#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);} #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 /* Table of constant values */ static real c_b9 = 0.f; static real c_b10 = 1.f; static integer c__3 = 3; static integer c__1 = 1; /* > \brief \b SLAROR */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* Definition: */ /* =========== */ /* SUBROUTINE SLAROR( SIDE, INIT, M, N, A, LDA, ISEED, X, INFO ) */ /* CHARACTER INIT, SIDE */ /* INTEGER INFO, LDA, M, N */ /* INTEGER ISEED( 4 ) */ /* REAL A( LDA, * ), X( * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > SLAROR pre- or post-multiplies an M by N matrix A by a random */ /* > orthogonal matrix U, overwriting A. A may optionally be initialized */ /* > to the identity matrix before multiplying by U. U is generated using */ /* > the method of G.W. Stewart (SIAM J. Numer. Anal. 17, 1980, 403-409). */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \param[in] SIDE */ /* > \verbatim */ /* > SIDE is CHARACTER*1 */ /* > Specifies whether A is multiplied on the left or right by U. */ /* > = 'L': Multiply A on the left (premultiply) by U */ /* > = 'R': Multiply A on the right (postmultiply) by U' */ /* > = 'C' or 'T': Multiply A on the left by U and the right */ /* > by U' (Here, U' means U-transpose.) */ /* > \endverbatim */ /* > */ /* > \param[in] INIT */ /* > \verbatim */ /* > INIT is CHARACTER*1 */ /* > Specifies whether or not A should be initialized to the */ /* > identity matrix. */ /* > = 'I': Initialize A to (a section of) the identity matrix */ /* > before applying U. */ /* > = 'N': No initialization. Apply U to the input matrix A. */ /* > */ /* > INIT = 'I' may be used to generate square or rectangular */ /* > orthogonal matrices: */ /* > */ /* > For M = N and SIDE = 'L' or 'R', the rows will be orthogonal */ /* > to each other, as will the columns. */ /* > */ /* > If M < N, SIDE = 'R' produces a dense matrix whose rows are */ /* > orthogonal and whose columns are not, while SIDE = 'L' */ /* > produces a matrix whose rows are orthogonal, and whose first */ /* > M columns are orthogonal, and whose remaining columns are */ /* > zero. */ /* > */ /* > If M > N, SIDE = 'L' produces a dense matrix whose columns */ /* > are orthogonal and whose rows are not, while SIDE = 'R' */ /* > produces a matrix whose columns are orthogonal, and whose */ /* > first M rows are orthogonal, and whose remaining rows are */ /* > zero. */ /* > \endverbatim */ /* > */ /* > \param[in] M */ /* > \verbatim */ /* > M is INTEGER */ /* > The number of rows of A. */ /* > \endverbatim */ /* > */ /* > \param[in] N */ /* > \verbatim */ /* > N is INTEGER */ /* > The number of columns of A. */ /* > \endverbatim */ /* > */ /* > \param[in,out] A */ /* > \verbatim */ /* > A is REAL array, dimension (LDA, N) */ /* > On entry, the array A. */ /* > On exit, overwritten by U A ( if SIDE = 'L' ), */ /* > or by A U ( if SIDE = 'R' ), */ /* > or by U A U' ( if SIDE = 'C' or 'T'). */ /* > \endverbatim */ /* > */ /* > \param[in] LDA */ /* > \verbatim */ /* > LDA is INTEGER */ /* > The leading dimension of the array A. LDA >= f2cmax(1,M). */ /* > \endverbatim */ /* > */ /* > \param[in,out] ISEED */ /* > \verbatim */ /* > ISEED is INTEGER array, dimension (4) */ /* > On entry ISEED specifies the seed of the random number */ /* > generator. The array elements should be between 0 and 4095; */ /* > if not they will be reduced mod 4096. Also, ISEED(4) must */ /* > 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 SLAROR to continue the same random number */ /* > sequence. */ /* > \endverbatim */ /* > */ /* > \param[out] X */ /* > \verbatim */ /* > X is REAL array, dimension (3*MAX( M, N )) */ /* > Workspace of length */ /* > 2*M + N if SIDE = 'L', */ /* > 2*N + M if SIDE = 'R', */ /* > 3*N if SIDE = 'C' or 'T'. */ /* > \endverbatim */ /* > */ /* > \param[out] INFO */ /* > \verbatim */ /* > INFO is INTEGER */ /* > An error flag. It is set to: */ /* > = 0: normal return */ /* > < 0: if INFO = -k, the k-th argument had an illegal value */ /* > = 1: if the random numbers generated by SLARND are bad. */ /* > \endverbatim */ /* Authors: */ /* ======== */ /* > \author Univ. of Tennessee */ /* > \author Univ. of California Berkeley */ /* > \author Univ. of Colorado Denver */ /* > \author NAG Ltd. */ /* > \date December 2016 */ /* > \ingroup real_matgen */ /* ===================================================================== */ /* Subroutine */ void slaror_(char *side, char *init, integer *m, integer *n, real *a, integer *lda, integer *iseed, real *x, integer *info) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2; real r__1; /* Local variables */ integer kbeg, jcol; extern /* Subroutine */ void sger_(integer *, integer *, real *, real *, integer *, real *, integer *, real *, integer *); integer irow; extern real snrm2_(integer *, real *, integer *); integer j; extern logical lsame_(char *, char *); extern /* Subroutine */ void sscal_(integer *, real *, real *, integer *), sgemv_(char *, integer *, integer *, real *, real *, integer *, real *, integer *, real *, real *, integer *); integer ixfrm, itype, nxfrm; real xnorm; extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); real factor; extern real slarnd_(integer *, integer *); extern /* Subroutine */ void slaset_(char *, integer *, integer *, real *, real *, real *, integer *); real xnorms; /* -- 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; --iseed; --x; /* Function Body */ *info = 0; if (*n == 0 || *m == 0) { return; } itype = 0; if (lsame_(side, "L")) { itype = 1; } else if (lsame_(side, "R")) { itype = 2; } else if (lsame_(side, "C") || lsame_(side, "T")) { itype = 3; } /* Check for argument errors. */ if (itype == 0) { *info = -1; } else if (*m < 0) { *info = -3; } else if (*n < 0 || itype == 3 && *n != *m) { *info = -4; } else if (*lda < *m) { *info = -6; } if (*info != 0) { i__1 = -(*info); xerbla_("SLAROR", &i__1, 6); return; } if (itype == 1) { nxfrm = *m; } else { nxfrm = *n; } /* Initialize A to the identity matrix if desired */ if (lsame_(init, "I")) { slaset_("Full", m, n, &c_b9, &c_b10, &a[a_offset], lda); } /* If no rotation possible, multiply by random +/-1 */ /* Compute rotation by computing Householder transformations */ /* H(2), H(3), ..., H(nhouse) */ i__1 = nxfrm; for (j = 1; j <= i__1; ++j) { x[j] = 0.f; /* L10: */ } i__1 = nxfrm; for (ixfrm = 2; ixfrm <= i__1; ++ixfrm) { kbeg = nxfrm - ixfrm + 1; /* Generate independent normal( 0, 1 ) random numbers */ i__2 = nxfrm; for (j = kbeg; j <= i__2; ++j) { x[j] = slarnd_(&c__3, &iseed[1]); /* L20: */ } /* Generate a Householder transformation from the random vector X */ xnorm = snrm2_(&ixfrm, &x[kbeg], &c__1); xnorms = r_sign(&xnorm, &x[kbeg]); r__1 = -x[kbeg]; x[kbeg + nxfrm] = r_sign(&c_b10, &r__1); factor = xnorms * (xnorms + x[kbeg]); if (abs(factor) < 1e-20f) { *info = 1; xerbla_("SLAROR", info, 6); return; } else { factor = 1.f / factor; } x[kbeg] += xnorms; /* Apply Householder transformation to A */ if (itype == 1 || itype == 3) { /* Apply H(k) from the left. */ sgemv_("T", &ixfrm, n, &c_b10, &a[kbeg + a_dim1], lda, &x[kbeg], & c__1, &c_b9, &x[(nxfrm << 1) + 1], &c__1); r__1 = -factor; sger_(&ixfrm, n, &r__1, &x[kbeg], &c__1, &x[(nxfrm << 1) + 1], & c__1, &a[kbeg + a_dim1], lda); } if (itype == 2 || itype == 3) { /* Apply H(k) from the right. */ sgemv_("N", m, &ixfrm, &c_b10, &a[kbeg * a_dim1 + 1], lda, &x[ kbeg], &c__1, &c_b9, &x[(nxfrm << 1) + 1], &c__1); r__1 = -factor; sger_(m, &ixfrm, &r__1, &x[(nxfrm << 1) + 1], &c__1, &x[kbeg], & c__1, &a[kbeg * a_dim1 + 1], lda); } /* L30: */ } r__1 = slarnd_(&c__3, &iseed[1]); x[nxfrm * 2] = r_sign(&c_b10, &r__1); /* Scale the matrix A by D. */ if (itype == 1 || itype == 3) { i__1 = *m; for (irow = 1; irow <= i__1; ++irow) { sscal_(n, &x[nxfrm + irow], &a[irow + a_dim1], lda); /* L40: */ } } if (itype == 2 || itype == 3) { i__1 = *n; for (jcol = 1; jcol <= i__1; ++jcol) { sscal_(m, &x[nxfrm + jcol], &a[jcol * a_dim1 + 1], &c__1); /* L50: */ } } return; /* End of SLAROR */ } /* slaror_ */