?trtri
?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(
of a triangular matrix A
)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 whetherAis upper or lower triangular:If, thenuplo='U'Ais upper triangular.If, thenuplo='L'Ais lower triangular.
- diag
- Must be'N'or'U'.If, thendiag='N'Ais not a unit triangular matrix.If,diag='U'Ais unit triangular: diagonal elements ofAare assumed to be 1 and not referenced in the arraya.
- n
- The order of the matrixA;.n≥0
- a
- Array: . Contains the matrixA.
- lda
- The first dimension ofa;.lda≥max(1,n)
Output Parameters
- a
- Overwritten by the matrixinv(.A)
Return Values
This function returns a value
info
.If , the execution is successful.
info
= 0If
info
= -i
, parameter i
had an illegal value.If , the
info
= i
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 is a modest linear function of
c
(n
)n
; ε
is the machine precision; I
denotes the identity matrix.The total number of floating-point operations is approximately
(1/3)
for real flavors and n
3
(4/3)
for complex flavors.n
3