Multi-shift Trsm¶
Solve for \(X\) in the linear system
\[T^\# X - X D^\# = Y\]
or
\[X T^\# - D^\# X = Y\]
where \(T\) is triangular, \(D\) is diagonal, and
\(A^\#\) is defined to be one of \(\{A,A^T,A^H\}\).
The data movement requires almost no modification from that of Trsm().
Note
There is no corresponding BLAS routine, but it is a natural modification of Trsm.
C++ API¶
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void
MultiShiftTrsm(LeftOrRight side, UpperOrLower uplo, Orientation orientation, F alpha, const Matrix<F> &T, const Matrix<F> &shifts, Matrix<F> &X)¶
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void
MultiShiftTrsm(LeftOrRight side, UpperOrLower uplo, Orientation orientation, F alpha, const AbstractDistMatrix<F> &T, const AbstractDistMatrix<F> &shifts, AbstractDistMatrix<F> &X)¶ Overwrite the columns of X with the solutions to the shifted linear systems.
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void
MultiShiftTrsm(LeftOrRight side, UpperOrLower uplo, Orientation orientation, Complex<Real> alpha, const Matrix<Real> &T, const Matrix<Complex<Real>> &shifts, Matrix<Real> &XReal, Matrix<Real> &XImag)¶
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void
MultiShiftTrsm(LeftOrRight side, UpperOrLower uplo, Orientation orientation, Complex<Real> alpha, const AbstractDistMatrix<Real> &T, const AbstractDistMatrix<Complex<Real>> &shifts, AbstractDistMatrix<Real> &XReal, AbstractDistMatrix<Real> &XImag)¶ Overwrite the columns of the real and imaginary parts of X with the solutions to the shifted linear systems.
C API¶
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ElError
ElMultiShiftTrsm_s(ElLeftOrRight side, ElUpperOrLower uplo, ElOrientation orientation, float alpha, ElMatrix_s A, ElConstMatrix_s shifts, ElMatrix_s B)¶
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ElError
ElMultiShiftTrsm_d(ElLeftOrRight side, ElUpperOrLower uplo, ElOrientation orientation, double alpha, ElMatrix_d A, ElConstMatrix_d shifts, ElMatrix_d B)¶
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ElError
ElMultiShiftTrsm_c(ElLeftOrRight side, ElUpperOrLower uplo, ElOrientation orientation, complex_float alpha, ElMatrix_c A, ElConstMatrix_c shifts, ElMatrix_c B)¶
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ElError
ElMultiShiftTrsm_z(ElLeftOrRight side, ElUpperOrLower uplo, ElOrientation orientation, complex_double alpha, ElMatrix_z A, ElConstMatrix_z shifts, ElMatrix_z B)¶
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ElError
ElMultiShiftTrsmDist_s(ElLeftOrRight side, ElUpperOrLower uplo, ElOrientation orientation, float alpha, ElDistMatrix_s A, ElConstDistMatrix_s shifts, ElDistMatrix_s B)¶
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ElError
ElMultiShiftTrsmDist_d(ElLeftOrRight side, ElUpperOrLower uplo, ElOrientation orientation, double alpha, ElDistMatrix_d A, ElConstDistMatrix_d shifts, ElDistMatrix_d B)¶
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ElError
ElMultiShiftTrsmDist_c(ElLeftOrRight side, ElUpperOrLower uplo, ElOrientation orientation, complex_float alpha, ElDistMatrix_c A, ElConstDistMatrix_c shifts, ElDistMatrix_c B)¶
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ElError
ElMultiShiftTrsmDist_z(ElLeftOrRight side, ElUpperOrLower uplo, ElOrientation orientation, complex_double alpha, ElDistMatrix_z A, ElConstDistMatrix_z shifts, ElDistMatrix_z B)¶