1ZTPSV(1)                         BLAS routine                         ZTPSV(1)
2
3
4

NAME

6       ZTPSV  -  one  of  the  systems of equations   A*x = b, or A'*x = b, or
7       conjg( A' )*x = b,
8

SYNOPSIS

10       SUBROUTINE ZTPSV(UPLO,TRANS,DIAG,N,AP,X,INCX)
11
12           INTEGER                                   INCX,N
13
14           CHARACTER                                 DIAG,TRANS,UPLO
15
16           DOUBLE                                    COMPLEX AP(*),X(*)
17

PURPOSE

19       ZTPSV  solves one of the systems of equations
20
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.
23
24       No  test  for  singularity or near-singularity is included in this rou‐
25       tine. Such tests must be performed before calling this routine.
26
27

ARGUMENTS

29       UPLO   - CHARACTER*1.
30              On entry, UPLO specifies whether the matrix is an upper or lower
31              triangular matrix as follows:
32
33              UPLO = 'U' or 'u'   A is an upper triangular matrix.
34
35              UPLO = 'L' or 'l'   A is a lower triangular matrix.
36
37              Unchanged on exit.
38
39       TRANS  - CHARACTER*1.
40              On entry, TRANS specifies the equations to be solved as follows:
41
42              TRANS = 'N' or 'n'   A*x = b.
43
44              TRANS = 'T' or 't'   A'*x = b.
45
46              TRANS = 'C' or 'c'   conjg( A' )*x = b.
47
48              Unchanged on exit.
49
50       DIAG   - CHARACTER*1.
51              On  entry, DIAG specifies whether or not A is unit triangular as
52              follows:
53
54              DIAG = 'U' or 'u'   A is assumed to be unit triangular.
55
56              DIAG = 'N' or 'n'   A is not assumed to be unit triangular.
57
58              Unchanged on exit.
59
60       N      - INTEGER.
61              On entry, N specifies the order of the matrix A.  N must  be  at
62              least zero.  Unchanged on exit.
63
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.
76
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.
81
82       INCX   - INTEGER.
83              On  entry,  INCX  specifies the increment for the elements of X.
84              INCX must not be zero.  Unchanged on exit.
85
86              Level 2 Blas routine.
87
88              -- Written on 22-October-1986.  Jack Dongarra, Argonne  National
89              Lab.   Jeremy Du Croz, Nag Central Office.  Sven Hammarling, Nag
90              Central Office.  Richard Hanson, Sandia National Labs.
91
92
93
94BLAS routine                     November 2006                        ZTPSV(1)