.TH "stevx" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME stevx \- stevx: eig, bisection .SH SYNOPSIS .br .PP .SS "Functions" .in +1c .ti -1c .RI "subroutine \fBdstevx\fP (jobz, range, n, d, e, vl, vu, il, iu, abstol, m, w, z, ldz, work, iwork, ifail, info)" .br .RI "\fB DSTEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices\fP " .ti -1c .RI "subroutine \fBsstevx\fP (jobz, range, n, d, e, vl, vu, il, iu, abstol, m, w, z, ldz, work, iwork, ifail, info)" .br .RI "\fB SSTEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices\fP " .in -1c .SH "Detailed Description" .PP .SH "Function Documentation" .PP .SS "subroutine dstevx (character jobz, character range, integer n, double precision, dimension( * ) d, double precision, dimension( * ) e, double precision vl, double precision vu, integer il, integer iu, double precision abstol, integer m, double precision, dimension( * ) w, double precision, dimension( ldz, * ) z, integer ldz, double precision, dimension( * ) work, integer, dimension( * ) iwork, integer, dimension( * ) ifail, integer info)" .PP \fB DSTEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices\fP .PP \fBPurpose:\fP .RS 4 .PP .nf DSTEVX computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix A\&. Eigenvalues and eigenvectors can be selected by specifying either a range of values or a range of indices for the desired eigenvalues\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIJOBZ\fP .PP .nf JOBZ is CHARACTER*1 = 'N': Compute eigenvalues only; = 'V': Compute eigenvalues and eigenvectors\&. .fi .PP .br \fIRANGE\fP .PP .nf RANGE is CHARACTER*1 = 'A': all eigenvalues will be found\&. = 'V': all eigenvalues in the half-open interval (VL,VU] will be found\&. = 'I': the IL-th through IU-th eigenvalues will be found\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The order of the matrix\&. N >= 0\&. .fi .PP .br \fID\fP .PP .nf D is DOUBLE PRECISION array, dimension (N) On entry, the n diagonal elements of the tridiagonal matrix A\&. On exit, D may be multiplied by a constant factor chosen to avoid over/underflow in computing the eigenvalues\&. .fi .PP .br \fIE\fP .PP .nf E is DOUBLE PRECISION array, dimension (max(1,N-1)) On entry, the (n-1) subdiagonal elements of the tridiagonal matrix A in elements 1 to N-1 of E\&. On exit, E may be multiplied by a constant factor chosen to avoid over/underflow in computing the eigenvalues\&. .fi .PP .br \fIVL\fP .PP .nf VL is DOUBLE PRECISION If RANGE='V', the lower bound of the interval to be searched for eigenvalues\&. VL < VU\&. Not referenced if RANGE = 'A' or 'I'\&. .fi .PP .br \fIVU\fP .PP .nf VU is DOUBLE PRECISION If RANGE='V', the upper bound of the interval to be searched for eigenvalues\&. VL < VU\&. Not referenced if RANGE = 'A' or 'I'\&. .fi .PP .br \fIIL\fP .PP .nf IL is INTEGER If RANGE='I', the index of the smallest eigenvalue to be returned\&. 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0\&. Not referenced if RANGE = 'A' or 'V'\&. .fi .PP .br \fIIU\fP .PP .nf IU is INTEGER If RANGE='I', the index of the largest eigenvalue to be returned\&. 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0\&. Not referenced if RANGE = 'A' or 'V'\&. .fi .PP .br \fIABSTOL\fP .PP .nf ABSTOL is DOUBLE PRECISION The absolute error tolerance for the eigenvalues\&. An approximate eigenvalue is accepted as converged when it is determined to lie in an interval [a,b] of width less than or equal to ABSTOL + EPS * max( |a|,|b| ) , where EPS is the machine precision\&. If ABSTOL is less than or equal to zero, then EPS*|T| will be used in its place, where |T| is the 1-norm of the tridiagonal matrix\&. Eigenvalues will be computed most accurately when ABSTOL is set to twice the underflow threshold 2*DLAMCH('S'), not zero\&. If this routine returns with INFO>0, indicating that some eigenvectors did not converge, try setting ABSTOL to 2*DLAMCH('S')\&. See 'Computing Small Singular Values of Bidiagonal Matrices with Guaranteed High Relative Accuracy,' by Demmel and Kahan, LAPACK Working Note #3\&. .fi .PP .br \fIM\fP .PP .nf M is INTEGER The total number of eigenvalues found\&. 0 <= M <= N\&. If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1\&. .fi .PP .br \fIW\fP .PP .nf W is DOUBLE PRECISION array, dimension (N) The first M elements contain the selected eigenvalues in ascending order\&. .fi .PP .br \fIZ\fP .PP .nf Z is DOUBLE PRECISION array, dimension (LDZ, max(1,M) ) If JOBZ = 'V', then if INFO = 0, the first M columns of Z contain the orthonormal eigenvectors of the matrix A corresponding to the selected eigenvalues, with the i-th column of Z holding the eigenvector associated with W(i)\&. If an eigenvector fails to converge (INFO > 0), then that column of Z contains the latest approximation to the eigenvector, and the index of the eigenvector is returned in IFAIL\&. If JOBZ = 'N', then Z is not referenced\&. Note: the user must ensure that at least max(1,M) columns are supplied in the array Z; if RANGE = 'V', the exact value of M is not known in advance and an upper bound must be used\&. .fi .PP .br \fILDZ\fP .PP .nf LDZ is INTEGER The leading dimension of the array Z\&. LDZ >= 1, and if JOBZ = 'V', LDZ >= max(1,N)\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is DOUBLE PRECISION array, dimension (5*N) .fi .PP .br \fIIWORK\fP .PP .nf IWORK is INTEGER array, dimension (5*N) .fi .PP .br \fIIFAIL\fP .PP .nf IFAIL is INTEGER array, dimension (N) If JOBZ = 'V', then if INFO = 0, the first M elements of IFAIL are zero\&. If INFO > 0, then IFAIL contains the indices of the eigenvectors that failed to converge\&. If JOBZ = 'N', then IFAIL 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, then i eigenvectors failed to converge\&. Their indices are stored in array IFAIL\&. .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 .SS "subroutine sstevx (character jobz, character range, integer n, real, dimension( * ) d, real, dimension( * ) e, real vl, real vu, integer il, integer iu, real abstol, integer m, real, dimension( * ) w, real, dimension( ldz, * ) z, integer ldz, real, dimension( * ) work, integer, dimension( * ) iwork, integer, dimension( * ) ifail, integer info)" .PP \fB SSTEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices\fP .PP \fBPurpose:\fP .RS 4 .PP .nf SSTEVX computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix A\&. Eigenvalues and eigenvectors can be selected by specifying either a range of values or a range of indices for the desired eigenvalues\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIJOBZ\fP .PP .nf JOBZ is CHARACTER*1 = 'N': Compute eigenvalues only; = 'V': Compute eigenvalues and eigenvectors\&. .fi .PP .br \fIRANGE\fP .PP .nf RANGE is CHARACTER*1 = 'A': all eigenvalues will be found\&. = 'V': all eigenvalues in the half-open interval (VL,VU] will be found\&. = 'I': the IL-th through IU-th eigenvalues will be found\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The order of the matrix\&. N >= 0\&. .fi .PP .br \fID\fP .PP .nf D is REAL array, dimension (N) On entry, the n diagonal elements of the tridiagonal matrix A\&. On exit, D may be multiplied by a constant factor chosen to avoid over/underflow in computing the eigenvalues\&. .fi .PP .br \fIE\fP .PP .nf E is REAL array, dimension (max(1,N-1)) On entry, the (n-1) subdiagonal elements of the tridiagonal matrix A in elements 1 to N-1 of E\&. On exit, E may be multiplied by a constant factor chosen to avoid over/underflow in computing the eigenvalues\&. .fi .PP .br \fIVL\fP .PP .nf VL is REAL If RANGE='V', the lower bound of the interval to be searched for eigenvalues\&. VL < VU\&. Not referenced if RANGE = 'A' or 'I'\&. .fi .PP .br \fIVU\fP .PP .nf VU is REAL If RANGE='V', the upper bound of the interval to be searched for eigenvalues\&. VL < VU\&. Not referenced if RANGE = 'A' or 'I'\&. .fi .PP .br \fIIL\fP .PP .nf IL is INTEGER If RANGE='I', the index of the smallest eigenvalue to be returned\&. 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0\&. Not referenced if RANGE = 'A' or 'V'\&. .fi .PP .br \fIIU\fP .PP .nf IU is INTEGER If RANGE='I', the index of the largest eigenvalue to be returned\&. 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0\&. Not referenced if RANGE = 'A' or 'V'\&. .fi .PP .br \fIABSTOL\fP .PP .nf ABSTOL is REAL The absolute error tolerance for the eigenvalues\&. An approximate eigenvalue is accepted as converged when it is determined to lie in an interval [a,b] of width less than or equal to ABSTOL + EPS * max( |a|,|b| ) , where EPS is the machine precision\&. If ABSTOL is less than or equal to zero, then EPS*|T| will be used in its place, where |T| is the 1-norm of the tridiagonal matrix\&. Eigenvalues will be computed most accurately when ABSTOL is set to twice the underflow threshold 2*SLAMCH('S'), not zero\&. If this routine returns with INFO>0, indicating that some eigenvectors did not converge, try setting ABSTOL to 2*SLAMCH('S')\&. See 'Computing Small Singular Values of Bidiagonal Matrices with Guaranteed High Relative Accuracy,' by Demmel and Kahan, LAPACK Working Note #3\&. .fi .PP .br \fIM\fP .PP .nf M is INTEGER The total number of eigenvalues found\&. 0 <= M <= N\&. If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1\&. .fi .PP .br \fIW\fP .PP .nf W is REAL array, dimension (N) The first M elements contain the selected eigenvalues in ascending order\&. .fi .PP .br \fIZ\fP .PP .nf Z is REAL array, dimension (LDZ, max(1,M) ) If JOBZ = 'V', then if INFO = 0, the first M columns of Z contain the orthonormal eigenvectors of the matrix A corresponding to the selected eigenvalues, with the i-th column of Z holding the eigenvector associated with W(i)\&. If an eigenvector fails to converge (INFO > 0), then that column of Z contains the latest approximation to the eigenvector, and the index of the eigenvector is returned in IFAIL\&. If JOBZ = 'N', then Z is not referenced\&. Note: the user must ensure that at least max(1,M) columns are supplied in the array Z; if RANGE = 'V', the exact value of M is not known in advance and an upper bound must be used\&. .fi .PP .br \fILDZ\fP .PP .nf LDZ is INTEGER The leading dimension of the array Z\&. LDZ >= 1, and if JOBZ = 'V', LDZ >= max(1,N)\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is REAL array, dimension (5*N) .fi .PP .br \fIIWORK\fP .PP .nf IWORK is INTEGER array, dimension (5*N) .fi .PP .br \fIIFAIL\fP .PP .nf IFAIL is INTEGER array, dimension (N) If JOBZ = 'V', then if INFO = 0, the first M elements of IFAIL are zero\&. If INFO > 0, then IFAIL contains the indices of the eigenvectors that failed to converge\&. If JOBZ = 'N', then IFAIL 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, then i eigenvectors failed to converge\&. Their indices are stored in array IFAIL\&. .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 .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.