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---
:name: dlaed7
:md5sum: 28c523ba917e198d63509b14a5f28ee1
:category: :subroutine
:arguments:
- icompq:
:type: integer
:intent: input
- n:
:type: integer
:intent: input
- qsiz:
:type: integer
:intent: input
- tlvls:
:type: integer
:intent: input
- curlvl:
:type: integer
:intent: input
- curpbm:
: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: output
:dims:
- n
- rho:
:type: doublereal
:intent: input
- cutpnt:
:type: integer
:intent: input
- qstore:
:type: doublereal
:intent: input/output
:dims:
- pow(n,2)+1
- qptr:
:type: integer
:intent: input/output
:dims:
- n+2
- prmptr:
:type: integer
:intent: input
:dims:
- n*LG(n)
- perm:
:type: integer
:intent: input
:dims:
- n*LG(n)
- givptr:
:type: integer
:intent: input
:dims:
- n*LG(n)
- givcol:
:type: integer
:intent: input
:dims:
- "2"
- n*LG(n)
- givnum:
:type: doublereal
:intent: input
:dims:
- "2"
- n*LG(n)
- work:
:type: doublereal
:intent: workspace
:dims:
- 3*n+qsiz*n
- iwork:
:type: integer
:intent: workspace
:dims:
- 4*n
- info:
:type: integer
:intent: output
:substitutions: {}
:fortran_help: " SUBROUTINE DLAED7( ICOMPQ, N, QSIZ, TLVLS, CURLVL, CURPBM, D, Q, LDQ, INDXQ, RHO, CUTPNT, QSTORE, QPTR, PRMPTR, PERM, GIVPTR, GIVCOL, GIVNUM, WORK, IWORK, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* DLAED7 computes the updated eigensystem of a diagonal\n\
* matrix after modification by a rank-one symmetric matrix. This\n\
* routine is used only for the eigenproblem which requires all\n\
* eigenvalues and optionally eigenvectors of a dense symmetric matrix\n\
* that has been reduced to tridiagonal form. DLAED1 handles\n\
* the case in which all eigenvalues and eigenvectors of a symmetric\n\
* tridiagonal matrix are desired.\n\
*\n\
* T = Q(in) ( D(in) + RHO * Z*Z' ) Q'(in) = Q(out) * D(out) * Q'(out)\n\
*\n\
* where Z = Q'u, u is a vector of length N with ones in the\n\
* CUTPNT and CUTPNT + 1 th elements and zeros elsewhere.\n\
*\n\
* The eigenvectors of the original matrix are stored in Q, and the\n\
* eigenvalues are in D. The algorithm consists of three stages:\n\
*\n\
* The first stage consists of deflating the size of the problem\n\
* when there are multiple eigenvalues or if there is a zero in\n\
* the Z vector. For each such occurrence the dimension of the\n\
* secular equation problem is reduced by one. This stage is\n\
* performed by the routine DLAED8.\n\
*\n\
* The second stage consists of calculating the updated\n\
* eigenvalues. This is done by finding the roots of the secular\n\
* equation via the routine DLAED4 (as called by DLAED9).\n\
* This routine also calculates the eigenvectors of the current\n\
* problem.\n\
*\n\
* The final stage consists of computing the updated eigenvectors\n\
* directly using the updated eigenvalues. The eigenvectors for\n\
* the current problem are multiplied with the eigenvectors from\n\
* the overall problem.\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\
* 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\
* TLVLS (input) INTEGER\n\
* The total number of merging levels in the overall divide and\n\
* conquer tree.\n\
*\n\
* CURLVL (input) INTEGER\n\
* The current level in the overall merge routine,\n\
* 0 <= CURLVL <= TLVLS.\n\
*\n\
* CURPBM (input) INTEGER\n\
* The current problem in the current level in the overall\n\
* merge routine (counting from upper left to lower right).\n\
*\n\
* D (input/output) DOUBLE PRECISION array, dimension (N)\n\
* On entry, the eigenvalues of the rank-1-perturbed matrix.\n\
* On exit, the eigenvalues of the repaired matrix.\n\
*\n\
* Q (input/output) DOUBLE PRECISION array, dimension (LDQ, N)\n\
* On entry, the eigenvectors of the rank-1-perturbed matrix.\n\
* On exit, the eigenvectors of the repaired tridiagonal matrix.\n\
*\n\
* LDQ (input) INTEGER\n\
* The leading dimension of the array Q. LDQ >= max(1,N).\n\
*\n\
* INDXQ (output) INTEGER array, dimension (N)\n\
* The permutation which will reintegrate the subproblem just\n\
* solved back into sorted order, i.e., D( INDXQ( I = 1, N ) )\n\
* will be in ascending order.\n\
*\n\
* RHO (input) DOUBLE PRECISION\n\
* The subdiagonal element used to create the rank-1\n\
* modification.\n\
*\n\
* CUTPNT (input) INTEGER\n\
* Contains the location of the last eigenvalue in the leading\n\
* sub-matrix. min(1,N) <= CUTPNT <= N.\n\
*\n\
* QSTORE (input/output) DOUBLE PRECISION array, dimension (N**2+1)\n\
* Stores eigenvectors of submatrices encountered during\n\
* divide and conquer, packed together. QPTR points to\n\
* beginning of the submatrices.\n\
*\n\
* QPTR (input/output) INTEGER array, dimension (N+2)\n\
* List of indices pointing to beginning of submatrices stored\n\
* in QSTORE. The submatrices are numbered starting at the\n\
* bottom left of the divide and conquer tree, from left to\n\
* right and bottom to top.\n\
*\n\
* PRMPTR (input) INTEGER array, dimension (N lg N)\n\
* Contains a list of pointers which indicate where in PERM a\n\
* level's permutation is stored. PRMPTR(i+1) - PRMPTR(i)\n\
* indicates the size of the permutation and also the size of\n\
* the full, non-deflated problem.\n\
*\n\
* PERM (input) INTEGER array, dimension (N lg N)\n\
* Contains the permutations (from deflation and sorting) to be\n\
* applied to each eigenblock.\n\
*\n\
* GIVPTR (input) INTEGER array, dimension (N lg N)\n\
* Contains a list of pointers which indicate where in GIVCOL a\n\
* level's Givens rotations are stored. GIVPTR(i+1) - GIVPTR(i)\n\
* indicates the number of Givens rotations.\n\
*\n\
* GIVCOL (input) INTEGER array, dimension (2, N lg N)\n\
* Each pair of numbers indicates a pair of columns to take place\n\
* in a Givens rotation.\n\
*\n\
* GIVNUM (input) DOUBLE PRECISION array, dimension (2, N lg N)\n\
* Each number indicates the S value to be used in the\n\
* corresponding Givens rotation.\n\
*\n\
* WORK (workspace) DOUBLE PRECISION array, dimension (3*N+QSIZ*N)\n\
*\n\
* IWORK (workspace) INTEGER array, dimension (4*N)\n\
*\n\
* INFO (output) INTEGER\n\
* = 0: successful exit.\n\
* < 0: if INFO = -i, the i-th argument had an illegal value.\n\
* > 0: if INFO = 1, an eigenvalue did not converge\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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