Arithmetic Matrix Operations

Direct Sum.

The direct sum of the matrices A₁,...,A_n is the matrix C = A₁ ⊕ ... ⊕ A_n given by the matrix

C =  ⌈ A1 0 ···  0 ⌉ | 0 A2 ···  0 | | ··· ··· ··· ··· | ⌊ 0 0 ···  An ⌋

Function List

• void Direct_Sum( double *C, int nrows, int ncols, int number_of_summands, double *A1, int nrows1, int ncols1, ... , double *Am, int nrowsm, int ncolsm, double *Alast )
  
  This routine initializes the nrows×ncols matrix C as the direct sum of number_of_summands matrices A1, … , Alast, where last = number_of_summands. The number of rows of C, nrows, is equal to the sum of the number of rows of the individual summands:
  nrows = nrows1 + … + nrowsm + nrowslast,
  and the number of columns of C, ncols, is equal to the sum of the number of columns of the individual summands:
  ncols = ncols1 + … + ncolsm + ncolslast.
  
  Note that the number of rows and columns of the last summand, Alast, are not arguments, but rather are calculated internally.
  
  
• void CDirect_Sum( double complex *C, int nrows, int ncols, int number_of_summands, double complex*A1, int nrows1, int ncols1, ... , double complex *Am, int nrowsm, int ncolsm, double complex *Alast )
  
  This routine initializes the nrows×ncols matrix C as the direct sum of number_of_summands matrices A1, … , Alast, where last = number_of_summands. The number of rows of C, nrows, is equal to the sum of the number of rows of the individual summands:
  nrows = nrows1 + … + nrowsm + nrowslast,
  and the number of columns of C, ncols, is equal to the sum of the number of columns of the individual summands:
  ncols = ncols1 + … + ncolsm + ncolslast.
  
  Note that the number of rows and columns of the last summand, Alast, are not arguments, but rather are calculated internally.
  
  

C Source Code

• The file, direct_sum.c, contains the version of Direct_Sum( ) written in C.
  
  


• The file, cdirect_sum.c, contains the version of CDirect_Sum( ) written in C.
  
  

C Test Code, Test Results, and Build Shell Script

• The file, testdirectsum_C.c, contains a test program of Direct_Sum( ). This test program requires the file direct_sum.c listed above.
  
  
• The file, DirectSumTests_C.txt, contains the results of the test program testdirectsum_C.c.
  
  
• The file, testdirectsum_C.sh, contains the shell script used to compile, link, and execute the test program testdirectsum_C.c.
  
  


• The file, testcdirectsum.c, contains a test program of CDirect_Sum( ). This test program requires the file cdirect_sum.c listed above.
  
  
• The file, CDirectSumTests.txt, contains the results of the test program testcdirectsum.c.
  
  
• The file, testcdirectsum.sh, contains the shell script used to compile, link, and execute the test program testcdirectsum.c.
  
  

NASM Source Code
For Linux gcc Users

• The file, direct_sum.asm, contains the version of Direct_Sum( ) written in NASM.
  
  

Nasm Test Code, Test Results, and Build Shell Script

• The file, testdirectsum_A.c, contains a test program of Zero_Vector( ). This test program requires the file zero_vector.asm listed above.
  
  
• The file, DirectSumTests_A.txt, contains the results of the test program testdirectsum_A.c.
  
  
• The file, testdirectsum_A.sh, contains the shell script used to compile, link, and execute the test program testdirectsum_A.c.
  
  

Timing For Direct_Sum
Number of Clock Cycles

Routine 3 ×3 ⊕ 3×3 direct_sum.c 1016 direct_sum.asm 494