.TH "chsein.f" 3 "Wed Oct 15 2014" "Version 3.4.2" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME chsein.f \- .SH SYNOPSIS .br .PP .SS "Functions/Subroutines" .in +1c .ti -1c .RI "subroutine \fBchsein\fP (SIDE, EIGSRC, INITV, SELECT, N, H, LDH, W, VL, LDVL, VR, LDVR, MM, M, WORK, RWORK, IFAILL, IFAILR, INFO)" .br .RI "\fI\fBCHSEIN\fP \fP" .in -1c .SH "Function/Subroutine Documentation" .PP .SS "subroutine chsein (characterSIDE, characterEIGSRC, characterINITV, logical, dimension( * )SELECT, integerN, complex, dimension( ldh, * )H, integerLDH, complex, dimension( * )W, complex, dimension( ldvl, * )VL, integerLDVL, complex, dimension( ldvr, * )VR, integerLDVR, integerMM, integerM, complex, dimension( * )WORK, real, dimension( * )RWORK, integer, dimension( * )IFAILL, integer, dimension( * )IFAILR, integerINFO)" .PP \fBCHSEIN\fP .PP \fBPurpose: \fP .RS 4 .PP .nf CHSEIN uses inverse iteration to find specified right and/or left eigenvectors of a complex upper Hessenberg matrix H. The right eigenvector x and the left eigenvector y of the matrix H corresponding to an eigenvalue w are defined by: H * x = w * x, y**h * H = w * y**h where y**h denotes the conjugate transpose of the vector y. .fi .PP .RE .PP \fBParameters:\fP .RS 4 \fISIDE\fP .PP .nf SIDE is CHARACTER*1 = 'R': compute right eigenvectors only; = 'L': compute left eigenvectors only; = 'B': compute both right and left eigenvectors. .fi .PP .br \fIEIGSRC\fP .PP .nf EIGSRC is CHARACTER*1 Specifies the source of eigenvalues supplied in W: = 'Q': the eigenvalues were found using CHSEQR; thus, if H has zero subdiagonal elements, and so is block-triangular, then the j-th eigenvalue can be assumed to be an eigenvalue of the block containing the j-th row/column. This property allows CHSEIN to perform inverse iteration on just one diagonal block. = 'N': no assumptions are made on the correspondence between eigenvalues and diagonal blocks. In this case, CHSEIN must always perform inverse iteration using the whole matrix H. .fi .PP .br \fIINITV\fP .PP .nf INITV is CHARACTER*1 = 'N': no initial vectors are supplied; = 'U': user-supplied initial vectors are stored in the arrays VL and/or VR. .fi .PP .br \fISELECT\fP .PP .nf SELECT is LOGICAL array, dimension (N) Specifies the eigenvectors to be computed. To select the eigenvector corresponding to the eigenvalue W(j), SELECT(j) must be set to .TRUE.. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The order of the matrix H. N >= 0. .fi .PP .br \fIH\fP .PP .nf H is COMPLEX array, dimension (LDH,N) The upper Hessenberg matrix H. If a NaN is detected in H, the routine will return with INFO=-6. .fi .PP .br \fILDH\fP .PP .nf LDH is INTEGER The leading dimension of the array H. LDH >= max(1,N). .fi .PP .br \fIW\fP .PP .nf W is COMPLEX array, dimension (N) On entry, the eigenvalues of H. On exit, the real parts of W may have been altered since close eigenvalues are perturbed slightly in searching for independent eigenvectors. .fi .PP .br \fIVL\fP .PP .nf VL is COMPLEX array, dimension (LDVL,MM) On entry, if INITV = 'U' and SIDE = 'L' or 'B', VL must contain starting vectors for the inverse iteration for the left eigenvectors; the starting vector for each eigenvector must be in the same column in which the eigenvector will be stored. On exit, if SIDE = 'L' or 'B', the left eigenvectors specified by SELECT will be stored consecutively in the columns of VL, in the same order as their eigenvalues. If SIDE = 'R', VL is not referenced. .fi .PP .br \fILDVL\fP .PP .nf LDVL is INTEGER The leading dimension of the array VL. LDVL >= max(1,N) if SIDE = 'L' or 'B'; LDVL >= 1 otherwise. .fi .PP .br \fIVR\fP .PP .nf VR is COMPLEX array, dimension (LDVR,MM) On entry, if INITV = 'U' and SIDE = 'R' or 'B', VR must contain starting vectors for the inverse iteration for the right eigenvectors; the starting vector for each eigenvector must be in the same column in which the eigenvector will be stored. On exit, if SIDE = 'R' or 'B', the right eigenvectors specified by SELECT will be stored consecutively in the columns of VR, in the same order as their eigenvalues. If SIDE = 'L', VR is not referenced. .fi .PP .br \fILDVR\fP .PP .nf LDVR is INTEGER The leading dimension of the array VR. LDVR >= max(1,N) if SIDE = 'R' or 'B'; LDVR >= 1 otherwise. .fi .PP .br \fIMM\fP .PP .nf MM is INTEGER The number of columns in the arrays VL and/or VR. MM >= M. .fi .PP .br \fIM\fP .PP .nf M is INTEGER The number of columns in the arrays VL and/or VR required to store the eigenvectors (= the number of .TRUE. elements in SELECT). .fi .PP .br \fIWORK\fP .PP .nf WORK is COMPLEX array, dimension (N*N) .fi .PP .br \fIRWORK\fP .PP .nf RWORK is REAL array, dimension (N) .fi .PP .br \fIIFAILL\fP .PP .nf IFAILL is INTEGER array, dimension (MM) If SIDE = 'L' or 'B', IFAILL(i) = j > 0 if the left eigenvector in the i-th column of VL (corresponding to the eigenvalue w(j)) failed to converge; IFAILL(i) = 0 if the eigenvector converged satisfactorily. If SIDE = 'R', IFAILL is not referenced. .fi .PP .br \fIIFAILR\fP .PP .nf IFAILR is INTEGER array, dimension (MM) If SIDE = 'R' or 'B', IFAILR(i) = j > 0 if the right eigenvector in the i-th column of VR (corresponding to the eigenvalue w(j)) failed to converge; IFAILR(i) = 0 if the eigenvector converged satisfactorily. If SIDE = 'L', IFAILR is not referenced. .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, i is the number of eigenvectors which failed to converge; see IFAILL and IFAILR for further details. .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 \fBDate:\fP .RS 4 November 2013 .RE .PP \fBFurther Details: \fP .RS 4 .PP .nf Each eigenvector is normalized so that the element of largest magnitude has magnitude 1; here the magnitude of a complex number (x,y) is taken to be |x|+|y|. .fi .PP .RE .PP .PP Definition at line 244 of file chsein\&.f\&. .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.