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SUBROUTINE <a name="DGTSVX.1"></a><a href="dgtsvx.f.html#DGTSVX.1">DGTSVX</a>( FACT, TRANS, N, NRHS, DL, D, DU, DLF, DF, DUF,
$ DU2, IPIV, B, LDB, X, LDX, RCOND, FERR, BERR,
$ WORK, IWORK, INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> -- LAPACK 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> CHARACTER FACT, TRANS
INTEGER INFO, LDB, LDX, N, NRHS
DOUBLE PRECISION RCOND
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Array Arguments ..
</span> INTEGER IPIV( * ), IWORK( * )
DOUBLE PRECISION B( LDB, * ), BERR( * ), D( * ), DF( * ),
$ DL( * ), DLF( * ), DU( * ), DU2( * ), DUF( * ),
$ FERR( * ), WORK( * ), X( LDX, * )
<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="DGTSVX.24"></a><a href="dgtsvx.f.html#DGTSVX.1">DGTSVX</a> uses the LU factorization to compute the solution to a real
</span><span class="comment">*</span><span class="comment"> system of linear equations A * X = B or A**T * X = B,
</span><span class="comment">*</span><span class="comment"> where A is a tridiagonal matrix of order N and X and B are N-by-NRHS
</span><span class="comment">*</span><span class="comment"> matrices.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Error bounds on the solution and a condition estimate are also
</span><span class="comment">*</span><span class="comment"> provided.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Description
</span><span class="comment">*</span><span class="comment"> ===========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> The following steps are performed:
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> 1. If FACT = 'N', the LU decomposition is used to factor the matrix A
</span><span class="comment">*</span><span class="comment"> as A = L * U, where L is a product of permutation and unit lower
</span><span class="comment">*</span><span class="comment"> bidiagonal matrices and U is upper triangular with nonzeros in
</span><span class="comment">*</span><span class="comment"> only the main diagonal and first two superdiagonals.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> 2. If some U(i,i)=0, so that U is exactly singular, then the routine
</span><span class="comment">*</span><span class="comment"> returns with INFO = i. Otherwise, the factored form of A is used
</span><span class="comment">*</span><span class="comment"> to estimate the condition number of the matrix A. If the
</span><span class="comment">*</span><span class="comment"> reciprocal of the condition number is less than machine precision,
</span><span class="comment">*</span><span class="comment"> INFO = N+1 is returned as a warning, but the routine still goes on
</span><span class="comment">*</span><span class="comment"> to solve for X and compute error bounds as described below.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> 3. The system of equations is solved for X using the factored form
</span><span class="comment">*</span><span class="comment"> of A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> 4. Iterative refinement is applied to improve the computed solution
</span><span class="comment">*</span><span class="comment"> matrix and calculate error bounds and backward error estimates
</span><span class="comment">*</span><span class="comment"> for it.
</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"> FACT (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment"> Specifies whether or not the factored form of A has been
</span><span class="comment">*</span><span class="comment"> supplied on entry.
</span><span class="comment">*</span><span class="comment"> = 'F': DLF, DF, DUF, DU2, and IPIV contain the factored
</span><span class="comment">*</span><span class="comment"> form of A; DL, D, DU, DLF, DF, DUF, DU2 and IPIV
</span><span class="comment">*</span><span class="comment"> will not be modified.
</span><span class="comment">*</span><span class="comment"> = 'N': The matrix will be copied to DLF, DF, and DUF
</span><span class="comment">*</span><span class="comment"> and factored.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> TRANS (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment"> Specifies the form of the system of equations:
</span><span class="comment">*</span><span class="comment"> = 'N': A * X = B (No transpose)
</span><span class="comment">*</span><span class="comment"> = 'T': A**T * X = B (Transpose)
</span><span class="comment">*</span><span class="comment"> = 'C': A**H * X = B (Conjugate transpose = 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. N >= 0.
</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) DOUBLE PRECISION array, dimension (N-1)
</span><span class="comment">*</span><span class="comment"> The (n-1) subdiagonal elements of A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> D (input) DOUBLE PRECISION array, dimension (N)
</span><span class="comment">*</span><span class="comment"> The n diagonal elements of A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> DU (input) DOUBLE PRECISION array, dimension (N-1)
</span><span class="comment">*</span><span class="comment"> The (n-1) superdiagonal elements of A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> DLF (input or output) DOUBLE PRECISION array, dimension (N-1)
</span><span class="comment">*</span><span class="comment"> If FACT = 'F', then DLF is an input argument and on entry
</span><span class="comment">*</span><span class="comment"> contains the (n-1) multipliers that define the matrix L from
</span><span class="comment">*</span><span class="comment"> the LU factorization of A as computed by <a name="DGTTRF.93"></a><a href="dgttrf.f.html#DGTTRF.1">DGTTRF</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> If FACT = 'N', then DLF is an output argument and on exit
</span><span class="comment">*</span><span class="comment"> contains the (n-1) multipliers that define the matrix L 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"> DF (input or output) DOUBLE PRECISION array, dimension (N)
</span><span class="comment">*</span><span class="comment"> If FACT = 'F', then DF is an input argument and on entry
</span><span class="comment">*</span><span class="comment"> contains the n diagonal elements of the upper triangular
</span><span class="comment">*</span><span class="comment"> matrix U from the LU factorization of A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> If FACT = 'N', then DF is an output argument and on exit
</span><span class="comment">*</span><span class="comment"> contains the n diagonal elements of the upper triangular
</span><span class="comment">*</span><span class="comment"> matrix U from the LU factorization of A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> DUF (input or output) DOUBLE PRECISION array, dimension (N-1)
</span><span class="comment">*</span><span class="comment"> If FACT = 'F', then DUF is an input argument and on entry
</span><span class="comment">*</span><span class="comment"> contains the (n-1) elements of the first superdiagonal of U.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> If FACT = 'N', then DUF is an output argument and on exit
</span><span class="comment">*</span><span class="comment"> contains the (n-1) elements of the first superdiagonal of U.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> DU2 (input or output) DOUBLE PRECISION array, dimension (N-2)
</span><span class="comment">*</span><span class="comment"> If FACT = 'F', then DU2 is an input argument and on entry
</span><span class="comment">*</span><span class="comment"> contains the (n-2) elements of the second superdiagonal of
</span><span class="comment">*</span><span class="comment"> U.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> If FACT = 'N', then DU2 is an output argument and on exit
</span><span class="comment">*</span><span class="comment"> contains the (n-2) elements of the second superdiagonal of
</span><span class="comment">*</span><span class="comment"> U.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> IPIV (input or output) INTEGER array, dimension (N)
</span><span class="comment">*</span><span class="comment"> If FACT = 'F', then IPIV is an input argument and on entry
</span><span class="comment">*</span><span class="comment"> contains the pivot indices from the LU factorization of A as
</span><span class="comment">*</span><span class="comment"> computed by <a name="DGTTRF.127"></a><a href="dgttrf.f.html#DGTTRF.1">DGTTRF</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> If FACT = 'N', then IPIV is an output argument and on exit
</span><span class="comment">*</span><span class="comment"> contains the pivot indices from the LU factorization of A;
</span><span class="comment">*</span><span class="comment"> row i of the matrix was interchanged with row IPIV(i).
</span><span class="comment">*</span><span class="comment"> IPIV(i) will always be either i or i+1; IPIV(i) = i indicates
</span><span class="comment">*</span><span class="comment"> a row interchange was not required.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> B (input) DOUBLE PRECISION array, dimension (LDB,NRHS)
</span><span class="comment">*</span><span class="comment"> The N-by-NRHS right hand side matrix B.
</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).
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