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.
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.
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.
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.
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.
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.
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.
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.

Detailed Description

Function Documentation

magma_cgeev()

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]	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	COMPLEX 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]	w	COMPLEX array, dimension (N) w contains the computed eigenvalues.
[out]	VL	COMPLEX 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	COMPLEX 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) COMPLEX 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 >= (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]	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_cgeev_m()

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]	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	COMPLEX 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]	w	COMPLEX array, dimension (N) W contains the computed eigenvalues.
[out]	VL	COMPLEX 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	COMPLEX 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) COMPLEX 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 >= (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]	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_dgeev()

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]	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. If the j-th eigenvalue is real, then u(j) = VL(:,j), the j-th column of VL. If the j-th and (j+1)-st eigenvalues form a complex conjugate pair, then u(j) = VL(:,j) + i*VL(:,j+1) and u(j+1) = VL(:,j) - i*VL(:,j+1).
[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. If the j-th eigenvalue is real, then v(j) = VR(:,j), the j-th column of VR. If the j-th and (j+1)-st eigenvalues form a complex conjugate pair, then v(j) = VR(:,j) + i*VR(:,j+1) and v(j+1) = VR(:,j) - i*VR(:,j+1).
[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_dgeev_m()

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]	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. If the j-th eigenvalue is real, then u(j) = VL(:,j), the j-th column of VL. If the j-th and (j+1)-st eigenvalues form a complex conjugate pair, then u(j) = VL(:,j) + i*VL(:,j+1) and u(j+1) = VL(:,j) - i*VL(:,j+1).
[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. If the j-th eigenvalue is real, then v(j) = VR(:,j), the j-th column of VR. If the j-th and (j+1)-st eigenvalues form a complex conjugate pair, then v(j) = VR(:,j) + i*VR(:,j+1) and v(j+1) = VR(:,j) - i*VR(:,j+1).
[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 + 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]	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_sgeev()

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]	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	REAL 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	REAL array, dimension (N)
[out]	wi	REAL 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	REAL 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. If the j-th eigenvalue is real, then u(j) = VL(:,j), the j-th column of VL. If the j-th and (j+1)-st eigenvalues form a complex conjugate pair, then u(j) = VL(:,j) + i*VL(:,j+1) and u(j+1) = VL(:,j) - i*VL(:,j+1).
[in]	ldvl	INTEGER The leading dimension of the array VL. LDVL >= 1; if JOBVL = MagmaVec, LDVL >= N.
[out]	VR	REAL 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. If the j-th eigenvalue is real, then v(j) = VR(:,j), the j-th column of VR. If the j-th and (j+1)-st eigenvalues form a complex conjugate pair, then v(j) = VR(:,j) + i*VR(:,j+1) and v(j+1) = VR(:,j) - i*VR(:,j+1).
[in]	ldvr	INTEGER 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]	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_sgeev_m()

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]	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	REAL 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	REAL array, dimension (N)
[out]	wi	REAL 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	REAL 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. If the j-th eigenvalue is real, then u(j) = VL(:,j), the j-th column of VL. If the j-th and (j+1)-st eigenvalues form a complex conjugate pair, then u(j) = VL(:,j) + i*VL(:,j+1) and u(j+1) = VL(:,j) - i*VL(:,j+1).
[in]	ldvl	INTEGER The leading dimension of the array VL. LDVL >= 1; if JOBVL = MagmaVec, LDVL >= N.
[out]	VR	REAL 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. If the j-th eigenvalue is real, then v(j) = VR(:,j), the j-th column of VR. If the j-th and (j+1)-st eigenvalues form a complex conjugate pair, then v(j) = VR(:,j) + i*VR(:,j+1) and v(j+1) = VR(:,j) - i*VR(:,j+1).
[in]	ldvr	INTEGER 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]	lwork	INTEGER 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]	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_zgeev()

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]	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	COMPLEX_16 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]	w	COMPLEX_16 array, dimension (N) w contains the computed eigenvalues.
[out]	VL	COMPLEX_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]	ldvl	INTEGER The leading dimension of the array VL. LDVL >= 1; if JOBVL = MagmaVec, LDVL >= N.
[out]	VR	COMPLEX_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]	ldvr	INTEGER 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]	lwork	INTEGER 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]	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_zgeev_m()

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]	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	COMPLEX_16 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]	w	COMPLEX_16 array, dimension (N) W contains the computed eigenvalues.
[out]	VL	COMPLEX_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]	ldvl	INTEGER The leading dimension of the array VL. LDVL >= 1; if JOBVL = MagmaVec, LDVL >= N.
[out]	VR	COMPLEX_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]	ldvr	INTEGER 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]	lwork	INTEGER 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]	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.