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---
:name: zgeev
:md5sum: a2f45f145f9a86dc68d7611fb89512e0
:category: :subroutine
:arguments:
- jobvl:
:type: char
:intent: input
- jobvr:
:type: char
:intent: input
- n:
:type: integer
:intent: input
- a:
:type: doublecomplex
:intent: input/output
:dims:
- lda
- n
- lda:
:type: integer
:intent: input
- w:
:type: doublecomplex
:intent: output
:dims:
- n
- vl:
:type: doublecomplex
:intent: output
:dims:
- ldvl
- n
- ldvl:
:type: integer
:intent: input
- vr:
:type: doublecomplex
:intent: output
:dims:
- ldvr
- n
- ldvr:
:type: integer
:intent: input
- work:
:type: doublecomplex
:intent: output
:dims:
- MAX(1,lwork)
- lwork:
:type: integer
:intent: input
:option: true
:default: 2*n
- rwork:
:type: doublereal
:intent: workspace
:dims:
- 2*n
- info:
:type: integer
:intent: output
:substitutions:
ldvr: "lsame_(&jobvr,\"V\") ? n : 1"
ldvl: "lsame_(&jobvl,\"V\") ? n : 1"
:fortran_help: " SUBROUTINE ZGEEV( JOBVL, JOBVR, N, A, LDA, W, VL, LDVL, VR, LDVR, WORK, LWORK, RWORK, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* ZGEEV computes for an N-by-N complex nonsymmetric matrix A, the\n\
* eigenvalues and, optionally, the left and/or right eigenvectors.\n\
*\n\
* The right eigenvector v(j) of A satisfies\n\
* A * v(j) = lambda(j) * v(j)\n\
* where lambda(j) is its eigenvalue.\n\
* The left eigenvector u(j) of A satisfies\n\
* u(j)**H * A = lambda(j) * u(j)**H\n\
* where u(j)**H denotes the conjugate transpose of u(j).\n\
*\n\
* The computed eigenvectors are normalized to have Euclidean norm\n\
* equal to 1 and largest component real.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* JOBVL (input) CHARACTER*1\n\
* = 'N': left eigenvectors of A are not computed;\n\
* = 'V': left eigenvectors of are computed.\n\
*\n\
* JOBVR (input) CHARACTER*1\n\
* = 'N': right eigenvectors of A are not computed;\n\
* = 'V': right eigenvectors of A are computed.\n\
*\n\
* N (input) INTEGER\n\
* The order of the matrix A. N >= 0.\n\
*\n\
* A (input/output) COMPLEX*16 array, dimension (LDA,N)\n\
* On entry, the N-by-N matrix A.\n\
* On exit, A has been overwritten.\n\
*\n\
* LDA (input) INTEGER\n\
* The leading dimension of the array A. LDA >= max(1,N).\n\
*\n\
* W (output) COMPLEX*16 array, dimension (N)\n\
* W contains the computed eigenvalues.\n\
*\n\
* VL (output) COMPLEX*16 array, dimension (LDVL,N)\n\
* If JOBVL = 'V', the left eigenvectors u(j) are stored one\n\
* after another in the columns of VL, in the same order\n\
* as their eigenvalues.\n\
* If JOBVL = 'N', VL is not referenced.\n\
* u(j) = VL(:,j), the j-th column of VL.\n\
*\n\
* LDVL (input) INTEGER\n\
* The leading dimension of the array VL. LDVL >= 1; if\n\
* JOBVL = 'V', LDVL >= N.\n\
*\n\
* VR (output) COMPLEX*16 array, dimension (LDVR,N)\n\
* If JOBVR = 'V', the right eigenvectors v(j) are stored one\n\
* after another in the columns of VR, in the same order\n\
* as their eigenvalues.\n\
* If JOBVR = 'N', VR is not referenced.\n\
* v(j) = VR(:,j), the j-th column of VR.\n\
*\n\
* LDVR (input) INTEGER\n\
* The leading dimension of the array VR. LDVR >= 1; if\n\
* JOBVR = 'V', LDVR >= N.\n\
*\n\
* WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))\n\
* On exit, if INFO = 0, WORK(1) returns the optimal LWORK.\n\
*\n\
* LWORK (input) INTEGER\n\
* The dimension of the array WORK. LWORK >= max(1,2*N).\n\
* For good performance, LWORK must generally be larger.\n\
*\n\
* If LWORK = -1, then a workspace query is assumed; the routine\n\
* only calculates the optimal size of the WORK array, returns\n\
* this value as the first entry of the WORK array, and no error\n\
* message related to LWORK is issued by XERBLA.\n\
*\n\
* RWORK (workspace) DOUBLE PRECISION array, dimension (2*N)\n\
*\n\
* INFO (output) INTEGER\n\
* = 0: successful exit\n\
* < 0: if INFO = -i, the i-th argument had an illegal value.\n\
* > 0: if INFO = i, the QR algorithm failed to compute all the\n\
* eigenvalues, and no eigenvectors have been computed;\n\
* elements and i+1:N of W contain eigenvalues which have\n\
* converged.\n\
*\n\n\
* =====================================================================\n\
*\n"
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