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---
:name: dlaed9
:md5sum: e45625c97ed5b50036009a7a23bf1afd
:category: :subroutine
:arguments:
- k:
:type: integer
:intent: input
- kstart:
:type: integer
:intent: input
- kstop:
:type: integer
:intent: input
- n:
:type: integer
:intent: input
- d:
:type: doublereal
:intent: output
:dims:
- MAX(1,n)
- q:
:type: doublereal
:intent: workspace
:dims:
- ldq
- MAX(1,n)
- ldq:
:type: integer
:intent: input
- rho:
:type: doublereal
:intent: input
- dlamda:
:type: doublereal
:intent: input
:dims:
- k
- w:
:type: doublereal
:intent: input
:dims:
- k
- s:
:type: doublereal
:intent: output
:dims:
- lds
- k
- lds:
:type: integer
:intent: input
- info:
:type: integer
:intent: output
:substitutions:
ldq: MAX( 1, n )
lds: MAX( 1, k )
:fortran_help: " SUBROUTINE DLAED9( K, KSTART, KSTOP, N, D, Q, LDQ, RHO, DLAMDA, W, S, LDS, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* DLAED9 finds the roots of the secular equation, as defined by the\n\
* values in D, Z, and RHO, between KSTART and KSTOP. It makes the\n\
* appropriate calls to DLAED4 and then stores the new matrix of\n\
* eigenvectors for use in calculating the next level of Z vectors.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* K (input) INTEGER\n\
* The number of terms in the rational function to be solved by\n\
* DLAED4. K >= 0.\n\
*\n\
* KSTART (input) INTEGER\n\
* KSTOP (input) INTEGER\n\
* The updated eigenvalues Lambda(I), KSTART <= I <= KSTOP\n\
* are to be computed. 1 <= KSTART <= KSTOP <= K.\n\
*\n\
* N (input) INTEGER\n\
* The number of rows and columns in the Q matrix.\n\
* N >= K (delation may result in N > K).\n\
*\n\
* D (output) DOUBLE PRECISION array, dimension (N)\n\
* D(I) contains the updated eigenvalues\n\
* for KSTART <= I <= KSTOP.\n\
*\n\
* Q (workspace) DOUBLE PRECISION array, dimension (LDQ,N)\n\
*\n\
* LDQ (input) INTEGER\n\
* The leading dimension of the array Q. LDQ >= max( 1, N ).\n\
*\n\
* RHO (input) DOUBLE PRECISION\n\
* The value of the parameter in the rank one update equation.\n\
* RHO >= 0 required.\n\
*\n\
* DLAMDA (input) DOUBLE PRECISION array, dimension (K)\n\
* The first K elements of this array contain the old roots\n\
* of the deflated updating problem. These are the poles\n\
* of the secular equation.\n\
*\n\
* W (input) DOUBLE PRECISION array, dimension (K)\n\
* The first K elements of this array contain the components\n\
* of the deflation-adjusted updating vector.\n\
*\n\
* S (output) DOUBLE PRECISION array, dimension (LDS, K)\n\
* Will contain the eigenvectors of the repaired matrix which\n\
* will be stored for subsequent Z vector calculation and\n\
* multiplied by the previously accumulated eigenvectors\n\
* to update the system.\n\
*\n\
* LDS (input) INTEGER\n\
* The leading dimension of S. LDS >= max( 1, K ).\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\
* .. Local Scalars ..\n INTEGER I, J\n DOUBLE PRECISION TEMP\n\
* ..\n\
* .. External Functions ..\n DOUBLE PRECISION DLAMC3, DNRM2\n EXTERNAL DLAMC3, DNRM2\n\
* ..\n\
* .. External Subroutines ..\n EXTERNAL DCOPY, DLAED4, XERBLA\n\
* ..\n\
* .. Intrinsic Functions ..\n INTRINSIC MAX, SIGN, SQRT\n\
* ..\n"
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