#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int dlaqsb_(char *uplo, integer *n, integer *kd, doublereal * ab, integer *ldab, doublereal *s, doublereal *scond, doublereal *amax, char *equed) { /* -- LAPACK auxiliary routine (version 3.1) -- Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. November 2006 Purpose ======= DLAQSB equilibrates a symmetric band matrix A using the scaling factors in the vector S. Arguments ========= UPLO (input) CHARACTER*1 Specifies whether the upper or lower triangular part of the symmetric matrix A is stored. = 'U': Upper triangular = 'L': Lower triangular N (input) INTEGER The order of the matrix A. N >= 0. KD (input) INTEGER The number of super-diagonals of the matrix A if UPLO = 'U', or the number of sub-diagonals if UPLO = 'L'. KD >= 0. AB (input/output) DOUBLE PRECISION array, dimension (LDAB,N) On entry, the upper or lower triangle of the symmetric 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). On exit, if INFO = 0, the triangular factor U or L from the Cholesky factorization A = U'*U or A = L*L' of the band matrix A, in the same storage format as A. LDAB (input) INTEGER The leading dimension of the array AB. LDAB >= KD+1. S (input) DOUBLE PRECISION array, dimension (N) The scale factors for A. SCOND (input) DOUBLE PRECISION Ratio of the smallest S(i) to the largest S(i). AMAX (input) DOUBLE PRECISION Absolute value of largest matrix entry. EQUED (output) CHARACTER*1 Specifies whether or not equilibration was done. = 'N': No equilibration. = 'Y': Equilibration was done, i.e., A has been replaced by diag(S) * A * diag(S). Internal Parameters =================== THRESH is a threshold value used to decide if scaling should be done based on the ratio of the scaling factors. If SCOND < THRESH, scaling is done. LARGE and SMALL are threshold values used to decide if scaling should be done based on the absolute size of the largest matrix element. If AMAX > LARGE or AMAX < SMALL, scaling is done. ===================================================================== Quick return if possible Parameter adjustments */ /* System generated locals */ integer ab_dim1, ab_offset, i__1, i__2, i__3, i__4; /* Local variables */ static integer i__, j; static doublereal cj, large; extern logical lsame_(char *, char *); static doublereal small; extern doublereal dlamch_(char *); ab_dim1 = *ldab; ab_offset = 1 + ab_dim1; ab -= ab_offset; --s; /* Function Body */ if (*n <= 0) { *(unsigned char *)equed = 'N'; return 0; } /* Initialize LARGE and SMALL. */ small = dlamch_("Safe minimum") / dlamch_("Precision"); large = 1. / small; if (*scond >= .1 && *amax >= small && *amax <= large) { /* No equilibration */ *(unsigned char *)equed = 'N'; } else { /* Replace A by diag(S) * A * diag(S). */ if (lsame_(uplo, "U")) { /* Upper triangle of A is stored in band format. */ i__1 = *n; for (j = 1; j <= i__1; ++j) { cj = s[j]; /* Computing MAX */ i__2 = 1, i__3 = j - *kd; i__4 = j; for (i__ = max(i__2,i__3); i__ <= i__4; ++i__) { ab[*kd + 1 + i__ - j + j * ab_dim1] = cj * s[i__] * ab[* kd + 1 + i__ - j + j * ab_dim1]; /* L10: */ } /* L20: */ } } else { /* Lower triangle of A is stored. */ i__1 = *n; for (j = 1; j <= i__1; ++j) { cj = s[j]; /* Computing MIN */ i__2 = *n, i__3 = j + *kd; i__4 = min(i__2,i__3); for (i__ = j; i__ <= i__4; ++i__) { ab[i__ + 1 - j + j * ab_dim1] = cj * s[i__] * ab[i__ + 1 - j + j * ab_dim1]; /* L30: */ } /* L40: */ } } *(unsigned char *)equed = 'Y'; } return 0; /* End of DLAQSB */ } /* dlaqsb_ */