ssytrs_3.f - Man Page



subroutine ssytrs_3 (UPLO, N, NRHS, A, LDA, E, IPIV, B, LDB, INFO)

Function/Subroutine Documentation

subroutine ssytrs_3 (character UPLO, integer N, integer NRHS, real, dimension( lda, * ) A, integer LDA, real, dimension( * ) E, integer, dimension( * ) IPIV, real, dimension( ldb, * ) B, integer LDB, integer INFO)



 SSYTRS_3 solves a system of linear equations A * X = B with a real
 symmetric matrix A using the factorization computed

    A = P*U*D*(U**T)*(P**T) or A = P*L*D*(L**T)*(P**T),

 where U (or L) is unit upper (or lower) triangular matrix,
 U**T (or L**T) is the transpose of U (or L), P is a permutation
 matrix, P**T is the transpose of P, and D is symmetric and block
 diagonal with 1-by-1 and 2-by-2 diagonal blocks.

 This algorithm is using Level 3 BLAS.


          UPLO is CHARACTER*1
          Specifies whether the details of the factorization are
          stored as an upper or lower triangular matrix:
          = 'U':  Upper triangular, form is A = P*U*D*(U**T)*(P**T);
          = 'L':  Lower triangular, form is A = P*L*D*(L**T)*(P**T).


          N is INTEGER
          The order of the matrix A.  N >= 0.


          NRHS is INTEGER
          The number of right hand sides, i.e., the number of columns
          of the matrix B.  NRHS >= 0.


          A is REAL array, dimension (LDA,N)
          Diagonal of the block diagonal matrix D and factors U or L
          as computed by SSYTRF_RK and SSYTRF_BK:
            a) ONLY diagonal elements of the symmetric block diagonal
               matrix D on the diagonal of A, i.e. D(k,k) = A(k,k);
               (superdiagonal (or subdiagonal) elements of D
                should be provided on entry in array E), and
            b) If UPLO = 'U': factor U in the superdiagonal part of A.
               If UPLO = 'L': factor L in the subdiagonal part of A.


          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).


          E is REAL array, dimension (N)
          On entry, contains the superdiagonal (or subdiagonal)
          elements of the symmetric block diagonal matrix D
          with 1-by-1 or 2-by-2 diagonal blocks, where
          If UPLO = 'U': E(i) = D(i-1,i),i=2:N, E(1) not referenced;
          If UPLO = 'L': E(i) = D(i+1,i),i=1:N-1, E(N) not referenced.

          NOTE: For 1-by-1 diagonal block D(k), where
          1 <= k <= N, the element E(k) is not referenced in both
          UPLO = 'U' or UPLO = 'L' cases.


          IPIV is INTEGER array, dimension (N)
          Details of the interchanges and the block structure of D
          as determined by SSYTRF_RK or SSYTRF_BK.


          B is REAL array, dimension (LDB,NRHS)
          On entry, the right hand side matrix B.
          On exit, the solution matrix X.


          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).


          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.


  June 2017,  Igor Kozachenko,
                  Computer Science Division,
                  University of California, Berkeley

  September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
                  School of Mathematics,
                  University of Manchester

Definition at line 163 of file ssytrs_3.f.


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Referenced By

The man page ssytrs_3(3) is an alias of ssytrs_3.f(3).

Mon Jun 28 2021 Version 3.10.0 LAPACK