# pptri - Man Page

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

## 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

NAG Ltd.

Definition at line 92 of file cpptri.f.

### 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

NAG Ltd.

Definition at line 92 of file dpptri.f.

### 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

NAG Ltd.

Definition at line 92 of file spptri.f.

### 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