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SUBROUTINE <a name="CGBRFS.1"></a><a href="cgbrfs.f.html#CGBRFS.1">CGBRFS</a>( TRANS, N, KL, KU, NRHS, AB, LDAB, AFB, LDAFB,
$ IPIV, B, LDB, X, LDX, 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"> Modified to call <a name="CLACN2.9"></a><a href="clacn2.f.html#CLACN2.1">CLACN2</a> in place of <a name="CLACON.9"></a><a href="clacon.f.html#CLACON.1">CLACON</a>, 10 Feb 03, SJH.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> .. Scalar Arguments ..
</span> CHARACTER TRANS
INTEGER INFO, KL, KU, LDAB, LDAFB, LDB, LDX, N, NRHS
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Array Arguments ..
</span> INTEGER IPIV( * )
REAL BERR( * ), FERR( * ), RWORK( * )
COMPLEX AB( LDAB, * ), AFB( LDAFB, * ), B( LDB, * ),
$ 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="CGBRFS.25"></a><a href="cgbrfs.f.html#CGBRFS.1">CGBRFS</a> improves the computed solution to a system of linear
</span><span class="comment">*</span><span class="comment"> equations when the coefficient matrix is banded, and provides
</span><span class="comment">*</span><span class="comment"> error bounds and backward error estimates for the solution.
</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"> 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)
</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"> KL (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The number of subdiagonals within the band of A. KL >= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> KU (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The number of superdiagonals within the band of A. KU >= 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"> AB (input) COMPLEX array, dimension (LDAB,N)
</span><span class="comment">*</span><span class="comment"> The original band matrix A, stored in rows 1 to KL+KU+1.
</span><span class="comment">*</span><span class="comment"> The j-th column of A is stored in the j-th column of the
</span><span class="comment">*</span><span class="comment"> array AB as follows:
</span><span class="comment">*</span><span class="comment"> AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDAB (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The leading dimension of the array AB. LDAB >= KL+KU+1.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> AFB (input) COMPLEX array, dimension (LDAFB,N)
</span><span class="comment">*</span><span class="comment"> Details of the LU factorization of the band matrix A, as
</span><span class="comment">*</span><span class="comment"> computed by <a name="CGBTRF.62"></a><a href="cgbtrf.f.html#CGBTRF.1">CGBTRF</a>. U is stored as an upper triangular band
</span><span class="comment">*</span><span class="comment"> matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and
</span><span class="comment">*</span><span class="comment"> the multipliers used during the factorization are stored in
</span><span class="comment">*</span><span class="comment"> rows KL+KU+2 to 2*KL+KU+1.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDAFB (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The leading dimension of the array AFB. LDAFB >= 2*KL*KU+1.
</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 from <a name="CGBTRF.71"></a><a href="cgbtrf.f.html#CGBTRF.1">CGBTRF</a>; for 1<=i<=N, row i of the
</span><span class="comment">*</span><span class="comment"> matrix was interchanged with row IPIV(i).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> B (input) COMPLEX array, dimension (LDB,NRHS)
</span><span class="comment">*</span><span class="comment"> The 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 (input/output) COMPLEX array, dimension (LDX,NRHS)
</span><span class="comment">*</span><span class="comment"> On entry, the solution matrix X, as computed by <a name="CGBTRS.81"></a><a href="cgbtrs.f.html#CGBTRS.1">CGBTRS</a>.
</span><span class="comment">*</span><span class="comment"> On exit, the improved 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"> FERR (output) REAL array, dimension (NRHS)
</span><span class="comment">*</span><span class="comment"> The estimated forward error bound for each solution vector
</span><span class="comment">*</span><span class="comment"> X(j) (the j-th column of the solution matrix X).
</span><span class="comment">*</span><span class="comment"> If XTRUE is the true solution corresponding to X(j), FERR(j)
</span><span class="comment">*</span><span class="comment"> is an estimated upper bound for the magnitude of the largest
</span><span class="comment">*</span><span class="comment"> element in (X(j) - XTRUE) divided by the magnitude of the
</span><span class="comment">*</span><span class="comment"> largest element in X(j). The estimate is as reliable as
</span><span class="comment">*</span><span class="comment"> the estimate for RCOND, and is almost always a slight
</span><span class="comment">*</span><span class="comment"> overestimate of the true error.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> BERR (output) REAL array, dimension (NRHS)
</span><span class="comment">*</span><span class="comment"> The componentwise relative backward error of each solution
</span><span class="comment">*</span><span class="comment"> vector X(j) (i.e., the smallest relative change in
</span><span class="comment">*</span><span class="comment"> any element of A or B that makes X(j) an exact solution).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> WORK (workspace) COMPLEX array, dimension (2*N)
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> RWORK (workspace) REAL array, dimension (N)
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> INFO (output) INTEGER
</span><span class="comment">*</span><span class="comment"> = 0: successful exit
</span><span class="comment">*</span><span class="comment"> < 0: if INFO = -i, the i-th argument had an illegal value
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Internal Parameters
</span><span class="comment">*</span><span class="comment"> ===================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> ITMAX is the maximum number of steps of iterative refinement.
</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"> .. Parameters ..
</span> INTEGER ITMAX
PARAMETER ( ITMAX = 5 )
REAL ZERO
PARAMETER ( ZERO = 0.0E+0 )
COMPLEX CONE
PARAMETER ( CONE = ( 1.0E+0, 0.0E+0 ) )
REAL TWO
PARAMETER ( TWO = 2.0E+0 )
REAL THREE
PARAMETER ( THREE = 3.0E+0 )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Local Scalars ..
</span> LOGICAL NOTRAN
CHARACTER TRANSN, TRANST
INTEGER COUNT, I, J, K, KASE, KK, NZ
REAL EPS, LSTRES, S, SAFE1, SAFE2, SAFMIN, XK
COMPLEX ZDUM
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Local Arrays ..
</span> INTEGER ISAVE( 3 )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Subroutines ..
</span> EXTERNAL CAXPY, CCOPY, CGBMV, <a name="CGBTRS.140"></a><a href="cgbtrs.f.html#CGBTRS.1">CGBTRS</a>, <a name="CLACN2.140"></a><a href="clacn2.f.html#CLACN2.1">CLACN2</a>, <a name="XERBLA.140"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Intrinsic Functions ..
</span> INTRINSIC ABS, AIMAG, MAX, MIN, REAL
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Functions ..
</span> LOGICAL <a name="LSAME.146"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
REAL <a name="SLAMCH.147"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>
EXTERNAL <a name="LSAME.148"></a><a href="lsame.f.html#LSAME.1">LSAME</a>, <a name="SLAMCH.148"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Statement Functions ..
</span> REAL CABS1
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Statement Function definitions ..
</span> CABS1( ZDUM ) = ABS( REAL( ZDUM ) ) + ABS( AIMAG( ZDUM ) )
<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"> Test the input parameters.
</span><span class="comment">*</span><span class="comment">
</span> INFO = 0
NOTRAN = <a name="LSAME.161"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( TRANS, <span class="string">'N'</span> )
IF( .NOT.NOTRAN .AND. .NOT.<a name="LSAME.162"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( TRANS, <span class="string">'T'</span> ) .AND. .NOT.
$ <a name="LSAME.163"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( TRANS, <span class="string">'C'</span> ) ) THEN
INFO = -1
ELSE IF( N.LT.0 ) THEN
INFO = -2
ELSE IF( KL.LT.0 ) THEN
INFO = -3
ELSE IF( KU.LT.0 ) THEN
INFO = -4
ELSE IF( NRHS.LT.0 ) THEN
INFO = -5
ELSE IF( LDAB.LT.KL+KU+1 ) THEN
INFO = -7
ELSE IF( LDAFB.LT.2*KL+KU+1 ) THEN
INFO = -9
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