Numerical Methods Contents - SAM

4 {
5 a ssert ( this−>n==B. n && this−>m==B .m) ; / / only support square matrices
6 ColumnMajorMatrix C( n ,m) ; / / important: must be zero: (done in constructor)
7 double alpha ( 1 . 0 ) , beta ( 1 . 0 ) ;
8 cblas_dgemm ( CblasColMajor , CblasNoTrans , CblasNoTrans , n , m,
B .m, alpha , data , n , B . data , B . n , beta , C. data , C. n ) ;
9 return C;
10 }
Code 1.4.10: Timings of different Matrix Multiplications in C++, Ex. 1.4.1
1 #include
2 #include < cstdio >
3 #include < c s t d l i b >
4 #include
5 #include " simpleTimer . h "
6 #include " unixTimer . h "
7 #include " ColumnMajorMatrix . h "
8 /∗ Main Routine f o r the t i m i n g o f d i f f e r e n t
9 ∗ M a trix M a trix M u l t i p l i c a t i o n implementations ∗/
10 i n t main ( i n t argc , char ∗ const argv [ ] ) {
Ôº ½º
13 simpleTimer watch ;
11
12 double T0(1 e20 ) ,T1(1 e20 ) ,T2(1 e20 ) ,T3(1 e20 ) ;
33 p r i n t f ( "N: %i d o t M u l t i p l y : %g , e r r o r : %g \ n " ,n , T1 ,D. CalcErr (C) ) ;
34 p r i n t f ( "N: %i gemvMultiply : %g , e r r o r : %g \ n " ,n , T2 , E . CalcErr (C) ) ;
35 p r i n t f ( "N: %i gemmMultiply : %g , e r r o r : %g \ n " ,n , T3 , F . CalcErr (C) ) ;
36 }
CPU−Time: [s]
trivial
dot
gemv
gemm
Slope Order
10 3
10 2
10 1
10 0
10 −1
10 −2
10 −3
10 −4
10 −5
10 −6
10 0 3
10 1 10 2
Matrix Size: N
10 3 10 4
✁ timings for different implementations of matrix
multiplication (see C++-codes above)
OS: Mac OS X
Processor: Intel Core 2 Duo 2GB 667 MHz DDR2
SDRAM
Compiler: intel v.11.0 (-O3 option)
✸
Ôº ½º
14 i n t rep ( 1 ) , n ( 5 ) ;
15 i f ( argc >1) n= a t o i ( argv [ 1 ] ) ;
16 i f ( argc >2) rep= a t o i ( argv [ 2 ] ) ;
17 / / Declare Input Data
18 ColumnMajorMatrix A( n , n ) ;
19 A . i n i tRand ( ) ; / / A.initGrow();
20 ColumnMajorMatrix B(A) ;
21 / / The Results:
22 ColumnMajorMatrix C( n , n ) ,D( n , n ) ,E( n , n ) ,F ( n , n ) ;
23 / / loop for repetitions (always take timing results over several measurements!)
24 for ( i n t r =0; r