--- 
:name: dspsv
:md5sum: 0fac3d384951ed9358ca786e7d72fd2b
:category: :subroutine
:arguments: 
- uplo: 
    :type: char
    :intent: input
- n: 
    :type: integer
    :intent: input
- nrhs: 
    :type: integer
    :intent: input
- ap: 
    :type: doublereal
    :intent: input/output
    :dims: 
    - n*(n+1)/2
- ipiv: 
    :type: integer
    :intent: output
    :dims: 
    - n
- b: 
    :type: doublereal
    :intent: input/output
    :dims: 
    - ldb
    - nrhs
- ldb: 
    :type: integer
    :intent: input
- info: 
    :type: integer
    :intent: output
:substitutions: 
  n: ldb
:fortran_help: "      SUBROUTINE DSPSV( UPLO, N, NRHS, AP, IPIV, B, LDB, INFO )\n\n\
  *  Purpose\n\
  *  =======\n\
  *\n\
  *  DSPSV computes the solution to a real system of linear equations\n\
  *     A * X = B,\n\
  *  where A is an N-by-N symmetric matrix stored in packed format and X\n\
  *  and B are N-by-NRHS matrices.\n\
  *\n\
  *  The diagonal pivoting method is used to factor A as\n\
  *     A = U * D * U**T,  if UPLO = 'U', or\n\
  *     A = L * D * L**T,  if UPLO = 'L',\n\
  *  where U (or L) is a product of permutation and unit upper (lower)\n\
  *  triangular matrices, D is symmetric and block diagonal with 1-by-1\n\
  *  and 2-by-2 diagonal blocks.  The factored form of A is then used to\n\
  *  solve the system of equations A * X = B.\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\
  *  AP      (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2)\n\
  *          On entry, the upper or lower triangle of the symmetric matrix\n\
  *          A, packed columnwise in a linear array.  The j-th column of A\n\
  *          is stored in the array AP as follows:\n\
  *          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;\n\
  *          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.\n\
  *          See below for further details.\n\
  *\n\
  *          On exit, the block diagonal matrix D and the multipliers used\n\
  *          to obtain the factor U or L from the factorization\n\
  *          A = U*D*U**T or A = L*D*L**T as computed by DSPTRF, stored as\n\
  *          a packed triangular matrix in the same storage format as A.\n\
  *\n\
  *  IPIV    (output) INTEGER array, dimension (N)\n\
  *          Details of the interchanges and the block structure of D, as\n\
  *          determined by DSPTRF.  If IPIV(k) > 0, then rows and columns\n\
  *          k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1\n\
  *          diagonal block.  If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0,\n\
  *          then rows and columns k-1 and -IPIV(k) were interchanged and\n\
  *          D(k-1:k,k-1:k) is a 2-by-2 diagonal block.  If UPLO = 'L' and\n\
  *          IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and\n\
  *          -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2\n\
  *          diagonal block.\n\
  *\n\
  *  B       (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)\n\
  *          On entry, the N-by-NRHS right hand side matrix B.\n\
  *          On exit, if INFO = 0, the N-by-NRHS solution matrix X.\n\
  *\n\
  *  LDB     (input) INTEGER\n\
  *          The leading dimension of the array B.  LDB >= max(1,N).\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, D(i,i) is exactly zero.  The factorization\n\
  *                has been completed, but the block diagonal matrix D is\n\
  *                exactly singular, so the solution could not be\n\
  *                computed.\n\
  *\n\n\
  *  Further Details\n\
  *  ===============\n\
  *\n\
  *  The packed storage scheme is illustrated by the following example\n\
  *  when N = 4, UPLO = 'U':\n\
  *\n\
  *  Two-dimensional storage of the symmetric matrix A:\n\
  *\n\
  *     a11 a12 a13 a14\n\
  *         a22 a23 a24\n\
  *             a33 a34     (aij = aji)\n\
  *                 a44\n\
  *\n\
  *  Packed storage of the upper triangle of A:\n\
  *\n\
  *  AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]\n\
  *\n\
  *  =====================================================================\n\
  *\n\
  *     .. External Functions ..\n      LOGICAL            LSAME\n      EXTERNAL           LSAME\n\
  *     ..\n\
  *     .. External Subroutines ..\n      EXTERNAL           DSPTRF, DSPTRS, XERBLA\n\
  *     ..\n\
  *     .. Intrinsic Functions ..\n      INTRINSIC          MAX\n\
  *     ..\n"
