#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 ZUNHR_COL */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download ZUNHR_COL + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > */ /* Definition: */ /* =========== */ /* SUBROUTINE ZUNHR_COL( M, N, NB, A, LDA, T, LDT, D, INFO ) */ /* INTEGER INFO, LDA, LDT, M, N, NB */ /* COMPLEX*16 A( LDA, * ), D( * ), T( LDT, * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > ZUNHR_COL takes an M-by-N complex matrix Q_in with orthonormal columns */ /* > as input, stored in A, and performs Householder Reconstruction (HR), */ /* > i.e. reconstructs Householder vectors V(i) implicitly representing */ /* > another M-by-N matrix Q_out, with the property that Q_in = Q_out*S, */ /* > where S is an N-by-N diagonal matrix with diagonal entries */ /* > equal to +1 or -1. The Householder vectors (columns V(i) of V) are */ /* > stored in A on output, and the diagonal entries of S are stored in D. */ /* > Block reflectors are also returned in T */ /* > (same output format as ZGEQRT). */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \param[in] M */ /* > \verbatim */ /* > M is INTEGER */ /* > The number of rows of the matrix A. M >= 0. */ /* > \endverbatim */ /* > */ /* > \param[in] N */ /* > \verbatim */ /* > N is INTEGER */ /* > The number of columns of the matrix A. M >= N >= 0. */ /* > \endverbatim */ /* > */ /* > \param[in] NB */ /* > \verbatim */ /* > NB is INTEGER */ /* > The column block size to be used in the reconstruction */ /* > of Householder column vector blocks in the array A and */ /* > corresponding block reflectors in the array T. NB >= 1. */ /* > (Note that if NB > N, then N is used instead of NB */ /* > as the column block size.) */ /* > \endverbatim */ /* > */ /* > \param[in,out] A */ /* > \verbatim */ /* > A is COMPLEX*16 array, dimension (LDA,N) */ /* > */ /* > On entry: */ /* > */ /* > The array A contains an M-by-N orthonormal matrix Q_in, */ /* > i.e the columns of A are orthogonal unit vectors. */ /* > */ /* > On exit: */ /* > */ /* > The elements below the diagonal of A represent the unit */ /* > lower-trapezoidal matrix V of Householder column vectors */ /* > V(i). The unit diagonal entries of V are not stored */ /* > (same format as the output below the diagonal in A from */ /* > ZGEQRT). The matrix T and the matrix V stored on output */ /* > in A implicitly define Q_out. */ /* > */ /* > The elements above the diagonal contain the factor U */ /* > of the "modified" LU-decomposition: */ /* > Q_in - ( S ) = V * U */ /* > ( 0 ) */ /* > where 0 is a (M-N)-by-(M-N) zero matrix. */ /* > \endverbatim */ /* > */ /* > \param[in] LDA */ /* > \verbatim */ /* > LDA is INTEGER */ /* > The leading dimension of the array A. LDA >= f2cmax(1,M). */ /* > \endverbatim */ /* > */ /* > \param[out] T */ /* > \verbatim */ /* > T is COMPLEX*16 array, */ /* > dimension (LDT, N) */ /* > */ /* > Let NOCB = Number_of_output_col_blocks */ /* > = CEIL(N/NB) */ /* > */ /* > On exit, T(1:NB, 1:N) contains NOCB upper-triangular */ /* > block reflectors used to define Q_out stored in compact */ /* > form as a sequence of upper-triangular NB-by-NB column */ /* > blocks (same format as the output T in ZGEQRT). */ /* > The matrix T and the matrix V stored on output in A */ /* > implicitly define Q_out. NOTE: The lower triangles */ /* > below the upper-triangular blcoks will be filled with */ /* > zeros. See Further Details. */ /* > \endverbatim */ /* > */ /* > \param[in] LDT */ /* > \verbatim */ /* > LDT is INTEGER */ /* > The leading dimension of the array T. */ /* > LDT >= f2cmax(1,f2cmin(NB,N)). */ /* > \endverbatim */ /* > */ /* > \param[out] D */ /* > \verbatim */ /* > D is COMPLEX*16 array, dimension f2cmin(M,N). */ /* > The elements can be only plus or minus one. */ /* > */ /* > D(i) is constructed as D(i) = -SIGN(Q_in_i(i,i)), where */ /* > 1 <= i <= f2cmin(M,N), and Q_in_i is Q_in after performing */ /* > i-1 steps of “modified” Gaussian elimination. */ /* > See Further Details. */ /* > \endverbatim */ /* > */ /* > \param[out] INFO */ /* > \verbatim */ /* > INFO is INTEGER */ /* > = 0: successful exit */ /* > < 0: if INFO = -i, the i-th argument had an illegal value */ /* > \endverbatim */ /* > */ /* > \par Further Details: */ /* ===================== */ /* > */ /* > \verbatim */ /* > */ /* > The computed M-by-M unitary factor Q_out is defined implicitly as */ /* > a product of unitary matrices Q_out(i). Each Q_out(i) is stored in */ /* > the compact WY-representation format in the corresponding blocks of */ /* > matrices V (stored in A) and T. */ /* > */ /* > The M-by-N unit lower-trapezoidal matrix V stored in the M-by-N */ /* > matrix A contains the column vectors V(i) in NB-size column */ /* > blocks VB(j). For example, VB(1) contains the columns */ /* > V(1), V(2), ... V(NB). NOTE: The unit entries on */ /* > the diagonal of Y are not stored in A. */ /* > */ /* > The number of column blocks is */ /* > */ /* > NOCB = Number_of_output_col_blocks = CEIL(N/NB) */ /* > */ /* > where each block is of order NB except for the last block, which */ /* > is of order LAST_NB = N - (NOCB-1)*NB. */ /* > */ /* > For example, if M=6, N=5 and NB=2, the matrix V is */ /* > */ /* > */ /* > V = ( VB(1), VB(2), VB(3) ) = */ /* > */ /* > = ( 1 ) */ /* > ( v21 1 ) */ /* > ( v31 v32 1 ) */ /* > ( v41 v42 v43 1 ) */ /* > ( v51 v52 v53 v54 1 ) */ /* > ( v61 v62 v63 v54 v65 ) */ /* > */ /* > */ /* > For each of the column blocks VB(i), an upper-triangular block */ /* > reflector TB(i) is computed. These blocks are stored as */ /* > a sequence of upper-triangular column blocks in the NB-by-N */ /* > matrix T. The size of each TB(i) block is NB-by-NB, except */ /* > for the last block, whose size is LAST_NB-by-LAST_NB. */ /* > */ /* > For example, if M=6, N=5 and NB=2, the matrix T is */ /* > */ /* > T = ( TB(1), TB(2), TB(3) ) = */ /* > */ /* > = ( t11 t12 t13 t14 t15 ) */ /* > ( t22 t24 ) */ /* > */ /* > */ /* > The M-by-M factor Q_out is given as a product of NOCB */ /* > unitary M-by-M matrices Q_out(i). */ /* > */ /* > Q_out = Q_out(1) * Q_out(2) * ... * Q_out(NOCB), */ /* > */ /* > where each matrix Q_out(i) is given by the WY-representation */ /* > using corresponding blocks from the matrices V and T: */ /* > */ /* > Q_out(i) = I - VB(i) * TB(i) * (VB(i))**T, */ /* > */ /* > where I is the identity matrix. Here is the formula with matrix */ /* > dimensions: */ /* > */ /* > Q(i){M-by-M} = I{M-by-M} - */ /* > VB(i){M-by-INB} * TB(i){INB-by-INB} * (VB(i))**T {INB-by-M}, */ /* > */ /* > where INB = NB, except for the last block NOCB */ /* > for which INB=LAST_NB. */ /* > */ /* > ===== */ /* > NOTE: */ /* > ===== */ /* > */ /* > If Q_in is the result of doing a QR factorization */ /* > B = Q_in * R_in, then: */ /* > */ /* > B = (Q_out*S) * R_in = Q_out * (S * R_in) = O_out * R_out. */ /* > */ /* > So if one wants to interpret Q_out as the result */ /* > of the QR factorization of B, then corresponding R_out */ /* > should be obtained by R_out = S * R_in, i.e. some rows of R_in */ /* > should be multiplied by -1. */ /* > */ /* > For the details of the algorithm, see [1]. */ /* > */ /* > [1] "Reconstructing Householder vectors from tall-skinny QR", */ /* > G. Ballard, J. Demmel, L. Grigori, M. Jacquelin, H.D. Nguyen, */ /* > E. Solomonik, J. Parallel Distrib. Comput., */ /* > vol. 85, pp. 3-31, 2015. */ /* > \endverbatim */ /* > */ /* Authors: */ /* ======== */ /* > \author Univ. of Tennessee */ /* > \author Univ. of California Berkeley */ /* > \author Univ. of Colorado Denver */ /* > \author NAG Ltd. */ /* > \date November 2019 */ /* > \ingroup complex16OTHERcomputational */ /* > \par Contributors: */ /* ================== */ /* > */ /* > \verbatim */ /* > */ /* > November 2019, Igor Kozachenko, */ /* > Computer Science Division, */ /* > University of California, Berkeley */ /* > */ /* > \endverbatim */ /* ===================================================================== */ /* Subroutine */ int zunhr_col_(integer *m, integer *n, integer *nb, doublecomplex *a, integer *lda, doublecomplex *t, integer *ldt, doublecomplex *d__, integer *info) { /* System generated locals */ integer a_dim1, a_offset, t_dim1, t_offset, i__1, i__2, i__3, i__4, i__5; doublecomplex z__1; /* Local variables */ extern /* Subroutine */ int zlaunhr_col_getrfnp_(integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *); integer nplusone, i__, j, iinfo; extern /* Subroutine */ int zscal_(integer *, doublecomplex *, doublecomplex *, integer *), zcopy_(integer *, doublecomplex *, integer *, doublecomplex *, integer *), ztrsm_(char *, char *, char *, char *, integer *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *); integer jb; extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); integer jbtemp1, jbtemp2, jnb; /* -- LAPACK computational routine (version 3.9.0) -- */ /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ /* November 2019 */ /* ===================================================================== */ /* Test the input parameters */ /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1 * 1; a -= a_offset; t_dim1 = *ldt; t_offset = 1 + t_dim1 * 1; t -= t_offset; --d__; /* Function Body */ *info = 0; if (*m < 0) { *info = -1; } else if (*n < 0 || *n > *m) { *info = -2; } else if (*nb < 1) { *info = -3; } else if (*lda < f2cmax(1,*m)) { *info = -5; } else /* if(complicated condition) */ { /* Computing MAX */ i__1 = 1, i__2 = f2cmin(*nb,*n); if (*ldt < f2cmax(i__1,i__2)) { *info = -7; } } /* Handle error in the input parameters. */ if (*info != 0) { i__1 = -(*info); xerbla_("ZUNHR_COL", &i__1, (ftnlen)9); return 0; } /* Quick return if possible */ if (f2cmin(*m,*n) == 0) { return 0; } /* On input, the M-by-N matrix A contains the unitary */ /* M-by-N matrix Q_in. */ /* (1) Compute the unit lower-trapezoidal V (ones on the diagonal */ /* are not stored) by performing the "modified" LU-decomposition. */ /* Q_in - ( S ) = V * U = ( V1 ) * U, */ /* ( 0 ) ( V2 ) */ /* where 0 is an (M-N)-by-N zero matrix. */ /* (1-1) Factor V1 and U. */ zlaunhr_col_getrfnp_(n, n, &a[a_offset], lda, &d__[1], &iinfo); /* (1-2) Solve for V2. */ if (*m > *n) { i__1 = *m - *n; ztrsm_("R", "U", "N", "N", &i__1, n, &c_b1, &a[a_offset], lda, &a[*n + 1 + a_dim1], lda); } /* (2) Reconstruct the block reflector T stored in T(1:NB, 1:N) */ /* as a sequence of upper-triangular blocks with NB-size column */ /* blocking. */ /* Loop over the column blocks of size NB of the array A(1:M,1:N) */ /* and the array T(1:NB,1:N), JB is the column index of a column */ /* block, JNB is the column block size at each step JB. */ nplusone = *n + 1; i__1 = *n; i__2 = *nb; for (jb = 1; i__2 < 0 ? jb >= i__1 : jb <= i__1; jb += i__2) { /* (2-0) Determine the column block size JNB. */ /* Computing MIN */ i__3 = nplusone - jb; jnb = f2cmin(i__3,*nb); /* (2-1) Copy the upper-triangular part of the current JNB-by-JNB */ /* diagonal block U(JB) (of the N-by-N matrix U) stored */ /* in A(JB:JB+JNB-1,JB:JB+JNB-1) into the upper-triangular part */ /* of the current JNB-by-JNB block T(1:JNB,JB:JB+JNB-1) */ /* column-by-column, total JNB*(JNB+1)/2 elements. */ jbtemp1 = jb - 1; i__3 = jb + jnb - 1; for (j = jb; j <= i__3; ++j) { i__4 = j - jbtemp1; zcopy_(&i__4, &a[jb + j * a_dim1], &c__1, &t[j * t_dim1 + 1], & c__1); } /* (2-2) Perform on the upper-triangular part of the current */ /* JNB-by-JNB diagonal block U(JB) (of the N-by-N matrix U) stored */ /* in T(1:JNB,JB:JB+JNB-1) the following operation in place: */ /* (-1)*U(JB)*S(JB), i.e the result will be stored in the upper- */ /* triangular part of T(1:JNB,JB:JB+JNB-1). This multiplication */ /* of the JNB-by-JNB diagonal block U(JB) by the JNB-by-JNB */ /* diagonal block S(JB) of the N-by-N sign matrix S from the */ /* right means changing the sign of each J-th column of the block */ /* U(JB) according to the sign of the diagonal element of the block */ /* S(JB), i.e. S(J,J) that is stored in the array element D(J). */ i__3 = jb + jnb - 1; for (j = jb; j <= i__3; ++j) { i__4 = j; if (d__[i__4].r == 1. && d__[i__4].i == 0.) { i__4 = j - jbtemp1; z__1.r = -1., z__1.i = 0.; zscal_(&i__4, &z__1, &t[j * t_dim1 + 1], &c__1); } } /* (2-3) Perform the triangular solve for the current block */ /* matrix X(JB): */ /* X(JB) * (A(JB)**T) = B(JB), where: */ /* A(JB)**T is a JNB-by-JNB unit upper-triangular */ /* coefficient block, and A(JB)=V1(JB), which */ /* is a JNB-by-JNB unit lower-triangular block */ /* stored in A(JB:JB+JNB-1,JB:JB+JNB-1). */ /* The N-by-N matrix V1 is the upper part */ /* of the M-by-N lower-trapezoidal matrix V */ /* stored in A(1:M,1:N); */ /* B(JB) is a JNB-by-JNB upper-triangular right-hand */ /* side block, B(JB) = (-1)*U(JB)*S(JB), and */ /* B(JB) is stored in T(1:JNB,JB:JB+JNB-1); */ /* X(JB) is a JNB-by-JNB upper-triangular solution */ /* block, X(JB) is the upper-triangular block */ /* reflector T(JB), and X(JB) is stored */ /* in T(1:JNB,JB:JB+JNB-1). */ /* In other words, we perform the triangular solve for the */ /* upper-triangular block T(JB): */ /* T(JB) * (V1(JB)**T) = (-1)*U(JB)*S(JB). */ /* Even though the blocks X(JB) and B(JB) are upper- */ /* triangular, the routine ZTRSM will access all JNB**2 */ /* elements of the square T(1:JNB,JB:JB+JNB-1). Therefore, */ /* we need to set to zero the elements of the block */ /* T(1:JNB,JB:JB+JNB-1) below the diagonal before the call */ /* to ZTRSM. */ /* (2-3a) Set the elements to zero. */ jbtemp2 = jb - 2; i__3 = jb + jnb - 2; for (j = jb; j <= i__3; ++j) { i__4 = *nb; for (i__ = j - jbtemp2; i__ <= i__4; ++i__) { i__5 = i__ + j * t_dim1; t[i__5].r = 0., t[i__5].i = 0.; } } /* (2-3b) Perform the triangular solve. */ ztrsm_("R", "L", "C", "U", &jnb, &jnb, &c_b1, &a[jb + jb * a_dim1], lda, &t[jb * t_dim1 + 1], ldt); } return 0; /* End of ZUNHR_COL */ } /* zunhr_col__ */