.TH "SRC/claed8.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME SRC/claed8.f .SH SYNOPSIS .br .PP .SS "Functions/Subroutines" .in +1c .ti -1c .RI "subroutine \fBclaed8\fP (k, n, qsiz, q, ldq, d, rho, cutpnt, z, dlambda, q2, ldq2, w, indxp, indx, indxq, perm, givptr, givcol, givnum, info)" .br .RI "\fBCLAED8\fP used by CSTEDC\&. Merges eigenvalues and deflates secular equation\&. Used when the original matrix is dense\&. " .in -1c .SH "Function/Subroutine Documentation" .PP .SS "subroutine claed8 (integer k, integer n, integer qsiz, complex, dimension( ldq, * ) q, integer ldq, real, dimension( * ) d, real rho, integer cutpnt, real, dimension( * ) z, real, dimension( * ) dlambda, complex, dimension( ldq2, * ) q2, integer ldq2, real, dimension( * ) w, integer, dimension( * ) indxp, integer, dimension( * ) indx, integer, dimension( * ) indxq, integer, dimension( * ) perm, integer givptr, integer, dimension( 2, * ) givcol, real, dimension( 2, * ) givnum, integer info)" .PP \fBCLAED8\fP used by CSTEDC\&. Merges eigenvalues and deflates secular equation\&. Used when the original matrix is dense\&. .PP \fBPurpose:\fP .RS 4 .PP .nf CLAED8 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 element 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 Contains the number of non-deflated eigenvalues\&. This is the order of the related secular equation\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The dimension of the symmetric tridiagonal matrix\&. N >= 0\&. .fi .PP .br \fIQSIZ\fP .PP .nf QSIZ is INTEGER The dimension of the unitary matrix used to reduce the dense or band matrix to tridiagonal form\&. QSIZ >= N if ICOMPQ = 1\&. .fi .PP .br \fIQ\fP .PP .nf Q is COMPLEX array, dimension (LDQ,N) On entry, Q contains the eigenvectors of the partially solved system which has been previously updated in matrix multiplies with other partially solved eigensystems\&. 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 \fID\fP .PP .nf D is REAL 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 \fIRHO\fP .PP .nf RHO is REAL Contains the off diagonal element associated with the rank-1 cut which originally split the two submatrices which are now being recombined\&. RHO is modified during the computation to the value required by SLAED3\&. .fi .PP .br \fICUTPNT\fP .PP .nf CUTPNT is INTEGER Contains the location of the last eigenvalue in the leading sub-matrix\&. MIN(1,N) <= CUTPNT <= N\&. .fi .PP .br \fIZ\fP .PP .nf Z is REAL array, dimension (N) On input this vector contains the updating vector (the last row of the first sub-eigenvector matrix and the first row of the second sub-eigenvector matrix)\&. The contents of Z are destroyed during the updating process\&. .fi .PP .br \fIDLAMBDA\fP .PP .nf DLAMBDA is REAL array, dimension (N) Contains a copy of the first K eigenvalues which will be used by SLAED3 to form the secular equation\&. .fi .PP .br \fIQ2\fP .PP .nf Q2 is COMPLEX array, dimension (LDQ2,N) If ICOMPQ = 0, Q2 is not referenced\&. Otherwise, Contains a copy of the first K eigenvectors which will be used by SLAED7 in a matrix multiply (SGEMM) to update the new eigenvectors\&. .fi .PP .br \fILDQ2\fP .PP .nf LDQ2 is INTEGER The leading dimension of the array Q2\&. LDQ2 >= max( 1, N )\&. .fi .PP .br \fIW\fP .PP .nf W is REAL array, dimension (N) This will hold the first k values of the final deflation-altered z-vector and will be passed to SLAED3\&. .fi .PP .br \fIINDXP\fP .PP .nf INDXP is INTEGER array, dimension (N) This will contain the permutation used to place deflated values of D at the end of the array\&. On output INDXP(1:K) points to the nondeflated D-values and INDXP(K+1:N) points to the deflated eigenvalues\&. .fi .PP .br \fIINDX\fP .PP .nf INDX is INTEGER array, dimension (N) This will contain the permutation used to sort the contents of D into ascending order\&. .fi .PP .br \fIINDXQ\fP .PP .nf INDXQ is INTEGER array, dimension (N) This contains 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 CUTPNT added to their values in order to be accurate\&. .fi .PP .br \fIPERM\fP .PP .nf PERM is INTEGER array, dimension (N) Contains the permutations (from deflation and sorting) to be applied to each eigenblock\&. .fi .PP .br \fIGIVPTR\fP .PP .nf GIVPTR is INTEGER Contains the number of Givens rotations which took place in this subproblem\&. .fi .PP .br \fIGIVCOL\fP .PP .nf GIVCOL is INTEGER array, dimension (2, N) Each pair of numbers indicates a pair of columns to take place in a Givens rotation\&. .fi .PP .br \fIGIVNUM\fP .PP .nf GIVNUM is REAL array, dimension (2, N) Each number indicates the S value to be used in the corresponding Givens rotation\&. .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 .PP Definition at line \fB225\fP of file \fBclaed8\&.f\fP\&. .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.