Fixup: clean up my mess (no deviations from paper yet)

Author: eisenwave

source/numerics.tex

@@ -11354,21 +11354,21 @@
                                         Scalar alpha, InVec x, OutMat A, Triangle t);
 
   // updating symmetric rank-1 matrix update
-  template<class Scalar, @\exposconcept{in-vector}@ InVec, @\exposconcept{in-matrix}@ InMat, @\exposconcept{possibly-packed-out-matrix}@ OutMat,
+  template<@\exposconcept{scalar}@ Scalar, @\exposconcept{in-vector}@ InVec, @\exposconcept{in-matrix}@ InMat, @\exposconcept{possibly-packed-out-matrix}@ OutMat,
            class Triangle>
     void symmetric_matrix_rank_1_update(Scalar alpha, InVec x, InMat E, OutMat A, Triangle t);
   template<class ExecutionPolicy,
-           class Scalar, @\exposconcept{in-vector InVec}@, @\exposconcept{in-matrix}@ InMat, @\exposconcept{possibly-packed-out-matrix}@ OutMat,
+           @\exposconcept{scalar}@ Scalar, @\exposconcept{in-vector}@ InVec, @\exposconcept{in-matrix}@ InMat, @\exposconcept{possibly-packed-out-matrix}@ OutMat,
            class Triangle>
     void symmetric_matrix_rank_1_update(ExecutionPolicy&& exec,
                                         Scalar alpha, InVec x, InMat E, OutMat A, Triangle t);
 
   // updating Hermitian rank-1 matrix update
-  template<class Scalar, @\exposconcept{in-vector}@ InVec, @\exposconcept{in-matrix}@ InMat, @\exposconcept{possibly-packed-out-matrix}@ OutMat,
+  template<@\exposconcept{scalar}@ Scalar, @\exposconcept{in-vector}@ InVec, @\exposconcept{in-matrix}@ InMat, @\exposconcept{possibly-packed-out-matrix}@ OutMat,
            class Triangle>
     void hermitian_matrix_rank_1_update(Scalar alpha, InVec x, InMat E, OutMat A, Triangle t);
   template<class ExecutionPolicy,
-           class Scalar, @\exposconcept{in-vector}@ InVec, @\exposconcept{in-matrix}@ InMat, @\exposconcept{possibly-packed-out-matrix}@ OutMat,
+           @\exposconcept{scalar}@ Scalar, @\exposconcept{in-vector}@ InVec, @\exposconcept{in-matrix}@ InMat, @\exposconcept{possibly-packed-out-matrix}@ OutMat,
            class Triangle>
     void hermitian_matrix_rank_1_update(ExecutionPolicy&& exec,
                                         Scalar alpha, InVec x, InMat E, OutMat A, Triangle t);
@@ -11571,40 +11571,24 @@
                                         Scalar alpha, InMat A, OutMat C, Triangle t);
 
   // updating rank-k symmetric matrix update
-  template<class Scalar,
-           @\exposconcept{in-matrix}@ InMat1,
-           @\exposconcept{in-matrix}@ InMat2,
-           @\exposconcept{possibly-packed-out-matrix}@ OutMat,
-           class Triangle>
-    void symmetric_matrix_rank_k_update(
-      Scalar alpha,
-      InMat1 A, InMat2 E, OutMat C, Triangle t);
-  template<class ExecutionPolicy, class Scalar,
-           @\exposconcept{in-matrix}@ InMat1,
-           @\exposconcept{in-matrix}@ InMat2,
-           @\exposconcept{possibly-packed-out-matrix}@ OutMat,
-           class Triangle>
-    void symmetric_matrix_rank_k_update(
-      ExecutionPolicy&& exec, Scalar alpha,
-      InMat1 A, InMat2 E, OutMat C, Triangle t);
+  template<@\exposconcept{scalar}@ Scalar, @\exposconcept{in-matrix}@ InMat1, @\exposconcept{in-matrix}@ InMat2,
+           @\exposconcept{possibly-packed-out-matrix}@ OutMat, class Triangle>
+    void symmetric_matrix_rank_k_update(Scalar alpha, InMat1 A, InMat2 E, OutMat C, Triangle t);
+  template<class ExecutionPolicy,
+           @\exposconcept{scalar}@ Scalar, @\exposconcept{in-matrix}@ InMat1, @\exposconcept{in-matrix}@ InMat2,
+           @\exposconcept{possibly-packed-out-matrix}@ OutMat, class Triangle>
+    void symmetric_matrix_rank_k_update(ExecutionPolicy&& exec, Scalar alpha,
+                                        InMat1 A, InMat2 E, OutMat C, Triangle t);
 
   // updating rank-k Hermitian matrix update
-  template<class Scalar,
-           @\exposconcept{in-matrix}@ InMat1,
-           @\exposconcept{in-matrix}@ InMat2,
-           @\exposconcept{possibly-packed-out-matrix}@ OutMat,
-           class Triangle>
-    void hermitian_matrix_rank_k_update(
-      Scalar alpha,
-      InMat1 A, InMat2 E, OutMat C, Triangle t);
-  template<class ExecutionPolicy, class Scalar,
-           @\exposconcept{in-matrix}@ InMat1,
-           @\exposconcept{in-matrix}@ InMat2,
-           @\exposconcept{possibly-packed-out-matrix}@ OutMat,
-           class Triangle>
-    void hermitian_matrix_rank_k_update(
-      ExecutionPolicy&& exec, Scalar alpha,
-      InMat1 A, InMat2 E, OutMat C, Triangle t);
+  template<@\exposconcept{scalar}@ Scalar, @\exposconcept{in-matrix}@ InMat1, @\exposconcept{in-matrix}@ InMat2,
+           @\exposconcept{possibly-packed-out-matrix}@ OutMat, class Triangle>
+    void hermitian_matrix_rank_k_update(Scalar alpha, InMat1 A, InMat2 E, OutMat C, Triangle t);
+  template<class ExecutionPolicy,
+           @\exposconcept{scalar}@ Scalar, @\exposconcept{in-matrix}@ InMat1, @\exposconcept{in-matrix}@ InMat2,
+           @\exposconcept{possibly-packed-out-matrix}@ OutMat, class Triangle>
+    void hermitian_matrix_rank_k_update(ExecutionPolicy&& exec, Scalar alpha,
+                                        InMat1 A, InMat2 E, OutMat C, Triangle t);
 
   // \ref{linalg.algs.blas3.rank2k}, rank-2k update of a symmetric or Hermitian matrix
 
@@ -11629,25 +11613,21 @@
                                          InMat1 A, InMat2 B, OutMat C, Triangle t);
 
   // updating symmetric rank-2k matrix update
-  template<@\exposconcept{in-matrix}@ InMat1, @\exposconcept{in-matrix}@ InMat2,
-           @\exposconcept{in-matrix}@ InMat3,
+  template<@\exposconcept{in-matrix}@ InMat1, @\exposconcept{in-matrix}@ InMat2, @\exposconcept{in-matrix}@ InMat3,
            @\exposconcept{possibly-packed-out-matrix}@ OutMat, class Triangle>
     void symmetric_matrix_rank_2k_update(InMat1 A, InMat2 B, InMat3 E, OutMat C, Triangle t);
   template<class ExecutionPolicy,
-           @\exposconcept{in-matrix}@ InMat1, @\exposconcept{in-matrix}@ InMat2,
-           @\exposconcept{in-matrix}@ InMat3,
+           @\exposconcept{in-matrix}@ InMat1, @\exposconcept{in-matrix}@ InMat2, @\exposconcept{in-matrix}@ InMat3,
            @\exposconcept{possibly-packed-out-matrix}@ OutMat, class Triangle>
     void symmetric_matrix_rank_2k_update(ExecutionPolicy&& exec,
                                          InMat1 A, InMat2 B, InMat3 E, OutMat C, Triangle t);
 
   // updating Hermitian rank-2k matrix update
-  template<@\exposconcept{in-matrix}@ InMat1, @\exposconcept{in-matrix}@ InMat2,
-           @\exposconcept{in-matrix}@ InMat3,
+  template<@\exposconcept{in-matrix}@ InMat1, @\exposconcept{in-matrix}@ InMat2, @\exposconcept{in-matrix}@ InMat3,
            @\exposconcept{possibly-packed-out-matrix}@ OutMat, class Triangle>
     void hermitian_matrix_rank_2k_update(InMat1 A, InMat2 B, InMat3 E, OutMat C, Triangle t);
   template<class ExecutionPolicy,
-           @\exposconcept{in-matrix}@ InMat1, @\exposconcept{in-matrix}@ InMat2,
-           @\exposconcept{in-matrix}@ InMat3,
+           @\exposconcept{in-matrix}@ InMat1, @\exposconcept{in-matrix}@ InMat2, @\exposconcept{in-matrix}@ InMat3,
            @\exposconcept{possibly-packed-out-matrix}@ OutMat, class Triangle>
     void hermitian_matrix_rank_2k_update(ExecutionPolicy&& exec,
                                          InMat1 A, InMat2 B, InMat3 E, OutMat C, Triangle t);
@@ -12549,7 +12529,7 @@
 
 template<class T>
   concept @\defexposconcept{scalar}@ =
-    @\libconcept{semiregular}@<T> && (!@\exposconcept{is-mdspan}@<T>) && (!is_execution_policy_v<T>);
+    @\libconcept{semiregular}@<T> && (!@\exposid{is-mdspan}@<T>) && (!is_execution_policy_v<T>);
 \end{codeblock}
 
 \pnum
@@ -14929,10 +14909,10 @@
 \mandates
 \begin{itemize}
 \item
-\tcode{\exposconcept{possibly-multipliable}<OutMat, InVec2, InVec1>()}
+\tcode{\exposid{possibly-multipliable}<OutMat, InVec2, InVec1>()}
 is \tcode{true}, and
 \item
-\tcode{\exposconcept{possibly-addable}<OutMat, InMat, OutMat>()}
+\tcode{\exposid{possibly-addable}<OutMat, InMat, OutMat>()}
 is \tcode{true} for those overloads with an \tcode{E} parameter.
 \end{itemize}
 
@@ -15166,8 +15146,8 @@
 template<@\exposconcept{scalar}@ Scalar, @\exposconcept{in-vector}@ InVec, @\exposconcept{in-matrix}@ InMat, @\exposconcept{possibly-packed-out-matrix}@ OutMat,
          class Triangle>
   void symmetric_matrix_rank_1_update(Scalar alpha, InVec x, InMat E, OutMat A, Triangle t);
-template<class ExecutionPolicy,
-         @\exposconcept{scalar}@ Scalar, @\exposconcept{in-vector}@ InVec, @\exposconcept{in-matrix}@ InMat, @\exposconcept{possibly-packed-out-matrix}@ OutMat, class Triangle>
+template<class ExecutionPolicy, @\exposconcept{scalar}@ Scalar, @\exposconcept{in-vector}@ InVec, @\exposconcept{in-matrix}@ InMat,
+         @\exposconcept{possibly-packed-out-matrix}@ OutMat, class Triangle>
   void symmetric_matrix_rank_1_update(ExecutionPolicy&& exec,
                                       Scalar alpha, InVec x, InMat E, OutMat A, Triangle t);
 \end{itemdecl}
@@ -15225,13 +15205,14 @@
 \begin{itemdescr}
 \pnum
 These functions perform
-an updating Hermitian rank-1 update of the Hermitian matrix \tcode{E},
+an updating Hermitian rank-1 update of the Hermitian matrix \tcode{A}
+using the Hermitian matrix \tcode{E},
 taking into account the \tcode{Triangle} parameter
 that applies to \tcode{A} and \tcode{E}\iref{linalg.general}.
 
 \pnum
 \effects
-Computes a matrix $A = E + \alpha x x^H$,
+Computes $A = E + \alpha x x^H$,
 where the scalar $\alpha$ is \tcode{\exposid{real-if-needed}(alpha)}.
 
 \pnum
@@ -15256,15 +15237,19 @@
 an \tcode{InMat} template parameter, and
 a function parameter \tcode{InMat E},
 \tcode{t} applies to accesses done through the parameter \tcode{E}.
-\tcode{F} only accesses the triangle of \tcode{E} specified by \tcodee{t}.
+\tcode{F} only accesses the triangle of \tcode{E} specified by \tcode{t}.
 For accesses of diagonal elements \tcode{E[i, i]},
 \tcode{F} only uses the value \tcode{\exposid{real-if-needed}(E[i, i])}
 if the name of \tcode{F} starts with \tcode{hermitian}.
 For accesses \tcode{E[i, j]} outside the triangle specified by \tcode{t},
 \tcode{F} only uses the value
 \begin{itemize}
-\item \tcode{\exposid{conj-if-needed}(E[j, i])} if the name of F starts with hermitian, or
-\item \tcode{E[j, i]} if the name of F starts with symmetric.
+\item
+\tcode{\exposid{conj-if-needed}(E[j, i])}
+if the name of F starts with \tcode{hermitian}, or
+\item
+\tcode{E[j, i]}
+if the name of F starts with \tcode{symmetric}.
 \end{itemize}
 
 \pnum
@@ -15331,12 +15316,10 @@
 
 \indexlibraryglobal{symmetric_matrix_rank_2_update}%
 \begin{itemdecl}
-template<@\exposconcept{in-vector}@ InVec1, @\exposconcept{in-vector}@ InVec2,
-         @\exposconcept{in-matrix}@ InMat,
+template<@\exposconcept{in-vector}@ InVec1, @\exposconcept{in-vector}@ InVec2, @\exposconcept{in-matrix}@ InMat,
          @\exposconcept{possibly-packed-out-matrix}@ OutMat, class Triangle>
   void symmetric_matrix_rank_2_update(InVec1 x, InVec2 y, InMat E, OutMat A, Triangle t);
-template<class ExecutionPolicy, @\exposconcept{in-vector}@ InVec1, @\exposconcept{in-vector}@ InVec2,
-         @\exposconcept{in-matrix}@ InMat,
+template<class ExecutionPolicy, @\exposconcept{in-vector}@ InVec1, @\exposconcept{in-vector}@ InVec2, @\exposconcept{in-matrix}@ InMat,
          @\exposconcept{possibly-packed-out-matrix}@ OutMat, class Triangle>
   void symmetric_matrix_rank_2_update(ExecutionPolicy&& exec,
                                       InVec1 x, InVec2 y, InMat E, OutMat A, Triangle t);
@@ -15384,12 +15367,10 @@
 
 \indexlibraryglobal{hermitian_matrix_rank_2_update}%
 \begin{itemdecl}
-template<@\exposconcept{in-vector}@ InVec1, @\exposconcept{in-vector}@ InVec2,
-         @\exposconcept{in-matrix}@ InMat,
+template<@\exposconcept{in-vector}@ InVec1, @\exposconcept{in-vector}@ InVec2, @\exposconcept{in-matrix}@ InMat,
          @\exposconcept{possibly-packed-out-matrix}@ OutMat, class Triangle>
   void hermitian_matrix_rank_2_update(InVec1 x, InVec2 y, InMat E, OutMat A, Triangle t);
-template<class ExecutionPolicy, @\exposconcept{in-vector}@ InVec1, @\exposconcept{in-vector}@ InVec2,
-         @\exposconcept{in-matrix}@ InMat,
+template<class ExecutionPolicy, @\exposconcept{in-vector}@ InVec1, @\exposconcept{in-vector}@ InVec2, @\exposconcept{in-matrix}@ InMat,
          @\exposconcept{possibly-packed-out-matrix}@ OutMat, class Triangle>
   void hermitian_matrix_rank_2_update(ExecutionPolicy&& exec,
                                       InVec1 x, InVec2 y, InMat E, OutMat A, Triangle t);
@@ -15409,7 +15390,7 @@
 
 \pnum
 \remarks
-\tcode{A} my alias \tcode{E}.
+\tcode{A} may alias \tcode{E}.
 \end{itemdescr}
 
 \rSec2[linalg.algs.blas3]{BLAS 3 algorithms}
@@ -15904,7 +15885,7 @@
 \begin{itemize}
 \item
 \tcode{\exposid{multipliable}(A, transposed(A), C)}
-is \tcode{true};
+is \tcode{true}; and
 \begin{note}
 This implies that \tcode{C} is square.
 \end{note}
@@ -15958,10 +15939,10 @@
 
 \indexlibraryglobal{hermitian_matrix_rank_k_update}%
 \begin{itemdecl}
-template<class Scalar, @\exposconcept{in-matrix}@ InMat1, @\exposconcept{in-matrix}@ InMat2, @\exposconcept{possibly-packed-out-matrix}@ OutMat,
+template<@\exposconcept{scalar}@ Scalar, @\exposconcept{in-matrix}@ InMat1, @\exposconcept{in-matrix}@ InMat2, @\exposconcept{possibly-packed-out-matrix}@ OutMat,
          class Triangle>
 void hermitian_matrix_rank_k_update(Scalar alpha, InMat1 A, InMat2 E, OutMat C, Triangle t);
-template<class ExecutionPolicy, class Scalar, @\exposconcept{in-matrix}@ InMat1, @\exposconcept{in-matrix}@ InMat2,
+template<class ExecutionPolicy, @\exposconcept{scalar}@ Scalar, @\exposconcept{in-matrix}@ InMat1, @\exposconcept{in-matrix}@ InMat2,
          @\exposconcept{possibly-packed-out-matrix}@ OutMat, class Triangle>
 void hermitian_matrix_rank_k_update(ExecutionPolicy&& exec, Scalar alpha, InMat1 A, InMat2 E,
                                     OutMat C, Triangle t);
@@ -16091,30 +16072,13 @@
 
 \indexlibraryglobal{symmetric_matrix_rank_2k_update}%
 \begin{itemdecl}
-template<in-matrix InMat1,
-         in-matrix InMat2,
-         in-matrix InMat3,
-         possibly-packed-out-matrix OutMat,
-         class Triangle>
-void symmetric_matrix_rank_2k_update(
-  InMat1 A,
-  InMat2 B,
-  InMat3 E,
-  OutMat C,
-  Triangle t);
-template<class ExecutionPolicy,
-         in-matrix InMat1,
-         in-matrix InMat2,
-         in-matrix InMat3,
-         possibly-packed-out-matrix OutMat,
-         class Triangle>
-void symmetric_matrix_rank_2k_update(
-  ExecutionPolicy&& exec,
-  InMat1 A,
-  InMat2 B,
-  InMat3 E,
-  OutMat C,
-  Triangle t);
+template<@\exposconcept{in-matrix}@ InMat1, @\exposconcept{in-matrix}@ InMat2, @\exposconcept{in-matrix}@ InMat3,
+         @\exposconcept{possibly-packed-out-matrix}@ OutMat, class Triangle>
+void symmetric_matrix_rank_2k_update(InMat1 A, InMat2 B, InMat3 E, OutMat C, Triangle t);
+template<class ExecutionPolicy, @\exposconcept{in-matrix}@ InMat1, @\exposconcept{in-matrix}@ InMat2, @\exposconcept{in-matrix}@ InMat3,
+         @\exposconcept{possibly-packed-out-matrix}@ OutMat, class Triangle>
+void symmetric_matrix_rank_2k_update(ExecutionPolicy&& exec,
+                                     InMat1 A, InMat2 B, InMat3 E, OutMat C, Triangle t);
 \end{itemdecl}
 
 \begin{itemdescr}