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---
:name: dlasd3
:md5sum: eea845f53351b22e245c27f4d81cd078
:category: :subroutine
:arguments:
- nl:
:type: integer
:intent: input
- nr:
:type: integer
:intent: input
- sqre:
:type: integer
:intent: input
- k:
:type: integer
:intent: input
- d:
:type: doublereal
:intent: output
:dims:
- k
- q:
:type: doublereal
:intent: workspace
:dims:
- ldq
- k
- ldq:
:type: integer
:intent: input
- dsigma:
:type: doublereal
:intent: input
:dims:
- k
- u:
:type: doublereal
:intent: output
:dims:
- ldu
- n
- ldu:
:type: integer
:intent: input
- u2:
:type: doublereal
:intent: input/output
:dims:
- ldu2
- n
- ldu2:
:type: integer
:intent: input
- vt:
:type: doublereal
:intent: output
:dims:
- ldvt
- m
- ldvt:
:type: integer
:intent: input
- vt2:
:type: doublereal
:intent: input/output
:dims:
- ldvt2
- n
- ldvt2:
:type: integer
:intent: input
- idxc:
:type: integer
:intent: input
:dims:
- n
- ctot:
:type: integer
:intent: input
:dims:
- "4"
- z:
:type: doublereal
:intent: input
:dims:
- k
- info:
:type: integer
:intent: output
:substitutions:
m: n + sqre
ldq: k
n: nl + nr + 1
ldu2: n
ldvt: n
ldvt2: n
ldu: n
:fortran_help: " SUBROUTINE DLASD3( NL, NR, SQRE, K, D, Q, LDQ, DSIGMA, U, LDU, U2, LDU2, VT, LDVT, VT2, LDVT2, IDXC, CTOT, Z, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* DLASD3 finds all the square roots of the roots of the secular\n\
* equation, as defined by the values in D and Z. It makes the\n\
* appropriate calls to DLASD4 and then updates the singular\n\
* vectors by matrix multiplication.\n\
*\n\
* This code makes very mild assumptions about floating point\n\
* arithmetic. It will work on machines with a guard digit in\n\
* add/subtract, or on those binary machines without guard digits\n\
* which subtract like the Cray XMP, Cray YMP, Cray C 90, or Cray 2.\n\
* It could conceivably fail on hexadecimal or decimal machines\n\
* without guard digits, but we know of none.\n\
*\n\
* DLASD3 is called from DLASD1.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* NL (input) INTEGER\n\
* The row dimension of the upper block. NL >= 1.\n\
*\n\
* NR (input) INTEGER\n\
* The row dimension of the lower block. NR >= 1.\n\
*\n\
* SQRE (input) INTEGER\n\
* = 0: the lower block is an NR-by-NR square matrix.\n\
* = 1: the lower block is an NR-by-(NR+1) rectangular matrix.\n\
*\n\
* The bidiagonal matrix has N = NL + NR + 1 rows and\n\
* M = N + SQRE >= N columns.\n\
*\n\
* K (input) INTEGER\n\
* The size of the secular equation, 1 =< K = < N.\n\
*\n\
* D (output) DOUBLE PRECISION array, dimension(K)\n\
* On exit the square roots of the roots of the secular equation,\n\
* in ascending order.\n\
*\n\
* Q (workspace) DOUBLE PRECISION array,\n\
* dimension at least (LDQ,K).\n\
*\n\
* LDQ (input) INTEGER\n\
* The leading dimension of the array Q. LDQ >= K.\n\
*\n\
* DSIGMA (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\
* U (output) DOUBLE PRECISION array, dimension (LDU, N)\n\
* The last N - K columns of this matrix contain the deflated\n\
* left singular vectors.\n\
*\n\
* LDU (input) INTEGER\n\
* The leading dimension of the array U. LDU >= N.\n\
*\n\
* U2 (input/output) DOUBLE PRECISION array, dimension (LDU2, N)\n\
* The first K columns of this matrix contain the non-deflated\n\
* left singular vectors for the split problem.\n\
*\n\
* LDU2 (input) INTEGER\n\
* The leading dimension of the array U2. LDU2 >= N.\n\
*\n\
* VT (output) DOUBLE PRECISION array, dimension (LDVT, M)\n\
* The last M - K columns of VT' contain the deflated\n\
* right singular vectors.\n\
*\n\
* LDVT (input) INTEGER\n\
* The leading dimension of the array VT. LDVT >= N.\n\
*\n\
* VT2 (input/output) DOUBLE PRECISION array, dimension (LDVT2, N)\n\
* The first K columns of VT2' contain the non-deflated\n\
* right singular vectors for the split problem.\n\
*\n\
* LDVT2 (input) INTEGER\n\
* The leading dimension of the array VT2. LDVT2 >= N.\n\
*\n\
* IDXC (input) INTEGER array, dimension ( N )\n\
* The permutation used to arrange the columns of U (and rows of\n\
* VT) into three groups: the first group contains non-zero\n\
* entries only at and above (or before) NL +1; the second\n\
* contains non-zero entries only at and below (or after) NL+2;\n\
* and the third is dense. The first column of U and the row of\n\
* VT are treated separately, however.\n\
*\n\
* The rows of the singular vectors found by DLASD4\n\
* must be likewise permuted before the matrix multiplies can\n\
* take place.\n\
*\n\
* CTOT (input) INTEGER array, dimension ( 4 )\n\
* A count of the total number of the various types of columns\n\
* in U (or rows in VT), as described in IDXC. The fourth column\n\
* type is any column which has been deflated.\n\
*\n\
* Z (input) DOUBLE PRECISION array, dimension (K)\n\
* The first K elements of this array contain the components\n\
* of the deflation-adjusted updating row vector.\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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