y);
    double dot(uvector_cx_view &x, ovector_cx_view &y);
    double dot(uvector_cx_view &x, uvector_cx_view &y);

    ovector operator*(double x, ovector_const_view &y);
    uvector operator*(double x, uvector_const_view &y);
    ovector operator*(ovector_const_view &x, double y);
    uvector operator*(uvector_const_view &x, double y);
    
    ovector pair_prod(ovector_const_view &x, ovector_const_view &y);
    ovector pair_prod(ovector_const_view &x, uvector_const_view &y);
    ovector pair_prod(uvector_const_view &x, ovector_const_view &y);
    uvector pair_prod(uvector_const_view &x, uvector_const_view &y);

    ovector_cx pair_prod(ovector_cx_view &x, ovector_const_view &y);
    ovector_cx pair_prod(ovector_cx_view &x, uvector_const_view &y);
    ovector_cx pair_prod(uvector_cx_view &x, ovector_const_view &y);
    uvector_cx pair_prod(uvector_cx_view &x, uvector_const_view &y);
    ovector_cx pair_prod(ovector_const_view &x, ovector_cx_view &y);
    ovector_cx pair_prod(ovector_const_view &x, uvector_cx_view &y);
    ovector_cx pair_prod(uvector_const_view &x, ovector_cx_view &y);
    uvector_cx pair_prod(uvector_const_view &x, uvector_cx_view &y);
    ovector_cx pair_prod(ovector_cx_view &x, ovector_cx_view &y);
    ovector_cx pair_prod(ovector_cx_view &x, uvector_cx_view &y);
    ovector_cx pair_prod(uvector_cx_view &x, ovector_cx_view &y);
    uvector_cx pair_prod(uvector_cx_view &x, uvector_cx_view &y);

    bool operator==(ovector_const_view &x, ovector_const_view &y);
    bool operator==(ovector_const_view &x, uvector_const_view &y);
    bool operator==(uvector_const_view &x, ovector_const_view &y);
    bool operator==(uvector_const_view &x, uvector_const_view &y);

    bool operator!=(ovector_const_view &x, ovector_const_view &y);
    bool operator!=(ovector_const_view &x, uvector_const_view &y);
    bool operator!=(uvector_const_view &x, ovector_const_view &y);
    bool operator!=(uvector_const_view &x, uvector_const_view &y);

Note:
This used to be in a separate namespace, called o2scl_arith, but this causes problems with Koenig lookup in template classes for operator*() when defined for vector addition (for example).
Todo:
Properly document the operators defined as macros
Idea for future:
Define operators for complex vector * real matrix
Idea for future:
These should be replaced by the BLAS routines where possible?

Definition in file vec_arith.h.


Defines

#define O2SCL_OP_VEC_VEC_ADD(vec1, vec2, vec3)
 The header macro for vector-vector addition.
#define O2SCL_OP_VEC_VEC_SUB(vec1, vec2, vec3)
 The header macro for vector-vector subtraction.
#define O2SCL_OP_MAT_VEC_MULT(vec1, vec2, mat)
 The header macro for matrix-vector (right) multiplication.
#define O2SCL_OP_CMAT_CVEC_MULT(vec1, vec2, mat)
 The header macro for complex matrix-vector (right) multiplication.
#define O2SCL_OP_VEC_MAT_MULT(vec1, vec2, mat)
 The header macro for vector-matrix (left) multiplication.
#define O2SCL_OP_TRANS_MULT(vec1, vec2, mat)
 The header macro for the trans_mult form of vector * matrix.
#define O2SCL_OP_DOT_PROD(dtype, vec1, vec2)
 The header macro for vector scalar (dot) product.
#define O2SCL_OP_CX_DOT_PROD(dtype, vec1, vec2)
 The header macro for complex vector scalar (dot) product.
#define O2SCL_OP_SCA_VEC_MULT(dtype, vecv, vec)
 The header macro for scalar-vector multiplication.
#define O2SCL_OP_VEC_SCA_MULT(dtype, vecv, vec)
 The header macro for vector-scalar multiplication.
#define O2SCL_OP_VEC_VEC_PRO(vec1, vec2, vec3)
 The header macro for pairwise vector * vector (where either vector can be real or complex).
#define O2SCL_OPSRC_VEC_VEC_ADD(vec1, vec2, vec3)
 The source code macro for vector-vector addition.
#define O2SCL_OPSRC_VEC_VEC_SUB(vec1, vec2, vec3)
 The source code macro for vector-vector subtraction.
#define O2SCL_OPSRC_MAT_VEC_MULT(vec1, vec2, mat)
 The source code macro for matrix * vector.
#define O2SCL_OPSRC_CMAT_CVEC_MULT(vec1, vec2, mat)
 The source code macro for complex matrix * complex vector.
#define O2SCL_OPSRC_VEC_MAT_MULT(vec1, vec2, mat)
 The source code macro for the operator form of vector * matrix.
#define O2SCL_OPSRC_TRANS_MULT(vec1, vec2, mat)
 The source code macro for the trans_mult form of vector * matrix.
#define O2SCL_OPSRC_DOT_PROD(dtype, vec1, vec2)
 The source code macro for a vector dot product.
#define O2SCL_OPSRC_CX_DOT_PROD(dtype, vec1, vec2)
 The source code macro for a complex vector dot product.
#define O2SCL_OPSRC_SCA_VEC_MULT(dtype, vecv, vec)
 The source code macro for vector=scalar*vector.
#define O2SCL_OPSRC_VEC_SCA_MULT(dtype, vecv, vec)
 The source code macro for vector=vector*scalar.
#define O2SCL_OPSRC_VEC_VEC_PRO(vec1, vec2, vec3)
 The source code macro for pairwise vector * vector (where either vector can be real or complex).
#define O2SCL_OP_VEC_VEC_EQUAL(vec1, vec2)
 The header macro for vector==vector.
#define O2SCL_OPSRC_VEC_VEC_EQUAL(vec1, vec2)
 The source code macro vector==vector.
#define O2SCL_OP_VEC_VEC_NEQUAL(vec1, vec2)
 The header macro for vector!=vector.
#define O2SCL_OPSRC_VEC_VEC_NEQUAL(vec1, vec2)
 The source code macro vector!=vector.

Define Documentation

#define O2SCL_OP_CMAT_CVEC_MULT ( vec1,
vec2,
mat   ) 

Value:

vec1 operator*  \
    (const mat &m, const vec2 &x);
The header macro for complex matrix-vector (right) multiplication.

Given types vec1, vec2, and mat, this macro provides the function declaration for adding two vectors using the form

      vec1 operator*(const mat &m, const vec3 &x);

The corresponding definition is given in O2SCL_OPSRC_CMAT_CVEC_MULT.

Definition at line 283 of file vec_arith.h.

#define O2SCL_OP_CX_DOT_PROD ( dtype,
vec1,
vec2   ) 

Value:

dtype dot       \
    (const vec1 &x, const vec2 &y);
The header macro for complex vector scalar (dot) product.

Given types vec1, vec2, and dtype, this macro provides the function declaration for adding two vectors using the form

      dtype operator*(const vec1 &x, const vec2 &y);

The corresponding definition is given in O2SCL_OPSRC_CX_DOT_PROD.

Definition at line 409 of file vec_arith.h.

#define O2SCL_OP_DOT_PROD ( dtype,
vec1,
vec2   ) 

Value:

dtype dot       \
    (const vec1 &x, const vec2 &y);
The header macro for vector scalar (dot) product.

Given types vec1, vec2, and dtype, this macro provides the function declaration for adding two vectors using the form

      dtype operator*(const vec1 &x, const vec2 &y);

The corresponding definition is given in O2SCL_OPSRC_DOT_PROD.

Definition at line 374 of file vec_arith.h.

#define O2SCL_OP_MAT_VEC_MULT ( vec1,
vec2,
mat   ) 

Value:

vec1 operator*  \
    (const mat &m, const vec2 &x);
The header macro for matrix-vector (right) multiplication.

Given types vec1, vec2, and mat, this macro provides the function declaration for adding two vectors using the form

      vec1 operator*(const mat &m, const vec3 &x);

See also the blas version of this function dgemv().

The corresponding definition is given in O2SCL_OPSRC_MAT_VEC_MULT.

Definition at line 247 of file vec_arith.h.

#define O2SCL_OP_SCA_VEC_MULT ( dtype,
vecv,
vec   ) 

Value:

vec operator*   \
    (const dtype &x, const vecv &y);
The header macro for scalar-vector multiplication.

Given types vecv, vec, and dtype, this macro provides the function declaration for adding two vectors using the form

      vec operator*(const dtype &x, const vecv &y);

The corresponding definition is given in O2SCL_OPSRC_SCA_VEC_MULT.

Definition at line 443 of file vec_arith.h.

#define O2SCL_OP_TRANS_MULT ( vec1,
vec2,
mat   ) 

Value:

vec1 trans_mult \
    (const vec2 &x, const mat &m);
The header macro for the trans_mult form of vector * matrix.

Definition at line 340 of file vec_arith.h.

#define O2SCL_OP_VEC_MAT_MULT ( vec1,
vec2,
mat   ) 

Value:

vec1 operator*  \
    (const vec2 &x, const mat &m);
The header macro for vector-matrix (left) multiplication.

Given types vec1, vec2, and mat, this macro provides the function declaration for adding two vectors using the form

      vec1 operator*(const vec3 &x, const mat &m);

The corresponding definition is given in O2SCL_OPSRC_VEC_MAT_MULT.

Definition at line 318 of file vec_arith.h.

#define O2SCL_OP_VEC_SCA_MULT ( dtype,
vecv,
vec   ) 

Value:

vec operator*   \
    (const vecv &x, const dtype &y);
The header macro for vector-scalar multiplication.

Given types vecv, vec, and dtype, this macro provides the function declaration for adding two vectors using the form

      vec operator*(const vecv &x, const dtype &y);

The corresponding definition is given in O2SCL_OPSRC_VEC_SCA_MULT.

Definition at line 471 of file vec_arith.h.

#define O2SCL_OP_VEC_VEC_ADD ( vec1,
vec2,
vec3   ) 

Value:

vec1 operator+  \
    (const vec2 &x, const vec3 &y);
The header macro for vector-vector addition.

Given types vec1, vec2, and vec_3, this macro provides the function declaration for adding two vectors using the form

      vec1 operator+(const vec2 &x, const vec3 &y);

The corresponding definition is given in O2SCL_OPSRC_VEC_VEC_ADD.

Note:
This used to be in a separate namespace, called o2scl_arith, but this causes problems with Koenig lookup in template classes for operator*() when defined for vector addition (for example).

Definition at line 160 of file vec_arith.h.

#define O2SCL_OP_VEC_VEC_EQUAL ( vec1,
vec2   ) 

Value:

bool operator== \
      (const vec1 &x, const vec2 &y);
The header macro for vector==vector.

Given types vec1 and vec2, this macro provides the function declaration for vector equality comparisons using

        bool operator==(const vec1 &x, const vec2 &y);

Note:
Two vectors with different sizes are defined to be not equal, no matter what their contents.
The corresponding definition is given in O2SCL_OPSRC_VEC_VEC_EQUAL.

Definition at line 762 of file vec_arith.h.

#define O2SCL_OP_VEC_VEC_NEQUAL ( vec1,
vec2   ) 

Value:

bool operator!= \
    (const vec1 &x, const vec2 &y);
The header macro for vector!=vector.

Given types vec1 and vec2, this macro provides the function declaration for vector inequality comparisons using

      bool operator==(const vec1 &x, const vec2 &y);

Note:
Two vectors with different sizes are defined to be not equal, no matter what their contents.
The corresponding definition is given in O2SCL_OPSRC_VEC_VEC_NEQUAL.

Definition at line 844 of file vec_arith.h.

#define O2SCL_OP_VEC_VEC_PRO ( vec1,
vec2,
vec3   ) 

Value:

vec1 pair_prod  \
    (const vec2 &x, const vec3 &y);
The header macro for pairwise vector * vector (where either vector can be real or complex).

Given types vec1, vec2, and vec3, this macro provides the function declaration for adding two vectors using the form

      vec1 pair_prod(const vec2 &x, const vec3 &y);

The corresponding definition is given in O2SCL_OPSRC_VEC_VEC_PRO.

Definition at line 500 of file vec_arith.h.

#define O2SCL_OP_VEC_VEC_SUB ( vec1,
vec2,
vec3   ) 

Value:

vec1 operator-  \
    (const vec2 &x, const vec3 &y);
The header macro for vector-vector subtraction.

Given types vec1, vec2, and vec_3, this macro provides the function declaration for adding two vectors using the form

      vec1 operator-(const vec2 &x, const vec3 &y);

The corresponding definition is given in O2SCL_OPSRC_VEC_VEC_SUB.

Definition at line 202 of file vec_arith.h.

#define O2SCL_OPSRC_CMAT_CVEC_MULT ( vec1,
vec2,
mat   ) 

The source code macro for complex matrix * complex vector.

This define macro generates the function definition. See the function declaration O2SCL_OP_CMAT_CVEC_MULT

Definition at line 601 of file vec_arith.h.

#define O2SCL_OPSRC_CX_DOT_PROD ( dtype,
vec1,
vec2   ) 

The source code macro for a complex vector dot product.

This define macro generates the function definition. See the function declaration O2SCL_OP_CX_DOT_PROD

Definition at line 686 of file vec_arith.h.

#define O2SCL_OPSRC_DOT_PROD ( dtype,
vec1,
vec2   ) 

The source code macro for a vector dot product.

This define macro generates the function definition. See the function declaration O2SCL_OP_DOT_PROD

Definition at line 669 of file vec_arith.h.

#define O2SCL_OPSRC_MAT_VEC_MULT ( vec1,
vec2,
mat   ) 

The source code macro for matrix * vector.

This define macro generates the function definition. See the function declaration O2SCL_OP_MAT_VEC_MULT

Definition at line 580 of file vec_arith.h.

#define O2SCL_OPSRC_SCA_VEC_MULT ( dtype,
vecv,
vec   ) 

The source code macro for vector=scalar*vector.

This define macro generates the function definition. See the function declaration O2SCL_OP_SCA_VEC_MULT

Definition at line 703 of file vec_arith.h.

#define O2SCL_OPSRC_TRANS_MULT ( vec1,
vec2,
mat   ) 

The source code macro for the trans_mult form of vector * matrix.

This define macro generates the function definition. See the function declaration O2SCL_OP_TRANS_MULT

Definition at line 648 of file vec_arith.h.

#define O2SCL_OPSRC_VEC_MAT_MULT ( vec1,
vec2,
mat   ) 

The source code macro for the operator form of vector * matrix.

This define macro generates the function definition. See the function declaration O2SCL_OP_VEC_MAT_MULT

Definition at line 626 of file vec_arith.h.

#define O2SCL_OPSRC_VEC_SCA_MULT ( dtype,
vecv,
vec   ) 

The source code macro for vector=vector*scalar.

This define macro generates the function definition. See the function declaration O2SCL_OP_VEC_SCA_MULT

Definition at line 719 of file vec_arith.h.

#define O2SCL_OPSRC_VEC_VEC_ADD ( vec1,
vec2,
vec3   ) 

The source code macro for vector-vector addition.

This define macro generates the function definition. See the function declaration O2SCL_OP_VEC_VEC_ADD

Definition at line 546 of file vec_arith.h.

#define O2SCL_OPSRC_VEC_VEC_EQUAL ( vec1,
vec2   ) 

The source code macro vector==vector.

Note:
Two vectors with different sizes are defined to be not equal, no matter what their contents.
This define macro generates the function definition. See the function declaration O2SCL_OP_VEC_VEC_EQUAL

Definition at line 818 of file vec_arith.h.

#define O2SCL_OPSRC_VEC_VEC_NEQUAL ( vec1,
vec2   ) 

The source code macro vector!=vector.

Note:
Two vectors with different sizes are defined to be not equal, no matter what their contents.
This define macro generates the function definition. See the function declaration O2SCL_OP_VEC_VEC_NEQUAL

Definition at line 900 of file vec_arith.h.

#define O2SCL_OPSRC_VEC_VEC_PRO ( vec1,
vec2,
vec3   ) 

The source code macro for pairwise vector * vector (where either vector can be real or complex).

This define macro generates the function definition. See the function declaration O2SCL_OP_VEC_VEC_PRO

Definition at line 736 of file vec_arith.h.

#define O2SCL_OPSRC_VEC_VEC_SUB ( vec1,
vec2,
vec3   ) 

The source code macro for vector-vector subtraction.

This define macro generates the function definition. See the function declaration O2SCL_OP_VEC_VEC_SUB

Definition at line 563 of file vec_arith.h.


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