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---
:name: dlasd8
:md5sum: da4e64c91be87e67d70f49ec5f695f5e
:category: :subroutine
:arguments:
- icompq:
:type: integer
:intent: input
- k:
:type: integer
:intent: input
- d:
:type: doublereal
:intent: output
:dims:
- k
- z:
:type: doublereal
:intent: input/output
:dims:
- k
- vf:
:type: doublereal
:intent: input/output
:dims:
- k
- vl:
:type: doublereal
:intent: input/output
:dims:
- k
- difl:
:type: doublereal
:intent: output
:dims:
- k
- difr:
:type: doublereal
:intent: output
:dims:
- "icompq == 1 ? lddifr : icompq == 0 ? k : 0"
- "icompq == 1 ? 2 : 0"
- lddifr:
:type: integer
:intent: input
- dsigma:
:type: doublereal
:intent: input/output
:dims:
- k
- work:
:type: doublereal
:intent: workspace
:dims:
- 3 * k
- info:
:type: integer
:intent: output
:substitutions:
lddifr: k
:fortran_help: " SUBROUTINE DLASD8( ICOMPQ, K, D, Z, VF, VL, DIFL, DIFR, LDDIFR, DSIGMA, WORK, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* DLASD8 finds the square roots of the roots of the secular equation,\n\
* as defined by the values in DSIGMA and Z. It makes the appropriate\n\
* calls to DLASD4, and stores, for each element in D, the distance\n\
* to its two nearest poles (elements in DSIGMA). It also updates\n\
* the arrays VF and VL, the first and last components of all the\n\
* right singular vectors of the original bidiagonal matrix.\n\
*\n\
* DLASD8 is called from DLASD6.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* ICOMPQ (input) INTEGER\n\
* Specifies whether singular vectors are to be computed in\n\
* factored form in the calling routine:\n\
* = 0: Compute singular values only.\n\
* = 1: Compute singular vectors in factored form as well.\n\
*\n\
* K (input) INTEGER\n\
* The number of terms in the rational function to be solved\n\
* by DLASD4. K >= 1.\n\
*\n\
* D (output) DOUBLE PRECISION array, dimension ( K )\n\
* On output, D contains the updated singular values.\n\
*\n\
* Z (input/output) DOUBLE PRECISION array, dimension ( K )\n\
* On entry, the first K elements of this array contain the\n\
* components of the deflation-adjusted updating row vector.\n\
* On exit, Z is updated.\n\
*\n\
* VF (input/output) DOUBLE PRECISION array, dimension ( K )\n\
* On entry, VF contains information passed through DBEDE8.\n\
* On exit, VF contains the first K components of the first\n\
* components of all right singular vectors of the bidiagonal\n\
* matrix.\n\
*\n\
* VL (input/output) DOUBLE PRECISION array, dimension ( K )\n\
* On entry, VL contains information passed through DBEDE8.\n\
* On exit, VL contains the first K components of the last\n\
* components of all right singular vectors of the bidiagonal\n\
* matrix.\n\
*\n\
* DIFL (output) DOUBLE PRECISION array, dimension ( K )\n\
* On exit, DIFL(I) = D(I) - DSIGMA(I).\n\
*\n\
* DIFR (output) DOUBLE PRECISION array,\n\
* dimension ( LDDIFR, 2 ) if ICOMPQ = 1 and\n\
* dimension ( K ) if ICOMPQ = 0.\n\
* On exit, DIFR(I,1) = D(I) - DSIGMA(I+1), DIFR(K,1) is not\n\
* defined and will not be referenced.\n\
*\n\
* If ICOMPQ = 1, DIFR(1:K,2) is an array containing the\n\
* normalizing factors for the right singular vector matrix.\n\
*\n\
* LDDIFR (input) INTEGER\n\
* The leading dimension of DIFR, must be at least K.\n\
*\n\
* DSIGMA (input/output) DOUBLE PRECISION array, dimension ( K )\n\
* On entry, the first K elements of this array contain the old\n\
* roots of the deflated updating problem. These are the poles\n\
* of the secular equation.\n\
* On exit, the elements of DSIGMA may be very slightly altered\n\
* in value.\n\
*\n\
* WORK (workspace) DOUBLE PRECISION array, dimension at least 3 * 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, a singular value did not converge\n\
*\n\n\
* Further Details\n\
* ===============\n\
*\n\
* Based on contributions by\n\
* Ming Gu and Huan Ren, Computer Science Division, University of\n\
* California at Berkeley, USA\n\
*\n\
* =====================================================================\n\
*\n"
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