#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 SLARFB_GETT */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download SLARFB_GETT + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE SLARFB_GETT( IDENT, M, N, K, T, LDT, A, LDA, B, LDB, */ /* $ WORK, LDWORK ) */ /* IMPLICIT NONE */ /* CHARACTER IDENT */ /* INTEGER K, LDA, LDB, LDT, LDWORK, M, N */ /* REAL A( LDA, * ), B( LDB, * ), T( LDT, * ), */ /* $ WORK( LDWORK, * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > SLARFB_GETT applies a real Householder block reflector H from the */ /* > left to a real (K+M)-by-N "triangular-pentagonal" matrix */ /* > composed of two block matrices: an upper trapezoidal K-by-N matrix A */ /* > stored in the array A, and a rectangular M-by-(N-K) matrix B, stored */ /* > in the array B. The block reflector H is stored in a compact */ /* > WY-representation, where the elementary reflectors are in the */ /* > arrays A, B and T. See Further Details section. */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \param[in] IDENT */ /* > \verbatim */ /* > IDENT is CHARACTER*1 */ /* > If IDENT = not 'I', or not 'i', then V1 is unit */ /* > lower-triangular and stored in the left K-by-K block of */ /* > the input matrix A, */ /* > If IDENT = 'I' or 'i', then V1 is an identity matrix and */ /* > not stored. */ /* > See Further Details section. */ /* > \endverbatim */ /* > */ /* > \param[in] M */ /* > \verbatim */ /* > M is INTEGER */ /* > The number of rows of the matrix B. */ /* > M >= 0. */ /* > \endverbatim */ /* > */ /* > \param[in] N */ /* > \verbatim */ /* > N is INTEGER */ /* > The number of columns of the matrices A and B. */ /* > N >= 0. */ /* > \endverbatim */ /* > */ /* > \param[in] K */ /* > \verbatim */ /* > K is INTEGER */ /* > The number or rows of the matrix A. */ /* > K is also order of the matrix T, i.e. the number of */ /* > elementary reflectors whose product defines the block */ /* > reflector. 0 <= K <= N. */ /* > \endverbatim */ /* > */ /* > \param[in] T */ /* > \verbatim */ /* > T is REAL array, dimension (LDT,K) */ /* > The upper-triangular K-by-K matrix T in the representation */ /* > of the block reflector. */ /* > \endverbatim */ /* > */ /* > \param[in] LDT */ /* > \verbatim */ /* > LDT is INTEGER */ /* > The leading dimension of the array T. LDT >= K. */ /* > \endverbatim */ /* > */ /* > \param[in,out] A */ /* > \verbatim */ /* > A is REAL array, dimension (LDA,N) */ /* > */ /* > On entry: */ /* > a) In the K-by-N upper-trapezoidal part A: input matrix A. */ /* > b) In the columns below the diagonal: columns of V1 */ /* > (ones are not stored on the diagonal). */ /* > */ /* > On exit: */ /* > A is overwritten by rectangular K-by-N product H*A. */ /* > */ /* > See Further Details section. */ /* > \endverbatim */ /* > */ /* > \param[in] LDA */ /* > \verbatim */ /* > LDB is INTEGER */ /* > The leading dimension of the array A. LDA >= f2cmax(1,K). */ /* > \endverbatim */ /* > */ /* > \param[in,out] B */ /* > \verbatim */ /* > B is REAL array, dimension (LDB,N) */ /* > */ /* > On entry: */ /* > a) In the M-by-(N-K) right block: input matrix B. */ /* > b) In the M-by-N left block: columns of V2. */ /* > */ /* > On exit: */ /* > B is overwritten by rectangular M-by-N product H*B. */ /* > */ /* > See Further Details section. */ /* > \endverbatim */ /* > */ /* > \param[in] LDB */ /* > \verbatim */ /* > LDB is INTEGER */ /* > The leading dimension of the array B. LDB >= f2cmax(1,M). */ /* > \endverbatim */ /* > */ /* > \param[out] WORK */ /* > \verbatim */ /* > WORK is REAL array, */ /* > dimension (LDWORK,f2cmax(K,N-K)) */ /* > \endverbatim */ /* > */ /* > \param[in] LDWORK */ /* > \verbatim */ /* > LDWORK is INTEGER */ /* > The leading dimension of the array WORK. LDWORK>=f2cmax(1,K). */ /* > */ /* > \endverbatim */ /* Authors: */ /* ======== */ /* > \author Univ. of Tennessee */ /* > \author Univ. of California Berkeley */ /* > \author Univ. of Colorado Denver */ /* > \author NAG Ltd. */ /* > \ingroup singleOTHERauxiliary */ /* > \par Contributors: */ /* ================== */ /* > */ /* > \verbatim */ /* > */ /* > November 2020, Igor Kozachenko, */ /* > Computer Science Division, */ /* > University of California, Berkeley */ /* > */ /* > \endverbatim */ /* > \par Further Details: */ /* ===================== */ /* > */ /* > \verbatim */ /* > */ /* > (1) Description of the Algebraic Operation. */ /* > */ /* > The matrix A is a K-by-N matrix composed of two column block */ /* > matrices, A1, which is K-by-K, and A2, which is K-by-(N-K): */ /* > A = ( A1, A2 ). */ /* > The matrix B is an M-by-N matrix composed of two column block */ /* > matrices, B1, which is M-by-K, and B2, which is M-by-(N-K): */ /* > B = ( B1, B2 ). */ /* > */ /* > Perform the operation: */ /* > */ /* > ( A_out ) := H * ( A_in ) = ( I - V * T * V**T ) * ( A_in ) = */ /* > ( B_out ) ( B_in ) ( B_in ) */ /* > = ( I - ( V1 ) * T * ( V1**T, V2**T ) ) * ( A_in ) */ /* > ( V2 ) ( B_in ) */ /* > On input: */ /* > */ /* > a) ( A_in ) consists of two block columns: */ /* > ( B_in ) */ /* > */ /* > ( A_in ) = (( A1_in ) ( A2_in )) = (( A1_in ) ( A2_in )) */ /* > ( B_in ) (( B1_in ) ( B2_in )) (( 0 ) ( B2_in )), */ /* > */ /* > where the column blocks are: */ /* > */ /* > ( A1_in ) is a K-by-K upper-triangular matrix stored in the */ /* > upper triangular part of the array A(1:K,1:K). */ /* > ( B1_in ) is an M-by-K rectangular ZERO matrix and not stored. */ /* > */ /* > ( A2_in ) is a K-by-(N-K) rectangular matrix stored */ /* > in the array A(1:K,K+1:N). */ /* > ( B2_in ) is an M-by-(N-K) rectangular matrix stored */ /* > in the array B(1:M,K+1:N). */ /* > */ /* > b) V = ( V1 ) */ /* > ( V2 ) */ /* > */ /* > where: */ /* > 1) if IDENT == 'I',V1 is a K-by-K identity matrix, not stored; */ /* > 2) if IDENT != 'I',V1 is a K-by-K unit lower-triangular matrix, */ /* > stored in the lower-triangular part of the array */ /* > A(1:K,1:K) (ones are not stored), */ /* > and V2 is an M-by-K rectangular stored the array B(1:M,1:K), */ /* > (because on input B1_in is a rectangular zero */ /* > matrix that is not stored and the space is */ /* > used to store V2). */ /* > */ /* > c) T is a K-by-K upper-triangular matrix stored */ /* > in the array T(1:K,1:K). */ /* > */ /* > On output: */ /* > */ /* > a) ( A_out ) consists of two block columns: */ /* > ( B_out ) */ /* > */ /* > ( A_out ) = (( A1_out ) ( A2_out )) */ /* > ( B_out ) (( B1_out ) ( B2_out )), */ /* > */ /* > where the column blocks are: */ /* > */ /* > ( A1_out ) is a K-by-K square matrix, or a K-by-K */ /* > upper-triangular matrix, if V1 is an */ /* > identity matrix. AiOut is stored in */ /* > the array A(1:K,1:K). */ /* > ( B1_out ) is an M-by-K rectangular matrix stored */ /* > in the array B(1:M,K:N). */ /* > */ /* > ( A2_out ) is a K-by-(N-K) rectangular matrix stored */ /* > in the array A(1:K,K+1:N). */ /* > ( B2_out ) is an M-by-(N-K) rectangular matrix stored */ /* > in the array B(1:M,K+1:N). */ /* > */ /* > */ /* > The operation above can be represented as the same operation */ /* > on each block column: */ /* > */ /* > ( A1_out ) := H * ( A1_in ) = ( I - V * T * V**T ) * ( A1_in ) */ /* > ( B1_out ) ( 0 ) ( 0 ) */ /* > */ /* > ( A2_out ) := H * ( A2_in ) = ( I - V * T * V**T ) * ( A2_in ) */ /* > ( B2_out ) ( B2_in ) ( B2_in ) */ /* > */ /* > If IDENT != 'I': */ /* > */ /* > The computation for column block 1: */ /* > */ /* > A1_out: = A1_in - V1*T*(V1**T)*A1_in */ /* > */ /* > B1_out: = - V2*T*(V1**T)*A1_in */ /* > */ /* > The computation for column block 2, which exists if N > K: */ /* > */ /* > A2_out: = A2_in - V1*T*( (V1**T)*A2_in + (V2**T)*B2_in ) */ /* > */ /* > B2_out: = B2_in - V2*T*( (V1**T)*A2_in + (V2**T)*B2_in ) */ /* > */ /* > If IDENT == 'I': */ /* > */ /* > The operation for column block 1: */ /* > */ /* > A1_out: = A1_in - V1*T**A1_in */ /* > */ /* > B1_out: = - V2*T**A1_in */ /* > */ /* > The computation for column block 2, which exists if N > K: */ /* > */ /* > A2_out: = A2_in - T*( A2_in + (V2**T)*B2_in ) */ /* > */ /* > B2_out: = B2_in - V2*T*( A2_in + (V2**T)*B2_in ) */ /* > */ /* > (2) Description of the Algorithmic Computation. */ /* > */ /* > In the first step, we compute column block 2, i.e. A2 and B2. */ /* > Here, we need to use the K-by-(N-K) rectangular workspace */ /* > matrix W2 that is of the same size as the matrix A2. */ /* > W2 is stored in the array WORK(1:K,1:(N-K)). */ /* > */ /* > In the second step, we compute column block 1, i.e. A1 and B1. */ /* > Here, we need to use the K-by-K square workspace matrix W1 */ /* > that is of the same size as the as the matrix A1. */ /* > W1 is stored in the array WORK(1:K,1:K). */ /* > */ /* > NOTE: Hence, in this routine, we need the workspace array WORK */ /* > only of size WORK(1:K,1:f2cmax(K,N-K)) so it can hold both W2 from */ /* > the first step and W1 from the second step. */ /* > */ /* > Case (A), when V1 is unit lower-triangular, i.e. IDENT != 'I', */ /* > more computations than in the Case (B). */ /* > */ /* > if( IDENT != 'I' ) then */ /* > if ( N > K ) then */ /* > (First Step - column block 2) */ /* > col2_(1) W2: = A2 */ /* > col2_(2) W2: = (V1**T) * W2 = (unit_lower_tr_of_(A1)**T) * W2 */ /* > col2_(3) W2: = W2 + (V2**T) * B2 = W2 + (B1**T) * B2 */ /* > col2_(4) W2: = T * W2 */ /* > col2_(5) B2: = B2 - V2 * W2 = B2 - B1 * W2 */ /* > col2_(6) W2: = V1 * W2 = unit_lower_tr_of_(A1) * W2 */ /* > col2_(7) A2: = A2 - W2 */ /* > else */ /* > (Second Step - column block 1) */ /* > col1_(1) W1: = A1 */ /* > col1_(2) W1: = (V1**T) * W1 = (unit_lower_tr_of_(A1)**T) * W1 */ /* > col1_(3) W1: = T * W1 */ /* > col1_(4) B1: = - V2 * W1 = - B1 * W1 */ /* > col1_(5) square W1: = V1 * W1 = unit_lower_tr_of_(A1) * W1 */ /* > col1_(6) square A1: = A1 - W1 */ /* > end if */ /* > end if */ /* > */ /* > Case (B), when V1 is an identity matrix, i.e. IDENT == 'I', */ /* > less computations than in the Case (A) */ /* > */ /* > if( IDENT == 'I' ) then */ /* > if ( N > K ) then */ /* > (First Step - column block 2) */ /* > col2_(1) W2: = A2 */ /* > col2_(3) W2: = W2 + (V2**T) * B2 = W2 + (B1**T) * B2 */ /* > col2_(4) W2: = T * W2 */ /* > col2_(5) B2: = B2 - V2 * W2 = B2 - B1 * W2 */ /* > col2_(7) A2: = A2 - W2 */ /* > else */ /* > (Second Step - column block 1) */ /* > col1_(1) W1: = A1 */ /* > col1_(3) W1: = T * W1 */ /* > col1_(4) B1: = - V2 * W1 = - B1 * W1 */ /* > col1_(6) upper-triangular_of_(A1): = A1 - W1 */ /* > end if */ /* > end if */ /* > */ /* > Combine these cases (A) and (B) together, this is the resulting */ /* > algorithm: */ /* > */ /* > if ( N > K ) then */ /* > */ /* > (First Step - column block 2) */ /* > */ /* > col2_(1) W2: = A2 */ /* > if( IDENT != 'I' ) then */ /* > col2_(2) W2: = (V1**T) * W2 */ /* > = (unit_lower_tr_of_(A1)**T) * W2 */ /* > end if */ /* > col2_(3) W2: = W2 + (V2**T) * B2 = W2 + (B1**T) * B2] */ /* > col2_(4) W2: = T * W2 */ /* > col2_(5) B2: = B2 - V2 * W2 = B2 - B1 * W2 */ /* > if( IDENT != 'I' ) then */ /* > col2_(6) W2: = V1 * W2 = unit_lower_tr_of_(A1) * W2 */ /* > end if */ /* > col2_(7) A2: = A2 - W2 */ /* > */ /* > else */ /* > */ /* > (Second Step - column block 1) */ /* > */ /* > col1_(1) W1: = A1 */ /* > if( IDENT != 'I' ) then */ /* > col1_(2) W1: = (V1**T) * W1 */ /* > = (unit_lower_tr_of_(A1)**T) * W1 */ /* > end if */ /* > col1_(3) W1: = T * W1 */ /* > col1_(4) B1: = - V2 * W1 = - B1 * W1 */ /* > if( IDENT != 'I' ) then */ /* > col1_(5) square W1: = V1 * W1 = unit_lower_tr_of_(A1) * W1 */ /* > col1_(6_a) below_diag_of_(A1): = - below_diag_of_(W1) */ /* > end if */ /* > col1_(6_b) up_tr_of_(A1): = up_tr_of_(A1) - up_tr_of_(W1) */ /* > */ /* > end if */ /* > */ /* > \endverbatim */ /* > */ /* ===================================================================== */ /* Subroutine */ int slarfb_gett_(char *ident, integer *m, integer *n, integer *k, real *t, integer *ldt, real *a, integer *lda, real *b, integer *ldb, real *work, integer *ldwork) { /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, t_dim1, t_offset, work_dim1, work_offset, i__1, i__2; /* Local variables */ integer i__, j; extern logical lsame_(char *, char *); extern /* Subroutine */ int sgemm_(char *, char *, integer *, integer *, integer *, real *, real *, integer *, real *, integer *, real *, real *, integer *), scopy_(integer *, real *, integer *, real *, integer *), strmm_(char *, char *, char *, char *, integer *, integer *, real *, real *, integer *, real *, integer *); logical lnotident; /* -- LAPACK auxiliary routine -- */ /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ /* ===================================================================== */ /* Quick return if possible */ /* Parameter adjustments */ t_dim1 = *ldt; t_offset = 1 + t_dim1 * 1; t -= t_offset; a_dim1 = *lda; a_offset = 1 + a_dim1 * 1; a -= a_offset; b_dim1 = *ldb; b_offset = 1 + b_dim1 * 1; b -= b_offset; work_dim1 = *ldwork; work_offset = 1 + work_dim1 * 1; work -= work_offset; /* Function Body */ if (*m < 0 || *n <= 0 || *k == 0 || *k > *n) { return 0; } lnotident = ! lsame_(ident, "I"); /* ------------------------------------------------------------------ */ /* First Step. Computation of the Column Block 2: */ /* ( A2 ) := H * ( A2 ) */ /* ( B2 ) ( B2 ) */ /* ------------------------------------------------------------------ */ if (*n > *k) { /* col2_(1) Compute W2: = A2. Therefore, copy A2 = A(1:K, K+1:N) */ /* into W2=WORK(1:K, 1:N-K) column-by-column. */ i__1 = *n - *k; for (j = 1; j <= i__1; ++j) { scopy_(k, &a[(*k + j) * a_dim1 + 1], &c__1, &work[j * work_dim1 + 1], &c__1); } if (lnotident) { /* col2_(2) Compute W2: = (V1**T) * W2 = (A1**T) * W2, */ /* V1 is not an identy matrix, but unit lower-triangular */ /* V1 stored in A1 (diagonal ones are not stored). */ i__1 = *n - *k; strmm_("L", "L", "T", "U", k, &i__1, &c_b9, &a[a_offset], lda, & work[work_offset], ldwork); } /* col2_(3) Compute W2: = W2 + (V2**T) * B2 = W2 + (B1**T) * B2 */ /* V2 stored in B1. */ if (*m > 0) { i__1 = *n - *k; sgemm_("T", "N", k, &i__1, m, &c_b9, &b[b_offset], ldb, &b[(*k + 1) * b_dim1 + 1], ldb, &c_b9, &work[work_offset], ldwork); } /* col2_(4) Compute W2: = T * W2, */ /* T is upper-triangular. */ i__1 = *n - *k; strmm_("L", "U", "N", "N", k, &i__1, &c_b9, &t[t_offset], ldt, &work[ work_offset], ldwork); /* col2_(5) Compute B2: = B2 - V2 * W2 = B2 - B1 * W2, */ /* V2 stored in B1. */ if (*m > 0) { i__1 = *n - *k; sgemm_("N", "N", m, &i__1, k, &c_b21, &b[b_offset], ldb, &work[ work_offset], ldwork, &c_b9, &b[(*k + 1) * b_dim1 + 1], ldb); } if (lnotident) { /* col2_(6) Compute W2: = V1 * W2 = A1 * W2, */ /* V1 is not an identity matrix, but unit lower-triangular, */ /* V1 stored in A1 (diagonal ones are not stored). */ i__1 = *n - *k; strmm_("L", "L", "N", "U", k, &i__1, &c_b9, &a[a_offset], lda, & work[work_offset], ldwork); } /* col2_(7) Compute A2: = A2 - W2 = */ /* = A(1:K, K+1:N-K) - WORK(1:K, 1:N-K), */ /* column-by-column. */ i__1 = *n - *k; for (j = 1; j <= i__1; ++j) { i__2 = *k; for (i__ = 1; i__ <= i__2; ++i__) { a[i__ + (*k + j) * a_dim1] -= work[i__ + j * work_dim1]; } } } /* ------------------------------------------------------------------ */ /* Second Step. Computation of the Column Block 1: */ /* ( A1 ) := H * ( A1 ) */ /* ( B1 ) ( 0 ) */ /* ------------------------------------------------------------------ */ /* col1_(1) Compute W1: = A1. Copy the upper-triangular */ /* A1 = A(1:K, 1:K) into the upper-triangular */ /* W1 = WORK(1:K, 1:K) column-by-column. */ i__1 = *k; for (j = 1; j <= i__1; ++j) { scopy_(&j, &a[j * a_dim1 + 1], &c__1, &work[j * work_dim1 + 1], &c__1) ; } /* Set the subdiagonal elements of W1 to zero column-by-column. */ i__1 = *k - 1; for (j = 1; j <= i__1; ++j) { i__2 = *k; for (i__ = j + 1; i__ <= i__2; ++i__) { work[i__ + j * work_dim1] = 0.f; } } if (lnotident) { /* col1_(2) Compute W1: = (V1**T) * W1 = (A1**T) * W1, */ /* V1 is not an identity matrix, but unit lower-triangular */ /* V1 stored in A1 (diagonal ones are not stored), */ /* W1 is upper-triangular with zeroes below the diagonal. */ strmm_("L", "L", "T", "U", k, k, &c_b9, &a[a_offset], lda, &work[ work_offset], ldwork); } /* col1_(3) Compute W1: = T * W1, */ /* T is upper-triangular, */ /* W1 is upper-triangular with zeroes below the diagonal. */ strmm_("L", "U", "N", "N", k, k, &c_b9, &t[t_offset], ldt, &work[ work_offset], ldwork); /* col1_(4) Compute B1: = - V2 * W1 = - B1 * W1, */ /* V2 = B1, W1 is upper-triangular with zeroes below the diagonal. */ if (*m > 0) { strmm_("R", "U", "N", "N", m, k, &c_b21, &work[work_offset], ldwork, & b[b_offset], ldb); } if (lnotident) { /* col1_(5) Compute W1: = V1 * W1 = A1 * W1, */ /* V1 is not an identity matrix, but unit lower-triangular */ /* V1 stored in A1 (diagonal ones are not stored), */ /* W1 is upper-triangular on input with zeroes below the diagonal, */ /* and square on output. */ strmm_("L", "L", "N", "U", k, k, &c_b9, &a[a_offset], lda, &work[ work_offset], ldwork); /* col1_(6) Compute A1: = A1 - W1 = A(1:K, 1:K) - WORK(1:K, 1:K) */ /* column-by-column. A1 is upper-triangular on input. */ /* If IDENT, A1 is square on output, and W1 is square, */ /* if NOT IDENT, A1 is upper-triangular on output, */ /* W1 is upper-triangular. */ /* col1_(6)_a Compute elements of A1 below the diagonal. */ i__1 = *k - 1; for (j = 1; j <= i__1; ++j) { i__2 = *k; for (i__ = j + 1; i__ <= i__2; ++i__) { a[i__ + j * a_dim1] = -work[i__ + j * work_dim1]; } } } /* col1_(6)_b Compute elements of A1 on and above the diagonal. */ i__1 = *k; for (j = 1; j <= i__1; ++j) { i__2 = j; for (i__ = 1; i__ <= i__2; ++i__) { a[i__ + j * a_dim1] -= work[i__ + j * work_dim1]; } } return 0; /* End of SLARFB_GETT */ } /* slarfb_gett__ */