dspsv.f man page

dspsv.f —



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

Function/Subroutine Documentation

subroutine dspsv (characterUPLO, integerN, integerNRHS, double precision, dimension( * )AP, integer, dimension( * )IPIV, double precision, dimension( ldb, * )B, integerLDB, integerINFO)

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


 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 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 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 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 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 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, 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

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 = aji)

  Packed storage of the upper triangle of A:

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

Definition at line 163 of file dspsv.f.


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Referenced By

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

Sat Nov 16 2013 Version 3.4.2 LAPACK