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---
:name: dlaed2
:md5sum: d8f308f281405229efe4f87a4a67b923
:category: :subroutine
:arguments:
- k:
:type: integer
:intent: output
- n:
:type: integer
:intent: input
- n1:
:type: integer
:intent: input
- d:
:type: doublereal
:intent: input/output
:dims:
- n
- q:
:type: doublereal
:intent: input/output
:dims:
- ldq
- n
- ldq:
:type: integer
:intent: input
- indxq:
:type: integer
:intent: input/output
:dims:
- n
- rho:
:type: doublereal
:intent: input/output
- z:
:type: doublereal
:intent: input
:dims:
- n
- dlamda:
:type: doublereal
:intent: output
:dims:
- n
- w:
:type: doublereal
:intent: output
:dims:
- n
- q2:
:type: doublereal
:intent: output
:dims:
- pow(n1,2)+pow(n-n1,2)
- indx:
:type: integer
:intent: workspace
:dims:
- n
- indxc:
:type: integer
:intent: output
:dims:
- n
- indxp:
:type: integer
:intent: workspace
:dims:
- n
- coltyp:
:type: integer
:intent: output
:dims:
- n
- info:
:type: integer
:intent: output
:substitutions: {}
:fortran_help: " SUBROUTINE DLAED2( K, N, N1, D, Q, LDQ, INDXQ, RHO, Z, DLAMDA, W, Q2, INDX, INDXC, INDXP, COLTYP, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* DLAED2 merges the two sets of eigenvalues together into a single\n\
* sorted set. Then it tries to deflate the size of the problem.\n\
* There are two ways in which deflation can occur: when two or more\n\
* eigenvalues are close together or if there is a tiny entry in the\n\
* Z vector. For each such occurrence the order of the related secular\n\
* equation problem is reduced by one.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* K (output) INTEGER\n\
* The number of non-deflated eigenvalues, and the order of the\n\
* related secular equation. 0 <= K <=N.\n\
*\n\
* N (input) INTEGER\n\
* The dimension of the symmetric tridiagonal matrix. N >= 0.\n\
*\n\
* N1 (input) INTEGER\n\
* The location of the last eigenvalue in the leading sub-matrix.\n\
* min(1,N) <= N1 <= N/2.\n\
*\n\
* D (input/output) DOUBLE PRECISION array, dimension (N)\n\
* On entry, D contains the eigenvalues of the two submatrices to\n\
* be combined.\n\
* On exit, D contains the trailing (N-K) updated eigenvalues\n\
* (those which were deflated) sorted into increasing order.\n\
*\n\
* Q (input/output) DOUBLE PRECISION array, dimension (LDQ, N)\n\
* On entry, Q contains the eigenvectors of two submatrices in\n\
* the two square blocks with corners at (1,1), (N1,N1)\n\
* and (N1+1, N1+1), (N,N).\n\
* On exit, Q contains the trailing (N-K) updated eigenvectors\n\
* (those which were deflated) in its last N-K columns.\n\
*\n\
* LDQ (input) INTEGER\n\
* The leading dimension of the array Q. LDQ >= max(1,N).\n\
*\n\
* INDXQ (input/output) INTEGER array, dimension (N)\n\
* The permutation which separately sorts the two sub-problems\n\
* in D into ascending order. Note that elements in the second\n\
* half of this permutation must first have N1 added to their\n\
* values. Destroyed on exit.\n\
*\n\
* RHO (input/output) DOUBLE PRECISION\n\
* On entry, the off-diagonal element associated with the rank-1\n\
* cut which originally split the two submatrices which are now\n\
* being recombined.\n\
* On exit, RHO has been modified to the value required by\n\
* DLAED3.\n\
*\n\
* Z (input) DOUBLE PRECISION array, dimension (N)\n\
* On entry, Z contains the updating vector (the last\n\
* row of the first sub-eigenvector matrix and the first row of\n\
* the second sub-eigenvector matrix).\n\
* On exit, the contents of Z have been destroyed by the updating\n\
* process.\n\
*\n\
* DLAMDA (output) DOUBLE PRECISION array, dimension (N)\n\
* A copy of the first K eigenvalues which will be used by\n\
* DLAED3 to form the secular equation.\n\
*\n\
* W (output) DOUBLE PRECISION array, dimension (N)\n\
* The first k values of the final deflation-altered z-vector\n\
* which will be passed to DLAED3.\n\
*\n\
* Q2 (output) DOUBLE PRECISION array, dimension (N1**2+(N-N1)**2)\n\
* A copy of the first K eigenvectors which will be used by\n\
* DLAED3 in a matrix multiply (DGEMM) to solve for the new\n\
* eigenvectors.\n\
*\n\
* INDX (workspace) INTEGER array, dimension (N)\n\
* The permutation used to sort the contents of DLAMDA into\n\
* ascending order.\n\
*\n\
* INDXC (output) INTEGER array, dimension (N)\n\
* The permutation used to arrange the columns of the deflated\n\
* Q matrix into three groups: the first group contains non-zero\n\
* elements only at and above N1, the second contains\n\
* non-zero elements only below N1, and the third is dense.\n\
*\n\
* INDXP (workspace) INTEGER array, dimension (N)\n\
* The permutation used to place deflated values of D at the end\n\
* of the array. INDXP(1:K) points to the nondeflated D-values\n\
* and INDXP(K+1:N) points to the deflated eigenvalues.\n\
*\n\
* COLTYP (workspace/output) INTEGER array, dimension (N)\n\
* During execution, a label which will indicate which of the\n\
* following types a column in the Q2 matrix is:\n\
* 1 : non-zero in the upper half only;\n\
* 2 : dense;\n\
* 3 : non-zero in the lower half only;\n\
* 4 : deflated.\n\
* On exit, COLTYP(i) is the number of columns of type i,\n\
* for i=1 to 4 only.\n\
*\n\
* INFO (output) INTEGER\n\
* = 0: successful exit.\n\
* < 0: if INFO = -i, the i-th argument had an illegal value.\n\
*\n\n\
* Further Details\n\
* ===============\n\
*\n\
* Based on contributions by\n\
* Jeff Rutter, Computer Science Division, University of California\n\
* at Berkeley, USA\n\
* Modified by Francoise Tisseur, University of Tennessee.\n\
*\n\
* =====================================================================\n\
*\n"
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