MAGMA  2.3.0
Matrix Algebra for GPU and Multicore Architectures
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geev: Non-symmetric eigenvalues (driver)

Functions

magma_int_t magma_cgeev (magma_vec_t jobvl, magma_vec_t jobvr, magma_int_t n, magmaFloatComplex *A, magma_int_t lda, magmaFloatComplex *w, magmaFloatComplex *VL, magma_int_t ldvl, magmaFloatComplex *VR, magma_int_t ldvr, magmaFloatComplex *work, magma_int_t lwork, float *rwork, magma_int_t *info)
 CGEEV computes for an N-by-N complex nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors. More...
 
magma_int_t magma_cgeev_m (magma_vec_t jobvl, magma_vec_t jobvr, magma_int_t n, magmaFloatComplex *A, magma_int_t lda, magmaFloatComplex *w, magmaFloatComplex *VL, magma_int_t ldvl, magmaFloatComplex *VR, magma_int_t ldvr, magmaFloatComplex *work, magma_int_t lwork, float *rwork, magma_int_t *info)
 CGEEV computes for an N-by-N complex nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors. More...
 
magma_int_t magma_dgeev (magma_vec_t jobvl, magma_vec_t jobvr, magma_int_t n, double *A, magma_int_t lda, double *wr, double *wi, double *VL, magma_int_t ldvl, double *VR, magma_int_t ldvr, double *work, magma_int_t lwork, 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. More...
 
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 *wr, double *wi, double *VL, magma_int_t ldvl, double *VR, magma_int_t ldvr, double *work, magma_int_t lwork, 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. More...
 
magma_int_t magma_sgeev (magma_vec_t jobvl, magma_vec_t jobvr, magma_int_t n, float *A, magma_int_t lda, float *wr, float *wi, float *VL, magma_int_t ldvl, float *VR, magma_int_t ldvr, float *work, magma_int_t lwork, magma_int_t *info)
 SGEEV computes for an N-by-N real nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors. More...
 
magma_int_t magma_sgeev_m (magma_vec_t jobvl, magma_vec_t jobvr, magma_int_t n, float *A, magma_int_t lda, float *wr, float *wi, float *VL, magma_int_t ldvl, float *VR, magma_int_t ldvr, float *work, magma_int_t lwork, magma_int_t *info)
 SGEEV computes for an N-by-N real nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors. More...
 
magma_int_t magma_zgeev (magma_vec_t jobvl, magma_vec_t jobvr, magma_int_t n, magmaDoubleComplex *A, magma_int_t lda, magmaDoubleComplex *w, magmaDoubleComplex *VL, magma_int_t ldvl, magmaDoubleComplex *VR, magma_int_t ldvr, magmaDoubleComplex *work, magma_int_t lwork, double *rwork, magma_int_t *info)
 ZGEEV computes for an N-by-N complex nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors. More...
 
magma_int_t magma_zgeev_m (magma_vec_t jobvl, magma_vec_t jobvr, magma_int_t n, magmaDoubleComplex *A, magma_int_t lda, magmaDoubleComplex *w, magmaDoubleComplex *VL, magma_int_t ldvl, magmaDoubleComplex *VR, magma_int_t ldvr, magmaDoubleComplex *work, magma_int_t lwork, double *rwork, magma_int_t *info)
 ZGEEV computes for an N-by-N complex nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors. More...
 

Detailed Description

Function Documentation

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

CGEEV computes for an N-by-N complex 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.

Parameters
[in]jobvlmagma_vec_t
  • = MagmaNoVec: left eigenvectors of A are not computed;
  • = MagmaVec: left eigenvectors of are computed.
[in]jobvrmagma_vec_t
  • = MagmaNoVec: right eigenvectors of A are not computed;
  • = MagmaVec: right eigenvectors of A are computed.
[in]nINTEGER The order of the matrix A. N >= 0.
[in,out]ACOMPLEX array, dimension (LDA,N) On entry, the N-by-N matrix A. On exit, A has been overwritten.
[in]ldaINTEGER The leading dimension of the array A. LDA >= max(1,N).
[out]wCOMPLEX array, dimension (N) w contains the computed eigenvalues.
[out]VLCOMPLEX 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]ldvlINTEGER The leading dimension of the array VL. LDVL >= 1; if JOBVL = MagmaVec, LDVL >= N.
[out]VRCOMPLEX 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]ldvrINTEGER The leading dimension of the array VR. LDVR >= 1; if JOBVR = MagmaVec, LDVR >= N.
[out]work(workspace) COMPLEX array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
[in]lworkINTEGER The dimension of the array WORK. LWORK >= (1 + nb)*N. For optimal performance, LWORK >= (1 + 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.
rwork(workspace) REAL array, dimension (2*N)
[out]infoINTEGER
  • = 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_cgeev_m ( magma_vec_t  jobvl,
magma_vec_t  jobvr,
magma_int_t  n,
magmaFloatComplex *  A,
magma_int_t  lda,
magmaFloatComplex *  w,
magmaFloatComplex *  VL,
magma_int_t  ldvl,
magmaFloatComplex *  VR,
magma_int_t  ldvr,
magmaFloatComplex *  work,
magma_int_t  lwork,
float *  rwork,
magma_int_t *  info 
)

CGEEV computes for an N-by-N complex 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.

Parameters
[in]jobvlmagma_vec_t
  • = MagmaNoVec: left eigenvectors of A are not computed;
  • = MagmaVec: left eigenvectors of are computed.
[in]jobvrmagma_vec_t
  • = MagmaNoVec: right eigenvectors of A are not computed;
  • = MagmaVec: right eigenvectors of A are computed.
[in]nINTEGER The order of the matrix A. N >= 0.
[in,out]ACOMPLEX array, dimension (LDA,N) On entry, the N-by-N matrix A. On exit, A has been overwritten.
[in]ldaINTEGER The leading dimension of the array A. LDA >= max(1,N).
[out]wCOMPLEX array, dimension (N) W contains the computed eigenvalues.
[out]VLCOMPLEX 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]ldvlINTEGER The leading dimension of the array VL. LDVL >= 1; if JOBVL = MagmaVec, LDVL >= N.
[out]VRCOMPLEX 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]ldvrINTEGER The leading dimension of the array VR. LDVR >= 1; if JOBVR = MagmaVec, LDVR >= N.
[out]work(workspace) COMPLEX array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
[in]lworkINTEGER The dimension of the array WORK. LWORK >= (1 + nb + nb*ngpu)*N. For optimal performance, LWORK >= (1 + 2*nb + nb*ngpu)*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.
rwork(workspace) REAL array, dimension (2*N)
[out]infoINTEGER
  • = 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 ( magma_vec_t  jobvl,
magma_vec_t  jobvr,
magma_int_t  n,
double *  A,
magma_int_t  lda,
double *  wr,
double *  wi,
double *  VL,
magma_int_t  ldvl,
double *  VR,
magma_int_t  ldvr,
double *  work,
magma_int_t  lwork,
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]jobvlmagma_vec_t
  • = MagmaNoVec: left eigenvectors of A are not computed;
  • = MagmaVec: left eigenvectors of are computed.
[in]jobvrmagma_vec_t
  • = MagmaNoVec: right eigenvectors of A are not computed;
  • = MagmaVec: right eigenvectors of A are computed.
[in]nINTEGER The order of the matrix A. N >= 0.
[in,out]ADOUBLE PRECISION array, dimension (LDA,N) On entry, the N-by-N matrix A. On exit, A has been overwritten.
[in]ldaINTEGER The leading dimension of the array A. LDA >= max(1,N).
[out]wrDOUBLE PRECISION array, dimension (N)
[out]wiDOUBLE 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]VLDOUBLE 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]ldvlINTEGER The leading dimension of the array VL. LDVL >= 1; if JOBVL = MagmaVec, LDVL >= N.
[out]VRDOUBLE 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]ldvrINTEGER 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]lworkINTEGER 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]infoINTEGER
  • = 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 *  wr,
double *  wi,
double *  VL,
magma_int_t  ldvl,
double *  VR,
magma_int_t  ldvr,
double *  work,
magma_int_t  lwork,
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]jobvlmagma_vec_t
  • = MagmaNoVec: left eigenvectors of A are not computed;
  • = MagmaVec: left eigenvectors of are computed.
[in]jobvrmagma_vec_t
  • = MagmaNoVec: right eigenvectors of A are not computed;
  • = MagmaVec: right eigenvectors of A are computed.
[in]nINTEGER The order of the matrix A. N >= 0.
[in,out]ADOUBLE PRECISION array, dimension (LDA,N) On entry, the N-by-N matrix A. On exit, A has been overwritten.
[in]ldaINTEGER The leading dimension of the array A. LDA >= max(1,N).
[out]wrDOUBLE PRECISION array, dimension (N)
[out]wiDOUBLE 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]VLDOUBLE 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]ldvlINTEGER The leading dimension of the array VL. LDVL >= 1; if JOBVL = MagmaVec, LDVL >= N.
[out]VRDOUBLE 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]ldvrINTEGER 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]lworkINTEGER The dimension of the array WORK. LWORK >= (2 + nb + nb*ngpu)*N. For optimal performance, LWORK >= (2 + 2*nb + nb*ngpu)*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]infoINTEGER
  • = 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_sgeev ( magma_vec_t  jobvl,
magma_vec_t  jobvr,
magma_int_t  n,
float *  A,
magma_int_t  lda,
float *  wr,
float *  wi,
float *  VL,
magma_int_t  ldvl,
float *  VR,
magma_int_t  ldvr,
float *  work,
magma_int_t  lwork,
magma_int_t *  info 
)

SGEEV 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]jobvlmagma_vec_t
  • = MagmaNoVec: left eigenvectors of A are not computed;
  • = MagmaVec: left eigenvectors of are computed.
[in]jobvrmagma_vec_t
  • = MagmaNoVec: right eigenvectors of A are not computed;
  • = MagmaVec: right eigenvectors of A are computed.
[in]nINTEGER The order of the matrix A. N >= 0.
[in,out]AREAL array, dimension (LDA,N) On entry, the N-by-N matrix A. On exit, A has been overwritten.
[in]ldaINTEGER The leading dimension of the array A. LDA >= max(1,N).
[out]wrREAL array, dimension (N)
[out]wiREAL 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]VLREAL 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]ldvlINTEGER The leading dimension of the array VL. LDVL >= 1; if JOBVL = MagmaVec, LDVL >= N.
[out]VRREAL 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]ldvrINTEGER The leading dimension of the array VR. LDVR >= 1; if JOBVR = MagmaVec, LDVR >= N.
[out]work(workspace) REAL array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
[in]lworkINTEGER 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]infoINTEGER
  • = 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_sgeev_m ( magma_vec_t  jobvl,
magma_vec_t  jobvr,
magma_int_t  n,
float *  A,
magma_int_t  lda,
float *  wr,
float *  wi,
float *  VL,
magma_int_t  ldvl,
float *  VR,
magma_int_t  ldvr,
float *  work,
magma_int_t  lwork,
magma_int_t *  info 
)

SGEEV 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]jobvlmagma_vec_t
  • = MagmaNoVec: left eigenvectors of A are not computed;
  • = MagmaVec: left eigenvectors of are computed.
[in]jobvrmagma_vec_t
  • = MagmaNoVec: right eigenvectors of A are not computed;
  • = MagmaVec: right eigenvectors of A are computed.
[in]nINTEGER The order of the matrix A. N >= 0.
[in,out]AREAL array, dimension (LDA,N) On entry, the N-by-N matrix A. On exit, A has been overwritten.
[in]ldaINTEGER The leading dimension of the array A. LDA >= max(1,N).
[out]wrREAL array, dimension (N)
[out]wiREAL 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]VLREAL 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]ldvlINTEGER The leading dimension of the array VL. LDVL >= 1; if JOBVL = MagmaVec, LDVL >= N.
[out]VRREAL 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]ldvrINTEGER The leading dimension of the array VR. LDVR >= 1; if JOBVR = MagmaVec, LDVR >= N.
[out]work(workspace) REAL array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
[in]lworkINTEGER The dimension of the array WORK. LWORK >= (2 + nb + nb*ngpu)*N. For optimal performance, LWORK >= (2 + 2*nb + nb*ngpu)*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]infoINTEGER
  • = 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_zgeev ( magma_vec_t  jobvl,
magma_vec_t  jobvr,
magma_int_t  n,
magmaDoubleComplex *  A,
magma_int_t  lda,
magmaDoubleComplex *  w,
magmaDoubleComplex *  VL,
magma_int_t  ldvl,
magmaDoubleComplex *  VR,
magma_int_t  ldvr,
magmaDoubleComplex *  work,
magma_int_t  lwork,
double *  rwork,
magma_int_t *  info 
)

ZGEEV computes for an N-by-N complex 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.

Parameters
[in]jobvlmagma_vec_t
  • = MagmaNoVec: left eigenvectors of A are not computed;
  • = MagmaVec: left eigenvectors of are computed.
[in]jobvrmagma_vec_t
  • = MagmaNoVec: right eigenvectors of A are not computed;
  • = MagmaVec: right eigenvectors of A are computed.
[in]nINTEGER The order of the matrix A. N >= 0.
[in,out]ACOMPLEX_16 array, dimension (LDA,N) On entry, the N-by-N matrix A. On exit, A has been overwritten.
[in]ldaINTEGER The leading dimension of the array A. LDA >= max(1,N).
[out]wCOMPLEX_16 array, dimension (N) w contains the computed eigenvalues.
[out]VLCOMPLEX_16 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]ldvlINTEGER The leading dimension of the array VL. LDVL >= 1; if JOBVL = MagmaVec, LDVL >= N.
[out]VRCOMPLEX_16 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]ldvrINTEGER The leading dimension of the array VR. LDVR >= 1; if JOBVR = MagmaVec, LDVR >= N.
[out]work(workspace) COMPLEX_16 array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
[in]lworkINTEGER The dimension of the array WORK. LWORK >= (1 + nb)*N. For optimal performance, LWORK >= (1 + 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.
rwork(workspace) DOUBLE PRECISION array, dimension (2*N)
[out]infoINTEGER
  • = 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_zgeev_m ( magma_vec_t  jobvl,
magma_vec_t  jobvr,
magma_int_t  n,
magmaDoubleComplex *  A,
magma_int_t  lda,
magmaDoubleComplex *  w,
magmaDoubleComplex *  VL,
magma_int_t  ldvl,
magmaDoubleComplex *  VR,
magma_int_t  ldvr,
magmaDoubleComplex *  work,
magma_int_t  lwork,
double *  rwork,
magma_int_t *  info 
)

ZGEEV computes for an N-by-N complex 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.

Parameters
[in]jobvlmagma_vec_t
  • = MagmaNoVec: left eigenvectors of A are not computed;
  • = MagmaVec: left eigenvectors of are computed.
[in]jobvrmagma_vec_t
  • = MagmaNoVec: right eigenvectors of A are not computed;
  • = MagmaVec: right eigenvectors of A are computed.
[in]nINTEGER The order of the matrix A. N >= 0.
[in,out]ACOMPLEX_16 array, dimension (LDA,N) On entry, the N-by-N matrix A. On exit, A has been overwritten.
[in]ldaINTEGER The leading dimension of the array A. LDA >= max(1,N).
[out]wCOMPLEX_16 array, dimension (N) W contains the computed eigenvalues.
[out]VLCOMPLEX_16 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]ldvlINTEGER The leading dimension of the array VL. LDVL >= 1; if JOBVL = MagmaVec, LDVL >= N.
[out]VRCOMPLEX_16 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]ldvrINTEGER The leading dimension of the array VR. LDVR >= 1; if JOBVR = MagmaVec, LDVR >= N.
[out]work(workspace) COMPLEX_16 array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
[in]lworkINTEGER The dimension of the array WORK. LWORK >= (1 + nb + nb*ngpu)*N. For optimal performance, LWORK >= (1 + 2*nb + nb*ngpu)*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.
rwork(workspace) DOUBLE PRECISION array, dimension (2*N)
[out]infoINTEGER
  • = 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.