geev(3)

NAME
geev - geev: eig

SYNOPSIS

  Functions
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

Detailed Description

Function Documentation

  subroutine cgeev (character jobvl, character jobvr, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) w, complex, dimension( ldvl, * ) vl, integer ldvl, complex, dimension( ldvr, * ) vr, integer ldvr, complex, dimension( * ) work, integer lwork, real, dimension( * ) rwork, integer info)

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.

  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.

Definition at line 190 of file dgeev.f.

  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.

  subroutine zgeev (character jobvl, character jobvr, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) w, complex*16, dimension( ldvl, * ) vl, integer ldvl, complex*16, dimension( ldvr, * ) vr, integer ldvr, complex*16, dimension( * ) work, integer lwork, double precision, dimension( * ) rwork, integer info)

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.

Author

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