Contents

# ?tptri

Computes the inverse of a triangular matrix using packed storage.

## Syntax

Include Files
• mkl.h
Description
The routine computes the inverse
inv(
A
)
of a packed triangular matrix
A
.
Input Parameters
matrix_layout
Specifies whether matrix storage layout is row major (
LAPACK_ROW_MAJOR
) or column major (
LAPACK_COL_MAJOR
).
uplo
Must be
'U'
or
'L'
.
Indicates whether
A
is upper or lower triangular:
If
uplo
=
'U'
, then
A
is upper triangular.
If
uplo
=
'L'
, then
A
is lower triangular.
diag
Must be
'N'
or
'U'
.
If
diag
=
'N'
, then
A
is not a unit triangular matrix.
If
diag
=
'U'
,
A
is unit triangular: diagonal elements of
A
are assumed to be 1 and not referenced in the array
ap
.
n
The order of the matrix
A
;
n
0
.
ap
Array, size at least
max(1,
n
(
n
+1)/2)
.
Contains the packed triangular matrix A.
Output Parameters
ap
Overwritten by the packed
n
-by-
n
matrix
inv(
A
)
.
Return Values
This function returns a value
info
.
If
info
= 0
, the execution is successful.
If
info
=
-i
, parameter
i
If
info
=
i
, the
i
-th diagonal element of
A
is zero,
A
is singular, and the inversion could not be completed.
Application Notes
The computed inverse
X
satisfies the following error bounds:
`|XA - I| ≤ c(n)ε |X||A|`
`|X - A-1| ≤ c(n)ε |A-1||A||X|,`
where
c
(
n
)
is a modest linear function of
n
;
ε
is the machine precision;
I
denotes the identity matrix.
The total number of floating-point operations is approximately
(1/3)
n
3
for real flavors and
(4/3)
n
3
for complex flavors.

#### Product and Performance Information

1

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.