BLAS.md

@@ -4,8 +4,9 @@ All these operations are now supported for CPU and GPU memory, real and complex.
 |---     |---                     | ---                           | ---                  | ---             | --- |
 | SWAP   |`blas::swap(x, y)`      | $`x_i \leftrightarrow y_i`$ | `(x^y)` |    | `swap_ranges(begin(x), end(x), begin(y))` |
 | COPY   |`blas::copy(x, y)`      | $`y_i \leftrightarrow x_i`$ | `y << x` |  `y = blas::copy(x)` | `copy(begin(x), end(x), begin(y))` |
-| ASUM   |`blas::asum(x, res)`    | $`r \leftarrow \sum_i \|\Re x_i\| + \|\Im x_i\|`$ | `x == 0` or `x != 0` | `res = blas::asum(x)` | `transform_reduce(begin(x), end(x), 0.0, plus<>{}, [](auto const& e){return abs(e.real()) + abs(e.imag());})` |
-| NRM2   |`blas::nrm2(x, res)`     | $`r \leftarrow \sqrt{\sum_i \|x_i\|^2}`$ | `abs(x)` | `res = blas::nrm2(x);` | `sqrt(trasnform_reduce(begin(x), end(x), 0.0, plus<>{}, [](auto const& e){return norm(e);}));` |
+| ASUM   |`blas::asum(x, res)`    | $`r \leftarrow \sum_i \|\Re x_i\| + \|\Im x_i\|`$ | `x==0`/`x!=0`/`isinf(x)`/`isnan(x)` | `res = blas::asum(x)` | `transform_reduce(begin(x), end(x), 0.0, plus<>{}, [](auto const& e){return abs(e.real()) + abs(e.imag());})` |
+| NRM2   |`blas::
+nrm2(x, res)`     | $`r \leftarrow \sqrt{\sum_i \|x_i\|^2}`$ | `abs(x)` | `res = blas::nrm2(x);` | `sqrt(trasnform_reduce(begin(x), end(x), 0.0, plus<>{}, [](auto const& e){return norm(e);}));` |
 | SCAL   |`blas::scal(aa, x);`    | $`x_i \leftarrow \alpha x_i`$ | `x*=aa;`           |                 | `for_each(begin(x), end(x), [aa](auto& e){return e*=aa;})` |
 | AXPY   |`blas::axpy(aa, x, y)`  | $`y_i \leftarrow \alpha x_i + y_i`$ | `y+=x` `y-=x` `y+=aa*x` `y-=aa*x` |     | `transform(x.begin(), x.end(), y.begin(), y.begin(), [aa](auto ex, auto ey) {return aa*ex + ey;}` |
 | DOT    | `blas::dot(x, y, res)` | $`r = \sum_i x_i y_i`$        | `res = (x, y);`       | `res = blas::dot(x, y)`                | `inner_product(begin(x), end(x), begin(y), T{});` |
@@ -20,4 +21,4 @@ All these operations are now supported for CPU and GPU memory, real and complex.
 |      | `blas::gemm(aa, A, blas::T(B), bb, C)` | $`C_{ij} \leftarrow \alpha \sum_k A_{ik} B_{jk} + \beta C_{ij}`$ | `C = aa*(A* ~B)` | `C = blas::gemm(aa, A, blas::T(B))` `C += blas::gemm(aa, A, blas::T(B))` | `transform(begin(A), end(A), begin(C), begin(C), [&B, aa, bb] (auto const& Ar, auto&& Cr) {return blas::gemv(aa, B, Ar, bb, move(Cr));})` |
 |        | `blas::gemm(aa, blas::T(A), B, bb, C)` | $`C_{ij} \leftarrow \alpha \sum_k A_{ki} B_{kj} + \beta C_{ij}`$ | `C =~A * B` `C = aa*(~A * B)` `C+=~A * B` `C+=aa*(~A * B)` | `C = blas::gemm(aa, blas::T(A), B, bb, C)` (or `+=`) | `transform(begin(transposed(A)), end(transposed(A)), begin(C), begin(C), [&B, aa, bb] (auto const& Ar, auto&& Cr) {return blas::gemv(aa, blas::T(B), Ar, bb, std::move(Cr));})` |
 |        | `blas::gemm(aa, blas::T(A), blas::T(B), bb, C)` | $`C_{ij} \leftarrow \alpha \sum_k A_{ki} B_{jk} + \beta C_{ij}`$ | `C =~A * ~B` `C = aa*(~A * ~B)` `C+=~A * ~B` `C+=aa*(~A * ~B)` | `C = blas::gemm(aa, blas::T(A), blas::T(B), bb, C)` (or `+=`) | `transform(begin(transposed(A)), end(transposed(A)), begin(C), begin(C), [&B, aa, bb] (auto const& Ar, auto&& Cr) {return blas::gemv(aa, B, Ar, bb, std::move(Cr));})` |
-|      | <s>`blas::gemm(aa, A, blas::J(B), bb, C)`</s> (use `blas::gemm(..., blas::T(B), blas::H(A), ..., C_copy)` and conjtranspose result) | $`C_{ij} \leftarrow \alpha \sum_k A_{ik} B_{kj}^* + \beta C_{ij}`$ (not BLAS-implemented) |    |   | `transform(begin(A), end(A), begin(C), begin(C), [BT=transposed(B)](auto const& Ar, auto&& Cr) {transform(begin(BT), end(BT), begin(Cr), begin(Cr), [&Ar](auto const& BCr, auto&& Ce) {return aa*blas::dot(Ar, blas::C(BCr)) + bb*Ce;}); return std::move(Cr);});` |
+|      | <s>`blas::gemm(aa, A, blas::J(B), bb, C)`</s> (use `blas::gemm(..., blas::T(B), blas::H(A), ..., HC)` and conjtranspose result) | $`C_{ij} \leftarrow \alpha \sum_k A_{ik} B_{kj}^* + \beta C_{ij}`$ (not BLAS-implemented) |    |   | `transform(begin(A), end(A), begin(C), begin(C), [BT=transposed(B)](auto const& Ar, auto&& Cr) {transform(begin(BT), end(BT), begin(Cr), begin(Cr), [&Ar](auto const& BCr, auto&& Ce) {return aa*blas::dot(Ar, blas::C(BCr)) + bb*Ce;}); return std::move(Cr);});` |