#include #include #include #include #include #ifdef complex #undef complex #endif #ifdef I #undef I #endif #if defined(_WIN64) typedef long long BLASLONG; typedef unsigned long long BLASULONG; #else typedef long BLASLONG; typedef unsigned long BLASULONG; #endif #ifdef LAPACK_ILP64 typedef BLASLONG blasint; #if defined(_WIN64) #define blasabs(x) llabs(x) #else #define blasabs(x) labs(x) #endif #else typedef int blasint; #define blasabs(x) abs(x) #endif typedef blasint integer; typedef unsigned int uinteger; typedef char *address; typedef short int shortint; typedef float real; typedef double doublereal; typedef struct { real r, i; } complex; typedef struct { doublereal r, i; } doublecomplex; #ifdef _MSC_VER static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;} static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;} static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;} static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;} #else static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;} static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;} static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;} static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;} #endif #define pCf(z) (*_pCf(z)) #define pCd(z) (*_pCd(z)) typedef int logical; typedef short int shortlogical; typedef char logical1; typedef char integer1; #define TRUE_ (1) #define FALSE_ (0) /* Extern is for use with -E */ #ifndef Extern #define Extern extern #endif /* I/O stuff */ typedef int flag; typedef int ftnlen; typedef int ftnint; /*external read, write*/ typedef struct { flag cierr; ftnint ciunit; flag ciend; char *cifmt; ftnint cirec; } cilist; /*internal read, write*/ typedef struct { flag icierr; char *iciunit; flag iciend; char *icifmt; ftnint icirlen; ftnint icirnum; } icilist; /*open*/ typedef struct { flag oerr; ftnint ounit; char *ofnm; ftnlen ofnmlen; char *osta; char *oacc; char *ofm; ftnint orl; char *oblnk; } olist; /*close*/ typedef struct { flag cerr; ftnint cunit; char *csta; } cllist; /*rewind, backspace, endfile*/ typedef struct { flag aerr; ftnint aunit; } alist; /* inquire */ typedef struct { flag inerr; ftnint inunit; char *infile; ftnlen infilen; ftnint *inex; /*parameters in standard's order*/ ftnint *inopen; ftnint *innum; ftnint *innamed; char *inname; ftnlen innamlen; char *inacc; ftnlen inacclen; char *inseq; ftnlen inseqlen; char *indir; ftnlen indirlen; char *infmt; ftnlen infmtlen; char *inform; ftnint informlen; char *inunf; ftnlen inunflen; ftnint *inrecl; ftnint *innrec; char *inblank; ftnlen inblanklen; } inlist; #define VOID void union Multitype { /* for multiple entry points */ integer1 g; shortint h; integer i; /* longint j; */ real r; doublereal d; complex c; doublecomplex z; }; typedef union Multitype Multitype; struct Vardesc { /* for Namelist */ char *name; char *addr; ftnlen *dims; int type; }; typedef struct Vardesc Vardesc; struct Namelist { char *name; Vardesc **vars; int nvars; }; typedef struct Namelist Namelist; #define abs(x) ((x) >= 0 ? (x) : -(x)) #define dabs(x) (fabs(x)) #define f2cmin(a,b) ((a) <= (b) ? (a) : (b)) #define f2cmax(a,b) ((a) >= (b) ? (a) : (b)) #define dmin(a,b) (f2cmin(a,b)) #define dmax(a,b) (f2cmax(a,b)) #define bit_test(a,b) ((a) >> (b) & 1) #define bit_clear(a,b) ((a) & ~((uinteger)1 << (b))) #define bit_set(a,b) ((a) | ((uinteger)1 << (b))) #define abort_() { sig_die("Fortran abort routine called", 1); } #define c_abs(z) (cabsf(Cf(z))) #define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); } #ifdef _MSC_VER #define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);} #define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/df(b)._Val[1]);} #else #define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);} #define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);} #endif #define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));} #define c_log(R, Z) {pCf(R) = clogf(Cf(Z));} #define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));} //#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));} #define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));} #define d_abs(x) (fabs(*(x))) #define d_acos(x) (acos(*(x))) #define d_asin(x) (asin(*(x))) #define d_atan(x) (atan(*(x))) #define d_atn2(x, y) (atan2(*(x),*(y))) #define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); } #define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); } #define d_cos(x) (cos(*(x))) #define d_cosh(x) (cosh(*(x))) #define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 ) #define d_exp(x) (exp(*(x))) #define d_imag(z) (cimag(Cd(z))) #define r_imag(z) (cimagf(Cf(z))) #define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x))) #define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x))) #define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) ) #define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) ) #define d_log(x) (log(*(x))) #define d_mod(x, y) (fmod(*(x), *(y))) #define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x))) #define d_nint(x) u_nint(*(x)) #define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a))) #define d_sign(a,b) u_sign(*(a),*(b)) #define r_sign(a,b) u_sign(*(a),*(b)) #define d_sin(x) (sin(*(x))) #define d_sinh(x) (sinh(*(x))) #define d_sqrt(x) (sqrt(*(x))) #define d_tan(x) (tan(*(x))) #define d_tanh(x) (tanh(*(x))) #define i_abs(x) abs(*(x)) #define i_dnnt(x) ((integer)u_nint(*(x))) #define i_len(s, n) (n) #define i_nint(x) ((integer)u_nint(*(x))) #define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b))) #define pow_dd(ap, bp) ( pow(*(ap), *(bp))) #define pow_si(B,E) spow_ui(*(B),*(E)) #define pow_ri(B,E) spow_ui(*(B),*(E)) #define pow_di(B,E) dpow_ui(*(B),*(E)) #define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));} #define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));} #define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));} #define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; } #define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d)))) #define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; } #define sig_die(s, kill) { exit(1); } #define s_stop(s, n) {exit(0);} static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n"; #define z_abs(z) (cabs(Cd(z))) #define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));} #define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));} #define myexit_() break; #define mycycle() continue; #define myceiling(w) {ceil(w)} #define myhuge(w) {HUGE_VAL} //#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);} #define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)} /* procedure parameter types for -A and -C++ */ #define F2C_proc_par_types 1 #ifdef __cplusplus typedef logical (*L_fp)(...); #else typedef logical (*L_fp)(); #endif static float spow_ui(float x, integer n) { float pow=1.0; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x = 1/x; for(u = n; ; ) { if(u & 01) pow *= x; if(u >>= 1) x *= x; else break; } } return pow; } static double dpow_ui(double x, integer n) { double pow=1.0; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x = 1/x; for(u = n; ; ) { if(u & 01) pow *= x; if(u >>= 1) x *= x; else break; } } return pow; } #ifdef _MSC_VER static _Fcomplex cpow_ui(complex x, integer n) { complex pow={1.0,0.0}; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i; for(u = n; ; ) { if(u & 01) pow.r *= x.r, pow.i *= x.i; if(u >>= 1) x.r *= x.r, x.i *= x.i; else break; } } _Fcomplex p={pow.r, pow.i}; return p; } #else static _Complex float cpow_ui(_Complex float x, integer n) { _Complex float pow=1.0; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x = 1/x; for(u = n; ; ) { if(u & 01) pow *= x; if(u >>= 1) x *= x; else break; } } return pow; } #endif #ifdef _MSC_VER static _Dcomplex zpow_ui(_Dcomplex x, integer n) { _Dcomplex pow={1.0,0.0}; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1]; for(u = n; ; ) { if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1]; if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1]; else break; } } _Dcomplex p = {pow._Val[0], pow._Val[1]}; return p; } #else static _Complex double zpow_ui(_Complex double x, integer n) { _Complex double pow=1.0; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x = 1/x; for(u = n; ; ) { if(u & 01) pow *= x; if(u >>= 1) x *= x; else break; } } return pow; } #endif static integer pow_ii(integer x, integer n) { integer pow; unsigned long int u; if (n <= 0) { if (n == 0 || x == 1) pow = 1; else if (x != -1) pow = x == 0 ? 1/x : 0; else n = -n; } if ((n > 0) || !(n == 0 || x == 1 || x != -1)) { u = n; for(pow = 1; ; ) { if(u & 01) pow *= x; if(u >>= 1) x *= x; else break; } } return pow; } static integer dmaxloc_(double *w, integer s, integer e, integer *n) { double m; integer i, mi; for(m=w[s-1], mi=s, i=s+1; i<=e; i++) if (w[i-1]>m) mi=i ,m=w[i-1]; return mi-s+1; } static integer smaxloc_(float *w, integer s, integer e, integer *n) { float m; integer i, mi; for(m=w[s-1], mi=s, i=s+1; i<=e; i++) if (w[i-1]>m) mi=i ,m=w[i-1]; return mi-s+1; } static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) { integer n = *n_, incx = *incx_, incy = *incy_, i; #ifdef _MSC_VER _Fcomplex zdotc = {0.0, 0.0}; if (incx == 1 && incy == 1) { for (i=0;i \brief \b CLAQPS computes a step of QR factorization with column pivoting of a real m-by-n matrix A by us ing BLAS level 3. */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download CLAQPS + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE CLAQPS( M, N, OFFSET, NB, KB, A, LDA, JPVT, TAU, VN1, */ /* VN2, AUXV, F, LDF ) */ /* INTEGER KB, LDA, LDF, M, N, NB, OFFSET */ /* INTEGER JPVT( * ) */ /* REAL VN1( * ), VN2( * ) */ /* COMPLEX A( LDA, * ), AUXV( * ), F( LDF, * ), TAU( * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > CLAQPS computes a step of QR factorization with column pivoting */ /* > of a complex M-by-N matrix A by using Blas-3. It tries to factorize */ /* > NB columns from A starting from the row OFFSET+1, and updates all */ /* > of the matrix with Blas-3 xGEMM. */ /* > */ /* > In some cases, due to catastrophic cancellations, it cannot */ /* > factorize NB columns. Hence, the actual number of factorized */ /* > columns is returned in KB. */ /* > */ /* > Block A(1:OFFSET,1:N) is accordingly pivoted, but not factorized. */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \param[in] M */ /* > \verbatim */ /* > M is INTEGER */ /* > The number of rows of the matrix A. M >= 0. */ /* > \endverbatim */ /* > */ /* > \param[in] N */ /* > \verbatim */ /* > N is INTEGER */ /* > The number of columns of the matrix A. N >= 0 */ /* > \endverbatim */ /* > */ /* > \param[in] OFFSET */ /* > \verbatim */ /* > OFFSET is INTEGER */ /* > The number of rows of A that have been factorized in */ /* > previous steps. */ /* > \endverbatim */ /* > */ /* > \param[in] NB */ /* > \verbatim */ /* > NB is INTEGER */ /* > The number of columns to factorize. */ /* > \endverbatim */ /* > */ /* > \param[out] KB */ /* > \verbatim */ /* > KB is INTEGER */ /* > The number of columns actually factorized. */ /* > \endverbatim */ /* > */ /* > \param[in,out] A */ /* > \verbatim */ /* > A is COMPLEX array, dimension (LDA,N) */ /* > On entry, the M-by-N matrix A. */ /* > On exit, block A(OFFSET+1:M,1:KB) is the triangular */ /* > factor obtained and block A(1:OFFSET,1:N) has been */ /* > accordingly pivoted, but no factorized. */ /* > The rest of the matrix, block A(OFFSET+1:M,KB+1:N) has */ /* > been updated. */ /* > \endverbatim */ /* > */ /* > \param[in] LDA */ /* > \verbatim */ /* > LDA is INTEGER */ /* > The leading dimension of the array A. LDA >= f2cmax(1,M). */ /* > \endverbatim */ /* > */ /* > \param[in,out] JPVT */ /* > \verbatim */ /* > JPVT is INTEGER array, dimension (N) */ /* > JPVT(I) = K <==> Column K of the full matrix A has been */ /* > permuted into position I in AP. */ /* > \endverbatim */ /* > */ /* > \param[out] TAU */ /* > \verbatim */ /* > TAU is COMPLEX array, dimension (KB) */ /* > The scalar factors of the elementary reflectors. */ /* > \endverbatim */ /* > */ /* > \param[in,out] VN1 */ /* > \verbatim */ /* > VN1 is REAL array, dimension (N) */ /* > The vector with the partial column norms. */ /* > \endverbatim */ /* > */ /* > \param[in,out] VN2 */ /* > \verbatim */ /* > VN2 is REAL array, dimension (N) */ /* > The vector with the exact column norms. */ /* > \endverbatim */ /* > */ /* > \param[in,out] AUXV */ /* > \verbatim */ /* > AUXV is COMPLEX array, dimension (NB) */ /* > Auxiliary vector. */ /* > \endverbatim */ /* > */ /* > \param[in,out] F */ /* > \verbatim */ /* > F is COMPLEX array, dimension (LDF,NB) */ /* > Matrix F**H = L * Y**H * A. */ /* > \endverbatim */ /* > */ /* > \param[in] LDF */ /* > \verbatim */ /* > LDF is INTEGER */ /* > The leading dimension of the array F. LDF >= f2cmax(1,N). */ /* > \endverbatim */ /* Authors: */ /* ======== */ /* > \author Univ. of Tennessee */ /* > \author Univ. of California Berkeley */ /* > \author Univ. of Colorado Denver */ /* > \author NAG Ltd. */ /* > \date December 2016 */ /* > \ingroup complexOTHERauxiliary */ /* > \par Contributors: */ /* ================== */ /* > */ /* > G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain */ /* > X. Sun, Computer Science Dept., Duke University, USA */ /* > */ /* > \n */ /* > Partial column norm updating strategy modified on April 2011 */ /* > Z. Drmac and Z. Bujanovic, Dept. of Mathematics, */ /* > University of Zagreb, Croatia. */ /* > \par References: */ /* ================ */ /* > */ /* > LAPACK Working Note 176 */ /* > \htmlonly */ /* > [PDF] */ /* > \endhtmlonly */ /* ===================================================================== */ /* Subroutine */ int claqps_(integer *m, integer *n, integer *offset, integer *nb, integer *kb, complex *a, integer *lda, integer *jpvt, complex * tau, real *vn1, real *vn2, complex *auxv, complex *f, integer *ldf) { /* System generated locals */ integer a_dim1, a_offset, f_dim1, f_offset, i__1, i__2, i__3; real r__1, r__2; complex q__1; /* Local variables */ real temp, temp2; integer j, k; real tol3z; extern /* Subroutine */ int cgemm_(char *, char *, integer *, integer *, integer *, complex *, complex *, integer *, complex *, integer *, complex *, complex *, integer *), cgemv_(char *, integer *, integer *, complex *, complex *, integer *, complex *, integer *, complex *, complex *, integer *), cswap_( integer *, complex *, integer *, complex *, integer *); integer itemp; extern real scnrm2_(integer *, complex *, integer *); integer rk; extern /* Subroutine */ int clarfg_(integer *, complex *, complex *, integer *, complex *); extern real slamch_(char *); integer lsticc; extern integer isamax_(integer *, real *, integer *); integer lastrk; complex akk; integer pvt; /* -- LAPACK auxiliary routine (version 3.7.0) -- */ /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ /* December 2016 */ /* ===================================================================== */ /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1 * 1; a -= a_offset; --jpvt; --tau; --vn1; --vn2; --auxv; f_dim1 = *ldf; f_offset = 1 + f_dim1 * 1; f -= f_offset; /* Function Body */ /* Computing MIN */ i__1 = *m, i__2 = *n + *offset; lastrk = f2cmin(i__1,i__2); lsticc = 0; k = 0; tol3z = sqrt(slamch_("Epsilon")); /* Beginning of while loop. */ L10: if (k < *nb && lsticc == 0) { ++k; rk = *offset + k; /* Determine ith pivot column and swap if necessary */ i__1 = *n - k + 1; pvt = k - 1 + isamax_(&i__1, &vn1[k], &c__1); if (pvt != k) { cswap_(m, &a[pvt * a_dim1 + 1], &c__1, &a[k * a_dim1 + 1], &c__1); i__1 = k - 1; cswap_(&i__1, &f[pvt + f_dim1], ldf, &f[k + f_dim1], ldf); itemp = jpvt[pvt]; jpvt[pvt] = jpvt[k]; jpvt[k] = itemp; vn1[pvt] = vn1[k]; vn2[pvt] = vn2[k]; } /* Apply previous Householder reflectors to column K: */ /* A(RK:M,K) := A(RK:M,K) - A(RK:M,1:K-1)*F(K,1:K-1)**H. */ if (k > 1) { i__1 = k - 1; for (j = 1; j <= i__1; ++j) { i__2 = k + j * f_dim1; r_cnjg(&q__1, &f[k + j * f_dim1]); f[i__2].r = q__1.r, f[i__2].i = q__1.i; /* L20: */ } i__1 = *m - rk + 1; i__2 = k - 1; q__1.r = -1.f, q__1.i = 0.f; cgemv_("No transpose", &i__1, &i__2, &q__1, &a[rk + a_dim1], lda, &f[k + f_dim1], ldf, &c_b2, &a[rk + k * a_dim1], &c__1); i__1 = k - 1; for (j = 1; j <= i__1; ++j) { i__2 = k + j * f_dim1; r_cnjg(&q__1, &f[k + j * f_dim1]); f[i__2].r = q__1.r, f[i__2].i = q__1.i; /* L30: */ } } /* Generate elementary reflector H(k). */ if (rk < *m) { i__1 = *m - rk + 1; clarfg_(&i__1, &a[rk + k * a_dim1], &a[rk + 1 + k * a_dim1], & c__1, &tau[k]); } else { clarfg_(&c__1, &a[rk + k * a_dim1], &a[rk + k * a_dim1], &c__1, & tau[k]); } i__1 = rk + k * a_dim1; akk.r = a[i__1].r, akk.i = a[i__1].i; i__1 = rk + k * a_dim1; a[i__1].r = 1.f, a[i__1].i = 0.f; /* Compute Kth column of F: */ /* Compute F(K+1:N,K) := tau(K)*A(RK:M,K+1:N)**H*A(RK:M,K). */ if (k < *n) { i__1 = *m - rk + 1; i__2 = *n - k; cgemv_("Conjugate transpose", &i__1, &i__2, &tau[k], &a[rk + (k + 1) * a_dim1], lda, &a[rk + k * a_dim1], &c__1, &c_b1, &f[ k + 1 + k * f_dim1], &c__1); } /* Padding F(1:K,K) with zeros. */ i__1 = k; for (j = 1; j <= i__1; ++j) { i__2 = j + k * f_dim1; f[i__2].r = 0.f, f[i__2].i = 0.f; /* L40: */ } /* Incremental updating of F: */ /* F(1:N,K) := F(1:N,K) - tau(K)*F(1:N,1:K-1)*A(RK:M,1:K-1)**H */ /* *A(RK:M,K). */ if (k > 1) { i__1 = *m - rk + 1; i__2 = k - 1; i__3 = k; q__1.r = -tau[i__3].r, q__1.i = -tau[i__3].i; cgemv_("Conjugate transpose", &i__1, &i__2, &q__1, &a[rk + a_dim1] , lda, &a[rk + k * a_dim1], &c__1, &c_b1, &auxv[1], &c__1); i__1 = k - 1; cgemv_("No transpose", n, &i__1, &c_b2, &f[f_dim1 + 1], ldf, & auxv[1], &c__1, &c_b2, &f[k * f_dim1 + 1], &c__1); } /* Update the current row of A: */ /* A(RK,K+1:N) := A(RK,K+1:N) - A(RK,1:K)*F(K+1:N,1:K)**H. */ if (k < *n) { i__1 = *n - k; q__1.r = -1.f, q__1.i = 0.f; cgemm_("No transpose", "Conjugate transpose", &c__1, &i__1, &k, & q__1, &a[rk + a_dim1], lda, &f[k + 1 + f_dim1], ldf, & c_b2, &a[rk + (k + 1) * a_dim1], lda); } /* Update partial column norms. */ if (rk < lastrk) { i__1 = *n; for (j = k + 1; j <= i__1; ++j) { if (vn1[j] != 0.f) { /* NOTE: The following 4 lines follow from the analysis in */ /* Lapack Working Note 176. */ temp = c_abs(&a[rk + j * a_dim1]) / vn1[j]; /* Computing MAX */ r__1 = 0.f, r__2 = (temp + 1.f) * (1.f - temp); temp = f2cmax(r__1,r__2); /* Computing 2nd power */ r__1 = vn1[j] / vn2[j]; temp2 = temp * (r__1 * r__1); if (temp2 <= tol3z) { vn2[j] = (real) lsticc; lsticc = j; } else { vn1[j] *= sqrt(temp); } } /* L50: */ } } i__1 = rk + k * a_dim1; a[i__1].r = akk.r, a[i__1].i = akk.i; /* End of while loop. */ goto L10; } *kb = k; rk = *offset + *kb; /* Apply the block reflector to the rest of the matrix: */ /* A(OFFSET+KB+1:M,KB+1:N) := A(OFFSET+KB+1:M,KB+1:N) - */ /* A(OFFSET+KB+1:M,1:KB)*F(KB+1:N,1:KB)**H. */ /* Computing MIN */ i__1 = *n, i__2 = *m - *offset; if (*kb < f2cmin(i__1,i__2)) { i__1 = *m - rk; i__2 = *n - *kb; q__1.r = -1.f, q__1.i = 0.f; cgemm_("No transpose", "Conjugate transpose", &i__1, &i__2, kb, &q__1, &a[rk + 1 + a_dim1], lda, &f[*kb + 1 + f_dim1], ldf, &c_b2, & a[rk + 1 + (*kb + 1) * a_dim1], lda); } /* Recomputation of difficult columns. */ L60: if (lsticc > 0) { itemp = i_nint(&vn2[lsticc]); i__1 = *m - rk; vn1[lsticc] = scnrm2_(&i__1, &a[rk + 1 + lsticc * a_dim1], &c__1); /* NOTE: The computation of VN1( LSTICC ) relies on the fact that */ /* SNRM2 does not fail on vectors with norm below the value of */ /* SQRT(DLAMCH('S')) */ vn2[lsticc] = vn1[lsticc]; lsticc = itemp; goto L60; } return 0; /* End of CLAQPS */ } /* claqps_ */