LAPACK 3.12.0
LAPACK: Linear Algebra PACKage

subroutine ssysv_aa_2stage  (  character  uplo, 
integer  n,  
integer  nrhs,  
real, dimension( lda, * )  a,  
integer  lda,  
real, dimension( * )  tb,  
integer  ltb,  
integer, dimension( * )  ipiv,  
integer, dimension( * )  ipiv2,  
real, dimension( ldb, * )  b,  
integer  ldb,  
real, dimension( * )  work,  
integer  lwork,  
integer  info  
) 
SSYSV_AA_2STAGE computes the solution to system of linear equations A * X = B for SY matrices
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SSYSV_AA_2STAGE computes the solution to a real system of linear equations A * X = B, where A is an NbyN symmetric matrix and X and B are NbyNRHS matrices. Aasen's 2stage 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 LUfactored 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.
[in]  UPLO  UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. 
[in]  N  N is INTEGER The order of the matrix A. N >= 0. 
[in]  NRHS  NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0. 
[in,out]  A  A is REAL array, dimension (LDA,N) On entry, the symmetric matrix A. If UPLO = 'U', the leading NbyN 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 NbyN 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'). 
[in]  LDA  LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N). 
[out]  TB  TB is REAL array, dimension (LTB) On exit, details of the LU factorization of the band matrix. 
[in]  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. 
[out]  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). 
[out]  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). 
[in,out]  B  B is REAL array, dimension (LDB,NRHS) On entry, the right hand side matrix B. On exit, the solution matrix X. 
[in]  LDB  LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N). 
[out]  WORK  WORK is REAL workspace of size LWORK 
[in]  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. 
[out]  INFO  INFO is INTEGER = 0: successful exit < 0: if INFO = i, the ith argument had an illegal value. > 0: if INFO = i, band LU factorization failed on ith column 
Definition at line 184 of file ssysv_aa_2stage.f.