DSYTRS_3 solves a system of linear equations A * X = B with a real


 symmetric matrix A using the factorization computed


 by DSYTRF_RK or DSYTRF_BK:


    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

          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

          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)


          Diagonal of the block diagonal matrix D and factors U or L


          as computed by DSYTRF_RK and DSYTRF_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

          LDA is INTEGER


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

E

          E is DOUBLE PRECISION 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

          IPIV is INTEGER array, dimension (N)


          Details of the interchanges and the block structure of D


          as determined by DSYTRF_RK or DSYTRF_BK.

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).

INFO

          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

  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