#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 DLATME */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* Definition: */ /* =========== */ /* SUBROUTINE DLATME( N, DIST, ISEED, D, MODE, COND, DMAX, EI, */ /* RSIGN, */ /* UPPER, SIM, DS, MODES, CONDS, KL, KU, ANORM, */ /* A, */ /* LDA, WORK, INFO ) */ /* CHARACTER DIST, RSIGN, SIM, UPPER */ /* INTEGER INFO, KL, KU, LDA, MODE, MODES, N */ /* DOUBLE PRECISION ANORM, COND, CONDS, DMAX */ /* CHARACTER EI( * ) */ /* INTEGER ISEED( 4 ) */ /* DOUBLE PRECISION A( LDA, * ), D( * ), DS( * ), WORK( * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > DLATME generates random non-symmetric square matrices with */ /* > specified eigenvalues for testing LAPACK programs. */ /* > */ /* > DLATME operates by applying the following sequence of */ /* > operations: */ /* > */ /* > 1. Set the diagonal to D, where D may be input or */ /* > computed according to MODE, COND, DMAX, and RSIGN */ /* > as described below. */ /* > */ /* > 2. If complex conjugate pairs are desired (MODE=0 and EI(1)='R', */ /* > or MODE=5), certain pairs of adjacent elements of D are */ /* > interpreted as the real and complex parts of a complex */ /* > conjugate pair; A thus becomes block diagonal, with 1x1 */ /* > and 2x2 blocks. */ /* > */ /* > 3. If UPPER='T', the upper triangle of A is set to random values */ /* > out of distribution DIST. */ /* > */ /* > 4. If SIM='T', A is multiplied on the left by a random matrix */ /* > X, whose singular values are specified by DS, MODES, and */ /* > CONDS, and on the right by X inverse. */ /* > */ /* > 5. If KL < N-1, the lower bandwidth is reduced to KL using */ /* > Householder transformations. If KU < N-1, the upper */ /* > bandwidth is reduced to KU. */ /* > */ /* > 6. If ANORM is not negative, the matrix is scaled to have */ /* > maximum-element-norm ANORM. */ /* > */ /* > (Note: since the matrix cannot be reduced beyond Hessenberg form, */ /* > no packing options are available.) */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \param[in] N */ /* > \verbatim */ /* > N is INTEGER */ /* > The number of columns (or rows) of A. Not modified. */ /* > \endverbatim */ /* > */ /* > \param[in] DIST */ /* > \verbatim */ /* > DIST is CHARACTER*1 */ /* > On entry, DIST specifies the type of distribution to be used */ /* > to generate the random eigen-/singular values, and for the */ /* > upper triangle (see UPPER). */ /* > 'U' => UNIFORM( 0, 1 ) ( 'U' for uniform ) */ /* > 'S' => UNIFORM( -1, 1 ) ( 'S' for symmetric ) */ /* > 'N' => NORMAL( 0, 1 ) ( 'N' for normal ) */ /* > 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. They should lie between 0 and 4095 inclusive, */ /* > and ISEED(4) should be odd. 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 DLATME */ /* > to continue the same random number sequence. */ /* > Changed on exit. */ /* > \endverbatim */ /* > */ /* > \param[in,out] D */ /* > \verbatim */ /* > D is DOUBLE PRECISION array, dimension ( N ) */ /* > This array is used to specify the eigenvalues of A. If */ /* > MODE=0, then D is assumed to contain the eigenvalues (but */ /* > see the description of EI), otherwise they will be */ /* > computed according to MODE, COND, DMAX, and RSIGN and */ /* > placed in D. */ /* > Modified if MODE is nonzero. */ /* > \endverbatim */ /* > */ /* > \param[in] MODE */ /* > \verbatim */ /* > MODE is INTEGER */ /* > On entry this describes how the eigenvalues are to */ /* > be specified: */ /* > MODE = 0 means use D (with EI) as input */ /* > 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. Each odd-even pair */ /* > of elements will be either used as two real */ /* > eigenvalues or as the real and imaginary part */ /* > of a complex conjugate pair of eigenvalues; */ /* > the choice of which is done is random, with */ /* > 50-50 probability, for each pair. */ /* > 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 between 1 and 4, D has entries ranging */ /* > from 1 to 1/COND, if between -1 and -4, D has entries */ /* > ranging from 1/COND to 1, */ /* > Not modified. */ /* > \endverbatim */ /* > */ /* > \param[in] COND */ /* > \verbatim */ /* > COND is DOUBLE PRECISION */ /* > On entry, this is used as described under MODE above. */ /* > If used, it must be >= 1. Not modified. */ /* > \endverbatim */ /* > */ /* > \param[in] DMAX */ /* > \verbatim */ /* > DMAX is DOUBLE PRECISION */ /* > If MODE is neither -6, 0 nor 6, the contents of D, as */ /* > computed according to MODE and COND, will be scaled by */ /* > DMAX / f2cmax(abs(D(i))). Note that DMAX need not be */ /* > positive: if DMAX is negative (or zero), D will be */ /* > scaled by a negative number (or zero). */ /* > Not modified. */ /* > \endverbatim */ /* > */ /* > \param[in] EI */ /* > \verbatim */ /* > EI is CHARACTER*1 array, dimension ( N ) */ /* > If MODE is 0, and EI(1) is not ' ' (space character), */ /* > this array specifies which elements of D (on input) are */ /* > real eigenvalues and which are the real and imaginary parts */ /* > of a complex conjugate pair of eigenvalues. The elements */ /* > of EI may then only have the values 'R' and 'I'. If */ /* > EI(j)='R' and EI(j+1)='I', then the j-th eigenvalue is */ /* > CMPLX( D(j) , D(j+1) ), and the (j+1)-th is the complex */ /* > conjugate thereof. If EI(j)=EI(j+1)='R', then the j-th */ /* > eigenvalue is D(j) (i.e., real). EI(1) may not be 'I', */ /* > nor may two adjacent elements of EI both have the value 'I'. */ /* > If MODE is not 0, then EI is ignored. If MODE is 0 and */ /* > EI(1)=' ', then the eigenvalues will all be real. */ /* > Not modified. */ /* > \endverbatim */ /* > */ /* > \param[in] RSIGN */ /* > \verbatim */ /* > RSIGN is CHARACTER*1 */ /* > If MODE is not 0, 6, or -6, and RSIGN='T', then the */ /* > elements of D, as computed according to MODE and COND, will */ /* > be multiplied by a random sign (+1 or -1). If RSIGN='F', */ /* > they will not be. RSIGN may only have the values 'T' or */ /* > 'F'. */ /* > Not modified. */ /* > \endverbatim */ /* > */ /* > \param[in] UPPER */ /* > \verbatim */ /* > UPPER is CHARACTER*1 */ /* > If UPPER='T', then the elements of A above the diagonal */ /* > (and above the 2x2 diagonal blocks, if A has complex */ /* > eigenvalues) will be set to random numbers out of DIST. */ /* > If UPPER='F', they will not. UPPER may only have the */ /* > values 'T' or 'F'. */ /* > Not modified. */ /* > \endverbatim */ /* > */ /* > \param[in] SIM */ /* > \verbatim */ /* > SIM is CHARACTER*1 */ /* > If SIM='T', then A will be operated on by a "similarity */ /* > transform", i.e., multiplied on the left by a matrix X and */ /* > on the right by X inverse. X = U S V, where U and V are */ /* > random unitary matrices and S is a (diagonal) matrix of */ /* > singular values specified by DS, MODES, and CONDS. If */ /* > SIM='F', then A will not be transformed. */ /* > Not modified. */ /* > \endverbatim */ /* > */ /* > \param[in,out] DS */ /* > \verbatim */ /* > DS is DOUBLE PRECISION array, dimension ( N ) */ /* > This array is used to specify the singular values of X, */ /* > in the same way that D specifies the eigenvalues of A. */ /* > If MODE=0, the DS contains the singular values, which */ /* > may not be zero. */ /* > Modified if MODE is nonzero. */ /* > \endverbatim */ /* > */ /* > \param[in] MODES */ /* > \verbatim */ /* > MODES is INTEGER */ /* > \endverbatim */ /* > */ /* > \param[in] CONDS */ /* > \verbatim */ /* > CONDS is DOUBLE PRECISION */ /* > Same as MODE and COND, but for specifying the diagonal */ /* > of S. MODES=-6 and +6 are not allowed (since they would */ /* > result in randomly ill-conditioned eigenvalues.) */ /* > \endverbatim */ /* > */ /* > \param[in] KL */ /* > \verbatim */ /* > KL is INTEGER */ /* > This specifies the lower bandwidth of the matrix. KL=1 */ /* > specifies upper Hessenberg form. If KL is at least N-1, */ /* > then A will have full lower bandwidth. KL must be at */ /* > least 1. */ /* > Not modified. */ /* > \endverbatim */ /* > */ /* > \param[in] KU */ /* > \verbatim */ /* > KU is INTEGER */ /* > This specifies the upper bandwidth of the matrix. KU=1 */ /* > specifies lower Hessenberg form. If KU is at least N-1, */ /* > then A will have full upper bandwidth; if KU and KL */ /* > are both at least N-1, then A will be dense. Only one of */ /* > KU and KL may be less than N-1. KU must be at least 1. */ /* > Not modified. */ /* > \endverbatim */ /* > */ /* > \param[in] ANORM */ /* > \verbatim */ /* > ANORM is DOUBLE PRECISION */ /* > If ANORM is not negative, then A will be scaled by a non- */ /* > negative real number to make the maximum-element-norm of A */ /* > to be ANORM. */ /* > Not modified. */ /* > \endverbatim */ /* > */ /* > \param[out] A */ /* > \verbatim */ /* > A is DOUBLE PRECISION array, dimension ( LDA, N ) */ /* > On exit A is the desired test matrix. */ /* > Modified. */ /* > \endverbatim */ /* > */ /* > \param[in] LDA */ /* > \verbatim */ /* > LDA is INTEGER */ /* > LDA specifies the first dimension of A as declared in the */ /* > calling program. LDA must be at least N. */ /* > Not modified. */ /* > \endverbatim */ /* > */ /* > \param[out] WORK */ /* > \verbatim */ /* > WORK is DOUBLE PRECISION array, dimension ( 3*N ) */ /* > Workspace. */ /* > Modified. */ /* > \endverbatim */ /* > */ /* > \param[out] INFO */ /* > \verbatim */ /* > INFO is INTEGER */ /* > Error code. On exit, INFO will be set to one of the */ /* > following values: */ /* > 0 => normal return */ /* > -1 => N negative */ /* > -2 => DIST illegal string */ /* > -5 => MODE not in range -6 to 6 */ /* > -6 => COND less than 1.0, and MODE neither -6, 0 nor 6 */ /* > -8 => EI(1) is not ' ' or 'R', EI(j) is not 'R' or 'I', or */ /* > two adjacent elements of EI are 'I'. */ /* > -9 => RSIGN is not 'T' or 'F' */ /* > -10 => UPPER is not 'T' or 'F' */ /* > -11 => SIM is not 'T' or 'F' */ /* > -12 => MODES=0 and DS has a zero singular value. */ /* > -13 => MODES is not in the range -5 to 5. */ /* > -14 => MODES is nonzero and CONDS is less than 1. */ /* > -15 => KL is less than 1. */ /* > -16 => KU is less than 1, or KL and KU are both less than */ /* > N-1. */ /* > -19 => LDA is less than N. */ /* > 1 => Error return from DLATM1 (computing D) */ /* > 2 => Cannot scale to DMAX (f2cmax. eigenvalue is 0) */ /* > 3 => Error return from DLATM1 (computing DS) */ /* > 4 => Error return from DLARGE */ /* > 5 => Zero singular value from DLATM1. */ /* > \endverbatim */ /* Authors: */ /* ======== */ /* > \author Univ. of Tennessee */ /* > \author Univ. of California Berkeley */ /* > \author Univ. of Colorado Denver */ /* > \author NAG Ltd. */ /* > \date December 2016 */ /* > \ingroup double_matgen */ /* ===================================================================== */ /* Subroutine */ int dlatme_(integer *n, char *dist, integer *iseed, doublereal *d__, integer *mode, doublereal *cond, doublereal *dmax__, char *ei, char *rsign, char *upper, char *sim, doublereal *ds, integer *modes, doublereal *conds, integer *kl, integer *ku, doublereal *anorm, doublereal *a, integer *lda, doublereal *work, integer *info) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2; doublereal d__1, d__2, d__3; /* Local variables */ logical bads; extern /* Subroutine */ int dger_(integer *, integer *, doublereal *, doublereal *, integer *, doublereal *, integer *, doublereal *, integer *); integer isim; doublereal temp; logical badei; integer i__, j; doublereal alpha; extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, integer *); extern logical lsame_(char *, char *); extern /* Subroutine */ int dgemv_(char *, integer *, integer *, doublereal *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *); integer iinfo; doublereal tempa[1]; integer icols; logical useei; integer idist; extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, doublereal *, integer *); integer irows; extern /* Subroutine */ int dlatm1_(integer *, doublereal *, integer *, integer *, integer *, doublereal *, integer *, integer *); integer ic, jc; extern doublereal dlange_(char *, integer *, integer *, doublereal *, integer *, doublereal *); integer ir, jr; extern /* Subroutine */ int dlarge_(integer *, doublereal *, integer *, integer *, doublereal *, integer *), dlarfg_(integer *, doublereal *, doublereal *, integer *, doublereal *); extern doublereal dlaran_(integer *); extern /* Subroutine */ int dlaset_(char *, integer *, integer *, doublereal *, doublereal *, doublereal *, integer *), xerbla_(char *, integer *), dlarnv_(integer *, integer *, integer *, doublereal *); integer irsign, iupper; doublereal xnorms; integer jcr; doublereal tau; /* -- LAPACK computational 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 */ /* ===================================================================== */ /* 1) Decode and Test the input parameters. */ /* Initialize flags & seed. */ /* Parameter adjustments */ --iseed; --d__; --ei; --ds; a_dim1 = *lda; a_offset = 1 + a_dim1 * 1; a -= a_offset; --work; /* Function Body */ *info = 0; /* Quick return if possible */ if (*n == 0) { return 0; } /* Decode DIST */ if (lsame_(dist, "U")) { idist = 1; } else if (lsame_(dist, "S")) { idist = 2; } else if (lsame_(dist, "N")) { idist = 3; } else { idist = -1; } /* Check EI */ useei = TRUE_; badei = FALSE_; if (lsame_(ei + 1, " ") || *mode != 0) { useei = FALSE_; } else { if (lsame_(ei + 1, "R")) { i__1 = *n; for (j = 2; j <= i__1; ++j) { if (lsame_(ei + j, "I")) { if (lsame_(ei + (j - 1), "I")) { badei = TRUE_; } } else { if (! lsame_(ei + j, "R")) { badei = TRUE_; } } /* L10: */ } } else { badei = TRUE_; } } /* Decode RSIGN */ if (lsame_(rsign, "T")) { irsign = 1; } else if (lsame_(rsign, "F")) { irsign = 0; } else { irsign = -1; } /* Decode UPPER */ if (lsame_(upper, "T")) { iupper = 1; } else if (lsame_(upper, "F")) { iupper = 0; } else { iupper = -1; } /* Decode SIM */ if (lsame_(sim, "T")) { isim = 1; } else if (lsame_(sim, "F")) { isim = 0; } else { isim = -1; } /* Check DS, if MODES=0 and ISIM=1 */ bads = FALSE_; if (*modes == 0 && isim == 1) { i__1 = *n; for (j = 1; j <= i__1; ++j) { if (ds[j] == 0.) { bads = TRUE_; } /* L20: */ } } /* Set INFO if an error */ if (*n < 0) { *info = -1; } else if (idist == -1) { *info = -2; } else if (abs(*mode) > 6) { *info = -5; } else if (*mode != 0 && abs(*mode) != 6 && *cond < 1.) { *info = -6; } else if (badei) { *info = -8; } else if (irsign == -1) { *info = -9; } else if (iupper == -1) { *info = -10; } else if (isim == -1) { *info = -11; } else if (bads) { *info = -12; } else if (isim == 1 && abs(*modes) > 5) { *info = -13; } else if (isim == 1 && *modes != 0 && *conds < 1.) { *info = -14; } else if (*kl < 1) { *info = -15; } else if (*ku < 1 || *ku < *n - 1 && *kl < *n - 1) { *info = -16; } else if (*lda < f2cmax(1,*n)) { *info = -19; } if (*info != 0) { i__1 = -(*info); xerbla_("DLATME", &i__1); return 0; } /* Initialize random number generator */ for (i__ = 1; i__ <= 4; ++i__) { iseed[i__] = (i__1 = iseed[i__], abs(i__1)) % 4096; /* L30: */ } if (iseed[4] % 2 != 1) { ++iseed[4]; } /* 2) Set up diagonal of A */ /* Compute D according to COND and MODE */ dlatm1_(mode, cond, &irsign, &idist, &iseed[1], &d__[1], n, &iinfo); if (iinfo != 0) { *info = 1; return 0; } if (*mode != 0 && abs(*mode) != 6) { /* Scale by DMAX */ temp = abs(d__[1]); i__1 = *n; for (i__ = 2; i__ <= i__1; ++i__) { /* Computing MAX */ d__2 = temp, d__3 = (d__1 = d__[i__], abs(d__1)); temp = f2cmax(d__2,d__3); /* L40: */ } if (temp > 0.) { alpha = *dmax__ / temp; } else if (*dmax__ != 0.) { *info = 2; return 0; } else { alpha = 0.; } dscal_(n, &alpha, &d__[1], &c__1); } dlaset_("Full", n, n, &c_b23, &c_b23, &a[a_offset], lda); i__1 = *lda + 1; dcopy_(n, &d__[1], &c__1, &a[a_offset], &i__1); /* Set up complex conjugate pairs */ if (*mode == 0) { if (useei) { i__1 = *n; for (j = 2; j <= i__1; ++j) { if (lsame_(ei + j, "I")) { a[j - 1 + j * a_dim1] = a[j + j * a_dim1]; a[j + (j - 1) * a_dim1] = -a[j + j * a_dim1]; a[j + j * a_dim1] = a[j - 1 + (j - 1) * a_dim1]; } /* L50: */ } } } else if (abs(*mode) == 5) { i__1 = *n; for (j = 2; j <= i__1; j += 2) { if (dlaran_(&iseed[1]) > .5) { a[j - 1 + j * a_dim1] = a[j + j * a_dim1]; a[j + (j - 1) * a_dim1] = -a[j + j * a_dim1]; a[j + j * a_dim1] = a[j - 1 + (j - 1) * a_dim1]; } /* L60: */ } } /* 3) If UPPER='T', set upper triangle of A to random numbers. */ /* (but don't modify the corners of 2x2 blocks.) */ if (iupper != 0) { i__1 = *n; for (jc = 2; jc <= i__1; ++jc) { if (a[jc - 1 + jc * a_dim1] != 0.) { jr = jc - 2; } else { jr = jc - 1; } dlarnv_(&idist, &iseed[1], &jr, &a[jc * a_dim1 + 1]); /* L70: */ } } /* 4) If SIM='T', apply similarity transformation. */ /* -1 */ /* Transform is X A X , where X = U S V, thus */ /* it is U S V A V' (1/S) U' */ if (isim != 0) { /* Compute S (singular values of the eigenvector matrix) */ /* according to CONDS and MODES */ dlatm1_(modes, conds, &c__0, &c__0, &iseed[1], &ds[1], n, &iinfo); if (iinfo != 0) { *info = 3; return 0; } /* Multiply by V and V' */ dlarge_(n, &a[a_offset], lda, &iseed[1], &work[1], &iinfo); if (iinfo != 0) { *info = 4; return 0; } /* Multiply by S and (1/S) */ i__1 = *n; for (j = 1; j <= i__1; ++j) { dscal_(n, &ds[j], &a[j + a_dim1], lda); if (ds[j] != 0.) { d__1 = 1. / ds[j]; dscal_(n, &d__1, &a[j * a_dim1 + 1], &c__1); } else { *info = 5; return 0; } /* L80: */ } /* Multiply by U and U' */ dlarge_(n, &a[a_offset], lda, &iseed[1], &work[1], &iinfo); if (iinfo != 0) { *info = 4; return 0; } } /* 5) Reduce the bandwidth. */ if (*kl < *n - 1) { /* Reduce bandwidth -- kill column */ i__1 = *n - 1; for (jcr = *kl + 1; jcr <= i__1; ++jcr) { ic = jcr - *kl; irows = *n + 1 - jcr; icols = *n + *kl - jcr; dcopy_(&irows, &a[jcr + ic * a_dim1], &c__1, &work[1], &c__1); xnorms = work[1]; dlarfg_(&irows, &xnorms, &work[2], &c__1, &tau); work[1] = 1.; dgemv_("T", &irows, &icols, &c_b39, &a[jcr + (ic + 1) * a_dim1], lda, &work[1], &c__1, &c_b23, &work[irows + 1], &c__1); d__1 = -tau; dger_(&irows, &icols, &d__1, &work[1], &c__1, &work[irows + 1], & c__1, &a[jcr + (ic + 1) * a_dim1], lda); dgemv_("N", n, &irows, &c_b39, &a[jcr * a_dim1 + 1], lda, &work[1] , &c__1, &c_b23, &work[irows + 1], &c__1); d__1 = -tau; dger_(n, &irows, &d__1, &work[irows + 1], &c__1, &work[1], &c__1, &a[jcr * a_dim1 + 1], lda); a[jcr + ic * a_dim1] = xnorms; i__2 = irows - 1; dlaset_("Full", &i__2, &c__1, &c_b23, &c_b23, &a[jcr + 1 + ic * a_dim1], lda); /* L90: */ } } else if (*ku < *n - 1) { /* Reduce upper bandwidth -- kill a row at a time. */ i__1 = *n - 1; for (jcr = *ku + 1; jcr <= i__1; ++jcr) { ir = jcr - *ku; irows = *n + *ku - jcr; icols = *n + 1 - jcr; dcopy_(&icols, &a[ir + jcr * a_dim1], lda, &work[1], &c__1); xnorms = work[1]; dlarfg_(&icols, &xnorms, &work[2], &c__1, &tau); work[1] = 1.; dgemv_("N", &irows, &icols, &c_b39, &a[ir + 1 + jcr * a_dim1], lda, &work[1], &c__1, &c_b23, &work[icols + 1], &c__1); d__1 = -tau; dger_(&irows, &icols, &d__1, &work[icols + 1], &c__1, &work[1], & c__1, &a[ir + 1 + jcr * a_dim1], lda); dgemv_("C", &icols, n, &c_b39, &a[jcr + a_dim1], lda, &work[1], & c__1, &c_b23, &work[icols + 1], &c__1); d__1 = -tau; dger_(&icols, n, &d__1, &work[1], &c__1, &work[icols + 1], &c__1, &a[jcr + a_dim1], lda); a[ir + jcr * a_dim1] = xnorms; i__2 = icols - 1; dlaset_("Full", &c__1, &i__2, &c_b23, &c_b23, &a[ir + (jcr + 1) * a_dim1], lda); /* L100: */ } } /* Scale the matrix to have norm ANORM */ if (*anorm >= 0.) { temp = dlange_("M", n, n, &a[a_offset], lda, tempa); if (temp > 0.) { alpha = *anorm / temp; i__1 = *n; for (j = 1; j <= i__1; ++j) { dscal_(n, &alpha, &a[j * a_dim1 + 1], &c__1); /* L110: */ } } } return 0; /* End of DLATME */ } /* dlatme_ */