.TH "SRC/dlaed2.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME SRC/dlaed2.f .SH SYNOPSIS .br .PP .SS "Functions/Subroutines" .in +1c .ti -1c .RI "subroutine \fBdlaed2\fP (k, n, n1, d, q, ldq, indxq, rho, z, dlambda, w, q2, indx, indxc, indxp, coltyp, info)" .br .RI "\fBDLAED2\fP used by DSTEDC\&. Merges eigenvalues and deflates secular equation\&. Used when the original matrix is tridiagonal\&. " .in -1c .SH "Function/Subroutine Documentation" .PP .SS "subroutine dlaed2 (integer k, integer n, integer n1, double precision, dimension( * ) d, double precision, dimension( ldq, * ) q, integer ldq, integer, dimension( * ) indxq, double precision rho, double precision, dimension( * ) z, double precision, dimension( * ) dlambda, double precision, dimension( * ) w, double precision, dimension( * ) q2, integer, dimension( * ) indx, integer, dimension( * ) indxc, integer, dimension( * ) indxp, integer, dimension( * ) coltyp, integer info)" .PP \fBDLAED2\fP used by DSTEDC\&. Merges eigenvalues and deflates secular equation\&. Used when the original matrix is tridiagonal\&. .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> DLAED2 merges the two sets of eigenvalues together into a single !> sorted set\&. Then it tries to deflate the size of the problem\&. !> There are two ways in which deflation can occur: when two or more !> eigenvalues are close together or if there is a tiny entry in the !> Z vector\&. For each such occurrence the order of the related secular !> equation problem is reduced by one\&. !> .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIK\fP .PP .nf !> K is INTEGER !> The number of non-deflated eigenvalues, and the order of the !> related secular equation\&. 0 <= K <=N\&. !> .fi .PP .br \fIN\fP .PP .nf !> N is INTEGER !> The dimension of the symmetric tridiagonal matrix\&. N >= 0\&. !> .fi .PP .br \fIN1\fP .PP .nf !> N1 is INTEGER !> The location of the last eigenvalue in the leading sub-matrix\&. !> min(1,N) <= N1 <= N/2\&. !> .fi .PP .br \fID\fP .PP .nf !> D is DOUBLE PRECISION array, dimension (N) !> On entry, D contains the eigenvalues of the two submatrices to !> be combined\&. !> On exit, D contains the trailing (N-K) updated eigenvalues !> (those which were deflated) sorted into increasing order\&. !> .fi .PP .br \fIQ\fP .PP .nf !> Q is DOUBLE PRECISION array, dimension (LDQ, N) !> On entry, Q contains the eigenvectors of two submatrices in !> the two square blocks with corners at (1,1), (N1,N1) !> and (N1+1, N1+1), (N,N)\&. !> On exit, Q contains the trailing (N-K) updated eigenvectors !> (those which were deflated) in its last N-K columns\&. !> .fi .PP .br \fILDQ\fP .PP .nf !> LDQ is INTEGER !> The leading dimension of the array Q\&. LDQ >= max(1,N)\&. !> .fi .PP .br \fIINDXQ\fP .PP .nf !> INDXQ is INTEGER array, dimension (N) !> The permutation which separately sorts the two sub-problems !> in D into ascending order\&. Note that elements in the second !> half of this permutation must first have N1 added to their !> values\&. Destroyed on exit\&. !> .fi .PP .br \fIRHO\fP .PP .nf !> RHO is DOUBLE PRECISION !> On entry, the off-diagonal element associated with the rank-1 !> cut which originally split the two submatrices which are now !> being recombined\&. !> On exit, RHO has been modified to the value required by !> DLAED3\&. !> .fi .PP .br \fIZ\fP .PP .nf !> Z is DOUBLE PRECISION array, dimension (N) !> On entry, Z contains the updating vector (the last !> row of the first sub-eigenvector matrix and the first row of !> the second sub-eigenvector matrix)\&. !> On exit, the contents of Z have been destroyed by the updating !> process\&. !> .fi .PP .br \fIDLAMBDA\fP .PP .nf !> DLAMBDA is DOUBLE PRECISION array, dimension (N) !> A copy of the first K eigenvalues which will be used by !> DLAED3 to form the secular equation\&. !> .fi .PP .br \fIW\fP .PP .nf !> W is DOUBLE PRECISION array, dimension (N) !> The first k values of the final deflation-altered z-vector !> which will be passed to DLAED3\&. !> .fi .PP .br \fIQ2\fP .PP .nf !> Q2 is DOUBLE PRECISION array, dimension (N1**2+(N-N1)**2) !> A copy of the first K eigenvectors which will be used by !> DLAED3 in a matrix multiply (DGEMM) to solve for the new !> eigenvectors\&. !> .fi .PP .br \fIINDX\fP .PP .nf !> INDX is INTEGER array, dimension (N) !> The permutation used to sort the contents of DLAMBDA into !> ascending order\&. !> .fi .PP .br \fIINDXC\fP .PP .nf !> INDXC is INTEGER array, dimension (N) !> The permutation used to arrange the columns of the deflated !> Q matrix into three groups: the first group contains non-zero !> elements only at and above N1, the second contains !> non-zero elements only below N1, and the third is dense\&. !> .fi .PP .br \fIINDXP\fP .PP .nf !> INDXP is INTEGER array, dimension (N) !> The permutation used to place deflated values of D at the end !> of the array\&. INDXP(1:K) points to the nondeflated D-values !> and INDXP(K+1:N) points to the deflated eigenvalues\&. !> .fi .PP .br \fICOLTYP\fP .PP .nf !> COLTYP is INTEGER array, dimension (N) !> During execution, a label which will indicate which of the !> following types a column in the Q2 matrix is: !> 1 : non-zero in the upper half only; !> 2 : dense; !> 3 : non-zero in the lower half only; !> 4 : deflated\&. !> On exit, COLTYP(i) is the number of columns of type i, !> for i=1 to 4 only\&. !> .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\&. !> .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 Jeff Rutter, Computer Science Division, University of California at Berkeley, USA .br Modified by Francoise Tisseur, University of Tennessee .RE .PP .PP Definition at line \fB210\fP of file \fBdlaed2\&.f\fP\&. .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.