# Arithmetic Vector Operations

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## Vector Addition / Subtraction

The functionality of vector routines in this collection are routines which could be implemented for vectors defined over an arbitrary group but the implementation presented here is for real vectors declared as double v[N] or for dynamically defined vectors declared as double* v and for complex vectors declared as double complex v[N] or for dynamically defined complex vectors declared as double complex *v.

The function for adding two real vectors is Add_Vectors( ) and the function for adding two complex vectors is Add_CVectors( ).. There are special versions of these routines for the cases of the ubiquitous 2-d and 3-d vectors. Inversely the function for subtracting two vectors is Subtract_Vectors( ) and the function for subtracting a complex vector from another complex vector is Subtract_CVectors( ). There are also special versions of these routines for the cases of the ubiquitous 2-d and 3-d vectors.

There are 2 versions for both Add_Vectors( ) and Subtract_Vectors( ), 1 version is written in C and 1 version written in NASM. There is one version for both Add_CVectors( ) and Subtract_Vectors( ) both written in C. For the special 2×2 and 3×3 cases there is an additional version which is written as a macro.

Additional routines for adding and subtracting complex vectors in which at least one of the summands is a real vector can be found at More Complex Vector Addition / Subtraction.

By abuse of language, a complex vector in which all of its components are real and is stored as an array double [n] is referred to as a real vector. Similarly a complex vector in which all of its components are purely imaginary and is stored as an array double [n] is called an imaginary vector.

### Function List

• void Add_Vectors( double w[ ], double u[ ], double v[ ], int n )

This routine calculates the vector w = u + v. All vectors, u, v, and w, should be declared in the calling routine as double [n].

• void Add_Vectors_2d( double w[ ], double u[ ], double v[ ] )

This routine calculates the vector w = u + v for the special case in which all vectors, u, v, and w, are 2d vectors. The vectors, u, v, and w, should be declared in the calling routine as double [2].

• void Add_Vectors_3d( double w[ ], double u[ ], double v[] )

This routine calculates the vector w = u + vx for the special case in which all vectors, u, v, and w, are 3d vectors. The vectors, u, v, and w, should be declared in the calling routine as double [3].

• void Subtract_Vectors( double w[ ], double u[ ], double v[ ], int n )

This routine calculates the vector w = u - v. All vectors, u, v, and w, should be declared in the calling routine as double [n].

• void Subtract_Vectors_2d( double w[ ], double u[ ], double v[ ] )

This routine calculates the vector w = u - v for the special case in which all vectors, u, v, and w, are 2d vectors. The vectors, u, v, and w, should be declared in the calling routine as double [2].

• void Subtract_Vectors_3d( double w[ ], double u[ ], double v[ ] )

This routine calculates the vector w = u - v for the special case in which all vectors, u, v, and w, are 3d vectors. The vectors, u, v, and w, should be declared in the calling routine as double [3].

• void Add_CVectors( double complex w[ ], double complex u[ ], double complex v[ ], int n )

This routine calculates the vector w = u + v. All vectors, u, v, and w, should be declared in the calling routine as double complex [n].

• void Add_CVectors_2d( double complex w[ ], double complex u[ ], double complex v[ ] )

This routine calculates the vector w = u + v for the special case in which all vectors, u, v, and w, are 2d vectors. The vectors, u, v, and w, should be declared in the calling routine as double complex [2].

• void Add_CVectors_3d( double complex w[ ], double complex u[ ], double complex v[] )

This routine calculates the vector w = u + vx for the special case in which all vectors, u, v, and w, are 3d vectors. The vectors, u, v, and w, should be declared in the calling routine as double complex [3].

• void Subtract_CVectors( double complex w[ ], double complex u[ ], double complex v[ ], int n )

This routine calculates the vector w = u - v. All vectors, u, v, and w, should be declared in the calling routine as double complex [n].

• void Subtract_CVectors_2d( double complex w[ ], double complex u[ ], double complex v[ ] )

This routine calculates the vector w = u - v for the special case in which all vectors, u, v, and w, are 2d vectors. The vectors, u, v, and w, should be declared in the calling routine as double complex [2].

• void Subtract_CVectors_3d( double complex w[ ], double complex u[ ], double complex v[ ] )

This routine calculates the vector w = u - v for the special case in which all vectors, u, v, and w, are 3d vectors. The vectors, u, v, and w, should be declared in the calling routine as double complex [3].

#### C Source Code - Macros

As a rule, the macros presented here are faster and require less memory than either the C version or the NASM version of the corresponding routines. The major draw back is that when calling these macros DO NOT use expressions for the arguments. I.e. do not call MyMacro(&A[2], n+m) but rather set variables double * pA, int k then set pA = A + 2; k = n+m; and then call the macro MyMacro(pA,k). It would be easy to change the macro to allow such expressions but in general not all versions of C have a typeof "keyword" which would facilitate the changes and moreover make the macro run slower. For C compilers which have the inline keyword, a better alternative would be to make the corresponding C functions inline.
• The file, add_vectors_2d.h, contains the version of Add_Vectors_2d( ) written as a macro. This macro is also suitable for adding complex vectors and for adding real vectors with complex vectors.

• The file, add_vectors_3d.h, contains the version of Add_Vectors_3d( ) written as a macro. This macro is also suitable for adding complex vectors and for adding real vectors with complex vectors.

• The file, subtract_vectors_2d.h, contains the version of Subtract_Vectors_2d( ) written as a macro. This macro is also suitable for subtracting complex vectors, subtracting a real vector from a complex vector and subtracting a complex vector from a real vector.

• The file, subtract_vectors_3d.h, contains the version of Subtract_Vectors_3d( ) written as a macro. This macro is also suitable for subtracting complex vectors, subtracting a real vector from a complex vector and subtracting a complex vector from a real vector.

#### C Test Code, Test Results, and Build Shell Script

• The file, testaddvectors.c, contains a test program of Add_Vectors( ) in the file add_vectors.c. This test program requires the file add_vectors.c listed above.

• The file, AddVectorsTest.txt, contains the results of the test program testaddvectors.c.

• The file, testaddvectors.sh, contains the shell script used to compile, link, and execute the test program testaddvectors.c.

• The file, testaddvectors2d.c, contains a test program of Add_Vectors_2d( ) in the file add_vectors_2d.c. This test program requires the file add_vectors_2d.c listed above.

• The file, AddVectors2dTest.txt, contains the results of the test program testaddvectors2d.c.

• The file, testaddvectors2d.sh, contains the shell script used to compile, link, and execute the test program testaddvectors2d.c.

• The file, testaddvectors2d_h.c, contains a test program of the macro Add_Vectors_2d( ) in the file add_vectors_2d.h for the case in which the arguments are the same as in add_vectors_2d.c. This test program requires the file add_vectors_2d.h listed above.

• The file, AddVectors2d_hTest.txt, contains the results of the test program testaddvectors2d_h.c.

• The file, testaddvectors2d_h.sh, contains the shell script used to compile, link, and execute the test program testaddvectors2d_h.c.

• The file, testaddvectors3d.c, contains a test program of Add_Vectors_3d( ) in the file add_vectors_3d.c. This test program requires the file add_vectors_3d.c listed above.

• The file, AddVectors3dTest.txt, contains the results of the test program testaddvectors3d.c.

• The file, testaddvectors3d.sh, contains the shell script used to compile, link, and execute the test program testaddvectors3d.c.

• The file, testaddvectors3d_h.c, contains a test program of the macro Add_Vectors_3d( ) in the file add_vectors_3d.h for the case in which the arguments are the same as in add_vectors_3d.c. This test program requires the file add_vectors_3d.h listed above.

• The file, AddVectors3d_hTest.txt, contains the results of the test program testaddvectors3d_h.c.

• The file, testaddvectors3d_h.sh, contains the shell script used to compile, link, and execute the test program testaddvectors3d_h.c.

• The file, testaddcvectors.c, contains a test program of Add_CVectors( ) in the file add_cvectors.c. This test program requires the file add_cvectors.c listed above.

• The file, AddCVectorsTest.txt, contains the results of the test program testaddcvectors.c.

• The file, testaddcvectors.sh, contains the shell script used to compile, link, and execute the test program testaddcvectors.c.

• The file, testaddcvectors2d.c, contains a test program of Add_CVectors_2d( ) in the file add_cvectors_2d.c. This test program requires the file add_cvectors_2d.c listed above.

• The file, AddCVectors2dTest.txt, contains the results of the test program testaddcvectors2d.c.

• The file, testaddcvectors2d.sh, contains the shell script used to compile, link, and execute the test program testaddcvectors2d.c.

• The file, testaddcvectors2d_h.c, contains a test program of the macro Add_Vectors_2d( ) in the file add_vectors_2d.h for the case in which the arguments are the same as in add_cvectors_2d.c. This test program requires the file add_vectors_2d.h listed above.

• The file, AddCVectors2d_hTest.txt, contains the results of the test program testaddcvectors2d_h.c.

• The file, testaddcvectors2d_h.sh, contains the shell script used to compile, link, and execute the test program testaddcvectors2d_h.c.

• The file, testaddcvectors3d.c, contains a test program of Add_CVectors_3d( ) in the file add_cvectors_3d.c. This test program requires the file add_cvectors_3d.c listed above.

• The file, AddCVectors3dTest.txt, contains the results of the test program testaddcvectors3d.c.

• The file, testaddcvectors3d.sh, contains the shell script used to compile, link, and execute the test program testaddcvectors3d.c.

• The file, testaddcvectors3d_h.c, contains a test program of the macro Add_Vectors_3d( ) in the file add_vectors_3d.h for the case in which the arguments are the same as in add_cvectors_3d.c. This test program requires the file add_vectors_3d.h listed above.

• The file, AddCVectors3d_hTest.txt, contains the results of the test program testaddcvectors3d_h.c.

• The file, testaddcvectors3d_h.sh, contains the shell script used to compile, link, and execute the test program testaddcvectors3d_h.c.

• The file, testsubvectors.c, contains a test program of Subtract_Vectors( ) in the file subtract_vectors.c. This test program requires the file subtract_vectors.c listed above.

• The file, SubtractVectorsTest.txt, contains the results of the test program testsubtractmatrices.c.

• The file, testsubvectors.sh, contains the shell script used to compile, link, and execute the test program testsubtractvectors.c.

• The file, testsubvectors2d.c, contains a test program of Subtract_Vectors_2d( ) in the file subtract_vectors_2d.c. This test program requires the file subtract_vectors_2d.c listed above.

• The file, SubtractVectors2dTest.txt, contains the results of the test program testsubtractvectors2d.c.

• The file, testsubvectors2d.sh, contains the shell script used to compile, link, and execute the test program testsubtractvectors2d.c.

• The file, testsubvectors2d_h.c, contains a test program of the macro Subtract_Vectors_2d( ) in the file subtract_vectors_2d.h for the case in which the arguments are the same as in subtract_vectors_2d.c. This test program requires the file subtract_vectors_2d.h listed above.

• The file, SubtractVectors2d_hTest.txt, contains the results of the test program testsubtractvectors2d_h.c.

• The file, testsubvectors2d_h.sh, contains the shell script used to compile, link, and execute the test program testsubtractvectors2d_h.c.

• The file, testsubvectors3d.c, contains a test program of Subtract_Vectors_3d( ) in the file subtract_vectors_3d.c. This test program requires the file subtract_vectors_3d.c listed above.

• The file, SubtractVectors3dTest.txt, contains the results of the test program testsubtractvectors3d.c.

• The file, testsubvectors3d.sh, contains the shell script used to compile, link, and execute the test program testsubtractvectors3d.c.

• The file, testsubvectors3d_h.c, contains a test program of the macro Subtract_Vectors_3d( ) in the file subtract_vectors_3d.h for the case in which the arguments are the same as in subtract_vectors_3d.c. This test program requires the file subtract_vectors_3d.h listed above.

• The file, SubtractVectors3d_hTest.txt, contains the results of the test program testsubtractvectors3d_h.c.

• The file, testsubvectors3d_h.sh, contains the shell script used to compile, link, and execute the test program testsubtractvectors3d_h.c.

• The file, testsubcvectors.c, contains a test program of Subtract_CVectors( ) in the file subtract_cvectors.c. This test program requires the file subtract_cvectors.c listed above.

• The file, SubtractCVectorsTest.txt, contains the results of the test program testsubcvectors.c.

• The file, testsubcvectors.sh, contains the shell script used to compile, link, and execute the test program testsubcvectors.c.

• The file, testsubcvectors2d.c, contains a test program of Subtract_CVectors_2d( ) in the file subtract_cvectors_2d.c. This test program requires the file subtract_cvectors_2d.c listed above.

• The file, SubtractCVectors2dTest.txt, contains the results of the test program testsubcvectors2d.c.

• The file, testsubcvectors2d.sh, contains the shell script used to compile, link, and execute the test program testssubcvectors2d.c.

• The file, testsubcvectors2d_h.c, contains a test program of the macro Subtract_Vectors_2d( ) in the file subtract_vectors_2d.h for the case in which the arguments are the same as in subtract_cvectors_2d.c. This test program requires the file subtract_vectors_2d.h listed above.

• The file, SubtractCVectors2d_hTest.txt, contains the results of the test program testsubcvectors2d_h.c.

• The file, testsubcvectors2d_h.sh, contains the shell script used to compile, link, and execute the test program testsubcvectors2d_h.c.

• The file, testsubcvectors3d.c, contains a test program of Subtract_CVectors_3d( ) in the file subtract_cvectors_3d.c. This test program requires the file subtract_cvectors_3d.c listed above.

• The file, SubtractCVectors3dTest.txt, contains the results of the test program testsubcvectors3d.c.

• The file, testsubcvectors3d.sh, contains the shell script used to compile, link, and execute the test program testsubcvectors3d.c.

• The file, testsubcvectors3d_h.c, contains a test program of the macro Subtract_Vectors_3d( ) in the file subtract_vectors_3d.h for the case in which the arguments are the same as in subtract_cvectors_3d.c. This test program requires the file subtract_vectors_3d.h listed above.

• The file, SubtractCVectors3d_hTest.txt, contains the results of the test program testsubcvectors3d_h.c.

• The file, testsubcvectors3d_h.sh, contains the shell script used to compile, link, and execute the test program testsubcvectors3d_h.c.