#include "blaswrap.h" /* stbt06.f -- translated by f2c (version 20061008). You must link the resulting object file with libf2c: on Microsoft Windows system, link with libf2c.lib; on Linux or Unix systems, link with .../path/to/libf2c.a -lm or, if you install libf2c.a in a standard place, with -lf2c -lm -- in that order, at the end of the command line, as in cc *.o -lf2c -lm Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., http://www.netlib.org/f2c/libf2c.zip */ #include "f2c.h" /* Subroutine */ int stbt06_(real *rcond, real *rcondc, char *uplo, char * diag, integer *n, integer *kd, real *ab, integer *ldab, real *work, real *rat) { /* System generated locals */ integer ab_dim1, ab_offset; real r__1, r__2; /* Local variables */ static real eps, rmin, rmax, anorm; extern /* Subroutine */ int slabad_(real *, real *); extern doublereal slamch_(char *); static real bignum; extern doublereal slantb_(char *, char *, char *, integer *, integer *, real *, integer *, real *); static real smlnum; /* -- LAPACK test routine (version 3.1) -- Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. November 2006 Purpose ======= STBT06 computes a test ratio comparing RCOND (the reciprocal condition number of a triangular matrix A) and RCONDC, the estimate computed by STBCON. 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 STBCON. 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) REAL 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. WORK (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. ===================================================================== Parameter adjustments */ ab_dim1 = *ldab; ab_offset = 1 + ab_dim1; ab -= ab_offset; --work; /* Function Body */ eps = slamch_("Epsilon"); rmax = dmax(*rcond,*rcondc); rmin = dmin(*rcond,*rcondc); /* Do the easy cases first. */ if (rmin < 0.f) { /* Invalid value for RCOND or RCONDC, return 1/EPS. */ *rat = 1.f / eps; } else if (rmin > 0.f) { /* Both estimates are positive, return RMAX/RMIN - 1. */ *rat = rmax / rmin - 1.f; } else if (rmax == 0.f) { /* Both estimates zero. */ *rat = 0.f; } 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. */ smlnum = slamch_("Safe minimum"); bignum = 1.f / smlnum; slabad_(&smlnum, &bignum); anorm = slantb_("M", uplo, diag, n, kd, &ab[ab_offset], ldab, &work[1] ); /* Computing MIN */ r__1 = bignum / dmax(1.f,anorm), r__2 = 1.f / eps; *rat = rmax * dmin(r__1,r__2); } return 0; /* End of STBT06 */ } /* stbt06_ */