# 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**

## 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.

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

Univ. of Colorado Denver

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

Univ. of Colorado Denver

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**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***Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **92** of file **zpptri.f**.

## Author

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