#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 SLAROT */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* Definition: */ /* =========== */ /* SUBROUTINE SLAROT( LROWS, LLEFT, LRIGHT, NL, C, S, A, LDA, XLEFT, */ /* XRIGHT ) */ /* LOGICAL LLEFT, LRIGHT, LROWS */ /* INTEGER LDA, NL */ /* REAL C, S, XLEFT, XRIGHT */ /* REAL A( * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > SLAROT applies a (Givens) rotation to two adjacent rows or */ /* > columns, where one element of the first and/or last column/row */ /* > for use on matrices stored in some format other than GE, so */ /* > that elements of the matrix may be used or modified for which */ /* > no array element is provided. */ /* > */ /* > One example is a symmetric matrix in SB format (bandwidth=4), for */ /* > which UPLO='L': Two adjacent rows will have the format: */ /* > */ /* > row j: C> C> C> C> C> . . . . */ /* > row j+1: C> C> C> C> C> . . . . */ /* > */ /* > '*' indicates elements for which storage is provided, */ /* > '.' indicates elements for which no storage is provided, but */ /* > are not necessarily zero; their values are determined by */ /* > symmetry. ' ' indicates elements which are necessarily zero, */ /* > and have no storage provided. */ /* > */ /* > Those columns which have two '*'s can be handled by SROT. */ /* > Those columns which have no '*'s can be ignored, since as long */ /* > as the Givens rotations are carefully applied to preserve */ /* > symmetry, their values are determined. */ /* > Those columns which have one '*' have to be handled separately, */ /* > by using separate variables "p" and "q": */ /* > */ /* > row j: C> C> C> C> C> p . . . */ /* > row j+1: q C> C> C> C> C> . . . . */ /* > */ /* > The element p would have to be set correctly, then that column */ /* > is rotated, setting p to its new value. The next call to */ /* > SLAROT would rotate columns j and j+1, using p, and restore */ /* > symmetry. The element q would start out being zero, and be */ /* > made non-zero by the rotation. Later, rotations would presumably */ /* > be chosen to zero q out. */ /* > */ /* > Typical Calling Sequences: rotating the i-th and (i+1)-st rows. */ /* > ------- ------- --------- */ /* > */ /* > General dense matrix: */ /* > */ /* > CALL SLAROT(.TRUE.,.FALSE.,.FALSE., N, C,S, */ /* > A(i,1),LDA, DUMMY, DUMMY) */ /* > */ /* > General banded matrix in GB format: */ /* > */ /* > j = MAX(1, i-KL ) */ /* > NL = MIN( N, i+KU+1 ) + 1-j */ /* > CALL SLAROT( .TRUE., i-KL.GE.1, i+KU.LT.N, NL, C,S, */ /* > A(KU+i+1-j,j),LDA-1, XLEFT, XRIGHT ) */ /* > */ /* > [ note that i+1-j is just MIN(i,KL+1) ] */ /* > */ /* > Symmetric banded matrix in SY format, bandwidth K, */ /* > lower triangle only: */ /* > */ /* > j = MAX(1, i-K ) */ /* > NL = MIN( K+1, i ) + 1 */ /* > CALL SLAROT( .TRUE., i-K.GE.1, .TRUE., NL, C,S, */ /* > A(i,j), LDA, XLEFT, XRIGHT ) */ /* > */ /* > Same, but upper triangle only: */ /* > */ /* > NL = MIN( K+1, N-i ) + 1 */ /* > CALL SLAROT( .TRUE., .TRUE., i+K.LT.N, NL, C,S, */ /* > A(i,i), LDA, XLEFT, XRIGHT ) */ /* > */ /* > Symmetric banded matrix in SB format, bandwidth K, */ /* > lower triangle only: */ /* > */ /* > [ same as for SY, except:] */ /* > . . . . */ /* > A(i+1-j,j), LDA-1, XLEFT, XRIGHT ) */ /* > */ /* > [ note that i+1-j is just MIN(i,K+1) ] */ /* > */ /* > Same, but upper triangle only: */ /* > . . . */ /* > A(K+1,i), LDA-1, XLEFT, XRIGHT ) */ /* > */ /* > Rotating columns is just the transpose of rotating rows, except */ /* > for GB and SB: (rotating columns i and i+1) */ /* > */ /* > GB: */ /* > j = MAX(1, i-KU ) */ /* > NL = MIN( N, i+KL+1 ) + 1-j */ /* > CALL SLAROT( .TRUE., i-KU.GE.1, i+KL.LT.N, NL, C,S, */ /* > A(KU+j+1-i,i),LDA-1, XTOP, XBOTTM ) */ /* > */ /* > [note that KU+j+1-i is just MAX(1,KU+2-i)] */ /* > */ /* > SB: (upper triangle) */ /* > */ /* > . . . . . . */ /* > A(K+j+1-i,i),LDA-1, XTOP, XBOTTM ) */ /* > */ /* > SB: (lower triangle) */ /* > */ /* > . . . . . . */ /* > A(1,i),LDA-1, XTOP, XBOTTM ) */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \verbatim */ /* > LROWS - LOGICAL */ /* > If .TRUE., then SLAROT will rotate two rows. If .FALSE., */ /* > then it will rotate two columns. */ /* > Not modified. */ /* > */ /* > LLEFT - LOGICAL */ /* > If .TRUE., then XLEFT will be used instead of the */ /* > corresponding element of A for the first element in the */ /* > second row (if LROWS=.FALSE.) or column (if LROWS=.TRUE.) */ /* > If .FALSE., then the corresponding element of A will be */ /* > used. */ /* > Not modified. */ /* > */ /* > LRIGHT - LOGICAL */ /* > If .TRUE., then XRIGHT will be used instead of the */ /* > corresponding element of A for the last element in the */ /* > first row (if LROWS=.FALSE.) or column (if LROWS=.TRUE.) If */ /* > .FALSE., then the corresponding element of A will be used. */ /* > Not modified. */ /* > */ /* > NL - INTEGER */ /* > The length of the rows (if LROWS=.TRUE.) or columns (if */ /* > LROWS=.FALSE.) to be rotated. If XLEFT and/or XRIGHT are */ /* > used, the columns/rows they are in should be included in */ /* > NL, e.g., if LLEFT = LRIGHT = .TRUE., then NL must be at */ /* > least 2. The number of rows/columns to be rotated */ /* > exclusive of those involving XLEFT and/or XRIGHT may */ /* > not be negative, i.e., NL minus how many of LLEFT and */ /* > LRIGHT are .TRUE. must be at least zero; if not, XERBLA */ /* > will be called. */ /* > Not modified. */ /* > */ /* > C, S - REAL */ /* > Specify the Givens rotation to be applied. If LROWS is */ /* > true, then the matrix ( c s ) */ /* > (-s c ) is applied from the left; */ /* > if false, then the transpose thereof is applied from the */ /* > right. For a Givens rotation, C**2 + S**2 should be 1, */ /* > but this is not checked. */ /* > Not modified. */ /* > */ /* > A - REAL array. */ /* > The array containing the rows/columns to be rotated. The */ /* > first element of A should be the upper left element to */ /* > be rotated. */ /* > Read and modified. */ /* > */ /* > LDA - INTEGER */ /* > The "effective" leading dimension of A. If A contains */ /* > a matrix stored in GE or SY format, then this is just */ /* > the leading dimension of A as dimensioned in the calling */ /* > routine. If A contains a matrix stored in band (GB or SB) */ /* > format, then this should be *one less* than the leading */ /* > dimension used in the calling routine. Thus, if */ /* > A were dimensioned A(LDA,*) in SLAROT, then A(1,j) would */ /* > be the j-th element in the first of the two rows */ /* > to be rotated, and A(2,j) would be the j-th in the second, */ /* > regardless of how the array may be stored in the calling */ /* > routine. [A cannot, however, actually be dimensioned thus, */ /* > since for band format, the row number may exceed LDA, which */ /* > is not legal FORTRAN.] */ /* > If LROWS=.TRUE., then LDA must be at least 1, otherwise */ /* > it must be at least NL minus the number of .TRUE. values */ /* > in XLEFT and XRIGHT. */ /* > Not modified. */ /* > */ /* > XLEFT - REAL */ /* > If LLEFT is .TRUE., then XLEFT will be used and modified */ /* > instead of A(2,1) (if LROWS=.TRUE.) or A(1,2) */ /* > (if LROWS=.FALSE.). */ /* > Read and modified. */ /* > */ /* > XRIGHT - REAL */ /* > If LRIGHT is .TRUE., then XRIGHT will be used and modified */ /* > instead of A(1,NL) (if LROWS=.TRUE.) or A(NL,1) */ /* > (if LROWS=.FALSE.). */ /* > Read and modified. */ /* > \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 */ int slarot_(logical *lrows, logical *lleft, logical *lright, integer *nl, real *c__, real *s, real *a, integer *lda, real *xleft, real *xright) { /* System generated locals */ integer i__1; /* Local variables */ integer iinc; extern /* Subroutine */ int srot_(integer *, real *, integer *, real *, integer *, real *, real *); integer inext, ix, iy, nt; real xt[2], yt[2]; extern /* Subroutine */ int xerbla_(char *, integer *); integer iyt; /* -- 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 */ /* ===================================================================== */ /* Set up indices, arrays for ends */ /* Parameter adjustments */ --a; /* Function Body */ if (*lrows) { iinc = *lda; inext = 1; } else { iinc = 1; inext = *lda; } if (*lleft) { nt = 1; ix = iinc + 1; iy = *lda + 2; xt[0] = a[1]; yt[0] = *xleft; } else { nt = 0; ix = 1; iy = inext + 1; } if (*lright) { iyt = inext + 1 + (*nl - 1) * iinc; ++nt; xt[nt - 1] = *xright; yt[nt - 1] = a[iyt]; } /* Check for errors */ if (*nl < nt) { xerbla_("SLAROT", &c__4); return 0; } if (*lda <= 0 || ! (*lrows) && *lda < *nl - nt) { xerbla_("SLAROT", &c__8); return 0; } /* Rotate */ i__1 = *nl - nt; srot_(&i__1, &a[ix], &iinc, &a[iy], &iinc, c__, s); srot_(&nt, xt, &c__1, yt, &c__1, c__, s); /* Stuff values back into XLEFT, XRIGHT, etc. */ if (*lleft) { a[1] = xt[0]; *xleft = yt[0]; } if (*lright) { *xright = xt[nt - 1]; a[iyt] = yt[nt - 1]; } return 0; /* End of SLAROT */ } /* slarot_ */