?pptri
?pptri
Computes the inverse of a packed symmetric (Hermitian) positive-definite matrix using Cholesky factorization.
Syntax
lapack_int
LAPACKE_spptri
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
float
*
ap
);
lapack_int
LAPACKE_dpptri
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
double
*
ap
);
lapack_int
LAPACKE_cpptri
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
lapack_complex_float
*
ap
);
lapack_int
LAPACKE_zpptri
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
lapack_complex_double
*
ap
);
Include Files
- mkl.h
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 the upper or lower triangular factor is stored inap:If, then the upper triangular factor is stored.uplo='U'If, then the lower triangular factor is stored.uplo='L'
- n
- The order of the matrixA;.n≥0
- ap
- Array, size at least max(1,n(n+1)/2).Contains the factorization of the packed matrixA, as returned by?pptrf.The dimensionapmust be at least max(1,n(n+1)/2).
Output Parameters
- ap
- Overwritten by the packedn-by-nmatrixinv(.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 the Cholesky factor (and therefore the factor itself) is zero, and the inversion could not be completed.Application Notes
The computed inverse
X
satisfies the following error bounds: ||XA - I||2≤ c(n)εκ2(A), ||AX - I||2≤ c(n)εκ2(A),
where is a modest linear function of
c
(n
)n
, and ε
is the machine precision; I
denotes the identity matrix.The 2-norm is defined by .
||
of a matrix A
||2
A
is defined by ||(
, and the condition number A
||2
=max
x
·
x
=1A
x
·
A
x
)1/2
κ
2
(A
)κ
2
(A
) = ||A
||2
||A
-1
||2
The total number of floating-point operations is approximately
(2/3)
for real flavors and n
3
(8/3)
for complex flavors.n
3