LAPACK++
2022.07.00
LAPACK C++ API
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Functions | |
int64_t | lapack::geev (lapack::Job jobvl, lapack::Job jobvr, int64_t n, double *A, int64_t lda, std::complex< double > *W, double *VL, int64_t ldvl, double *VR, int64_t ldvr) |
int64_t | lapack::geev (lapack::Job jobvl, lapack::Job jobvr, int64_t n, float *A, int64_t lda, std::complex< float > *W, float *VL, int64_t ldvl, float *VR, int64_t ldvr) |
int64_t | lapack::geev (lapack::Job jobvl, lapack::Job jobvr, int64_t n, std::complex< double > *A, int64_t lda, std::complex< double > *W, std::complex< double > *VL, int64_t ldvl, std::complex< double > *VR, int64_t ldvr) |
Computes for an n-by-n nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors. More... | |
int64_t | lapack::geev (lapack::Job jobvl, lapack::Job jobvr, int64_t n, std::complex< float > *A, int64_t lda, std::complex< float > *W, std::complex< float > *VL, int64_t ldvl, std::complex< float > *VR, int64_t ldvr) |
int64_t lapack::geev | ( | lapack::Job | jobvl, |
lapack::Job | jobvr, | ||
int64_t | n, | ||
std::complex< double > * | A, | ||
int64_t | lda, | ||
std::complex< double > * | W, | ||
std::complex< double > * | VL, | ||
int64_t | ldvl, | ||
std::complex< double > * | VR, | ||
int64_t | ldvr | ||
) |
Computes for an n-by-n nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors.
The right eigenvector v_j of A satisfies
\[ A v_j = \lambda_j v_j \]
where \(\lambda_j\) is its eigenvalue. The left eigenvector \(u_j\) of A satisfies
\[ u_j^H A = \lambda_j u_j^H \]
where \(u_j^H\) denotes the conjugate transpose of \(u_j\).
The computed eigenvectors are normalized to have Euclidean norm equal to 1 and largest component real.
Overloaded versions are available for float
, double
, std::complex<float>
, and std::complex<double>
.
[in] | jobvl |
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[in] | jobvr |
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[in] | n | The order of the matrix A. n >= 0. |
[in,out] | A | The n-by-n matrix A, stored in an lda-by-n array. On entry, the n-by-n matrix A. On exit, A has been overwritten. |
[in] | lda | The leading dimension of the array A. lda >= max(1,n). |
[out] | W | The vector W of length n. W contains the computed eigenvalues. Note: In LAPACK++, W is always complex, whereas LAPACK with a real matrix A uses a split-complex representation (WR, WI) for W. |
[out] | VL | The n-by-n matrix VL, stored in an ldvl-by-n array.
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[in] | ldvl | The leading dimension of the array VL. ldvl >= 1; if jobvl = Vec, ldvl >= n. |
[out] | VR | The n-by-n matrix VR, stored in an ldvr-by-n array.
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[in] | ldvr | The leading dimension of the array VR. ldvr >= 1; if jobvr = Vec, ldvr >= n. |