1CTRSV(1)                         BLAS routine                         CTRSV(1)
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NAME

6       CTRSV  - 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 CTRSV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX)
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12           INTEGER                                      INCX,LDA,N
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14           CHARACTER                                    DIAG,TRANS,UPLO
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16           COMPLEX                                      A(LDA,*),X(*)
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PURPOSE

19       CTRSV  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.
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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       A      - COMPLEX          array of DIMENSION ( LDA, n ).
65              Before  entry  with  UPLO = 'U' or 'u', the leading n by n upper
66              triangular part of the array A must contain the upper triangular
67              matrix and the strictly lower triangular part of A is not refer‐
68              enced.  Before entry with UPLO = 'L' or 'l', the leading n by  n
69              lower triangular part of the array A must contain the lower tri‐
70              angular matrix and the strictly upper triangular part  of  A  is
71              not referenced.  Note that when  DIAG = 'U' or 'u', the diagonal
72              elements of A are not referenced either, but are assumed  to  be
73              unity.  Unchanged on exit.
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75       LDA    - INTEGER.
76              On  entry, LDA specifies the first dimension of A as declared in
77              the calling (sub) program. LDA must be at least  max(  1,  n  ).
78              Unchanged on exit.
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80       X      - COMPLEX          array of dimension at least
81              (  1  +  ( n - 1 )*abs( INCX ) ).  Before entry, the incremented
82              array X must contain the n element right-hand side vector b.  On
83              exit, X is overwritten with the solution vector x.
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85       INCX   - INTEGER.
86              On  entry,  INCX  specifies the increment for the elements of X.
87              INCX must not be zero.  Unchanged on exit.
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FURTHER DETAILS

90       Level 2 Blas routine.
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92       -- Written on 22-October-1986.
93          Jack Dongarra, Argonne National Lab.
94          Jeremy Du Croz, Nag Central Office.
95          Sven Hammarling, Nag Central Office.
96          Richard Hanson, Sandia National Labs.
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101BLAS routine                     November 2008                        CTRSV(1)