sppsv.f man page

sppsv.f —



subroutine sppsv (UPLO, N, NRHS, AP, B, LDB, INFO)
SPPSV computes the solution to system of linear equations A * X = B for OTHER matrices

Function/Subroutine Documentation

subroutine sppsv (characterUPLO, integerN, integerNRHS, real, dimension( * )AP, real, dimension( ldb, * )B, integerLDB, integerINFO)

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


 SPPSV computes the solution to a real system of linear equations
    A * X = B,
 where A is an N-by-N symmetric 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**T* U,  if UPLO = 'U', or
    A = L * L**T,  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 is CHARACTER*1
          = 'U':  Upper triangle of A is stored;
          = 'L':  Lower triangle of A is stored.


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


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


          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, if INFO = 0, the factor U or L from the Cholesky
          factorization A = U**T*U or A = L*L**T, in the same storage
          format as A.


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


          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

Further Details:

  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 = conjg(aji))

  Packed storage of the upper triangle of A:

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

Definition at line 145 of file sppsv.f.


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Referenced By

sppsv(3) is an alias of sppsv.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK