## Developer Reference

• 2020.2
• 07/15/2020
• Public Content
Contents

# ?laqtr

Solves a real quasi-triangular system of equations, or a complex quasi-triangular system of special form, in real arithmetic.

## Syntax

Include Files
• mkl.fi
Description
The routine
?laqtr
solves the real quasi-triangular system
op
(
T
) *
p
=
scale
*
c
, if
lreal
=
.TRUE.
or the complex quasi-triangular systems
op
(
T
+
i
B
)*(
p
+
i
q
) =
scale
*(
c
+
i
d
)
, 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 op
(A)
=
A
or
A
T
,
A
T
denotes the transpose of matrix
A
.
On input, This routine is designed for the condition number estimation in routine
?trsna
.
Input Parameters
ltran
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
LOGICAL
.
On entry,
lreal
specifies the input matrix structure:
=
.FALSE.
, the input is complex
=
.TRUE.
, the input is real.
n
INTEGER
.
On entry,
n
specifies the order of
T
+
i
B
.
n
0
.
t
REAL
for
slaqtr
DOUBLE PRECISION
for
dlaqtr
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
INTEGER
. The leading dimension of the matrix
T
.
ldt
max(1,
n
)
.
b
REAL
for
slaqtr
DOUBLE PRECISION
for
dlaqtr
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
REAL
for
slaqtr
DOUBLE PRECISION
for
dlaqtr
On entry,
w
is the diagonal element of the matrix
B
.
If
lreal
=
.TRUE.
,
w
is not referenced.
x
REAL
for
slaqtr
DOUBLE PRECISION
for
dlaqtr
Array, dimension (2
n
). On entry,
x
contains the right hand side of the system.