.TH "geev" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME geev \- geev: eig .SH SYNOPSIS .br .PP .SS "Functions" .in +1c .ti -1c .RI "subroutine \fBcgeev\fP (jobvl, jobvr, n, a, lda, w, vl, ldvl, vr, ldvr, work, lwork, rwork, info)" .br .RI "\fB CGEEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices\fP " .ti -1c .RI "subroutine \fBdgeev\fP (jobvl, jobvr, n, a, lda, wr, wi, vl, ldvl, vr, ldvr, work, lwork, info)" .br .RI "\fB DGEEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices\fP " .ti -1c .RI "subroutine \fBsgeev\fP (jobvl, jobvr, n, a, lda, wr, wi, vl, ldvl, vr, ldvr, work, lwork, info)" .br .RI "\fB SGEEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices\fP " .ti -1c .RI "subroutine \fBzgeev\fP (jobvl, jobvr, n, a, lda, w, vl, ldvl, vr, ldvr, work, lwork, rwork, info)" .br .RI "\fB ZGEEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices\fP " .in -1c .SH "Detailed Description" .PP .SH "Function Documentation" .PP .SS "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)" .PP \fB CGEEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> 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\&. !> .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIJOBVL\fP .PP .nf !> JOBVL is CHARACTER*1 !> = 'N': left eigenvectors of A are not computed; !> = 'V': left eigenvectors of are computed\&. !> .fi .PP .br \fIJOBVR\fP .PP .nf !> JOBVR is CHARACTER*1 !> = 'N': right eigenvectors of A are not computed; !> = 'V': right eigenvectors of A are computed\&. !> .fi .PP .br \fIN\fP .PP .nf !> N is INTEGER !> The order of the matrix A\&. N >= 0\&. !> .fi .PP .br \fIA\fP .PP .nf !> A is COMPLEX array, dimension (LDA,N) !> On entry, the N-by-N matrix A\&. !> On exit, A has been overwritten\&. !> .fi .PP .br \fILDA\fP .PP .nf !> LDA is INTEGER !> The leading dimension of the array A\&. LDA >= max(1,N)\&. !> .fi .PP .br \fIW\fP .PP .nf !> W is COMPLEX array, dimension (N) !> W contains the computed eigenvalues\&. !> .fi .PP .br \fIVL\fP .PP .nf !> 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\&. !> .fi .PP .br \fILDVL\fP .PP .nf !> LDVL is INTEGER !> The leading dimension of the array VL\&. LDVL >= 1; if !> JOBVL = 'V', LDVL >= N\&. !> .fi .PP .br \fIVR\fP .PP .nf !> 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\&. !> .fi .PP .br \fILDVR\fP .PP .nf !> LDVR is INTEGER !> The leading dimension of the array VR\&. LDVR >= 1; if !> JOBVR = 'V', LDVR >= N\&. !> .fi .PP .br \fIWORK\fP .PP .nf !> WORK is COMPLEX array, dimension (MAX(1,LWORK)) !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&. !> .fi .PP .br \fILWORK\fP .PP .nf !> 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\&. !> .fi .PP .br \fIRWORK\fP .PP .nf !> RWORK is REAL array, dimension (2*N) !> .fi .PP .br \fIINFO\fP .PP .nf !> 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\&. !> .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP .PP Definition at line \fB178\fP of file \fBcgeev\&.f\fP\&. .SS "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)" .PP \fB DGEEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> 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\&. !> .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIJOBVL\fP .PP .nf !> JOBVL is CHARACTER*1 !> = 'N': left eigenvectors of A are not computed; !> = 'V': left eigenvectors of A are computed\&. !> .fi .PP .br \fIJOBVR\fP .PP .nf !> JOBVR is CHARACTER*1 !> = 'N': right eigenvectors of A are not computed; !> = 'V': right eigenvectors of A are computed\&. !> .fi .PP .br \fIN\fP .PP .nf !> N is INTEGER !> The order of the matrix A\&. N >= 0\&. !> .fi .PP .br \fIA\fP .PP .nf !> A is DOUBLE PRECISION array, dimension (LDA,N) !> On entry, the N-by-N matrix A\&. !> On exit, A has been overwritten\&. !> .fi .PP .br \fILDA\fP .PP .nf !> LDA is INTEGER !> The leading dimension of the array A\&. LDA >= max(1,N)\&. !> .fi .PP .br \fIWR\fP .PP .nf !> WR is DOUBLE PRECISION array, dimension (N) !> .fi .PP .br \fIWI\fP .PP .nf !> 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\&. !> .fi .PP .br \fIVL\fP .PP .nf !> 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)\&. !> .fi .PP .br \fILDVL\fP .PP .nf !> LDVL is INTEGER !> The leading dimension of the array VL\&. LDVL >= 1; if !> JOBVL = 'V', LDVL >= N\&. !> .fi .PP .br \fIVR\fP .PP .nf !> 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)\&. !> .fi .PP .br \fILDVR\fP .PP .nf !> LDVR is INTEGER !> The leading dimension of the array VR\&. LDVR >= 1; if !> JOBVR = 'V', LDVR >= N\&. !> .fi .PP .br \fIWORK\fP .PP .nf !> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&. !> .fi .PP .br \fILWORK\fP .PP .nf !> 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\&. !> .fi .PP .br \fIINFO\fP .PP .nf !> 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\&. !> .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP .PP Definition at line \fB190\fP of file \fBdgeev\&.f\fP\&. .SS "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)" .PP \fB SGEEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> 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\&. !> .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIJOBVL\fP .PP .nf !> JOBVL is CHARACTER*1 !> = 'N': left eigenvectors of A are not computed; !> = 'V': left eigenvectors of A are computed\&. !> .fi .PP .br \fIJOBVR\fP .PP .nf !> JOBVR is CHARACTER*1 !> = 'N': right eigenvectors of A are not computed; !> = 'V': right eigenvectors of A are computed\&. !> .fi .PP .br \fIN\fP .PP .nf !> N is INTEGER !> The order of the matrix A\&. N >= 0\&. !> .fi .PP .br \fIA\fP .PP .nf !> A is REAL array, dimension (LDA,N) !> On entry, the N-by-N matrix A\&. !> On exit, A has been overwritten\&. !> .fi .PP .br \fILDA\fP .PP .nf !> LDA is INTEGER !> The leading dimension of the array A\&. LDA >= max(1,N)\&. !> .fi .PP .br \fIWR\fP .PP .nf !> WR is REAL array, dimension (N) !> .fi .PP .br \fIWI\fP .PP .nf !> 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\&. !> .fi .PP .br \fIVL\fP .PP .nf !> 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)\&. !> .fi .PP .br \fILDVL\fP .PP .nf !> LDVL is INTEGER !> The leading dimension of the array VL\&. LDVL >= 1; if !> JOBVL = 'V', LDVL >= N\&. !> .fi .PP .br \fIVR\fP .PP .nf !> 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)\&. !> .fi .PP .br \fILDVR\fP .PP .nf !> LDVR is INTEGER !> The leading dimension of the array VR\&. LDVR >= 1; if !> JOBVR = 'V', LDVR >= N\&. !> .fi .PP .br \fIWORK\fP .PP .nf !> WORK is REAL array, dimension (MAX(1,LWORK)) !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&. !> .fi .PP .br \fILWORK\fP .PP .nf !> 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\&. !> .fi .PP .br \fIINFO\fP .PP .nf !> 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\&. !> .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP .PP Definition at line \fB190\fP of file \fBsgeev\&.f\fP\&. .SS "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)" .PP \fB ZGEEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> 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\&. !> .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIJOBVL\fP .PP .nf !> JOBVL is CHARACTER*1 !> = 'N': left eigenvectors of A are not computed; !> = 'V': left eigenvectors of are computed\&. !> .fi .PP .br \fIJOBVR\fP .PP .nf !> JOBVR is CHARACTER*1 !> = 'N': right eigenvectors of A are not computed; !> = 'V': right eigenvectors of A are computed\&. !> .fi .PP .br \fIN\fP .PP .nf !> N is INTEGER !> The order of the matrix A\&. N >= 0\&. !> .fi .PP .br \fIA\fP .PP .nf !> A is COMPLEX*16 array, dimension (LDA,N) !> On entry, the N-by-N matrix A\&. !> On exit, A has been overwritten\&. !> .fi .PP .br \fILDA\fP .PP .nf !> LDA is INTEGER !> The leading dimension of the array A\&. LDA >= max(1,N)\&. !> .fi .PP .br \fIW\fP .PP .nf !> W is COMPLEX*16 array, dimension (N) !> W contains the computed eigenvalues\&. !> .fi .PP .br \fIVL\fP .PP .nf !> 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\&. !> .fi .PP .br \fILDVL\fP .PP .nf !> LDVL is INTEGER !> The leading dimension of the array VL\&. LDVL >= 1; if !> JOBVL = 'V', LDVL >= N\&. !> .fi .PP .br \fIVR\fP .PP .nf !> 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\&. !> .fi .PP .br \fILDVR\fP .PP .nf !> LDVR is INTEGER !> The leading dimension of the array VR\&. LDVR >= 1; if !> JOBVR = 'V', LDVR >= N\&. !> .fi .PP .br \fIWORK\fP .PP .nf !> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&. !> .fi .PP .br \fILWORK\fP .PP .nf !> 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\&. !> .fi .PP .br \fIRWORK\fP .PP .nf !> RWORK is DOUBLE PRECISION array, dimension (2*N) !> .fi .PP .br \fIINFO\fP .PP .nf !> 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\&. !> .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP .PP Definition at line \fB178\fP of file \fBzgeev\&.f\fP\&. .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.