/// <summary>Performs a Hermitian rank-2 update, i.e. C := \alpha*A*B^h + conjg(\alpha)*B*A^h + \beta * C or C := \alpha*B^h*A + conjg(\alpha)*A^h*B + beta*C, where C is an Hermitian matrix.
/// </summary>
/// <param name="n">The order of matrix C.</param>
/// <param name="k">The number of columns of matrix A if to calculate C := \alpha*A*B^h + conjg(\alpha)*B*A^h + \beta * C; the number of rows of the matrix A otherwise.</param>
/// <param name="alpha">The scalar \alpha.</param>
/// <param name="a">The matrix A supplied column-by-column of dimension (<paramref name="lda" />, ka), where ka equals to <paramref name="k" /> if to calculate C := \alpha*A*B^h + conjg(\alpha)*B*A^h + \beta * C; <paramref name="n" /> otherwise.</param>
/// <param name="b">The matrix B supplied column-by-column of dimension (<paramref name="ldb" />, kb), where kb equals to <paramref name="k" /> if to calculate C := \alpha*A*B^h + conjg(\alpha)*B*A^h + \beta * C; <paramref name="n" /> otherwise.</param>
/// <param name="beta">The scalar \beta.</param>
/// <param name="c">The Hermitian matrix C supplied column-by-column of dimension (<paramref name="ldc" />, <paramref name="n" />).</param>
/// <param name="lda">The leading dimension of <paramref name="a" />, must be at least max(1,<paramref name="n" />) if to calculate C := \alpha*A*B^h + conjg(\alpha)*B*A^h + \beta * C; max(1, <paramref name="k" />) otherwise.</param>
/// <param name="ldb">The leading dimension of <paramref name="b" />, must be at least max(1,<paramref name="n" />) if to calculate C := \alpha*A*B^h + conjg(\alpha)*B*A^h + \beta * C; max(1, <paramref name="k" />) otherwise.</param>
/// <param name="ldc">The leading dimension of <paramref name="c" />, must be at least max(1, <paramref name="n" />).</param>
/// <param name="triangularMatrixType">A value whether matrix C is in its upper or lower triangular representation.</param>
/// <param name="operation">A value indicating whether to calculate C := \alpha*A*B^h + conjg(\alpha)*B*A^h + \beta * C or C := \alpha*B^h*A + conjg(\alpha)*A^h*B + beta*C.</param>
public void zher2k(int n, int k, Complex alpha, Complex[] a, Complex[] b, double beta, Complex[] c, int lda, int ldb, int ldc, BLAS.TriangularMatrixType triangularMatrixType = BLAS.TriangularMatrixType.UpperTriangularMatrix, BLAS.Zher2kOperation operation = BLAS.Zher2kOperation.ATimesBHermitePlusBTimesAHermite)
{
if (n == 0 || ((alpha == 0.0 || k == 0) && (beta == 1.0)))
{
return; // nothing to do
}
if (operation == BLAS.Zher2kOperation.ATimesBHermitePlusBTimesAHermite) // C := \alpha * A*conjg(B') + conjg(\alpha) *B*conjg(A') + \beta * C
{
if (triangularMatrixType == BLAS.TriangularMatrixType.UpperTriangularMatrix)
{
for (int j = 0; j < n; j++)
{
for (int i = 0; i <= j - 1; i++)
{
c[i + j * ldc] *= beta;
}
c[j + j * ldc] = beta * c[j + j * ldc].Real;
for (int ell = 0; ell < k; ell++)
{
Complex temp = alpha * Complex.Conjugate(b[j + ell * ldb]);
Complex temp2 = Complex.Conjugate(alpha * a[j + ell * lda]);
for (int i = 0; i <= j - 1; i++)
{
c[i + j * ldc] += a[i + ell * lda] * temp + b[i + ell * ldb] * temp2;
}
c[j + j * ldc] += a[j + ell * lda] * temp + b[j + ell * ldb] * temp2;
}
}
}
else
{
for (int j = 0; j < n; j++)
{
for (int i = j + 1; i < n; i++)
{
c[i + j * ldc] *= beta;
}
c[j + j * ldc] = beta * c[j + j * ldc].Real;
for (int ell = 0; ell < k; ell++)
{
Complex temp = alpha * Complex.Conjugate(b[j + ell * ldb]);
Complex temp2 = Complex.Conjugate(alpha * a[j + ell * lda]);
for (int i = j + 1; i < n; i++)
{
c[i + j * ldc] += a[i + ell * lda] * temp + b[i + ell * ldb] * temp2;
}
c[j + j * ldc] += a[j + ell * lda] * temp + b[j + ell * ldb] * temp2;
}
}
}
}
else // C := \alpha * conjg(A')*B + conjg(\alpha) * conjg(B')*A + C
{
if (triangularMatrixType == BLAS.TriangularMatrixType.UpperTriangularMatrix)
{
for (int j = 0; j < n; j++)
{
for (int i = 0; i <= j; i++)
{
Complex temp = 0.0;
Complex temp2 = 0.0;
for (int ell = 0; ell < k; ell++)
{
temp += Complex.Conjugate(a[ell + i * lda]) * b[ell + j * ldb];
temp2 += Complex.Conjugate(b[ell + i * ldb]) * a[ell + j * lda];
}
if (i == j)
{
c[j + j * ldc] = (beta * c[j + j * ldc] + alpha * temp + Complex.Conjugate(alpha) * temp2).Real;
}
else
{
c[i + j * ldc] = beta * c[i + j * ldc] + alpha * temp + Complex.Conjugate(alpha) * temp2;
}
}
}
}
else
{
for (int j = 0; j < n; j++)
{
for (int i = j; i < n; i++)
{
Complex temp = 0.0;
Complex temp2 = 0.0;
for (int ell = 0; ell < k; ell++)
{
temp += Complex.Conjugate(a[ell + i * lda]) * b[ell + j * ldb];
temp2 += Complex.Conjugate(b[ell + i * ldb]) * a[ell + j * lda];
}
if (i == j)
{
c[j + j * ldc] = (beta * c[j + j * ldc] + alpha * temp + Complex.Conjugate(alpha) * temp2).Real;
}
else
{
c[i + j * ldc] = beta * c[i + j * ldc] + alpha * temp + Complex.Conjugate(alpha) * temp2;
}
}
}
}
}
}
/// <summary>Performs a Hermitian rank-2 update, i.e. C := \alpha*A*B^h + conjg(\alpha)*B*A^h + \beta * C or C := \alpha*B^h*A + conjg(\alpha)*A^h*B + beta*C, where C is an Hermitian matrix.
/// </summary>
/// <param name="level3">The BLAS level 3 implementation.</param>
/// <param name="n">The order of matrix C.</param>
/// <param name="k">The number of columns of matrix A if to calculate C := \alpha*A*B^h + conjg(\alpha)*B*A^h + \beta * C; the number of rows of the matrix A otherwise.</param>
/// <param name="alpha">The scalar \alpha.</param>
/// <param name="a">The matrix A supplied column-by-column of dimension (s, ka), where s must be at least max(1,<paramref name="n"/>) and ka equals to <paramref name="k"/> if to calculate C := \alpha*A*B^h + conjg(\alpha)*B*A^h + \beta * C; s = max(1, <paramref name="k"/>), ka = <paramref name="n"/> otherwise.</param>
/// <param name="b">The matrix B supplied column-by-column of dimension (s, kb), where s must be at least max(1,<paramref name="n"/>) and kb equals to <paramref name="k"/> if to calculate C := \alpha*A*B^h + conjg(\alpha)*B*A^h + \beta * C; s = max(1, <paramref name="k"/>), ka = <paramref name="n"/> otherwise.</param>
/// <param name="beta">The scalar \beta.</param>
/// <param name="c">The Hermitian matrix C supplied column-by-column of dimension (<paramref name="n"/>, <paramref name="n"/>).</param>
/// <param name="triangularMatrixType">A value whether matrix C is in its upper or lower triangular representation.</param>
/// <param name="operation">A value indicating whether to calculate C := \alpha*A*B^h + conjg(\alpha)*B*A^h + \beta * C or C := \alpha*B^h*A + conjg(\alpha)*A^h*B + beta*C.</param>
public static void zher2k(this ILevel3BLAS level3, int n, int k, Complex alpha, Complex[] a, Complex[] b, double beta, Complex[] c, BLAS.TriangularMatrixType triangularMatrixType = BLAS.TriangularMatrixType.UpperTriangularMatrix, BLAS.Zher2kOperation operation = BLAS.Zher2kOperation.ATimesBHermitePlusBTimesAHermite)
{
level3.zher2k(n, k, alpha, a, b, beta, c, operation == BLAS.Zher2kOperation.ATimesBHermitePlusBTimesAHermite ? n : k, operation == BLAS.Zher2kOperation.ATimesBHermitePlusBTimesAHermite ? n : k, n, triangularMatrixType, operation);
}