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SUBROUTINE <a name="ZPTSVX.1"></a><a href="zptsvx.f.html#ZPTSVX.1">ZPTSVX</a>( FACT, N, NRHS, D, E, DF, EF, B, LDB, X, LDX,
$ RCOND, FERR, BERR, WORK, RWORK, 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
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> DOUBLE PRECISION BERR( * ), D( * ), DF( * ), FERR( * ),
$ RWORK( * )
COMPLEX*16 B( LDB, * ), E( * ), EF( * ), 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="ZPTSVX.23"></a><a href="zptsvx.f.html#ZPTSVX.1">ZPTSVX</a> uses the factorization A = L*D*L**H to compute the solution
</span><span class="comment">*</span><span class="comment"> to a complex system of linear equations A*X = B, where A is an
</span><span class="comment">*</span><span class="comment"> N-by-N Hermitian positive definite tridiagonal matrix and X and B
</span><span class="comment">*</span><span class="comment"> are N-by-NRHS 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 matrix A is factored as A = L*D*L**H, where L
</span><span class="comment">*</span><span class="comment"> is a unit lower bidiagonal matrix and D is diagonal. The
</span><span class="comment">*</span><span class="comment"> factorization can also be regarded as having the form
</span><span class="comment">*</span><span class="comment"> A = U**H*D*U.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> 2. If the leading i-by-i principal minor is not positive definite,
</span><span class="comment">*</span><span class="comment"> then the routine returns with INFO = i. Otherwise, the factored
</span><span class="comment">*</span><span class="comment"> form of A is used to estimate the condition number of the matrix
</span><span class="comment">*</span><span class="comment"> A. If the reciprocal of the condition number is less than machine
</span><span class="comment">*</span><span class="comment"> precision, INFO = N+1 is returned as a warning, but the routine
</span><span class="comment">*</span><span class="comment"> still goes on to solve for X and compute error bounds as
</span><span class="comment">*</span><span class="comment"> 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 the matrix
</span><span class="comment">*</span><span class="comment"> A is supplied on entry.
</span><span class="comment">*</span><span class="comment"> = 'F': On entry, DF and EF contain the factored form of A.
</span><span class="comment">*</span><span class="comment"> D, E, DF, and EF will not be modified.
</span><span class="comment">*</span><span class="comment"> = 'N': The matrix A will be copied to DF and EF and
</span><span class="comment">*</span><span class="comment"> factored.
</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 matrices B and X. NRHS >= 0.
</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 the tridiagonal matrix A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> E (input) COMPLEX*16 array, dimension (N-1)
</span><span class="comment">*</span><span class="comment"> The (n-1) subdiagonal elements of the tridiagonal matrix 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 diagonal matrix D
</span><span class="comment">*</span><span class="comment"> from the L*D*L**H factorization of A.
</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 diagonal matrix D
</span><span class="comment">*</span><span class="comment"> from the L*D*L**H factorization of A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> EF (input or output) COMPLEX*16 array, dimension (N-1)
</span><span class="comment">*</span><span class="comment"> If FACT = 'F', then EF is an input argument and on entry
</span><span class="comment">*</span><span class="comment"> contains the (n-1) subdiagonal elements of the unit
</span><span class="comment">*</span><span class="comment"> bidiagonal factor L from the L*D*L**H factorization of A.
</span><span class="comment">*</span><span class="comment"> If FACT = 'N', then EF is an output argument and on exit
</span><span class="comment">*</span><span class="comment"> contains the (n-1) subdiagonal elements of the unit
</span><span class="comment">*</span><span class="comment"> bidiagonal factor L from the L*D*L**H factorization of A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> B (input) COMPLEX*16 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).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> X (output) COMPLEX*16 array, dimension (LDX,NRHS)
</span><span class="comment">*</span><span class="comment"> If INFO = 0 or INFO = N+1, the N-by-NRHS solution matrix X.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDX (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The leading dimension of the array X. LDX >= max(1,N).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> RCOND (output) DOUBLE PRECISION
</span><span class="comment">*</span><span class="comment"> The reciprocal condition number of the matrix A. If RCOND
</span><span class="comment">*</span><span class="comment"> is less than the machine precision (in particular, if
</span><span class="comment">*</span><span class="comment"> RCOND = 0), the matrix is singular to working precision.
</span><span class="comment">*</span><span class="comment"> This condition is indicated by a return code of INFO > 0.
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