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---
:name: dlaqtr
:md5sum: 3ddbfae11a027af905ef99908a20b4bc
:category: :subroutine
:arguments:
- ltran:
:type: logical
:intent: input
- lreal:
:type: logical
:intent: input
- n:
:type: integer
:intent: input
- t:
:type: doublereal
:intent: input
:dims:
- ldt
- n
- ldt:
:type: integer
:intent: input
- b:
:type: doublereal
:intent: input
:dims:
- n
- w:
:type: doublereal
:intent: input
- scale:
:type: doublereal
:intent: output
- x:
:type: doublereal
:intent: input/output
:dims:
- 2*n
- work:
:type: doublereal
:intent: workspace
:dims:
- n
- info:
:type: integer
:intent: output
:substitutions: {}
:fortran_help: " SUBROUTINE DLAQTR( LTRAN, LREAL, N, T, LDT, B, W, SCALE, X, WORK, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* DLAQTR solves the real quasi-triangular system\n\
*\n\
* op(T)*p = scale*c, if LREAL = .TRUE.\n\
*\n\
* or the complex quasi-triangular systems\n\
*\n\
* op(T + iB)*(p+iq) = scale*(c+id), if LREAL = .FALSE.\n\
*\n\
* in real arithmetic, where T is upper quasi-triangular.\n\
* If LREAL = .FALSE., then the first diagonal block of T must be\n\
* 1 by 1, B is the specially structured matrix\n\
*\n\
* B = [ b(1) b(2) ... b(n) ]\n\
* [ w ]\n\
* [ w ]\n\
* [ . ]\n\
* [ w ]\n\
*\n\
* op(A) = A or A', A' denotes the conjugate transpose of\n\
* matrix A.\n\
*\n\
* On input, X = [ c ]. On output, X = [ p ].\n\
* [ d ] [ q ]\n\
*\n\
* This subroutine is designed for the condition number estimation\n\
* in routine DTRSNA.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* LTRAN (input) LOGICAL\n\
* On entry, LTRAN specifies the option of conjugate transpose:\n\
* = .FALSE., op(T+i*B) = T+i*B,\n\
* = .TRUE., op(T+i*B) = (T+i*B)'.\n\
*\n\
* LREAL (input) LOGICAL\n\
* On entry, LREAL specifies the input matrix structure:\n\
* = .FALSE., the input is complex\n\
* = .TRUE., the input is real\n\
*\n\
* N (input) INTEGER\n\
* On entry, N specifies the order of T+i*B. N >= 0.\n\
*\n\
* T (input) DOUBLE PRECISION array, dimension (LDT,N)\n\
* On entry, T contains a matrix in Schur canonical form.\n\
* If LREAL = .FALSE., then the first diagonal block of T mu\n\
* be 1 by 1.\n\
*\n\
* LDT (input) INTEGER\n\
* The leading dimension of the matrix T. LDT >= max(1,N).\n\
*\n\
* B (input) DOUBLE PRECISION array, dimension (N)\n\
* On entry, B contains the elements to form the matrix\n\
* B as described above.\n\
* If LREAL = .TRUE., B is not referenced.\n\
*\n\
* W (input) DOUBLE PRECISION\n\
* On entry, W is the diagonal element of the matrix B.\n\
* If LREAL = .TRUE., W is not referenced.\n\
*\n\
* SCALE (output) DOUBLE PRECISION\n\
* On exit, SCALE is the scale factor.\n\
*\n\
* X (input/output) DOUBLE PRECISION array, dimension (2*N)\n\
* On entry, X contains the right hand side of the system.\n\
* On exit, X is overwritten by the solution.\n\
*\n\
* WORK (workspace) DOUBLE PRECISION array, dimension (N)\n\
*\n\
* INFO (output) INTEGER\n\
* On exit, INFO is set to\n\
* 0: successful exit.\n\
* 1: the some diagonal 1 by 1 block has been perturbed by\n\
* a small number SMIN to keep nonsingularity.\n\
* 2: the some diagonal 2 by 2 block has been perturbed by\n\
* a small number in DLALN2 to keep nonsingularity.\n\
* NOTE: In the interests of speed, this routine does not\n\
* check the inputs for errors.\n\
*\n\n\
* =====================================================================\n\
*\n"
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