134 lines
4.0 KiB
FortranFixed
134 lines
4.0 KiB
FortranFixed
SUBROUTINE CTBT06( RCOND, RCONDC, UPLO, DIAG, N, KD, AB, LDAB,
|
|
$ RWORK, RAT )
|
|
*
|
|
* -- LAPACK test routine (version 3.1) --
|
|
* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
|
|
* November 2006
|
|
*
|
|
* .. Scalar Arguments ..
|
|
CHARACTER DIAG, UPLO
|
|
INTEGER KD, LDAB, N
|
|
REAL RAT, RCOND, RCONDC
|
|
* ..
|
|
* .. Array Arguments ..
|
|
REAL RWORK( * )
|
|
COMPLEX AB( LDAB, * )
|
|
* ..
|
|
*
|
|
* Purpose
|
|
* =======
|
|
*
|
|
* CTBT06 computes a test ratio comparing RCOND (the reciprocal
|
|
* condition number of a triangular matrix A) and RCONDC, the estimate
|
|
* computed by CTBCON. Information about the triangular matrix A is
|
|
* used if one estimate is zero and the other is non-zero to decide if
|
|
* underflow in the estimate is justified.
|
|
*
|
|
* Arguments
|
|
* =========
|
|
*
|
|
* RCOND (input) REAL
|
|
* The estimate of the reciprocal condition number obtained by
|
|
* forming the explicit inverse of the matrix A and computing
|
|
* RCOND = 1/( norm(A) * norm(inv(A)) ).
|
|
*
|
|
* RCONDC (input) REAL
|
|
* The estimate of the reciprocal condition number computed by
|
|
* CTBCON.
|
|
*
|
|
* UPLO (input) CHARACTER
|
|
* Specifies whether the matrix A is upper or lower triangular.
|
|
* = 'U': Upper triangular
|
|
* = 'L': Lower triangular
|
|
*
|
|
* DIAG (input) CHARACTER
|
|
* 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.
|
|
*
|
|
* 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.
|
|
*
|
|
* RWORK (workspace) REAL array, dimension (N)
|
|
*
|
|
* RAT (output) REAL
|
|
* The test ratio. If both RCOND and RCONDC are nonzero,
|
|
* RAT = MAX( RCOND, RCONDC )/MIN( RCOND, RCONDC ) - 1.
|
|
* If RAT = 0, the two estimates are exactly the same.
|
|
*
|
|
* =====================================================================
|
|
*
|
|
* .. Parameters ..
|
|
REAL ZERO, ONE
|
|
PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
|
|
* ..
|
|
* .. Local Scalars ..
|
|
REAL ANORM, BIGNUM, EPS, RMAX, RMIN
|
|
* ..
|
|
* .. External Functions ..
|
|
REAL CLANTB, SLAMCH
|
|
EXTERNAL CLANTB, SLAMCH
|
|
* ..
|
|
* .. Intrinsic Functions ..
|
|
INTRINSIC MAX, MIN
|
|
* ..
|
|
* .. Executable Statements ..
|
|
*
|
|
EPS = SLAMCH( 'Epsilon' )
|
|
RMAX = MAX( RCOND, RCONDC )
|
|
RMIN = MIN( RCOND, RCONDC )
|
|
*
|
|
* Do the easy cases first.
|
|
*
|
|
IF( RMIN.LT.ZERO ) THEN
|
|
*
|
|
* Invalid value for RCOND or RCONDC, return 1/EPS.
|
|
*
|
|
RAT = ONE / EPS
|
|
*
|
|
ELSE IF( RMIN.GT.ZERO ) THEN
|
|
*
|
|
* Both estimates are positive, return RMAX/RMIN - 1.
|
|
*
|
|
RAT = RMAX / RMIN - ONE
|
|
*
|
|
ELSE IF( RMAX.EQ.ZERO ) THEN
|
|
*
|
|
* Both estimates zero.
|
|
*
|
|
RAT = ZERO
|
|
*
|
|
ELSE
|
|
*
|
|
* One estimate is zero, the other is non-zero. If the matrix is
|
|
* ill-conditioned, return the nonzero estimate multiplied by
|
|
* 1/EPS; if the matrix is badly scaled, return the nonzero
|
|
* estimate multiplied by BIGNUM/TMAX, where TMAX is the maximum
|
|
* element in absolute value in A.
|
|
*
|
|
BIGNUM = ONE / SLAMCH( 'Safe minimum' )
|
|
ANORM = CLANTB( 'M', UPLO, DIAG, N, KD, AB, LDAB, RWORK )
|
|
*
|
|
RAT = RMAX*( MIN( BIGNUM / MAX( ONE, ANORM ), ONE / EPS ) )
|
|
END IF
|
|
*
|
|
RETURN
|
|
*
|
|
* End of CTBT06
|
|
*
|
|
END
|