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---
:name: dlasq1
:md5sum: 64432270af33eae03a6a5fd907dae092
:category: :subroutine
:arguments:
- n:
:type: integer
:intent: input
- d:
:type: doublereal
:intent: input/output
:dims:
- n
- e:
:type: doublereal
:intent: input/output
:dims:
- n
- work:
:type: doublereal
:intent: workspace
:dims:
- 4*n
- info:
:type: integer
:intent: output
:substitutions: {}
:fortran_help: " SUBROUTINE DLASQ1( N, D, E, WORK, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* DLASQ1 computes the singular values of a real N-by-N bidiagonal\n\
* matrix with diagonal D and off-diagonal E. The singular values\n\
* are computed to high relative accuracy, in the absence of\n\
* denormalization, underflow and overflow. The algorithm was first\n\
* presented in\n\
*\n\
* \"Accurate singular values and differential qd algorithms\" by K. V.\n\
* Fernando and B. N. Parlett, Numer. Math., Vol-67, No. 2, pp. 191-230,\n\
* 1994,\n\
*\n\
* and the present implementation is described in \"An implementation of\n\
* the dqds Algorithm (Positive Case)\", LAPACK Working Note.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* N (input) INTEGER\n\
* The number of rows and columns in the matrix. N >= 0.\n\
*\n\
* D (input/output) DOUBLE PRECISION array, dimension (N)\n\
* On entry, D contains the diagonal elements of the\n\
* bidiagonal matrix whose SVD is desired. On normal exit,\n\
* D contains the singular values in decreasing order.\n\
*\n\
* E (input/output) DOUBLE PRECISION array, dimension (N)\n\
* On entry, elements E(1:N-1) contain the off-diagonal elements\n\
* of the bidiagonal matrix whose SVD is desired.\n\
* On exit, E is overwritten.\n\
*\n\
* WORK (workspace) DOUBLE PRECISION 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: the algorithm failed\n\
* = 1, a split was marked by a positive value in E\n\
* = 2, current block of Z not diagonalized after 30*N\n\
* iterations (in inner while loop)\n\
* = 3, termination criterion of outer while loop not met \n\
* (program created more than N unreduced blocks)\n\
*\n\n\
* =====================================================================\n\
*\n"
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