#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]/Cd(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 ZLATM1 */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* Definition: */ /* =========== */ /* SUBROUTINE ZLATM1( MODE, COND, IRSIGN, IDIST, ISEED, D, N, INFO ) */ /* INTEGER IDIST, INFO, IRSIGN, MODE, N */ /* DOUBLE PRECISION COND */ /* INTEGER ISEED( 4 ) */ /* COMPLEX*16 D( * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > ZLATM1 computes the entries of D(1..N) as specified by */ /* > MODE, COND and IRSIGN. IDIST and ISEED determine the generation */ /* > of random numbers. ZLATM1 is called by ZLATMR to generate */ /* > random test matrices for LAPACK programs. */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \param[in] MODE */ /* > \verbatim */ /* > MODE is INTEGER */ /* > On entry describes how D is to be computed: */ /* > MODE = 0 means do not change D. */ /* > MODE = 1 sets D(1)=1 and D(2:N)=1.0/COND */ /* > MODE = 2 sets D(1:N-1)=1 and D(N)=1.0/COND */ /* > MODE = 3 sets D(I)=COND**(-(I-1)/(N-1)) */ /* > MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND) */ /* > MODE = 5 sets D to random numbers in the range */ /* > ( 1/COND , 1 ) such that their logarithms */ /* > are uniformly distributed. */ /* > MODE = 6 set D to random numbers from same distribution */ /* > as the rest of the matrix. */ /* > MODE < 0 has the same meaning as ABS(MODE), except that */ /* > the order of the elements of D is reversed. */ /* > Thus if MODE is positive, D has entries ranging from */ /* > 1 to 1/COND, if negative, from 1/COND to 1, */ /* > Not modified. */ /* > \endverbatim */ /* > */ /* > \param[in] COND */ /* > \verbatim */ /* > COND is DOUBLE PRECISION */ /* > On entry, used as described under MODE above. */ /* > If used, it must be >= 1. Not modified. */ /* > \endverbatim */ /* > */ /* > \param[in] IRSIGN */ /* > \verbatim */ /* > IRSIGN is INTEGER */ /* > On entry, if MODE neither -6, 0 nor 6, determines sign of */ /* > entries of D */ /* > 0 => leave entries of D unchanged */ /* > 1 => multiply each entry of D by random complex number */ /* > uniformly distributed with absolute value 1 */ /* > \endverbatim */ /* > */ /* > \param[in] IDIST */ /* > \verbatim */ /* > IDIST is INTEGER */ /* > On entry, IDIST specifies the type of distribution to be */ /* > used to generate a random matrix . */ /* > 1 => real and imaginary parts each UNIFORM( 0, 1 ) */ /* > 2 => real and imaginary parts each UNIFORM( -1, 1 ) */ /* > 3 => real and imaginary parts each NORMAL( 0, 1 ) */ /* > 4 => complex number uniform in DISK( 0, 1 ) */ /* > Not modified. */ /* > \endverbatim */ /* > */ /* > \param[in,out] ISEED */ /* > \verbatim */ /* > ISEED is INTEGER array, dimension ( 4 ) */ /* > On entry ISEED specifies the seed of the random number */ /* > generator. The random number generator uses a */ /* > linear congruential sequence limited to small */ /* > integers, and so should produce machine independent */ /* > random numbers. The values of ISEED are changed on */ /* > exit, and can be used in the next call to ZLATM1 */ /* > to continue the same random number sequence. */ /* > Changed on exit. */ /* > \endverbatim */ /* > */ /* > \param[in,out] D */ /* > \verbatim */ /* > D is COMPLEX*16 array, dimension ( N ) */ /* > Array to be computed according to MODE, COND and IRSIGN. */ /* > May be changed on exit if MODE is nonzero. */ /* > \endverbatim */ /* > */ /* > \param[in] N */ /* > \verbatim */ /* > N is INTEGER */ /* > Number of entries of D. Not modified. */ /* > \endverbatim */ /* > */ /* > \param[out] INFO */ /* > \verbatim */ /* > INFO is INTEGER */ /* > 0 => normal termination */ /* > -1 => if MODE not in range -6 to 6 */ /* > -2 => if MODE neither -6, 0 nor 6, and */ /* > IRSIGN neither 0 nor 1 */ /* > -3 => if MODE neither -6, 0 nor 6 and COND less than 1 */ /* > -4 => if MODE equals 6 or -6 and IDIST not in range 1 to 4 */ /* > -7 => if N negative */ /* > \endverbatim */ /* Authors: */ /* ======== */ /* > \author Univ. of Tennessee */ /* > \author Univ. of California Berkeley */ /* > \author Univ. of Colorado Denver */ /* > \author NAG Ltd. */ /* > \date December 2016 */ /* > \ingroup complex16_matgen */ /* ===================================================================== */ /* Subroutine */ int zlatm1_(integer *mode, doublereal *cond, integer *irsign, integer *idist, integer *iseed, doublecomplex *d__, integer *n, integer *info) { /* System generated locals */ integer i__1, i__2, i__3; doublereal d__1; doublecomplex z__1, z__2; /* Local variables */ doublereal temp; integer i__; doublereal alpha; doublecomplex ctemp; extern doublereal dlaran_(integer *); extern /* Subroutine */ int xerbla_(char *, integer *); //extern /* Double Complex */ VOID zlarnd_(doublecomplex *, integer *, extern doublecomplex zlarnd_(integer *, integer *); extern /* Subroutine */ int zlarnv_(integer *, integer *, integer *, doublecomplex *); /* -- 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 */ /* ===================================================================== */ /* Decode and Test the input parameters. Initialize flags & seed. */ /* Parameter adjustments */ --d__; --iseed; /* Function Body */ *info = 0; /* Quick return if possible */ if (*n == 0) { return 0; } /* Set INFO if an error */ if (*mode < -6 || *mode > 6) { *info = -1; } else if (*mode != -6 && *mode != 0 && *mode != 6 && (*irsign != 0 && * irsign != 1)) { *info = -2; } else if (*mode != -6 && *mode != 0 && *mode != 6 && *cond < 1.) { *info = -3; } else if ((*mode == 6 || *mode == -6) && (*idist < 1 || *idist > 4)) { *info = -4; } else if (*n < 0) { *info = -7; } if (*info != 0) { i__1 = -(*info); xerbla_("ZLATM1", &i__1); return 0; } /* Compute D according to COND and MODE */ if (*mode != 0) { switch (abs(*mode)) { case 1: goto L10; case 2: goto L30; case 3: goto L50; case 4: goto L70; case 5: goto L90; case 6: goto L110; } /* One large D value: */ L10: i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = i__; d__1 = 1. / *cond; d__[i__2].r = d__1, d__[i__2].i = 0.; /* L20: */ } d__[1].r = 1., d__[1].i = 0.; goto L120; /* One small D value: */ L30: i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = i__; d__[i__2].r = 1., d__[i__2].i = 0.; /* L40: */ } i__1 = *n; d__1 = 1. / *cond; d__[i__1].r = d__1, d__[i__1].i = 0.; goto L120; /* Exponentially distributed D values: */ L50: d__[1].r = 1., d__[1].i = 0.; if (*n > 1) { d__1 = -1. / (doublereal) (*n - 1); alpha = pow_dd(cond, &d__1); i__1 = *n; for (i__ = 2; i__ <= i__1; ++i__) { i__2 = i__; i__3 = i__ - 1; d__1 = pow_di(&alpha, &i__3); d__[i__2].r = d__1, d__[i__2].i = 0.; /* L60: */ } } goto L120; /* Arithmetically distributed D values: */ L70: d__[1].r = 1., d__[1].i = 0.; if (*n > 1) { temp = 1. / *cond; alpha = (1. - temp) / (doublereal) (*n - 1); i__1 = *n; for (i__ = 2; i__ <= i__1; ++i__) { i__2 = i__; d__1 = (doublereal) (*n - i__) * alpha + temp; d__[i__2].r = d__1, d__[i__2].i = 0.; /* L80: */ } } goto L120; /* Randomly distributed D values on ( 1/COND , 1): */ L90: alpha = log(1. / *cond); i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = i__; d__1 = exp(alpha * dlaran_(&iseed[1])); d__[i__2].r = d__1, d__[i__2].i = 0.; /* L100: */ } goto L120; /* Randomly distributed D values from IDIST */ L110: zlarnv_(idist, &iseed[1], n, &d__[1]); L120: /* If MODE neither -6 nor 0 nor 6, and IRSIGN = 1, assign */ /* random signs to D */ if (*mode != -6 && *mode != 0 && *mode != 6 && *irsign == 1) { i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { //zlarnd_(&z__1, &c__3, &iseed[1]); z__1=zlarnd_(&c__3, &iseed[1]); ctemp.r = z__1.r, ctemp.i = z__1.i; i__2 = i__; i__3 = i__; d__1 = z_abs(&ctemp); z__2.r = ctemp.r / d__1, z__2.i = ctemp.i / d__1; z__1.r = d__[i__3].r * z__2.r - d__[i__3].i * z__2.i, z__1.i = d__[i__3].r * z__2.i + d__[i__3].i * z__2.r; d__[i__2].r = z__1.r, d__[i__2].i = z__1.i; /* L130: */ } } /* Reverse if MODE < 0 */ if (*mode < 0) { i__1 = *n / 2; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = i__; ctemp.r = d__[i__2].r, ctemp.i = d__[i__2].i; i__2 = i__; i__3 = *n + 1 - i__; d__[i__2].r = d__[i__3].r, d__[i__2].i = d__[i__3].i; i__2 = *n + 1 - i__; d__[i__2].r = ctemp.r, d__[i__2].i = ctemp.i; /* L140: */ } } } return 0; /* End of ZLATM1 */ } /* zlatm1_ */