# Arithmetic Matrix Operations

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## Sum over a Row(s) / Column(s) / Diagonal of a Matrix.

The functionality of matrix routines in this collection are routines which could be implemented for matrices defined over an arbitrary commutative semigroup but the routines below are implemented for the Abelian group of Reals under addition for which the matrices are declared as double A[M][N] or for dynamically defined matrices declared as double* A and for the Abelian group of complex numbers under addition for which the complex matrices are declared as double complex A[M][N] or for dynamically defined complex matrices declared as double complex *A.

The function for summing over a particular row of a real matrix is called Sum_over_Row( ) and the function for summing over all the rows of a real matrix the function is called Sum_over_Rows( ). The function for summing over a particular row of a complex matrix is called Sum_over_CMatrix_Row( ) and the function for summing over all the rows of a complex matrix the function is called Sum_over_CMatrix_Rows( ).

The function for summing over a particular column of a real matrix is called Sum_over_Column( ) and for summing over all the columns of a real matrix the function is called Sum_over_Columns( ). The function for summing over a particular column of a complex matrix is called Sum_over_CMatrix_Column( ) and for summing over all the columns of a complex matrix the function is called
Sum_over_CMatrix_Columns( ).

The function for summing over the diagonal of a square real matrix is called Trace_of_Matrix( ). The function for summing over the diagonal of a square complex matrix is called Trace_of_CMatrix( ). There are special versions of the Trace_of_Matrix( ) routine and the for Trace_of_CMatrix( ) routine for the cases of the ubiquitous 2×2 and 3×3 matrices.

### Function List

• double Sum_over_Row( double *A, int ncols, int row )

Return the sum over row row of the nrows×ncols matrix A.

• void Sum_over_Rows( double v[ ], double *A, int nrows, int ncols )

The array element v[i] is set to the sum over row i of the nrows×ncols matrix A.

• double Sum_over_Column( double *A, int nrows, int ncols, int col )

Return the sum over column col of the nrows×ncols matrix A.

• void Sum_over_Columns( double v[ ], double *A, int nrows, int ncols )

The array element v[i] is set to the sum over column i of the nrows×ncols matrix A.

• double Trace_of_Matrix( double *A, int n )

Return the trace of the n×n matrix A.

• double Trace_of_Matrix_2x2( double *A )

Return the trace of the 2×2 matrix A.

• double Trace_of_Matrix_3x3( double *A )

Return the trace of the 3×3 matrix A.

• double complex Sum_over_CMatrix_Row( double complex *A, int ncols, int row )

Return the sum over row row of the nrows×ncols complex matrix A.

• void Sum_over_CMatrix_Rows( double complex v[ ], double complex *A, int nrows, int ncols )

The array element v[i] is set to the sum over row i of the nrows×ncols complex matrix A.

• double complex Sum_over_CMatrix_Column( double complex *A, int nrows, int ncols, int col )

Return the sum over column col of the nrows×ncols matrix A.

• void Sum_over_CMatrix_Columns( double complex v[ ], double complex *A, int nrows, int ncols )

The array element v[i] is set to the sum over column i of the nrows×ncols matrix A.

• double complex Trace_of_CMatrix( double complex *A, int n )

Return the trace of the n×n complex matrix A.

• double complex Trace_of_CMatrix_2x2( double complex *A )

Return the trace of the 2×2 complex matrix A.

• double complex Trace_of_CMatrix_3x3( double complex *A )

Return the trace of the 3×3 complex matrix A.

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

• The file, testsumoverrow.c, contains a test program of Sum_over_Row( ) in the file sum_over_row.c. This test program requires the file sum_over_row.c listed above.

• The file, SumOverRowTests.txt, contains the results of the test program testsumoverrow.c.

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

• The file, testsumoverrows.c, contains a test program of Sum_over_Rows( ) in the file sum_over_rows.c. This test program requires the file sum_over_rows.c listed above.

• The file, SumOverRowsTests.txt, contains the results of the test program testsumoverrows.c.

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

• The file, testsumovercol.c, contains a test program of Sum_over_Column( ) in the file sum_over_col.c. This test program requires the file sum_over_col.c listed above.

• The file, SumOverColTests.txt, contains the results of the test program testsumovercol.c.

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

• The file, testsumovercols.c, contains a test program of Sum_over_Columns( ) in the file sum_over_cols.c. This test program requires the file sum_over_cols.c listed above.

• The file, SumOverColsTests.txt, contains the results of the test program ttestsumovercols.c.

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

• The file, testtrace.c, contains a test program of Trace_of_Matrix( ) in the file trace_of_matrix.c. This test program requires the file trace_of_matrix.c listed above.

• The file, TraceTests.txt, contains the results of the test program testtrace.c.

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

• The file, testtrace2x2.c, contains a test program of Trace_of_Matrix_2x2( ) in the file trace_of_matrix_2x2.c. This test program requires the file trace_of_matrix_2x2.c listed above.

• The file, Trace2x2Tests.txt, contains the results of the test program testtrace2x2.c.

• The file, testtrace2x2.sh, contains the shell script used to compile, link, and execute the test program ttesttrace2x2.c.

• The file, testtrace3x3.c, contains a test program of Trace_of_Matrix_3x3( ) in the file trace_of_matrix_3x3.c. This test program requires the file trace_of_matrix_3x3.c listed above.

• The file, Trace3x3Tests.txt, contains the results of the test program testtrace3x3.c.

• The file, testtrace3x3.sh, contains the shell script used to compile, link, and execute the test program testtrace3x3.c.

• The file, testsumovercmatrixrow.c, contains a test program of Sum_over_CMatrix_Row( ) in the file sum_over_cmatrix_row.c. This test program requires the file sum_over_cmatrix_row.c listed above.

• The file, SumOverCMatrixRowTests.txt, contains the results of the test program testsumovercmatrixrow.c.

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

• The file, testsumovercmatrixrows.c, contains a test program of Sum_over_CMatrix_Rows( ) in the file sum_over_cmatrix_rows.c. This test program requires the file sum_over_cmatrix_rows.c listed above.

• The file, SumOverCMatrixRowsTests.txt, contains the results of the test program testsumovercmatrixrows.c

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

• The file, testsumovercmatrixcol.c, contains a test program of Sum_over_CMatrix_Column( ) in the file sum_over_cmatrix_col.c. This test program requires the file sum_over_cmatrix_col.c listed above.

• The file, SumOverCMatrixColTests.txt, contains the results of the test program testsumovercmatrixcol.c.

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

• The file, testsumovercmatrixcols.c, contains a test program of Sum_over_CMatrix_Columns( ) in the file sum_over_cmatrix_cols.c. This test program requires the file sum_over_cmatrix_cols.c listed above.

• The file, SumOverCMatrixColsTests.txt, contains the results of the test program testsumovercmatrixcols.c.

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

• The file, testtracecmatrix.c, contains a test program of Trace_of_CMatrix( ) in the file trace_of_cmatrix.c. This test program requires the file trace_of_cmatrix.c listed above.

• The file, TraceCMatrixTests.txt, contains the results of the test program testtracecmatrix.c.

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

• The file, testtracecmatrix2x2.c, contains a test program of Trace_of_CMatrix_2x2( ) in the file trace_of_cmatrix_2x2.c. This test program requires the file trace_of_cmatrix_2x2.c listed above.

• The file, TraceCMatrix2x2Tests.txt, contains the results of the test program testtracecmatrix2x2.c.

• The file, testtracecmatrix2x2.sh, contains the shell script used to compile, link, and execute the test program ttesttracecmatrix2x2.c.

• The file, testtracecmatrix3x3.c, contains a test program of Trace_of_CMatrix_3x3( ) in the file trace_of_cmatrix_3x3.c. This test program requires the file trace_of_cmatrix_3x3.c listed above.

• The file, TraceCMatrix3x3Tests.txt, contains the results of the test program testtracecmatrix3x3.c.

• The file, testtracecmatrix3x3.sh, contains the shell script used to compile, link, and execute the test program testtracecmatrix3x3.c.