hetrf_aa_2stage - {he,sy}trf_aa_2stage: triangular factor

Generated automatically by Doxygen for LAPACK from the source code. Version 3.12.0 Thu Aug 7 2025 17:26:25 hetrf_aa_2stage(3)

subroutinechetrf_aa_2stage(characteruplo,integern,complex,dimension(lda,*)a,integerlda,complex,dimension(*)tb,integerltb,integer,dimension(*)ipiv,integer,dimension(*)ipiv2,complex,dimension(*)work,integerlwork,integerinfo)CHETRF_AA_2STAGEPurpose: CHETRF_AA_2STAGE computes the factorization of a real hermitian 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 hermitian band matrix with the bandwidth of NB (NB is internally selected and stored in TB( 1 ), and T is LU factorized with partial pivoting). This is the blocked version of the algorithm, calling Level 3 BLAS. ParametersUPLO 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, L is stored below (or above) the subdiagonal blocks, when UPLO is 'L' (or 'U'). LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N). TB TB is COMPLEX array, dimension (MAX(1,LTB)) On exit, details of the LU factorization of the band matrix. LTB LTB is INTEGER The size of the array TB. LTB >= MAX(1,4*N), internally used to select NB such that LTB >= (3*NB+1)*N. If LTB = -1, then a workspace query is assumed; the routine only calculates the optimal size of LTB, returns this value as the first entry of TB, and no error message related to LTB is issued by XERBLA. 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). IPIV2 IPIV2 is INTEGER array, dimension (N) On exit, it contains the details of the interchanges, i.e., the row and column k of T were interchanged with the row and column IPIV(k). WORK WORK is COMPLEX workspace of size (MAX(1,LWORK)) LWORK LWORK is INTEGER The size of WORK. LWORK >= MAX(1,N), internally used to select NB such that LWORK >= N*NB. 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. > 0: if INFO = i, band LU factorization failed on i-th column Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. subroutinecsytrf_aa_2stage(characteruplo,integern,complex,dimension(lda,*)a,integerlda,complex,dimension(*)tb,integerltb,integer,dimension(*)ipiv,integer,dimension(*)ipiv2,complex,dimension(*)work,integerlwork,integerinfo)CSYTRF_AA_2STAGEPurpose: CSYTRF_AA_2STAGE 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 band matrix with the bandwidth of NB (NB is internally selected and stored in TB( 1 ), and T is LU factorized with partial pivoting). This is the blocked version of the algorithm, calling Level 3 BLAS. ParametersUPLO 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, L is stored below (or above) the subdiagonal blocks, when UPLO is 'L' (or 'U'). LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N). TB TB is COMPLEX array, dimension (LTB) On exit, details of the LU factorization of the band matrix. LTB LTB is INTEGER The size of the array TB. LTB >= 4*N, internally used to select NB such that LTB >= (3*NB+1)*N. If LTB = -1, then a workspace query is assumed; the routine only calculates the optimal size of LTB, returns this value as the first entry of TB, and no error message related to LTB is issued by XERBLA. 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). IPIV2 IPIV2 is INTEGER array, dimension (N) On exit, it contains the details of the interchanges, i.e., the row and column k of T were interchanged with the row and column IPIV(k). WORK WORK is COMPLEX workspace of size LWORK LWORK LWORK is INTEGER The size of WORK. LWORK >= N, internally used to select NB such that LWORK >= N*NB. 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. > 0: if INFO = i, band LU factorization failed on i-th column Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. subroutinedsytrf_aa_2stage(characteruplo,integern,doubleprecision,dimension(lda,*)a,integerlda,doubleprecision,dimension(*)tb,integerltb,integer,dimension(*)ipiv,integer,dimension(*)ipiv2,doubleprecision,dimension(*)work,integerlwork,integerinfo)DSYTRF_AA_2STAGEPurpose: DSYTRF_AA_2STAGE 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 band matrix with the bandwidth of NB (NB is internally selected and stored in TB( 1 ), and T is LU factorized with partial pivoting). This is the blocked version of the algorithm, calling Level 3 BLAS. ParametersUPLO 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, L is stored below (or above) the subdiagonal blocks, when UPLO is 'L' (or 'U'). LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N). TB TB is DOUBLE PRECISION array, dimension (MAX(1,LTB)) On exit, details of the LU factorization of the band matrix. LTB LTB is INTEGER The size of the array TB. LTB >= MAX(1,4*N), internally used to select NB such that LTB >= (3*NB+1)*N. If LTB = -1, then a workspace query is assumed; the routine only calculates the optimal size of LTB, returns this value as the first entry of TB, and no error message related to LTB is issued by XERBLA. 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). IPIV2 IPIV2 is INTEGER array, dimension (N) On exit, it contains the details of the interchanges, i.e., the row and column k of T were interchanged with the row and column IPIV2(k). WORK WORK is DOUBLE PRECISION workspace of size (MAX(1,LWORK)) LWORK LWORK is INTEGER The size of WORK. LWORK >= MAX(1,N), internally used to select NB such that LWORK >= N*NB. 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. > 0: if INFO = i, band LU factorization failed on i-th column Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. subroutinessytrf_aa_2stage(characteruplo,integern,real,dimension(lda,*)a,integerlda,real,dimension(*)tb,integerltb,integer,dimension(*)ipiv,integer,dimension(*)ipiv2,real,dimension(*)work,integerlwork,integerinfo)SSYTRF_AA_2STAGEPurpose: SSYTRF_AA_2STAGE 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 band matrix with the bandwidth of NB (NB is internally selected and stored in TB( 1 ), and T is LU factorized with partial pivoting). This is the blocked version of the algorithm, calling Level 3 BLAS. ParametersUPLO 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, L is stored below (or above) the subdiagonal blocks, when UPLO is 'L' (or 'U'). LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N). TB TB is REAL array, dimension (LTB) On exit, details of the LU factorization of the band matrix. LTB LTB is INTEGER The size of the array TB. LTB >= MAX(1,4*N), internally used to select NB such that LTB >= (3*NB+1)*N. If LTB = -1, then a workspace query is assumed; the routine only calculates the optimal size of LTB, returns this value as the first entry of TB, and no error message related to LTB is issued by XERBLA. 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). IPIV2 IPIV2 is INTEGER array, dimension (N) On exit, it contains the details of the interchanges, i.e., the row and column k of T were interchanged with the row and column IPIV(k). WORK WORK is REAL workspace of size (MAX(1,LWORK)) LWORK LWORK is INTEGER The size of WORK. LWORK >= MAX(1,N), internally used to select NB such that LWORK >= N*NB. 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. > 0: if INFO = i, band LU factorization failed on i-th column Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. subroutinezhetrf_aa_2stage(characteruplo,integern,complex*16,dimension(lda,*)a,integerlda,complex*16,dimension(*)tb,integerltb,integer,dimension(*)ipiv,integer,dimension(*)ipiv2,complex*16,dimension(*)work,integerlwork,integerinfo)ZHETRF_AA_2STAGEPurpose: ZHETRF_AA_2STAGE computes the factorization of a double 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 band matrix with the bandwidth of NB (NB is internally selected and stored in TB( 1 ), and T is LU factorized with partial pivoting). This is the blocked version of the algorithm, calling Level 3 BLAS. ParametersUPLO 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, L is stored below (or above) the subdiagonal blocks, when UPLO is 'L' (or 'U'). LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N). TB TB is COMPLEX*16 array, dimension (MAX(1,LTB)) On exit, details of the LU factorization of the band matrix. LTB LTB is INTEGER The size of the array TB. LTB >= MAX(1,4*N), internally used to select NB such that LTB >= (3*NB+1)*N. If LTB = -1, then a workspace query is assumed; the routine only calculates the optimal size of LTB, returns this value as the first entry of TB, and no error message related to LTB is issued by XERBLA. 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). IPIV2 IPIV2 is INTEGER array, dimension (N) On exit, it contains the details of the interchanges, i.e., the row and column k of T were interchanged with the row and column IPIV(k). WORK WORK is COMPLEX*16 workspace of size (MAX(1,LWORK)) LWORK LWORK is INTEGER The size of WORK. LWORK >= MAX(1,N), internally used to select NB such that LWORK >= N*NB. 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. > 0: if INFO = i, band LU factorization failed on i-th column Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. subroutinezsytrf_aa_2stage(characteruplo,integern,complex*16,dimension(lda,*)a,integerlda,complex*16,dimension(*)tb,integerltb,integer,dimension(*)ipiv,integer,dimension(*)ipiv2,complex*16,dimension(*)work,integerlwork,integerinfo)ZSYTRF_AA_2STAGEPurpose: ZSYTRF_AA_2STAGE 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 band matrix with the bandwidth of NB (NB is internally selected and stored in TB( 1 ), and T is LU factorized with partial pivoting). This is the blocked version of the algorithm, calling Level 3 BLAS. ParametersUPLO 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, L is stored below (or above) the subdiagonal blocks, when UPLO is 'L' (or 'U'). LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N). TB TB is COMPLEX*16 array, dimension (LTB) On exit, details of the LU factorization of the band matrix. LTB LTB is INTEGER The size of the array TB. LTB >= 4*N, internally used to select NB such that LTB >= (3*NB+1)*N. If LTB = -1, then a workspace query is assumed; the routine only calculates the optimal size of LTB, returns this value as the first entry of TB, and no error message related to LTB is issued by XERBLA. 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). IPIV2 IPIV2 is INTEGER array, dimension (N) On exit, it contains the details of the interchanges, i.e., the row and column k of T were interchanged with the row and column IPIV(k). WORK WORK is COMPLEX*16 workspace of size LWORK LWORK LWORK is INTEGER The size of WORK. LWORK >= N, internally used to select NB such that LWORK >= N*NB. 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. > 0: if INFO = i, band LU factorization failed on i-th column Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd.

hetrf_aa_2stage - {he,sy}trf_aa_2stage: triangular factor

Functions subroutine chetrf_aa_2stage (uplo, n, a, lda, tb, ltb, ipiv, ipiv2, work, lwork, info) CHETRF_AA_2STAGE subroutine csytrf_aa_2stage (uplo, n, a, lda, tb, ltb, ipiv, ipiv2, work, lwork, info) CSYTRF_AA_2STAGE subroutine dsytrf_aa_2stage (uplo, n, a, lda, tb, ltb, ipiv, ipiv2, work, lwork, info) DSYTRF_AA_2STAGE subroutine ssytrf_aa_2stage (uplo, n, a, lda, tb, ltb, ipiv, ipiv2, work, lwork, info) SSYTRF_AA_2STAGE subroutine zhetrf_aa_2stage (uplo, n, a, lda, tb, ltb, ipiv, ipiv2, work, lwork, info) ZHETRF_AA_2STAGE subroutine zsytrf_aa_2stage (uplo, n, a, lda, tb, ltb, ipiv, ipiv2, work, lwork, info) ZSYTRF_AA_2STAGE