Swift BLAS cblas_cgemv复数

Question

在所有值都是实值的情况下，我一直能够使用cblas_sgemv。但是，如果没有“cblas_cgemv”错误，我就不能使用EXC_BAD_ACCESS。对于这个函数，我是否正确地假设，复杂部分直接出现在函数作为参数的数组中的真实部分之后？例如，如果我有一个矩阵：

1 + 2i, 3 + 4i
5 + 6i, 7 + 8i

然后表示为1.0,2.0,3.0,4.0,5.0,6.0,7.0,8.0。对于任何给定的矩阵和向量，关于它在数组中的表示，N，M，lda，incX和incY应该有什么值？

完整的示例:对于cblas_sgemv，函数原型是：

func cblas_sgemv(_ __Order: CBLAS_ORDER, _ __TransA: CBLAS_TRANSPOSE, _ __M: Int32, _ __N: Int32, _ __alpha: Float, _ __A: UnsafePointer<Float>, _ __lda: Int32, _ __X: UnsafePointer<Float>, _ __incX: Int32, _ __beta: Float, _ __Y: UnsafeMutablePointer<Float>, _ __incY: Int32)

此代码适用于：

let matrix: [Float] = [1.0,2.0,3.0,4.0]
let vector: [Float] = [1.0,2.0]
let matrixConverted: UnsafePointer<Float> = UnsafePointer<Float>(matrix)
let vectorConverted: UnsafePointer<Float> = UnsafePointer<Float>(vector)
let matrixSize = sqrt(Double(matrix.count)
let total: [Float] = [Float](count: Int(matrixSize), repeatedValue: 0.0)
let totalConverted: UnsafeMutablePointer<Float> = UnsafeMutablePointer<Float>(total)
cblas_sgemv(CblasRowMajor, CblasNoTrans, Int32(matrixSize), Int32(matrixSize), 1.0, matrixConverted, Int32(matrixSize), vectorConverted, 1, 0, totalConverted, 1)

答案全部存储在一起。那么，除了上面的复杂矩阵和带有prototype的函数cblas_cgemv，做同样的事情会是什么样子：

func cblas_cgemv(_ __Order: CBLAS_ORDER, _ __TransA: CBLAS_TRANSPOSE, _ __M: Int32, _ __N: Int32, _ __alpha: UnsafePointer<Void>, _ __A: UnsafePointer<Void>, _ __lda: Int32, _ __X: UnsafePointer<Void>, _ __incX: Int32, _ __beta: UnsafePointer<Void>, _ __Y: UnsafeMutablePointer<Void>, _ __incY: Int32) 

更多的信息和参考可以在这里找到：ref/doc/uid/TP30000414-SW55

Answer 1

您的现有代码有点过于复杂，并且有一个错误：

• 输入矩阵和向量可以直接传递给cblas_sgemv()函数，不需要matrixConverted和vectorConverted。
• 不允许创建指向常量数组total的可变指针。结果向量必须是可变的(而且也不需要totalConverted )。

因此，您的代码可以简化为：

let matrix: [Float] = [1.0,2.0,3.0,4.0]
let vector: [Float] = [1.0,2.0]

let matrixSize = sqrt(Double(matrix.count))
var total = [Float](count: Int(matrixSize), repeatedValue: 0.0)

cblas_sgemv(CblasRowMajor, CblasNoTrans, Int32(matrixSize), Int32(matrixSize), 1.0, matrix, Int32(matrixSize), vector, 1, 0, &total, 1)

<cblas.h>中记录了BLAS例程中复数的布局。

 * A note on complex data layouts:
 *
 * In order to allow straightforward interoperation with other libraries and
 * complex types in C and C++, complex data in BLAS is passed through an opaque
 * pointer (void *).  The layout requirements on this complex data are that
 * the real and imaginary parts are stored consecutively in memory, and have
 * the alignment of the corresponding real type (float or double).  The BLAS
 * complex interfaces are compatible with the following types:
 *
 *     - The C complex types, defined in <complex.h>.
 *     - The C++ std::complex types, defined in <complex>.
 *     - The LAPACK complex types, defined in <Accelerate/vecLib/clapack.h>.
 *     - The vDSP types DSPComplex and DSPDoubleComplex, defined in <Accelerate/vecLib/vDSP.h>.
 *     - An array of size two of the corresponding real type.
 *     - A structure containing two elements, each of the corresponding real type.

因此，要乘

| 1 + 2i  3 + 4i |    | 1 + 2i |
|                |  * |        |
| 5 + 6i  7 + 8i |    | 3 + 4i |

您可以将每个复数表示为连续存储的两个浮点数：

let matrix: [Float] = [1.0,2.0, 3.0,4.0, 5.0,6.0, 7.0,8.0]
let vector: [Float] = [1.0,2.0, 3.0,4.0]

let matrixSize = sqrt(Double(matrix.count/2))
var total = [Float](count: vector.count, repeatedValue: 0.0)

let alpha : [Float] = [1.0, 0.0]
let beta : [Float] = [1.0, 0.0]

cblas_cgemv(CblasRowMajor, CblasNoTrans, Int32(matrixSize), Int32(matrixSize), beta, matrix, Int32(matrixSize), vector, 1, alpha, &total, 1)

也可以使用DSPComplex、COMPLEX或__CLPK_complex结构(它们都具有相同的布局)来表示复数：

let matrix = [DSPComplex(real: 1.0, imag: 2.0), DSPComplex(real: 3.0, imag: 4.0),
              DSPComplex(real: 5.0, imag: 6.0), DSPComplex(real: 7.0, imag: 8.0)]

let vector = [DSPComplex(real: 1.0, imag: 2.0), DSPComplex(real: 3.0, imag: 4.0)]

let matrixSize = sqrt(Double(matrix.count))
var total  =  [DSPComplex](count: Int(matrixSize), repeatedValue: DSPComplex())

var alpha = [DSPComplex(real: 1.0, imag: 0.0)]
var beta  = [DSPComplex(real: 1.0, imag: 0.0)]

cblas_cgemv(CblasRowMajor, CblasNoTrans, Int32(matrixSize), Int32(matrixSize), alpha, matrix, Int32(matrixSize), vector, 1, beta, &total, 1)

在这两种情况下，维度M、N等都是指复数的计数，因此它们与实数示例中的值M=N=2相同，而alpha和beta也是表示复杂因子的数组。