hetrf_aa(3) Library Functions Manual hetrf_aa(3) NAME hetrf_aa - {he,sy}trf_aa: triangular factor SYNOPSIS Functions subroutine chetrf_aa (uplo, n, a, lda, ipiv, work, lwork, info) CHETRF_AA subroutine csytrf_aa (uplo, n, a, lda, ipiv, work, lwork, info) CSYTRF_AA subroutine dsytrf_aa (uplo, n, a, lda, ipiv, work, lwork, info) DSYTRF_AA subroutine ssytrf_aa (uplo, n, a, lda, ipiv, work, lwork, info) SSYTRF_AA subroutine zhetrf_aa (uplo, n, a, lda, ipiv, work, lwork, info) ZHETRF_AA subroutine zsytrf_aa (uplo, n, a, lda, ipiv, work, lwork, info) ZSYTRF_AA Detailed Description Function Documentation subroutine chetrf_aa (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex, dimension( * ) work, integer lwork, integer info) CHETRF_AA Purpose: !> !> CHETRF_AA computes the factorization of a complex hermitian matrix A !> using the Aasen's algorithm. The form of the factorization is !> !> A = U**H*T*U or A = L*T*L**H !> !> where U (or L) is a product of permutation and unit upper (lower) !> triangular matrices, and T is a hermitian tridiagonal matrix. !> !> This is the blocked version of the algorithm, calling Level 3 BLAS. !> 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 hermitian matrix A. If UPLO = 'U', the leading !> N-by-N upper triangular part of A contains the upper !> triangular part of the matrix A, and the strictly lower !> triangular part of A is not referenced. If UPLO = 'L', the !> leading N-by-N lower triangular part of A contains the lower !> triangular part of the matrix A, and the strictly upper !> triangular part of A is not referenced. !> !> On exit, the tridiagonal matrix is stored in the diagonals !> and the subdiagonals of A just below (or above) the diagonals, !> and L is stored below (or above) the subdiagonals, when UPLO !> is 'L' (or 'U'). !> LDA !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !> IPIV !> IPIV is INTEGER array, dimension (N) !> On exit, it contains the details of the interchanges, i.e., !> the row and column k of A were interchanged with the !> row and column IPIV(k). !> WORK !> WORK is COMPLEX array, dimension (MAX(1,LWORK)) !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. !> LWORK !> LWORK is INTEGER !> The length of WORK. !> LWORK >= 1, if N <= 1, and LWORK >= 2*N, otherwise. !> For optimum performance LWORK >= N*(1+NB), where NB is !> the optimal blocksize, returned by ILAENV. !> !> If LWORK = -1, then a workspace query is assumed; the routine !> only calculates the optimal size of the WORK array, returns !> this value as the first entry of the WORK array, and no error !> message related to LWORK is issued by XERBLA. !> INFO !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value. !> Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line 133 of file chetrf_aa.f. subroutine csytrf_aa (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex, dimension( * ) work, integer lwork, integer info) CSYTRF_AA Purpose: !> !> CSYTRF_AA computes the factorization of a complex symmetric matrix A !> using the Aasen's algorithm. The form of the factorization is !> !> A = U**T*T*U or A = L*T*L**T !> !> where U (or L) is a product of permutation and unit upper (lower) !> triangular matrices, and T is a complex symmetric tridiagonal matrix. !> !> This is the blocked version of the algorithm, calling Level 3 BLAS. !> 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 symmetric matrix A. If UPLO = 'U', the leading !> N-by-N upper triangular part of A contains the upper !> triangular part of the matrix A, and the strictly lower !> triangular part of A is not referenced. If UPLO = 'L', the !> leading N-by-N lower triangular part of A contains the lower !> triangular part of the matrix A, and the strictly upper !> triangular part of A is not referenced. !> !> On exit, the tridiagonal matrix is stored in the diagonals !> and the subdiagonals of A just below (or above) the diagonals, !> and L is stored below (or above) the subdiagonals, when UPLO !> is 'L' (or 'U'). !> LDA !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !> IPIV !> IPIV is INTEGER array, dimension (N) !> On exit, it contains the details of the interchanges, i.e., !> the row and column k of A were interchanged with the !> row and column IPIV(k). !> WORK !> WORK is COMPLEX array, dimension (MAX(1,LWORK)) !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. !> LWORK !> LWORK is INTEGER !> The length of WORK. LWORK >= MAX(1,2*N). For optimum performance !> LWORK >= N*(1+NB), where NB is the optimal blocksize. !> !> If LWORK = -1, then a workspace query is assumed; the routine !> only calculates the optimal size of the WORK array, returns !> this value as the first entry of the WORK array, and no error !> message related to LWORK is issued by XERBLA. !> INFO !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value. !> Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line 131 of file csytrf_aa.f. subroutine dsytrf_aa (character uplo, integer n, double precision, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, double precision, dimension( * ) work, integer lwork, integer info) DSYTRF_AA Purpose: !> !> DSYTRF_AA computes the factorization of a real symmetric matrix A !> using the Aasen's algorithm. The form of the factorization is !> !> A = U**T*T*U or A = L*T*L**T !> !> where U (or L) is a product of permutation and unit upper (lower) !> triangular matrices, and T is a symmetric tridiagonal matrix. !> !> This is the blocked version of the algorithm, calling Level 3 BLAS. !> 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 symmetric matrix A. If UPLO = 'U', the leading !> N-by-N upper triangular part of A contains the upper !> triangular part of the matrix A, and the strictly lower !> triangular part of A is not referenced. If UPLO = 'L', the !> leading N-by-N lower triangular part of A contains the lower !> triangular part of the matrix A, and the strictly upper !> triangular part of A is not referenced. !> !> On exit, the tridiagonal matrix is stored in the diagonals !> and the subdiagonals of A just below (or above) the diagonals, !> and L is stored below (or above) the subdiagonals, when UPLO !> is 'L' (or 'U'). !> LDA !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !> IPIV !> IPIV is INTEGER array, dimension (N) !> On exit, it contains the details of the interchanges, i.e., !> the row and column k of A were interchanged with the !> row and column IPIV(k). !> WORK !> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. !> LWORK !> LWORK is INTEGER !> The length of WORK. !> LWORK >= 1, if N <= 1, and LWORK >= 2*N, otherwise. !> For optimum performance LWORK >= N*(1+NB), where NB is !> the optimal blocksize, returned by ILAENV. !> !> If LWORK = -1, then a workspace query is assumed; the routine !> only calculates the optimal size of the WORK array, returns !> this value as the first entry of the WORK array, and no error !> message related to LWORK is issued by XERBLA. !> INFO !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value. !> Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line 133 of file dsytrf_aa.f. subroutine ssytrf_aa (character uplo, integer n, real, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, real, dimension( * ) work, integer lwork, integer info) SSYTRF_AA Purpose: !> !> SSYTRF_AA computes the factorization of a real symmetric matrix A !> using the Aasen's algorithm. The form of the factorization is !> !> A = U**T*T*U or A = L*T*L**T !> !> where U (or L) is a product of permutation and unit upper (lower) !> triangular matrices, and T is a symmetric tridiagonal matrix. !> !> This is the blocked version of the algorithm, calling Level 3 BLAS. !> 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 symmetric matrix A. If UPLO = 'U', the leading !> N-by-N upper triangular part of A contains the upper !> triangular part of the matrix A, and the strictly lower !> triangular part of A is not referenced. If UPLO = 'L', the !> leading N-by-N lower triangular part of A contains the lower !> triangular part of the matrix A, and the strictly upper !> triangular part of A is not referenced. !> !> On exit, the tridiagonal matrix is stored in the diagonals !> and the subdiagonals of A just below (or above) the diagonals, !> and L is stored below (or above) the subdiagonals, when UPLO !> is 'L' (or 'U'). !> LDA !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !> IPIV !> IPIV is INTEGER array, dimension (N) !> On exit, it contains the details of the interchanges, i.e., !> the row and column k of A were interchanged with the !> row and column IPIV(k). !> WORK !> WORK is REAL array, dimension (MAX(1,LWORK)) !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. !> LWORK !> LWORK is INTEGER !> The length of WORK. !> LWORK >= 1, if N <= 1, and LWORK >= 2*N, otherwise. !> For optimum performance LWORK >= N*(1+NB), where NB is !> the optimal blocksize, returned by ILAENV. !> !> If LWORK = -1, then a workspace query is assumed; the routine !> only calculates the optimal size of the WORK array, returns !> this value as the first entry of the WORK array, and no error !> message related to LWORK is issued by XERBLA. !> INFO !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value. !> Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line 133 of file ssytrf_aa.f. subroutine zhetrf_aa (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex*16, dimension( * ) work, integer lwork, integer info) ZHETRF_AA Purpose: !> !> ZHETRF_AA computes the factorization of a complex hermitian matrix A !> using the Aasen's algorithm. The form of the factorization is !> !> A = U**H*T*U or A = L*T*L**H !> !> where U (or L) is a product of permutation and unit upper (lower) !> triangular matrices, and T is a hermitian tridiagonal matrix. !> !> This is the blocked version of the algorithm, calling Level 3 BLAS. !> 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 hermitian matrix A. If UPLO = 'U', the leading !> N-by-N upper triangular part of A contains the upper !> triangular part of the matrix A, and the strictly lower !> triangular part of A is not referenced. If UPLO = 'L', the !> leading N-by-N lower triangular part of A contains the lower !> triangular part of the matrix A, and the strictly upper !> triangular part of A is not referenced. !> !> On exit, the tridiagonal matrix is stored in the diagonals !> and the subdiagonals of A just below (or above) the diagonals, !> and L is stored below (or above) the subdiagonals, when UPLO !> is 'L' (or 'U'). !> LDA !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !> IPIV !> IPIV is INTEGER array, dimension (N) !> On exit, it contains the details of the interchanges, i.e., !> the row and column k of A were interchanged with the !> row and column IPIV(k). !> WORK !> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. !> LWORK !> LWORK is INTEGER !> The length of WORK. !> LWORK >= 1, if N >= 1, and LWORK >= 2*N, otherwise. !> For optimum performance LWORK >= N*(1+NB), where NB is !> the optimal blocksize, returned by ILAENV. !> !> If LWORK = -1, then a workspace query is assumed; the routine !> only calculates the optimal size of the WORK array, returns !> this value as the first entry of the WORK array, and no error !> message related to LWORK is issued by XERBLA. !> INFO !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value. !> Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line 133 of file zhetrf_aa.f. subroutine zsytrf_aa (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex*16, dimension( * ) work, integer lwork, integer info) ZSYTRF_AA Purpose: !> !> ZSYTRF_AA computes the factorization of a complex symmetric matrix A !> using the Aasen's algorithm. The form of the factorization is !> !> A = U**T*T*U or A = L*T*L**T !> !> where U (or L) is a product of permutation and unit upper (lower) !> triangular matrices, and T is a complex symmetric tridiagonal matrix. !> !> This is the blocked version of the algorithm, calling Level 3 BLAS. !> 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 symmetric matrix A. If UPLO = 'U', the leading !> N-by-N upper triangular part of A contains the upper !> triangular part of the matrix A, and the strictly lower !> triangular part of A is not referenced. If UPLO = 'L', the !> leading N-by-N lower triangular part of A contains the lower !> triangular part of the matrix A, and the strictly upper !> triangular part of A is not referenced. !> !> On exit, the tridiagonal matrix is stored in the diagonals !> and the subdiagonals of A just below (or above) the diagonals, !> and L is stored below (or above) the subdiagonals, when UPLO !> is 'L' (or 'U'). !> LDA !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !> IPIV !> IPIV is INTEGER array, dimension (N) !> On exit, it contains the details of the interchanges, i.e., !> the row and column k of A were interchanged with the !> row and column IPIV(k). !> WORK !> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. !> LWORK !> LWORK is INTEGER !> The length of WORK. LWORK >=MAX(1,2*N). For optimum performance !> LWORK >= N*(1+NB), where NB is the optimal blocksize. !> !> If LWORK = -1, then a workspace query is assumed; the routine !> only calculates the optimal size of the WORK array, returns !> this value as the first entry of the WORK array, and no error !> message related to LWORK is issued by XERBLA. !> INFO !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value. !> Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line 131 of file zsytrf_aa.f. Author Generated automatically by Doxygen for LAPACK from the source code. LAPACK Version 3.12.0 hetrf_aa(3)