--- name: "hetri_rook" 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_rook" --- # hetri\_rook(3) {he,sy}tri\_rook: triangular inverse ## NAME hetri\_rook - {he,sy}tri\_rook: triangular inverse ## SYNOPSIS ### Functions subroutine **chetri\_rook** (uplo, n, a, lda, ipiv, work, info)\ **CHETRI\_ROOK** computes the inverse of HE matrix using the factorization obtained with the bounded Bunch-Kaufman (*rook")*diagonal*pivoting*method. subroutine **csytri\_rook** (uplo, n, a, lda, ipiv, work, info)\ **CSYTRI\_ROOK** subroutine **dsytri\_rook** (uplo, n, a, lda, ipiv, work, info)\ **DSYTRI\_ROOK** subroutine **ssytri\_rook** (uplo, n, a, lda, ipiv, work, info)\ **SSYTRI\_ROOK** subroutine **zhetri\_rook** (uplo, n, a, lda, ipiv, work, info)\ **ZHETRI\_ROOK** computes the inverse of HE matrix using the factorization obtained with the bounded Bunch-Kaufman (*rook")*diagonal*pivoting*method. subroutine **zsytri\_rook** (uplo, n, a, lda, ipiv, work, info)\ **ZSYTRI\_ROOK** ## Detailed Description ## Function Documentation ### subroutine chetri\_rook (character uplo, integer n, complex, dimension( lda, \* ) a, integer lda, integer, dimension( \* ) ipiv, complex, dimension( \* ) work, integer info) **CHETRI\_ROOK** computes the inverse of HE matrix using the factorization obtained with the bounded Bunch-Kaufman ("rook") diagonal pivoting method. **Purpose:** ``` !> !> CHETRI_ROOK 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_ROOK. !> ``` **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_ROOK. !> !> 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_ROOK. !> ``` *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. **Contributors:** ``` !> !> November 2013, Igor Kozachenko, !> Computer Science Division, !> University of California, Berkeley !> !> September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas, !> School of Mathematics, !> University of Manchester !> ``` Definition at line **127** of file **chetri\_rook.f**. ### subroutine csytri\_rook (character uplo, integer n, complex, dimension( lda, \* ) a, integer lda, integer, dimension( \* ) ipiv, complex, dimension( \* ) work, integer info) **CSYTRI\_ROOK** **Purpose:** ``` !> !> CSYTRI_ROOK computes the inverse of a complex symmetric !> matrix A using the factorization A = U*D*U**T or A = L*D*L**T !> computed by CSYTRF_ROOK. !> ``` **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_ROOK. !> !> 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_ROOK. !> ``` *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. **Contributors:** ``` !> !> December 2016, Igor Kozachenko, !> Computer Science Division, !> University of California, Berkeley !> !> September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas, !> School of Mathematics, !> University of Manchester !> !> ``` Definition at line **128** of file **csytri\_rook.f**. ### subroutine dsytri\_rook (character uplo, integer n, double precision, dimension( lda, \* ) a, integer lda, integer, dimension( \* ) ipiv, double precision, dimension( \* ) work, integer info) **DSYTRI\_ROOK** **Purpose:** ``` !> !> DSYTRI_ROOK computes the inverse of a real symmetric !> matrix A using the factorization A = U*D*U**T or A = L*D*L**T !> computed by DSYTRF_ROOK. !> ``` **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_ROOK. !> !> 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_ROOK. !> ``` *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. **Contributors:** ``` !> !> April 2012, Igor Kozachenko, !> Computer Science Division, !> University of California, Berkeley !> !> September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas, !> School of Mathematics, !> University of Manchester !> !> ``` Definition at line **128** of file **dsytri\_rook.f**. ### subroutine ssytri\_rook (character uplo, integer n, real, dimension( lda, \* ) a, integer lda, integer, dimension( \* ) ipiv, real, dimension( \* ) work, integer info) **SSYTRI\_ROOK** **Purpose:** ``` !> !> SSYTRI_ROOK computes the inverse of a real symmetric !> matrix A using the factorization A = U*D*U**T or A = L*D*L**T !> computed by SSYTRF_ROOK. !> ``` **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_ROOK. !> !> 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_ROOK. !> ``` *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. **Contributors:** ``` !> !> April 2012, Igor Kozachenko, !> Computer Science Division, !> University of California, Berkeley !> !> September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas, !> School of Mathematics, !> University of Manchester !> !> ``` Definition at line **128** of file **ssytri\_rook.f**. ### subroutine zhetri\_rook (character uplo, integer n, complex\*16, dimension( lda, \* ) a, integer lda, integer, dimension( \* ) ipiv, complex\*16, dimension( \* ) work, integer info) **ZHETRI\_ROOK** computes the inverse of HE matrix using the factorization obtained with the bounded Bunch-Kaufman ("rook") diagonal pivoting method. **Purpose:** ``` !> !> ZHETRI_ROOK 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_ROOK. !> ``` **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_ROOK. !> !> 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_ROOK. !> ``` *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. **Contributors:** ``` !> !> November 2013, Igor Kozachenko, !> Computer Science Division, !> University of California, Berkeley !> !> September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas, !> School of Mathematics, !> University of Manchester !> ``` Definition at line **127** of file **zhetri\_rook.f**. ### subroutine zsytri\_rook (character uplo, integer n, complex\*16, dimension( lda, \* ) a, integer lda, integer, dimension( \* ) ipiv, complex\*16, dimension( \* ) work, integer info) **ZSYTRI\_ROOK** **Purpose:** ``` !> !> ZSYTRI_ROOK computes the inverse of a complex symmetric !> matrix A using the factorization A = U*D*U**T or A = L*D*L**T !> computed by ZSYTRF_ROOK. !> ``` **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_ROOK. !> !> 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_ROOK. !> ``` *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. **Contributors:** ``` !> !> December 2016, Igor Kozachenko, !> Computer Science Division, !> University of California, Berkeley !> !> September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas, !> School of Mathematics, !> University of Manchester !> !> ``` Definition at line **128** of file **zsytri\_rook.f**. ## Author Generated automatically by Doxygen for LAPACK from the source code.