--- name: "hetri" 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/hetri" --- # hetri(3) {he,sy}tri: triangular inverse ## NAME hetri - {he,sy}tri: triangular inverse ## SYNOPSIS ### Functions subroutine **chetri** (uplo, n, a, lda, ipiv, work, info)\ **CHETRI** subroutine **csytri** (uplo, n, a, lda, ipiv, work, info)\ **CSYTRI** subroutine **dsytri** (uplo, n, a, lda, ipiv, work, info)\ **DSYTRI** subroutine **ssytri** (uplo, n, a, lda, ipiv, work, info)\ **SSYTRI** subroutine **zhetri** (uplo, n, a, lda, ipiv, work, info)\ **ZHETRI** subroutine **zsytri** (uplo, n, a, lda, ipiv, work, info)\ **ZSYTRI** ## Detailed Description ## Function Documentation ### subroutine chetri (character uplo, integer n, complex, dimension( lda, \* ) a, integer lda, integer, dimension( \* ) ipiv, complex, dimension( \* ) work, integer info) **CHETRI** **Purpose:** ``` !> !> CHETRI computes the inverse of a complex Hermitian indefinite matrix !> A using the factorization A = U*D*U**H or A = L*D*L**H computed by !> CHETRF. !> ``` **Parameters** *UPLO* ``` !> UPLO is CHARACTER*1 !> Specifies whether the details of the factorization are stored !> as an upper or lower triangular matrix. !> = 'U': Upper triangular, form is A = U*D*U**H; !> = 'L': Lower triangular, form is A = L*D*L**H. !> ``` *N* ``` !> N is INTEGER !> The order of the matrix A. N >= 0. !> ``` *A* ``` !> A is COMPLEX array, dimension (LDA,N) !> On entry, the block diagonal matrix D and the multipliers !> used to obtain the factor U or L as computed by CHETRF. !> !> On exit, if INFO = 0, the (Hermitian) inverse of the original !> matrix. If UPLO = 'U', the upper triangular part of the !> inverse is formed and the part of A below the diagonal is not !> referenced; if UPLO = 'L' the lower triangular part of the !> inverse is formed and the part of A above the diagonal is !> not referenced. !> ``` *LDA* ``` !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !> ``` *IPIV* ``` !> IPIV is INTEGER array, dimension (N) !> Details of the interchanges and the block structure of D !> as determined by CHETRF. !> ``` *WORK* ``` !> WORK is COMPLEX array, dimension (N) !> ``` *INFO* ``` !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its !> inverse could not be computed. !> ``` **Author** Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line **113** of file **chetri.f**. ### subroutine csytri (character uplo, integer n, complex, dimension( lda, \* ) a, integer lda, integer, dimension( \* ) ipiv, complex, dimension( \* ) work, integer info) **CSYTRI** **Purpose:** ``` !> !> CSYTRI computes the inverse of a complex symmetric indefinite matrix !> A using the factorization A = U*D*U**T or A = L*D*L**T computed by !> CSYTRF. !> ``` **Parameters** *UPLO* ``` !> UPLO is CHARACTER*1 !> Specifies whether the details of the factorization are stored !> as an upper or lower triangular matrix. !> = 'U': Upper triangular, form is A = U*D*U**T; !> = 'L': Lower triangular, form is A = L*D*L**T. !> ``` *N* ``` !> N is INTEGER !> The order of the matrix A. N >= 0. !> ``` *A* ``` !> A is COMPLEX array, dimension (LDA,N) !> On entry, the block diagonal matrix D and the multipliers !> used to obtain the factor U or L as computed by CSYTRF. !> !> On exit, if INFO = 0, the (symmetric) inverse of the original !> matrix. If UPLO = 'U', the upper triangular part of the !> inverse is formed and the part of A below the diagonal is not !> referenced; if UPLO = 'L' the lower triangular part of the !> inverse is formed and the part of A above the diagonal is !> not referenced. !> ``` *LDA* ``` !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !> ``` *IPIV* ``` !> IPIV is INTEGER array, dimension (N) !> Details of the interchanges and the block structure of D !> as determined by CSYTRF. !> ``` *WORK* ``` !> WORK is COMPLEX array, dimension (2*N) !> ``` *INFO* ``` !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its !> inverse could not be computed. !> ``` **Author** Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line **113** of file **csytri.f**. ### subroutine dsytri (character uplo, integer n, double precision, dimension( lda, \* ) a, integer lda, integer, dimension( \* ) ipiv, double precision, dimension( \* ) work, integer info) **DSYTRI** **Purpose:** ``` !> !> DSYTRI computes the inverse of a real symmetric indefinite matrix !> A using the factorization A = U*D*U**T or A = L*D*L**T computed by !> DSYTRF. !> ``` **Parameters** *UPLO* ``` !> UPLO is CHARACTER*1 !> Specifies whether the details of the factorization are stored !> as an upper or lower triangular matrix. !> = 'U': Upper triangular, form is A = U*D*U**T; !> = 'L': Lower triangular, form is A = L*D*L**T. !> ``` *N* ``` !> N is INTEGER !> The order of the matrix A. N >= 0. !> ``` *A* ``` !> A is DOUBLE PRECISION array, dimension (LDA,N) !> On entry, the block diagonal matrix D and the multipliers !> used to obtain the factor U or L as computed by DSYTRF. !> !> On exit, if INFO = 0, the (symmetric) inverse of the original !> matrix. If UPLO = 'U', the upper triangular part of the !> inverse is formed and the part of A below the diagonal is not !> referenced; if UPLO = 'L' the lower triangular part of the !> inverse is formed and the part of A above the diagonal is !> not referenced. !> ``` *LDA* ``` !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !> ``` *IPIV* ``` !> IPIV is INTEGER array, dimension (N) !> Details of the interchanges and the block structure of D !> as determined by DSYTRF. !> ``` *WORK* ``` !> WORK is DOUBLE PRECISION array, dimension (N) !> ``` *INFO* ``` !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its !> inverse could not be computed. !> ``` **Author** Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line **113** of file **dsytri.f**. ### subroutine ssytri (character uplo, integer n, real, dimension( lda, \* ) a, integer lda, integer, dimension( \* ) ipiv, real, dimension( \* ) work, integer info) **SSYTRI** **Purpose:** ``` !> !> SSYTRI computes the inverse of a real symmetric indefinite matrix !> A using the factorization A = U*D*U**T or A = L*D*L**T computed by !> SSYTRF. !> ``` **Parameters** *UPLO* ``` !> UPLO is CHARACTER*1 !> Specifies whether the details of the factorization are stored !> as an upper or lower triangular matrix. !> = 'U': Upper triangular, form is A = U*D*U**T; !> = 'L': Lower triangular, form is A = L*D*L**T. !> ``` *N* ``` !> N is INTEGER !> The order of the matrix A. N >= 0. !> ``` *A* ``` !> A is REAL array, dimension (LDA,N) !> On entry, the block diagonal matrix D and the multipliers !> used to obtain the factor U or L as computed by SSYTRF. !> !> On exit, if INFO = 0, the (symmetric) inverse of the original !> matrix. If UPLO = 'U', the upper triangular part of the !> inverse is formed and the part of A below the diagonal is not !> referenced; if UPLO = 'L' the lower triangular part of the !> inverse is formed and the part of A above the diagonal is !> not referenced. !> ``` *LDA* ``` !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !> ``` *IPIV* ``` !> IPIV is INTEGER array, dimension (N) !> Details of the interchanges and the block structure of D !> as determined by SSYTRF. !> ``` *WORK* ``` !> WORK is REAL array, dimension (N) !> ``` *INFO* ``` !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its !> inverse could not be computed. !> ``` **Author** Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line **113** of file **ssytri.f**. ### subroutine zhetri (character uplo, integer n, complex\*16, dimension( lda, \* ) a, integer lda, integer, dimension( \* ) ipiv, complex\*16, dimension( \* ) work, integer info) **ZHETRI** **Purpose:** ``` !> !> ZHETRI computes the inverse of a complex Hermitian indefinite matrix !> A using the factorization A = U*D*U**H or A = L*D*L**H computed by !> ZHETRF. !> ``` **Parameters** *UPLO* ``` !> UPLO is CHARACTER*1 !> Specifies whether the details of the factorization are stored !> as an upper or lower triangular matrix. !> = 'U': Upper triangular, form is A = U*D*U**H; !> = 'L': Lower triangular, form is A = L*D*L**H. !> ``` *N* ``` !> N is INTEGER !> The order of the matrix A. N >= 0. !> ``` *A* ``` !> A is COMPLEX*16 array, dimension (LDA,N) !> On entry, the block diagonal matrix D and the multipliers !> used to obtain the factor U or L as computed by ZHETRF. !> !> On exit, if INFO = 0, the (Hermitian) inverse of the original !> matrix. If UPLO = 'U', the upper triangular part of the !> inverse is formed and the part of A below the diagonal is not !> referenced; if UPLO = 'L' the lower triangular part of the !> inverse is formed and the part of A above the diagonal is !> not referenced. !> ``` *LDA* ``` !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !> ``` *IPIV* ``` !> IPIV is INTEGER array, dimension (N) !> Details of the interchanges and the block structure of D !> as determined by ZHETRF. !> ``` *WORK* ``` !> WORK is COMPLEX*16 array, dimension (N) !> ``` *INFO* ``` !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its !> inverse could not be computed. !> ``` **Author** Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line **113** of file **zhetri.f**. ### subroutine zsytri (character uplo, integer n, complex\*16, dimension( lda, \* ) a, integer lda, integer, dimension( \* ) ipiv, complex\*16, dimension( \* ) work, integer info) **ZSYTRI** **Purpose:** ``` !> !> ZSYTRI computes the inverse of a complex symmetric indefinite matrix !> A using the factorization A = U*D*U**T or A = L*D*L**T computed by !> ZSYTRF. !> ``` **Parameters** *UPLO* ``` !> UPLO is CHARACTER*1 !> Specifies whether the details of the factorization are stored !> as an upper or lower triangular matrix. !> = 'U': Upper triangular, form is A = U*D*U**T; !> = 'L': Lower triangular, form is A = L*D*L**T. !> ``` *N* ``` !> N is INTEGER !> The order of the matrix A. N >= 0. !> ``` *A* ``` !> A is COMPLEX*16 array, dimension (LDA,N) !> On entry, the block diagonal matrix D and the multipliers !> used to obtain the factor U or L as computed by ZSYTRF. !> !> On exit, if INFO = 0, the (symmetric) inverse of the original !> matrix. If UPLO = 'U', the upper triangular part of the !> inverse is formed and the part of A below the diagonal is not !> referenced; if UPLO = 'L' the lower triangular part of the !> inverse is formed and the part of A above the diagonal is !> not referenced. !> ``` *LDA* ``` !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !> ``` *IPIV* ``` !> IPIV is INTEGER array, dimension (N) !> Details of the interchanges and the block structure of D !> as determined by ZSYTRF. !> ``` *WORK* ``` !> WORK is COMPLEX*16 array, dimension (2*N) !> ``` *INFO* ``` !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its !> inverse could not be computed. !> ``` **Author** Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line **113** of file **zsytri.f**. ## Author Generated automatically by Doxygen for LAPACK from the source code.