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SUBROUTINE <a name="CGTTS2.1"></a><a href="cgtts2.f.html#CGTTS2.1">CGTTS2</a>( ITRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> -- LAPACK auxiliary routine (version 3.1) --
</span><span class="comment">*</span><span class="comment"> Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment"> November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> .. Scalar Arguments ..
</span> INTEGER ITRANS, LDB, N, NRHS
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Array Arguments ..
</span> INTEGER IPIV( * )
COMPLEX B( LDB, * ), D( * ), DL( * ), DU( * ), DU2( * )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Purpose
</span><span class="comment">*</span><span class="comment"> =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> <a name="CGTTS2.18"></a><a href="cgtts2.f.html#CGTTS2.1">CGTTS2</a> solves one of the systems of equations
</span><span class="comment">*</span><span class="comment"> A * X = B, A**T * X = B, or A**H * X = B,
</span><span class="comment">*</span><span class="comment"> with a tridiagonal matrix A using the LU factorization computed
</span><span class="comment">*</span><span class="comment"> by <a name="CGTTRF.21"></a><a href="cgttrf.f.html#CGTTRF.1">CGTTRF</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Arguments
</span><span class="comment">*</span><span class="comment"> =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> ITRANS (input) INTEGER
</span><span class="comment">*</span><span class="comment"> Specifies the form of the system of equations.
</span><span class="comment">*</span><span class="comment"> = 0: A * X = B (No transpose)
</span><span class="comment">*</span><span class="comment"> = 1: A**T * X = B (Transpose)
</span><span class="comment">*</span><span class="comment"> = 2: A**H * X = B (Conjugate transpose)
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> N (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The order of the matrix A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> NRHS (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The number of right hand sides, i.e., the number of columns
</span><span class="comment">*</span><span class="comment"> of the matrix B. NRHS >= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> DL (input) COMPLEX array, dimension (N-1)
</span><span class="comment">*</span><span class="comment"> The (n-1) multipliers that define the matrix L from the
</span><span class="comment">*</span><span class="comment"> LU factorization of A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> D (input) COMPLEX array, dimension (N)
</span><span class="comment">*</span><span class="comment"> The n diagonal elements of the upper triangular matrix U from
</span><span class="comment">*</span><span class="comment"> the LU factorization of A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> DU (input) COMPLEX array, dimension (N-1)
</span><span class="comment">*</span><span class="comment"> The (n-1) elements of the first super-diagonal of U.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> DU2 (input) COMPLEX array, dimension (N-2)
</span><span class="comment">*</span><span class="comment"> The (n-2) elements of the second super-diagonal of U.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> IPIV (input) INTEGER array, dimension (N)
</span><span class="comment">*</span><span class="comment"> The pivot indices; for 1 <= i <= n, row i of the matrix was
</span><span class="comment">*</span><span class="comment"> interchanged with row IPIV(i). IPIV(i) will always be either
</span><span class="comment">*</span><span class="comment"> i or i+1; IPIV(i) = i indicates a row interchange was not
</span><span class="comment">*</span><span class="comment"> required.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> B (input/output) COMPLEX array, dimension (LDB,NRHS)
</span><span class="comment">*</span><span class="comment"> On entry, the matrix of right hand side vectors B.
</span><span class="comment">*</span><span class="comment"> On exit, B is overwritten by the solution vectors X.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDB (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The leading dimension of the array B. LDB >= max(1,N).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> .. Local Scalars ..
</span> INTEGER I, J
COMPLEX TEMP
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Intrinsic Functions ..
</span> INTRINSIC CONJG
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Quick return if possible
</span><span class="comment">*</span><span class="comment">
</span> IF( N.EQ.0 .OR. NRHS.EQ.0 )
$ RETURN
<span class="comment">*</span><span class="comment">
</span> IF( ITRANS.EQ.0 ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Solve A*X = B using the LU factorization of A,
</span><span class="comment">*</span><span class="comment"> overwriting each right hand side vector with its solution.
</span><span class="comment">*</span><span class="comment">
</span> IF( NRHS.LE.1 ) THEN
J = 1
10 CONTINUE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Solve L*x = b.
</span><span class="comment">*</span><span class="comment">
</span> DO 20 I = 1, N - 1
IF( IPIV( I ).EQ.I ) THEN
B( I+1, J ) = B( I+1, J ) - DL( I )*B( I, J )
ELSE
TEMP = B( I, J )
B( I, J ) = B( I+1, J )
B( I+1, J ) = TEMP - DL( I )*B( I, J )
END IF
20 CONTINUE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Solve U*x = b.
</span><span class="comment">*</span><span class="comment">
</span> B( N, J ) = B( N, J ) / D( N )
IF( N.GT.1 )
$ B( N-1, J ) = ( B( N-1, J )-DU( N-1 )*B( N, J ) ) /
$ D( N-1 )
DO 30 I = N - 2, 1, -1
B( I, J ) = ( B( I, J )-DU( I )*B( I+1, J )-DU2( I )*
$ B( I+2, J ) ) / D( I )
30 CONTINUE
IF( J.LT.NRHS ) THEN
J = J + 1
GO TO 10
END IF
ELSE
DO 60 J = 1, NRHS
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Solve L*x = b.
</span><span class="comment">*</span><span class="comment">
</span> DO 40 I = 1, N - 1
IF( IPIV( I ).EQ.I ) THEN
B( I+1, J ) = B( I+1, J ) - DL( I )*B( I, J )
ELSE
TEMP = B( I, J )
B( I, J ) = B( I+1, J )
B( I+1, J ) = TEMP - DL( I )*B( I, J )
END IF
40 CONTINUE
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