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SUBROUTINE CTBT02( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, X,
$ LDX, B, LDB, WORK, RWORK, RESID )
*
* -- LAPACK test routine (version 3.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* February 29, 1992
*
* .. Scalar Arguments ..
CHARACTER DIAG, TRANS, UPLO
INTEGER KD, LDAB, LDB, LDX, N, NRHS
REAL RESID
* ..
* .. Array Arguments ..
REAL RWORK( * )
COMPLEX AB( LDAB, * ), B( LDB, * ), WORK( * ),
$ X( LDX, * )
* ..
*
* Purpose
* =======
*
* CTBT02 computes the residual for the computed solution to a
* triangular system of linear equations A*x = b, A**T *x = b, or
* A**H *x = b when A is a triangular band matrix. Here A**T denotes
* the transpose of A, A**H denotes the conjugate transpose of A, and
* x and b are N by NRHS matrices. The test ratio is the maximum over
* the number of right hand sides of
* norm(b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
* where op(A) denotes A, A**T, or A**H, and EPS is the machine epsilon.
*
* Arguments
* =========
*
* UPLO (input) CHARACTER*1
* Specifies whether the matrix A is upper or lower triangular.
* = 'U': Upper triangular
* = 'L': Lower triangular
*
* TRANS (input) CHARACTER*1
* Specifies the operation applied to A.
* = 'N': A *x = b (No transpose)
* = 'T': A**T *x = b (Transpose)
* = 'C': A**H *x = b (Conjugate transpose)
*
* DIAG (input) CHARACTER*1
* Specifies whether or not the matrix A is unit triangular.
* = 'N': Non-unit triangular
* = 'U': Unit triangular
*
* N (input) INTEGER
* The order of the matrix A. N >= 0.
*
* KD (input) INTEGER
* The number of superdiagonals or subdiagonals of the
* triangular band matrix A. KD >= 0.
*
* NRHS (input) INTEGER
* The number of right hand sides, i.e., the number of columns
* of the matrices X and B. NRHS >= 0.
*
* AB (input) COMPLEX array, dimension (LDA,N)
* The upper or lower triangular band matrix A, stored in the
* first kd+1 rows of the array. The j-th column of A is stored
* in the j-th column of the array AB as follows:
* if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
* if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
*
* LDAB (input) INTEGER
* The leading dimension of the array AB. LDAB >= max(1,KD+1).
*
* X (input) COMPLEX array, dimension (LDX,NRHS)
* The computed solution vectors for the system of linear
* equations.
*
* LDX (input) INTEGER
* The leading dimension of the array X. LDX >= max(1,N).
*
* B (input) COMPLEX array, dimension (LDB,NRHS)
* The right hand side vectors for the system of linear
* equations.
*
* LDB (input) INTEGER
* The leading dimension of the array B. LDB >= max(1,N).
*
* WORK (workspace) COMPLEX array, dimension (N)
*
* RWORK (workspace) REAL array, dimension (N)
*
* RESID (output) REAL
* The maximum over the number of right hand sides of
* norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ).
*
* =====================================================================
*
* .. Parameters ..
REAL ZERO, ONE
PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
* ..
* .. Local Scalars ..
INTEGER J
REAL ANORM, BNORM, EPS, XNORM
* ..
* .. External Functions ..
LOGICAL LSAME
REAL CLANTB, SCASUM, SLAMCH
EXTERNAL LSAME, CLANTB, SCASUM, SLAMCH
* ..
* .. External Subroutines ..
EXTERNAL CAXPY, CCOPY, CTBMV
* ..
* .. Intrinsic Functions ..
INTRINSIC CMPLX, MAX
* ..
* .. Executable Statements ..
*
* Quick exit if N = 0 or NRHS = 0
*
IF( N.LE.0 .OR. NRHS.LE.0 ) THEN
RESID = ZERO
RETURN
END IF
*
* Compute the 1-norm of A or A'.
*
IF( LSAME( TRANS, 'N' ) ) THEN
ANORM = CLANTB( '1', UPLO, DIAG, N, KD, AB, LDAB, RWORK )
ELSE
ANORM = CLANTB( 'I', UPLO, DIAG, N, KD, AB, LDAB, RWORK )
END IF
*
* Exit with RESID = 1/EPS if ANORM = 0.
*
EPS = SLAMCH( 'Epsilon' )
IF( ANORM.LE.ZERO ) THEN
RESID = ONE / EPS
RETURN
END IF
*
* Compute the maximum over the number of right hand sides of
* norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ).
*
RESID = ZERO
DO 10 J = 1, NRHS
CALL CCOPY( N, X( 1, J ), 1, WORK, 1 )
CALL CTBMV( UPLO, TRANS, DIAG, N, KD, AB, LDAB, WORK, 1 )
CALL CAXPY( N, CMPLX( -ONE ), B( 1, J ), 1, WORK, 1 )
BNORM = SCASUM( N, WORK, 1 )
XNORM = SCASUM( N, X( 1, J ), 1 )
IF( XNORM.LE.ZERO ) THEN
RESID = ONE / EPS
ELSE
RESID = MAX( RESID, ( ( BNORM / ANORM ) / XNORM ) / EPS )
END IF
10 CONTINUE
*
RETURN
*
* End of CTBT02
*
END
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