Simple BLAS
Intro
What? A better simpler website to illustrate BLAS operations.
Why? The current website is an artifact straight outta 2000. Look at it: https://www.netlib.org/blas/.
Who? For those with some understanding of BLAS operations, intended as a reference not a tutorial.
Levels
- Vector operations.
- Matrix-vector operations.
- Matrix-matrix operations.
Parameters
- Scalars: \alpha and \beta.
- Dimensions: m, n and k.
- Vectors: x and y.
- Matricies: A, B and C.
Animations
Animated Vs Un-animated
Disclaimer: Some operations have animations illustrating them, it is important you know these animations do not illustrate how the underlying code performs the operation, they simply illustrate the result and how you might think about it.
Level 1
| Name | Description | Equation |
|---|---|---|
| SROTG | setup Givens rotation |
|
| SROTMG | setup modified Givens rotation |
|
| SROT | apply Givens rotation |
|
| SROTM | apply modified Givens rotation |
|
SSWAP |
swap x and y |
x\Leftrightarrow y |
SSCAL |
x = a*x |
x\leftarrow \alpha x |
SCOPY |
copy x into y |
y\leftarrow x |
SAXPY |
y = a*x + y |
y\leftarrow \alpha x + y |
SDOT |
dot product |
dot\leftarrow x^T y |
| SDSDOT |
dot product with extended precision accumulation |
dot\leftarrow x^T y |
SNRM2 |
Euclidean norm |
nrm2\leftarrow ||x||_2 |
| SCNRM2 |
Euclidean norm |
nrm2\leftarrow ||x||_2 |
SASUM |
sum of absolute values |
asum\leftarrow ||re(x)||_1 +||im(x)||_1 |
| ISAMAX | index of max abs value |
\text{amax}\leftarrow 1^{st}\ni |re(x_k)|+|im(x_k)|=max(|re(x_i)|+|im(x_i)|) |
| Name | Description | Equation |
|---|---|---|
| DROTG | setup Givens rotation |
|
| DROTMG | setup modified Givens rotation |
|
| DROT | apply Givens rotation |
|
| DROTM | apply modified Givens rotation |
|
| DSWAP |
swap x and y |
x\Leftrightarrow y |
| DSCAL |
x = a*x |
x\leftarrow \alpha x |
| DCOPY |
copy x into y |
y\leftarrow x |
| DAXPY |
y = a*x + y |
y\leftarrow \alpha x + y |
| DDOT |
dot product |
dot\leftarrow x^T y |
| DSDOT |
dot product with extended precision accumulation |
dot\leftarrow x^T y |
| DNRM2 |
Euclidean norm |
nrm2\leftarrow ||x||_2 |
| DCNRM2 |
Euclidean norm |
nrm2\leftarrow ||x||_2 |
| DASUM |
sum of absolute values |
asum\leftarrow ||re(x)||_1 +||im(x)||_1 |
| IDAMAX | index of max abs value |
\text{amax}\leftarrow 1^{st}\ni |re(x_k)|+|im(x_k)|=max(|re(x_i)|+|im(x_i)|) |
| Name | Description | Equation |
|---|---|---|
| CROTG | setup Givens rotation |
|
| CSROT | apply Givens rotation |
|
| CSWAP | swap x and y |
x\Leftrightarrow y |
| CSCAL | x = a*x |
x\leftarrow \alpha x |
| CSSCAL | x = a*x |
x\leftarrow \alpha x |
| CCOPY | copy x into y |
y\leftarrow x |
| CAXPY | y = a*x + y |
y\leftarrow \alpha x + y |
| CDOTU | dot product |
dot\leftarrow x^T y |
| CDOTC | dot product, conjugating the first vector |
|
| SCASUM | sum of absolute values |
asum\leftarrow ||re(x)||_1 +||im(x)||_1 |
| ICAMAX | index of max abs value |
\text{amax}\leftarrow 1^{st}\ni |re(x_k)|+|im(x_k)|=max(|re(x_i)|+|im(x_i)|) |
| Name | Description | Equation |
|---|---|---|
| ZROTG | setup Givens rotation |
|
| ZDROTF | apply Givens rotation |
|
| ZSWAP | swap x and y |
x\Leftrightarrow y |
| ZSCAL | x = a*x |
x\leftarrow \alpha x |
| ZDSCAL | x = a*x |
x\leftarrow \alpha x |
| ZCOPY | copy x into y |
y\leftarrow x |
| ZAXPY | y = a*x + y |
y\leftarrow \alpha x + y |
| ZDOTU | dot product |
dot\leftarrow x^T y |
| ZDOTC | dot product, conjugating the first vector |
|
| DZASUM | sum of absolute values |
asum\leftarrow ||re(x)||_1 +||im(x)||_1 |
| IZAMAX | index of max abs value |
\text{amax}\leftarrow 1^{st}\ni |re(x_k)|+|im(x_k)|=max(|re(x_i)|+|im(x_i)|) |
Level 2
| Name | Description |
|---|---|
SGEMV |
matrix vector multiply |
SGBMV |
banded matrix vector multiply |
SSYMV |
symmetric matrix vector multiply |
SSBMV |
symmetric banded matrix vector multiply |
| SSPMV |
symmetric packed matrix vector multiply |
STRMV |
triangular matrix vector multiply |
| STBMV |
triangular banded matrix vector multiply |
| STPMV |
triangular packed matrix vector multiply |
| STRSV | solving triangular matrix problems |
| STBSV | solving triangular banded matrix problems |
| STPSV | solving triangular packed matrix problems |
| SGER | performs the rank 1 operation A := alpha*x*y' + A |
| SSYR | performs the symmetric rank 1 operation A := alpha*x*x' + A |
| SSPR | symmetric packed rank 1 operation A := alpha*x*x' + A |
| SSYR2 | performs the symmetric rank 2 operation, A := alpha*x*y' + alpha*y*x' + A |
| SSPR2 | performs the symmetric packed rank 2 operation, A := alpha*x*y' + alpha*y*x' + A |
| Name | Description |
|---|---|
| DGEMV |
matrix vector multiply |
| DGBMV |
banded matrix vector multiply |
| DSYMV |
symmetric matrix vector multiply |
| DSBMV |
symmetric banded matrix vector multiply |
| DSPMV |
symmetric packed matrix vector multiply |
| DTRMV |
triangular matrix vector multiply |
| DTBMV |
triangular banded matrix vector multiply |
| DTPMV |
triangular packed matrix vector multiply |
| DTRSV | solving triangular matrix problems |
| DTBSV | solving triangular banded matrix problems |
| DTPSV | solving triangular packed matrix problems |
| DGER | performs the rank 1 operation A := alpha*x*y' + A |
| DSYR | performs the symmetric rank 1 operation A := alpha*x*x' + A |
| DSPR | symmetric packed rank 1 operation A := alpha*x*x' + A |
| DSYR2 | performs the symmetric rank 2 operation, A := alpha*x*y' + alpha*y*x' + A |
| DSPR2 | performs the symmetric packed rank 2 operation, A := alpha*x*y' + alpha*y*x' + A |
| Name | Description |
|---|---|
| CGEMV | matrix vector multiply |
| CGBMV | banded matrix vector multiply |
| CHEMV | hermitian matrix vector multiply |
| CHBMV | hermitian banded matrix vector multiply |
| CHPMV | hermitian packed matrix vector multiply |
| CTRMV | triangular matrix vector multiply |
| CTBMV | triangular banded matrix vector multiply |
| CTPMV | triangular packed matrix vector multiply |
| CTRSV | solving triangular matrix problems |
| CTBSV | solving triangular banded matrix problems |
| CTPSV | solving triangular packed matrix problems |
| CGERU | performs the rank 1 operation A := alpha*x*y' + A |
| CGERC | performs the rank 1 operation A := alpha*x*conjg( y' ) + A |
| CHER | hermitian rank 1 operation A := alpha*x*conjg(x') + A |
| CHPR | hermitian packed rank 1 operation A := alpha*x*conjg( x' ) + A |
| CHER2 | hermitian rank 2 operation |
| CHRP2 | hermitian packed rank 2 operation |
| Name | Description |
|---|---|
| ZGEMV | matrix vector multiply |
| ZGBMV | banded matrix vector multiply |
| ZHEMV | hermitian matrix vector multiply |
| ZHBMV | hermitian banded matrix vector multiply |
| ZHPMV | hermitian packed matrix vector multiply |
| ZTRMV | triangular matrix vector multiply |
| ZTBMV | triangular banded matrix vector multiply |
| ZTPMV | triangular packed matrix vector multiply |
| ZTRSV | solving triangular matrix problems |
| ZTBSV | solving triangular banded matrix problems |
| ZTPSV | solving triangular packed matrix problems |
| ZGERU | performs the rank 1 operation A := alpha*x*y' + A |
| ZGERC | performs the rank 1 operation A := alpha*x*conjg( y' ) + A |
| ZHER | hermitian rank 1 operation A := alpha*x*conjg(x') + A |
| ZHPR | hermitian packed rank 1 operation A := alpha*x*conjg( x' ) + A |
| ZHER2 | hermitian rank 2 operation |
| ZHRP2 | hermitian packed rank 2 operation |
Level 3
| Name | Description |
|---|---|
| SGEMM | matrix matrix multiply |
| SSYMM | symmetric matrix matrix multiply |
| SSYRK | symmetric rank-k update to a matrix |
| SSYR2k | symmetric rank-2k update to a matrix |
| STRMM | triangular matrix matrix multiply |
| STRSM | solving triangular matrix with multiple right hand sides |
| Name | Description |
|---|---|
| DGEMM | matrix matrix multiply |
| DSYMM | symmetric matrix matrix multiply |
| DSYRK | symmetric rank-k update to a matrix |
| DSYR2k | symmetric rank-2k update to a matrix |
| DTRMM | triangular matrix matrix multiply |
| DTRSM | solving triangular matrix with multiple right hand sides |
| Name | Description |
|---|---|
| CGEMM | matrix matrix multiply |
| CSYMM | symmetric matrix matrix multiply |
| CHEMM | hermitian matrix matrix multiply |
| CSYRK | symmetric rank-k update to a matrix |
| CHERK | hermitian rank-k update to a matrix |
| CSYR2k | symmetric rank-2k update to a matrix |
| CHER2K | hermitian rank-2k update to a matrix |
| CTRMM | triangular matrix matrix multiply |
| CTRSM | solving triangular matrix with multiple right hand sides |
| Name | Description |
|---|---|
| ZGEMM | matrix matrix multiply |
| ZSYMM | symmetric matrix matrix multiply |
| ZHEMM | hermitian matrix matrix multiply |
| ZSYRK | symmetric rank-k update to a matrix |
| ZHERK | hermitian rank-k update to a matrix |
| ZSYR2K | symmetric rank-2k update to a matrix |
| ZHER2K | hermitian rank-2k update to a matrix |
| ZTRMM | triangular matrix matrix multiply |
| ZTRSM | solving triangular matrix with multiple right hand sides |