---
name: "slaqtr"
section: "3lapack"
platform: "linux"
package: "liblapack-doc"
version: "3.2.1-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/slaqtr/3lapack"
---

# slaqtr(3lapack)

solves the real quasi-triangular system op(T)\*p = scale\*c, if LREAL = .TRUE

## NAME

SLAQTR - solves the real quasi-triangular system   op(T)\*p = scale\*c, if LREAL = .TRUE

## SYNOPSIS

- SUBROUTINE SLAQTR(

  LTRAN, LREAL, N, T, LDT, B, W, SCALE, X, WORK, INFO )

- LOGICAL

  LREAL, LTRAN

- INTEGER

  INFO, LDT, N

- REAL

  SCALE, W

- REAL

  B( \* ), T( LDT, \* ), WORK( \* ), X( \* )

## PURPOSE

SLAQTR solves the real quasi-triangular system or the complex quasi-triangular systems\
\
            op(T + iB)\*(p+iq) = scale\*(c+id),  if LREAL = .FALSE. in real arithmetic, where T is upper quasi-triangular.\
 If LREAL = .FALSE., then the first diagonal block of T must be 1 by 1, B is the specially structured matrix\
\
                B = \[ b(1) b(2) ... b(n) \]\
\
                    \[       w            \]\
\
                    \[           w        \]\
\
                    \[              .     \]\
\
                    \[                 w  \]\
 op(A) = A or A', A' denotes the conjugate transpose of\
 matrix A.\
 On input, X = \[ c \].  On output, X = \[ p \].\
\
               \[ d \]                  \[ q \]\
 This subroutine is designed for the condition number estimation in routine STRSNA.\

## ARGUMENTS

- LTRAN (input) LOGICAL

  On entry, LTRAN specifies the option of conjugate transpose: = .FALSE.,    op(T+i\*B) = T+i\*B, = .TRUE.,     op(T+i\*B) = (T+i\*B)'.

- LREAL (input) LOGICAL

  On entry, LREAL specifies the input matrix structure: = .FALSE.,    the input is complex = .TRUE.,     the input is real

- N (input) INTEGER

  On entry, N specifies the order of T+i\*B. N \>= 0.

- T (input) REAL array, dimension (LDT,N)

  On entry, T contains a matrix in Schur canonical form. If LREAL = .FALSE., then the first diagonal block of T must be 1 by 1.

- LDT (input) INTEGER

  The leading dimension of the matrix T. LDT \>= max(1,N).

- B (input) REAL array, dimension (N)

  On entry, B contains the elements to form the matrix B as described above. If LREAL = .TRUE., B is not referenced.

- W (input) REAL

  On entry, W is the diagonal element of the matrix B. If LREAL = .TRUE., W is not referenced.

- SCALE (output) REAL

  On exit, SCALE is the scale factor.

- X (input/output) REAL array, dimension (2\*N)

  On entry, X contains the right hand side of the system. On exit, X is overwritten by the solution.

- WORK (workspace) REAL array, dimension (N)

  - INFO (output) INTEGER

  On exit, INFO is set to 0: successful exit.\
   1: the some diagonal 1 by 1 block has been perturbed by a small number SMIN to keep nonsingularity. 2: the some diagonal 2 by 2 block has been perturbed by a small number in SLALN2 to keep nonsingularity. NOTE: In the interests of speed, this routine does not check the inputs for errors.