geev - Man Page

subroutine cgeev (jobvl, jobvr, n, a, lda, w, vl, ldvl, vr, ldvr, work, lwork, rwork, info)
CGEEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices
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
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
subroutine zgeev (jobvl, jobvr, n, a, lda, w, vl, ldvl, vr, ldvr, work, lwork, rwork, info)
ZGEEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices

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

Purpose:

 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

JOBVL

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

W

          W is COMPLEX array, dimension (N)
          W contains the computed eigenvalues.

VL

          VL is COMPLEX 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.
          u(j) = VL(:,j), the j-th column of VL.

LDVL

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

VR

          VR is COMPLEX 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.
          v(j) = VR(:,j), the j-th column of VR.

LDVR

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

WORK

          WORK is COMPLEX 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(1,2*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.

RWORK

          RWORK is REAL array, dimension (2*N)

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 W contain eigenvalues which have
                converged.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 178 of file cgeev.f.

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.

Definition at line 190 of file dgeev.f.

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.

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

Purpose:

 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

JOBVL

          JOBVL is CHARACTER*1
          = 'N': left eigenvectors of A are not computed;
          = 'V': left eigenvectors of 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 COMPLEX*16 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).

W

          W is COMPLEX*16 array, dimension (N)
          W contains the computed eigenvalues.

VL

          VL is COMPLEX*16 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.
          u(j) = VL(:,j), the j-th column of VL.

LDVL

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

VR

          VR is COMPLEX*16 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.
          v(j) = VR(:,j), the j-th column of VR.

LDVR

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

WORK

          WORK is COMPLEX*16 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(1,2*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.

RWORK

          RWORK is DOUBLE PRECISION array, dimension (2*N)

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 W contain eigenvalues which have
                converged.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 178 of file zgeev.f.