CPPSV computes the solution to a complex system of linear equations


    A * X = B,


 where A is an N-by-N Hermitian positive definite matrix stored in


 packed format and X and B are N-by-NRHS matrices.


 The Cholesky decomposition is used to factor A as


    A = U**H * U,  if UPLO = 'U', or


    A = L * L**H,  if UPLO = 'L',


 where U is an upper triangular matrix and L is a lower triangular


 matrix.  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 COMPLEX array, dimension (N*(N+1)/2)


          On entry, the upper or lower triangle of the Hermitian 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, if INFO = 0, the factor U or L from the Cholesky


          factorization A = U**H*U or A = L*L**H, in the same storage


          format as A.

B

          B is COMPLEX 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, the leading minor of order i of A is not


                positive definite, so the factorization could not be


                completed, and the solution has not been computed.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

November 2011

  The packed storage scheme is illustrated by the following example


  when N = 4, UPLO = 'U':


  Two-dimensional storage of the Hermitian matrix A:


     a11 a12 a13 a14


         a22 a23 a24


             a33 a34     (aij = conjg(aji))


                 a44


  Packed storage of the upper triangle of A:


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