/// <summary>
/// Computes the product of square metrices X = AB
/// </summary>
/// <param name="A">The left matrix</param>
/// <param name="B">The right matrix</param>
/// <param name="X">The target matrix</param>
/// <param name="N">The number of columns in B and C</param>
public static ref Matrix256 <N, double> gemm <N>(Matrix256 <N, double> A, Matrix256 <N, double> B, ref Matrix256 <N, double> X)
where N : unmanaged, ITypeNat
{
var n = nat32i <N>();
var ld = n;
CBLAS.cblas_dgemm(RowMajor, NoTranspose, NoTranspose, n, n, n, 1, ref head(A), ld, ref head(B), ld, 0, ref head(X), ld);
return(ref X);
}
/// <summary>
/// Computes the product of square metrices X = AB
/// </summary>
/// <param name="A">The left matrix</param>
/// <param name="B">The right matrix</param>
/// <param name="X">The target matrix</param>
/// <param name="N">The number of columns in B and C</param>
public static ref BlockMatrix <N, double> gemm <N>(BlockMatrix <N, double> A, BlockMatrix <N, double> B, ref BlockMatrix <N, double> X)
where N : ITypeNat, new()
{
var n = nati <N>();
var ld = n;
CBLAS.cblas_dgemm(RowMajor, NoTranspose, NoTranspose, n, n, n, 1, ref head(A), ld, ref head(B), ld, 0, ref head(X), ld);
return(ref X);
}
/// <summary>
/// Computes the matrix-vector product y = A*x;
/// </summary>
/// <param name="A">A source matrix of dimension MxN</param>
/// <param name="x">A source vector of length N</param>
/// <param name="y">A target vector of length M</param>
/// <typeparam name="M">The row dimension type of A</typeparam>
/// <typeparam name="N">The column dimension type of A</typeparam>
public static ref Block256 <M, float> gemv <M, N>(Matrix256 <M, N, float> A, Block256 <N, float> x, ref Block256 <M, float> y)
where M : unmanaged, ITypeNat
where N : unmanaged, ITypeNat
{
var m = nat32i <M>();
var n = nat32i <N>();
var lda = n;
CBLAS.cblas_sgemv(RowMajor, NoTranspose, m, n, alpha: 1f, ref head(A), lda, ref head(x), incX: 1, beta: 0, ref head(y), incY: 1);
return(ref y);
}
/// <summary>
/// Computes the matrix-vector product y = A*x;
/// </summary>
/// <param name="A">A source matrix of dimension MxN</param>
/// <param name="x">A source vector of length N</param>
/// <param name="y">A target vector of length M</param>
/// <typeparam name="M">The row dimension type of A</typeparam>
/// <typeparam name="N">The column dimension type of A</typeparam>
public static ref BlockVector <M, float> gemv <M, N>(BlockMatrix <M, N, float> A, BlockVector <N, float> x, ref BlockVector <M, float> y)
where M : ITypeNat, new()
where N : ITypeNat, new()
{
var m = nati <M>();
var n = nati <N>();
var lda = n;
CBLAS.cblas_sgemv(RowMajor, NoTranspose, m, n, alpha: 1f, ref head(A), lda, ref head(x), incX: 1, beta: 0, ref head(y), incY: 1);
return(ref y);
}
/// <summary>
/// Populates a target matrix with the product of the operands
/// </summary>
/// <param name="A">The left matrix</param>
/// <param name="B">The right matrix</param>
/// <param name="M">The number of rows in A and C</param>
/// <param name="N">The number of columns in B and C</param>
/// <param name="K">The number of columns in A and rows in B</param>
public static ref BlockMatrix <M, N, double> gemm <M, K, N>(BlockMatrix <M, K, double> A, BlockMatrix <K, N, double> B, ref BlockMatrix <M, N, double> X)
where M : ITypeNat, new()
where K : ITypeNat, new()
where N : ITypeNat, new()
{
var m = nati <M>();
var k = nati <K>();
var n = nati <N>();
var lda = k;
var ldb = n;
var ldx = n;
CBLAS.cblas_dgemm(RowMajor, NoTranspose, NoTranspose, m, n, k, 1d, ref head(A), lda, ref head(B), ldb, 0, ref head(X), ldx);
return(ref X);
}
/// <summary>
/// Populates a target matrix with the product of the operands
/// </summary>
/// <param name="A">The left matrix</param>
/// <param name="B">The right matrix</param>
/// <param name="M">The number of rows in A and C</param>
/// <param name="N">The number of columns in B and C</param>
/// <param name="K">The number of columns in A and rows in B</param>
public static ref Matrix256 <M, N, double> gemm <M, K, N>(Matrix256 <M, K, double> A, Matrix256 <K, N, double> B, ref Matrix256 <M, N, double> X)
where M : unmanaged, ITypeNat
where K : unmanaged, ITypeNat
where N : unmanaged, ITypeNat
{
var m = nat32i <M>();
var k = nat32i <K>();
var n = nat32i <N>();
var lda = k;
var ldb = n;
var ldx = n;
CBLAS.cblas_dgemm(RowMajor, NoTranspose, NoTranspose, m, n, k, 1d, ref head(A), lda, ref head(B), ldb, 0, ref head(X), ldx);
return(ref X);
}
/// <summary>
/// Allocates a target matrix and populates it with the product of the operands
/// </summary>
/// <param name="A">The left matrix</param>
/// <param name="B">The right matrix</param>
/// <param name="M">The number of rows in A and C</param>
/// <param name="N">The number of columns in B and C</param>
/// <param name="K">The number of columns in A and rows in B</param>
public static Matrix256 <M, N, float> gemm <M, K, N>(Matrix256 <M, K, float> A, Matrix256 <K, N, float> B)
where M : unmanaged, ITypeNat
where K : unmanaged, ITypeNat
where N : unmanaged, ITypeNat
{
var m = nat32i <M>();
var k = nat32i <K>();
var n = nat32i <N>();
var lda = k;
var ldb = n;
var ldx = n;
var X = Matrix.blockalloc <M, N, float>();
CBLAS.cblas_sgemm(RowMajor, NoTranspose, NoTranspose, m, n, k, 1.0f, ref head(A), lda, ref head(B), ldb, 0, ref head(X), ldx);
return(X);
}
/// <summary>
/// Allocates a target matrix and populates it with the product of the operands
/// </summary>
/// <param name="A">The left matrix</param>
/// <param name="B">The right matrix</param>
/// <param name="M">The number of rows in A and C</param>
/// <param name="N">The number of columns in B and C</param>
/// <param name="K">The number of columns in A and rows in B</param>
public static BlockMatrix <M, N, float> gemm <M, K, N>(BlockMatrix <M, K, float> A, BlockMatrix <K, N, float> B)
where M : ITypeNat, new()
where K : ITypeNat, new()
where N : ITypeNat, new()
{
var m = nati <M>();
var k = nati <K>();
var n = nati <N>();
var lda = k;
var ldb = n;
var ldx = n;
var X = BlockMatrix.Alloc <M, N, float>();
CBLAS.cblas_sgemm(RowMajor, NoTranspose, NoTranspose, m, n, k, 1.0f, ref head(A), lda, ref head(B), ldb, 0, ref head(X), ldx);
return(X);
}
public static void sasum()
{
var silent = true;
(var method, var msg) = intro(silent);
var n = 10;
var incx = 1;
var x = floats(1.0, -2.0, 3.0, 4.0, -5.0, 6.0, -7.0, 8.0, -9.0, 10.0);
input(x.FormatVector());
var sw = stopwatch();
var result = CBLAS.cblas_sasum(n, ref x[0], incx);
var time = snapshot(sw);
msg += output(result, silent);
msg += eol();
msg += conclude(time, silent);
}
public static void sasum()
{
var silent = true;
(var method, var msg) = intro(silent);
var n = 10;
var incx = 1;
Span <float> x = new float[] { 1.0f, -2.0f, 3.0f, 4.0f, -5.0f, 6.0f, -7.0f, 8.0f, -9.0f, 10.0f };
input(x.FormatVector());
var sw = Time.stopwatch();
var result = CBLAS.cblas_sasum(n, ref x[0], incx);
var ss = snap(sw);
msg += output(result, silent);
msg += Eol;
msg += conclude(ss, silent);
}
public static void saxpy()
{
(var method, var msg) = intro();
var n = 5;
var incx = 1;
var incy = 1;
var alpha = .5f;
Span <float> x = new float[] { 1, 2, 3, 4, 5 };
Span <float> y = new float[] { .5f, .5f, .5f, .5f, .5f };
input($"alpha={alpha}, x = {x.FormatVector()}, y = {y.FormatVector()}");
var sw = Time.stopwatch();
CBLAS.cblas_saxpy(n, alpha, ref x[0], incx, ref y[0], incy);
var ss = snap(sw);
output(y.FormatVector());
conclude(ss);
}
public static void saxpy()
{
(var method, var msg) = intro();
var n = 5;
var incx = 1;
var incy = 1;
var alpha = .5f;
var x = floats(1, 2, 3, 4, 5);
var y = floats(.5, .5, .5, .5, .5);
input($"alpha={alpha}, x = {x.FormatVector()}, y = {y.FormatVector()}");
var sw = stopwatch();
CBLAS.cblas_saxpy(n, alpha, ref x[0], incx, ref y[0], incy);
var time = snapshot(sw);
output(y.FormatVector());
conclude(time);
}
public static void dzasum()
{
var silent = true;
(var method, var msg) = intro(silent);
var n = 4;
var incx = 1;
var x = ComplexF64.Load(doubles(1.2, 2.5, 3.0, 1.7, 4.0, 0.53, -5.5, -0.29));
msg += input(x.FormatVector(), silent);
var expect = x.Map(z => Math.Abs(z.re) + Math.Abs(z.im)).Reduce((a, b) => a + b);
expected(expect);
var time = start();
var result = CBLAS.cblas_dzasum(n, ref x[0], incx);
output("result", result, snapshot(time));
}
public static void axpy <N>(float a, BlockVector <N, float> X, BlockVector <N, float> Y, ref BlockVector <N, float> Z)
where N : ITypeNat, new()
{
Y.CopyTo(ref Z);
CBLAS.cblas_saxpy(nati <N>(), a, ref head(X), 1, ref head(Z), 1);
}
static double asum(Span <ComplexF64> X) => CBLAS.cblas_dzasum(X.Length, ref X[0], 1);
static float asum(Span <ComplexF32> X) => CBLAS.cblas_scasum(X.Length, ref X[0], 1);
public static double asum(BlockVector <double> X) => CBLAS.cblas_dasum(X.Length, ref head(X), 1);
static double dot(Span <double> X, Span <double> Y) => CBLAS.cblas_ddot(length(X, Y), ref head(X), 1, ref head(Y), 1);
static float dot(Span <float> X, Span <float> Y) => CBLAS.cblas_sdot(length(X, Y), ref head(X), 1, ref head(Y), 1);
public static void axpy(double a, BlockVector <double> X, BlockVector <double> Y, ref BlockVector <double> Z)
{
Y.CopyTo(ref Z);
CBLAS.cblas_daxpy(length(X, Y), a, ref head(X), 1, ref head(Z), 1);
}
static float norm(Span <ComplexF32> X) => CBLAS.cblas_scnrm2(X.Length, ref head(X), 1);
public static double norm(BlockVector <double> X) => CBLAS.cblas_dnrm2(X.Length, ref head(X), 1);
public static float norm(BlockVector <float> X) => CBLAS.cblas_snrm2(X.Length, ref head(X), 1);
public static int iamin(RowVector256 <double> X) => (int)CBLAS.cblas_idamin(X.Length, ref head(X), 1);
public static int iamin(RowVector256 <float> X) => (int)CBLAS.cblas_isamin(X.Length, ref head(X), 1);
public static void axpy(float a, BlockVector <float> X, BlockVector <float> Y, ref BlockVector <float> Z)
{
Y.CopyTo(ref Z);
CBLAS.cblas_saxpy(length(X, Y), a, ref head(X), 1, ref head(Z), 1);
}
public static int iamin(BlockVector <float> X) => (int)CBLAS.cblas_isamin(X.Length, ref head(X), 1);
static double norm(Span <ComplexF64> X) => CBLAS.cblas_dznrm2(X.Length, ref head(X), 1);
public static int iamin(BlockVector <double> X) => (int)CBLAS.cblas_idamin(X.Length, ref head(X), 1);