195 lines
6.3 KiB
FortranFixed
195 lines
6.3 KiB
FortranFixed
SUBROUTINE CTBT03( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB,
|
|
$ SCALE, CNORM, TSCAL, X, LDX, B, LDB, WORK,
|
|
$ RESID )
|
|
*
|
|
* -- LAPACK test routine (version 3.1) --
|
|
* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
|
|
* November 2006
|
|
*
|
|
* .. Scalar Arguments ..
|
|
CHARACTER DIAG, TRANS, UPLO
|
|
INTEGER KD, LDAB, LDB, LDX, N, NRHS
|
|
REAL RESID, SCALE, TSCAL
|
|
* ..
|
|
* .. Array Arguments ..
|
|
REAL CNORM( * )
|
|
COMPLEX AB( LDAB, * ), B( LDB, * ), WORK( * ),
|
|
$ X( LDX, * )
|
|
* ..
|
|
*
|
|
* Purpose
|
|
* =======
|
|
*
|
|
* CTBT03 computes the residual for the solution to a scaled triangular
|
|
* system of equations A*x = s*b, A**T *x = s*b, or A**H *x = s*b
|
|
* when A is a triangular band matrix. Here A**T denotes the transpose
|
|
* of A, A**H denotes the conjugate transpose of A, s is a scalar, and
|
|
* x and b are N by NRHS matrices. The test ratio is the maximum over
|
|
* the number of right hand sides of
|
|
* norm(s*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 = s*b (No transpose)
|
|
* = 'T': A**T *x = s*b (Transpose)
|
|
* = 'C': A**H *x = s*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 (LDAB,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 >= KD+1.
|
|
*
|
|
* SCALE (input) REAL
|
|
* The scaling factor s used in solving the triangular system.
|
|
*
|
|
* CNORM (input) REAL array, dimension (N)
|
|
* The 1-norms of the columns of A, not counting the diagonal.
|
|
*
|
|
* TSCAL (input) REAL
|
|
* The scaling factor used in computing the 1-norms in CNORM.
|
|
* CNORM actually contains the column norms of TSCAL*A.
|
|
*
|
|
* 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)
|
|
*
|
|
* RESID (output) REAL
|
|
* The maximum over the number of right hand sides of
|
|
* norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ).
|
|
*
|
|
* =====================================================================
|
|
*
|
|
*
|
|
* .. Parameters ..
|
|
REAL ONE, ZERO
|
|
PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
|
|
* ..
|
|
* .. Local Scalars ..
|
|
INTEGER IX, J
|
|
REAL EPS, ERR, SMLNUM, TNORM, XNORM, XSCAL
|
|
* ..
|
|
* .. External Functions ..
|
|
LOGICAL LSAME
|
|
INTEGER ICAMAX
|
|
REAL SLAMCH
|
|
EXTERNAL LSAME, ICAMAX, SLAMCH
|
|
* ..
|
|
* .. External Subroutines ..
|
|
EXTERNAL CAXPY, CCOPY, CSSCAL, CTBMV
|
|
* ..
|
|
* .. Intrinsic Functions ..
|
|
INTRINSIC ABS, CMPLX, MAX, REAL
|
|
* ..
|
|
* .. Executable Statements ..
|
|
*
|
|
* Quick exit if N = 0
|
|
*
|
|
IF( N.LE.0 .OR. NRHS.LE.0 ) THEN
|
|
RESID = ZERO
|
|
RETURN
|
|
END IF
|
|
EPS = SLAMCH( 'Epsilon' )
|
|
SMLNUM = SLAMCH( 'Safe minimum' )
|
|
*
|
|
* Compute the norm of the triangular matrix A using the column
|
|
* norms already computed by CLATBS.
|
|
*
|
|
TNORM = ZERO
|
|
IF( LSAME( DIAG, 'N' ) ) THEN
|
|
IF( LSAME( UPLO, 'U' ) ) THEN
|
|
DO 10 J = 1, N
|
|
TNORM = MAX( TNORM, TSCAL*ABS( AB( KD+1, J ) )+
|
|
$ CNORM( J ) )
|
|
10 CONTINUE
|
|
ELSE
|
|
DO 20 J = 1, N
|
|
TNORM = MAX( TNORM, TSCAL*ABS( AB( 1, J ) )+CNORM( J ) )
|
|
20 CONTINUE
|
|
END IF
|
|
ELSE
|
|
DO 30 J = 1, N
|
|
TNORM = MAX( TNORM, TSCAL+CNORM( J ) )
|
|
30 CONTINUE
|
|
END IF
|
|
*
|
|
* Compute the maximum over the number of right hand sides of
|
|
* norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ).
|
|
*
|
|
RESID = ZERO
|
|
DO 40 J = 1, NRHS
|
|
CALL CCOPY( N, X( 1, J ), 1, WORK, 1 )
|
|
IX = ICAMAX( N, WORK, 1 )
|
|
XNORM = MAX( ONE, ABS( X( IX, J ) ) )
|
|
XSCAL = ( ONE / XNORM ) / REAL( KD+1 )
|
|
CALL CSSCAL( N, XSCAL, WORK, 1 )
|
|
CALL CTBMV( UPLO, TRANS, DIAG, N, KD, AB, LDAB, WORK, 1 )
|
|
CALL CAXPY( N, CMPLX( -SCALE*XSCAL ), B( 1, J ), 1, WORK, 1 )
|
|
IX = ICAMAX( N, WORK, 1 )
|
|
ERR = TSCAL*ABS( WORK( IX ) )
|
|
IX = ICAMAX( N, X( 1, J ), 1 )
|
|
XNORM = ABS( X( IX, J ) )
|
|
IF( ERR*SMLNUM.LE.XNORM ) THEN
|
|
IF( XNORM.GT.ZERO )
|
|
$ ERR = ERR / XNORM
|
|
ELSE
|
|
IF( ERR.GT.ZERO )
|
|
$ ERR = ONE / EPS
|
|
END IF
|
|
IF( ERR*SMLNUM.LE.TNORM ) THEN
|
|
IF( TNORM.GT.ZERO )
|
|
$ ERR = ERR / TNORM
|
|
ELSE
|
|
IF( ERR.GT.ZERO )
|
|
$ ERR = ONE / EPS
|
|
END IF
|
|
RESID = MAX( RESID, ERR )
|
|
40 CONTINUE
|
|
*
|
|
RETURN
|
|
*
|
|
* End of CTBT03
|
|
*
|
|
END
|