From Jason Turner

[linalg.algs.blas3.rankk]

Diff to HTML by rtfpessoa

Files changed (1) hide show
  1. tmp/tmpxnextqra/{from.md → to.md} +76 -0
tmp/tmpxnextqra/{from.md → to.md} RENAMED
@@ -0,0 +1,76 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ #### Rank-k update of a symmetric or Hermitian matrix <a id="linalg.algs.blas3.rankk">[[linalg.algs.blas3.rankk]]</a>
2
+
3
+ [*Note 1*: These functions correspond to the BLAS functions `xSYRK` and
4
+ `xHERK`. — *end note*]
5
+
6
+ The following elements apply to all functions in
7
+ [[linalg.algs.blas3.rankk]].
8
+
9
+ *Mandates:*
10
+
11
+ - If `InOutMat` has `layout_blas_packed` layout, then the layout’s
12
+ `Triangle` template argument has the same type as the function’s
13
+ `Triangle` template argument;
14
+ - `compatible-static-extents<decltype(A), decltype(A)>(0, 1)` is `true`;
15
+ - `compatible-static-extents<decltype(C), decltype(C)>(0, 1)` is `true`;
16
+ and
17
+ - `compatible-static-extents<decltype(A), decltype(C)>(0, 0)` is `true`.
18
+
19
+ *Preconditions:*
20
+
21
+ - `A.extent(0)` equals `A.extent(1)`,
22
+ - `C.extent(0)` equals `C.extent(1)`, and
23
+ - `A.extent(0)` equals `C.extent(0)`.
24
+
25
+ *Complexity:* 𝑂(`A.extent(0)` × `A.extent(1)` × `C.extent(0)`).
26
+
27
+ ``` cpp
28
+ template<class Scalar, in-matrix InMat, possibly-packed-inout-matrix InOutMat, class Triangle>
29
+ void symmetric_matrix_rank_k_update(Scalar alpha, InMat A, InOutMat C, Triangle t);
30
+ template<class ExecutionPolicy, class Scalar,
31
+ in-matrix InMat, possibly-packed-inout-matrix InOutMat, class Triangle>
32
+ void symmetric_matrix_rank_k_update(ExecutionPolicy&& exec,
33
+ Scalar alpha, InMat A, InOutMat C, Triangle t);
34
+ ```
35
+
36
+ *Effects:* Computes a matrix C' such that $C' = C + \alpha A A^T$, where
37
+ the scalar α is `alpha`, and assigns each element of C' to the
38
+ corresponding element of C.
39
+
40
+ ``` cpp
41
+ template<in-matrix InMat, possibly-packed-inout-matrix InOutMat, class Triangle>
42
+ void symmetric_matrix_rank_k_update(InMat A, InOutMat C, Triangle t);
43
+ template<class ExecutionPolicy,
44
+ in-matrix InMat, possibly-packed-inout-matrix InOutMat, class Triangle>
45
+ void symmetric_matrix_rank_k_update(ExecutionPolicy&& exec,
46
+ InMat A, InOutMat C, Triangle t);
47
+ ```
48
+
49
+ *Effects:* Computes a matrix C' such that $C' = C + A A^T$, and assigns
50
+ each element of C' to the corresponding element of C.
51
+
52
+ ``` cpp
53
+ template<class Scalar, in-matrix InMat, possibly-packed-inout-matrix InOutMat, class Triangle>
54
+ void hermitian_matrix_rank_k_update(Scalar alpha, InMat A, InOutMat C, Triangle t);
55
+ template<class ExecutionPolicy,
56
+ class Scalar, in-matrix InMat, possibly-packed-inout-matrix InOutMat, class Triangle>
57
+ void hermitian_matrix_rank_k_update(ExecutionPolicy&& exec,
58
+ Scalar alpha, InMat A, InOutMat C, Triangle t);
59
+ ```
60
+
61
+ *Effects:* Computes a matrix C' such that $C' = C + \alpha A A^H$, where
62
+ the scalar α is `alpha`, and assigns each element of C' to the
63
+ corresponding element of C.
64
+
65
+ ``` cpp
66
+ template<in-matrix InMat, possibly-packed-inout-matrix InOutMat, class Triangle>
67
+ void hermitian_matrix_rank_k_update(InMat A, InOutMat C, Triangle t);
68
+ template<class ExecutionPolicy,
69
+ in-matrix InMat, possibly-packed-inout-matrix InOutMat, class Triangle>
70
+ void hermitian_matrix_rank_k_update(ExecutionPolicy&& exec,
71
+ InMat A, InOutMat C, Triangle t);
72
+ ```
73
+
74
+ *Effects:* Computes a matrix C' such that $C' = C + A A^H$, and assigns
75
+ each element of C' to the corresponding element of C.
76
+