hesv_aa_2stage - {he,sy}sv_aa_2stage: Aasen, blocked 2-stage

Generated automatically by Doxygen for LAPACK from the source code. Version 3.12.0 Sun Jul 20 2025 01:40:05 hesv_aa_2stage(3)

subroutinechesv_aa_2stage(characteruplo,integern,integernrhs,complex,dimension(lda,*)a,integerlda,complex,dimension(*)tb,integerltb,integer,dimension(*)ipiv,integer,dimension(*)ipiv2,complex,dimension(ldb,*)b,integerldb,complex,dimension(*)work,integerlwork,integerinfo)CHESV_AA_2STAGEcomputesthesolutiontosystemoflinearequationsA*X=BforHEmatricesPurpose: CHESV_AA_2STAGE computes the solution to a complex system of linear equations A * X = B, where A is an N-by-N Hermitian matrix and X and B are N-by-NRHS matrices. Aasen's 2-stage algorithm is used to factor A as A = U**H * T * U, if UPLO = 'U', or A = L * T * L**H, if UPLO = 'L', where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and T is Hermitian and band. The matrix T is then LU-factored with partial pivoting. The factored form of A is then used to solve the system of equations A * X = B. 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. NRHS NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 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). B B is COMPLEX array, dimension (LDB,NRHS) On entry, the right hand side matrix B. On exit, the solution matrix X. LDB LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N). WORK WORK is COMPLEX workspace of size (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal 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. subroutinecsysv_aa_2stage(characteruplo,integern,integernrhs,complex,dimension(lda,*)a,integerlda,complex,dimension(*)tb,integerltb,integer,dimension(*)ipiv,integer,dimension(*)ipiv2,complex,dimension(ldb,*)b,integerldb,complex,dimension(*)work,integerlwork,integerinfo)CSYSV_AA_2STAGEcomputesthesolutiontosystemoflinearequationsA*X=BforSYmatricesPurpose: CSYSV_AA_2STAGE computes the solution to a complex system of linear equations A * X = B, where A is an N-by-N symmetric matrix and X and B are N-by-NRHS matrices. Aasen's 2-stage algorithm is used to factor A as A = U**T * T * U, if UPLO = 'U', or A = L * T * L**T, if UPLO = 'L', where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and T is symmetric and band. The matrix T is then LU-factored with partial pivoting. The factored form of A is then used to solve the system of equations A * X = B. 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. NRHS NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 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, 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). B B is COMPLEX array, dimension (LDB,NRHS) On entry, the right hand side matrix B. On exit, the solution matrix X. LDB LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N). 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. subroutinedsysv_aa_2stage(characteruplo,integern,integernrhs,doubleprecision,dimension(lda,*)a,integerlda,doubleprecision,dimension(*)tb,integerltb,integer,dimension(*)ipiv,integer,dimension(*)ipiv2,doubleprecision,dimension(ldb,*)b,integerldb,doubleprecision,dimension(*)work,integerlwork,integerinfo)DSYSV_AA_2STAGEcomputesthesolutiontosystemoflinearequationsA*X=BforSYmatricesPurpose: DSYSV_AA_2STAGE computes the solution to a real system of linear equations A * X = B, where A is an N-by-N symmetric matrix and X and B are N-by-NRHS matrices. Aasen's 2-stage algorithm is used to factor A as A = U**T * T * U, if UPLO = 'U', or A = L * T * L**T, if UPLO = 'L', where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and T is symmetric and band. The matrix T is then LU-factored with partial pivoting. The factored form of A is then used to solve the system of equations A * X = B. 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. NRHS NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 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 IPIV(k). B B is DOUBLE PRECISION array, dimension (LDB,NRHS) On entry, the right hand side matrix B. On exit, the solution matrix X. LDB LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N). WORK WORK is DOUBLE PRECISION workspace of size (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal 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. subroutinessysv_aa_2stage(characteruplo,integern,integernrhs,real,dimension(lda,*)a,integerlda,real,dimension(*)tb,integerltb,integer,dimension(*)ipiv,integer,dimension(*)ipiv2,real,dimension(ldb,*)b,integerldb,real,dimension(*)work,integerlwork,integerinfo)SSYSV_AA_2STAGEcomputesthesolutiontosystemoflinearequationsA*X=BforSYmatricesPurpose: SSYSV_AA_2STAGE computes the solution to a real system of linear equations A * X = B, where A is an N-by-N symmetric matrix and X and B are N-by-NRHS matrices. Aasen's 2-stage algorithm is used to factor A as A = U**T * T * U, if UPLO = 'U', or A = L * T * L**T, if UPLO = 'L', where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and T is symmetric and band. The matrix T is then LU-factored with partial pivoting. The factored form of A is then used to solve the system of equations A * X = B. 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. NRHS NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 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 (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). B B is REAL array, dimension (LDB,NRHS) On entry, the right hand side matrix B. On exit, the solution matrix X. LDB LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N). WORK WORK is REAL workspace of size (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal 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. subroutinezhesv_aa_2stage(characteruplo,integern,integernrhs,complex*16,dimension(lda,*)a,integerlda,complex*16,dimension(*)tb,integerltb,integer,dimension(*)ipiv,integer,dimension(*)ipiv2,complex*16,dimension(ldb,*)b,integerldb,complex*16,dimension(*)work,integerlwork,integerinfo)ZHESV_AA_2STAGEcomputesthesolutiontosystemoflinearequationsA*X=BforHEmatricesPurpose: ZHESV_AA_2STAGE computes the solution to a complex system of linear equations A * X = B, where A is an N-by-N Hermitian matrix and X and B are N-by-NRHS matrices. Aasen's 2-stage algorithm is used to factor A as A = U**H * T * U, if UPLO = 'U', or A = L * T * L**H, if UPLO = 'L', where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and T is Hermitian and band. The matrix T is then LU-factored with partial pivoting. The factored form of A is then used to solve the system of equations A * X = B. 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. NRHS NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 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). B B is COMPLEX*16 array, dimension (LDB,NRHS) On entry, the right hand side matrix B. On exit, the solution matrix X. LDB LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N). WORK WORK is COMPLEX*16 workspace of size (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal 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. subroutinezsysv_aa_2stage(characteruplo,integern,integernrhs,complex*16,dimension(lda,*)a,integerlda,complex*16,dimension(*)tb,integerltb,integer,dimension(*)ipiv,integer,dimension(*)ipiv2,complex*16,dimension(ldb,*)b,integerldb,complex*16,dimension(*)work,integerlwork,integerinfo)ZSYSV_AA_2STAGEcomputesthesolutiontosystemoflinearequationsA*X=BforSYmatricesPurpose: ZSYSV_AA_2STAGE computes the solution to a complex system of linear equations A * X = B, where A is an N-by-N symmetric matrix and X and B are N-by-NRHS matrices. Aasen's 2-stage algorithm is used to factor A as A = U**T * T * U, if UPLO = 'U', or A = L * T * L**T, if UPLO = 'L', where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and T is symmetric and band. The matrix T is then LU-factored with partial pivoting. The factored form of A is then used to solve the system of equations A * X = B. 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. NRHS NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 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, 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). B B is COMPLEX*16 array, dimension (LDB,NRHS) On entry, the right hand side matrix B. On exit, the solution matrix X. LDB LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N). 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.

hesv_aa_2stage - {he,sy}sv_aa_2stage: Aasen, blocked 2-stage

Functions subroutine chesv_aa_2stage (uplo, n, nrhs, a, lda, tb, ltb, ipiv, ipiv2, b, ldb, work, lwork, info) CHESV_AA_2STAGEcomputesthesolutiontosystemoflinearequationsA*X=BforHEmatrices subroutine csysv_aa_2stage (uplo, n, nrhs, a, lda, tb, ltb, ipiv, ipiv2, b, ldb, work, lwork, info) CSYSV_AA_2STAGEcomputesthesolutiontosystemoflinearequationsA*X=BforSYmatrices subroutine dsysv_aa_2stage (uplo, n, nrhs, a, lda, tb, ltb, ipiv, ipiv2, b, ldb, work, lwork, info) DSYSV_AA_2STAGEcomputesthesolutiontosystemoflinearequationsA*X=BforSYmatrices subroutine ssysv_aa_2stage (uplo, n, nrhs, a, lda, tb, ltb, ipiv, ipiv2, b, ldb, work, lwork, info) SSYSV_AA_2STAGEcomputesthesolutiontosystemoflinearequationsA*X=BforSYmatrices subroutine zhesv_aa_2stage (uplo, n, nrhs, a, lda, tb, ltb, ipiv, ipiv2, b, ldb, work, lwork, info) ZHESV_AA_2STAGEcomputesthesolutiontosystemoflinearequationsA*X=BforHEmatrices subroutine zsysv_aa_2stage (uplo, n, nrhs, a, lda, tb, ltb, ipiv, ipiv2, b, ldb, work, lwork, info) ZSYSV_AA_2STAGEcomputesthesolutiontosystemoflinearequationsA*X=BforSYmatrices