Man page - geev(3)

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Manual

geev

NAME
SYNOPSIS
Functions
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)
subroutine dgeev (character jobvl, character jobvr, integer n, doubleprecision, dimension( lda, * ) a, integer lda, double precision,dimension( * ) wr, double precision, dimension( * ) wi, doubleprecision, dimension( ldvl, * ) vl, integer ldvl, double precision,dimension( ldvr, * ) vr, integer ldvr, double precision, dimension( * )work, integer lwork, integer info)
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)
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)
Author

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
= ā€™Nā€™: left eigenvectors of A are not computed;
= ā€™Vā€™: left eigenvectors of are computed.

JOBVR

JOBVR is CHARACTER*1
= ā€™Nā€™: right eigenvectors of A are not computed;
= ā€™Vā€™: 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 = ā€™Vā€™, the left eigenvectors u(j) are stored one
after another in the columns of VL, in the same order
as their eigenvalues.
If JOBVL = ā€™Nā€™, 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 = ā€™Vā€™, LDVL >= N.

VR

VR is COMPLEX array, dimension (LDVR,N)
If JOBVR = ā€™Vā€™, the right eigenvectors v(j) are stored one
after another in the columns of VR, in the same order
as their eigenvalues.
If JOBVR = ā€™Nā€™, 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 = ā€™Vā€™, 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.

subroutine dgeev (character jobvl, character jobvr, integer n, doubleprecision, dimension( lda, * ) a, integer lda, double precision,dimension( * ) wr, double precision, dimension( * ) wi, doubleprecision, 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
= ā€™Nā€™: left eigenvectors of A are not computed;
= ā€™Vā€™: left eigenvectors of A are computed.

JOBVR

JOBVR is CHARACTER*1
= ā€™Nā€™: right eigenvectors of A are not computed;
= ā€™Vā€™: 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 = ā€™Vā€™, the left eigenvectors u(j) are stored one
after another in the columns of VL, in the same order
as their eigenvalues.
If JOBVL = ā€™Nā€™, 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 = ā€™Vā€™, LDVL >= N.

VR

VR is DOUBLE PRECISION array, dimension (LDVR,N)
If JOBVR = ā€™Vā€™, the right eigenvectors v(j) are stored one
after another in the columns of VR, in the same order
as their eigenvalues.
If JOBVR = ā€™Nā€™, 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 = ā€™Vā€™, 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 = ā€™Vā€™ or JOBVR = ā€™Vā€™, 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.

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
= ā€™Nā€™: left eigenvectors of A are not computed;
= ā€™Vā€™: left eigenvectors of A are computed.

JOBVR

JOBVR is CHARACTER*1
= ā€™Nā€™: right eigenvectors of A are not computed;
= ā€™Vā€™: 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 = ā€™Vā€™, the left eigenvectors u(j) are stored one
after another in the columns of VL, in the same order
as their eigenvalues.
If JOBVL = ā€™Nā€™, 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 = ā€™Vā€™, LDVL >= N.

VR

VR is REAL array, dimension (LDVR,N)
If JOBVR = ā€™Vā€™, the right eigenvectors v(j) are stored one
after another in the columns of VR, in the same order
as their eigenvalues.
If JOBVR = ā€™Nā€™, 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 = ā€™Vā€™, 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 = ā€™Vā€™ or JOBVR = ā€™Vā€™, 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.

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
= ā€™Nā€™: left eigenvectors of A are not computed;
= ā€™Vā€™: left eigenvectors of are computed.

JOBVR

JOBVR is CHARACTER*1
= ā€™Nā€™: right eigenvectors of A are not computed;
= ā€™Vā€™: 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 = ā€™Vā€™, the left eigenvectors u(j) are stored one
after another in the columns of VL, in the same order
as their eigenvalues.
If JOBVL = ā€™Nā€™, 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 = ā€™Vā€™, LDVL >= N.

VR

VR is COMPLEX*16 array, dimension (LDVR,N)
If JOBVR = ā€™Vā€™, the right eigenvectors v(j) are stored one
after another in the columns of VR, in the same order
as their eigenvalues.
If JOBVR = ā€™Nā€™, 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 = ā€™Vā€™, 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.

Author

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