#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int cgeequ_(integer *m, integer *n, complex *a, integer *lda, real *r__, real *c__, real *rowcnd, real *colcnd, real *amax, integer *info) { /* -- LAPACK routine (version 3.1) -- Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. November 2006 Purpose ======= CGEEQU computes row and column scalings intended to equilibrate an M-by-N 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. A (input) COMPLEX array, dimension (LDA,N) The M-by-N matrix whose equilibration factors are to be computed. LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,M). R (output) REAL array, dimension (M) If INFO = 0 or INFO > M, R contains the row scale factors for A. C (output) REAL array, dimension (N) If INFO = 0, C contains the column scale factors for A. ROWCND (output) REAL 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) REAL 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) REAL 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 a_dim1, a_offset, i__1, i__2, i__3; real r__1, r__2, r__3, r__4; /* Builtin functions */ double r_imag(complex *); /* Local variables */ static integer i__, j; static real rcmin, rcmax; extern doublereal slamch_(char *); extern /* Subroutine */ int xerbla_(char *, integer *); static real bignum, smlnum; a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --r__; --c__; /* Function Body */ *info = 0; if (*m < 0) { *info = -1; } else if (*n < 0) { *info = -2; } else if (*lda < max(1,*m)) { *info = -4; } if (*info != 0) { i__1 = -(*info); xerbla_("CGEEQU", &i__1); return 0; } /* Quick return if possible */ if (*m == 0 || *n == 0) { *rowcnd = 1.f; *colcnd = 1.f; *amax = 0.f; return 0; } /* Get machine constants. */ smlnum = slamch_("S"); bignum = 1.f / smlnum; /* Compute row scale factors. */ i__1 = *m; for (i__ = 1; i__ <= i__1; ++i__) { r__[i__] = 0.f; /* L10: */ } /* Find the maximum element in each row. */ i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { /* Computing MAX */ i__3 = i__ + j * a_dim1; r__3 = r__[i__], r__4 = (r__1 = a[i__3].r, dabs(r__1)) + (r__2 = r_imag(&a[i__ + j * a_dim1]), dabs(r__2)); r__[i__] = dmax(r__3,r__4); /* L20: */ } /* L30: */ } /* Find the maximum and minimum scale factors. */ rcmin = bignum; rcmax = 0.f; i__1 = *m; for (i__ = 1; i__ <= i__1; ++i__) { /* Computing MAX */ r__1 = rcmax, r__2 = r__[i__]; rcmax = dmax(r__1,r__2); /* Computing MIN */ r__1 = rcmin, r__2 = r__[i__]; rcmin = dmin(r__1,r__2); /* L40: */ } *amax = rcmax; if (rcmin == 0.f) { /* 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.f) { *info = i__; return 0; } /* L50: */ } } else { /* Invert the scale factors. */ i__1 = *m; for (i__ = 1; i__ <= i__1; ++i__) { /* Computing MIN Computing MAX */ r__2 = r__[i__]; r__1 = dmax(r__2,smlnum); r__[i__] = 1.f / dmin(r__1,bignum); /* L60: */ } /* Compute ROWCND = min(R(I)) / max(R(I)) */ *rowcnd = dmax(rcmin,smlnum) / dmin(rcmax,bignum); } /* Compute column scale factors */ i__1 = *n; for (j = 1; j <= i__1; ++j) { c__[j] = 0.f; /* L70: */ } /* Find the maximum element in each column, assuming the row scaling computed above. */ i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { /* Computing MAX */ i__3 = i__ + j * a_dim1; r__3 = c__[j], r__4 = ((r__1 = a[i__3].r, dabs(r__1)) + (r__2 = r_imag(&a[i__ + j * a_dim1]), dabs(r__2))) * r__[i__]; c__[j] = dmax(r__3,r__4); /* L80: */ } /* L90: */ } /* Find the maximum and minimum scale factors. */ rcmin = bignum; rcmax = 0.f; i__1 = *n; for (j = 1; j <= i__1; ++j) { /* Computing MIN */ r__1 = rcmin, r__2 = c__[j]; rcmin = dmin(r__1,r__2); /* Computing MAX */ r__1 = rcmax, r__2 = c__[j]; rcmax = dmax(r__1,r__2); /* L100: */ } if (rcmin == 0.f) { /* 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.f) { *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 */ r__2 = c__[j]; r__1 = dmax(r__2,smlnum); c__[j] = 1.f / dmin(r__1,bignum); /* L120: */ } /* Compute COLCND = min(C(J)) / max(C(J)) */ *colcnd = dmax(rcmin,smlnum) / dmin(rcmax,bignum); } return 0; /* End of CGEEQU */ } /* cgeequ_ */