SPSV - 5.2 English - 68552

SPSV computes the solution to system of linear equations A * X = B for OTHER matrices.

Purpose:

    SPSV 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.

Parameters:

• UPLO – [in]

  UPLO is CHARACTER*1

  = ‘U’: Upper triangle of A is stored;

  = ‘L’: Lower triangle of A is stored.

• N – [in]

  N is INTEGER

  The number of linear equations, i.e., the order of the matrix A. N >= 0.

• NRHS – [in]

  NRHS is INTEGER

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

• AP – [inout]

  AP is REAL 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 SSPTRF, stored as a packed triangular matrix in the same storage format as A.

• IPIV – [out]

  IPIV is INTEGER array, dimension (N)

  Details of the interchanges and the block structure of D, as determined by SSPTRF. 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 – [inout]

  B is REAL 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 – [in]

  LDB is INTEGER

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

• INFO – [out]

  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.