internal void Dpotrs(StoredTriangle triangle, int orderA, int numRhs, double[] factorizedMatrixA, int offsetA,
int leadingDimA, double[] rhsB, int offsetB, int leadingDimB)
{
int info = DefaultInfo;
Provider.Dpotrs(triangle.Translate(), orderA, numRhs, factorizedMatrixA, offsetA, leadingDimA,
rhsB, offsetB, leadingDimB, ref info);
if (info < 0) // info can only be 0 or negative
{
// The indices of negative pivots must take into account the offset parameters
if (info == -5)
{
info = -6;
}
else if (info == -6)
{
info = -7;
}
else if (info == -7)
{
info = -9;
}
ProcessNegativeInfo(info);
}
}
/// <summary>
/// If the return value is a non-negative int i, then the entry (i, i) of the factor U or L is 0 and the inverse could
/// not be computed.
/// </summary>
internal int Dpotri(StoredTriangle triangle, int orderA, double[] factorizedMatrixA, int offsetA, int leadingDimA)
{
int info = DefaultInfo;
Provider.Dpotri(triangle.Translate(), orderA, factorizedMatrixA, offsetA, leadingDimA, ref info);
if (info < 0)
{
// The indices of negative pivots must take into account the offset parameters
if (info == -4)
{
info = -5;
}
ProcessNegativeInfo(info);
}
//TODO: is there the same problem as LU, i.e. can the last minor not be positive definite, while the info = 0?
if (info > 0)
{
return(info - 1);
}
else
{
return(int.MinValue);
}
}
public void Dspmv(StoredTriangle uplo, int n,
double alpha, double[] a, int offsetA, double[] x, int offsetX, int incX,
double beta, double[] y, int offsetY, int incY)
{
// y = alpha * L * x + beta * y
CblasLevel2Implementations.LowerTimesVectorPackedRowMajor(
CblasLevel2Implementations.Diagonal.Regular, n, alpha, a, offsetA, x, offsetX, incX, beta, y, offsetY, incY);
// y = alpha * U * x + y, where U has 0 diagonal
CblasLevel2Implementations.UpperTimesVectorPackedColMajor(
CblasLevel2Implementations.Diagonal.Zero, n, alpha, a, offsetA, x, offsetX, incX, 1.0, y, offsetY, incY);
}
public void Dtpsv(StoredTriangle uplo, TransposeMatrix transA, DiagonalValues diag, int n,
double[] a, int offsetA, double[] x, int offsetX, int incX)
{
bool unit = (diag == DiagonalValues.Unit) ? true : false;
if (UseUpperImplementation(uplo, transA))
{
CblasLevel2Implementations.BackSubstitutionPackedColMajor(unit, n, a, offsetA, x, offsetX, incX);
}
else
{
CblasLevel2Implementations.ForwardSubstitutionPackedRowMajor(unit, n, a, offsetA, x, offsetX, incX);
}
}
internal void Dsyev(EigensystemJob job, StoredTriangle triangle, int orderA, double[] matrixA, int offsetA,
int leadingDimA, double[] eigenvalues, int offsetEigenvalues)
{
int info = DefaultInfo;
QueryWorkspaceAndExecute((work, offsetWork, lWork) => Provider.Dsyev(
job.Translate(), triangle.Translate(), orderA, ref matrixA, offsetA, leadingDimA, ref eigenvalues,
offsetEigenvalues, ref work, offsetWork, lWork, ref info));
if (info > 0)
{
throw new LapackException($"The algorithm failed to converge. There were {info} elements of an intermediate"
+ " tridiagonal form which did not converge to zero");
}
else if (info < 0)
{
ProcessNegativeInfo(info);
}
}
public void Dtpmv(StoredTriangle uplo, TransposeMatrix transA, DiagonalValues diag, int n,
double[] a, int offsetA, double[] x, int offsetX, int incX)
{
// The copy may be avoidable in trangular operations, if we start the dot products from the bottom
var input = new double[x.Length];
Array.Copy(x, input, x.Length);
CblasLevel2Implementations.Diagonal managedDiag = (diag == DiagonalValues.NonUnit) ?
CblasLevel2Implementations.Diagonal.Regular : CblasLevel2Implementations.Diagonal.Unit;
if (UseUpperImplementation(uplo, transA))
{
CblasLevel2Implementations.UpperTimesVectorPackedColMajor(
managedDiag, n, 1.0, a, offsetA, input, offsetX, incX, 0.0, x, offsetX, incX);
}
else
{
CblasLevel2Implementations.LowerTimesVectorPackedRowMajor(
managedDiag, n, 1.0, a, offsetA, input, offsetX, incX, 0.0, x, offsetX, incX);
}
}
/// <summary>
/// If the return value is a non-negative int i, then the entry (i, i) of the factor U or L is 0 and the inverse could
/// not be computed.
/// </summary>
internal int Dpptri(StoredTriangle triangle, int orderA, double[] factorizedMatrixA, int offsetA)
{
int info = DefaultInfo;
Provider.Dpptri(triangle.Translate(), orderA, factorizedMatrixA, offsetA, ref info);
if (info < 0)
{
ProcessNegativeInfo(info);
}
//TODO: is there the same problem as LU, i.e. can the last minor not be positive definite, while the info = 0?
if (info > 0)
{
return(info - 1);
}
else
{
return(int.MinValue);
}
}
private static bool UseUpperImplementation(StoredTriangle uplo, TransposeMatrix transA)
{
//if (transA == TransposeMatrix.ConjugateTranspose)
// throw new ArgumentException("Cannot use conjugate transpose operations for double matrices and vectors.");
if (uplo == StoredTriangle.Upper && transA == TransposeMatrix.NoTranspose)
{
return(true);
}
if (uplo == StoredTriangle.Upper && transA == TransposeMatrix.Transpose)
{
return(false);
}
if (uplo == StoredTriangle.Lower && transA == TransposeMatrix.NoTranspose)
{
return(true);
}
if (uplo == StoredTriangle.Lower && transA == TransposeMatrix.Transpose)
{
return(false);
}
throw new Exception("This code should not have been reached");
}
/// <summary>
/// See http://www.dotnumerics.com/NumericalLibraries/LinearAlgebra/CSharpCodeFiles/dtrsv.aspx
/// </summary>
public void Dtrsv(StoredTriangle uplo, TransposeMatrix transA, DiagonalValues diag, int n,
double[] a, int offsetA, int ldA, double[] x, int offsetX, int incX)
=> dtrsv.Run(uplo.Translate(), transA.Translate(), diag.Translate(), n, a, offsetA, ldA, ref x, offsetX, incX);
/// <summary>
/// See https://software.intel.com/en-us/mkl-developer-reference-fortran-trsv#D8733073-F041-4AA1-B82C-123DFA993AD7
/// </summary>
public void Dtrsv(StoredTriangle uplo, TransposeMatrix transA, DiagonalValues diag, int n,
double[] a, int offsetA, int ldA, double[] x, int offsetX, int incX)
=> Blas.Dtrsv(uplo.Translate(), transA.Translate(), diag.Translate(), ref n, ref a[offsetA], ref ldA,
ref x[offsetX], ref incX);
/// <summary>
/// See https://software.intel.com/en-us/mkl-developer-reference-fortran-spmv#16CB58C4-105B-486C-B6AA-42BB0C721A76
/// </summary>
public void Dspmv(StoredTriangle uplo, int n,
double alpha, double[] a, int offsetA, double[] x, int offsetX, int incX,
double beta, double[] y, int offsetY, int incY)
=> Blas.Dspmv(uplo.Translate(), ref n, ref alpha, ref a[offsetA],
ref x[offsetX], ref incX, ref beta, ref y[offsetY], ref incY);
internal static string Translate(this StoredTriangle uplo) => (uplo == StoredTriangle.Upper) ? "U" : "L";