#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int dgbequ_(integer *m, integer *n, integer *kl, integer *ku, doublereal *ab, integer *ldab, doublereal *r__, doublereal *c__, doublereal *rowcnd, doublereal *colcnd, doublereal *amax, integer * info) { /* -- LAPACK routine (version 3.0) -- Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., Courant Institute, Argonne National Lab, and Rice University March 31, 1993 Purpose ======= DGBEQU computes row and column scalings intended to equilibrate an M-by-N band matrix A and reduce its condition number. R returns the row scale factors and C the column scale factors, chosen to try to make the largest element in each row and column of the matrix B with elements B(i,j)=R(i)*A(i,j)*C(j) have absolute value 1. R(i) and C(j) are restricted to be between SMLNUM = smallest safe number and BIGNUM = largest safe number. Use of these scaling factors is not guaranteed to reduce the condition number of A but works well in practice. Arguments ========= M (input) INTEGER The number of rows of the matrix A. M >= 0. N (input) INTEGER The number of columns of the matrix A. N >= 0. KL (input) INTEGER The number of subdiagonals within the band of A. KL >= 0. KU (input) INTEGER The number of superdiagonals within the band of A. KU >= 0. AB (input) DOUBLE PRECISION array, dimension (LDAB,N) The band matrix A, stored in rows 1 to KL+KU+1. The j-th column of A is stored in the j-th column of the array AB as follows: AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl). LDAB (input) INTEGER The leading dimension of the array AB. LDAB >= KL+KU+1. R (output) DOUBLE PRECISION array, dimension (M) If INFO = 0, or INFO > M, R contains the row scale factors for A. C (output) DOUBLE PRECISION array, dimension (N) If INFO = 0, C contains the column scale factors for A. ROWCND (output) DOUBLE PRECISION If INFO = 0 or INFO > M, ROWCND contains the ratio of the smallest R(i) to the largest R(i). If ROWCND >= 0.1 and AMAX is neither too large nor too small, it is not worth scaling by R. COLCND (output) DOUBLE PRECISION If INFO = 0, COLCND contains the ratio of the smallest C(i) to the largest C(i). If COLCND >= 0.1, it is not worth scaling by C. AMAX (output) DOUBLE PRECISION Absolute value of largest matrix element. If AMAX is very close to overflow or very close to underflow, the matrix should be scaled. INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, and i is <= M: the i-th row of A is exactly zero > M: the (i-M)-th column of A is exactly zero ===================================================================== Test the input parameters Parameter adjustments */ /* System generated locals */ integer ab_dim1, ab_offset, i__1, i__2, i__3, i__4; doublereal d__1, d__2, d__3; /* Local variables */ static integer i__, j; static doublereal rcmin, rcmax; static integer kd; extern doublereal dlamch_(char *); extern /* Subroutine */ int xerbla_(char *, integer *); static doublereal bignum, smlnum; #define ab_ref(a_1,a_2) ab[(a_2)*ab_dim1 + a_1] ab_dim1 = *ldab; ab_offset = 1 + ab_dim1 * 1; ab -= ab_offset; --r__; --c__; /* Function Body */ *info = 0; if (*m < 0) { *info = -1; } else if (*n < 0) { *info = -2; } else if (*kl < 0) { *info = -3; } else if (*ku < 0) { *info = -4; } else if (*ldab < *kl + *ku + 1) { *info = -6; } if (*info != 0) { i__1 = -(*info); xerbla_("DGBEQU", &i__1); return 0; } /* Quick return if possible */ if (*m == 0 || *n == 0) { *rowcnd = 1.; *colcnd = 1.; *amax = 0.; return 0; } /* Get machine constants. */ smlnum = dlamch_("S"); bignum = 1. / smlnum; /* Compute row scale factors. */ i__1 = *m; for (i__ = 1; i__ <= i__1; ++i__) { r__[i__] = 0.; /* L10: */ } /* Find the maximum element in each row. */ kd = *ku + 1; i__1 = *n; for (j = 1; j <= i__1; ++j) { /* Computing MAX */ i__2 = j - *ku; /* Computing MIN */ i__4 = j + *kl; i__3 = min(i__4,*m); for (i__ = max(i__2,1); i__ <= i__3; ++i__) { /* Computing MAX */ d__2 = r__[i__], d__3 = (d__1 = ab_ref(kd + i__ - j, j), abs(d__1) ); r__[i__] = max(d__2,d__3); /* L20: */ } /* L30: */ } /* Find the maximum and minimum scale factors. */ rcmin = bignum; rcmax = 0.; i__1 = *m; for (i__ = 1; i__ <= i__1; ++i__) { /* Computing MAX */ d__1 = rcmax, d__2 = r__[i__]; rcmax = max(d__1,d__2); /* Computing MIN */ d__1 = rcmin, d__2 = r__[i__]; rcmin = min(d__1,d__2); /* L40: */ } *amax = rcmax; if (rcmin == 0.) { /* Find the first zero scale factor and return an error code. */ i__1 = *m; for (i__ = 1; i__ <= i__1; ++i__) { if (r__[i__] == 0.) { *info = i__; return 0; } /* L50: */ } } else { /* Invert the scale factors. */ i__1 = *m; for (i__ = 1; i__ <= i__1; ++i__) { /* Computing MIN Computing MAX */ d__2 = r__[i__]; d__1 = max(d__2,smlnum); r__[i__] = 1. / min(d__1,bignum); /* L60: */ } /* Compute ROWCND = min(R(I)) / max(R(I)) */ *rowcnd = max(rcmin,smlnum) / min(rcmax,bignum); } /* Compute column scale factors */ i__1 = *n; for (j = 1; j <= i__1; ++j) { c__[j] = 0.; /* L70: */ } /* Find the maximum element in each column, assuming the row scaling computed above. */ kd = *ku + 1; i__1 = *n; for (j = 1; j <= i__1; ++j) { /* Computing MAX */ i__3 = j - *ku; /* Computing MIN */ i__4 = j + *kl; i__2 = min(i__4,*m); for (i__ = max(i__3,1); i__ <= i__2; ++i__) { /* Computing MAX */ d__2 = c__[j], d__3 = (d__1 = ab_ref(kd + i__ - j, j), abs(d__1)) * r__[i__]; c__[j] = max(d__2,d__3); /* L80: */ } /* L90: */ } /* Find the maximum and minimum scale factors. */ rcmin = bignum; rcmax = 0.; i__1 = *n; for (j = 1; j <= i__1; ++j) { /* Computing MIN */ d__1 = rcmin, d__2 = c__[j]; rcmin = min(d__1,d__2); /* Computing MAX */ d__1 = rcmax, d__2 = c__[j]; rcmax = max(d__1,d__2); /* L100: */ } if (rcmin == 0.) { /* Find the first zero scale factor and return an error code. */ i__1 = *n; for (j = 1; j <= i__1; ++j) { if (c__[j] == 0.) { *info = *m + j; return 0; } /* L110: */ } } else { /* Invert the scale factors. */ i__1 = *n; for (j = 1; j <= i__1; ++j) { /* Computing MIN Computing MAX */ d__2 = c__[j]; d__1 = max(d__2,smlnum); c__[j] = 1. / min(d__1,bignum); /* L120: */ } /* Compute COLCND = min(C(J)) / max(C(J)) */ *colcnd = max(rcmin,smlnum) / min(rcmax,bignum); } return 0; /* End of DGBEQU */ } /* dgbequ_ */ #undef ab_ref