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- #include <math.h>
- #include <stdlib.h>
- #include <string.h>
- #include <stdio.h>
- #include <complex.h>
- #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<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
- zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
- zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
- }
- } else {
- for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
- zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
- zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
- }
- }
- pCf(z) = zdotc;
- }
- #else
- _Complex float zdotc = 0.0;
- if (incx == 1 && incy == 1) {
- for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
- zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
- }
- } else {
- for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
- zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
- }
- }
- pCf(z) = zdotc;
- }
- #endif
- static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
- integer n = *n_, incx = *incx_, incy = *incy_, i;
- #ifdef _MSC_VER
- _Dcomplex zdotc = {0.0, 0.0};
- if (incx == 1 && incy == 1) {
- for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
- zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
- zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
- }
- } else {
- for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
- zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
- zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
- }
- }
- pCd(z) = zdotc;
- }
- #else
- _Complex double zdotc = 0.0;
- if (incx == 1 && incy == 1) {
- for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
- zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
- }
- } else {
- for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
- zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
- }
- }
- pCd(z) = zdotc;
- }
- #endif
- static inline void cdotu_(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<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
- zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
- zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
- }
- } else {
- for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
- zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
- zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
- }
- }
- pCf(z) = zdotc;
- }
- #else
- _Complex float zdotc = 0.0;
- if (incx == 1 && incy == 1) {
- for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
- zdotc += Cf(&x[i]) * Cf(&y[i]);
- }
- } else {
- for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
- zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
- }
- }
- pCf(z) = zdotc;
- }
- #endif
- static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
- integer n = *n_, incx = *incx_, incy = *incy_, i;
- #ifdef _MSC_VER
- _Dcomplex zdotc = {0.0, 0.0};
- if (incx == 1 && incy == 1) {
- for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
- zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
- zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
- }
- } else {
- for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
- zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
- zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
- }
- }
- pCd(z) = zdotc;
- }
- #else
- _Complex double zdotc = 0.0;
- if (incx == 1 && incy == 1) {
- for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
- zdotc += Cd(&x[i]) * Cd(&y[i]);
- }
- } else {
- for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
- zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
- }
- }
- pCd(z) = zdotc;
- }
- #endif
- /* -- translated by f2c (version 20000121).
- You must link the resulting object file with the libraries:
- -lf2c -lm (in that order)
- */
-
-
-
-
-
- /* Table of constant values */
-
- static doublereal c_b1 = 0.;
- static doublereal c_b15 = 1.;
- static integer c__1 = 1;
- static doublereal c_b44 = -1.;
-
- /* > \brief \b DTGSJA */
-
- /* =========== DOCUMENTATION =========== */
-
- /* Online html documentation available at */
- /* http://www.netlib.org/lapack/explore-html/ */
-
- /* > \htmlonly */
- /* > Download DTGSJA + dependencies */
- /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dtgsja.
- f"> */
- /* > [TGZ]</a> */
- /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dtgsja.
- f"> */
- /* > [ZIP]</a> */
- /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dtgsja.
- f"> */
- /* > [TXT]</a> */
- /* > \endhtmlonly */
-
- /* Definition: */
- /* =========== */
-
- /* SUBROUTINE DTGSJA( JOBU, JOBV, JOBQ, M, P, N, K, L, A, LDA, B, */
- /* LDB, TOLA, TOLB, ALPHA, BETA, U, LDU, V, LDV, */
- /* Q, LDQ, WORK, NCALL MYCYCLE, INFO ) */
-
- /* CHARACTER JOBQ, JOBU, JOBV */
- /* INTEGER INFO, K, L, LDA, LDB, LDQ, LDU, LDV, M, N, */
- /* $ NCALL MYCYCLE, P */
- /* DOUBLE PRECISION TOLA, TOLB */
- /* DOUBLE PRECISION A( LDA, * ), ALPHA( * ), B( LDB, * ), */
- /* $ BETA( * ), Q( LDQ, * ), U( LDU, * ), */
- /* $ V( LDV, * ), WORK( * ) */
-
-
- /* > \par Purpose: */
- /* ============= */
- /* > */
- /* > \verbatim */
- /* > */
- /* > DTGSJA computes the generalized singular value decomposition (GSVD) */
- /* > of two real upper triangular (or trapezoidal) matrices A and B. */
- /* > */
- /* > On entry, it is assumed that matrices A and B have the following */
- /* > forms, which may be obtained by the preprocessing subroutine DGGSVP */
- /* > from a general M-by-N matrix A and P-by-N matrix B: */
- /* > */
- /* > N-K-L K L */
- /* > A = K ( 0 A12 A13 ) if M-K-L >= 0; */
- /* > L ( 0 0 A23 ) */
- /* > M-K-L ( 0 0 0 ) */
- /* > */
- /* > N-K-L K L */
- /* > A = K ( 0 A12 A13 ) if M-K-L < 0; */
- /* > M-K ( 0 0 A23 ) */
- /* > */
- /* > N-K-L K L */
- /* > B = L ( 0 0 B13 ) */
- /* > P-L ( 0 0 0 ) */
- /* > */
- /* > where the K-by-K matrix A12 and L-by-L matrix B13 are nonsingular */
- /* > upper triangular; A23 is L-by-L upper triangular if M-K-L >= 0, */
- /* > otherwise A23 is (M-K)-by-L upper trapezoidal. */
- /* > */
- /* > On exit, */
- /* > */
- /* > U**T *A*Q = D1*( 0 R ), V**T *B*Q = D2*( 0 R ), */
- /* > */
- /* > where U, V and Q are orthogonal matrices. */
- /* > R is a nonsingular upper triangular matrix, and D1 and D2 are */
- /* > ``diagonal'' matrices, which are of the following structures: */
- /* > */
- /* > If M-K-L >= 0, */
- /* > */
- /* > K L */
- /* > D1 = K ( I 0 ) */
- /* > L ( 0 C ) */
- /* > M-K-L ( 0 0 ) */
- /* > */
- /* > K L */
- /* > D2 = L ( 0 S ) */
- /* > P-L ( 0 0 ) */
- /* > */
- /* > N-K-L K L */
- /* > ( 0 R ) = K ( 0 R11 R12 ) K */
- /* > L ( 0 0 R22 ) L */
- /* > */
- /* > where */
- /* > */
- /* > C = diag( ALPHA(K+1), ... , ALPHA(K+L) ), */
- /* > S = diag( BETA(K+1), ... , BETA(K+L) ), */
- /* > C**2 + S**2 = I. */
- /* > */
- /* > R is stored in A(1:K+L,N-K-L+1:N) on exit. */
- /* > */
- /* > If M-K-L < 0, */
- /* > */
- /* > K M-K K+L-M */
- /* > D1 = K ( I 0 0 ) */
- /* > M-K ( 0 C 0 ) */
- /* > */
- /* > K M-K K+L-M */
- /* > D2 = M-K ( 0 S 0 ) */
- /* > K+L-M ( 0 0 I ) */
- /* > P-L ( 0 0 0 ) */
- /* > */
- /* > N-K-L K M-K K+L-M */
- /* > ( 0 R ) = K ( 0 R11 R12 R13 ) */
- /* > M-K ( 0 0 R22 R23 ) */
- /* > K+L-M ( 0 0 0 R33 ) */
- /* > */
- /* > where */
- /* > C = diag( ALPHA(K+1), ... , ALPHA(M) ), */
- /* > S = diag( BETA(K+1), ... , BETA(M) ), */
- /* > C**2 + S**2 = I. */
- /* > */
- /* > R = ( R11 R12 R13 ) is stored in A(1:M, N-K-L+1:N) and R33 is stored */
- /* > ( 0 R22 R23 ) */
- /* > in B(M-K+1:L,N+M-K-L+1:N) on exit. */
- /* > */
- /* > The computation of the orthogonal transformation matrices U, V or Q */
- /* > is optional. These matrices may either be formed explicitly, or they */
- /* > may be postmultiplied into input matrices U1, V1, or Q1. */
- /* > \endverbatim */
-
- /* Arguments: */
- /* ========== */
-
- /* > \param[in] JOBU */
- /* > \verbatim */
- /* > JOBU is CHARACTER*1 */
- /* > = 'U': U must contain an orthogonal matrix U1 on entry, and */
- /* > the product U1*U is returned; */
- /* > = 'I': U is initialized to the unit matrix, and the */
- /* > orthogonal matrix U is returned; */
- /* > = 'N': U is not computed. */
- /* > \endverbatim */
- /* > */
- /* > \param[in] JOBV */
- /* > \verbatim */
- /* > JOBV is CHARACTER*1 */
- /* > = 'V': V must contain an orthogonal matrix V1 on entry, and */
- /* > the product V1*V is returned; */
- /* > = 'I': V is initialized to the unit matrix, and the */
- /* > orthogonal matrix V is returned; */
- /* > = 'N': V is not computed. */
- /* > \endverbatim */
- /* > */
- /* > \param[in] JOBQ */
- /* > \verbatim */
- /* > JOBQ is CHARACTER*1 */
- /* > = 'Q': Q must contain an orthogonal matrix Q1 on entry, and */
- /* > the product Q1*Q is returned; */
- /* > = 'I': Q is initialized to the unit matrix, and the */
- /* > orthogonal matrix Q is returned; */
- /* > = 'N': Q is not computed. */
- /* > \endverbatim */
- /* > */
- /* > \param[in] M */
- /* > \verbatim */
- /* > M is INTEGER */
- /* > The number of rows of the matrix A. M >= 0. */
- /* > \endverbatim */
- /* > */
- /* > \param[in] P */
- /* > \verbatim */
- /* > P is INTEGER */
- /* > The number of rows of the matrix B. P >= 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 */
- /* > \endverbatim */
- /* > */
- /* > \param[in] L */
- /* > \verbatim */
- /* > L is INTEGER */
- /* > */
- /* > K and L specify the subblocks in the input matrices A and B: */
- /* > A23 = A(K+1:MIN(K+L,M),N-L+1:N) and B13 = B(1:L,N-L+1:N) */
- /* > of A and B, whose GSVD is going to be computed by DTGSJA. */
- /* > See Further Details. */
- /* > \endverbatim */
- /* > */
- /* > \param[in,out] A */
- /* > \verbatim */
- /* > A is DOUBLE PRECISION array, dimension (LDA,N) */
- /* > On entry, the M-by-N matrix A. */
- /* > On exit, A(N-K+1:N,1:MIN(K+L,M) ) contains the triangular */
- /* > matrix R or part of R. See Purpose for details. */
- /* > \endverbatim */
- /* > */
- /* > \param[in] LDA */
- /* > \verbatim */
- /* > LDA is INTEGER */
- /* > The leading dimension of the array A. LDA >= f2cmax(1,M). */
- /* > \endverbatim */
- /* > */
- /* > \param[in,out] B */
- /* > \verbatim */
- /* > B is DOUBLE PRECISION array, dimension (LDB,N) */
- /* > On entry, the P-by-N matrix B. */
- /* > On exit, if necessary, B(M-K+1:L,N+M-K-L+1:N) contains */
- /* > a part of R. See Purpose for details. */
- /* > \endverbatim */
- /* > */
- /* > \param[in] LDB */
- /* > \verbatim */
- /* > LDB is INTEGER */
- /* > The leading dimension of the array B. LDB >= f2cmax(1,P). */
- /* > \endverbatim */
- /* > */
- /* > \param[in] TOLA */
- /* > \verbatim */
- /* > TOLA is DOUBLE PRECISION */
- /* > \endverbatim */
- /* > */
- /* > \param[in] TOLB */
- /* > \verbatim */
- /* > TOLB is DOUBLE PRECISION */
- /* > */
- /* > TOLA and TOLB are the convergence criteria for the Jacobi- */
- /* > Kogbetliantz iteration procedure. Generally, they are the */
- /* > same as used in the preprocessing step, say */
- /* > TOLA = f2cmax(M,N)*norm(A)*MAZHEPS, */
- /* > TOLB = f2cmax(P,N)*norm(B)*MAZHEPS. */
- /* > \endverbatim */
- /* > */
- /* > \param[out] ALPHA */
- /* > \verbatim */
- /* > ALPHA is DOUBLE PRECISION array, dimension (N) */
- /* > \endverbatim */
- /* > */
- /* > \param[out] BETA */
- /* > \verbatim */
- /* > BETA is DOUBLE PRECISION array, dimension (N) */
- /* > */
- /* > On exit, ALPHA and BETA contain the generalized singular */
- /* > value pairs of A and B; */
- /* > ALPHA(1:K) = 1, */
- /* > BETA(1:K) = 0, */
- /* > and if M-K-L >= 0, */
- /* > ALPHA(K+1:K+L) = diag(C), */
- /* > BETA(K+1:K+L) = diag(S), */
- /* > or if M-K-L < 0, */
- /* > ALPHA(K+1:M)= C, ALPHA(M+1:K+L)= 0 */
- /* > BETA(K+1:M) = S, BETA(M+1:K+L) = 1. */
- /* > Furthermore, if K+L < N, */
- /* > ALPHA(K+L+1:N) = 0 and */
- /* > BETA(K+L+1:N) = 0. */
- /* > \endverbatim */
- /* > */
- /* > \param[in,out] U */
- /* > \verbatim */
- /* > U is DOUBLE PRECISION array, dimension (LDU,M) */
- /* > On entry, if JOBU = 'U', U must contain a matrix U1 (usually */
- /* > the orthogonal matrix returned by DGGSVP). */
- /* > On exit, */
- /* > if JOBU = 'I', U contains the orthogonal matrix U; */
- /* > if JOBU = 'U', U contains the product U1*U. */
- /* > If JOBU = 'N', U is not referenced. */
- /* > \endverbatim */
- /* > */
- /* > \param[in] LDU */
- /* > \verbatim */
- /* > LDU is INTEGER */
- /* > The leading dimension of the array U. LDU >= f2cmax(1,M) if */
- /* > JOBU = 'U'; LDU >= 1 otherwise. */
- /* > \endverbatim */
- /* > */
- /* > \param[in,out] V */
- /* > \verbatim */
- /* > V is DOUBLE PRECISION array, dimension (LDV,P) */
- /* > On entry, if JOBV = 'V', V must contain a matrix V1 (usually */
- /* > the orthogonal matrix returned by DGGSVP). */
- /* > On exit, */
- /* > if JOBV = 'I', V contains the orthogonal matrix V; */
- /* > if JOBV = 'V', V contains the product V1*V. */
- /* > If JOBV = 'N', V is not referenced. */
- /* > \endverbatim */
- /* > */
- /* > \param[in] LDV */
- /* > \verbatim */
- /* > LDV is INTEGER */
- /* > The leading dimension of the array V. LDV >= f2cmax(1,P) if */
- /* > JOBV = 'V'; LDV >= 1 otherwise. */
- /* > \endverbatim */
- /* > */
- /* > \param[in,out] Q */
- /* > \verbatim */
- /* > Q is DOUBLE PRECISION array, dimension (LDQ,N) */
- /* > On entry, if JOBQ = 'Q', Q must contain a matrix Q1 (usually */
- /* > the orthogonal matrix returned by DGGSVP). */
- /* > On exit, */
- /* > if JOBQ = 'I', Q contains the orthogonal matrix Q; */
- /* > if JOBQ = 'Q', Q contains the product Q1*Q. */
- /* > If JOBQ = 'N', Q is not referenced. */
- /* > \endverbatim */
- /* > */
- /* > \param[in] LDQ */
- /* > \verbatim */
- /* > LDQ is INTEGER */
- /* > The leading dimension of the array Q. LDQ >= f2cmax(1,N) if */
- /* > JOBQ = 'Q'; LDQ >= 1 otherwise. */
- /* > \endverbatim */
- /* > */
- /* > \param[out] WORK */
- /* > \verbatim */
- /* > WORK is DOUBLE PRECISION array, dimension (2*N) */
- /* > \endverbatim */
- /* > */
- /* > \param[out] NCALL MYCYCLE */
- /* > \verbatim */
- /* > NCALL MYCYCLE is INTEGER */
- /* > The number of cycles required for convergence. */
- /* > \endverbatim */
- /* > */
- /* > \param[out] INFO */
- /* > \verbatim */
- /* > INFO is INTEGER */
- /* > = 0: successful exit */
- /* > < 0: if INFO = -i, the i-th argument had an illegal value. */
- /* > = 1: the procedure does not converge after MAXIT cycles. */
- /* > \endverbatim */
- /* > */
- /* > \verbatim */
- /* > Internal Parameters */
- /* > =================== */
- /* > */
- /* > MAXIT INTEGER */
- /* > MAXIT specifies the total loops that the iterative procedure */
- /* > may take. If after MAXIT cycles, the routine fails to */
- /* > converge, we return INFO = 1. */
- /* > \endverbatim */
-
- /* Authors: */
- /* ======== */
-
- /* > \author Univ. of Tennessee */
- /* > \author Univ. of California Berkeley */
- /* > \author Univ. of Colorado Denver */
- /* > \author NAG Ltd. */
-
- /* > \date December 2016 */
-
- /* > \ingroup doubleOTHERcomputational */
-
- /* > \par Further Details: */
- /* ===================== */
- /* > */
- /* > \verbatim */
- /* > */
- /* > DTGSJA essentially uses a variant of Kogbetliantz algorithm to reduce */
- /* > f2cmin(L,M-K)-by-L triangular (or trapezoidal) matrix A23 and L-by-L */
- /* > matrix B13 to the form: */
- /* > */
- /* > U1**T *A13*Q1 = C1*R1; V1**T *B13*Q1 = S1*R1, */
- /* > */
- /* > where U1, V1 and Q1 are orthogonal matrix, and Z**T is the transpose */
- /* > of Z. C1 and S1 are diagonal matrices satisfying */
- /* > */
- /* > C1**2 + S1**2 = I, */
- /* > */
- /* > and R1 is an L-by-L nonsingular upper triangular matrix. */
- /* > \endverbatim */
- /* > */
- /* ===================================================================== */
- /* Subroutine */ void dtgsja_(char *jobu, char *jobv, char *jobq, integer *m,
- integer *p, integer *n, integer *k, integer *l, doublereal *a,
- integer *lda, doublereal *b, integer *ldb, doublereal *tola,
- doublereal *tolb, doublereal *alpha, doublereal *beta, doublereal *u,
- integer *ldu, doublereal *v, integer *ldv, doublereal *q, integer *
- ldq, doublereal *work, integer *ncallmycycle, integer *info)
- {
- /* System generated locals */
- integer a_dim1, a_offset, b_dim1, b_offset, q_dim1, q_offset, u_dim1,
- u_offset, v_dim1, v_offset, i__1, i__2, i__3, i__4;
- doublereal d__1;
-
- /* Local variables */
- extern /* Subroutine */ void drot_(integer *, doublereal *, integer *,
- doublereal *, integer *, doublereal *, doublereal *);
- integer kcallmycycle, i__, j;
- doublereal gamma;
- extern /* Subroutine */ void dscal_(integer *, doublereal *, doublereal *,
- integer *);
- extern logical lsame_(char *, char *);
- extern /* Subroutine */ void dcopy_(integer *, doublereal *, integer *,
- doublereal *, integer *);
- doublereal a1;
- logical initq;
- doublereal a2, a3, b1;
- logical initu, initv, wantq, upper;
- doublereal b2, b3;
- logical wantu, wantv;
- doublereal error, ssmin;
- extern /* Subroutine */ void dlags2_(logical *, doublereal *, doublereal *,
- doublereal *, doublereal *, doublereal *, doublereal *,
- doublereal *, doublereal *, doublereal *, doublereal *,
- doublereal *, doublereal *), dlapll_(integer *, doublereal *,
- integer *, doublereal *, integer *, doublereal *), dlartg_(
- doublereal *, doublereal *, doublereal *, doublereal *,
- doublereal *), dlaset_(char *, integer *, integer *, doublereal *,
- doublereal *, doublereal *, integer *);
- extern int xerbla_(char *, integer *, ftnlen);
- // extern integer myhuge_(doublereal *);
- doublereal csq, csu, csv, snq, rwk, snu, snv;
-
-
- /* -- LAPACK computational 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 */
-
-
- /* ===================================================================== */
-
-
-
- /* Decode and test the input parameters */
-
- /* Parameter adjustments */
- a_dim1 = *lda;
- a_offset = 1 + a_dim1 * 1;
- a -= a_offset;
- b_dim1 = *ldb;
- b_offset = 1 + b_dim1 * 1;
- b -= b_offset;
- --alpha;
- --beta;
- u_dim1 = *ldu;
- u_offset = 1 + u_dim1 * 1;
- u -= u_offset;
- v_dim1 = *ldv;
- v_offset = 1 + v_dim1 * 1;
- v -= v_offset;
- q_dim1 = *ldq;
- q_offset = 1 + q_dim1 * 1;
- q -= q_offset;
- --work;
-
- /* Function Body */
- initu = lsame_(jobu, "I");
- wantu = initu || lsame_(jobu, "U");
-
- initv = lsame_(jobv, "I");
- wantv = initv || lsame_(jobv, "V");
-
- initq = lsame_(jobq, "I");
- wantq = initq || lsame_(jobq, "Q");
-
- *info = 0;
- if (! (initu || wantu || lsame_(jobu, "N"))) {
- *info = -1;
- } else if (! (initv || wantv || lsame_(jobv, "N")))
- {
- *info = -2;
- } else if (! (initq || wantq || lsame_(jobq, "N")))
- {
- *info = -3;
- } else if (*m < 0) {
- *info = -4;
- } else if (*p < 0) {
- *info = -5;
- } else if (*n < 0) {
- *info = -6;
- } else if (*lda < f2cmax(1,*m)) {
- *info = -10;
- } else if (*ldb < f2cmax(1,*p)) {
- *info = -12;
- } else if (*ldu < 1 || wantu && *ldu < *m) {
- *info = -18;
- } else if (*ldv < 1 || wantv && *ldv < *p) {
- *info = -20;
- } else if (*ldq < 1 || wantq && *ldq < *n) {
- *info = -22;
- }
- if (*info != 0) {
- i__1 = -(*info);
- xerbla_("DTGSJA", &i__1, (ftnlen)6);
- return;
- }
-
- /* Initialize U, V and Q, if necessary */
-
- if (initu) {
- dlaset_("Full", m, m, &c_b1, &c_b15, &u[u_offset], ldu);
- }
- if (initv) {
- dlaset_("Full", p, p, &c_b1, &c_b15, &v[v_offset], ldv);
- }
- if (initq) {
- dlaset_("Full", n, n, &c_b1, &c_b15, &q[q_offset], ldq);
- }
-
- /* Loop until convergence */
-
- upper = FALSE_;
- for (kcallmycycle = 1; kcallmycycle <= 40; ++kcallmycycle) {
-
- upper = ! upper;
-
- i__1 = *l - 1;
- for (i__ = 1; i__ <= i__1; ++i__) {
- i__2 = *l;
- for (j = i__ + 1; j <= i__2; ++j) {
-
- a1 = 0.;
- a2 = 0.;
- a3 = 0.;
- if (*k + i__ <= *m) {
- a1 = a[*k + i__ + (*n - *l + i__) * a_dim1];
- }
- if (*k + j <= *m) {
- a3 = a[*k + j + (*n - *l + j) * a_dim1];
- }
-
- b1 = b[i__ + (*n - *l + i__) * b_dim1];
- b3 = b[j + (*n - *l + j) * b_dim1];
-
- if (upper) {
- if (*k + i__ <= *m) {
- a2 = a[*k + i__ + (*n - *l + j) * a_dim1];
- }
- b2 = b[i__ + (*n - *l + j) * b_dim1];
- } else {
- if (*k + j <= *m) {
- a2 = a[*k + j + (*n - *l + i__) * a_dim1];
- }
- b2 = b[j + (*n - *l + i__) * b_dim1];
- }
-
- dlags2_(&upper, &a1, &a2, &a3, &b1, &b2, &b3, &csu, &snu, &
- csv, &snv, &csq, &snq);
-
- /* Update (K+I)-th and (K+J)-th rows of matrix A: U**T *A */
-
- if (*k + j <= *m) {
- drot_(l, &a[*k + j + (*n - *l + 1) * a_dim1], lda, &a[*k
- + i__ + (*n - *l + 1) * a_dim1], lda, &csu, &snu);
- }
-
- /* Update I-th and J-th rows of matrix B: V**T *B */
-
- drot_(l, &b[j + (*n - *l + 1) * b_dim1], ldb, &b[i__ + (*n - *
- l + 1) * b_dim1], ldb, &csv, &snv);
-
- /* Update (N-L+I)-th and (N-L+J)-th columns of matrices */
- /* A and B: A*Q and B*Q */
-
- /* Computing MIN */
- i__4 = *k + *l;
- i__3 = f2cmin(i__4,*m);
- drot_(&i__3, &a[(*n - *l + j) * a_dim1 + 1], &c__1, &a[(*n - *
- l + i__) * a_dim1 + 1], &c__1, &csq, &snq);
-
- drot_(l, &b[(*n - *l + j) * b_dim1 + 1], &c__1, &b[(*n - *l +
- i__) * b_dim1 + 1], &c__1, &csq, &snq);
-
- if (upper) {
- if (*k + i__ <= *m) {
- a[*k + i__ + (*n - *l + j) * a_dim1] = 0.;
- }
- b[i__ + (*n - *l + j) * b_dim1] = 0.;
- } else {
- if (*k + j <= *m) {
- a[*k + j + (*n - *l + i__) * a_dim1] = 0.;
- }
- b[j + (*n - *l + i__) * b_dim1] = 0.;
- }
-
- /* Update orthogonal matrices U, V, Q, if desired. */
-
- if (wantu && *k + j <= *m) {
- drot_(m, &u[(*k + j) * u_dim1 + 1], &c__1, &u[(*k + i__) *
- u_dim1 + 1], &c__1, &csu, &snu);
- }
-
- if (wantv) {
- drot_(p, &v[j * v_dim1 + 1], &c__1, &v[i__ * v_dim1 + 1],
- &c__1, &csv, &snv);
- }
-
- if (wantq) {
- drot_(n, &q[(*n - *l + j) * q_dim1 + 1], &c__1, &q[(*n - *
- l + i__) * q_dim1 + 1], &c__1, &csq, &snq);
- }
-
- /* L10: */
- }
- /* L20: */
- }
-
- if (! upper) {
-
- /* The matrices A13 and B13 were lower triangular at the start */
- /* of the cycle, and are now upper triangular. */
-
- /* Convergence test: test the parallelism of the corresponding */
- /* rows of A and B. */
-
- error = 0.;
- /* Computing MIN */
- i__2 = *l, i__3 = *m - *k;
- i__1 = f2cmin(i__2,i__3);
- for (i__ = 1; i__ <= i__1; ++i__) {
- i__2 = *l - i__ + 1;
- dcopy_(&i__2, &a[*k + i__ + (*n - *l + i__) * a_dim1], lda, &
- work[1], &c__1);
- i__2 = *l - i__ + 1;
- dcopy_(&i__2, &b[i__ + (*n - *l + i__) * b_dim1], ldb, &work[*
- l + 1], &c__1);
- i__2 = *l - i__ + 1;
- dlapll_(&i__2, &work[1], &c__1, &work[*l + 1], &c__1, &ssmin);
- error = f2cmax(error,ssmin);
- /* L30: */
- }
-
- if (abs(error) <= f2cmin(*tola,*tolb)) {
- goto L50;
- }
- }
-
- /* End of cycle loop */
-
- /* L40: */
- }
-
- /* The algorithm has not converged after MAXIT cycles. */
-
- *info = 1;
- goto L100;
-
- L50:
-
- /* If ERROR <= MIN(TOLA,TOLB), then the algorithm has converged. */
- /* Compute the generalized singular value pairs (ALPHA, BETA), and */
- /* set the triangular matrix R to array A. */
-
- i__1 = *k;
- for (i__ = 1; i__ <= i__1; ++i__) {
- alpha[i__] = 1.;
- beta[i__] = 0.;
- /* L60: */
- }
-
- /* Computing MIN */
- i__2 = *l, i__3 = *m - *k;
- i__1 = f2cmin(i__2,i__3);
- for (i__ = 1; i__ <= i__1; ++i__) {
-
- a1 = a[*k + i__ + (*n - *l + i__) * a_dim1];
- b1 = b[i__ + (*n - *l + i__) * b_dim1];
- gamma = b1 / a1;
-
- if (gamma <= (doublereal) myhuge_(&c_b1) && gamma >= -((doublereal)
- myhuge_(&c_b1))) {
-
- /* change sign if necessary */
-
- if (gamma < 0.) {
- i__2 = *l - i__ + 1;
- dscal_(&i__2, &c_b44, &b[i__ + (*n - *l + i__) * b_dim1], ldb)
- ;
- if (wantv) {
- dscal_(p, &c_b44, &v[i__ * v_dim1 + 1], &c__1);
- }
- }
-
- d__1 = abs(gamma);
- dlartg_(&d__1, &c_b15, &beta[*k + i__], &alpha[*k + i__], &rwk);
-
- if (alpha[*k + i__] >= beta[*k + i__]) {
- i__2 = *l - i__ + 1;
- d__1 = 1. / alpha[*k + i__];
- dscal_(&i__2, &d__1, &a[*k + i__ + (*n - *l + i__) * a_dim1],
- lda);
- } else {
- i__2 = *l - i__ + 1;
- d__1 = 1. / beta[*k + i__];
- dscal_(&i__2, &d__1, &b[i__ + (*n - *l + i__) * b_dim1], ldb);
- i__2 = *l - i__ + 1;
- dcopy_(&i__2, &b[i__ + (*n - *l + i__) * b_dim1], ldb, &a[*k
- + i__ + (*n - *l + i__) * a_dim1], lda);
- }
-
- } else {
-
- alpha[*k + i__] = 0.;
- beta[*k + i__] = 1.;
- i__2 = *l - i__ + 1;
- dcopy_(&i__2, &b[i__ + (*n - *l + i__) * b_dim1], ldb, &a[*k +
- i__ + (*n - *l + i__) * a_dim1], lda);
-
- }
-
- /* L70: */
- }
-
- /* Post-assignment */
-
- i__1 = *k + *l;
- for (i__ = *m + 1; i__ <= i__1; ++i__) {
- alpha[i__] = 0.;
- beta[i__] = 1.;
- /* L80: */
- }
-
- if (*k + *l < *n) {
- i__1 = *n;
- for (i__ = *k + *l + 1; i__ <= i__1; ++i__) {
- alpha[i__] = 0.;
- beta[i__] = 0.;
- /* L90: */
- }
- }
-
- L100:
- *ncallmycycle = kcallmycycle;
- return;
-
- /* End of DTGSJA */
-
- } /* dtgsja_ */
-
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