ZSYSV_ROOK 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.


 The diagonal pivoting method is used to factor A as


    A = U * D * U**T,  if UPLO = 'U', or


    A = L * D * L**T,  if UPLO = 'L',


 where U (or L) is a product of permutation and unit upper (lower)


 triangular matrices, and D is symmetric and block diagonal with


 1-by-1 and 2-by-2 diagonal blocks.


 ZSYTRF_ROOK is called to compute the factorization of a complex


 symmetric matrix A using the bounded Bunch-Kaufman ("rook") diagonal


 pivoting method.


 The factored form of A is then used to solve the system


 of equations A * X = B by calling ZSYTRS_ROOK.

UPLO

          UPLO is CHARACTER*1


          = 'U':  Upper triangle of A is stored;


          = 'L':  Lower triangle of A is stored.

N

          N is INTEGER


          The number of linear equations, i.e., 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, if INFO = 0, the block diagonal matrix D and the


          multipliers used to obtain the factor U or L from the


          factorization A = U*D*U**T or A = L*D*L**T as computed by


          ZSYTRF_ROOK.

LDA

          LDA is INTEGER


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

IPIV

          IPIV is INTEGER array, dimension (N)


          Details of the interchanges and the block structure of D,


          as determined by ZSYTRF_ROOK.


          If UPLO = 'U':


               If IPIV(k) > 0, then rows and columns k and IPIV(k)


               were interchanged and D(k,k) is a 1-by-1 diagonal block.


               If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and


               columns k and -IPIV(k) were interchanged and rows and


               columns k-1 and -IPIV(k-1) were inerchaged,


               D(k-1:k,k-1:k) is a 2-by-2 diagonal block.


          If UPLO = 'L':


               If IPIV(k) > 0, then rows and columns k and IPIV(k)


               were interchanged and D(k,k) is a 1-by-1 diagonal block.


               If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and


               columns k and -IPIV(k) were interchanged and rows and


               columns k+1 and -IPIV(k+1) were inerchaged,


               D(k:k+1,k:k+1) is a 2-by-2 diagonal block.

B

          B is COMPLEX*16 array, dimension (LDB,NRHS)


          On entry, the N-by-NRHS right hand side matrix B.


          On exit, if INFO = 0, the N-by-NRHS solution matrix X.

LDB

          LDB is INTEGER


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

WORK

          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))


          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

          LWORK is INTEGER


          The length of WORK.  LWORK >= 1, and for best performance


          LWORK >= max(1,N*NB), where NB is the optimal blocksize for


          ZSYTRF_ROOK.


          TRS will be done with Level 2 BLAS


          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, D(i,i) is exactly zero.  The factorization


               has been completed, but the block diagonal matrix D is


               exactly singular, so the solution could not be computed.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

December 2016

   December 2016, Igor Kozachenko,


                  Computer Science Division,


                  University of California, Berkeley


  September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,


                  School of Mathematics,


                  University of Manchester