.TH "larrk" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME larrk \- larrk: step in stemr, compute one eigval .SH SYNOPSIS .br .PP .SS "Functions" .in +1c .ti -1c .RI "subroutine \fBdlarrk\fP (n, iw, gl, gu, d, e2, pivmin, reltol, w, werr, info)" .br .RI "\fBDLARRK\fP computes one eigenvalue of a symmetric tridiagonal matrix T to suitable accuracy\&. " .ti -1c .RI "subroutine \fBslarrk\fP (n, iw, gl, gu, d, e2, pivmin, reltol, w, werr, info)" .br .RI "\fBSLARRK\fP computes one eigenvalue of a symmetric tridiagonal matrix T to suitable accuracy\&. " .in -1c .SH "Detailed Description" .PP .SH "Function Documentation" .PP .SS "subroutine dlarrk (integer n, integer iw, double precision gl, double precision gu, double precision, dimension( * ) d, double precision, dimension( * ) e2, double precision pivmin, double precision reltol, double precision w, double precision werr, integer info)" .PP \fBDLARRK\fP computes one eigenvalue of a symmetric tridiagonal matrix T to suitable accuracy\&. .PP \fBPurpose:\fP .RS 4 .PP .nf DLARRK computes one eigenvalue of a symmetric tridiagonal matrix T to suitable accuracy\&. This is an auxiliary code to be called from DSTEMR\&. To avoid overflow, the matrix must be scaled so that its largest element is no greater than overflow**(1/2) * underflow**(1/4) in absolute value, and for greatest accuracy, it should not be much smaller than that\&. See W\&. Kahan 'Accurate Eigenvalues of a Symmetric Tridiagonal Matrix', Report CS41, Computer Science Dept\&., Stanford University, July 21, 1966\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIN\fP .PP .nf N is INTEGER The order of the tridiagonal matrix T\&. N >= 0\&. .fi .PP .br \fIIW\fP .PP .nf IW is INTEGER The index of the eigenvalues to be returned\&. .fi .PP .br \fIGL\fP .PP .nf GL is DOUBLE PRECISION .fi .PP .br \fIGU\fP .PP .nf GU is DOUBLE PRECISION An upper and a lower bound on the eigenvalue\&. .fi .PP .br \fID\fP .PP .nf D is DOUBLE PRECISION array, dimension (N) The n diagonal elements of the tridiagonal matrix T\&. .fi .PP .br \fIE2\fP .PP .nf E2 is DOUBLE PRECISION array, dimension (N-1) The (n-1) squared off-diagonal elements of the tridiagonal matrix T\&. .fi .PP .br \fIPIVMIN\fP .PP .nf PIVMIN is DOUBLE PRECISION The minimum pivot allowed in the Sturm sequence for T\&. .fi .PP .br \fIRELTOL\fP .PP .nf RELTOL is DOUBLE PRECISION The minimum relative width of an interval\&. When an interval is narrower than RELTOL times the larger (in magnitude) endpoint, then it is considered to be sufficiently small, i\&.e\&., converged\&. Note: this should always be at least radix*machine epsilon\&. .fi .PP .br \fIW\fP .PP .nf W is DOUBLE PRECISION .fi .PP .br \fIWERR\fP .PP .nf WERR is DOUBLE PRECISION The error bound on the corresponding eigenvalue approximation in W\&. .fi .PP .br \fIINFO\fP .PP .nf INFO is INTEGER = 0: Eigenvalue converged = -1: Eigenvalue did NOT converge .fi .PP .RE .PP \fBInternal Parameters:\fP .RS 4 .PP .nf FUDGE DOUBLE PRECISION, default = 2 A 'fudge factor' to widen the Gershgorin intervals\&. .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 slarrk (integer n, integer iw, real gl, real gu, real, dimension( * ) d, real, dimension( * ) e2, real pivmin, real reltol, real w, real werr, integer info)" .PP \fBSLARRK\fP computes one eigenvalue of a symmetric tridiagonal matrix T to suitable accuracy\&. .PP \fBPurpose:\fP .RS 4 .PP .nf SLARRK computes one eigenvalue of a symmetric tridiagonal matrix T to suitable accuracy\&. This is an auxiliary code to be called from SSTEMR\&. To avoid overflow, the matrix must be scaled so that its largest element is no greater than overflow**(1/2) * underflow**(1/4) in absolute value, and for greatest accuracy, it should not be much smaller than that\&. See W\&. Kahan 'Accurate Eigenvalues of a Symmetric Tridiagonal Matrix', Report CS41, Computer Science Dept\&., Stanford University, July 21, 1966\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIN\fP .PP .nf N is INTEGER The order of the tridiagonal matrix T\&. N >= 0\&. .fi .PP .br \fIIW\fP .PP .nf IW is INTEGER The index of the eigenvalues to be returned\&. .fi .PP .br \fIGL\fP .PP .nf GL is REAL .fi .PP .br \fIGU\fP .PP .nf GU is REAL An upper and a lower bound on the eigenvalue\&. .fi .PP .br \fID\fP .PP .nf D is REAL array, dimension (N) The n diagonal elements of the tridiagonal matrix T\&. .fi .PP .br \fIE2\fP .PP .nf E2 is REAL array, dimension (N-1) The (n-1) squared off-diagonal elements of the tridiagonal matrix T\&. .fi .PP .br \fIPIVMIN\fP .PP .nf PIVMIN is REAL The minimum pivot allowed in the Sturm sequence for T\&. .fi .PP .br \fIRELTOL\fP .PP .nf RELTOL is REAL The minimum relative width of an interval\&. When an interval is narrower than RELTOL times the larger (in magnitude) endpoint, then it is considered to be sufficiently small, i\&.e\&., converged\&. Note: this should always be at least radix*machine epsilon\&. .fi .PP .br \fIW\fP .PP .nf W is REAL .fi .PP .br \fIWERR\fP .PP .nf WERR is REAL The error bound on the corresponding eigenvalue approximation in W\&. .fi .PP .br \fIINFO\fP .PP .nf INFO is INTEGER = 0: Eigenvalue converged = -1: Eigenvalue did NOT converge .fi .PP .RE .PP \fBInternal Parameters:\fP .RS 4 .PP .nf FUDGE REAL , default = 2 A 'fudge factor' to widen the Gershgorin intervals\&. .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\&.