DSPSV computes the solution to a real system of linear equations


    A * X = B,


 where A is an N-by-N symmetric matrix stored in packed format 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, D is symmetric and block diagonal with 1-by-1


 and 2-by-2 diagonal blocks.  The factored form of A is then used to


 solve the system of equations A * X = B.

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.

AP

          AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)


          On entry, the upper or lower triangle of the symmetric matrix


          A, packed columnwise in a linear array.  The j-th column of A


          is stored in the array AP as follows:


          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;


          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.


          See below for further details.


          On exit, 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 DSPTRF, stored as


          a packed triangular matrix in the same storage format as A.

IPIV

          IPIV is INTEGER array, dimension (N)


          Details of the interchanges and the block structure of D, as


          determined by DSPTRF.  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 UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0,


          then rows and columns k-1 and -IPIV(k) were interchanged and


          D(k-1:k,k-1:k) is a 2-by-2 diagonal block.  If UPLO = 'L' and


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


          -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2


          diagonal block.

B

          B is DOUBLE PRECISION 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).

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

  The packed storage scheme is illustrated by the following example


  when N = 4, UPLO = 'U':


  Two-dimensional storage of the symmetric matrix A:


     a11 a12 a13 a14


         a22 a23 a24


             a33 a34     (aij = aji)


                 a44


  Packed storage of the upper triangle of A:


  AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]