1STPSV(1)                         BLAS routine                         STPSV(1)
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NAME

6       STPSV - solves one of the systems of equations   A*x = b, or A'*x = b,
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SYNOPSIS

9       SUBROUTINE STPSV(UPLO,TRANS,DIAG,N,AP,X,INCX)
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11           INTEGER                                   INCX,N
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13           CHARACTER                                 DIAG,TRANS,UPLO
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15           REAL                                      AP(*),X(*)
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PURPOSE

18       STPSV  solves one of the systems of equations
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20       where  b  and  x are n element vectors and A is an n by n unit, or non-
21       unit, upper or lower triangular matrix, supplied in packed form.
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23       No test for singularity or near-singularity is included  in  this  rou‐
24       tine. Such tests must be performed before calling this routine.
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ARGUMENTS

28       UPLO   - CHARACTER*1.
29              On entry, UPLO specifies whether the matrix is an upper or lower
30              triangular matrix as follows:
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32              UPLO = 'U' or 'u'   A is an upper triangular matrix.
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34              UPLO = 'L' or 'l'   A is a lower triangular matrix.
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36              Unchanged on exit.
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38       TRANS  - CHARACTER*1.
39              On entry, TRANS specifies the equations to be solved as follows:
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41              TRANS = 'N' or 'n'   A*x = b.
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43              TRANS = 'T' or 't'   A'*x = b.
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45              TRANS = 'C' or 'c'   A'*x = b.
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47              Unchanged on exit.
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49       DIAG   - CHARACTER*1.
50              On entry, DIAG specifies whether or not A is unit triangular  as
51              follows:
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53              DIAG = 'U' or 'u'   A is assumed to be unit triangular.
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55              DIAG = 'N' or 'n'   A is not assumed to be unit triangular.
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57              Unchanged on exit.
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59       N      - INTEGER.
60              On  entry,  N specifies the order of the matrix A.  N must be at
61              least zero.  Unchanged on exit.
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63       AP     - REAL             array of DIMENSION at least
64              ( ( n*( n + 1 ) )/2 ).  Before entry with  UPLO =  'U'  or  'u',
65              the  array  AP  must  contain the upper triangular matrix packed
66              sequentially, column by column, so that AP( 1 ) contains a( 1, 1
67              ),  AP(  2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) respec‐
68              tively, and so on.  Before entry with UPLO =  'L'  or  'l',  the
69              array AP must contain the lower triangular matrix packed sequen‐
70              tially, column by column, so that AP( 1 ) contains a(  1,  1  ),
71              AP(  2  )  and  AP(  3 ) contain a( 2, 1 ) and a( 3, 1 ) respec‐
72              tively, and so on.  Note that when  DIAG = 'U' or 'u', the diag‐
73              onal  elements  of  A  are not referenced, but are assumed to be
74              unity.  Unchanged on exit.
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76       X      - REAL             array of dimension at least
77              ( 1 + ( n - 1 )*abs( INCX ) ).  Before  entry,  the  incremented
78              array  X must contain the n element right-hand side vector b. On
79              exit, X is overwritten with the solution vector x.
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81       INCX   - INTEGER.
82              On entry, INCX specifies the increment for the  elements  of  X.
83              INCX must not be zero.  Unchanged on exit.
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FURTHER DETAILS

86       Level 2 Blas routine.
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88       -- Written on 22-October-1986.
89          Jack Dongarra, Argonne National Lab.
90          Jeremy Du Croz, Nag Central Office.
91          Sven Hammarling, Nag Central Office.
92          Richard Hanson, Sandia National Labs.
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97BLAS routine                     November 2008                        STPSV(1)
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