.TH "larra" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME larra \- larra: step in stemr .SH SYNOPSIS .br .PP .SS "Functions" .in +1c .ti -1c .RI "subroutine \fBdlarra\fP (n, d, e, e2, spltol, tnrm, nsplit, isplit, info)" .br .RI "\fBDLARRA\fP computes the splitting points with the specified threshold\&. " .ti -1c .RI "subroutine \fBslarra\fP (n, d, e, e2, spltol, tnrm, nsplit, isplit, info)" .br .RI "\fBSLARRA\fP computes the splitting points with the specified threshold\&. " .in -1c .SH "Detailed Description" .PP .SH "Function Documentation" .PP .SS "subroutine dlarra (integer n, double precision, dimension( * ) d, double precision, dimension( * ) e, double precision, dimension( * ) e2, double precision spltol, double precision tnrm, integer nsplit, integer, dimension( * ) isplit, integer info)" .PP \fBDLARRA\fP computes the splitting points with the specified threshold\&. .PP \fBPurpose:\fP .RS 4 .PP .nf Compute the splitting points with threshold SPLTOL\&. DLARRA sets any 'small' off-diagonal elements to zero\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \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 T\&. .fi .PP .br \fIE\fP .PP .nf E is DOUBLE PRECISION array, dimension (N) On entry, the first (N-1) entries contain the subdiagonal elements of the tridiagonal matrix T; E(N) need not be set\&. On exit, the entries E( ISPLIT( I ) ), 1 <= I <= NSPLIT, are set to zero, the other entries of E are untouched\&. .fi .PP .br \fIE2\fP .PP .nf E2 is DOUBLE PRECISION array, dimension (N) On entry, the first (N-1) entries contain the SQUARES of the subdiagonal elements of the tridiagonal matrix T; E2(N) need not be set\&. On exit, the entries E2( ISPLIT( I ) ), 1 <= I <= NSPLIT, have been set to zero .fi .PP .br \fISPLTOL\fP .PP .nf SPLTOL is DOUBLE PRECISION The threshold for splitting\&. Two criteria can be used: SPLTOL<0 : criterion based on absolute off-diagonal value SPLTOL>0 : criterion that preserves relative accuracy .fi .PP .br \fITNRM\fP .PP .nf TNRM is DOUBLE PRECISION The norm of the matrix\&. .fi .PP .br \fINSPLIT\fP .PP .nf NSPLIT is INTEGER The number of blocks T splits into\&. 1 <= NSPLIT <= N\&. .fi .PP .br \fIISPLIT\fP .PP .nf ISPLIT is INTEGER array, dimension (N) The splitting points, at which T breaks up into blocks\&. The first block consists of rows/columns 1 to ISPLIT(1), the second of rows/columns ISPLIT(1)+1 through ISPLIT(2), etc\&., and the NSPLIT-th consists of rows/columns ISPLIT(NSPLIT-1)+1 through ISPLIT(NSPLIT)=N\&. .fi .PP .br \fIINFO\fP .PP .nf INFO is INTEGER = 0: successful exit .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 \fBContributors:\fP .RS 4 Beresford Parlett, University of California, Berkeley, USA .br Jim Demmel, University of California, Berkeley, USA .br Inderjit Dhillon, University of Texas, Austin, USA .br Osni Marques, LBNL/NERSC, USA .br Christof Voemel, University of California, Berkeley, USA .RE .PP .SS "subroutine slarra (integer n, real, dimension( * ) d, real, dimension( * ) e, real, dimension( * ) e2, real spltol, real tnrm, integer nsplit, integer, dimension( * ) isplit, integer info)" .PP \fBSLARRA\fP computes the splitting points with the specified threshold\&. .PP \fBPurpose:\fP .RS 4 .PP .nf Compute the splitting points with threshold SPLTOL\&. SLARRA sets any 'small' off-diagonal elements to zero\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \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 T\&. .fi .PP .br \fIE\fP .PP .nf E is REAL array, dimension (N) On entry, the first (N-1) entries contain the subdiagonal elements of the tridiagonal matrix T; E(N) need not be set\&. On exit, the entries E( ISPLIT( I ) ), 1 <= I <= NSPLIT, are set to zero, the other entries of E are untouched\&. .fi .PP .br \fIE2\fP .PP .nf E2 is REAL array, dimension (N) On entry, the first (N-1) entries contain the SQUARES of the subdiagonal elements of the tridiagonal matrix T; E2(N) need not be set\&. On exit, the entries E2( ISPLIT( I ) ), 1 <= I <= NSPLIT, have been set to zero .fi .PP .br \fISPLTOL\fP .PP .nf SPLTOL is REAL The threshold for splitting\&. Two criteria can be used: SPLTOL<0 : criterion based on absolute off-diagonal value SPLTOL>0 : criterion that preserves relative accuracy .fi .PP .br \fITNRM\fP .PP .nf TNRM is REAL The norm of the matrix\&. .fi .PP .br \fINSPLIT\fP .PP .nf NSPLIT is INTEGER The number of blocks T splits into\&. 1 <= NSPLIT <= N\&. .fi .PP .br \fIISPLIT\fP .PP .nf ISPLIT is INTEGER array, dimension (N) The splitting points, at which T breaks up into blocks\&. The first block consists of rows/columns 1 to ISPLIT(1), the second of rows/columns ISPLIT(1)+1 through ISPLIT(2), etc\&., and the NSPLIT-th consists of rows/columns ISPLIT(NSPLIT-1)+1 through ISPLIT(NSPLIT)=N\&. .fi .PP .br \fIINFO\fP .PP .nf INFO is INTEGER = 0: successful exit .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 \fBContributors:\fP .RS 4 Beresford Parlett, University of California, Berkeley, USA .br Jim Demmel, University of California, Berkeley, USA .br Inderjit Dhillon, University of Texas, Austin, USA .br Osni Marques, LBNL/NERSC, USA .br Christof Voemel, University of California, Berkeley, USA .RE .PP .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.