Cauchy-like¶
An \(m \times n\) matrix \(A\) is called Cauchy-like if there exist vectors \(r\), \(s\), \(x\), and \(y\) such that
\[A(i,j) = \frac{r(i) s(j)}{x(i) - y(j)}.\]
The following routines generate a Cauchy-like matrix using the defining vectors: \(r\), \(s\), \(x\), and \(y\).
C++ API¶
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void
CauchyLike(Matrix<F> &A, const std::vector<F> &r, const std::vector<F> &s, const std::vector<F> &x, const std::vector<F> &y)¶
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void
CauchyLike(AbstractDistMatrix<F> &A, const std::vector<F> &r, const std::vector<F> &s, const std::vector<F> &x, const std::vector<F> &y)¶
C API¶
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ElError
ElCauchyLike_s(ElMatrix_s A, ElInt rSize, float* rBuf, ElInt sSize, float* sBuf, ElInt xSize, float* xBuf, ElInt ySize, float* yBuf)¶
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ElError
ElCauchyLike_d(ElMatrix_d A, ElInt rSize, double* rBuf, ElInt sSize, double* sBuf, ElInt xSize, double* xBuf, ElInt ySize, double* yBuf)¶
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ElError
ElCauchyLike_c(ElMatrix_c A, ElInt rSize, complex_float* rBuf, ElInt sSize, complex_float* sBuf, ElInt xSize, complex_float* xBuf, ElInt ySize, complex_float* yBuf)¶
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ElError
ElCauchyLike_z(ElMatrix_z A, ElInt rSize, complex_double* rBuf, ElInt sSize, complex_double* sBuf, ElInt xSize, complex_double* xBuf, ElInt ySize, complex_double* yBuf)¶
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ElError
ElCauchyLikeDist_s(ElDistMatrix_s A, ElInt rSize, float* rBuf, ElInt sSize, float* sBuf, ElInt xSize, float* xBuf, ElInt ySize, float* yBuf)¶
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ElError
ElCauchyLikeDist_d(ElDistMatrix_d A, ElInt rSize, double* rBuf, ElInt sSize, double* sBuf, ElInt xSize, double* xBuf, ElInt ySize, double* yBuf)¶
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ElError
ElCauchyLikeDist_c(ElDistMatrix_c A, ElInt rSize, complex_float* rBuf, ElInt sSize, complex_float* sBuf, ElInt xSize, complex_float* xBuf, ElInt ySize, complex_float* yBuf)¶
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ElError
ElCauchyLikeDist_z(ElDistMatrix_z A, ElInt rSize, complex_double* rBuf, ElInt sSize, complex_double* sBuf, ElInt xSize, complex_double* xBuf, ElInt ySize, complex_double* yBuf)¶