模板函数重载和 SFINAE 实现

首先，一些改进可以简化设计并提高可读性：

• biggest_dim.std::max自 C++14 年以来一直是 constexpr。您应该改用它。

不需要

• b_array_t.你可以写std::array< REAL_T, std::max(N1, N2)>

现在谈谈你的问题。C++17 中的一个好方法是：

template < typename REAL_T, std::size_t N1, std::size_t N2, std::size_t N3>
void solve(std::array< REAL_T, N1 * N2 > & A, std::array< REAL_T, N3> & b) {
if constexpr (N3 == std::max(N1, N2))
wrap::internal< N1, N2, N3 >(A, b);
else
static_assert(N3 == std::max(N1, N2), "invalid 3rd dimension");
// don't write static_assert(false)
// this would make the program ill-formed (*)
} 

或者，正如@max66所指出的

template < typename REAL_T, std::size_t N1, std::size_t N2, std::size_t N3>
void solve(std::array< REAL_T, N1 * N2 > & A, std::array< REAL_T, N3> & b) {
static_assert(N3 == std::max(N1, N2), "invalid 3rd dimension");
if constexpr (N3 == std::max(N1, N2))
wrap::internal< N1, N2, N3 >(A, b);
} 

哒！！简单，优雅，漂亮的错误消息。

constexpr if 版本和只是一个static_assert之间的区别，即：

void solve(...)
{
static_assert(...);
wrap::internal(...);
}

就是编译器即使失败static_assert也会尝试实例化wrap::internalstatic_assert，从而污染错误输出。使用 constexpr 如果对wrap::internal的调用不是正文的一部分，则条件失败，因此错误输出是干净的。

(*) 我之所以没有写static_asert(false, "error msg)，是因为这将使程序格式不正确，不需要诊断。参见 constexpr if 和 static_assert

如果需要，您还可以通过将模板参数移动到不可扣除参数之后来使float/double可扣除：

template < std::size_t N1, std::size_t N2, std::size_t N3,  typename REAL_T>
void solve(std::array< REAL_T, N1 * N2 > & A, std::array< REAL_T, N3> & b) {

因此，调用变为：

solve< n1_3, n2_3>(A_3, b_3);

你为什么不尝试将标签调度与一些static_assert结合起来呢？我希望以下是实现您想要解决的问题的一种方法。我的意思是，所有三个正确的案例都正确地管道到正确的blas调用，处理不同类型和维度不匹配，并且还处理了关于float和doubles 的违规行为，所有这些都以用户友好的方式处理，这要归功于static_assert.

我不确定您的C++版本要求，但以下是C++11友好的。

#include <algorithm>
#include <iostream>
#include <type_traits>
template <class value_t, int nrows, int ncols> struct Matrix {};
template <class value_t, int rows> struct Vector {};
template <class value_t> struct blas;
template <> struct blas<float> {
static void overdet(...) { std::cout << __PRETTY_FUNCTION__ << std::endl; }
static void underdet(...) { std::cout << __PRETTY_FUNCTION__ << std::endl; }
static void normal(...) { std::cout << __PRETTY_FUNCTION__ << std::endl; }
};
template <> struct blas<double> {
static void overdet(...) { std::cout << __PRETTY_FUNCTION__ << std::endl; }
static void underdet(...) { std::cout << __PRETTY_FUNCTION__ << std::endl; }
static void normal(...) { std::cout << __PRETTY_FUNCTION__ << std::endl; }
};
class overdet {};
class underdet {};
class normal {};
template <class T1, class T2, int nrows, int ncols, int dim>
void solve(const Matrix<T1, nrows, ncols> &lhs, Vector<T2, dim> &rhs) {
static_assert(std::is_same<T1, T2>::value,
"lhs and rhs must have the same value types");
static_assert(dim >= nrows && dim >= ncols,
"rhs does not have enough space");
static_assert(std::is_same<T1, float>::value ||
std::is_same<T1, double>::value,
"Only float or double are accepted");
solve_impl(lhs, rhs,
typename std::conditional<(nrows < ncols), underdet,
typename std::conditional<(nrows > ncols), overdet,
normal>::type>::type{});
}
template <class value_t, int nrows, int ncols, int dim>
void solve_impl(const Matrix<value_t, nrows, ncols> &lhs,
Vector<value_t, dim> &rhs, underdet) {
/* get the pointers and dimension information from lhs and rhs */
blas<value_t>::underdet(
/* trans, m, n, nrhs, A, lda, B, ldb, work, lwork, info */);
}
template <class value_t, int nrows, int ncols, int dim>
void solve_impl(const Matrix<value_t, nrows, ncols> &lhs,
Vector<value_t, dim> &rhs, overdet) {
/* get the pointers and dimension information from lhs and rhs */
blas<value_t>::overdet(
/* trans, m, n, nrhs, A, lda, B, ldb, work, lwork, info */);
}
template <class value_t, int nrows, int ncols, int dim>
void solve_impl(const Matrix<value_t, nrows, ncols> &lhs,
Vector<value_t, dim> &rhs, normal) {
/* get the pointers and dimension information from lhs and rhs */
blas<value_t>::normal(
/* trans, m, n, nrhs, A, lda, B, ldb, work, lwork, info */);
}
int main() {
/* valid types */
Matrix<float, 2, 4> A1;
Matrix<float, 4, 4> A2;
Matrix<float, 5, 4> A3;
Vector<float, 4> b1;
Vector<float, 5> b2;
solve(A1, b1);
solve(A2, b1);
solve(A3, b2);
Matrix<int, 4, 4> A4;
Vector<int, 4> b3;
// solve(A4, b3); // static_assert for float & double
Matrix<float, 4, 4> A5;
Vector<int, 4> b4;
// solve(A5, b4); // static_assert for different types
// solve(A3, b1); // static_assert for dimension problem
return 0;
}

<</div> div class="answers">你必须考虑为什么接口提供这种(复杂的)混乱的参数。作者想到了几件事。首先，您可以在一个函数中解决形式A x + b == 0和A^T x + b == 0的问题。其次，给定的A和b实际上可以指向大于 alg 所需矩阵中的内存。这可以通过LDA和LDB参数看到。

正是子寻址使事情变得复杂。如果你想要一个简单但可能足够有用的API，你可以选择忽略该部分：

using ::std::size_t;
using ::std::array;
template<typename T, size_t rows, size_t cols>
using matrix = array<T, rows * cols>;
enum class TransposeMode : bool {
None = false, Transposed = true
};
// See https://stackoverflow.com/questions/14637356/
template<typename T> struct always_false_t : std::false_type {};
template<typename T> constexpr bool always_false_v = always_false_t<T>::value;
template < typename T, size_t rowsA, size_t colsA, size_t rowsB, size_t colsB
, TransposeMode mode = TransposeMode::None >
void solve(matrix<T, rowsA, colsA>& A, matrix<T, rowsB, colsB>& B)
{
// Since the algorithm works in place, b needs to be able to store
// both input and output
static_assert(rowsB >= rowsA && rowsB >= colsA, "b is too small");
// LDA = rowsA, LDB = rowsB
if constexpr (::std::is_same_v<T, float>) {
// SGELS(mode == TransposeMode::None ? 'N' : 'T', ....);
} else if constexpr (::std::is_same_v<T, double>) {
// DGELS(mode == TransposeMode::None ? 'N' : 'T', ....);
} else {
static_assert(always_false_v<T>, "Unknown type");
}
}

现在，用LDA和LDB解决可能的子寻址。我建议你把这部分作为数据类型的一部分，而不是直接成为模板签名的一部分。您希望拥有自己的矩阵类型，该类型可以引用矩阵中的存储。也许是这样的：

// Since we store elements in a column-major order, we can always 
// pretend that our matrix has less columns than it actually has
// less rows than allocated. We can not equally pretend less rows
// otherwise the addressing into the array is off.
// Thus, we'd only four total parameters:
// offset = columnSkipped * actualRows + rowSkipped), actualRows, rows, cols
// We store the offset implicitly by adjusting our begin pointer
template<typename T, size_t rows, size_t cols, size_t actualRows>
class matrix_view { // Name derived from string_view :)
static_assert(actualRows >= rows);
T* start;
matrix_view(T* start) : start(start) {}
template<typename U, size_t r, size_t c, size_t ac>
friend class matrix_view;
public:
template<typename U>
matrix_view(matrix<U, rows, cols>& ref)
: start(ref.data()) { }
template<size_t rowSkipped, size_t colSkipped, size_t newRows, size_t newCols>
auto submat() {
static_assert(colSkipped + newCols <= cols, "can only shrink");
static_assert(rowSkipped + newRows <= rows, "can only shrink");
auto newStart = start + colSkipped * actualRows + rowSkipped;
using newType = matrix_view<T, newRows, newCols, actualRows>
return newType{ newStart };
}
T* data() {
return start;
}
};

现在，您需要使接口适应这种新数据类型，这基本上只是引入了一些新参数。检查基本保持不变。

// Using this instead of just type-defing allows us to use deducation guides
// Replaces: using matrix = std::array from above
template<typename T, size_t rows, size_t cols>
class matrix {
public:
std::array<T, rows * cols> storage;
auto data() { return storage.data(); }
auto data() const { return storage.data(); }
};
extern void dgels(char TRANS
, integer M, integer N , integer NRHS
, double* A, integer LDA
, double* B, integer LDB); // Mock, missing a few parameters at the end
// Replaces the solve method from above
template < typename T, size_t rowsA, size_t colsA, size_t actualRowsA
, size_t rowsB, size_t colsB, size_t actualRowsB
, TransposeMode mode = TransposeMode::None >
void solve(matrix_view<T, rowsA, colsA, actualRowsA> A, matrix_view<T, rowsB, colsB, actualRowsB> B)
{
static_assert(rowsB >= rowsA && rowsB >= colsA, "b is too small");
char transMode = mode == TransposeMode::None ? 'N' : 'T';
// LDA = rowsA, LDB = rowsB
if constexpr (::std::is_same_v<T, float>) {
fgels(transMode, rowsA, colsA, colsB, A.data(), actualRowsA, B.data(), actualRowsB);
} else if constexpr (::std::is_same_v<T, double>) {
dgels(transMode, rowsA, colsA, colsB, A.data(), actualRowsA, B.data(), actualRowsB);
// DGELS(, ....);
} else {
static_assert(always_false_v<T>, "Unknown type");
}
}

用法示例：

int main() {
matrix<float, 5, 5> A;
matrix<float, 4, 1> b;
auto viewA = matrix_view{A}.submat<1, 1, 4, 4>();
auto viewb = matrix_view{b};
solve(viewA, viewb);
// solve(viewA, viewb.submat<1, 0, 2, 1>()); // Error: b is too small
// solve(matrix_view{A}, viewb.submat<0, 0, 5, 1>()); // Error: can only shrink (b is 4x1 and can not be viewed as 5x1)
}