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---
:name: slaed8
:md5sum: 695bf39ffc8e6dd4d22f1ba3685aeddc
:category: :subroutine
:arguments:
- icompq:
:type: integer
:intent: input
- k:
:type: integer
:intent: output
- n:
:type: integer
:intent: input
- qsiz:
:type: integer
:intent: input
- d:
:type: real
:intent: input/output
:dims:
- n
- q:
:type: real
:intent: input/output
:dims:
- "icompq==0 ? 0 : ldq"
- "icompq==0 ? 0 : n"
- ldq:
:type: integer
:intent: input
- indxq:
:type: integer
:intent: input
:dims:
- n
- rho:
:type: real
:intent: input/output
- cutpnt:
:type: integer
:intent: input
- z:
:type: real
:intent: input
:dims:
- n
- dlamda:
:type: real
:intent: output
:dims:
- n
- q2:
:type: real
:intent: output
:dims:
- "icompq==0 ? 0 : ldq2"
- "icompq==0 ? 0 : n"
- ldq2:
:type: integer
:intent: input
- w:
:type: real
:intent: output
:dims:
- n
- perm:
:type: integer
:intent: output
:dims:
- n
- givptr:
:type: integer
:intent: output
- givcol:
:type: integer
:intent: output
:dims:
- "2"
- n
- givnum:
:type: real
:intent: output
:dims:
- "2"
- n
- indxp:
:type: integer
:intent: workspace
:dims:
- n
- indx:
:type: integer
:intent: workspace
:dims:
- n
- info:
:type: integer
:intent: output
:substitutions:
ldq2: MAX(1,n)
:fortran_help: " SUBROUTINE SLAED8( ICOMPQ, K, N, QSIZ, D, Q, LDQ, INDXQ, RHO, CUTPNT, Z, DLAMDA, Q2, LDQ2, W, PERM, GIVPTR, GIVCOL, GIVNUM, INDXP, INDX, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* SLAED8 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 element 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\
* ICOMPQ (input) INTEGER\n\
* = 0: Compute eigenvalues only.\n\
* = 1: Compute eigenvectors of original dense symmetric matrix\n\
* also. On entry, Q contains the orthogonal matrix used\n\
* to reduce the original matrix to tridiagonal form.\n\
*\n\
* K (output) INTEGER\n\
* The number of non-deflated eigenvalues, and the order of the\n\
* related secular equation.\n\
*\n\
* N (input) INTEGER\n\
* The dimension of the symmetric tridiagonal matrix. N >= 0.\n\
*\n\
* QSIZ (input) INTEGER\n\
* The dimension of the orthogonal matrix used to reduce\n\
* the full matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1.\n\
*\n\
* D (input/output) REAL array, dimension (N)\n\
* On entry, the eigenvalues of the two submatrices to be\n\
* combined. On exit, the trailing (N-K) updated eigenvalues\n\
* (those which were deflated) sorted into increasing order.\n\
*\n\
* Q (input/output) REAL array, dimension (LDQ,N)\n\
* If ICOMPQ = 0, Q is not referenced. Otherwise,\n\
* on entry, Q contains the eigenvectors of the partially solved\n\
* system which has been previously updated in matrix\n\
* multiplies with other partially solved eigensystems.\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) 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 CUTPNT added to\n\
* their values in order to be accurate.\n\
*\n\
* RHO (input/output) REAL\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\
* SLAED3.\n\
*\n\
* CUTPNT (input) INTEGER\n\
* The location of the last eigenvalue in the leading\n\
* sub-matrix. min(1,N) <= CUTPNT <= N.\n\
*\n\
* Z (input) REAL array, dimension (N)\n\
* On entry, Z contains the updating vector (the last row of\n\
* the first sub-eigenvector matrix and the first row of the\n\
* second sub-eigenvector matrix).\n\
* On exit, the contents of Z are destroyed by the updating\n\
* process.\n\
*\n\
* DLAMDA (output) REAL array, dimension (N)\n\
* A copy of the first K eigenvalues which will be used by\n\
* SLAED3 to form the secular equation.\n\
*\n\
* Q2 (output) REAL array, dimension (LDQ2,N)\n\
* If ICOMPQ = 0, Q2 is not referenced. Otherwise,\n\
* a copy of the first K eigenvectors which will be used by\n\
* SLAED7 in a matrix multiply (SGEMM) to update the new\n\
* eigenvectors.\n\
*\n\
* LDQ2 (input) INTEGER\n\
* The leading dimension of the array Q2. LDQ2 >= max(1,N).\n\
*\n\
* W (output) REAL array, dimension (N)\n\
* The first k values of the final deflation-altered z-vector and\n\
* will be passed to SLAED3.\n\
*\n\
* PERM (output) INTEGER array, dimension (N)\n\
* The permutations (from deflation and sorting) to be applied\n\
* to each eigenblock.\n\
*\n\
* GIVPTR (output) INTEGER\n\
* The number of Givens rotations which took place in this\n\
* subproblem.\n\
*\n\
* GIVCOL (output) INTEGER array, dimension (2, N)\n\
* Each pair of numbers indicates a pair of columns to take place\n\
* in a Givens rotation.\n\
*\n\
* GIVNUM (output) REAL array, dimension (2, N)\n\
* Each number indicates the S value to be used in the\n\
* corresponding Givens rotation.\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\
* INDX (workspace) INTEGER array, dimension (N)\n\
* The permutation used to sort the contents of D into ascending\n\
* order.\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\
*\n\
* =====================================================================\n\
*\n"
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