--- name: "potri" section: "3" platform: "linux" package: "lapack-doc" version: "3.12.1-2" release: "Arch Linux 2026-11-01" platforms: ["linux"] url: "https://new.carta.tech/potri" --- # potri(3) potri: triangular inverse ## NAME potri - potri: triangular inverse ## SYNOPSIS ### Functions subroutine **cpotri** (uplo, n, a, lda, info)\ **CPOTRI** subroutine **dpotri** (uplo, n, a, lda, info)\ **DPOTRI** subroutine **spotri** (uplo, n, a, lda, info)\ **SPOTRI** subroutine **zpotri** (uplo, n, a, lda, info)\ **ZPOTRI** ## Detailed Description ## Function Documentation ### subroutine cpotri (character uplo, integer n, complex, dimension( lda, \* ) a, integer lda, integer info) **CPOTRI** **Purpose:** ``` !> !> CPOTRI 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 CPOTRF. !> ``` **Parameters** *UPLO* ``` !> UPLO is CHARACTER*1 !> = 'U': Upper triangle of A is stored; !> = 'L': Lower triangle of A is stored. !> ``` *N* ``` !> N is INTEGER !> The order of the matrix A. N >= 0. !> ``` *A* ``` !> A is COMPLEX array, dimension (LDA,N) !> On entry, the triangular factor U or L from the Cholesky !> factorization A = U**H*U or A = L*L**H, as computed by !> CPOTRF. !> On exit, the upper or lower triangle of the (Hermitian) !> inverse of A, overwriting the input factor U or L. !> ``` *LDA* ``` !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !> ``` *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 **94** of file **cpotri.f**. ### subroutine dpotri (character uplo, integer n, double precision, dimension( lda, \* ) a, integer lda, integer info) **DPOTRI** **Purpose:** ``` !> !> DPOTRI 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 DPOTRF. !> ``` **Parameters** *UPLO* ``` !> UPLO is CHARACTER*1 !> = 'U': Upper triangle of A is stored; !> = 'L': Lower triangle of A is stored. !> ``` *N* ``` !> N is INTEGER !> The order of the matrix A. N >= 0. !> ``` *A* ``` !> A is DOUBLE PRECISION array, dimension (LDA,N) !> On entry, the triangular factor U or L from the Cholesky !> factorization A = U**T*U or A = L*L**T, as computed by !> DPOTRF. !> On exit, the upper or lower triangle of the (symmetric) !> inverse of A, overwriting the input factor U or L. !> ``` *LDA* ``` !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !> ``` *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 **94** of file **dpotri.f**. ### subroutine spotri (character uplo, integer n, real, dimension( lda, \* ) a, integer lda, integer info) **SPOTRI** **Purpose:** ``` !> !> SPOTRI 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 SPOTRF. !> ``` **Parameters** *UPLO* ``` !> UPLO is CHARACTER*1 !> = 'U': Upper triangle of A is stored; !> = 'L': Lower triangle of A is stored. !> ``` *N* ``` !> N is INTEGER !> The order of the matrix A. N >= 0. !> ``` *A* ``` !> A is REAL array, dimension (LDA,N) !> On entry, the triangular factor U or L from the Cholesky !> factorization A = U**T*U or A = L*L**T, as computed by !> SPOTRF. !> On exit, the upper or lower triangle of the (symmetric) !> inverse of A, overwriting the input factor U or L. !> ``` *LDA* ``` !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !> ``` *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 **94** of file **spotri.f**. ### subroutine zpotri (character uplo, integer n, complex\*16, dimension( lda, \* ) a, integer lda, integer info) **ZPOTRI** **Purpose:** ``` !> !> ZPOTRI 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 ZPOTRF. !> ``` **Parameters** *UPLO* ``` !> UPLO is CHARACTER*1 !> = 'U': Upper triangle of A is stored; !> = 'L': Lower triangle of A is stored. !> ``` *N* ``` !> N is INTEGER !> The order of the matrix A. N >= 0. !> ``` *A* ``` !> A is COMPLEX*16 array, dimension (LDA,N) !> On entry, the triangular factor U or L from the Cholesky !> factorization A = U**H*U or A = L*L**H, as computed by !> ZPOTRF. !> On exit, the upper or lower triangle of the (Hermitian) !> inverse of A, overwriting the input factor U or L. !> ``` *LDA* ``` !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !> ``` *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 **94** of file **zpotri.f**. ## Author Generated automatically by Doxygen for LAPACK from the source code.