#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int zlarfg_(integer *n, doublecomplex *alpha, doublecomplex * x, integer *incx, doublecomplex *tau) { /* -- LAPACK auxiliary routine (version 3.1) -- Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. November 2006 Purpose ======= ZLARFG generates a complex elementary reflector H of order n, such that H' * ( alpha ) = ( beta ), H' * H = I. ( x ) ( 0 ) where alpha and beta are scalars, with beta real, and x is an (n-1)-element complex vector. H is represented in the form H = I - tau * ( 1 ) * ( 1 v' ) , ( v ) where tau is a complex scalar and v is a complex (n-1)-element vector. Note that H is not hermitian. If the elements of x are all zero and alpha is real, then tau = 0 and H is taken to be the unit matrix. Otherwise 1 <= real(tau) <= 2 and abs(tau-1) <= 1 . Arguments ========= N (input) INTEGER The order of the elementary reflector. ALPHA (input/output) COMPLEX*16 On entry, the value alpha. On exit, it is overwritten with the value beta. X (input/output) COMPLEX*16 array, dimension (1+(N-2)*abs(INCX)) On entry, the vector x. On exit, it is overwritten with the vector v. INCX (input) INTEGER The increment between elements of X. INCX > 0. TAU (output) COMPLEX*16 The value tau. ===================================================================== Parameter adjustments */ /* Table of constant values */ static doublecomplex c_b5 = {1.,0.}; /* System generated locals */ integer i__1; doublereal d__1, d__2; doublecomplex z__1, z__2; /* Builtin functions */ double d_imag(doublecomplex *), d_sign(doublereal *, doublereal *); /* Local variables */ static integer j, knt; static doublereal beta, alphi, alphr; extern /* Subroutine */ int zscal_(integer *, doublecomplex *, doublecomplex *, integer *); static doublereal xnorm; extern doublereal dlapy3_(doublereal *, doublereal *, doublereal *), dznrm2_(integer *, doublecomplex *, integer *), dlamch_(char *); static doublereal safmin; extern /* Subroutine */ int zdscal_(integer *, doublereal *, doublecomplex *, integer *); static doublereal rsafmn; extern /* Double Complex */ VOID zladiv_(doublecomplex *, doublecomplex *, doublecomplex *); --x; /* Function Body */ if (*n <= 0) { tau->r = 0., tau->i = 0.; return 0; } i__1 = *n - 1; xnorm = dznrm2_(&i__1, &x[1], incx); alphr = alpha->r; alphi = d_imag(alpha); if (xnorm == 0. && alphi == 0.) { /* H = I */ tau->r = 0., tau->i = 0.; } else { /* general case */ d__1 = dlapy3_(&alphr, &alphi, &xnorm); beta = -d_sign(&d__1, &alphr); safmin = dlamch_("S") / dlamch_("E"); rsafmn = 1. / safmin; if (abs(beta) < safmin) { /* XNORM, BETA may be inaccurate; scale X and recompute them */ knt = 0; L10: ++knt; i__1 = *n - 1; zdscal_(&i__1, &rsafmn, &x[1], incx); beta *= rsafmn; alphi *= rsafmn; alphr *= rsafmn; if (abs(beta) < safmin) { goto L10; } /* New BETA is at most 1, at least SAFMIN */ i__1 = *n - 1; xnorm = dznrm2_(&i__1, &x[1], incx); z__1.r = alphr, z__1.i = alphi; alpha->r = z__1.r, alpha->i = z__1.i; d__1 = dlapy3_(&alphr, &alphi, &xnorm); beta = -d_sign(&d__1, &alphr); d__1 = (beta - alphr) / beta; d__2 = -alphi / beta; z__1.r = d__1, z__1.i = d__2; tau->r = z__1.r, tau->i = z__1.i; z__2.r = alpha->r - beta, z__2.i = alpha->i; zladiv_(&z__1, &c_b5, &z__2); alpha->r = z__1.r, alpha->i = z__1.i; i__1 = *n - 1; zscal_(&i__1, alpha, &x[1], incx); /* If ALPHA is subnormal, it may lose relative accuracy */ alpha->r = beta, alpha->i = 0.; i__1 = knt; for (j = 1; j <= i__1; ++j) { z__1.r = safmin * alpha->r, z__1.i = safmin * alpha->i; alpha->r = z__1.r, alpha->i = z__1.i; /* L20: */ } } else { d__1 = (beta - alphr) / beta; d__2 = -alphi / beta; z__1.r = d__1, z__1.i = d__2; tau->r = z__1.r, tau->i = z__1.i; z__2.r = alpha->r - beta, z__2.i = alpha->i; zladiv_(&z__1, &c_b5, &z__2); alpha->r = z__1.r, alpha->i = z__1.i; i__1 = *n - 1; zscal_(&i__1, alpha, &x[1], incx); alpha->r = beta, alpha->i = 0.; } } return 0; /* End of ZLARFG */ } /* zlarfg_ */