#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 blasint logical; 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);} #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++ */ /* Table of constant values */ static doublecomplex c_b1 = {0.,0.}; static doublecomplex c_b2 = {1.,0.}; static integer c__3 = 3; static integer c__1 = 1; /* > \brief \b ZLAROR */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* Definition: */ /* =========== */ /* SUBROUTINE ZLAROR( SIDE, INIT, M, N, A, LDA, ISEED, X, INFO ) */ /* CHARACTER INIT, SIDE */ /* INTEGER INFO, LDA, M, N */ /* INTEGER ISEED( 4 ) */ /* COMPLEX*16 A( LDA, * ), X( * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > ZLAROR pre- or post-multiplies an M by N matrix A by a random */ /* > unitary 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, pp. 403-409 ). */ /* > (BLAS-2 version) */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \param[in] SIDE */ /* > \verbatim */ /* > SIDE is CHARACTER*1 */ /* > SIDE specifies whether A is multiplied on the left or right */ /* > by U. */ /* > SIDE = 'L' Multiply A on the left (premultiply) by U */ /* > SIDE = 'R' Multiply A on the right (postmultiply) by UC> SIDE = 'C' Multiply A on the lef t by U and the right by UC> SIDE = 'T' Multiply A on the left by U and the right by U' */ /* > Not modified. */ /* > \endverbatim */ /* > */ /* > \param[in] INIT */ /* > \verbatim */ /* > INIT is CHARACTER*1 */ /* > INIT specifies whether or not A should be initialized to */ /* > the identity matrix. */ /* > INIT = 'I' Initialize A to (a section of) the */ /* > identity matrix before applying U. */ /* > INIT = 'N' No initialization. Apply U to the */ /* > input matrix A. */ /* > */ /* > INIT = 'I' may be used to generate square (i.e., unitary) */ /* > or rectangular orthogonal matrices (orthogonality being */ /* > in the sense of ZDOTC): */ /* > */ /* > For square matrices, M=N, and SIDE many be either 'L' or */ /* > 'R'; the rows will be orthogonal to each other, as will the */ /* > columns. */ /* > For rectangular matrices where M < N, SIDE = 'R' will */ /* > produce a dense matrix whose rows will be orthogonal and */ /* > whose columns will not, while SIDE = 'L' will produce a */ /* > matrix whose rows will be orthogonal, and whose first M */ /* > columns will be orthogonal, the remaining columns being */ /* > zero. */ /* > For matrices where M > N, just use the previous */ /* > explanation, interchanging 'L' and 'R' and "rows" and */ /* > "columns". */ /* > */ /* > Not modified. */ /* > \endverbatim */ /* > */ /* > \param[in] M */ /* > \verbatim */ /* > M is INTEGER */ /* > Number of rows of A. Not modified. */ /* > \endverbatim */ /* > */ /* > \param[in] N */ /* > \verbatim */ /* > N is INTEGER */ /* > Number of columns of A. Not modified. */ /* > \endverbatim */ /* > */ /* > \param[in,out] A */ /* > \verbatim */ /* > A is COMPLEX*16 array, dimension ( LDA, N ) */ /* > Input and output array. Overwritten by U A ( if SIDE = 'L' ) */ /* > or by A U ( if SIDE = 'R' ) */ /* > or by U A U* ( if SIDE = 'C') */ /* > or by U A U' ( if SIDE = 'T') on exit. */ /* > \endverbatim */ /* > */ /* > \param[in] LDA */ /* > \verbatim */ /* > LDA is INTEGER */ /* > Leading dimension of A. Must be at least MAX ( 1, M ). */ /* > 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 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 ZLAROR to continue the same random number */ /* > sequence. */ /* > Modified. */ /* > \endverbatim */ /* > */ /* > \param[out] X */ /* > \verbatim */ /* > X is COMPLEX*16 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'. */ /* > Modified. */ /* > \endverbatim */ /* > */ /* > \param[out] INFO */ /* > \verbatim */ /* > INFO is INTEGER */ /* > An error flag. It is set to: */ /* > 0 if no error. */ /* > 1 if ZLARND returned a bad random number (installation */ /* > problem) */ /* > -1 if SIDE is not L, R, C, or T. */ /* > -3 if M is negative. */ /* > -4 if N is negative or if SIDE is C or T and N is not equal */ /* > to M. */ /* > -6 if LDA is less than M. */ /* > \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 */ void zlaror_(char *side, char *init, integer *m, integer *n, doublecomplex *a, integer *lda, integer *iseed, doublecomplex *x, integer *info) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3; doublecomplex z__1, z__2; /* Local variables */ integer kbeg, jcol; doublereal xabs; integer irow, j; extern logical lsame_(char *, char *); doublecomplex csign; extern /* Subroutine */ void zgerc_(integer *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer *), zscal_(integer *, doublecomplex *, doublecomplex *, integer *); integer ixfrm; extern /* Subroutine */ void zgemv_(char *, integer *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *); integer itype, nxfrm; doublereal xnorm; extern doublereal dznrm2_(integer *, doublecomplex *, integer *); extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); doublereal factor; extern /* Subroutine */ void zlacgv_(integer *, doublecomplex *, integer *) ; //extern /* Double Complex */ VOID zlarnd_(doublecomplex *, integer *, extern doublecomplex zlarnd_(integer *, integer *); extern /* Subroutine */ void zlaset_(char *, integer *, integer *, doublecomplex *, doublecomplex *, doublecomplex *, integer *); doublecomplex 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")) { itype = 3; } else if (lsame_(side, "T")) { itype = 4; } /* 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_("ZLAROR", &i__1, 6); return; } if (itype == 1) { nxfrm = *m; } else { nxfrm = *n; } /* Initialize A to the identity matrix if desired */ if (lsame_(init, "I")) { zlaset_("Full", m, n, &c_b1, &c_b2, &a[a_offset], lda); } /* If no rotation possible, still multiply by */ /* a random complex number from the circle |x| = 1 */ /* 2) Compute Rotation by computing Householder */ /* Transformations H(2), H(3), ..., H(n). Note that the */ /* order in which they are computed is irrelevant. */ i__1 = nxfrm; for (j = 1; j <= i__1; ++j) { i__2 = j; x[i__2].r = 0., x[i__2].i = 0.; /* 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) { i__3 = j; //zlarnd_(&z__1, &c__3, &iseed[1]); z__1=zlarnd_(&c__3, &iseed[1]); x[i__3].r = z__1.r, x[i__3].i = z__1.i; /* L20: */ } /* Generate a Householder transformation from the random vector X */ xnorm = dznrm2_(&ixfrm, &x[kbeg], &c__1); xabs = z_abs(&x[kbeg]); if (xabs != 0.) { i__2 = kbeg; z__1.r = x[i__2].r / xabs, z__1.i = x[i__2].i / xabs; csign.r = z__1.r, csign.i = z__1.i; } else { csign.r = 1., csign.i = 0.; } z__1.r = xnorm * csign.r, z__1.i = xnorm * csign.i; xnorms.r = z__1.r, xnorms.i = z__1.i; i__2 = nxfrm + kbeg; z__1.r = -csign.r, z__1.i = -csign.i; x[i__2].r = z__1.r, x[i__2].i = z__1.i; factor = xnorm * (xnorm + xabs); if (abs(factor) < 1e-20) { *info = 1; i__2 = -(*info); xerbla_("ZLAROR", &i__2, 6); return; } else { factor = 1. / factor; } i__2 = kbeg; i__3 = kbeg; z__1.r = x[i__3].r + xnorms.r, z__1.i = x[i__3].i + xnorms.i; x[i__2].r = z__1.r, x[i__2].i = z__1.i; /* Apply Householder transformation to A */ if (itype == 1 || itype == 3 || itype == 4) { /* Apply H(k) on the left of A */ zgemv_("C", &ixfrm, n, &c_b2, &a[kbeg + a_dim1], lda, &x[kbeg], & c__1, &c_b1, &x[(nxfrm << 1) + 1], &c__1); z__2.r = factor, z__2.i = 0.; z__1.r = -z__2.r, z__1.i = -z__2.i; zgerc_(&ixfrm, n, &z__1, &x[kbeg], &c__1, &x[(nxfrm << 1) + 1], & c__1, &a[kbeg + a_dim1], lda); } if (itype >= 2 && itype <= 4) { /* Apply H(k)* (or H(k)') on the right of A */ if (itype == 4) { zlacgv_(&ixfrm, &x[kbeg], &c__1); } zgemv_("N", m, &ixfrm, &c_b2, &a[kbeg * a_dim1 + 1], lda, &x[kbeg] , &c__1, &c_b1, &x[(nxfrm << 1) + 1], &c__1); z__2.r = factor, z__2.i = 0.; z__1.r = -z__2.r, z__1.i = -z__2.i; zgerc_(m, &ixfrm, &z__1, &x[(nxfrm << 1) + 1], &c__1, &x[kbeg], & c__1, &a[kbeg * a_dim1 + 1], lda); } /* L30: */ } //zlarnd_(&z__1, &c__3, &iseed[1]); z__1=zlarnd_(&c__3, &iseed[1]); x[1].r = z__1.r, x[1].i = z__1.i; xabs = z_abs(&x[1]); if (xabs != 0.) { z__1.r = x[1].r / xabs, z__1.i = x[1].i / xabs; csign.r = z__1.r, csign.i = z__1.i; } else { csign.r = 1., csign.i = 0.; } i__1 = nxfrm << 1; x[i__1].r = csign.r, x[i__1].i = csign.i; /* Scale the matrix A by D. */ if (itype == 1 || itype == 3 || itype == 4) { i__1 = *m; for (irow = 1; irow <= i__1; ++irow) { d_cnjg(&z__1, &x[nxfrm + irow]); zscal_(n, &z__1, &a[irow + a_dim1], lda); /* L40: */ } } if (itype == 2 || itype == 3) { i__1 = *n; for (jcol = 1; jcol <= i__1; ++jcol) { zscal_(m, &x[nxfrm + jcol], &a[jcol * a_dim1 + 1], &c__1); /* L50: */ } } if (itype == 4) { i__1 = *n; for (jcol = 1; jcol <= i__1; ++jcol) { d_cnjg(&z__1, &x[nxfrm + jcol]); zscal_(m, &z__1, &a[jcol * a_dim1 + 1], &c__1); /* L60: */ } } return; /* End of ZLAROR */ } /* zlaror_ */