1ZTPSV(1)                         BLAS routine                         ZTPSV(1)
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NAME

6       ZTPSV  - solves one of the systems of equations   A*x = b, or A'*x = b,
7       or conjg( A' )*x = b,
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SYNOPSIS

10       SUBROUTINE ZTPSV(UPLO,TRANS,DIAG,N,AP,X,INCX)
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12           INTEGER                                   INCX,N
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14           CHARACTER                                 DIAG,TRANS,UPLO
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16           DOUBLE                                    COMPLEX AP(*),X(*)
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PURPOSE

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

29       UPLO   - CHARACTER*1.
30              On entry, UPLO specifies whether the matrix is an upper or lower
31              triangular matrix as follows:
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33              UPLO = 'U' or 'u'   A is an upper triangular matrix.
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35              UPLO = 'L' or 'l'   A is a lower triangular matrix.
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37              Unchanged on exit.
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39       TRANS  - CHARACTER*1.
40              On entry, TRANS specifies the equations to be solved as follows:
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42              TRANS = 'N' or 'n'   A*x = b.
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44              TRANS = 'T' or 't'   A'*x = b.
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46              TRANS = 'C' or 'c'   conjg( A' )*x = b.
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48              Unchanged on exit.
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50       DIAG   - CHARACTER*1.
51              On  entry, DIAG specifies whether or not A is unit triangular as
52              follows:
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54              DIAG = 'U' or 'u'   A is assumed to be unit triangular.
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56              DIAG = 'N' or 'n'   A is not assumed to be unit triangular.
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58              Unchanged on exit.
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60       N      - INTEGER.
61              On entry, N specifies the order of the matrix A.  N must  be  at
62              least zero.  Unchanged on exit.
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64       AP     - COMPLEX*16       array of DIMENSION at least
65              (  (  n*(  n + 1 ) )/2 ).  Before entry with  UPLO = 'U' or 'u',
66              the array AP must contain the  upper  triangular  matrix  packed
67              sequentially, column by column, so that AP( 1 ) contains a( 1, 1
68              ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2  )  respec‐
69              tively,  and  so  on.   Before entry with UPLO = 'L' or 'l', the
70              array AP must contain the lower triangular matrix packed sequen‐
71              tially,  column  by  column, so that AP( 1 ) contains a( 1, 1 ),
72              AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and  a(  3,  1  )  respec‐
73              tively, and so on.  Note that when  DIAG = 'U' or 'u', the diag‐
74              onal elements of A are not referenced, but  are  assumed  to  be
75              unity.  Unchanged on exit.
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77       X      - COMPLEX*16       array of dimension at least
78              (  1  +  ( n - 1 )*abs( INCX ) ).  Before entry, the incremented
79              array X must contain the n element right-hand side vector b.  On
80              exit, X is overwritten with the solution vector x.
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82       INCX   - INTEGER.
83              On  entry,  INCX  specifies the increment for the elements of X.
84              INCX must not be zero.  Unchanged on exit.
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FURTHER DETAILS

87       Level 2 Blas routine.
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89       -- Written on 22-October-1986.
90          Jack Dongarra, Argonne National Lab.
91          Jeremy Du Croz, Nag Central Office.
92          Sven Hammarling, Nag Central Office.
93          Richard Hanson, Sandia National Labs.
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98BLAS routine                     November 2008                        ZTPSV(1)