lahef_aa(3) Library Functions Manual lahef_aa(3) NAME lahef_aa - la{he,sy}f_aa: triangular factor partial factor SYNOPSIS Functions subroutine clahef_aa (uplo, j1, m, nb, a, lda, ipiv, h, ldh, work) CLAHEF_AA subroutine clasyf_aa (uplo, j1, m, nb, a, lda, ipiv, h, ldh, work) CLASYF_AA subroutine dlasyf_aa (uplo, j1, m, nb, a, lda, ipiv, h, ldh, work) DLASYF_AA subroutine slasyf_aa (uplo, j1, m, nb, a, lda, ipiv, h, ldh, work) SLASYF_AA subroutine zlahef_aa (uplo, j1, m, nb, a, lda, ipiv, h, ldh, work) ZLAHEF_AA subroutine zlasyf_aa (uplo, j1, m, nb, a, lda, ipiv, h, ldh, work) ZLASYF_AA Detailed Description Function Documentation subroutine clahef_aa (character uplo, integer j1, integer m, integer nb, complex, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex, dimension( ldh, * ) h, integer ldh, complex, dimension( * ) work) CLAHEF_AA Purpose: !> !> CLAHEF_AA factorizes a panel of a complex hermitian matrix A using !> the Aasen's algorithm. The panel consists of a set of NB rows of A !> when UPLO is U, or a set of NB columns when UPLO is L. !> !> In order to factorize the panel, the Aasen's algorithm requires the !> last row, or column, of the previous panel. The first row, or column, !> of A is set to be the first row, or column, of an identity matrix, !> which is used to factorize the first panel. !> !> The resulting J-th row of U, or J-th column of L, is stored in the !> (J-1)-th row, or column, of A (without the unit diagonals), while !> the diagonal and subdiagonal of A are overwritten by those of T. !> !> Parameters UPLO !> UPLO is CHARACTER*1 !> = 'U': Upper triangle of A is stored; !> = 'L': Lower triangle of A is stored. !> J1 !> J1 is INTEGER !> The location of the first row, or column, of the panel !> within the submatrix of A, passed to this routine, e.g., !> when called by CHETRF_AA, for the first panel, J1 is 1, !> while for the remaining panels, J1 is 2. !> M !> M is INTEGER !> The dimension of the submatrix. M >= 0. !> NB !> NB is INTEGER !> The dimension of the panel to be facotorized. !> A !> A is COMPLEX array, dimension (LDA,M) for !> the first panel, while dimension (LDA,M+1) for the !> remaining panels. !> !> On entry, A contains the last row, or column, of !> the previous panel, and the trailing submatrix of A !> to be factorized, except for the first panel, only !> the panel is passed. !> !> On exit, the leading panel is factorized. !> 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 row and column interchanges, !> the row and column k were interchanged with the row and !> column IPIV(k). !> H !> H is COMPLEX workspace, dimension (LDH,NB). !> !> LDH !> LDH is INTEGER !> The leading dimension of the workspace H. LDH >= max(1,M). !> WORK !> WORK is COMPLEX workspace, dimension (M). !> Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line 142 of file clahef_aa.f. subroutine clasyf_aa (character uplo, integer j1, integer m, integer nb, complex, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex, dimension( ldh, * ) h, integer ldh, complex, dimension( * ) work) CLASYF_AA Purpose: !> !> DLATRF_AA factorizes a panel of a complex symmetric matrix A using !> the Aasen's algorithm. The panel consists of a set of NB rows of A !> when UPLO is U, or a set of NB columns when UPLO is L. !> !> In order to factorize the panel, the Aasen's algorithm requires the !> last row, or column, of the previous panel. The first row, or column, !> of A is set to be the first row, or column, of an identity matrix, !> which is used to factorize the first panel. !> !> The resulting J-th row of U, or J-th column of L, is stored in the !> (J-1)-th row, or column, of A (without the unit diagonals), while !> the diagonal and subdiagonal of A are overwritten by those of T. !> !> Parameters UPLO !> UPLO is CHARACTER*1 !> = 'U': Upper triangle of A is stored; !> = 'L': Lower triangle of A is stored. !> J1 !> J1 is INTEGER !> The location of the first row, or column, of the panel !> within the submatrix of A, passed to this routine, e.g., !> when called by CSYTRF_AA, for the first panel, J1 is 1, !> while for the remaining panels, J1 is 2. !> M !> M is INTEGER !> The dimension of the submatrix. M >= 0. !> NB !> NB is INTEGER !> The dimension of the panel to be facotorized. !> A !> A is COMPLEX array, dimension (LDA,M) for !> the first panel, while dimension (LDA,M+1) for the !> remaining panels. !> !> On entry, A contains the last row, or column, of !> the previous panel, and the trailing submatrix of A !> to be factorized, except for the first panel, only !> the panel is passed. !> !> On exit, the leading panel is factorized. !> LDA !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,M). !> IPIV !> IPIV is INTEGER array, dimension (M) !> Details of the row and column interchanges, !> the row and column k were interchanged with the row and !> column IPIV(k). !> H !> H is COMPLEX workspace, dimension (LDH,NB). !> !> LDH !> LDH is INTEGER !> The leading dimension of the workspace H. LDH >= max(1,M). !> WORK !> WORK is COMPLEX workspace, dimension (M). !> Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line 142 of file clasyf_aa.f. subroutine dlasyf_aa (character uplo, integer j1, integer m, integer nb, double precision, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, double precision, dimension( ldh, * ) h, integer ldh, double precision, dimension( * ) work) DLASYF_AA Purpose: !> !> DLATRF_AA factorizes a panel of a real symmetric matrix A using !> the Aasen's algorithm. The panel consists of a set of NB rows of A !> when UPLO is U, or a set of NB columns when UPLO is L. !> !> In order to factorize the panel, the Aasen's algorithm requires the !> last row, or column, of the previous panel. The first row, or column, !> of A is set to be the first row, or column, of an identity matrix, !> which is used to factorize the first panel. !> !> The resulting J-th row of U, or J-th column of L, is stored in the !> (J-1)-th row, or column, of A (without the unit diagonals), while !> the diagonal and subdiagonal of A are overwritten by those of T. !> !> Parameters UPLO !> UPLO is CHARACTER*1 !> = 'U': Upper triangle of A is stored; !> = 'L': Lower triangle of A is stored. !> J1 !> J1 is INTEGER !> The location of the first row, or column, of the panel !> within the submatrix of A, passed to this routine, e.g., !> when called by DSYTRF_AA, for the first panel, J1 is 1, !> while for the remaining panels, J1 is 2. !> M !> M is INTEGER !> The dimension of the submatrix. M >= 0. !> NB !> NB is INTEGER !> The dimension of the panel to be facotorized. !> A !> A is DOUBLE PRECISION array, dimension (LDA,M) for !> the first panel, while dimension (LDA,M+1) for the !> remaining panels. !> !> On entry, A contains the last row, or column, of !> the previous panel, and the trailing submatrix of A !> to be factorized, except for the first panel, only !> the panel is passed. !> !> On exit, the leading panel is factorized. !> LDA !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,M). !> IPIV !> IPIV is INTEGER array, dimension (M) !> Details of the row and column interchanges, !> the row and column k were interchanged with the row and !> column IPIV(k). !> H !> H is DOUBLE PRECISION workspace, dimension (LDH,NB). !> !> LDH !> LDH is INTEGER !> The leading dimension of the workspace H. LDH >= max(1,M). !> WORK !> WORK is DOUBLE PRECISION workspace, dimension (M). !> Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line 142 of file dlasyf_aa.f. subroutine slasyf_aa (character uplo, integer j1, integer m, integer nb, real, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, real, dimension( ldh, * ) h, integer ldh, real, dimension( * ) work) SLASYF_AA Purpose: !> !> DLATRF_AA factorizes a panel of a real symmetric matrix A using !> the Aasen's algorithm. The panel consists of a set of NB rows of A !> when UPLO is U, or a set of NB columns when UPLO is L. !> !> In order to factorize the panel, the Aasen's algorithm requires the !> last row, or column, of the previous panel. The first row, or column, !> of A is set to be the first row, or column, of an identity matrix, !> which is used to factorize the first panel. !> !> The resulting J-th row of U, or J-th column of L, is stored in the !> (J-1)-th row, or column, of A (without the unit diagonals), while !> the diagonal and subdiagonal of A are overwritten by those of T. !> !> Parameters UPLO !> UPLO is CHARACTER*1 !> = 'U': Upper triangle of A is stored; !> = 'L': Lower triangle of A is stored. !> J1 !> J1 is INTEGER !> The location of the first row, or column, of the panel !> within the submatrix of A, passed to this routine, e.g., !> when called by SSYTRF_AA, for the first panel, J1 is 1, !> while for the remaining panels, J1 is 2. !> M !> M is INTEGER !> The dimension of the submatrix. M >= 0. !> NB !> NB is INTEGER !> The dimension of the panel to be facotorized. !> A !> A is REAL array, dimension (LDA,M) for !> the first panel, while dimension (LDA,M+1) for the !> remaining panels. !> !> On entry, A contains the last row, or column, of !> the previous panel, and the trailing submatrix of A !> to be factorized, except for the first panel, only !> the panel is passed. !> !> On exit, the leading panel is factorized. !> LDA !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,M). !> IPIV !> IPIV is INTEGER array, dimension (M) !> Details of the row and column interchanges, !> the row and column k were interchanged with the row and !> column IPIV(k). !> H !> H is REAL workspace, dimension (LDH,NB). !> !> LDH !> LDH is INTEGER !> The leading dimension of the workspace H. LDH >= max(1,M). !> WORK !> WORK is REAL workspace, dimension (M). !> Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line 142 of file slasyf_aa.f. subroutine zlahef_aa (character uplo, integer j1, integer m, integer nb, complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex*16, dimension( ldh, * ) h, integer ldh, complex*16, dimension( * ) work) ZLAHEF_AA Purpose: !> !> DLAHEF_AA factorizes a panel of a complex hermitian matrix A using !> the Aasen's algorithm. The panel consists of a set of NB rows of A !> when UPLO is U, or a set of NB columns when UPLO is L. !> !> In order to factorize the panel, the Aasen's algorithm requires the !> last row, or column, of the previous panel. The first row, or column, !> of A is set to be the first row, or column, of an identity matrix, !> which is used to factorize the first panel. !> !> The resulting J-th row of U, or J-th column of L, is stored in the !> (J-1)-th row, or column, of A (without the unit diagonals), while !> the diagonal and subdiagonal of A are overwritten by those of T. !> !> Parameters UPLO !> UPLO is CHARACTER*1 !> = 'U': Upper triangle of A is stored; !> = 'L': Lower triangle of A is stored. !> J1 !> J1 is INTEGER !> The location of the first row, or column, of the panel !> within the submatrix of A, passed to this routine, e.g., !> when called by ZHETRF_AA, for the first panel, J1 is 1, !> while for the remaining panels, J1 is 2. !> M !> M is INTEGER !> The dimension of the submatrix. M >= 0. !> NB !> NB is INTEGER !> The dimension of the panel to be facotorized. !> A !> A is COMPLEX*16 array, dimension (LDA,M) for !> the first panel, while dimension (LDA,M+1) for the !> remaining panels. !> !> On entry, A contains the last row, or column, of !> the previous panel, and the trailing submatrix of A !> to be factorized, except for the first panel, only !> the panel is passed. !> !> On exit, the leading panel is factorized. !> 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 row and column interchanges, !> the row and column k were interchanged with the row and !> column IPIV(k). !> H !> H is COMPLEX*16 workspace, dimension (LDH,NB). !> !> LDH !> LDH is INTEGER !> The leading dimension of the workspace H. LDH >= max(1,M). !> WORK !> WORK is COMPLEX*16 workspace, dimension (M). !> Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line 142 of file zlahef_aa.f. subroutine zlasyf_aa (character uplo, integer j1, integer m, integer nb, complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex*16, dimension( ldh, * ) h, integer ldh, complex*16, dimension( * ) work) ZLASYF_AA Purpose: !> !> DLATRF_AA factorizes a panel of a complex symmetric matrix A using !> the Aasen's algorithm. The panel consists of a set of NB rows of A !> when UPLO is U, or a set of NB columns when UPLO is L. !> !> In order to factorize the panel, the Aasen's algorithm requires the !> last row, or column, of the previous panel. The first row, or column, !> of A is set to be the first row, or column, of an identity matrix, !> which is used to factorize the first panel. !> !> The resulting J-th row of U, or J-th column of L, is stored in the !> (J-1)-th row, or column, of A (without the unit diagonals), while !> the diagonal and subdiagonal of A are overwritten by those of T. !> !> Parameters UPLO !> UPLO is CHARACTER*1 !> = 'U': Upper triangle of A is stored; !> = 'L': Lower triangle of A is stored. !> J1 !> J1 is INTEGER !> The location of the first row, or column, of the panel !> within the submatrix of A, passed to this routine, e.g., !> when called by ZSYTRF_AA, for the first panel, J1 is 1, !> while for the remaining panels, J1 is 2. !> M !> M is INTEGER !> The dimension of the submatrix. M >= 0. !> NB !> NB is INTEGER !> The dimension of the panel to be facotorized. !> A !> A is COMPLEX*16 array, dimension (LDA,M) for !> the first panel, while dimension (LDA,M+1) for the !> remaining panels. !> !> On entry, A contains the last row, or column, of !> the previous panel, and the trailing submatrix of A !> to be factorized, except for the first panel, only !> the panel is passed. !> !> On exit, the leading panel is factorized. !> LDA !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,M). !> IPIV !> IPIV is INTEGER array, dimension (M) !> Details of the row and column interchanges, !> the row and column k were interchanged with the row and !> column IPIV(k). !> H !> H is COMPLEX*16 workspace, dimension (LDH,NB). !> !> LDH !> LDH is INTEGER !> The leading dimension of the workspace H. LDH >= max(1,M). !> WORK !> WORK is COMPLEX*16 workspace, dimension (M). !> Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line 142 of file zlasyf_aa.f. Author Generated automatically by Doxygen for LAPACK from the source code. LAPACK Version 3.12.0 lahef_aa(3)