Unblocked LU: Variant based on GEMV and TRSV
Content |
In Session 12 we implemented the LU factorization based on the BLAS operation GER (rank 1 update). In this session we consider another variant that is based on the BLAS operations GEMV (matrix vector product) and TRSV (triangular solver).
Note that the term variant is used here to express that both algorithms (and implementation) carry out the same underlying floating point operations. However, because of the different BLAS building blocks the operations are carried out in a different order. So it is possible that each variant of an algorithm achieves a different different performance. That is because:
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Depending on an architecture different BLAS operations can be realized more or less efficient.
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Different BLAS operations might be implemented more or less efficient.
Algorithm
Input: |
An \(m \times n\) matrix \(A\). |
Output: |
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Return value: |
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For \(j=0, \dots, k-1\)
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Consider for the first \(j+1\) columns of \(A\) the partition
\[\left(\begin{array}{ccc} a_{0,0} & \dots & a_{0,j} \\ \vdots & & \vdots \\ a_{m,0} & \dots & a_{m,j} \\ \end{array}\right)=\left(\begin{array}{c|c} A_{0,0} & \vec{a_{0,j}} \\ \hline A_{j,0} & \vec{a_{j,j}} \\ \end{array}\right)\] -
TRSV operation
Compute \(\vec{a_{0,j}} \leftarrow L_{\text{unit}}^{-1}(A_{0,0}) \vec{a_{0,j}}\) where \(L_{\text{unit}}( \cdot )\) denotes that a matrix argument is considered as a lower unit triangular matrix.
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GEMV operation
Compute \(\vec{a_{j,j}} \leftarrow \vec{a_{j,j}} - A_{j,0} \vec{a_{0,j}}\).
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Partial pivoting
Find pivot index \(p_j\) from \(\vec{a_{j,j}}\), i.e.
\[p_j = j + \text{argmax}_{0 \leq \ell < m} a_{j,l}\]If \(p_j \neq j\) interchange in \(A\) rows with index \(j\) and \(p_j\).
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Consider for \(\vec{a_{j,j}}\) the sub-partition
\[\vec{a_{j,j}} =\left(\begin{array}{c} a_{j,j} \\ \hline \vec{a_{j+1,j}} \end{array}\right)\] -
If \(a_{j,j}\) is exactly zero return \(j\)
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Scale operation
Compute \(\vec{a_{j+1,j}} \leftarrow \frac{1}{a_{j,j}} \vec{a_{j+1,j}}\)
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For \(j=k, \dots, n-1\)
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Consider for \(A\) the partition
\[A = \left(\begin{array}{c|c|c|c} A_{0,0} & \vec{a_{0,k}} & \cdots & \vec{a_{0,n-1}} \\ \end{array}\right)\] -
TRSV operation
Compute \(\vec{a_{0,j}} \leftarrow L_{\text{unit}}^{-1}(A_{0,0}) \vec{a_{0,j}}\)
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Exercise
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Use the source file ulmblas.c from Session 12 as starting point. Or copy ulmblas.c from /home/numerik/pub/hpc/ss18/ulmblas/session13b/ulmblas.c
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Modify the code as follows, so that we can use a compiler switch to select the implementation for dgetrf:
/* Implementation of other BLAS functions */ ptrdiff_t dgetrf_ger(size_t m, size_t n, double *A, ptrdiff_t incRowA, ptrdiff_t incColA, size_t *p, ptrdiff_t incP) { /* Implementation from session 12 */ } ptrdiff_t dgetrf_gemv(size_t m, size_t n, double *A, ptrdiff_t incRowA, ptrdiff_t incColA, size_t *p, ptrdiff_t incP) { /* TODO: Your implementation based on dgemv and dtrsv */ } #define GETRF_GER 1 #define GETRF_GEMV 2 #ifndef GETRF #define GETRF 0 #endif // this pragma makes gcc stop immediately on '#error' #pragma GCC diagnostic error "-Wfatal-errors" ptrdiff_t dgetrf(size_t m, size_t n, double *A, ptrdiff_t incRowA, ptrdiff_t incColA, size_t *p, ptrdiff_t incP) { #if GETRF == GETRF_GER return dgetrf_ger(m, n, A, incRowA, incColA, p, incP); #elif GETRF == GETRF_GEMV return dgetrf_gemv(m, n, A, incRowA, incColA, p, incP); #else #error "Compile with either -DGETRF=GETRF_GER or -DGETRF=GETRF_GEMV" #endif }
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Implement function dgetrf_gemv. Use the GEMV/TRSV based algorithm. Test your implementation as described in the next section.
Test and Benchmark
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Compile with either -DGETRF=GETRF_GER or -DGETRF=GETRF_GER. Otherwise you get the following error:
heim$ gcc -Wall -std=c11 -I. -O3 -o test_dgetrf test_dgetrf.c ulmaux.c ulmblas.c ulmblas.c: In function ‘dgetrf’: ulmblas.c:328:2: error: #error "Compile with either -DGETRF=GETRF_GER or -DGETRF=GETRF_GEMV" #error "Compile with either -DGETRF=GETRF_GER or -DGETRF=GETRF_GEMV" ^ compilation terminated due to -Wfatal-errors. heim$
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Create different executables and check results:
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You can create an executable test_dgetrf_ger for testing and benchmarking the variant based on GER:
heim$ gcc -Wall -std=c11 -I. -O3 -o test_dgetrf_ger -DGETRF=GETRF_GER test_dgetrf.c ulmaux.c ulmblas.c heim$ ./test_dgetrf_ger check m n incRowA incColA incP err res 5 5 5 1 1 4.8e-02 PASS 5 5 1 5 1 9.7e-02 PASS 5 5 10 1 1 5.7e-02 PASS 5 5 2 10 1 4.7e-02 PASS 5 5 5 1 1 7.1e-02 PASS 5 5 -1 5 1 1.2e-01 PASS 5 5 10 1 1 1.3e-01 PASS 5 5 -2 10 1 1.1e-01 PASS 5 5 10 2 1 7.7e-02 PASS 5 5 1 10 1 8.0e-02 PASS 5 5 20 2 1 9.1e-02 PASS 5 5 2 20 1 4.8e-02 PASS 5 5 10 2 1 9.1e-02 PASS 5 5 -1 10 1 5.4e-02 PASS 5 5 20 2 1 1.1e-01 PASS 5 5 -2 20 1 3.6e-02 PASS 5 5 5 -1 1 1.8e-01 PASS 5 5 1 5 1 4.1e-02 PASS 5 5 10 -1 1 3.5e-02 PASS 5 5 2 10 1 7.7e-02 PASS 5 5 5 -1 1 7.6e-02 PASS 5 5 -1 5 1 8.9e-02 PASS 5 5 10 -1 1 8.6e-02 PASS 5 5 -2 10 1 4.8e-02 PASS 5 5 10 -2 1 1.5e-01 PASS 5 5 1 10 1 3.1e-02 PASS 5 5 20 -2 1 3.8e-02 PASS 5 5 2 20 1 7.4e-02 PASS 5 5 10 -2 1 3.4e-02 PASS 5 5 -1 10 1 7.7e-02 PASS 5 5 20 -2 1 6.0e-02 PASS 5 5 -2 20 1 7.3e-02 PASS 0 5 5 1 1 0.0e+00 PASS 0 5 1 0 1 0.0e+00 PASS 0 5 10 1 1 0.0e+00 PASS 0 5 2 0 1 0.0e+00 PASS 0 5 5 1 1 0.0e+00 PASS 0 5 -1 0 1 0.0e+00 PASS 0 5 10 1 1 0.0e+00 PASS 0 5 -2 0 1 0.0e+00 PASS 0 5 10 2 1 0.0e+00 PASS 0 5 1 0 1 0.0e+00 PASS 0 5 20 2 1 0.0e+00 PASS 0 5 2 0 1 0.0e+00 PASS 0 5 10 2 1 0.0e+00 PASS 0 5 -1 0 1 0.0e+00 PASS 0 5 20 2 1 0.0e+00 PASS 0 5 -2 0 1 0.0e+00 PASS 0 5 5 -1 1 0.0e+00 PASS 0 5 1 0 1 0.0e+00 PASS 0 5 10 -1 1 0.0e+00 PASS 0 5 2 0 1 0.0e+00 PASS 0 5 5 -1 1 0.0e+00 PASS 0 5 -1 0 1 0.0e+00 PASS 0 5 10 -1 1 0.0e+00 PASS 0 5 -2 0 1 0.0e+00 PASS 0 5 10 -2 1 0.0e+00 PASS 0 5 1 0 1 0.0e+00 PASS 0 5 20 -2 1 0.0e+00 PASS 0 5 2 0 1 0.0e+00 PASS 0 5 10 -2 1 0.0e+00 PASS 0 5 -1 0 1 0.0e+00 PASS 0 5 20 -2 1 0.0e+00 PASS 0 5 -2 0 1 0.0e+00 PASS 1 5 5 1 1 0.0e+00 PASS 1 5 1 1 1 0.0e+00 PASS 1 5 10 1 1 0.0e+00 PASS 1 5 2 2 1 0.0e+00 PASS 1 5 5 1 1 0.0e+00 PASS 1 5 -1 1 1 0.0e+00 PASS 1 5 10 1 1 0.0e+00 PASS 1 5 -2 2 1 0.0e+00 PASS 1 5 10 2 1 0.0e+00 PASS 1 5 1 2 1 0.0e+00 PASS 1 5 20 2 1 0.0e+00 PASS 1 5 2 4 1 0.0e+00 PASS 1 5 10 2 1 0.0e+00 PASS 1 5 -1 2 1 0.0e+00 PASS 1 5 20 2 1 0.0e+00 PASS 1 5 -2 4 1 0.0e+00 PASS 1 5 5 -1 1 0.0e+00 PASS 1 5 1 1 1 0.0e+00 PASS 1 5 10 -1 1 0.0e+00 PASS 1 5 2 2 1 0.0e+00 PASS 1 5 5 -1 1 0.0e+00 PASS 1 5 -1 1 1 0.0e+00 PASS 1 5 10 -1 1 0.0e+00 PASS 1 5 -2 2 1 0.0e+00 PASS 1 5 10 -2 1 0.0e+00 PASS 1 5 1 2 1 0.0e+00 PASS 1 5 20 -2 1 0.0e+00 PASS 1 5 2 4 1 0.0e+00 PASS 1 5 10 -2 1 0.0e+00 PASS 1 5 -1 2 1 0.0e+00 PASS 1 5 20 -2 1 0.0e+00 PASS 1 5 -2 4 1 0.0e+00 PASS 32 5 5 1 1 9.3e-02 PASS 32 5 1 32 1 1.5e-01 PASS 32 5 10 1 1 1.5e-01 PASS 32 5 2 64 1 8.3e-02 PASS 32 5 5 1 1 1.5e-01 PASS 32 5 -1 32 1 1.1e-01 PASS 32 5 10 1 1 1.4e-01 PASS 32 5 -2 64 1 1.1e-01 PASS 32 5 10 2 1 1.3e-01 PASS 32 5 1 64 1 1.2e-01 PASS 32 5 20 2 1 1.1e-01 PASS 32 5 2 128 1 1.7e-01 PASS 32 5 10 2 1 1.4e-01 PASS 32 5 -1 64 1 1.3e-01 PASS 32 5 20 2 1 1.3e-01 PASS 32 5 -2 128 1 1.0e-01 PASS 32 5 5 -1 1 1.5e-01 PASS 32 5 1 32 1 1.1e-01 PASS 32 5 10 -1 1 1.2e-01 PASS 32 5 2 64 1 1.2e-01 PASS 32 5 5 -1 1 1.3e-01 PASS 32 5 -1 32 1 1.4e-01 PASS 32 5 10 -1 1 1.9e-01 PASS 32 5 -2 64 1 9.3e-02 PASS 32 5 10 -2 1 2.1e-01 PASS 32 5 1 64 1 1.4e-01 PASS 32 5 20 -2 1 1.4e-01 PASS 32 5 2 128 1 1.3e-01 PASS 32 5 10 -2 1 1.3e-01 PASS 32 5 -1 64 1 1.0e-01 PASS 32 5 20 -2 1 1.3e-01 PASS 32 5 -2 128 1 1.4e-01 PASS 31 5 5 1 1 1.8e-01 PASS 31 5 1 31 1 1.2e-01 PASS 31 5 10 1 1 1.2e-01 PASS 31 5 2 62 1 1.6e-01 PASS 31 5 5 1 1 7.4e-02 PASS 31 5 -1 31 1 1.6e-01 PASS 31 5 10 1 1 1.3e-01 PASS 31 5 -2 62 1 9.1e-02 PASS 31 5 10 2 1 1.2e-01 PASS 31 5 1 62 1 1.1e-01 PASS 31 5 20 2 1 1.3e-01 PASS 31 5 2 124 1 1.2e-01 PASS 31 5 10 2 1 9.6e-02 PASS 31 5 -1 62 1 1.2e-01 PASS 31 5 20 2 1 1.2e-01 PASS 31 5 -2 124 1 1.2e-01 PASS 31 5 5 -1 1 1.6e-01 PASS 31 5 1 31 1 1.3e-01 PASS 31 5 10 -1 1 1.0e-01 PASS 31 5 2 62 1 1.5e-01 PASS 31 5 5 -1 1 1.5e-01 PASS 31 5 -1 31 1 8.9e-02 PASS 31 5 10 -1 1 9.4e-02 PASS 31 5 -2 62 1 1.1e-01 PASS 31 5 10 -2 1 9.4e-02 PASS 31 5 1 62 1 1.2e-01 PASS 31 5 20 -2 1 1.2e-01 PASS 31 5 2 124 1 1.4e-01 PASS 31 5 10 -2 1 1.5e-01 PASS 31 5 -1 62 1 1.5e-01 PASS 31 5 20 -2 1 1.3e-01 PASS 31 5 -2 124 1 1.3e-01 PASS 5 0 0 1 1 0.0e+00 PASS 5 0 1 5 1 0.0e+00 PASS 5 0 0 1 1 0.0e+00 PASS 5 0 2 10 1 0.0e+00 PASS 5 0 0 1 1 0.0e+00 PASS 5 0 -1 5 1 0.0e+00 PASS 5 0 0 1 1 0.0e+00 PASS 5 0 -2 10 1 0.0e+00 PASS 5 0 0 2 1 0.0e+00 PASS 5 0 1 10 1 0.0e+00 PASS 5 0 0 2 1 0.0e+00 PASS 5 0 2 20 1 0.0e+00 PASS 5 0 0 2 1 0.0e+00 PASS 5 0 -1 10 1 0.0e+00 PASS 5 0 0 2 1 0.0e+00 PASS 5 0 -2 20 1 0.0e+00 PASS 5 0 0 -1 1 0.0e+00 PASS 5 0 1 5 1 0.0e+00 PASS 5 0 0 -1 1 0.0e+00 PASS 5 0 2 10 1 0.0e+00 PASS 5 0 0 -1 1 0.0e+00 PASS 5 0 -1 5 1 0.0e+00 PASS 5 0 0 -1 1 0.0e+00 PASS 5 0 -2 10 1 0.0e+00 PASS 5 0 0 -2 1 0.0e+00 PASS 5 0 1 10 1 0.0e+00 PASS 5 0 0 -2 1 0.0e+00 PASS 5 0 2 20 1 0.0e+00 PASS 5 0 0 -2 1 0.0e+00 PASS 5 0 -1 10 1 0.0e+00 PASS 5 0 0 -2 1 0.0e+00 PASS 5 0 -2 20 1 0.0e+00 PASS 0 0 0 1 1 0.0e+00 PASS 0 0 1 0 1 0.0e+00 PASS 0 0 0 1 1 0.0e+00 PASS 0 0 2 0 1 0.0e+00 PASS 0 0 0 1 1 0.0e+00 PASS 0 0 -1 0 1 0.0e+00 PASS 0 0 0 1 1 0.0e+00 PASS 0 0 -2 0 1 0.0e+00 PASS 0 0 0 2 1 0.0e+00 PASS 0 0 1 0 1 0.0e+00 PASS 0 0 0 2 1 0.0e+00 PASS 0 0 2 0 1 0.0e+00 PASS 0 0 0 2 1 0.0e+00 PASS 0 0 -1 0 1 0.0e+00 PASS 0 0 0 2 1 0.0e+00 PASS 0 0 -2 0 1 0.0e+00 PASS 0 0 0 -1 1 0.0e+00 PASS 0 0 1 0 1 0.0e+00 PASS 0 0 0 -1 1 0.0e+00 PASS 0 0 2 0 1 0.0e+00 PASS 0 0 0 -1 1 0.0e+00 PASS 0 0 -1 0 1 0.0e+00 PASS 0 0 0 -1 1 0.0e+00 PASS 0 0 -2 0 1 0.0e+00 PASS 0 0 0 -2 1 0.0e+00 PASS 0 0 1 0 1 0.0e+00 PASS 0 0 0 -2 1 0.0e+00 PASS 0 0 2 0 1 0.0e+00 PASS 0 0 0 -2 1 0.0e+00 PASS 0 0 -1 0 1 0.0e+00 PASS 0 0 0 -2 1 0.0e+00 PASS 0 0 -2 0 1 0.0e+00 PASS 1 0 0 1 1 0.0e+00 PASS 1 0 1 1 1 0.0e+00 PASS 1 0 0 1 1 0.0e+00 PASS 1 0 2 2 1 0.0e+00 PASS 1 0 0 1 1 0.0e+00 PASS 1 0 -1 1 1 0.0e+00 PASS 1 0 0 1 1 0.0e+00 PASS 1 0 -2 2 1 0.0e+00 PASS 1 0 0 2 1 0.0e+00 PASS 1 0 1 2 1 0.0e+00 PASS 1 0 0 2 1 0.0e+00 PASS 1 0 2 4 1 0.0e+00 PASS 1 0 0 2 1 0.0e+00 PASS 1 0 -1 2 1 0.0e+00 PASS 1 0 0 2 1 0.0e+00 PASS 1 0 -2 4 1 0.0e+00 PASS 1 0 0 -1 1 0.0e+00 PASS 1 0 1 1 1 0.0e+00 PASS 1 0 0 -1 1 0.0e+00 PASS 1 0 2 2 1 0.0e+00 PASS 1 0 0 -1 1 0.0e+00 PASS 1 0 -1 1 1 0.0e+00 PASS 1 0 0 -1 1 0.0e+00 PASS 1 0 -2 2 1 0.0e+00 PASS 1 0 0 -2 1 0.0e+00 PASS 1 0 1 2 1 0.0e+00 PASS 1 0 0 -2 1 0.0e+00 PASS 1 0 2 4 1 0.0e+00 PASS 1 0 0 -2 1 0.0e+00 PASS 1 0 -1 2 1 0.0e+00 PASS 1 0 0 -2 1 0.0e+00 PASS 1 0 -2 4 1 0.0e+00 PASS 32 0 0 1 1 0.0e+00 PASS 32 0 1 32 1 0.0e+00 PASS 32 0 0 1 1 0.0e+00 PASS 32 0 2 64 1 0.0e+00 PASS 32 0 0 1 1 0.0e+00 PASS 32 0 -1 32 1 0.0e+00 PASS 32 0 0 1 1 0.0e+00 PASS 32 0 -2 64 1 0.0e+00 PASS 32 0 0 2 1 0.0e+00 PASS 32 0 1 64 1 0.0e+00 PASS 32 0 0 2 1 0.0e+00 PASS 32 0 2 128 1 0.0e+00 PASS 32 0 0 2 1 0.0e+00 PASS 32 0 -1 64 1 0.0e+00 PASS 32 0 0 2 1 0.0e+00 PASS 32 0 -2 128 1 0.0e+00 PASS 32 0 0 -1 1 0.0e+00 PASS 32 0 1 32 1 0.0e+00 PASS 32 0 0 -1 1 0.0e+00 PASS 32 0 2 64 1 0.0e+00 PASS 32 0 0 -1 1 0.0e+00 PASS 32 0 -1 32 1 0.0e+00 PASS 32 0 0 -1 1 0.0e+00 PASS 32 0 -2 64 1 0.0e+00 PASS 32 0 0 -2 1 0.0e+00 PASS 32 0 1 64 1 0.0e+00 PASS 32 0 0 -2 1 0.0e+00 PASS 32 0 2 128 1 0.0e+00 PASS 32 0 0 -2 1 0.0e+00 PASS 32 0 -1 64 1 0.0e+00 PASS 32 0 0 -2 1 0.0e+00 PASS 32 0 -2 128 1 0.0e+00 PASS 31 0 0 1 1 0.0e+00 PASS 31 0 1 31 1 0.0e+00 PASS 31 0 0 1 1 0.0e+00 PASS 31 0 2 62 1 0.0e+00 PASS 31 0 0 1 1 0.0e+00 PASS 31 0 -1 31 1 0.0e+00 PASS 31 0 0 1 1 0.0e+00 PASS 31 0 -2 62 1 0.0e+00 PASS 31 0 0 2 1 0.0e+00 PASS 31 0 1 62 1 0.0e+00 PASS 31 0 0 2 1 0.0e+00 PASS 31 0 2 124 1 0.0e+00 PASS 31 0 0 2 1 0.0e+00 PASS 31 0 -1 62 1 0.0e+00 PASS 31 0 0 2 1 0.0e+00 PASS 31 0 -2 124 1 0.0e+00 PASS 31 0 0 -1 1 0.0e+00 PASS 31 0 1 31 1 0.0e+00 PASS 31 0 0 -1 1 0.0e+00 PASS 31 0 2 62 1 0.0e+00 PASS 31 0 0 -1 1 0.0e+00 PASS 31 0 -1 31 1 0.0e+00 PASS 31 0 0 -1 1 0.0e+00 PASS 31 0 -2 62 1 0.0e+00 PASS 31 0 0 -2 1 0.0e+00 PASS 31 0 1 62 1 0.0e+00 PASS 31 0 0 -2 1 0.0e+00 PASS 31 0 2 124 1 0.0e+00 PASS 31 0 0 -2 1 0.0e+00 PASS 31 0 -1 62 1 0.0e+00 PASS 31 0 0 -2 1 0.0e+00 PASS 31 0 -2 124 1 0.0e+00 PASS 5 1 1 1 1 0.0e+00 PASS 5 1 1 5 1 5.2e-01 PASS 5 1 2 1 1 3.9e-01 PASS 5 1 2 10 1 4.0e-01 PASS 5 1 1 1 1 5.1e-01 PASS 5 1 -1 5 1 0.0e+00 PASS 5 1 2 1 1 5.7e-01 PASS 5 1 -2 10 1 2.7e-01 PASS 5 1 2 2 1 5.1e-01 PASS 5 1 1 10 1 0.0e+00 PASS 5 1 4 2 1 5.7e-01 PASS 5 1 2 20 1 5.0e-01 PASS 5 1 2 2 1 0.0e+00 PASS 5 1 -1 10 1 0.0e+00 PASS 5 1 4 2 1 0.0e+00 PASS 5 1 -2 20 1 1.5e-01 PASS 5 1 1 -1 1 0.0e+00 PASS 5 1 1 5 1 0.0e+00 PASS 5 1 2 -1 1 6.8e-01 PASS 5 1 2 10 1 0.0e+00 PASS 5 1 1 -1 1 4.9e-01 PASS 5 1 -1 5 1 0.0e+00 PASS 5 1 2 -1 1 6.3e-01 PASS 5 1 -2 10 1 4.2e-01 PASS 5 1 2 -2 1 0.0e+00 PASS 5 1 1 10 1 0.0e+00 PASS 5 1 4 -2 1 0.0e+00 PASS 5 1 2 20 1 2.7e-01 PASS 5 1 2 -2 1 5.6e-01 PASS 5 1 -1 10 1 0.0e+00 PASS 5 1 4 -2 1 1.8e-01 PASS 5 1 -2 20 1 0.0e+00 PASS 0 1 1 1 1 0.0e+00 PASS 0 1 1 0 1 0.0e+00 PASS 0 1 2 1 1 0.0e+00 PASS 0 1 2 0 1 0.0e+00 PASS 0 1 1 1 1 0.0e+00 PASS 0 1 -1 0 1 0.0e+00 PASS 0 1 2 1 1 0.0e+00 PASS 0 1 -2 0 1 0.0e+00 PASS 0 1 2 2 1 0.0e+00 PASS 0 1 1 0 1 0.0e+00 PASS 0 1 4 2 1 0.0e+00 PASS 0 1 2 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5.2e-01 PASS 31 1 4 -2 -2 5.1e-01 PASS 31 1 -2 124 -2 5.2e-01 PASS 5 32 32 1 -2 1.0e-01 PASS 5 32 1 5 -2 1.1e-01 PASS 5 32 64 1 -2 1.1e-01 PASS 5 32 2 10 -2 5.3e-02 PASS 5 32 32 1 -2 9.6e-02 PASS 5 32 -1 5 -2 1.1e-01 PASS 5 32 64 1 -2 8.1e-02 PASS 5 32 -2 10 -2 8.2e-02 PASS 5 32 64 2 -2 1.4e-01 PASS 5 32 1 10 -2 6.7e-02 PASS 5 32 128 2 -2 1.0e-01 PASS 5 32 2 20 -2 9.9e-02 PASS 5 32 64 2 -2 1.0e-01 PASS 5 32 -1 10 -2 1.0e-01 PASS 5 32 128 2 -2 8.9e-02 PASS 5 32 -2 20 -2 1.1e-01 PASS 5 32 32 -1 -2 1.2e-01 PASS 5 32 1 5 -2 1.2e-01 PASS 5 32 64 -1 -2 1.2e-01 PASS 5 32 2 10 -2 6.2e-02 PASS 5 32 32 -1 -2 9.8e-02 PASS 5 32 -1 5 -2 1.1e-01 PASS 5 32 64 -1 -2 1.3e-01 PASS 5 32 -2 10 -2 8.7e-02 PASS 5 32 64 -2 -2 1.2e-01 PASS 5 32 1 10 -2 1.2e-01 PASS 5 32 128 -2 -2 1.2e-01 PASS 5 32 2 20 -2 9.8e-02 PASS 5 32 64 -2 -2 1.1e-01 PASS 5 32 -1 10 -2 1.2e-01 PASS 5 32 128 -2 -2 6.5e-02 PASS 5 32 -2 20 -2 1.1e-01 PASS 0 32 32 1 -2 0.0e+00 PASS 0 32 1 0 -2 0.0e+00 PASS 0 32 64 1 -2 0.0e+00 PASS 0 32 2 0 -2 0.0e+00 PASS 0 32 32 1 -2 0.0e+00 PASS 0 32 -1 0 -2 0.0e+00 PASS 0 32 64 1 -2 0.0e+00 PASS 0 32 -2 0 -2 0.0e+00 PASS 0 32 64 2 -2 0.0e+00 PASS 0 32 1 0 -2 0.0e+00 PASS 0 32 128 2 -2 0.0e+00 PASS 0 32 2 0 -2 0.0e+00 PASS 0 32 64 2 -2 0.0e+00 PASS 0 32 -1 0 -2 0.0e+00 PASS 0 32 128 2 -2 0.0e+00 PASS 0 32 -2 0 -2 0.0e+00 PASS 0 32 32 -1 -2 0.0e+00 PASS 0 32 1 0 -2 0.0e+00 PASS 0 32 64 -1 -2 0.0e+00 PASS 0 32 2 0 -2 0.0e+00 PASS 0 32 32 -1 -2 0.0e+00 PASS 0 32 -1 0 -2 0.0e+00 PASS 0 32 64 -1 -2 0.0e+00 PASS 0 32 -2 0 -2 0.0e+00 PASS 0 32 64 -2 -2 0.0e+00 PASS 0 32 1 0 -2 0.0e+00 PASS 0 32 128 -2 -2 0.0e+00 PASS 0 32 2 0 -2 0.0e+00 PASS 0 32 64 -2 -2 0.0e+00 PASS 0 32 -1 0 -2 0.0e+00 PASS 0 32 128 -2 -2 0.0e+00 PASS 0 32 -2 0 -2 0.0e+00 PASS 1 32 32 1 -2 0.0e+00 PASS 1 32 1 1 -2 0.0e+00 PASS 1 32 64 1 -2 0.0e+00 PASS 1 32 2 2 -2 0.0e+00 PASS 1 32 32 1 -2 0.0e+00 PASS 1 32 -1 1 -2 0.0e+00 PASS 1 32 64 1 -2 0.0e+00 PASS 1 32 -2 2 -2 0.0e+00 PASS 1 32 64 2 -2 0.0e+00 PASS 1 32 1 2 -2 0.0e+00 PASS 1 32 128 2 -2 0.0e+00 PASS 1 32 2 4 -2 0.0e+00 PASS 1 32 64 2 -2 0.0e+00 PASS 1 32 -1 2 -2 0.0e+00 PASS 1 32 128 2 -2 0.0e+00 PASS 1 32 -2 4 -2 0.0e+00 PASS 1 32 32 -1 -2 0.0e+00 PASS 1 32 1 1 -2 0.0e+00 PASS 1 32 64 -1 -2 0.0e+00 PASS 1 32 2 2 -2 0.0e+00 PASS 1 32 32 -1 -2 0.0e+00 PASS 1 32 -1 1 -2 0.0e+00 PASS 1 32 64 -1 -2 0.0e+00 PASS 1 32 -2 2 -2 0.0e+00 PASS 1 32 64 -2 -2 0.0e+00 PASS 1 32 1 2 -2 0.0e+00 PASS 1 32 128 -2 -2 0.0e+00 PASS 1 32 2 4 -2 0.0e+00 PASS 1 32 64 -2 -2 0.0e+00 PASS 1 32 -1 2 -2 0.0e+00 PASS 1 32 128 -2 -2 0.0e+00 PASS 1 32 -2 4 -2 0.0e+00 PASS 32 32 32 1 -2 5.7e-02 PASS 32 32 1 32 -2 4.6e-02 PASS 32 32 64 1 -2 6.0e-02 PASS 32 32 2 64 -2 5.1e-02 PASS 32 32 32 1 -2 5.9e-02 PASS 32 32 -1 32 -2 5.0e-02 PASS 32 32 64 1 -2 4.2e-02 PASS 32 32 -2 64 -2 5.0e-02 PASS 32 32 64 2 -2 5.1e-02 PASS 32 32 1 64 -2 6.9e-02 PASS 32 32 128 2 -2 4.6e-02 PASS 32 32 2 128 -2 5.1e-02 PASS 32 32 64 2 -2 4.8e-02 PASS 32 32 -1 64 -2 4.2e-02 PASS 32 32 128 2 -2 5.4e-02 PASS 32 32 -2 128 -2 6.6e-02 PASS 32 32 32 -1 -2 6.0e-02 PASS 32 32 1 32 -2 4.8e-02 PASS 32 32 64 -1 -2 4.0e-02 PASS 32 32 2 64 -2 5.2e-02 PASS 32 32 32 -1 -2 4.9e-02 PASS 32 32 -1 32 -2 4.9e-02 PASS 32 32 64 -1 -2 4.6e-02 PASS 32 32 -2 64 -2 5.0e-02 PASS 32 32 64 -2 -2 4.7e-02 PASS 32 32 1 64 -2 6.1e-02 PASS 32 32 128 -2 -2 4.7e-02 PASS 32 32 2 128 -2 5.0e-02 PASS 32 32 64 -2 -2 5.3e-02 PASS 32 32 -1 64 -2 4.7e-02 PASS 32 32 128 -2 -2 5.1e-02 PASS 32 32 -2 128 -2 4.4e-02 PASS 31 32 32 1 -2 4.5e-02 PASS 31 32 1 31 -2 5.0e-02 PASS 31 32 64 1 -2 5.2e-02 PASS 31 32 2 62 -2 6.0e-02 PASS 31 32 32 1 -2 4.6e-02 PASS 31 32 -1 31 -2 6.3e-02 PASS 31 32 64 1 -2 6.4e-02 PASS 31 32 -2 62 -2 4.8e-02 PASS 31 32 64 2 -2 6.0e-02 PASS 31 32 1 62 -2 4.2e-02 PASS 31 32 128 2 -2 5.1e-02 PASS 31 32 2 124 -2 5.7e-02 PASS 31 32 64 2 -2 4.5e-02 PASS 31 32 -1 62 -2 4.2e-02 PASS 31 32 128 2 -2 6.0e-02 PASS 31 32 -2 124 -2 4.8e-02 PASS 31 32 32 -1 -2 4.6e-02 PASS 31 32 1 31 -2 4.5e-02 PASS 31 32 64 -1 -2 5.1e-02 PASS 31 32 2 62 -2 4.2e-02 PASS 31 32 32 -1 -2 4.5e-02 PASS 31 32 -1 31 -2 3.9e-02 PASS 31 32 64 -1 -2 4.6e-02 PASS 31 32 -2 62 -2 4.8e-02 PASS 31 32 64 -2 -2 4.6e-02 PASS 31 32 1 62 -2 5.9e-02 PASS 31 32 128 -2 -2 5.1e-02 PASS 31 32 2 124 -2 5.1e-02 PASS 31 32 64 -2 -2 5.2e-02 PASS 31 32 -1 62 -2 4.3e-02 PASS 31 32 128 -2 -2 5.6e-02 PASS 31 32 -2 124 -2 4.7e-02 PASS 5 31 31 1 -2 7.8e-02 PASS 5 31 1 5 -2 8.8e-02 PASS 5 31 62 1 -2 1.4e-01 PASS 5 31 2 10 -2 6.8e-02 PASS 5 31 31 1 -2 1.5e-01 PASS 5 31 -1 5 -2 1.0e-01 PASS 5 31 62 1 -2 9.4e-02 PASS 5 31 -2 10 -2 1.1e-01 PASS 5 31 62 2 -2 9.2e-02 PASS 5 31 1 10 -2 1.0e-01 PASS 5 31 124 2 -2 9.2e-02 PASS 5 31 2 20 -2 8.2e-02 PASS 5 31 62 2 -2 6.9e-02 PASS 5 31 -1 10 -2 1.2e-01 PASS 5 31 124 2 -2 7.0e-02 PASS 5 31 -2 20 -2 1.2e-01 PASS 5 31 31 -1 -2 8.4e-02 PASS 5 31 1 5 -2 6.1e-02 PASS 5 31 62 -1 -2 1.2e-01 PASS 5 31 2 10 -2 9.0e-02 PASS 5 31 31 -1 -2 1.1e-01 PASS 5 31 -1 5 -2 1.1e-01 PASS 5 31 62 -1 -2 1.4e-01 PASS 5 31 -2 10 -2 7.3e-02 PASS 5 31 62 -2 -2 1.1e-01 PASS 5 31 1 10 -2 8.4e-02 PASS 5 31 124 -2 -2 1.1e-01 PASS 5 31 2 20 -2 1.2e-01 PASS 5 31 62 -2 -2 9.2e-02 PASS 5 31 -1 10 -2 7.5e-02 PASS 5 31 124 -2 -2 9.0e-02 PASS 5 31 -2 20 -2 8.9e-02 PASS 0 31 31 1 -2 0.0e+00 PASS 0 31 1 0 -2 0.0e+00 PASS 0 31 62 1 -2 0.0e+00 PASS 0 31 2 0 -2 0.0e+00 PASS 0 31 31 1 -2 0.0e+00 PASS 0 31 -1 0 -2 0.0e+00 PASS 0 31 62 1 -2 0.0e+00 PASS 0 31 -2 0 -2 0.0e+00 PASS 0 31 62 2 -2 0.0e+00 PASS 0 31 1 0 -2 0.0e+00 PASS 0 31 124 2 -2 0.0e+00 PASS 0 31 2 0 -2 0.0e+00 PASS 0 31 62 2 -2 0.0e+00 PASS 0 31 -1 0 -2 0.0e+00 PASS 0 31 124 2 -2 0.0e+00 PASS 0 31 -2 0 -2 0.0e+00 PASS 0 31 31 -1 -2 0.0e+00 PASS 0 31 1 0 -2 0.0e+00 PASS 0 31 62 -1 -2 0.0e+00 PASS 0 31 2 0 -2 0.0e+00 PASS 0 31 31 -1 -2 0.0e+00 PASS 0 31 -1 0 -2 0.0e+00 PASS 0 31 62 -1 -2 0.0e+00 PASS 0 31 -2 0 -2 0.0e+00 PASS 0 31 62 -2 -2 0.0e+00 PASS 0 31 1 0 -2 0.0e+00 PASS 0 31 124 -2 -2 0.0e+00 PASS 0 31 2 0 -2 0.0e+00 PASS 0 31 62 -2 -2 0.0e+00 PASS 0 31 -1 0 -2 0.0e+00 PASS 0 31 124 -2 -2 0.0e+00 PASS 0 31 -2 0 -2 0.0e+00 PASS 1 31 31 1 -2 0.0e+00 PASS 1 31 1 1 -2 0.0e+00 PASS 1 31 62 1 -2 0.0e+00 PASS 1 31 2 2 -2 0.0e+00 PASS 1 31 31 1 -2 0.0e+00 PASS 1 31 -1 1 -2 0.0e+00 PASS 1 31 62 1 -2 0.0e+00 PASS 1 31 -2 2 -2 0.0e+00 PASS 1 31 62 2 -2 0.0e+00 PASS 1 31 1 2 -2 0.0e+00 PASS 1 31 124 2 -2 0.0e+00 PASS 1 31 2 4 -2 0.0e+00 PASS 1 31 62 2 -2 0.0e+00 PASS 1 31 -1 2 -2 0.0e+00 PASS 1 31 124 2 -2 0.0e+00 PASS 1 31 -2 4 -2 0.0e+00 PASS 1 31 31 -1 -2 0.0e+00 PASS 1 31 1 1 -2 0.0e+00 PASS 1 31 62 -1 -2 0.0e+00 PASS 1 31 2 2 -2 0.0e+00 PASS 1 31 31 -1 -2 0.0e+00 PASS 1 31 -1 1 -2 0.0e+00 PASS 1 31 62 -1 -2 0.0e+00 PASS 1 31 -2 2 -2 0.0e+00 PASS 1 31 62 -2 -2 0.0e+00 PASS 1 31 1 2 -2 0.0e+00 PASS 1 31 124 -2 -2 0.0e+00 PASS 1 31 2 4 -2 0.0e+00 PASS 1 31 62 -2 -2 0.0e+00 PASS 1 31 -1 2 -2 0.0e+00 PASS 1 31 124 -2 -2 0.0e+00 PASS 1 31 -2 4 -2 0.0e+00 PASS 32 31 31 1 -2 4.8e-02 PASS 32 31 1 32 -2 5.6e-02 PASS 32 31 62 1 -2 5.1e-02 PASS 32 31 2 64 -2 5.5e-02 PASS 32 31 31 1 -2 4.2e-02 PASS 32 31 -1 32 -2 5.5e-02 PASS 32 31 62 1 -2 6.6e-02 PASS 32 31 -2 64 -2 4.8e-02 PASS 32 31 62 2 -2 4.7e-02 PASS 32 31 1 64 -2 5.4e-02 PASS 32 31 124 2 -2 6.3e-02 PASS 32 31 2 128 -2 5.2e-02 PASS 32 31 62 2 -2 5.0e-02 PASS 32 31 -1 64 -2 5.5e-02 PASS 32 31 124 2 -2 5.2e-02 PASS 32 31 -2 128 -2 5.1e-02 PASS 32 31 31 -1 -2 5.1e-02 PASS 32 31 1 32 -2 4.4e-02 PASS 32 31 62 -1 -2 5.2e-02 PASS 32 31 2 64 -2 4.6e-02 PASS 32 31 31 -1 -2 5.2e-02 PASS 32 31 -1 32 -2 5.4e-02 PASS 32 31 62 -1 -2 4.9e-02 PASS 32 31 -2 64 -2 5.9e-02 PASS 32 31 62 -2 -2 4.7e-02 PASS 32 31 1 64 -2 4.6e-02 PASS 32 31 124 -2 -2 5.7e-02 PASS 32 31 2 128 -2 4.5e-02 PASS 32 31 62 -2 -2 6.7e-02 PASS 32 31 -1 64 -2 5.3e-02 PASS 32 31 124 -2 -2 5.9e-02 PASS 32 31 -2 128 -2 5.8e-02 PASS 31 31 31 1 -2 5.0e-02 PASS 31 31 1 31 -2 4.7e-02 PASS 31 31 62 1 -2 4.3e-02 PASS 31 31 2 62 -2 4.8e-02 PASS 31 31 31 1 -2 6.0e-02 PASS 31 31 -1 31 -2 4.6e-02 PASS 31 31 62 1 -2 5.1e-02 PASS 31 31 -2 62 -2 5.8e-02 PASS 31 31 62 2 -2 5.2e-02 PASS 31 31 1 62 -2 5.9e-02 PASS 31 31 124 2 -2 5.0e-02 PASS 31 31 2 124 -2 4.7e-02 PASS 31 31 62 2 -2 4.2e-02 PASS 31 31 -1 62 -2 4.8e-02 PASS 31 31 124 2 -2 5.9e-02 PASS 31 31 -2 124 -2 5.2e-02 PASS 31 31 31 -1 -2 5.4e-02 PASS 31 31 1 31 -2 4.7e-02 PASS 31 31 62 -1 -2 5.4e-02 PASS 31 31 2 62 -2 5.8e-02 PASS 31 31 31 -1 -2 5.9e-02 PASS 31 31 -1 31 -2 5.4e-02 PASS 31 31 62 -1 -2 4.5e-02 PASS 31 31 -2 62 -2 4.7e-02 PASS 31 31 62 -2 -2 4.9e-02 PASS 31 31 1 62 -2 5.8e-02 PASS 31 31 124 -2 -2 4.6e-02 PASS 31 31 2 124 -2 5.4e-02 PASS 31 31 62 -2 -2 5.7e-02 PASS 31 31 -1 62 -2 5.6e-02 PASS 31 31 124 -2 -2 4.6e-02 PASS 31 31 -2 124 -2 4.6e-02 PASS heim$
-
and test_dgetrf_gemv for benchmarking the variant based on GEMV and TRSV:
heim$ gcc -Wall -std=c11 -I. -O3 -o test_dgetrf_gemv -DGETRF=GETRF_GEMV test_dgetrf.c ulmaux.c ulmblas.c heim$ ./test_dgetrf_gemv check m n incRowA incColA incP err res 5 5 5 1 1 4.8e-02 PASS 5 5 1 5 1 9.7e-02 PASS 5 5 10 1 1 4.9e-02 PASS 5 5 2 10 1 4.7e-02 PASS 5 5 5 1 1 6.4e-02 PASS 5 5 -1 5 1 1.2e-01 PASS 5 5 10 1 1 6.2e-02 PASS 5 5 -2 10 1 1.1e-01 PASS 5 5 10 2 1 7.7e-02 PASS 5 5 1 10 1 8.0e-02 PASS 5 5 20 2 1 5.8e-02 PASS 5 5 2 20 1 4.8e-02 PASS 5 5 10 2 1 5.9e-02 PASS 5 5 -1 10 1 5.4e-02 PASS 5 5 20 2 1 1.1e-01 PASS 5 5 -2 20 1 3.6e-02 PASS 5 5 5 -1 1 7.5e-02 PASS 5 5 1 5 1 4.1e-02 PASS 5 5 10 -1 1 3.5e-02 PASS 5 5 2 10 1 7.7e-02 PASS 5 5 5 -1 1 7.6e-02 PASS 5 5 -1 5 1 8.9e-02 PASS 5 5 10 -1 1 5.2e-02 PASS 5 5 -2 10 1 4.8e-02 PASS 5 5 10 -2 1 1.4e-01 PASS 5 5 1 10 1 3.1e-02 PASS 5 5 20 -2 1 3.8e-02 PASS 5 5 2 20 1 7.4e-02 PASS 5 5 10 -2 1 3.2e-02 PASS 5 5 -1 10 1 7.7e-02 PASS 5 5 20 -2 1 3.4e-02 PASS 5 5 -2 20 1 7.3e-02 PASS 0 5 5 1 1 0.0e+00 PASS 0 5 1 0 1 0.0e+00 PASS 0 5 10 1 1 0.0e+00 PASS 0 5 2 0 1 0.0e+00 PASS 0 5 5 1 1 0.0e+00 PASS 0 5 -1 0 1 0.0e+00 PASS 0 5 10 1 1 0.0e+00 PASS 0 5 -2 0 1 0.0e+00 PASS 0 5 10 2 1 0.0e+00 PASS 0 5 1 0 1 0.0e+00 PASS 0 5 20 2 1 0.0e+00 PASS 0 5 2 0 1 0.0e+00 PASS 0 5 10 2 1 0.0e+00 PASS 0 5 -1 0 1 0.0e+00 PASS 0 5 20 2 1 0.0e+00 PASS 0 5 -2 0 1 0.0e+00 PASS 0 5 5 -1 1 0.0e+00 PASS 0 5 1 0 1 0.0e+00 PASS 0 5 10 -1 1 0.0e+00 PASS 0 5 2 0 1 0.0e+00 PASS 0 5 5 -1 1 0.0e+00 PASS 0 5 -1 0 1 0.0e+00 PASS 0 5 10 -1 1 0.0e+00 PASS 0 5 -2 0 1 0.0e+00 PASS 0 5 10 -2 1 0.0e+00 PASS 0 5 1 0 1 0.0e+00 PASS 0 5 20 -2 1 0.0e+00 PASS 0 5 2 0 1 0.0e+00 PASS 0 5 10 -2 1 0.0e+00 PASS 0 5 -1 0 1 0.0e+00 PASS 0 5 20 -2 1 0.0e+00 PASS 0 5 -2 0 1 0.0e+00 PASS 1 5 5 1 1 0.0e+00 PASS 1 5 1 1 1 0.0e+00 PASS 1 5 10 1 1 0.0e+00 PASS 1 5 2 2 1 0.0e+00 PASS 1 5 5 1 1 0.0e+00 PASS 1 5 -1 1 1 0.0e+00 PASS 1 5 10 1 1 0.0e+00 PASS 1 5 -2 2 1 0.0e+00 PASS 1 5 10 2 1 0.0e+00 PASS 1 5 1 2 1 0.0e+00 PASS 1 5 20 2 1 0.0e+00 PASS 1 5 2 4 1 0.0e+00 PASS 1 5 10 2 1 0.0e+00 PASS 1 5 -1 2 1 0.0e+00 PASS 1 5 20 2 1 0.0e+00 PASS 1 5 -2 4 1 0.0e+00 PASS 1 5 5 -1 1 0.0e+00 PASS 1 5 1 1 1 0.0e+00 PASS 1 5 10 -1 1 0.0e+00 PASS 1 5 2 2 1 0.0e+00 PASS 1 5 5 -1 1 0.0e+00 PASS 1 5 -1 1 1 0.0e+00 PASS 1 5 10 -1 1 0.0e+00 PASS 1 5 -2 2 1 0.0e+00 PASS 1 5 10 -2 1 0.0e+00 PASS 1 5 1 2 1 0.0e+00 PASS 1 5 20 -2 1 0.0e+00 PASS 1 5 2 4 1 0.0e+00 PASS 1 5 10 -2 1 0.0e+00 PASS 1 5 -1 2 1 0.0e+00 PASS 1 5 20 -2 1 0.0e+00 PASS 1 5 -2 4 1 0.0e+00 PASS 32 5 5 1 1 9.3e-02 PASS 32 5 1 32 1 1.5e-01 PASS 32 5 10 1 1 1.4e-01 PASS 32 5 2 64 1 8.3e-02 PASS 32 5 5 1 1 9.9e-02 PASS 32 5 -1 32 1 1.1e-01 PASS 32 5 10 1 1 1.4e-01 PASS 32 5 -2 64 1 1.1e-01 PASS 32 5 10 2 1 1.4e-01 PASS 32 5 1 64 1 1.2e-01 PASS 32 5 20 2 1 1.1e-01 PASS 32 5 2 128 1 1.7e-01 PASS 32 5 10 2 1 1.4e-01 PASS 32 5 -1 64 1 1.3e-01 PASS 32 5 20 2 1 1.3e-01 PASS 32 5 -2 128 1 1.0e-01 PASS 32 5 5 -1 1 1.5e-01 PASS 32 5 1 32 1 1.1e-01 PASS 32 5 10 -1 1 1.2e-01 PASS 32 5 2 64 1 1.2e-01 PASS 32 5 5 -1 1 1.3e-01 PASS 32 5 -1 32 1 1.4e-01 PASS 32 5 10 -1 1 1.2e-01 PASS 32 5 -2 64 1 9.3e-02 PASS 32 5 10 -2 1 1.8e-01 PASS 32 5 1 64 1 1.4e-01 PASS 32 5 20 -2 1 1.4e-01 PASS 32 5 2 128 1 1.3e-01 PASS 32 5 10 -2 1 1.4e-01 PASS 32 5 -1 64 1 1.0e-01 PASS 32 5 20 -2 1 1.3e-01 PASS 32 5 -2 128 1 1.4e-01 PASS 31 5 5 1 1 1.8e-01 PASS 31 5 1 31 1 1.2e-01 PASS 31 5 10 1 1 1.2e-01 PASS 31 5 2 62 1 1.6e-01 PASS 31 5 5 1 1 1.2e-01 PASS 31 5 -1 31 1 1.6e-01 PASS 31 5 10 1 1 1.1e-01 PASS 31 5 -2 62 1 9.1e-02 PASS 31 5 10 2 1 1.1e-01 PASS 31 5 1 62 1 1.1e-01 PASS 31 5 20 2 1 1.3e-01 PASS 31 5 2 124 1 1.2e-01 PASS 31 5 10 2 1 1.4e-01 PASS 31 5 -1 62 1 1.2e-01 PASS 31 5 20 2 1 1.2e-01 PASS 31 5 -2 124 1 1.2e-01 PASS 31 5 5 -1 1 1.7e-01 PASS 31 5 1 31 1 1.3e-01 PASS 31 5 10 -1 1 1.1e-01 PASS 31 5 2 62 1 1.5e-01 PASS 31 5 5 -1 1 1.5e-01 PASS 31 5 -1 31 1 8.9e-02 PASS 31 5 10 -1 1 1.2e-01 PASS 31 5 -2 62 1 1.1e-01 PASS 31 5 10 -2 1 9.4e-02 PASS 31 5 1 62 1 1.2e-01 PASS 31 5 20 -2 1 1.2e-01 PASS 31 5 2 124 1 1.4e-01 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62 -2 -2 0.0e+00 PASS 0 31 -1 0 -2 0.0e+00 PASS 0 31 124 -2 -2 0.0e+00 PASS 0 31 -2 0 -2 0.0e+00 PASS 1 31 31 1 -2 0.0e+00 PASS 1 31 1 1 -2 0.0e+00 PASS 1 31 62 1 -2 0.0e+00 PASS 1 31 2 2 -2 0.0e+00 PASS 1 31 31 1 -2 0.0e+00 PASS 1 31 -1 1 -2 0.0e+00 PASS 1 31 62 1 -2 0.0e+00 PASS 1 31 -2 2 -2 0.0e+00 PASS 1 31 62 2 -2 0.0e+00 PASS 1 31 1 2 -2 0.0e+00 PASS 1 31 124 2 -2 0.0e+00 PASS 1 31 2 4 -2 0.0e+00 PASS 1 31 62 2 -2 0.0e+00 PASS 1 31 -1 2 -2 0.0e+00 PASS 1 31 124 2 -2 0.0e+00 PASS 1 31 -2 4 -2 0.0e+00 PASS 1 31 31 -1 -2 0.0e+00 PASS 1 31 1 1 -2 0.0e+00 PASS 1 31 62 -1 -2 0.0e+00 PASS 1 31 2 2 -2 0.0e+00 PASS 1 31 31 -1 -2 0.0e+00 PASS 1 31 -1 1 -2 0.0e+00 PASS 1 31 62 -1 -2 0.0e+00 PASS 1 31 -2 2 -2 0.0e+00 PASS 1 31 62 -2 -2 0.0e+00 PASS 1 31 1 2 -2 0.0e+00 PASS 1 31 124 -2 -2 0.0e+00 PASS 1 31 2 4 -2 0.0e+00 PASS 1 31 62 -2 -2 0.0e+00 PASS 1 31 -1 2 -2 0.0e+00 PASS 1 31 124 -2 -2 0.0e+00 PASS 1 31 -2 4 -2 0.0e+00 PASS 32 31 31 1 -2 4.0e-02 PASS 32 31 1 32 -2 5.6e-02 PASS 32 31 62 1 -2 3.6e-02 PASS 32 31 2 64 -2 5.5e-02 PASS 32 31 31 1 -2 3.9e-02 PASS 32 31 -1 32 -2 5.5e-02 PASS 32 31 62 1 -2 3.4e-02 PASS 32 31 -2 64 -2 4.8e-02 PASS 32 31 62 2 -2 3.9e-02 PASS 32 31 1 64 -2 5.4e-02 PASS 32 31 124 2 -2 4.6e-02 PASS 32 31 2 128 -2 5.2e-02 PASS 32 31 62 2 -2 4.4e-02 PASS 32 31 -1 64 -2 5.5e-02 PASS 32 31 124 2 -2 3.3e-02 PASS 32 31 -2 128 -2 5.1e-02 PASS 32 31 31 -1 -2 3.8e-02 PASS 32 31 1 32 -2 4.4e-02 PASS 32 31 62 -1 -2 4.1e-02 PASS 32 31 2 64 -2 4.6e-02 PASS 32 31 31 -1 -2 4.3e-02 PASS 32 31 -1 32 -2 5.4e-02 PASS 32 31 62 -1 -2 4.3e-02 PASS 32 31 -2 64 -2 5.9e-02 PASS 32 31 62 -2 -2 3.4e-02 PASS 32 31 1 64 -2 4.6e-02 PASS 32 31 124 -2 -2 5.1e-02 PASS 32 31 2 128 -2 4.5e-02 PASS 32 31 62 -2 -2 3.7e-02 PASS 32 31 -1 64 -2 5.3e-02 PASS 32 31 124 -2 -2 3.9e-02 PASS 32 31 -2 128 -2 5.8e-02 PASS 31 31 31 1 -2 3.6e-02 PASS 31 31 1 31 -2 4.7e-02 PASS 31 31 62 1 -2 5.0e-02 PASS 31 31 2 62 -2 4.8e-02 PASS 31 31 31 1 -2 3.9e-02 PASS 31 31 -1 31 -2 4.6e-02 PASS 31 31 62 1 -2 3.4e-02 PASS 31 31 -2 62 -2 5.8e-02 PASS 31 31 62 2 -2 4.4e-02 PASS 31 31 1 62 -2 5.9e-02 PASS 31 31 124 2 -2 3.6e-02 PASS 31 31 2 124 -2 4.7e-02 PASS 31 31 62 2 -2 3.4e-02 PASS 31 31 -1 62 -2 4.8e-02 PASS 31 31 124 2 -2 3.8e-02 PASS 31 31 -2 124 -2 5.2e-02 PASS 31 31 31 -1 -2 4.3e-02 PASS 31 31 1 31 -2 4.7e-02 PASS 31 31 62 -1 -2 4.0e-02 PASS 31 31 2 62 -2 5.8e-02 PASS 31 31 31 -1 -2 3.8e-02 PASS 31 31 -1 31 -2 5.4e-02 PASS 31 31 62 -1 -2 4.3e-02 PASS 31 31 -2 62 -2 4.7e-02 PASS 31 31 62 -2 -2 4.4e-02 PASS 31 31 1 62 -2 5.8e-02 PASS 31 31 124 -2 -2 3.1e-02 PASS 31 31 2 124 -2 5.4e-02 PASS 31 31 62 -2 -2 3.5e-02 PASS 31 31 -1 62 -2 5.6e-02 PASS 31 31 124 -2 -2 3.9e-02 PASS 31 31 -2 124 -2 4.6e-02 PASS heim$
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Benchmark both variants:
heim$ ./test_dgetrf_ger bench > bench.dgetrf_ger heim$ ./test_dgetrf_gemv bench > bench.dgetrf_gemv heim$ cat bench.dgetrf_ger #colmajor = 1 #incP = 1 # m n incRowA incColA time mflops err 100 100 1 100 0.00 1822.23 3.5e-02 200 200 1 200 0.00 2156.59 3.0e-02 300 300 1 300 0.01 2154.60 2.9e-02 400 400 1 400 0.02 2214.51 2.7e-02 500 500 1 500 0.04 2240.22 2.4e-02 600 600 1 600 0.06 2256.00 2.3e-02 700 700 1 700 0.11 2154.92 2.4e-02 800 800 1 800 0.16 2200.09 2.2e-02 900 900 1 900 0.23 2142.33 2.2e-02 1000 1000 1 1000 0.31 2148.92 2.1e-02 heim$ cat bench.dgetrf_gemv #colmajor = 1 #incP = 1 # m n incRowA incColA time mflops err 100 100 1 100 0.00 2467.63 3.5e-02 200 200 1 200 0.00 2741.68 3.0e-02 300 300 1 300 0.01 2729.16 2.9e-02 400 400 1 400 0.02 2725.55 2.7e-02 500 500 1 500 0.03 2829.08 2.4e-02 600 600 1 600 0.05 2765.77 2.3e-02 700 700 1 700 0.08 2805.18 2.4e-02 800 800 1 800 0.12 2750.11 2.2e-02 900 900 1 900 0.18 2697.75 2.2e-02 1000 1000 1 1000 0.25 2700.68 2.1e-02 heim$
You can use the Gnuplot script
set terminal svg size 900, 500 set output "bench.getrf.svg" set xlabel "Matrix dimension M=N" set ylabel "MFLOPS" set yrange [0:4000] set title "GETRF (col major)" set key outside set pointsize 0.5 plot "bench.dgetrf_ger" using 1:6 with linespoints lt 2 lw 3 title "dgetrf with dger", \ "bench.dgetrf_gemv" using 1:6 with linespoints lt 3 lw 3 title "dgetrf with dgemv and dtrsv"
for plotting the performance:
heim$ gnuplot getrf.plot heim$
gives