#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int zpbequ_(char *uplo, integer *n, integer *kd, doublecomplex *ab, integer *ldab, doublereal *s, doublereal *scond, doublereal *amax, integer *info) { /* -- LAPACK routine (version 3.1) -- Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. November 2006 Purpose ======= ZPBEQU computes row and column scalings intended to equilibrate a Hermitian positive definite band matrix A and reduce its condition number (with respect to the two-norm). S contains the scale factors, S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with elements B(i,j) = S(i)*A(i,j)*S(j) has ones on the diagonal. This choice of S puts the condition number of B within a factor N of the smallest possible condition number over all possible diagonal scalings. Arguments ========= UPLO (input) CHARACTER*1 = 'U': Upper triangular of A is stored; = 'L': Lower triangular of A is stored. N (input) INTEGER The order of the matrix A. N >= 0. KD (input) INTEGER The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KD >= 0. AB (input) COMPLEX*16 array, dimension (LDAB,N) The upper or lower triangle of the Hermitian 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 A. LDAB >= KD+1. S (output) DOUBLE PRECISION array, dimension (N) If INFO = 0, S contains the scale factors for A. SCOND (output) DOUBLE PRECISION If INFO = 0, S contains the ratio of the smallest S(i) to the largest S(i). If SCOND >= 0.1 and AMAX is neither too large nor too small, it is not worth scaling by S. 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, the i-th diagonal element is nonpositive. ===================================================================== Test the input parameters. Parameter adjustments */ /* System generated locals */ integer ab_dim1, ab_offset, i__1, i__2; doublereal d__1, d__2; /* Builtin functions */ double sqrt(doublereal); /* Local variables */ static integer i__, j; static doublereal smin; extern logical lsame_(char *, char *); static logical upper; extern /* Subroutine */ int xerbla_(char *, integer *); ab_dim1 = *ldab; ab_offset = 1 + ab_dim1; ab -= ab_offset; --s; /* Function Body */ *info = 0; upper = lsame_(uplo, "U"); if (! upper && ! lsame_(uplo, "L")) { *info = -1; } else if (*n < 0) { *info = -2; } else if (*kd < 0) { *info = -3; } else if (*ldab < *kd + 1) { *info = -5; } if (*info != 0) { i__1 = -(*info); xerbla_("ZPBEQU", &i__1); return 0; } /* Quick return if possible */ if (*n == 0) { *scond = 1.; *amax = 0.; return 0; } if (upper) { j = *kd + 1; } else { j = 1; } /* Initialize SMIN and AMAX. */ i__1 = j + ab_dim1; s[1] = ab[i__1].r; smin = s[1]; *amax = s[1]; /* Find the minimum and maximum diagonal elements. */ i__1 = *n; for (i__ = 2; i__ <= i__1; ++i__) { i__2 = j + i__ * ab_dim1; s[i__] = ab[i__2].r; /* Computing MIN */ d__1 = smin, d__2 = s[i__]; smin = min(d__1,d__2); /* Computing MAX */ d__1 = *amax, d__2 = s[i__]; *amax = max(d__1,d__2); /* L10: */ } if (smin <= 0.) { /* Find the first non-positive diagonal element and return. */ i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { if (s[i__] <= 0.) { *info = i__; return 0; } /* L20: */ } } else { /* Set the scale factors to the reciprocals of the diagonal elements. */ i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { s[i__] = 1. / sqrt(s[i__]); /* L30: */ } /* Compute SCOND = min(S(I)) / max(S(I)) */ *scond = sqrt(smin) / sqrt(*amax); } return 0; /* End of ZPBEQU */ } /* zpbequ_ */