.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\&.