Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

Contents

?trtri

Computes the inverse of a triangular matrix.

Syntax

lapack_int
LAPACKE_strtri
(
int
matrix_layout
,
char
uplo
,
char
diag
,
lapack_int
n
,
float
*
a
,
lapack_int
lda
);
lapack_int
LAPACKE_dtrtri
(
int
matrix_layout
,
char
uplo
,
char
diag
,
lapack_int
n
,
double
*
a
,
lapack_int
lda
);
lapack_int
LAPACKE_ctrtri
(
int
matrix_layout
,
char
uplo
,
char
diag
,
lapack_int
n
,
lapack_complex_float
*
a
,
lapack_int
lda
);
lapack_int
LAPACKE_ztrtri
(
int
matrix_layout
,
char
uplo
,
char
diag
,
lapack_int
n
,
lapack_complex_double
*
a
,
lapack_int
lda
);
Include Files
  • mkl.h
Description
The routine computes the inverse
inv(
A
)
 of a 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
a
.
n
The order of the matrix
A
;
n
≥
 0
.
a
Array: . Contains the matrix
A
.
lda
The first dimension of
a
;
lda
≥
 max(1,
n
)
.
Output Parameters
a
Overwritten by the matrix
inv(
A
)
.
Return Values
This function returns a value
info
.
If
info
 = 0
, the execution is successful.
If
info
 =
-i
, parameter
i
 had an illegal value.
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|
|XA - I| ≤ 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.