double precision
[Non-symmetric eigenvalue: driver]

Functions

magma_int_t magma_dgeev (magma_vec_t jobvl, magma_vec_t jobvr, magma_int_t n, double *A, magma_int_t lda, double *w, double *VL, magma_int_t ldvl, double *VR, magma_int_t ldvr, double *work, magma_int_t lwork, double *rwork, magma_int_t *info)
 DGEEV computes for an N-by-N real nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors.
magma_int_t magma_dgeev_m (magma_vec_t jobvl, magma_vec_t jobvr, magma_int_t n, double *A, magma_int_t lda, double *w, double *VL, magma_int_t ldvl, double *VR, magma_int_t ldvr, double *work, magma_int_t lwork, double *rwork, magma_int_t *info)
 DGEEV computes for an N-by-N real nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors.

Function Documentation

magma_int_t magma_dgeev ( magma_vec_t  jobvl,
magma_vec_t  jobvr,
magma_int_t  n,
double *  A,
magma_int_t  lda,
double *  w,
double *  VL,
magma_int_t  ldvl,
double *  VR,
magma_int_t  ldvr,
double *  work,
magma_int_t  lwork,
double *  rwork,
magma_int_t *  info 
)

DGEEV computes for an N-by-N real 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)**T * A = lambda(j) * u(j)**T where u(j)**T denotes the transpose of u(j).

The computed eigenvectors are normalized to have Euclidean norm equal to 1 and largest component real.

Parameters:
[in] jobvl magma_vec_t

  • = MagmaNoVec: left eigenvectors of A are not computed;
  • = MagmaVec: left eigenvectors of are computed.
[in] jobvr magma_vec_t

  • = MagmaNoVec: right eigenvectors of A are not computed;
  • = MagmaVec: right eigenvectors of A are computed.
[in] n INTEGER The order of the matrix A. N >= 0.
[in,out] A DOUBLE PRECISION array, dimension (LDA,N) On entry, the N-by-N matrix A. On exit, A has been overwritten.
[in] lda INTEGER The leading dimension of the array A. LDA >= max(1,N).
[out] wr DOUBLE PRECISION array, dimension (N)
[out] wi DOUBLE PRECISION array, dimension (N) WR and WI contain the real and imaginary parts, respectively, of the computed eigenvalues. Complex conjugate pairs of eigenvalues appear consecutively with the eigenvalue having the positive imaginary part first.
[out] VL DOUBLE PRECISION array, dimension (LDVL,N) If JOBVL = MagmaVec, the left eigenvectors u(j) are stored one after another in the columns of VL, in the same order as their eigenvalues. If JOBVL = MagmaNoVec, VL is not referenced. u(j) = VL(:,j), the j-th column of VL.
[in] ldvl INTEGER The leading dimension of the array VL. LDVL >= 1; if JOBVL = MagmaVec, LDVL >= N.
[out] VR DOUBLE PRECISION array, dimension (LDVR,N) If JOBVR = MagmaVec, the right eigenvectors v(j) are stored one after another in the columns of VR, in the same order as their eigenvalues. If JOBVR = MagmaNoVec, VR is not referenced. v(j) = VR(:,j), the j-th column of VR.
[in] ldvr INTEGER The leading dimension of the array VR. LDVR >= 1; if JOBVR = MagmaVec, LDVR >= N.
[out] work (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
[in] lwork INTEGER The dimension of the array WORK. LWORK >= (2+nb)*N. For optimal performance, LWORK >= (2+2*nb)*N.
If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.
[out] info INTEGER

  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value.
  • > 0: if INFO = i, the QR algorithm failed to compute all the eigenvalues, and no eigenvectors have been computed; elements and i+1:N of w contain eigenvalues which have converged.
magma_int_t magma_dgeev_m ( magma_vec_t  jobvl,
magma_vec_t  jobvr,
magma_int_t  n,
double *  A,
magma_int_t  lda,
double *  w,
double *  VL,
magma_int_t  ldvl,
double *  VR,
magma_int_t  ldvr,
double *  work,
magma_int_t  lwork,
double *  rwork,
magma_int_t *  info 
)

DGEEV computes for an N-by-N real 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)**T * A = lambda(j) * u(j)**T where u(j)**T denotes the transpose of u(j).

The computed eigenvectors are normalized to have Euclidean norm equal to 1 and largest component real.

Parameters:
[in] jobvl magma_vec_t

  • = MagmaNoVec: left eigenvectors of A are not computed;
  • = MagmaVec: left eigenvectors of are computed.
[in] jobvr magma_vec_t

  • = MagmaNoVec: right eigenvectors of A are not computed;
  • = MagmaVec: right eigenvectors of A are computed.
[in] n INTEGER The order of the matrix A. N >= 0.
[in,out] A DOUBLE PRECISION array, dimension (LDA,N) On entry, the N-by-N matrix A. On exit, A has been overwritten.
[in] lda INTEGER The leading dimension of the array A. LDA >= max(1,N).
[out] wr DOUBLE PRECISION array, dimension (N)
[out] wi DOUBLE PRECISION array, dimension (N) WR and WI contain the real and imaginary parts, respectively, of the computed eigenvalues. Complex conjugate pairs of eigenvalues appear consecutively with the eigenvalue having the positive imaginary part first.
[out] VL DOUBLE PRECISION array, dimension (LDVL,N) If JOBVL = MagmaVec, the left eigenvectors u(j) are stored one after another in the columns of VL, in the same order as their eigenvalues. If JOBVL = MagmaNoVec, VL is not referenced. u(j) = VL(:,j), the j-th column of VL.
[in] ldvl INTEGER The leading dimension of the array VL. LDVL >= 1; if JOBVL = MagmaVec, LDVL >= N.
[out] VR DOUBLE PRECISION array, dimension (LDVR,N) If JOBVR = MagmaVec, the right eigenvectors v(j) are stored one after another in the columns of VR, in the same order as their eigenvalues. If JOBVR = MagmaNoVec, VR is not referenced. v(j) = VR(:,j), the j-th column of VR.
[in] ldvr INTEGER The leading dimension of the array VR. LDVR >= 1; if JOBVR = MagmaVec, LDVR >= N.
[out] work (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
[in] lwork INTEGER The dimension of the array WORK. LWORK >= (2+nb)*N. For optimal performance, LWORK >= (2+2*nb)*N.
If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.
[out] info INTEGER

  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value.
  • > 0: if INFO = i, the QR algorithm failed to compute all the eigenvalues, and no eigenvectors have been computed; elements and i+1:N of W contain eigenvalues which have converged.

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