--- 
:name: dsposv
:md5sum: afe420b5c200deccb5aa7fc0f0c8cf39
:category: :subroutine
:arguments: 
- uplo: 
    :type: char
    :intent: input
- n: 
    :type: integer
    :intent: input
- nrhs: 
    :type: integer
    :intent: input
- a: 
    :type: doublereal
    :intent: input/output
    :dims: 
    - lda
    - n
- lda: 
    :type: integer
    :intent: input
- b: 
    :type: doublereal
    :intent: input
    :dims: 
    - ldb
    - nrhs
- ldb: 
    :type: integer
    :intent: input
- x: 
    :type: doublereal
    :intent: output
    :dims: 
    - ldx
    - nrhs
- ldx: 
    :type: integer
    :intent: input
- work: 
    :type: doublereal
    :intent: workspace
    :dims: 
    - n
    - nrhs
- swork: 
    :type: real
    :intent: workspace
    :dims: 
    - n*(n+nrhs)
- iter: 
    :type: integer
    :intent: output
- info: 
    :type: integer
    :intent: output
:substitutions: 
  ldx: MAX(1,n)
:fortran_help: "      SUBROUTINE DSPOSV( UPLO, N, NRHS, A, LDA, B, LDB, X, LDX, WORK, SWORK, ITER, INFO )\n\n\
  *  Purpose\n\
  *  =======\n\
  *\n\
  *  DSPOSV computes the solution to a real system of linear equations\n\
  *     A * X = B,\n\
  *  where A is an N-by-N symmetric positive definite matrix and X and B\n\
  *  are N-by-NRHS matrices.\n\
  *\n\
  *  DSPOSV first attempts to factorize the matrix in SINGLE PRECISION\n\
  *  and use this factorization within an iterative refinement procedure\n\
  *  to produce a solution with DOUBLE PRECISION normwise backward error\n\
  *  quality (see below). If the approach fails the method switches to a\n\
  *  DOUBLE PRECISION factorization and solve.\n\
  *\n\
  *  The iterative refinement is not going to be a winning strategy if\n\
  *  the ratio SINGLE PRECISION performance over DOUBLE PRECISION\n\
  *  performance is too small. A reasonable strategy should take the\n\
  *  number of right-hand sides and the size of the matrix into account.\n\
  *  This might be done with a call to ILAENV in the future. Up to now, we\n\
  *  always try iterative refinement.\n\
  *\n\
  *  The iterative refinement process is stopped if\n\
  *      ITER > ITERMAX\n\
  *  or for all the RHS we have:\n\
  *      RNRM < SQRT(N)*XNRM*ANRM*EPS*BWDMAX\n\
  *  where\n\
  *      o ITER is the number of the current iteration in the iterative\n\
  *        refinement process\n\
  *      o RNRM is the infinity-norm of the residual\n\
  *      o XNRM is the infinity-norm of the solution\n\
  *      o ANRM is the infinity-operator-norm of the matrix A\n\
  *      o EPS is the machine epsilon returned by DLAMCH('Epsilon')\n\
  *  The value ITERMAX and BWDMAX are fixed to 30 and 1.0D+00\n\
  *  respectively.\n\
  *\n\n\
  *  Arguments\n\
  *  =========\n\
  *\n\
  *  UPLO    (input) CHARACTER*1\n\
  *          = 'U':  Upper triangle of A is stored;\n\
  *          = 'L':  Lower triangle of A is stored.\n\
  *\n\
  *  N       (input) INTEGER\n\
  *          The number of linear equations, i.e., the order of the\n\
  *          matrix A.  N >= 0.\n\
  *\n\
  *  NRHS    (input) INTEGER\n\
  *          The number of right hand sides, i.e., the number of columns\n\
  *          of the matrix B.  NRHS >= 0.\n\
  *\n\
  *  A       (input/output) DOUBLE PRECISION array,\n\
  *          dimension (LDA,N)\n\
  *          On entry, the symmetric matrix A.  If UPLO = 'U', the leading\n\
  *          N-by-N upper triangular part of A contains the upper\n\
  *          triangular part of the matrix A, and the strictly lower\n\
  *          triangular part of A is not referenced.  If UPLO = 'L', the\n\
  *          leading N-by-N lower triangular part of A contains the lower\n\
  *          triangular part of the matrix A, and the strictly upper\n\
  *          triangular part of A is not referenced.\n\
  *          On exit, if iterative refinement has been successfully used\n\
  *          (INFO.EQ.0 and ITER.GE.0, see description below), then A is\n\
  *          unchanged, if double precision factorization has been used\n\
  *          (INFO.EQ.0 and ITER.LT.0, see description below), then the\n\
  *          array A contains the factor U or L from the Cholesky\n\
  *          factorization A = U**T*U or A = L*L**T.\n\
  *\n\
  *\n\
  *  LDA     (input) INTEGER\n\
  *          The leading dimension of the array A.  LDA >= max(1,N).\n\
  *\n\
  *  B       (input) DOUBLE PRECISION array, dimension (LDB,NRHS)\n\
  *          The N-by-NRHS right hand side matrix B.\n\
  *\n\
  *  LDB     (input) INTEGER\n\
  *          The leading dimension of the array B.  LDB >= max(1,N).\n\
  *\n\
  *  X       (output) DOUBLE PRECISION array, dimension (LDX,NRHS)\n\
  *          If INFO = 0, the N-by-NRHS solution matrix X.\n\
  *\n\
  *  LDX     (input) INTEGER\n\
  *          The leading dimension of the array X.  LDX >= max(1,N).\n\
  *\n\
  *  WORK    (workspace) DOUBLE PRECISION array, dimension (N,NRHS)\n\
  *          This array is used to hold the residual vectors.\n\
  *\n\
  *  SWORK   (workspace) REAL array, dimension (N*(N+NRHS))\n\
  *          This array is used to use the single precision matrix and the\n\
  *          right-hand sides or solutions in single precision.\n\
  *\n\
  *  ITER    (output) INTEGER\n\
  *          < 0: iterative refinement has failed, double precision\n\
  *               factorization has been performed\n\
  *               -1 : the routine fell back to full precision for\n\
  *                    implementation- or machine-specific reasons\n\
  *               -2 : narrowing the precision induced an overflow,\n\
  *                    the routine fell back to full precision\n\
  *               -3 : failure of SPOTRF\n\
  *               -31: stop the iterative refinement after the 30th\n\
  *                    iterations\n\
  *          > 0: iterative refinement has been successfully used.\n\
  *               Returns the number of iterations\n\
  *\n\
  *  INFO    (output) INTEGER\n\
  *          = 0:  successful exit\n\
  *          < 0:  if INFO = -i, the i-th argument had an illegal value\n\
  *          > 0:  if INFO = i, the leading minor of order i of (DOUBLE\n\
  *                PRECISION) A is not positive definite, so the\n\
  *                factorization could not be completed, and the solution\n\
  *                has not been computed.\n\
  *\n\
  *  =========\n\
  *\n"
