## Developer Reference

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

# ?latps

Solves a triangular system of equations with the matrix held in packed storage.

## Syntax

Include Files
• mkl.fi
Description
The routine
?latps
solves one of the triangular systems
A
*x
=
s
*
b
, or
A
T
*x
=
s
*
b,
or
A
H
*x
=
s
*
b
(for complex flavors)
with scaling to prevent overflow, where
A
is an upper or lower triangular matrix stored in packed form. Here
A
T
denotes the transpose of
A
,
A
H
denotes the conjugate transpose of
A
,
x
and
b
are
n
-element vectors, and
s
is a scaling factor, usually less than or equal to 1, chosen so that the components of
x
will be less than the overflow threshold. If the unscaled problem does not cause overflow, the Level 2 BLAS routine
?tpsv
is called. If the matrix
A
is singular (
A
(
j
,
j
) = 0
for some
j
), then s is set to 0 and a non-trivial solution to
A
*
x
= 0
is returned.
Input Parameters
uplo
CHARACTER*1
.
Specifies whether the matrix
A
is upper or lower triangular.
=
'U'
: upper triangular
=
'L'
: uower triangular
trans
CHARACTER*1
.
Specifies the operation applied to
A
.
=
'N'
: solve
A
*
x
=
s
*
b
(no transpose)
=
'T'
: solve
A
T
*
x
=
s
*
b
(transpose)
=
'C'
: solve
A
H
*
x
=
s
*
b
(conjugate transpose)
diag
CHARACTER*1
.
Specifies whether the matrix
A
is unit triangular.
=
'N
': non-unit triangular
=
'U'
: unit triangular
normin
CHARACTER*1
.
Specifies whether
cnorm
is set.
=
'Y'
:
cnorm
contains the column norms on entry;
=
'N'
:
cnorm
is not set on entry. On exit, the norms will be computed and stored in cnorm.
n
INTEGER
. The order of the matrix
A
.
n
0
.
ap
REAL
for
slatps
DOUBLE PRECISION
for
dlatps
COMPLEX
for
clatps
DOUBLE COMPLEX
for
zlatps
.
Array,
DIMENSION
(
n
(
n
+1)/2).
The upper or lower triangular matrix
A
, packed columnwise in a linear array. The
j
-th column of
A
is stored in the array
ap
as follows: