table of contents
| pptri(3) | LAPACK | pptri(3) |
NAME¶
pptri - pptri: triangular inverse
SYNOPSIS¶
Functions¶
subroutine cpptri (uplo, n, ap, info)
CPPTRI subroutine dpptri (uplo, n, ap, info)
DPPTRI subroutine spptri (uplo, n, ap, info)
SPPTRI subroutine zpptri (uplo, n, ap, info)
ZPPTRI
Detailed Description¶
Function Documentation¶
subroutine cpptri (character uplo, integer n, complex, dimension( * ) ap, integer info)¶
CPPTRI
Purpose:
CPPTRI computes the inverse of a complex Hermitian positive definite
matrix A using the Cholesky factorization A = U**H*U or A = L*L**H
computed by CPPTRF.
Parameters
UPLO
UPLO is CHARACTER*1
= 'U': Upper triangular factor is stored in AP;
= 'L': Lower triangular factor is stored in AP.
N
N is INTEGER
The order of the matrix A. N >= 0.
AP
AP is COMPLEX array, dimension (N*(N+1)/2)
On entry, the triangular factor U or L from the Cholesky
factorization A = U**H*U or A = L*L**H, packed columnwise as
a linear array. The j-th column of U or L is stored in the
array AP as follows:
if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j;
if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n.
On exit, the upper or lower triangle of the (Hermitian)
inverse of A, overwriting the input factor U or L.
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, the (i,i) element of the factor U or L is
zero, and the inverse could not be computed.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine dpptri (character uplo, integer n, double precision, dimension( * ) ap, integer info)¶
DPPTRI
Purpose:
DPPTRI computes the inverse of a real symmetric positive definite
matrix A using the Cholesky factorization A = U**T*U or A = L*L**T
computed by DPPTRF.
Parameters
UPLO
UPLO is CHARACTER*1
= 'U': Upper triangular factor is stored in AP;
= 'L': Lower triangular factor is stored in AP.
N
N is INTEGER
The order of the matrix A. N >= 0.
AP
AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
On entry, the triangular factor U or L from the Cholesky
factorization A = U**T*U or A = L*L**T, packed columnwise as
a linear array. The j-th column of U or L is stored in the
array AP as follows:
if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j;
if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n.
On exit, the upper or lower triangle of the (symmetric)
inverse of A, overwriting the input factor U or L.
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, the (i,i) element of the factor U or L is
zero, and the inverse could not be computed.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine spptri (character uplo, integer n, real, dimension( * ) ap, integer info)¶
SPPTRI
Purpose:
SPPTRI computes the inverse of a real symmetric positive definite
matrix A using the Cholesky factorization A = U**T*U or A = L*L**T
computed by SPPTRF.
Parameters
UPLO
UPLO is CHARACTER*1
= 'U': Upper triangular factor is stored in AP;
= 'L': Lower triangular factor is stored in AP.
N
N is INTEGER
The order of the matrix A. N >= 0.
AP
AP is REAL array, dimension (N*(N+1)/2)
On entry, the triangular factor U or L from the Cholesky
factorization A = U**T*U or A = L*L**T, packed columnwise as
a linear array. The j-th column of U or L is stored in the
array AP as follows:
if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j;
if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n.
On exit, the upper or lower triangle of the (symmetric)
inverse of A, overwriting the input factor U or L.
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, the (i,i) element of the factor U or L is
zero, and the inverse could not be computed.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine zpptri (character uplo, integer n, complex*16, dimension( * ) ap, integer info)¶
ZPPTRI
Purpose:
ZPPTRI computes the inverse of a complex Hermitian positive definite
matrix A using the Cholesky factorization A = U**H*U or A = L*L**H
computed by ZPPTRF.
Parameters
UPLO
UPLO is CHARACTER*1
= 'U': Upper triangular factor is stored in AP;
= 'L': Lower triangular factor is stored in AP.
N
N is INTEGER
The order of the matrix A. N >= 0.
AP
AP is COMPLEX*16 array, dimension (N*(N+1)/2)
On entry, the triangular factor U or L from the Cholesky
factorization A = U**H*U or A = L*L**H, packed columnwise as
a linear array. The j-th column of U or L is stored in the
array AP as follows:
if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j;
if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n.
On exit, the upper or lower triangle of the (Hermitian)
inverse of A, overwriting the input factor U or L.
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, the (i,i) element of the factor U or L is
zero, and the inverse could not be computed.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Author¶
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| Wed Feb 7 2024 11:30:40 | Version 3.12.0 |