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OpenBLAS/lapack-netlib/SRC/DEPRECATED/dggsvd.c

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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 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]/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);}
#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++ */
/* -- 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 integer c__1 = 1;
/* > \brief <b> DGGSVD computes the singular value decomposition (SVD) for OTHER matrices</b> */
/* =========== DOCUMENTATION =========== */
/* Online html documentation available at */
/* http://www.netlib.org/lapack/explore-html/ */
/* > \htmlonly */
/* > Download DGGSVD + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dggsvd.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dggsvd.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dggsvd.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */
/* Definition: */
/* =========== */
/* SUBROUTINE DGGSVD( JOBU, JOBV, JOBQ, M, N, P, K, L, A, LDA, B, */
/* LDB, ALPHA, BETA, U, LDU, V, LDV, Q, LDQ, WORK, */
/* IWORK, INFO ) */
/* CHARACTER JOBQ, JOBU, JOBV */
/* INTEGER INFO, K, L, LDA, LDB, LDQ, LDU, LDV, M, N, P */
/* INTEGER IWORK( * ) */
/* DOUBLE PRECISION A( LDA, * ), ALPHA( * ), B( LDB, * ), */
/* $ BETA( * ), Q( LDQ, * ), U( LDU, * ), */
/* $ V( LDV, * ), WORK( * ) */
/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > This routine is deprecated and has been replaced by routine DGGSVD3. */
/* > */
/* > DGGSVD computes the generalized singular value decomposition (GSVD) */
/* > of an M-by-N real matrix A and P-by-N real matrix B: */
/* > */
/* > U**T*A*Q = D1*( 0 R ), V**T*B*Q = D2*( 0 R ) */
/* > */
/* > where U, V and Q are orthogonal matrices. */
/* > Let K+L = the effective numerical rank of the matrix (A**T,B**T)**T, */
/* > then R is a K+L-by-K+L nonsingular upper triangular matrix, D1 and */
/* > D2 are M-by-(K+L) and P-by-(K+L) "diagonal" matrices and of the */
/* > following structures, respectively: */
/* > */
/* > 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 ) */
/* > L ( 0 0 R22 ) */
/* > */
/* > 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. */
/* > */
/* > (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 routine computes C, S, R, and optionally the orthogonal */
/* > transformation matrices U, V and Q. */
/* > */
/* > In particular, if B is an N-by-N nonsingular matrix, then the GSVD of */
/* > A and B implicitly gives the SVD of A*inv(B): */
/* > A*inv(B) = U*(D1*inv(D2))*V**T. */
/* > If ( A**T,B**T)**T has orthonormal columns, then the GSVD of A and B is */
/* > also equal to the CS decomposition of A and B. Furthermore, the GSVD */
/* > can be used to derive the solution of the eigenvalue problem: */
/* > A**T*A x = lambda* B**T*B x. */
/* > In some literature, the GSVD of A and B is presented in the form */
/* > U**T*A*X = ( 0 D1 ), V**T*B*X = ( 0 D2 ) */
/* > where U and V are orthogonal and X is nonsingular, D1 and D2 are */
/* > ``diagonal''. The former GSVD form can be converted to the latter */
/* > form by taking the nonsingular matrix X as */
/* > */
/* > X = Q*( I 0 ) */
/* > ( 0 inv(R) ). */
/* > \endverbatim */
/* Arguments: */
/* ========== */
/* > \param[in] JOBU */
/* > \verbatim */
/* > JOBU is CHARACTER*1 */
/* > = 'U': Orthogonal matrix U is computed; */
/* > = 'N': U is not computed. */
/* > \endverbatim */
/* > */
/* > \param[in] JOBV */
/* > \verbatim */
/* > JOBV is CHARACTER*1 */
/* > = 'V': Orthogonal matrix V is computed; */
/* > = 'N': V is not computed. */
/* > \endverbatim */
/* > */
/* > \param[in] JOBQ */
/* > \verbatim */
/* > JOBQ is CHARACTER*1 */
/* > = 'Q': Orthogonal matrix Q is computed; */
/* > = '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] N */
/* > \verbatim */
/* > N is INTEGER */
/* > The number of columns of the matrices A and B. N >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in] P */
/* > \verbatim */
/* > P is INTEGER */
/* > The number of rows of the matrix B. P >= 0. */
/* > \endverbatim */
/* > */
/* > \param[out] K */
/* > \verbatim */
/* > K is INTEGER */
/* > \endverbatim */
/* > */
/* > \param[out] L */
/* > \verbatim */
/* > L is INTEGER */
/* > */
/* > On exit, K and L specify the dimension of the subblocks */
/* > described in Purpose. */
/* > K + L = effective numerical rank of (A**T,B**T)**T. */
/* > \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 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, B contains the triangular matrix R if M-K-L < 0. */
/* > 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[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) = C, */
/* > BETA(K+1:K+L) = 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 */
/* > and */
/* > ALPHA(K+L+1:N) = 0 */
/* > BETA(K+L+1:N) = 0 */
/* > \endverbatim */
/* > */
/* > \param[out] U */
/* > \verbatim */
/* > U is DOUBLE PRECISION array, dimension (LDU,M) */
/* > If JOBU = 'U', U contains the M-by-M orthogonal matrix 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[out] V */
/* > \verbatim */
/* > V is DOUBLE PRECISION array, dimension (LDV,P) */
/* > If JOBV = 'V', V contains the P-by-P orthogonal matrix 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[out] Q */
/* > \verbatim */
/* > Q is DOUBLE PRECISION array, dimension (LDQ,N) */
/* > If JOBQ = 'Q', Q contains the N-by-N orthogonal matrix 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 (f2cmax(3*N,M,P)+N) */
/* > \endverbatim */
/* > */
/* > \param[out] IWORK */
/* > \verbatim */
/* > IWORK is INTEGER array, dimension (N) */
/* > On exit, IWORK stores the sorting information. More */
/* > precisely, the following loop will sort ALPHA */
/* > for I = K+1, f2cmin(M,K+L) */
/* > swap ALPHA(I) and ALPHA(IWORK(I)) */
/* > endfor */
/* > such that ALPHA(1) >= ALPHA(2) >= ... >= ALPHA(N). */
/* > \endverbatim */
/* > */
/* > \param[out] INFO */
/* > \verbatim */
/* > INFO is INTEGER */
/* > = 0: successful exit */
/* > < 0: if INFO = -i, the i-th argument had an illegal value. */
/* > > 0: if INFO = 1, the Jacobi-type procedure failed to */
/* > converge. For further details, see subroutine DTGSJA. */
/* > \endverbatim */
/* > \par Internal Parameters: */
/* ========================= */
/* > */
/* > \verbatim */
/* > TOLA DOUBLE PRECISION */
/* > TOLB DOUBLE PRECISION */
/* > TOLA and TOLB are the thresholds to determine the effective */
/* > rank of (A',B')**T. Generally, they are set to */
/* > TOLA = MAX(M,N)*norm(A)*MAZHEPS, */
/* > TOLB = MAX(P,N)*norm(B)*MAZHEPS. */
/* > The size of TOLA and TOLB may affect the size of backward */
/* > errors of the decomposition. */
/* > \endverbatim */
/* Authors: */
/* ======== */
/* > \author Univ. of Tennessee */
/* > \author Univ. of California Berkeley */
/* > \author Univ. of Colorado Denver */
/* > \author NAG Ltd. */
/* > \date December 2016 */
/* > \ingroup doubleOTHERsing */
/* > \par Contributors: */
/* ================== */
/* > */
/* > Ming Gu and Huan Ren, Computer Science Division, University of */
/* > California at Berkeley, USA */
/* > */
/* ===================================================================== */
/* Subroutine */ void dggsvd_(char *jobu, char *jobv, char *jobq, integer *m,
integer *n, integer *p, integer *k, integer *l, doublereal *a,
integer *lda, doublereal *b, integer *ldb, doublereal *alpha,
doublereal *beta, doublereal *u, integer *ldu, doublereal *v, integer
*ldv, doublereal *q, integer *ldq, doublereal *work, integer *iwork,
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;
/* Local variables */
integer ibnd;
doublereal tola;
integer isub;
doublereal tolb, unfl, temp, smax;
integer ncallmycycle, i__, j;
extern logical lsame_(char *, char *);
doublereal anorm, bnorm;
extern /* Subroutine */ void dcopy_(integer *, doublereal *, integer *,
doublereal *, integer *);
logical wantq, wantu, wantv;
extern doublereal dlamch_(char *), dlange_(char *, integer *,
integer *, doublereal *, integer *, doublereal *);
extern /* Subroutine */ void dtgsja_(char *, char *, char *, integer *,
integer *, integer *, integer *, integer *, doublereal *, integer
*, doublereal *, integer *, doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *, integer *, doublereal *,
integer *, doublereal *, integer *, doublereal *, integer *,
integer *);
extern int xerbla_(char *, integer *, ftnlen);
extern void dggsvp_(char *, char *, char *, integer *, integer *,
integer *, doublereal *, integer *, doublereal *, integer *,
doublereal *, doublereal *, integer *, integer *, doublereal *,
integer *, doublereal *, integer *, doublereal *, integer *,
integer *, doublereal *, doublereal *, integer *);
doublereal ulp;
/* -- LAPACK driver 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 */
/* ===================================================================== */
/* 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;
--iwork;
/* Function Body */
wantu = lsame_(jobu, "U");
wantv = lsame_(jobv, "V");
wantq = lsame_(jobq, "Q");
*info = 0;
if (! (wantu || lsame_(jobu, "N"))) {
*info = -1;
} else if (! (wantv || lsame_(jobv, "N"))) {
*info = -2;
} else if (! (wantq || lsame_(jobq, "N"))) {
*info = -3;
} else if (*m < 0) {
*info = -4;
} else if (*n < 0) {
*info = -5;
} else if (*p < 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 = -16;
} else if (*ldv < 1 || wantv && *ldv < *p) {
*info = -18;
} else if (*ldq < 1 || wantq && *ldq < *n) {
*info = -20;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("DGGSVD", &i__1, 6);
return;
}
/* Compute the Frobenius norm of matrices A and B */
anorm = dlange_("1", m, n, &a[a_offset], lda, &work[1]);
bnorm = dlange_("1", p, n, &b[b_offset], ldb, &work[1]);
/* Get machine precision and set up threshold for determining */
/* the effective numerical rank of the matrices A and B. */
ulp = dlamch_("Precision");
unfl = dlamch_("Safe Minimum");
tola = f2cmax(*m,*n) * f2cmax(anorm,unfl) * ulp;
tolb = f2cmax(*p,*n) * f2cmax(bnorm,unfl) * ulp;
/* Preprocessing */
dggsvp_(jobu, jobv, jobq, m, p, n, &a[a_offset], lda, &b[b_offset], ldb, &
tola, &tolb, k, l, &u[u_offset], ldu, &v[v_offset], ldv, &q[
q_offset], ldq, &iwork[1], &work[1], &work[*n + 1], info);
/* Compute the GSVD of two upper "triangular" matrices */
dtgsja_(jobu, jobv, jobq, m, p, n, k, l, &a[a_offset], lda, &b[b_offset],
ldb, &tola, &tolb, &alpha[1], &beta[1], &u[u_offset], ldu, &v[
v_offset], ldv, &q[q_offset], ldq, &work[1], &ncallmycycle, info);
/* Sort the singular values and store the pivot indices in IWORK */
/* Copy ALPHA to WORK, then sort ALPHA in WORK */
dcopy_(n, &alpha[1], &c__1, &work[1], &c__1);
/* Computing MIN */
i__1 = *l, i__2 = *m - *k;
ibnd = f2cmin(i__1,i__2);
i__1 = ibnd;
for (i__ = 1; i__ <= i__1; ++i__) {
/* Scan for largest ALPHA(K+I) */
isub = i__;
smax = work[*k + i__];
i__2 = ibnd;
for (j = i__ + 1; j <= i__2; ++j) {
temp = work[*k + j];
if (temp > smax) {
isub = j;
smax = temp;
}
/* L10: */
}
if (isub != i__) {
work[*k + isub] = work[*k + i__];
work[*k + i__] = smax;
iwork[*k + i__] = *k + isub;
} else {
iwork[*k + i__] = *k + i__;
}
/* L20: */
}
return;
/* End of DGGSVD */
} /* dggsvd_ */
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