# dgeev.f man page

dgeev.f

## Synopsis

### Functions/Subroutines

subroutine **dgeev** (JOBVL, JOBVR, **N**, A, **LDA**, WR, WI, VL, LDVL, VR, LDVR, WORK, LWORK, INFO)

**DGEEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices**

## Function/Subroutine Documentation

### subroutine dgeev (character JOBVL, character JOBVR, integer N, double precision, dimension( lda, * ) A, integer LDA, double precision, dimension( * ) WR, double precision, dimension( * ) WI, double precision, dimension( ldvl, * ) VL, integer LDVL, double precision, dimension( ldvr, * ) VR, integer LDVR, double precision, dimension( * ) WORK, integer LWORK, integer INFO)

**DGEEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices**

**Purpose:**

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)**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:***JOBVL*JOBVL is CHARACTER*1 = 'N': left eigenvectors of A are not computed; = 'V': left eigenvectors of A are computed.

*JOBVR*JOBVR is CHARACTER*1 = 'N': right eigenvectors of A are not computed; = 'V': right eigenvectors of A are computed.

*N*N is INTEGER The order of the matrix A. N >= 0.

*A*A is DOUBLE PRECISION array, dimension (LDA,N) On entry, the N-by-N matrix A. On exit, A has been overwritten.

*LDA*LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).

*WR*WR is DOUBLE PRECISION array, dimension (N)

*WI*WI is 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.

*VL*VL is DOUBLE PRECISION array, dimension (LDVL,N) If JOBVL = 'V', the left eigenvectors u(j) are stored one after another in the columns of VL, in the same order as their eigenvalues. If JOBVL = 'N', 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).

*LDVL*LDVL is INTEGER The leading dimension of the array VL. LDVL >= 1; if JOBVL = 'V', LDVL >= N.

*VR*VR is DOUBLE PRECISION array, dimension (LDVR,N) If JOBVR = 'V', the right eigenvectors v(j) are stored one after another in the columns of VR, in the same order as their eigenvalues. If JOBVR = 'N', 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).

*LDVR*LDVR is INTEGER The leading dimension of the array VR. LDVR >= 1; if JOBVR = 'V', LDVR >= N.

*WORK*WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

*LWORK*LWORK is INTEGER The dimension of the array WORK. LWORK >= max(1,3*N), and if JOBVL = 'V' or JOBVR = 'V', LWORK >= 4*N. For good performance, LWORK must generally be larger. 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.

*INFO*INFO is 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 i+1:N of WR and WI contain eigenvalues which have converged.

**Author:**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date:**June 2016

Definition at line 193 of file dgeev.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page dgeev(3) is an alias of dgeev.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK