.TH "hsein" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME hsein \- hsein: Hessenberg inverse iteration for eigvec .SH SYNOPSIS .br .PP .SS "Functions" .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 "\fBCHSEIN\fP " .ti -1c .RI "subroutine \fBdhsein\fP (side, eigsrc, initv, select, n, h, ldh, wr, wi, vl, ldvl, vr, ldvr, mm, m, work, ifaill, ifailr, info)" .br .RI "\fBDHSEIN\fP " .ti -1c .RI "subroutine \fBshsein\fP (side, eigsrc, initv, select, n, h, ldh, wr, wi, vl, ldvl, vr, ldvr, mm, m, work, ifaill, ifailr, info)" .br .RI "\fBSHSEIN\fP " .ti -1c .RI "subroutine \fBzhsein\fP (side, eigsrc, initv, select, n, h, ldh, w, vl, ldvl, vr, ldvr, mm, m, work, rwork, ifaill, ifailr, info)" .br .RI "\fBZHSEIN\fP " .in -1c .SH "Detailed Description" .PP .SH "Function Documentation" .PP .SS "subroutine chsein (character side, character eigsrc, character initv, logical, dimension( * ) select, integer n, complex, dimension( ldh, * ) h, integer ldh, complex, dimension( * ) w, complex, dimension( ldvl, * ) vl, integer ldvl, complex, dimension( ldvr, * ) vr, integer ldvr, integer mm, integer m, complex, dimension( * ) work, real, dimension( * ) rwork, integer, dimension( * ) ifaill, integer, dimension( * ) ifailr, integer info)" .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 \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 .SS "subroutine dhsein (character side, character eigsrc, character initv, logical, dimension( * ) select, integer n, double precision, dimension( ldh, * ) h, integer ldh, double precision, dimension( * ) wr, double precision, dimension( * ) wi, double precision, dimension( ldvl, * ) vl, integer ldvl, double precision, dimension( ldvr, * ) vr, integer ldvr, integer mm, integer m, double precision, dimension( * ) work, integer, dimension( * ) ifaill, integer, dimension( * ) ifailr, integer info)" .PP \fBDHSEIN\fP .PP \fBPurpose:\fP .RS 4 .PP .nf DHSEIN uses inverse iteration to find specified right and/or left eigenvectors of a real 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 (WR,WI): = 'Q': the eigenvalues were found using DHSEQR; 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 DHSEIN 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, DHSEIN 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 real eigenvector corresponding to a real eigenvalue WR(j), SELECT(j) must be set to \&.TRUE\&.\&. To select the complex eigenvector corresponding to a complex eigenvalue (WR(j),WI(j)), with complex conjugate (WR(j+1),WI(j+1)), either SELECT(j) or SELECT(j+1) or both must be set to \&.TRUE\&.; then on exit SELECT(j) is \&.TRUE\&. and SELECT(j+1) is \&.FALSE\&.\&. .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 DOUBLE PRECISION 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 \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) On entry, the real and imaginary parts of the eigenvalues of H; a complex conjugate pair of eigenvalues must be stored in consecutive elements of WR and WI\&. On exit, WR may have been altered since close eigenvalues are perturbed slightly in searching for independent eigenvectors\&. .fi .PP .br \fIVL\fP .PP .nf VL is DOUBLE PRECISION 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(s) 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\&. A complex eigenvector corresponding to a complex eigenvalue is stored in two consecutive columns, the first holding the real part and the second the imaginary part\&. 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 DOUBLE PRECISION 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(s) 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\&. A complex eigenvector corresponding to a complex eigenvalue is stored in two consecutive columns, the first holding the real part and the second the imaginary part\&. 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; each selected real eigenvector occupies one column and each selected complex eigenvector occupies two columns\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is DOUBLE PRECISION array, dimension ((N+2)*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 the i-th and (i+1)th columns of VL hold a complex eigenvector, then IFAILL(i) and IFAILL(i+1) are set to the same value\&. 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 the i-th and (i+1)th columns of VR hold a complex eigenvector, then IFAILR(i) and IFAILR(i+1) are set to the same value\&. 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 \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 .SS "subroutine shsein (character side, character eigsrc, character initv, logical, dimension( * ) select, integer n, real, dimension( ldh, * ) h, integer ldh, real, dimension( * ) wr, real, dimension( * ) wi, real, dimension( ldvl, * ) vl, integer ldvl, real, dimension( ldvr, * ) vr, integer ldvr, integer mm, integer m, real, dimension( * ) work, integer, dimension( * ) ifaill, integer, dimension( * ) ifailr, integer info)" .PP \fBSHSEIN\fP .PP \fBPurpose:\fP .RS 4 .PP .nf SHSEIN uses inverse iteration to find specified right and/or left eigenvectors of a real 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 (WR,WI): = 'Q': the eigenvalues were found using SHSEQR; 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 SHSEIN 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, SHSEIN 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 real eigenvector corresponding to a real eigenvalue WR(j), SELECT(j) must be set to \&.TRUE\&.\&. To select the complex eigenvector corresponding to a complex eigenvalue (WR(j),WI(j)), with complex conjugate (WR(j+1),WI(j+1)), either SELECT(j) or SELECT(j+1) or both must be set to \&.TRUE\&.; then on exit SELECT(j) is \&.TRUE\&. and SELECT(j+1) is \&.FALSE\&.\&. .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 REAL 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 \fIWR\fP .PP .nf WR is REAL array, dimension (N) .fi .PP .br \fIWI\fP .PP .nf WI is REAL array, dimension (N) On entry, the real and imaginary parts of the eigenvalues of H; a complex conjugate pair of eigenvalues must be stored in consecutive elements of WR and WI\&. On exit, WR may have been altered since close eigenvalues are perturbed slightly in searching for independent eigenvectors\&. .fi .PP .br \fIVL\fP .PP .nf VL is REAL 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(s) 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\&. A complex eigenvector corresponding to a complex eigenvalue is stored in two consecutive columns, the first holding the real part and the second the imaginary part\&. 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 REAL 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(s) 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\&. A complex eigenvector corresponding to a complex eigenvalue is stored in two consecutive columns, the first holding the real part and the second the imaginary part\&. 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; each selected real eigenvector occupies one column and each selected complex eigenvector occupies two columns\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is REAL array, dimension ((N+2)*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 the i-th and (i+1)th columns of VL hold a complex eigenvector, then IFAILL(i) and IFAILL(i+1) are set to the same value\&. 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 the i-th and (i+1)th columns of VR hold a complex eigenvector, then IFAILR(i) and IFAILR(i+1) are set to the same value\&. 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 \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 .SS "subroutine zhsein (character side, character eigsrc, character initv, logical, dimension( * ) select, integer n, complex*16, dimension( ldh, * ) h, integer ldh, complex*16, dimension( * ) w, complex*16, dimension( ldvl, * ) vl, integer ldvl, complex*16, dimension( ldvr, * ) vr, integer ldvr, integer mm, integer m, complex*16, dimension( * ) work, double precision, dimension( * ) rwork, integer, dimension( * ) ifaill, integer, dimension( * ) ifailr, integer info)" .PP \fBZHSEIN\fP .PP \fBPurpose:\fP .RS 4 .PP .nf ZHSEIN 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 ZHSEQR; 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 ZHSEIN 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, ZHSEIN 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*16 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*16 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*16 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*16 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*16 array, dimension (N*N) .fi .PP .br \fIRWORK\fP .PP .nf RWORK is DOUBLE PRECISION 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 \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 .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.