#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 CLATBS solves a triangular banded system of equations. */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download CLATBS + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE CLATBS( UPLO, TRANS, DIAG, NORMIN, N, KD, AB, LDAB, X, */ /* SCALE, CNORM, INFO ) */ /* CHARACTER DIAG, NORMIN, TRANS, UPLO */ /* INTEGER INFO, KD, LDAB, N */ /* REAL SCALE */ /* REAL CNORM( * ) */ /* COMPLEX AB( LDAB, * ), X( * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > CLATBS solves one of the triangular systems */ /* > */ /* > A * x = s*b, A**T * x = s*b, or A**H * x = s*b, */ /* > */ /* > with scaling to prevent overflow, where A is an upper or lower */ /* > triangular band matrix. Here A**T denotes the transpose of A, x and b */ /* > are n-element vectors, and s is a scaling factor, usually less than */ /* > or equal to 1, chosen so that the components of x will be less than */ /* > the overflow threshold. If the unscaled problem will not cause */ /* > overflow, the Level 2 BLAS routine CTBSV is called. If the matrix A */ /* > is singular (A(j,j) = 0 for some j), then s is set to 0 and a */ /* > non-trivial solution to A*x = 0 is returned. */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \param[in] UPLO */ /* > \verbatim */ /* > UPLO is CHARACTER*1 */ /* > Specifies whether the matrix A is upper or lower triangular. */ /* > = 'U': Upper triangular */ /* > = 'L': Lower triangular */ /* > \endverbatim */ /* > */ /* > \param[in] TRANS */ /* > \verbatim */ /* > TRANS is CHARACTER*1 */ /* > Specifies the operation applied to A. */ /* > = 'N': Solve A * x = s*b (No transpose) */ /* > = 'T': Solve A**T * x = s*b (Transpose) */ /* > = 'C': Solve A**H * x = s*b (Conjugate transpose) */ /* > \endverbatim */ /* > */ /* > \param[in] DIAG */ /* > \verbatim */ /* > DIAG is CHARACTER*1 */ /* > Specifies whether or not the matrix A is unit triangular. */ /* > = 'N': Non-unit triangular */ /* > = 'U': Unit triangular */ /* > \endverbatim */ /* > */ /* > \param[in] NORMIN */ /* > \verbatim */ /* > NORMIN is CHARACTER*1 */ /* > Specifies whether CNORM has been set or not. */ /* > = 'Y': CNORM contains the column norms on entry */ /* > = 'N': CNORM is not set on entry. On exit, the norms will */ /* > be computed and stored in CNORM. */ /* > \endverbatim */ /* > */ /* > \param[in] N */ /* > \verbatim */ /* > N is INTEGER */ /* > The order of the matrix A. N >= 0. */ /* > \endverbatim */ /* > */ /* > \param[in] KD */ /* > \verbatim */ /* > KD is INTEGER */ /* > The number of subdiagonals or superdiagonals in the */ /* > triangular matrix A. KD >= 0. */ /* > \endverbatim */ /* > */ /* > \param[in] AB */ /* > \verbatim */ /* > AB is COMPLEX array, dimension (LDAB,N) */ /* > The upper or lower triangular 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 f2cmax(1,j-kd)<=i<=j; */ /* > if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=f2cmin(n,j+kd). */ /* > \endverbatim */ /* > */ /* > \param[in] LDAB */ /* > \verbatim */ /* > LDAB is INTEGER */ /* > The leading dimension of the array AB. LDAB >= KD+1. */ /* > \endverbatim */ /* > */ /* > \param[in,out] X */ /* > \verbatim */ /* > X is COMPLEX array, dimension (N) */ /* > On entry, the right hand side b of the triangular system. */ /* > On exit, X is overwritten by the solution vector x. */ /* > \endverbatim */ /* > */ /* > \param[out] SCALE */ /* > \verbatim */ /* > SCALE is REAL */ /* > The scaling factor s for the triangular system */ /* > A * x = s*b, A**T * x = s*b, or A**H * x = s*b. */ /* > If SCALE = 0, the matrix A is singular or badly scaled, and */ /* > the vector x is an exact or approximate solution to A*x = 0. */ /* > \endverbatim */ /* > */ /* > \param[in,out] CNORM */ /* > \verbatim */ /* > CNORM is REAL array, dimension (N) */ /* > */ /* > If NORMIN = 'Y', CNORM is an input argument and CNORM(j) */ /* > contains the norm of the off-diagonal part of the j-th column */ /* > of A. If TRANS = 'N', CNORM(j) must be greater than or equal */ /* > to the infinity-norm, and if TRANS = 'T' or 'C', CNORM(j) */ /* > must be greater than or equal to the 1-norm. */ /* > */ /* > If NORMIN = 'N', CNORM is an output argument and CNORM(j) */ /* > returns the 1-norm of the offdiagonal part of the j-th column */ /* > of A. */ /* > \endverbatim */ /* > */ /* > \param[out] INFO */ /* > \verbatim */ /* > INFO is INTEGER */ /* > = 0: successful exit */ /* > < 0: if INFO = -k, the k-th argument had an illegal value */ /* > \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 Further Details: */ /* ===================== */ /* > */ /* > \verbatim */ /* > */ /* > A rough bound on x is computed; if that is less than overflow, CTBSV */ /* > is called, otherwise, specific code is used which checks for possible */ /* > overflow or divide-by-zero at every operation. */ /* > */ /* > A columnwise scheme is used for solving A*x = b. The basic algorithm */ /* > if A is lower triangular is */ /* > */ /* > x[1:n] := b[1:n] */ /* > for j = 1, ..., n */ /* > x(j) := x(j) / A(j,j) */ /* > x[j+1:n] := x[j+1:n] - x(j) * A[j+1:n,j] */ /* > end */ /* > */ /* > Define bounds on the components of x after j iterations of the loop: */ /* > M(j) = bound on x[1:j] */ /* > G(j) = bound on x[j+1:n] */ /* > Initially, let M(0) = 0 and G(0) = f2cmax{x(i), i=1,...,n}. */ /* > */ /* > Then for iteration j+1 we have */ /* > M(j+1) <= G(j) / | A(j+1,j+1) | */ /* > G(j+1) <= G(j) + M(j+1) * | A[j+2:n,j+1] | */ /* > <= G(j) ( 1 + CNORM(j+1) / | A(j+1,j+1) | ) */ /* > */ /* > where CNORM(j+1) is greater than or equal to the infinity-norm of */ /* > column j+1 of A, not counting the diagonal. Hence */ /* > */ /* > G(j) <= G(0) product ( 1 + CNORM(i) / | A(i,i) | ) */ /* > 1<=i<=j */ /* > and */ /* > */ /* > |x(j)| <= ( G(0) / |A(j,j)| ) product ( 1 + CNORM(i) / |A(i,i)| ) */ /* > 1<=i< j */ /* > */ /* > Since |x(j)| <= M(j), we use the Level 2 BLAS routine CTBSV if the */ /* > reciprocal of the largest M(j), j=1,..,n, is larger than */ /* > f2cmax(underflow, 1/overflow). */ /* > */ /* > The bound on x(j) is also used to determine when a step in the */ /* > columnwise method can be performed without fear of overflow. If */ /* > the computed bound is greater than a large constant, x is scaled to */ /* > prevent overflow, but if the bound overflows, x is set to 0, x(j) to */ /* > 1, and scale to 0, and a non-trivial solution to A*x = 0 is found. */ /* > */ /* > Similarly, a row-wise scheme is used to solve A**T *x = b or */ /* > A**H *x = b. The basic algorithm for A upper triangular is */ /* > */ /* > for j = 1, ..., n */ /* > x(j) := ( b(j) - A[1:j-1,j]' * x[1:j-1] ) / A(j,j) */ /* > end */ /* > */ /* > We simultaneously compute two bounds */ /* > G(j) = bound on ( b(i) - A[1:i-1,i]' * x[1:i-1] ), 1<=i<=j */ /* > M(j) = bound on x(i), 1<=i<=j */ /* > */ /* > The initial values are G(0) = 0, M(0) = f2cmax{b(i), i=1,..,n}, and we */ /* > add the constraint G(j) >= G(j-1) and M(j) >= M(j-1) for j >= 1. */ /* > Then the bound on x(j) is */ /* > */ /* > M(j) <= M(j-1) * ( 1 + CNORM(j) ) / | A(j,j) | */ /* > */ /* > <= M(0) * product ( ( 1 + CNORM(i) ) / |A(i,i)| ) */ /* > 1<=i<=j */ /* > */ /* > and we can safely call CTBSV if 1/M(n) and 1/G(n) are both greater */ /* > than f2cmax(underflow, 1/overflow). */ /* > \endverbatim */ /* > */ /* ===================================================================== */ /* Subroutine */ int clatbs_(char *uplo, char *trans, char *diag, char * normin, integer *n, integer *kd, complex *ab, integer *ldab, complex * x, real *scale, real *cnorm, integer *info) { /* System generated locals */ integer ab_dim1, ab_offset, i__1, i__2, i__3, i__4, i__5; real r__1, r__2, r__3, r__4; complex q__1, q__2, q__3, q__4; /* Local variables */ integer jinc, jlen; real xbnd; integer imax; real tmax; complex tjjs; real xmax, grow; integer i__, j, maind; extern /* Complex */ VOID cdotc_(complex *, integer *, complex *, integer *, complex *, integer *); extern logical lsame_(char *, char *); extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *); real tscal; complex uscal; integer jlast; extern /* Complex */ VOID cdotu_(complex *, integer *, complex *, integer *, complex *, integer *); complex csumj; extern /* Subroutine */ int ctbsv_(char *, char *, char *, integer *, integer *, complex *, integer *, complex *, integer *), caxpy_(integer *, complex *, complex *, integer * , complex *, integer *); logical upper; extern /* Subroutine */ int slabad_(real *, real *); real xj; extern integer icamax_(integer *, complex *, integer *); extern /* Complex */ VOID cladiv_(complex *, complex *, complex *); extern real slamch_(char *); extern /* Subroutine */ int csscal_(integer *, real *, complex *, integer *), xerbla_(char *, integer *, ftnlen); real bignum; extern integer isamax_(integer *, real *, integer *); extern real scasum_(integer *, complex *, integer *); logical notran; integer jfirst; real smlnum; logical nounit; real rec, tjj; /* -- 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 */ ab_dim1 = *ldab; ab_offset = 1 + ab_dim1 * 1; ab -= ab_offset; --x; --cnorm; /* Function Body */ *info = 0; upper = lsame_(uplo, "U"); notran = lsame_(trans, "N"); nounit = lsame_(diag, "N"); /* Test the input parameters. */ if (! upper && ! lsame_(uplo, "L")) { *info = -1; } else if (! notran && ! lsame_(trans, "T") && ! lsame_(trans, "C")) { *info = -2; } else if (! nounit && ! lsame_(diag, "U")) { *info = -3; } else if (! lsame_(normin, "Y") && ! lsame_(normin, "N")) { *info = -4; } else if (*n < 0) { *info = -5; } else if (*kd < 0) { *info = -6; } else if (*ldab < *kd + 1) { *info = -8; } if (*info != 0) { i__1 = -(*info); xerbla_("CLATBS", &i__1, (ftnlen)6); return 0; } /* Quick return if possible */ if (*n == 0) { return 0; } /* Determine machine dependent parameters to control overflow. */ smlnum = slamch_("Safe minimum"); bignum = 1.f / smlnum; slabad_(&smlnum, &bignum); smlnum /= slamch_("Precision"); bignum = 1.f / smlnum; *scale = 1.f; if (lsame_(normin, "N")) { /* Compute the 1-norm of each column, not including the diagonal. */ if (upper) { /* A is upper triangular. */ i__1 = *n; for (j = 1; j <= i__1; ++j) { /* Computing MIN */ i__2 = *kd, i__3 = j - 1; jlen = f2cmin(i__2,i__3); cnorm[j] = scasum_(&jlen, &ab[*kd + 1 - jlen + j * ab_dim1], & c__1); /* L10: */ } } else { /* A is lower triangular. */ i__1 = *n; for (j = 1; j <= i__1; ++j) { /* Computing MIN */ i__2 = *kd, i__3 = *n - j; jlen = f2cmin(i__2,i__3); if (jlen > 0) { cnorm[j] = scasum_(&jlen, &ab[j * ab_dim1 + 2], &c__1); } else { cnorm[j] = 0.f; } /* L20: */ } } } /* Scale the column norms by TSCAL if the maximum element in CNORM is */ /* greater than BIGNUM/2. */ imax = isamax_(n, &cnorm[1], &c__1); tmax = cnorm[imax]; if (tmax <= bignum * .5f) { tscal = 1.f; } else { tscal = .5f / (smlnum * tmax); sscal_(n, &tscal, &cnorm[1], &c__1); } /* Compute a bound on the computed solution vector to see if the */ /* Level 2 BLAS routine CTBSV can be used. */ xmax = 0.f; i__1 = *n; for (j = 1; j <= i__1; ++j) { /* Computing MAX */ i__2 = j; r__3 = xmax, r__4 = (r__1 = x[i__2].r / 2.f, abs(r__1)) + (r__2 = r_imag(&x[j]) / 2.f, abs(r__2)); xmax = f2cmax(r__3,r__4); /* L30: */ } xbnd = xmax; if (notran) { /* Compute the growth in A * x = b. */ if (upper) { jfirst = *n; jlast = 1; jinc = -1; maind = *kd + 1; } else { jfirst = 1; jlast = *n; jinc = 1; maind = 1; } if (tscal != 1.f) { grow = 0.f; goto L60; } if (nounit) { /* A is non-unit triangular. */ /* Compute GROW = 1/G(j) and XBND = 1/M(j). */ /* Initially, G(0) = f2cmax{x(i), i=1,...,n}. */ grow = .5f / f2cmax(xbnd,smlnum); xbnd = grow; i__1 = jlast; i__2 = jinc; for (j = jfirst; i__2 < 0 ? j >= i__1 : j <= i__1; j += i__2) { /* Exit the loop if the growth factor is too small. */ if (grow <= smlnum) { goto L60; } i__3 = maind + j * ab_dim1; tjjs.r = ab[i__3].r, tjjs.i = ab[i__3].i; tjj = (r__1 = tjjs.r, abs(r__1)) + (r__2 = r_imag(&tjjs), abs( r__2)); if (tjj >= smlnum) { /* M(j) = G(j-1) / abs(A(j,j)) */ /* Computing MIN */ r__1 = xbnd, r__2 = f2cmin(1.f,tjj) * grow; xbnd = f2cmin(r__1,r__2); } else { /* M(j) could overflow, set XBND to 0. */ xbnd = 0.f; } if (tjj + cnorm[j] >= smlnum) { /* G(j) = G(j-1)*( 1 + CNORM(j) / abs(A(j,j)) ) */ grow *= tjj / (tjj + cnorm[j]); } else { /* G(j) could overflow, set GROW to 0. */ grow = 0.f; } /* L40: */ } grow = xbnd; } else { /* A is unit triangular. */ /* Compute GROW = 1/G(j), where G(0) = f2cmax{x(i), i=1,...,n}. */ /* Computing MIN */ r__1 = 1.f, r__2 = .5f / f2cmax(xbnd,smlnum); grow = f2cmin(r__1,r__2); i__2 = jlast; i__1 = jinc; for (j = jfirst; i__1 < 0 ? j >= i__2 : j <= i__2; j += i__1) { /* Exit the loop if the growth factor is too small. */ if (grow <= smlnum) { goto L60; } /* G(j) = G(j-1)*( 1 + CNORM(j) ) */ grow *= 1.f / (cnorm[j] + 1.f); /* L50: */ } } L60: ; } else { /* Compute the growth in A**T * x = b or A**H * x = b. */ if (upper) { jfirst = 1; jlast = *n; jinc = 1; maind = *kd + 1; } else { jfirst = *n; jlast = 1; jinc = -1; maind = 1; } if (tscal != 1.f) { grow = 0.f; goto L90; } if (nounit) { /* A is non-unit triangular. */ /* Compute GROW = 1/G(j) and XBND = 1/M(j). */ /* Initially, M(0) = f2cmax{x(i), i=1,...,n}. */ grow = .5f / f2cmax(xbnd,smlnum); xbnd = grow; i__1 = jlast; i__2 = jinc; for (j = jfirst; i__2 < 0 ? j >= i__1 : j <= i__1; j += i__2) { /* Exit the loop if the growth factor is too small. */ if (grow <= smlnum) { goto L90; } /* G(j) = f2cmax( G(j-1), M(j-1)*( 1 + CNORM(j) ) ) */ xj = cnorm[j] + 1.f; /* Computing MIN */ r__1 = grow, r__2 = xbnd / xj; grow = f2cmin(r__1,r__2); i__3 = maind + j * ab_dim1; tjjs.r = ab[i__3].r, tjjs.i = ab[i__3].i; tjj = (r__1 = tjjs.r, abs(r__1)) + (r__2 = r_imag(&tjjs), abs( r__2)); if (tjj >= smlnum) { /* M(j) = M(j-1)*( 1 + CNORM(j) ) / abs(A(j,j)) */ if (xj > tjj) { xbnd *= tjj / xj; } } else { /* M(j) could overflow, set XBND to 0. */ xbnd = 0.f; } /* L70: */ } grow = f2cmin(grow,xbnd); } else { /* A is unit triangular. */ /* Compute GROW = 1/G(j), where G(0) = f2cmax{x(i), i=1,...,n}. */ /* Computing MIN */ r__1 = 1.f, r__2 = .5f / f2cmax(xbnd,smlnum); grow = f2cmin(r__1,r__2); i__2 = jlast; i__1 = jinc; for (j = jfirst; i__1 < 0 ? j >= i__2 : j <= i__2; j += i__1) { /* Exit the loop if the growth factor is too small. */ if (grow <= smlnum) { goto L90; } /* G(j) = ( 1 + CNORM(j) )*G(j-1) */ xj = cnorm[j] + 1.f; grow /= xj; /* L80: */ } } L90: ; } if (grow * tscal > smlnum) { /* Use the Level 2 BLAS solve if the reciprocal of the bound on */ /* elements of X is not too small. */ ctbsv_(uplo, trans, diag, n, kd, &ab[ab_offset], ldab, &x[1], &c__1); } else { /* Use a Level 1 BLAS solve, scaling intermediate results. */ if (xmax > bignum * .5f) { /* Scale X so that its components are less than or equal to */ /* BIGNUM in absolute value. */ *scale = bignum * .5f / xmax; csscal_(n, scale, &x[1], &c__1); xmax = bignum; } else { xmax *= 2.f; } if (notran) { /* Solve A * x = b */ i__1 = jlast; i__2 = jinc; for (j = jfirst; i__2 < 0 ? j >= i__1 : j <= i__1; j += i__2) { /* Compute x(j) = b(j) / A(j,j), scaling x if necessary. */ i__3 = j; xj = (r__1 = x[i__3].r, abs(r__1)) + (r__2 = r_imag(&x[j]), abs(r__2)); if (nounit) { i__3 = maind + j * ab_dim1; q__1.r = tscal * ab[i__3].r, q__1.i = tscal * ab[i__3].i; tjjs.r = q__1.r, tjjs.i = q__1.i; } else { tjjs.r = tscal, tjjs.i = 0.f; if (tscal == 1.f) { goto L105; } } tjj = (r__1 = tjjs.r, abs(r__1)) + (r__2 = r_imag(&tjjs), abs( r__2)); if (tjj > smlnum) { /* abs(A(j,j)) > SMLNUM: */ if (tjj < 1.f) { if (xj > tjj * bignum) { /* Scale x by 1/b(j). */ rec = 1.f / xj; csscal_(n, &rec, &x[1], &c__1); *scale *= rec; xmax *= rec; } } i__3 = j; cladiv_(&q__1, &x[j], &tjjs); x[i__3].r = q__1.r, x[i__3].i = q__1.i; i__3 = j; xj = (r__1 = x[i__3].r, abs(r__1)) + (r__2 = r_imag(&x[j]) , abs(r__2)); } else if (tjj > 0.f) { /* 0 < abs(A(j,j)) <= SMLNUM: */ if (xj > tjj * bignum) { /* Scale x by (1/abs(x(j)))*abs(A(j,j))*BIGNUM */ /* to avoid overflow when dividing by A(j,j). */ rec = tjj * bignum / xj; if (cnorm[j] > 1.f) { /* Scale by 1/CNORM(j) to avoid overflow when */ /* multiplying x(j) times column j. */ rec /= cnorm[j]; } csscal_(n, &rec, &x[1], &c__1); *scale *= rec; xmax *= rec; } i__3 = j; cladiv_(&q__1, &x[j], &tjjs); x[i__3].r = q__1.r, x[i__3].i = q__1.i; i__3 = j; xj = (r__1 = x[i__3].r, abs(r__1)) + (r__2 = r_imag(&x[j]) , abs(r__2)); } else { /* A(j,j) = 0: Set x(1:n) = 0, x(j) = 1, and */ /* scale = 0, and compute a solution to A*x = 0. */ i__3 = *n; for (i__ = 1; i__ <= i__3; ++i__) { i__4 = i__; x[i__4].r = 0.f, x[i__4].i = 0.f; /* L100: */ } i__3 = j; x[i__3].r = 1.f, x[i__3].i = 0.f; xj = 1.f; *scale = 0.f; xmax = 0.f; } L105: /* Scale x if necessary to avoid overflow when adding a */ /* multiple of column j of A. */ if (xj > 1.f) { rec = 1.f / xj; if (cnorm[j] > (bignum - xmax) * rec) { /* Scale x by 1/(2*abs(x(j))). */ rec *= .5f; csscal_(n, &rec, &x[1], &c__1); *scale *= rec; } } else if (xj * cnorm[j] > bignum - xmax) { /* Scale x by 1/2. */ csscal_(n, &c_b36, &x[1], &c__1); *scale *= .5f; } if (upper) { if (j > 1) { /* Compute the update */ /* x(f2cmax(1,j-kd):j-1) := x(f2cmax(1,j-kd):j-1) - */ /* x(j)* A(f2cmax(1,j-kd):j-1,j) */ /* Computing MIN */ i__3 = *kd, i__4 = j - 1; jlen = f2cmin(i__3,i__4); i__3 = j; q__2.r = -x[i__3].r, q__2.i = -x[i__3].i; q__1.r = tscal * q__2.r, q__1.i = tscal * q__2.i; caxpy_(&jlen, &q__1, &ab[*kd + 1 - jlen + j * ab_dim1] , &c__1, &x[j - jlen], &c__1); i__3 = j - 1; i__ = icamax_(&i__3, &x[1], &c__1); i__3 = i__; xmax = (r__1 = x[i__3].r, abs(r__1)) + (r__2 = r_imag( &x[i__]), abs(r__2)); } } else if (j < *n) { /* Compute the update */ /* x(j+1:f2cmin(j+kd,n)) := x(j+1:f2cmin(j+kd,n)) - */ /* x(j) * A(j+1:f2cmin(j+kd,n),j) */ /* Computing MIN */ i__3 = *kd, i__4 = *n - j; jlen = f2cmin(i__3,i__4); if (jlen > 0) { i__3 = j; q__2.r = -x[i__3].r, q__2.i = -x[i__3].i; q__1.r = tscal * q__2.r, q__1.i = tscal * q__2.i; caxpy_(&jlen, &q__1, &ab[j * ab_dim1 + 2], &c__1, &x[ j + 1], &c__1); } i__3 = *n - j; i__ = j + icamax_(&i__3, &x[j + 1], &c__1); i__3 = i__; xmax = (r__1 = x[i__3].r, abs(r__1)) + (r__2 = r_imag(&x[ i__]), abs(r__2)); } /* L110: */ } } else if (lsame_(trans, "T")) { /* Solve A**T * x = b */ i__2 = jlast; i__1 = jinc; for (j = jfirst; i__1 < 0 ? j >= i__2 : j <= i__2; j += i__1) { /* Compute x(j) = b(j) - sum A(k,j)*x(k). */ /* k<>j */ i__3 = j; xj = (r__1 = x[i__3].r, abs(r__1)) + (r__2 = r_imag(&x[j]), abs(r__2)); uscal.r = tscal, uscal.i = 0.f; rec = 1.f / f2cmax(xmax,1.f); if (cnorm[j] > (bignum - xj) * rec) { /* If x(j) could overflow, scale x by 1/(2*XMAX). */ rec *= .5f; if (nounit) { i__3 = maind + j * ab_dim1; q__1.r = tscal * ab[i__3].r, q__1.i = tscal * ab[i__3] .i; tjjs.r = q__1.r, tjjs.i = q__1.i; } else { tjjs.r = tscal, tjjs.i = 0.f; } tjj = (r__1 = tjjs.r, abs(r__1)) + (r__2 = r_imag(&tjjs), abs(r__2)); if (tjj > 1.f) { /* Divide by A(j,j) when scaling x if A(j,j) > 1. */ /* Computing MIN */ r__1 = 1.f, r__2 = rec * tjj; rec = f2cmin(r__1,r__2); cladiv_(&q__1, &uscal, &tjjs); uscal.r = q__1.r, uscal.i = q__1.i; } if (rec < 1.f) { csscal_(n, &rec, &x[1], &c__1); *scale *= rec; xmax *= rec; } } csumj.r = 0.f, csumj.i = 0.f; if (uscal.r == 1.f && uscal.i == 0.f) { /* If the scaling needed for A in the dot product is 1, */ /* call CDOTU to perform the dot product. */ if (upper) { /* Computing MIN */ i__3 = *kd, i__4 = j - 1; jlen = f2cmin(i__3,i__4); cdotu_(&q__1, &jlen, &ab[*kd + 1 - jlen + j * ab_dim1] , &c__1, &x[j - jlen], &c__1); csumj.r = q__1.r, csumj.i = q__1.i; } else { /* Computing MIN */ i__3 = *kd, i__4 = *n - j; jlen = f2cmin(i__3,i__4); if (jlen > 1) { cdotu_(&q__1, &jlen, &ab[j * ab_dim1 + 2], &c__1, &x[j + 1], &c__1); csumj.r = q__1.r, csumj.i = q__1.i; } } } else { /* Otherwise, use in-line code for the dot product. */ if (upper) { /* Computing MIN */ i__3 = *kd, i__4 = j - 1; jlen = f2cmin(i__3,i__4); i__3 = jlen; for (i__ = 1; i__ <= i__3; ++i__) { i__4 = *kd + i__ - jlen + j * ab_dim1; q__3.r = ab[i__4].r * uscal.r - ab[i__4].i * uscal.i, q__3.i = ab[i__4].r * uscal.i + ab[i__4].i * uscal.r; i__5 = j - jlen - 1 + i__; q__2.r = q__3.r * x[i__5].r - q__3.i * x[i__5].i, q__2.i = q__3.r * x[i__5].i + q__3.i * x[ i__5].r; q__1.r = csumj.r + q__2.r, q__1.i = csumj.i + q__2.i; csumj.r = q__1.r, csumj.i = q__1.i; /* L120: */ } } else { /* Computing MIN */ i__3 = *kd, i__4 = *n - j; jlen = f2cmin(i__3,i__4); i__3 = jlen; for (i__ = 1; i__ <= i__3; ++i__) { i__4 = i__ + 1 + j * ab_dim1; q__3.r = ab[i__4].r * uscal.r - ab[i__4].i * uscal.i, q__3.i = ab[i__4].r * uscal.i + ab[i__4].i * uscal.r; i__5 = j + i__; q__2.r = q__3.r * x[i__5].r - q__3.i * x[i__5].i, q__2.i = q__3.r * x[i__5].i + q__3.i * x[ i__5].r; q__1.r = csumj.r + q__2.r, q__1.i = csumj.i + q__2.i; csumj.r = q__1.r, csumj.i = q__1.i; /* L130: */ } } } q__1.r = tscal, q__1.i = 0.f; if (uscal.r == q__1.r && uscal.i == q__1.i) { /* Compute x(j) := ( x(j) - CSUMJ ) / A(j,j) if 1/A(j,j) */ /* was not used to scale the dotproduct. */ i__3 = j; i__4 = j; q__1.r = x[i__4].r - csumj.r, q__1.i = x[i__4].i - csumj.i; x[i__3].r = q__1.r, x[i__3].i = q__1.i; i__3 = j; xj = (r__1 = x[i__3].r, abs(r__1)) + (r__2 = r_imag(&x[j]) , abs(r__2)); if (nounit) { /* Compute x(j) = x(j) / A(j,j), scaling if necessary. */ i__3 = maind + j * ab_dim1; q__1.r = tscal * ab[i__3].r, q__1.i = tscal * ab[i__3] .i; tjjs.r = q__1.r, tjjs.i = q__1.i; } else { tjjs.r = tscal, tjjs.i = 0.f; if (tscal == 1.f) { goto L145; } } tjj = (r__1 = tjjs.r, abs(r__1)) + (r__2 = r_imag(&tjjs), abs(r__2)); if (tjj > smlnum) { /* abs(A(j,j)) > SMLNUM: */ if (tjj < 1.f) { if (xj > tjj * bignum) { /* Scale X by 1/abs(x(j)). */ rec = 1.f / xj; csscal_(n, &rec, &x[1], &c__1); *scale *= rec; xmax *= rec; } } i__3 = j; cladiv_(&q__1, &x[j], &tjjs); x[i__3].r = q__1.r, x[i__3].i = q__1.i; } else if (tjj > 0.f) { /* 0 < abs(A(j,j)) <= SMLNUM: */ if (xj > tjj * bignum) { /* Scale x by (1/abs(x(j)))*abs(A(j,j))*BIGNUM. */ rec = tjj * bignum / xj; csscal_(n, &rec, &x[1], &c__1); *scale *= rec; xmax *= rec; } i__3 = j; cladiv_(&q__1, &x[j], &tjjs); x[i__3].r = q__1.r, x[i__3].i = q__1.i; } else { /* A(j,j) = 0: Set x(1:n) = 0, x(j) = 1, and */ /* scale = 0 and compute a solution to A**T *x = 0. */ i__3 = *n; for (i__ = 1; i__ <= i__3; ++i__) { i__4 = i__; x[i__4].r = 0.f, x[i__4].i = 0.f; /* L140: */ } i__3 = j; x[i__3].r = 1.f, x[i__3].i = 0.f; *scale = 0.f; xmax = 0.f; } L145: ; } else { /* Compute x(j) := x(j) / A(j,j) - CSUMJ if the dot */ /* product has already been divided by 1/A(j,j). */ i__3 = j; cladiv_(&q__2, &x[j], &tjjs); q__1.r = q__2.r - csumj.r, q__1.i = q__2.i - csumj.i; x[i__3].r = q__1.r, x[i__3].i = q__1.i; } /* Computing MAX */ i__3 = j; r__3 = xmax, r__4 = (r__1 = x[i__3].r, abs(r__1)) + (r__2 = r_imag(&x[j]), abs(r__2)); xmax = f2cmax(r__3,r__4); /* L150: */ } } else { /* Solve A**H * x = b */ i__1 = jlast; i__2 = jinc; for (j = jfirst; i__2 < 0 ? j >= i__1 : j <= i__1; j += i__2) { /* Compute x(j) = b(j) - sum A(k,j)*x(k). */ /* k<>j */ i__3 = j; xj = (r__1 = x[i__3].r, abs(r__1)) + (r__2 = r_imag(&x[j]), abs(r__2)); uscal.r = tscal, uscal.i = 0.f; rec = 1.f / f2cmax(xmax,1.f); if (cnorm[j] > (bignum - xj) * rec) { /* If x(j) could overflow, scale x by 1/(2*XMAX). */ rec *= .5f; if (nounit) { r_cnjg(&q__2, &ab[maind + j * ab_dim1]); q__1.r = tscal * q__2.r, q__1.i = tscal * q__2.i; tjjs.r = q__1.r, tjjs.i = q__1.i; } else { tjjs.r = tscal, tjjs.i = 0.f; } tjj = (r__1 = tjjs.r, abs(r__1)) + (r__2 = r_imag(&tjjs), abs(r__2)); if (tjj > 1.f) { /* Divide by A(j,j) when scaling x if A(j,j) > 1. */ /* Computing MIN */ r__1 = 1.f, r__2 = rec * tjj; rec = f2cmin(r__1,r__2); cladiv_(&q__1, &uscal, &tjjs); uscal.r = q__1.r, uscal.i = q__1.i; } if (rec < 1.f) { csscal_(n, &rec, &x[1], &c__1); *scale *= rec; xmax *= rec; } } csumj.r = 0.f, csumj.i = 0.f; if (uscal.r == 1.f && uscal.i == 0.f) { /* If the scaling needed for A in the dot product is 1, */ /* call CDOTC to perform the dot product. */ if (upper) { /* Computing MIN */ i__3 = *kd, i__4 = j - 1; jlen = f2cmin(i__3,i__4); cdotc_(&q__1, &jlen, &ab[*kd + 1 - jlen + j * ab_dim1] , &c__1, &x[j - jlen], &c__1); csumj.r = q__1.r, csumj.i = q__1.i; } else { /* Computing MIN */ i__3 = *kd, i__4 = *n - j; jlen = f2cmin(i__3,i__4); if (jlen > 1) { cdotc_(&q__1, &jlen, &ab[j * ab_dim1 + 2], &c__1, &x[j + 1], &c__1); csumj.r = q__1.r, csumj.i = q__1.i; } } } else { /* Otherwise, use in-line code for the dot product. */ if (upper) { /* Computing MIN */ i__3 = *kd, i__4 = j - 1; jlen = f2cmin(i__3,i__4); i__3 = jlen; for (i__ = 1; i__ <= i__3; ++i__) { r_cnjg(&q__4, &ab[*kd + i__ - jlen + j * ab_dim1]) ; q__3.r = q__4.r * uscal.r - q__4.i * uscal.i, q__3.i = q__4.r * uscal.i + q__4.i * uscal.r; i__4 = j - jlen - 1 + i__; q__2.r = q__3.r * x[i__4].r - q__3.i * x[i__4].i, q__2.i = q__3.r * x[i__4].i + q__3.i * x[ i__4].r; q__1.r = csumj.r + q__2.r, q__1.i = csumj.i + q__2.i; csumj.r = q__1.r, csumj.i = q__1.i; /* L160: */ } } else { /* Computing MIN */ i__3 = *kd, i__4 = *n - j; jlen = f2cmin(i__3,i__4); i__3 = jlen; for (i__ = 1; i__ <= i__3; ++i__) { r_cnjg(&q__4, &ab[i__ + 1 + j * ab_dim1]); q__3.r = q__4.r * uscal.r - q__4.i * uscal.i, q__3.i = q__4.r * uscal.i + q__4.i * uscal.r; i__4 = j + i__; q__2.r = q__3.r * x[i__4].r - q__3.i * x[i__4].i, q__2.i = q__3.r * x[i__4].i + q__3.i * x[ i__4].r; q__1.r = csumj.r + q__2.r, q__1.i = csumj.i + q__2.i; csumj.r = q__1.r, csumj.i = q__1.i; /* L170: */ } } } q__1.r = tscal, q__1.i = 0.f; if (uscal.r == q__1.r && uscal.i == q__1.i) { /* Compute x(j) := ( x(j) - CSUMJ ) / A(j,j) if 1/A(j,j) */ /* was not used to scale the dotproduct. */ i__3 = j; i__4 = j; q__1.r = x[i__4].r - csumj.r, q__1.i = x[i__4].i - csumj.i; x[i__3].r = q__1.r, x[i__3].i = q__1.i; i__3 = j; xj = (r__1 = x[i__3].r, abs(r__1)) + (r__2 = r_imag(&x[j]) , abs(r__2)); if (nounit) { /* Compute x(j) = x(j) / A(j,j), scaling if necessary. */ r_cnjg(&q__2, &ab[maind + j * ab_dim1]); q__1.r = tscal * q__2.r, q__1.i = tscal * q__2.i; tjjs.r = q__1.r, tjjs.i = q__1.i; } else { tjjs.r = tscal, tjjs.i = 0.f; if (tscal == 1.f) { goto L185; } } tjj = (r__1 = tjjs.r, abs(r__1)) + (r__2 = r_imag(&tjjs), abs(r__2)); if (tjj > smlnum) { /* abs(A(j,j)) > SMLNUM: */ if (tjj < 1.f) { if (xj > tjj * bignum) { /* Scale X by 1/abs(x(j)). */ rec = 1.f / xj; csscal_(n, &rec, &x[1], &c__1); *scale *= rec; xmax *= rec; } } i__3 = j; cladiv_(&q__1, &x[j], &tjjs); x[i__3].r = q__1.r, x[i__3].i = q__1.i; } else if (tjj > 0.f) { /* 0 < abs(A(j,j)) <= SMLNUM: */ if (xj > tjj * bignum) { /* Scale x by (1/abs(x(j)))*abs(A(j,j))*BIGNUM. */ rec = tjj * bignum / xj; csscal_(n, &rec, &x[1], &c__1); *scale *= rec; xmax *= rec; } i__3 = j; cladiv_(&q__1, &x[j], &tjjs); x[i__3].r = q__1.r, x[i__3].i = q__1.i; } else { /* A(j,j) = 0: Set x(1:n) = 0, x(j) = 1, and */ /* scale = 0 and compute a solution to A**H *x = 0. */ i__3 = *n; for (i__ = 1; i__ <= i__3; ++i__) { i__4 = i__; x[i__4].r = 0.f, x[i__4].i = 0.f; /* L180: */ } i__3 = j; x[i__3].r = 1.f, x[i__3].i = 0.f; *scale = 0.f; xmax = 0.f; } L185: ; } else { /* Compute x(j) := x(j) / A(j,j) - CSUMJ if the dot */ /* product has already been divided by 1/A(j,j). */ i__3 = j; cladiv_(&q__2, &x[j], &tjjs); q__1.r = q__2.r - csumj.r, q__1.i = q__2.i - csumj.i; x[i__3].r = q__1.r, x[i__3].i = q__1.i; } /* Computing MAX */ i__3 = j; r__3 = xmax, r__4 = (r__1 = x[i__3].r, abs(r__1)) + (r__2 = r_imag(&x[j]), abs(r__2)); xmax = f2cmax(r__3,r__4); /* L190: */ } } *scale /= tscal; } /* Scale the column norms by 1/TSCAL for return. */ if (tscal != 1.f) { r__1 = 1.f / tscal; sscal_(n, &r__1, &cnorm[1], &c__1); } return 0; /* End of CLATBS */ } /* clatbs_ */