# sgeev.f - Man Page

SRC/sgeev.f

## Synopsis

### Functions/Subroutines

subroutine **sgeev** (jobvl, jobvr, n, a, lda, wr, wi, vl, ldvl, vr, ldvr, work, lwork, info)

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

## Function/Subroutine Documentation

### subroutine sgeev (character jobvl, character jobvr, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) wr, real, dimension( * ) wi, real, dimension( ldvl, * ) vl, integer ldvl, real, dimension( ldvr, * ) vr, integer ldvr, real, dimension( * ) work, integer lwork, integer info)

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

**Purpose:**

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)**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 REAL 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 REAL array, dimension (N)

*WI*WI is 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.

*VL*VL is REAL 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 REAL 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 REAL 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.

Definition at line **190** of file **sgeev.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK