dlaqtr.f(3) LAPACK dlaqtr.f(3)
subroutine dlaqtr (LTRAN, LREAL, N, T, LDT, B, W, SCALE, X, WORK, INFO)
DLAQTR solves a real quasi-triangular system of equations, or a complex quasi-
triangular system of special form, in real arithmetic.
subroutine dlaqtr (logicalLTRAN, logicalLREAL, integerN, double precision, dimension( ldt, *
)T, integerLDT, double precision, dimension( * )B, double precisionW, double
precisionSCALE, double precision, dimension( * )X, double precision, dimension( * )WORK,
DLAQTR solves a real quasi-triangular system of equations, or a complex quasi-triangular
system of special form, in real arithmetic.
DLAQTR solves the real quasi-triangular system
op(T)*p = scale*c, if LREAL = .TRUE.
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**T, A**T denotes the transpose of
On input, X = [ c ]. On output, X = [ p ].
[ d ] [ q ]
This subroutine is designed for the condition number estimation
in routine DTRSNA.
LTRAN is 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)**T.
LREAL is LOGICAL
On entry, LREAL specifies the input matrix structure:
= .FALSE., the input is complex
= .TRUE., the input is real
N is INTEGER
On entry, N specifies the order of T+i*B. N >= 0.
T is DOUBLE PRECISION array, dimension (LDT,N)
On entry, T contains a matrix in Schur canonical form.
If LREAL = .FALSE., then the first diagonal block of T mu
be 1 by 1.
LDT is INTEGER
The leading dimension of the matrix T. LDT >= max(1,N).
B is DOUBLE PRECISION 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 is DOUBLE PRECISION
On entry, W is the diagonal element of the matrix B.
If LREAL = .TRUE., W is not referenced.
SCALE is DOUBLE PRECISION
On exit, SCALE is the scale factor.
X is DOUBLE PRECISION array, dimension (2*N)
On entry, X contains the right hand side of the system.
On exit, X is overwritten by the solution.
WORK is DOUBLE PRECISION array, dimension (N)
INFO is 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 DLALN2 to keep nonsingularity.
NOTE: In the interests of speed, this routine does not
check the inputs for errors.
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
Definition at line 165 of file dlaqtr.f.
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Version 3.4.2 Tue Sep 25 2012 dlaqtr.f(3)