/* Subroutine */ int derrbd_(char *path, integer *nunit)
{
/* Format strings */
static char fmt_9999[] = "(1x,a3,\002 routines passed the tests of the e"
"rror exits\002,\002 (\002,i3,\002 tests done)\002)";
static char fmt_9998[] = "(\002 *** \002,a3,\002 routines failed the tes"
"ts of the error \002,\002exits ***\002)";
/* Builtin functions */
integer s_wsle(cilist *), e_wsle(void);
/* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void);
/* Local variables */
doublereal a[16] /* was [4][4] */, d__[4], e[4];
integer i__, j;
doublereal q[16] /* was [4][4] */, u[16] /* was [4][4] */, v[16] /*
was [4][4] */, w[4];
char c2[2];
integer iq[16] /* was [4][4] */, iw[4], nt;
doublereal tp[4], tq[4];
integer info;
extern /* Subroutine */ int dgebd2_(integer *, integer *, doublereal *,
integer *, doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *, integer *), dbdsdc_(char *, char *, integer *,
doublereal *, doublereal *, doublereal *, integer *, doublereal *,
integer *, doublereal *, integer *, doublereal *, integer *,
integer *), dgebrd_(integer *, integer *,
doublereal *, integer *, doublereal *, doublereal *, doublereal *,
doublereal *, doublereal *, integer *, integer *);
extern logical lsamen_(integer *, char *, char *);
extern /* Subroutine */ int dbdsqr_(char *, integer *, integer *, integer
*, integer *, doublereal *, doublereal *, doublereal *, integer *,
doublereal *, integer *, doublereal *, integer *, doublereal *,
integer *), dorgbr_(char *, integer *, integer *, integer
*, doublereal *, integer *, doublereal *, doublereal *, integer *,
integer *), chkxer_(char *, integer *, integer *,
logical *, logical *), dormbr_(char *, char *, char *,
integer *, integer *, integer *, doublereal *, integer *,
doublereal *, doublereal *, integer *, doublereal *, integer *,
integer *);
/* Fortran I/O blocks */
static cilist io___1 = { 0, 0, 0, 0, 0 };
static cilist io___18 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___19 = { 0, 0, 0, fmt_9998, 0 };
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DERRBD tests the error exits for DGEBRD, DORGBR, DORMBR, DBDSQR and */
/* DBDSDC. */
/* Arguments */
/* ========= */
/* PATH (input) CHARACTER*3 */
/* The LAPACK path name for the routines to be tested. */
/* NUNIT (input) INTEGER */
/* The unit number for output. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Scalars in Common .. */
/* .. */
/* .. Common blocks .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
infoc_1.nout = *nunit;
io___1.ciunit = infoc_1.nout;
s_wsle(&io___1);
e_wsle();
s_copy(c2, path + 1, (ftnlen)2, (ftnlen)2);
/* Set the variables to innocuous values. */
for (j = 1; j <= 4; ++j) {
for (i__ = 1; i__ <= 4; ++i__) {
a[i__ + (j << 2) - 5] = 1. / (doublereal) (i__ + j);
/* L10: */
}
/* L20: */
}
infoc_1.ok = TRUE_;
nt = 0;
/* Test error exits of the SVD routines. */
if (lsamen_(&c__2, c2, "BD")) {
/* DGEBRD */
s_copy(srnamc_1.srnamt, "DGEBRD", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
dgebrd_(&c_n1, &c__0, a, &c__1, d__, e, tq, tp, w, &c__1, &info);
chkxer_("DGEBRD", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
dgebrd_(&c__0, &c_n1, a, &c__1, d__, e, tq, tp, w, &c__1, &info);
chkxer_("DGEBRD", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
dgebrd_(&c__2, &c__1, a, &c__1, d__, e, tq, tp, w, &c__2, &info);
chkxer_("DGEBRD", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
dgebrd_(&c__2, &c__1, a, &c__2, d__, e, tq, tp, w, &c__1, &info);
chkxer_("DGEBRD", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
nt += 4;
/* DGEBD2 */
s_copy(srnamc_1.srnamt, "DGEBD2", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
dgebd2_(&c_n1, &c__0, a, &c__1, d__, e, tq, tp, w, &info);
chkxer_("DGEBD2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
dgebd2_(&c__0, &c_n1, a, &c__1, d__, e, tq, tp, w, &info);
chkxer_("DGEBD2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
dgebd2_(&c__2, &c__1, a, &c__1, d__, e, tq, tp, w, &info);
chkxer_("DGEBD2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
nt += 3;
/* DORGBR */
s_copy(srnamc_1.srnamt, "DORGBR", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
dorgbr_("/", &c__0, &c__0, &c__0, a, &c__1, tq, w, &c__1, &info);
chkxer_("DORGBR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
dorgbr_("Q", &c_n1, &c__0, &c__0, a, &c__1, tq, w, &c__1, &info);
chkxer_("DORGBR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
dorgbr_("Q", &c__0, &c_n1, &c__0, a, &c__1, tq, w, &c__1, &info);
chkxer_("DORGBR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
dorgbr_("Q", &c__0, &c__1, &c__0, a, &c__1, tq, w, &c__1, &info);
chkxer_("DORGBR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
dorgbr_("Q", &c__1, &c__0, &c__1, a, &c__1, tq, w, &c__1, &info);
chkxer_("DORGBR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
dorgbr_("P", &c__1, &c__0, &c__0, a, &c__1, tq, w, &c__1, &info);
chkxer_("DORGBR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
dorgbr_("P", &c__0, &c__1, &c__1, a, &c__1, tq, w, &c__1, &info);
chkxer_("DORGBR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
dorgbr_("Q", &c__0, &c__0, &c_n1, a, &c__1, tq, w, &c__1, &info);
chkxer_("DORGBR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
dorgbr_("Q", &c__2, &c__1, &c__1, a, &c__1, tq, w, &c__1, &info);
chkxer_("DORGBR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 9;
dorgbr_("Q", &c__2, &c__2, &c__1, a, &c__2, tq, w, &c__1, &info);
chkxer_("DORGBR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
nt += 10;
/* DORMBR */
s_copy(srnamc_1.srnamt, "DORMBR", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
dormbr_("/", "L", "T", &c__0, &c__0, &c__0, a, &c__1, tq, u, &c__1, w,
&c__1, &info);
chkxer_("DORMBR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
dormbr_("Q", "/", "T", &c__0, &c__0, &c__0, a, &c__1, tq, u, &c__1, w,
&c__1, &info);
chkxer_("DORMBR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
dormbr_("Q", "L", "/", &c__0, &c__0, &c__0, a, &c__1, tq, u, &c__1, w,
&c__1, &info);
chkxer_("DORMBR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
dormbr_("Q", "L", "T", &c_n1, &c__0, &c__0, a, &c__1, tq, u, &c__1, w,
&c__1, &info);
chkxer_("DORMBR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
dormbr_("Q", "L", "T", &c__0, &c_n1, &c__0, a, &c__1, tq, u, &c__1, w,
&c__1, &info);
chkxer_("DORMBR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
dormbr_("Q", "L", "T", &c__0, &c__0, &c_n1, a, &c__1, tq, u, &c__1, w,
&c__1, &info);
chkxer_("DORMBR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
dormbr_("Q", "L", "T", &c__2, &c__0, &c__0, a, &c__1, tq, u, &c__2, w,
&c__1, &info);
chkxer_("DORMBR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
dormbr_("Q", "R", "T", &c__0, &c__2, &c__0, a, &c__1, tq, u, &c__1, w,
&c__1, &info);
chkxer_("DORMBR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
dormbr_("P", "L", "T", &c__2, &c__0, &c__2, a, &c__1, tq, u, &c__2, w,
&c__1, &info);
chkxer_("DORMBR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
dormbr_("P", "R", "T", &c__0, &c__2, &c__2, a, &c__1, tq, u, &c__1, w,
&c__1, &info);
chkxer_("DORMBR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 11;
dormbr_("Q", "R", "T", &c__2, &c__0, &c__0, a, &c__1, tq, u, &c__1, w,
&c__1, &info);
chkxer_("DORMBR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 13;
dormbr_("Q", "L", "T", &c__0, &c__2, &c__0, a, &c__1, tq, u, &c__1, w,
&c__1, &info);
chkxer_("DORMBR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 13;
dormbr_("Q", "R", "T", &c__2, &c__0, &c__0, a, &c__1, tq, u, &c__2, w,
&c__1, &info);
chkxer_("DORMBR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
nt += 13;
/* DBDSQR */
s_copy(srnamc_1.srnamt, "DBDSQR", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
dbdsqr_("/", &c__0, &c__0, &c__0, &c__0, d__, e, v, &c__1, u, &c__1,
a, &c__1, w, &info);
chkxer_("DBDSQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
dbdsqr_("U", &c_n1, &c__0, &c__0, &c__0, d__, e, v, &c__1, u, &c__1,
a, &c__1, w, &info);
chkxer_("DBDSQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
dbdsqr_("U", &c__0, &c_n1, &c__0, &c__0, d__, e, v, &c__1, u, &c__1,
a, &c__1, w, &info);
chkxer_("DBDSQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
dbdsqr_("U", &c__0, &c__0, &c_n1, &c__0, d__, e, v, &c__1, u, &c__1,
a, &c__1, w, &info);
chkxer_("DBDSQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
dbdsqr_("U", &c__0, &c__0, &c__0, &c_n1, d__, e, v, &c__1, u, &c__1,
a, &c__1, w, &info);
chkxer_("DBDSQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 9;
dbdsqr_("U", &c__2, &c__1, &c__0, &c__0, d__, e, v, &c__1, u, &c__1,
a, &c__1, w, &info);
chkxer_("DBDSQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 11;
dbdsqr_("U", &c__0, &c__0, &c__2, &c__0, d__, e, v, &c__1, u, &c__1,
a, &c__1, w, &info);
chkxer_("DBDSQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 13;
dbdsqr_("U", &c__2, &c__0, &c__0, &c__1, d__, e, v, &c__1, u, &c__1,
a, &c__1, w, &info);
chkxer_("DBDSQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
nt += 8;
/* DBDSDC */
s_copy(srnamc_1.srnamt, "DBDSDC", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
dbdsdc_("/", "N", &c__0, d__, e, u, &c__1, v, &c__1, q, iq, w, iw, &
info);
chkxer_("DBDSDC", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
dbdsdc_("U", "/", &c__0, d__, e, u, &c__1, v, &c__1, q, iq, w, iw, &
info);
chkxer_("DBDSDC", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
dbdsdc_("U", "N", &c_n1, d__, e, u, &c__1, v, &c__1, q, iq, w, iw, &
info);
chkxer_("DBDSDC", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
dbdsdc_("U", "I", &c__2, d__, e, u, &c__1, v, &c__1, q, iq, w, iw, &
info);
chkxer_("DBDSDC", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 9;
dbdsdc_("U", "I", &c__2, d__, e, u, &c__2, v, &c__1, q, iq, w, iw, &
info);
chkxer_("DBDSDC", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
nt += 5;
}
/* Print a summary line. */
if (infoc_1.ok) {
io___18.ciunit = infoc_1.nout;
s_wsfe(&io___18);
do_fio(&c__1, path, (ftnlen)3);
do_fio(&c__1, (char *)&nt, (ftnlen)sizeof(integer));
e_wsfe();
} else {
io___19.ciunit = infoc_1.nout;
s_wsfe(&io___19);
do_fio(&c__1, path, (ftnlen)3);
e_wsfe();
}
return 0;
/* End of DERRBD */
} /* derrbd_ */
/* Subroutine */ int dchkbd_(integer *nsizes, integer *mval, integer *nval,
integer *ntypes, logical *dotype, integer *nrhs, integer *iseed,
doublereal *thresh, doublereal *a, integer *lda, doublereal *bd,
doublereal *be, doublereal *s1, doublereal *s2, doublereal *x,
integer *ldx, doublereal *y, doublereal *z__, doublereal *q, integer *
ldq, doublereal *pt, integer *ldpt, doublereal *u, doublereal *vt,
doublereal *work, integer *lwork, integer *iwork, integer *nout,
integer *info)
{
/* Initialized data */
static integer ktype[16] = { 1,2,4,4,4,4,4,6,6,6,6,6,9,9,9,10 };
static integer kmagn[16] = { 1,1,1,1,1,2,3,1,1,1,2,3,1,2,3,0 };
static integer kmode[16] = { 0,0,4,3,1,4,4,4,3,1,4,4,0,0,0,0 };
/* Format strings */
static char fmt_9998[] = "(\002 DCHKBD: \002,a,\002 returned INFO=\002,i"
"6,\002.\002,/9x,\002M=\002,i6,\002, N=\002,i6,\002, JTYPE=\002,i"
"6,\002, ISEED=(\002,3(i5,\002,\002),i5,\002)\002)";
static char fmt_9999[] = "(\002 M=\002,i5,\002, N=\002,i5,\002, type "
"\002,i2,\002, seed=\002,4(i4,\002,\002),\002 test(\002,i2,\002)"
"=\002,g11.4)";
/* System generated locals */
integer a_dim1, a_offset, pt_dim1, pt_offset, q_dim1, q_offset, u_dim1,
u_offset, vt_dim1, vt_offset, x_dim1, x_offset, y_dim1, y_offset,
z_dim1, z_offset, i__1, i__2, i__3, i__4, i__5, i__6, i__7;
doublereal d__1, d__2, d__3, d__4, d__5, d__6, d__7;
/* Builtin functions */
/* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
double log(doublereal), sqrt(doublereal), exp(doublereal);
integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void);
/* Local variables */
integer i__, j, m, n, mq;
doublereal dum[1], ulp, cond;
integer jcol;
char path[3];
integer idum[1], mmax, nmax;
doublereal unfl, ovfl;
char uplo[1];
doublereal temp1, temp2;
extern /* Subroutine */ int dbdt01_(integer *, integer *, integer *,
doublereal *, integer *, doublereal *, integer *, doublereal *,
doublereal *, doublereal *, integer *, doublereal *, doublereal *)
, dbdt02_(integer *, integer *, doublereal *, integer *,
doublereal *, integer *, doublereal *, integer *, doublereal *,
doublereal *);
logical badmm;
extern /* Subroutine */ int dbdt03_(char *, integer *, integer *,
doublereal *, doublereal *, doublereal *, integer *, doublereal *,
doublereal *, integer *, doublereal *, doublereal *);
logical badnn;
integer nfail;
extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *,
integer *, doublereal *, doublereal *, integer *, doublereal *,
integer *, doublereal *, doublereal *, integer *);
integer imode;
doublereal dumma[1];
integer iinfo;
extern /* Subroutine */ int dort01_(char *, integer *, integer *,
doublereal *, integer *, doublereal *, integer *, doublereal *);
doublereal anorm;
integer mnmin;
extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *,
doublereal *, integer *);
integer mnmax, jsize, itype, jtype, ntest;
extern /* Subroutine */ int dlahd2_(integer *, char *);
integer log2ui;
extern /* Subroutine */ int dlabad_(doublereal *, doublereal *);
logical bidiag;
extern /* Subroutine */ int dbdsdc_(char *, char *, integer *, doublereal
*, doublereal *, doublereal *, integer *, doublereal *, integer *,
doublereal *, integer *, doublereal *, integer *, integer *), dgebrd_(integer *, integer *, doublereal *,
integer *, doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *, integer *, integer *);
extern doublereal dlamch_(char *), dlarnd_(integer *, integer *);
extern /* Subroutine */ int dlacpy_(char *, integer *, integer *,
doublereal *, integer *, doublereal *, integer *),
dlaset_(char *, integer *, integer *, doublereal *, doublereal *,
doublereal *, integer *);
integer ioldsd[4];
extern /* Subroutine */ int dbdsqr_(char *, integer *, integer *, integer
*, integer *, doublereal *, doublereal *, doublereal *, integer *,
doublereal *, integer *, doublereal *, integer *, doublereal *,
integer *), dorgbr_(char *, integer *, integer *, integer
*, doublereal *, integer *, doublereal *, doublereal *, integer *,
integer *), xerbla_(char *, integer *), alasum_(
char *, integer *, integer *, integer *, integer *),
dlatmr_(integer *, integer *, char *, integer *, char *,
doublereal *, integer *, doublereal *, doublereal *, char *, char
*, doublereal *, integer *, doublereal *, doublereal *, integer *,
doublereal *, char *, integer *, integer *, integer *,
doublereal *, doublereal *, char *, doublereal *, integer *,
integer *, integer *), dlatms_(integer *, integer *, char *, integer *, char *,
doublereal *, integer *, doublereal *, doublereal *, integer *,
integer *, char *, doublereal *, integer *, doublereal *, integer
*);
doublereal amninv;
integer minwrk;
doublereal rtunfl, rtovfl, ulpinv, result[19];
integer mtypes;
/* Fortran I/O blocks */
static cilist io___39 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___40 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___42 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___43 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___44 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___45 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___51 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___52 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___53 = { 0, 0, 0, fmt_9999, 0 };
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DCHKBD checks the singular value decomposition (SVD) routines. */
/* DGEBRD reduces a real general m by n matrix A to upper or lower */
/* bidiagonal form B by an orthogonal transformation: Q' * A * P = B */
/* (or A = Q * B * P'). The matrix B is upper bidiagonal if m >= n */
/* and lower bidiagonal if m < n. */
/* DORGBR generates the orthogonal matrices Q and P' from DGEBRD. */
/* Note that Q and P are not necessarily square. */
/* DBDSQR computes the singular value decomposition of the bidiagonal */
/* matrix B as B = U S V'. It is called three times to compute */
/* 1) B = U S1 V', where S1 is the diagonal matrix of singular */
/* values and the columns of the matrices U and V are the left */
/* and right singular vectors, respectively, of B. */
/* 2) Same as 1), but the singular values are stored in S2 and the */
/* singular vectors are not computed. */
/* 3) A = (UQ) S (P'V'), the SVD of the original matrix A. */
/* In addition, DBDSQR has an option to apply the left orthogonal matrix */
/* U to a matrix X, useful in least squares applications. */
/* DBDSDC computes the singular value decomposition of the bidiagonal */
/* matrix B as B = U S V' using divide-and-conquer. It is called twice */
/* to compute */
/* 1) B = U S1 V', where S1 is the diagonal matrix of singular */
/* values and the columns of the matrices U and V are the left */
/* and right singular vectors, respectively, of B. */
/* 2) Same as 1), but the singular values are stored in S2 and the */
/* singular vectors are not computed. */
/* For each pair of matrix dimensions (M,N) and each selected matrix */
/* type, an M by N matrix A and an M by NRHS matrix X are generated. */
/* The problem dimensions are as follows */
/* A: M x N */
/* Q: M x min(M,N) (but M x M if NRHS > 0) */
/* P: min(M,N) x N */
/* B: min(M,N) x min(M,N) */
/* U, V: min(M,N) x min(M,N) */
/* S1, S2 diagonal, order min(M,N) */
/* X: M x NRHS */
/* For each generated matrix, 14 tests are performed: */
/* Test DGEBRD and DORGBR */
/* (1) | A - Q B PT | / ( |A| max(M,N) ulp ), PT = P' */
/* (2) | I - Q' Q | / ( M ulp ) */
/* (3) | I - PT PT' | / ( N ulp ) */
/* Test DBDSQR on bidiagonal matrix B */
/* (4) | B - U S1 VT | / ( |B| min(M,N) ulp ), VT = V' */
/* (5) | Y - U Z | / ( |Y| max(min(M,N),k) ulp ), where Y = Q' X */
/* and Z = U' Y. */
/* (6) | I - U' U | / ( min(M,N) ulp ) */
/* (7) | I - VT VT' | / ( min(M,N) ulp ) */
/* (8) S1 contains min(M,N) nonnegative values in decreasing order. */
/* (Return 0 if true, 1/ULP if false.) */
/* (9) | S1 - S2 | / ( |S1| ulp ), where S2 is computed without */
/* computing U and V. */
/* (10) 0 if the true singular values of B are within THRESH of */
/* those in S1. 2*THRESH if they are not. (Tested using */
/* DSVDCH) */
/* Test DBDSQR on matrix A */
/* (11) | A - (QU) S (VT PT) | / ( |A| max(M,N) ulp ) */
/* (12) | X - (QU) Z | / ( |X| max(M,k) ulp ) */
/* (13) | I - (QU)'(QU) | / ( M ulp ) */
/* (14) | I - (VT PT) (PT'VT') | / ( N ulp ) */
/* Test DBDSDC on bidiagonal matrix B */
/* (15) | B - U S1 VT | / ( |B| min(M,N) ulp ), VT = V' */
/* (16) | I - U' U | / ( min(M,N) ulp ) */
/* (17) | I - VT VT' | / ( min(M,N) ulp ) */
/* (18) S1 contains min(M,N) nonnegative values in decreasing order. */
/* (Return 0 if true, 1/ULP if false.) */
/* (19) | S1 - S2 | / ( |S1| ulp ), where S2 is computed without */
/* computing U and V. */
/* The possible matrix types are */
/* (1) The zero matrix. */
/* (2) The identity matrix. */
/* (3) A diagonal matrix with evenly spaced entries */
/* 1, ..., ULP and random signs. */
/* (ULP = (first number larger than 1) - 1 ) */
/* (4) A diagonal matrix with geometrically spaced entries */
/* 1, ..., ULP and random signs. */
/* (5) A diagonal matrix with "clustered" entries 1, ULP, ..., ULP */
/* and random signs. */
/* (6) Same as (3), but multiplied by SQRT( overflow threshold ) */
/* (7) Same as (3), but multiplied by SQRT( underflow threshold ) */
/* (8) A matrix of the form U D V, where U and V are orthogonal and */
/* D has evenly spaced entries 1, ..., ULP with random signs */
/* on the diagonal. */
/* (9) A matrix of the form U D V, where U and V are orthogonal and */
/* D has geometrically spaced entries 1, ..., ULP with random */
/* signs on the diagonal. */
/* (10) A matrix of the form U D V, where U and V are orthogonal and */
/* D has "clustered" entries 1, ULP,..., ULP with random */
/* signs on the diagonal. */
/* (11) Same as (8), but multiplied by SQRT( overflow threshold ) */
/* (12) Same as (8), but multiplied by SQRT( underflow threshold ) */
/* (13) Rectangular matrix with random entries chosen from (-1,1). */
/* (14) Same as (13), but multiplied by SQRT( overflow threshold ) */
/* (15) Same as (13), but multiplied by SQRT( underflow threshold ) */
/* Special case: */
/* (16) A bidiagonal matrix with random entries chosen from a */
/* logarithmic distribution on [ulp^2,ulp^(-2)] (I.e., each */
/* entry is e^x, where x is chosen uniformly on */
/* [ 2 log(ulp), -2 log(ulp) ] .) For *this* type: */
/* (a) DGEBRD is not called to reduce it to bidiagonal form. */
/* (b) the bidiagonal is min(M,N) x min(M,N); if M<N, the */
/* matrix will be lower bidiagonal, otherwise upper. */
/* (c) only tests 5--8 and 14 are performed. */
/* A subset of the full set of matrix types may be selected through */
/* the logical array DOTYPE. */
/* Arguments */
/* ========== */
/* NSIZES (input) INTEGER */
/* The number of values of M and N contained in the vectors */
/* MVAL and NVAL. The matrix sizes are used in pairs (M,N). */
/* MVAL (input) INTEGER array, dimension (NM) */
/* The values of the matrix row dimension M. */
/* NVAL (input) INTEGER array, dimension (NM) */
/* The values of the matrix column dimension N. */
/* NTYPES (input) INTEGER */
/* The number of elements in DOTYPE. If it is zero, DCHKBD */
/* does nothing. It must be at least zero. If it is MAXTYP+1 */
/* and NSIZES is 1, then an additional type, MAXTYP+1 is */
/* defined, which is to use whatever matrices are in A and B. */
/* This is only useful if DOTYPE(1:MAXTYP) is .FALSE. and */
/* DOTYPE(MAXTYP+1) is .TRUE. . */
/* DOTYPE (input) LOGICAL array, dimension (NTYPES) */
/* If DOTYPE(j) is .TRUE., then for each size (m,n), a matrix */
/* of type j will be generated. If NTYPES is smaller than the */
/* maximum number of types defined (PARAMETER MAXTYP), then */
/* types NTYPES+1 through MAXTYP will not be generated. If */
/* NTYPES is larger than MAXTYP, DOTYPE(MAXTYP+1) through */
/* DOTYPE(NTYPES) will be ignored. */
/* NRHS (input) INTEGER */
/* The number of columns in the "right-hand side" matrices X, Y, */
/* and Z, used in testing DBDSQR. If NRHS = 0, then the */
/* operations on the right-hand side will not be tested. */
/* NRHS must be at least 0. */
/* ISEED (input/output) INTEGER array, dimension (4) */
/* On entry ISEED specifies the seed of the random number */
/* generator. The array elements should be between 0 and 4095; */
/* if not they will be reduced mod 4096. Also, ISEED(4) must */
/* be odd. The values of ISEED are changed on exit, and can be */
/* used in the next call to DCHKBD to continue the same random */
/* number sequence. */
/* THRESH (input) DOUBLE PRECISION */
/* The threshold value for the test ratios. A result is */
/* included in the output file if RESULT >= THRESH. To have */
/* every test ratio printed, use THRESH = 0. Note that the */
/* expected value of the test ratios is O(1), so THRESH should */
/* be a reasonably small multiple of 1, e.g., 10 or 100. */
/* A (workspace) DOUBLE PRECISION array, dimension (LDA,NMAX) */
/* where NMAX is the maximum value of N in NVAL. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,MMAX), */
/* where MMAX is the maximum value of M in MVAL. */
/* BD (workspace) DOUBLE PRECISION array, dimension */
/* (max(min(MVAL(j),NVAL(j)))) */
/* BE (workspace) DOUBLE PRECISION array, dimension */
/* (max(min(MVAL(j),NVAL(j)))) */
/* S1 (workspace) DOUBLE PRECISION array, dimension */
/* (max(min(MVAL(j),NVAL(j)))) */
/* S2 (workspace) DOUBLE PRECISION array, dimension */
/* (max(min(MVAL(j),NVAL(j)))) */
/* X (workspace) DOUBLE PRECISION array, dimension (LDX,NRHS) */
/* LDX (input) INTEGER */
/* The leading dimension of the arrays X, Y, and Z. */
/* LDX >= max(1,MMAX) */
/* Y (workspace) DOUBLE PRECISION array, dimension (LDX,NRHS) */
/* Z (workspace) DOUBLE PRECISION array, dimension (LDX,NRHS) */
/* Q (workspace) DOUBLE PRECISION array, dimension (LDQ,MMAX) */
/* LDQ (input) INTEGER */
/* The leading dimension of the array Q. LDQ >= max(1,MMAX). */
/* PT (workspace) DOUBLE PRECISION array, dimension (LDPT,NMAX) */
/* LDPT (input) INTEGER */
/* The leading dimension of the arrays PT, U, and V. */
/* LDPT >= max(1, max(min(MVAL(j),NVAL(j)))). */
/* U (workspace) DOUBLE PRECISION array, dimension */
/* (LDPT,max(min(MVAL(j),NVAL(j)))) */
/* V (workspace) DOUBLE PRECISION array, dimension */
/* (LDPT,max(min(MVAL(j),NVAL(j)))) */
/* WORK (workspace) DOUBLE PRECISION array, dimension (LWORK) */
/* LWORK (input) INTEGER */
/* The number of entries in WORK. This must be at least */
/* 3(M+N) and M(M + max(M,N,k) + 1) + N*min(M,N) for all */
/* pairs (M,N)=(MM(j),NN(j)) */
/* IWORK (workspace) INTEGER array, dimension at least 8*min(M,N) */
/* NOUT (input) INTEGER */
/* The FORTRAN unit number for printing out error messages */
/* (e.g., if a routine returns IINFO not equal to 0.) */
/* INFO (output) INTEGER */
/* If 0, then everything ran OK. */
/* -1: NSIZES < 0 */
/* -2: Some MM(j) < 0 */
/* -3: Some NN(j) < 0 */
/* -4: NTYPES < 0 */
/* -6: NRHS < 0 */
/* -8: THRESH < 0 */
/* -11: LDA < 1 or LDA < MMAX, where MMAX is max( MM(j) ). */
/* -17: LDB < 1 or LDB < MMAX. */
/* -21: LDQ < 1 or LDQ < MMAX. */
/* -23: LDPT< 1 or LDPT< MNMAX. */
/* -27: LWORK too small. */
/* If DLATMR, SLATMS, DGEBRD, DORGBR, or DBDSQR, */
/* returns an error code, the */
/* absolute value of it is returned. */
/* ----------------------------------------------------------------------- */
/* Some Local Variables and Parameters: */
/* ---- ----- --------- --- ---------- */
/* ZERO, ONE Real 0 and 1. */
/* MAXTYP The number of types defined. */
/* NTEST The number of tests performed, or which can */
/* be performed so far, for the current matrix. */
/* MMAX Largest value in NN. */
/* NMAX Largest value in NN. */
/* MNMIN min(MM(j), NN(j)) (the dimension of the bidiagonal */
/* matrix.) */
/* MNMAX The maximum value of MNMIN for j=1,...,NSIZES. */
/* NFAIL The number of tests which have exceeded THRESH */
/* COND, IMODE Values to be passed to the matrix generators. */
/* ANORM Norm of A; passed to matrix generators. */
/* OVFL, UNFL Overflow and underflow thresholds. */
/* RTOVFL, RTUNFL Square roots of the previous 2 values. */
/* ULP, ULPINV Finest relative precision and its inverse. */
/* The following four arrays decode JTYPE: */
/* KTYPE(j) The general type (1-10) for type "j". */
/* KMODE(j) The MODE value to be passed to the matrix */
/* generator for type "j". */
/* KMAGN(j) The order of magnitude ( O(1), */
/* O(overflow^(1/2) ), O(underflow^(1/2) ) */
/* ====================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Scalars in Common .. */
/* .. */
/* .. Common blocks .. */
/* .. */
/* .. Data statements .. */
/* Parameter adjustments */
--mval;
--nval;
--dotype;
--iseed;
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--bd;
--be;
--s1;
--s2;
z_dim1 = *ldx;
z_offset = 1 + z_dim1;
z__ -= z_offset;
y_dim1 = *ldx;
y_offset = 1 + y_dim1;
y -= y_offset;
x_dim1 = *ldx;
x_offset = 1 + x_dim1;
x -= x_offset;
q_dim1 = *ldq;
q_offset = 1 + q_dim1;
q -= q_offset;
vt_dim1 = *ldpt;
vt_offset = 1 + vt_dim1;
vt -= vt_offset;
u_dim1 = *ldpt;
u_offset = 1 + u_dim1;
u -= u_offset;
pt_dim1 = *ldpt;
pt_offset = 1 + pt_dim1;
pt -= pt_offset;
--work;
--iwork;
/* Function Body */
/* .. */
/* .. Executable Statements .. */
/* Check for errors */
*info = 0;
badmm = FALSE_;
badnn = FALSE_;
mmax = 1;
nmax = 1;
mnmax = 1;
minwrk = 1;
i__1 = *nsizes;
for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
i__2 = mmax, i__3 = mval[j];
mmax = max(i__2,i__3);
if (mval[j] < 0) {
badmm = TRUE_;
}
/* Computing MAX */
i__2 = nmax, i__3 = nval[j];
nmax = max(i__2,i__3);
if (nval[j] < 0) {
badnn = TRUE_;
}
/* Computing MAX */
/* Computing MIN */
i__4 = mval[j], i__5 = nval[j];
i__2 = mnmax, i__3 = min(i__4,i__5);
mnmax = max(i__2,i__3);
/* Computing MAX */
/* Computing MAX */
i__4 = mval[j], i__5 = nval[j], i__4 = max(i__4,i__5);
/* Computing MIN */
i__6 = nval[j], i__7 = mval[j];
i__2 = minwrk, i__3 = (mval[j] + nval[j]) * 3, i__2 = max(i__2,i__3),
i__3 = mval[j] * (mval[j] + max(i__4,*nrhs) + 1) + nval[j] *
min(i__6,i__7);
minwrk = max(i__2,i__3);
/* L10: */
}
/* Check for errors */
if (*nsizes < 0) {
*info = -1;
} else if (badmm) {
*info = -2;
} else if (badnn) {
*info = -3;
} else if (*ntypes < 0) {
*info = -4;
} else if (*nrhs < 0) {
*info = -6;
} else if (*lda < mmax) {
*info = -11;
} else if (*ldx < mmax) {
*info = -17;
} else if (*ldq < mmax) {
*info = -21;
} else if (*ldpt < mnmax) {
*info = -23;
} else if (minwrk > *lwork) {
*info = -27;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("DCHKBD", &i__1);
return 0;
}
/* Initialize constants */
s_copy(path, "Double precision", (ftnlen)1, (ftnlen)16);
s_copy(path + 1, "BD", (ftnlen)2, (ftnlen)2);
nfail = 0;
ntest = 0;
unfl = dlamch_("Safe minimum");
ovfl = dlamch_("Overflow");
dlabad_(&unfl, &ovfl);
ulp = dlamch_("Precision");
ulpinv = 1. / ulp;
log2ui = (integer) (log(ulpinv) / log(2.));
rtunfl = sqrt(unfl);
rtovfl = sqrt(ovfl);
infoc_1.infot = 0;
/* Loop over sizes, types */
i__1 = *nsizes;
for (jsize = 1; jsize <= i__1; ++jsize) {
m = mval[jsize];
n = nval[jsize];
mnmin = min(m,n);
/* Computing MAX */
i__2 = max(m,n);
amninv = 1. / max(i__2,1);
if (*nsizes != 1) {
mtypes = min(16,*ntypes);
} else {
mtypes = min(17,*ntypes);
}
i__2 = mtypes;
for (jtype = 1; jtype <= i__2; ++jtype) {
if (! dotype[jtype]) {
goto L190;
}
for (j = 1; j <= 4; ++j) {
ioldsd[j - 1] = iseed[j];
/* L20: */
}
for (j = 1; j <= 14; ++j) {
result[j - 1] = -1.;
/* L30: */
}
*(unsigned char *)uplo = ' ';
/* Compute "A" */
/* Control parameters: */
/* KMAGN KMODE KTYPE */
/* =1 O(1) clustered 1 zero */
/* =2 large clustered 2 identity */
/* =3 small exponential (none) */
/* =4 arithmetic diagonal, (w/ eigenvalues) */
/* =5 random symmetric, w/ eigenvalues */
/* =6 nonsymmetric, w/ singular values */
/* =7 random diagonal */
/* =8 random symmetric */
/* =9 random nonsymmetric */
/* =10 random bidiagonal (log. distrib.) */
if (mtypes > 16) {
goto L100;
}
itype = ktype[jtype - 1];
imode = kmode[jtype - 1];
/* Compute norm */
switch (kmagn[jtype - 1]) {
case 1: goto L40;
case 2: goto L50;
case 3: goto L60;
}
L40:
anorm = 1.;
goto L70;
L50:
anorm = rtovfl * ulp * amninv;
goto L70;
L60:
anorm = rtunfl * max(m,n) * ulpinv;
goto L70;
L70:
dlaset_("Full", lda, &n, &c_b20, &c_b20, &a[a_offset], lda);
iinfo = 0;
cond = ulpinv;
bidiag = FALSE_;
if (itype == 1) {
/* Zero matrix */
iinfo = 0;
} else if (itype == 2) {
/* Identity */
i__3 = mnmin;
for (jcol = 1; jcol <= i__3; ++jcol) {
a[jcol + jcol * a_dim1] = anorm;
/* L80: */
}
} else if (itype == 4) {
/* Diagonal Matrix, [Eigen]values Specified */
dlatms_(&mnmin, &mnmin, "S", &iseed[1], "N", &work[1], &imode,
&cond, &anorm, &c__0, &c__0, "N", &a[a_offset], lda,
&work[mnmin + 1], &iinfo);
} else if (itype == 5) {
/* Symmetric, eigenvalues specified */
dlatms_(&mnmin, &mnmin, "S", &iseed[1], "S", &work[1], &imode,
&cond, &anorm, &m, &n, "N", &a[a_offset], lda, &work[
mnmin + 1], &iinfo);
} else if (itype == 6) {
/* Nonsymmetric, singular values specified */
dlatms_(&m, &n, "S", &iseed[1], "N", &work[1], &imode, &cond,
&anorm, &m, &n, "N", &a[a_offset], lda, &work[mnmin +
1], &iinfo);
} else if (itype == 7) {
/* Diagonal, random entries */
dlatmr_(&mnmin, &mnmin, "S", &iseed[1], "N", &work[1], &c__6,
&c_b37, &c_b37, "T", "N", &work[mnmin + 1], &c__1, &
c_b37, &work[(mnmin << 1) + 1], &c__1, &c_b37, "N", &
iwork[1], &c__0, &c__0, &c_b20, &anorm, "NO", &a[
a_offset], lda, &iwork[1], &iinfo);
} else if (itype == 8) {
/* Symmetric, random entries */
dlatmr_(&mnmin, &mnmin, "S", &iseed[1], "S", &work[1], &c__6,
&c_b37, &c_b37, "T", "N", &work[mnmin + 1], &c__1, &
c_b37, &work[m + mnmin + 1], &c__1, &c_b37, "N", &
iwork[1], &m, &n, &c_b20, &anorm, "NO", &a[a_offset],
lda, &iwork[1], &iinfo);
} else if (itype == 9) {
/* Nonsymmetric, random entries */
dlatmr_(&m, &n, "S", &iseed[1], "N", &work[1], &c__6, &c_b37,
&c_b37, "T", "N", &work[mnmin + 1], &c__1, &c_b37, &
work[m + mnmin + 1], &c__1, &c_b37, "N", &iwork[1], &
m, &n, &c_b20, &anorm, "NO", &a[a_offset], lda, &
iwork[1], &iinfo);
} else if (itype == 10) {
/* Bidiagonal, random entries */
temp1 = log(ulp) * -2.;
i__3 = mnmin;
for (j = 1; j <= i__3; ++j) {
bd[j] = exp(temp1 * dlarnd_(&c__2, &iseed[1]));
if (j < mnmin) {
be[j] = exp(temp1 * dlarnd_(&c__2, &iseed[1]));
}
/* L90: */
}
iinfo = 0;
bidiag = TRUE_;
if (m >= n) {
*(unsigned char *)uplo = 'U';
} else {
*(unsigned char *)uplo = 'L';
}
} else {
iinfo = 1;
}
if (iinfo == 0) {
/* Generate Right-Hand Side */
if (bidiag) {
dlatmr_(&mnmin, nrhs, "S", &iseed[1], "N", &work[1], &
c__6, &c_b37, &c_b37, "T", "N", &work[mnmin + 1],
&c__1, &c_b37, &work[(mnmin << 1) + 1], &c__1, &
c_b37, "N", &iwork[1], &mnmin, nrhs, &c_b20, &
c_b37, "NO", &y[y_offset], ldx, &iwork[1], &iinfo);
} else {
dlatmr_(&m, nrhs, "S", &iseed[1], "N", &work[1], &c__6, &
c_b37, &c_b37, "T", "N", &work[m + 1], &c__1, &
c_b37, &work[(m << 1) + 1], &c__1, &c_b37, "N", &
iwork[1], &m, nrhs, &c_b20, &c_b37, "NO", &x[
x_offset], ldx, &iwork[1], &iinfo);
}
}
/* Error Exit */
if (iinfo != 0) {
io___39.ciunit = *nout;
s_wsfe(&io___39);
do_fio(&c__1, "Generator", (ftnlen)9);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&m, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
*info = abs(iinfo);
return 0;
}
L100:
/* Call DGEBRD and DORGBR to compute B, Q, and P, do tests. */
if (! bidiag) {
/* Compute transformations to reduce A to bidiagonal form: */
/* B := Q' * A * P. */
dlacpy_(" ", &m, &n, &a[a_offset], lda, &q[q_offset], ldq);
i__3 = *lwork - (mnmin << 1);
dgebrd_(&m, &n, &q[q_offset], ldq, &bd[1], &be[1], &work[1], &
work[mnmin + 1], &work[(mnmin << 1) + 1], &i__3, &
iinfo);
/* Check error code from DGEBRD. */
if (iinfo != 0) {
io___40.ciunit = *nout;
s_wsfe(&io___40);
do_fio(&c__1, "DGEBRD", (ftnlen)6);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&m, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer))
;
e_wsfe();
*info = abs(iinfo);
return 0;
}
dlacpy_(" ", &m, &n, &q[q_offset], ldq, &pt[pt_offset], ldpt);
if (m >= n) {
*(unsigned char *)uplo = 'U';
} else {
*(unsigned char *)uplo = 'L';
}
/* Generate Q */
mq = m;
if (*nrhs <= 0) {
mq = mnmin;
}
i__3 = *lwork - (mnmin << 1);
dorgbr_("Q", &m, &mq, &n, &q[q_offset], ldq, &work[1], &work[(
mnmin << 1) + 1], &i__3, &iinfo);
/* Check error code from DORGBR. */
if (iinfo != 0) {
io___42.ciunit = *nout;
s_wsfe(&io___42);
do_fio(&c__1, "DORGBR(Q)", (ftnlen)9);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&m, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer))
;
e_wsfe();
*info = abs(iinfo);
return 0;
}
/* Generate P' */
i__3 = *lwork - (mnmin << 1);
dorgbr_("P", &mnmin, &n, &m, &pt[pt_offset], ldpt, &work[
mnmin + 1], &work[(mnmin << 1) + 1], &i__3, &iinfo);
/* Check error code from DORGBR. */
if (iinfo != 0) {
io___43.ciunit = *nout;
s_wsfe(&io___43);
do_fio(&c__1, "DORGBR(P)", (ftnlen)9);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&m, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer))
;
e_wsfe();
*info = abs(iinfo);
return 0;
}
/* Apply Q' to an M by NRHS matrix X: Y := Q' * X. */
dgemm_("Transpose", "No transpose", &m, nrhs, &m, &c_b37, &q[
q_offset], ldq, &x[x_offset], ldx, &c_b20, &y[
y_offset], ldx);
/* Test 1: Check the decomposition A := Q * B * PT */
/* 2: Check the orthogonality of Q */
/* 3: Check the orthogonality of PT */
dbdt01_(&m, &n, &c__1, &a[a_offset], lda, &q[q_offset], ldq, &
bd[1], &be[1], &pt[pt_offset], ldpt, &work[1], result)
;
dort01_("Columns", &m, &mq, &q[q_offset], ldq, &work[1],
lwork, &result[1]);
dort01_("Rows", &mnmin, &n, &pt[pt_offset], ldpt, &work[1],
lwork, &result[2]);
}
/* Use DBDSQR to form the SVD of the bidiagonal matrix B: */
/* B := U * S1 * VT, and compute Z = U' * Y. */
dcopy_(&mnmin, &bd[1], &c__1, &s1[1], &c__1);
if (mnmin > 0) {
i__3 = mnmin - 1;
dcopy_(&i__3, &be[1], &c__1, &work[1], &c__1);
}
dlacpy_(" ", &m, nrhs, &y[y_offset], ldx, &z__[z_offset], ldx);
dlaset_("Full", &mnmin, &mnmin, &c_b20, &c_b37, &u[u_offset],
ldpt);
dlaset_("Full", &mnmin, &mnmin, &c_b20, &c_b37, &vt[vt_offset],
ldpt);
dbdsqr_(uplo, &mnmin, &mnmin, &mnmin, nrhs, &s1[1], &work[1], &vt[
vt_offset], ldpt, &u[u_offset], ldpt, &z__[z_offset], ldx,
&work[mnmin + 1], &iinfo);
/* Check error code from DBDSQR. */
if (iinfo != 0) {
io___44.ciunit = *nout;
s_wsfe(&io___44);
do_fio(&c__1, "DBDSQR(vects)", (ftnlen)13);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&m, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
*info = abs(iinfo);
if (iinfo < 0) {
return 0;
} else {
result[3] = ulpinv;
goto L170;
}
}
/* Use DBDSQR to compute only the singular values of the */
/* bidiagonal matrix B; U, VT, and Z should not be modified. */
dcopy_(&mnmin, &bd[1], &c__1, &s2[1], &c__1);
if (mnmin > 0) {
i__3 = mnmin - 1;
dcopy_(&i__3, &be[1], &c__1, &work[1], &c__1);
}
dbdsqr_(uplo, &mnmin, &c__0, &c__0, &c__0, &s2[1], &work[1], &vt[
vt_offset], ldpt, &u[u_offset], ldpt, &z__[z_offset], ldx,
&work[mnmin + 1], &iinfo);
/* Check error code from DBDSQR. */
if (iinfo != 0) {
io___45.ciunit = *nout;
s_wsfe(&io___45);
do_fio(&c__1, "DBDSQR(values)", (ftnlen)14);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&m, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
*info = abs(iinfo);
if (iinfo < 0) {
return 0;
} else {
result[8] = ulpinv;
goto L170;
}
}
/* Test 4: Check the decomposition B := U * S1 * VT */
/* 5: Check the computation Z := U' * Y */
/* 6: Check the orthogonality of U */
/* 7: Check the orthogonality of VT */
dbdt03_(uplo, &mnmin, &c__1, &bd[1], &be[1], &u[u_offset], ldpt, &
s1[1], &vt[vt_offset], ldpt, &work[1], &result[3]);
dbdt02_(&mnmin, nrhs, &y[y_offset], ldx, &z__[z_offset], ldx, &u[
u_offset], ldpt, &work[1], &result[4]);
dort01_("Columns", &mnmin, &mnmin, &u[u_offset], ldpt, &work[1],
lwork, &result[5]);
dort01_("Rows", &mnmin, &mnmin, &vt[vt_offset], ldpt, &work[1],
lwork, &result[6]);
/* Test 8: Check that the singular values are sorted in */
/* non-increasing order and are non-negative */
result[7] = 0.;
i__3 = mnmin - 1;
for (i__ = 1; i__ <= i__3; ++i__) {
if (s1[i__] < s1[i__ + 1]) {
result[7] = ulpinv;
}
if (s1[i__] < 0.) {
result[7] = ulpinv;
}
/* L110: */
}
if (mnmin >= 1) {
if (s1[mnmin] < 0.) {
result[7] = ulpinv;
}
}
/* Test 9: Compare DBDSQR with and without singular vectors */
temp2 = 0.;
i__3 = mnmin;
for (j = 1; j <= i__3; ++j) {
/* Computing MAX */
/* Computing MAX */
d__6 = (d__1 = s1[j], abs(d__1)), d__7 = (d__2 = s2[j], abs(
d__2));
d__4 = sqrt(unfl) * max(s1[1],1.), d__5 = ulp * max(d__6,d__7)
;
temp1 = (d__3 = s1[j] - s2[j], abs(d__3)) / max(d__4,d__5);
temp2 = max(temp1,temp2);
/* L120: */
}
result[8] = temp2;
/* Test 10: Sturm sequence test of singular values */
/* Go up by factors of two until it succeeds */
temp1 = *thresh * (.5 - ulp);
i__3 = log2ui;
for (j = 0; j <= i__3; ++j) {
/* CALL DSVDCH( MNMIN, BD, BE, S1, TEMP1, IINFO ) */
if (iinfo == 0) {
goto L140;
}
temp1 *= 2.;
/* L130: */
}
L140:
result[9] = temp1;
/* Use DBDSQR to form the decomposition A := (QU) S (VT PT) */
/* from the bidiagonal form A := Q B PT. */
if (! bidiag) {
dcopy_(&mnmin, &bd[1], &c__1, &s2[1], &c__1);
if (mnmin > 0) {
i__3 = mnmin - 1;
dcopy_(&i__3, &be[1], &c__1, &work[1], &c__1);
}
dbdsqr_(uplo, &mnmin, &n, &m, nrhs, &s2[1], &work[1], &pt[
pt_offset], ldpt, &q[q_offset], ldq, &y[y_offset],
ldx, &work[mnmin + 1], &iinfo);
/* Test 11: Check the decomposition A := Q*U * S2 * VT*PT */
/* 12: Check the computation Z := U' * Q' * X */
/* 13: Check the orthogonality of Q*U */
/* 14: Check the orthogonality of VT*PT */
dbdt01_(&m, &n, &c__0, &a[a_offset], lda, &q[q_offset], ldq, &
s2[1], dumma, &pt[pt_offset], ldpt, &work[1], &result[
10]);
dbdt02_(&m, nrhs, &x[x_offset], ldx, &y[y_offset], ldx, &q[
q_offset], ldq, &work[1], &result[11]);
dort01_("Columns", &m, &mq, &q[q_offset], ldq, &work[1],
lwork, &result[12]);
dort01_("Rows", &mnmin, &n, &pt[pt_offset], ldpt, &work[1],
lwork, &result[13]);
}
/* Use DBDSDC to form the SVD of the bidiagonal matrix B: */
/* B := U * S1 * VT */
dcopy_(&mnmin, &bd[1], &c__1, &s1[1], &c__1);
if (mnmin > 0) {
i__3 = mnmin - 1;
dcopy_(&i__3, &be[1], &c__1, &work[1], &c__1);
}
dlaset_("Full", &mnmin, &mnmin, &c_b20, &c_b37, &u[u_offset],
ldpt);
dlaset_("Full", &mnmin, &mnmin, &c_b20, &c_b37, &vt[vt_offset],
ldpt);
dbdsdc_(uplo, "I", &mnmin, &s1[1], &work[1], &u[u_offset], ldpt, &
vt[vt_offset], ldpt, dum, idum, &work[mnmin + 1], &iwork[
1], &iinfo);
/* Check error code from DBDSDC. */
if (iinfo != 0) {
io___51.ciunit = *nout;
s_wsfe(&io___51);
do_fio(&c__1, "DBDSDC(vects)", (ftnlen)13);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&m, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
*info = abs(iinfo);
if (iinfo < 0) {
return 0;
} else {
result[14] = ulpinv;
goto L170;
}
}
/* Use DBDSDC to compute only the singular values of the */
/* bidiagonal matrix B; U and VT should not be modified. */
dcopy_(&mnmin, &bd[1], &c__1, &s2[1], &c__1);
if (mnmin > 0) {
i__3 = mnmin - 1;
dcopy_(&i__3, &be[1], &c__1, &work[1], &c__1);
}
dbdsdc_(uplo, "N", &mnmin, &s2[1], &work[1], dum, &c__1, dum, &
c__1, dum, idum, &work[mnmin + 1], &iwork[1], &iinfo);
/* Check error code from DBDSDC. */
if (iinfo != 0) {
io___52.ciunit = *nout;
s_wsfe(&io___52);
do_fio(&c__1, "DBDSDC(values)", (ftnlen)14);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&m, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
*info = abs(iinfo);
if (iinfo < 0) {
return 0;
} else {
result[17] = ulpinv;
goto L170;
}
}
/* Test 15: Check the decomposition B := U * S1 * VT */
/* 16: Check the orthogonality of U */
/* 17: Check the orthogonality of VT */
dbdt03_(uplo, &mnmin, &c__1, &bd[1], &be[1], &u[u_offset], ldpt, &
s1[1], &vt[vt_offset], ldpt, &work[1], &result[14]);
dort01_("Columns", &mnmin, &mnmin, &u[u_offset], ldpt, &work[1],
lwork, &result[15]);
dort01_("Rows", &mnmin, &mnmin, &vt[vt_offset], ldpt, &work[1],
lwork, &result[16]);
/* Test 18: Check that the singular values are sorted in */
/* non-increasing order and are non-negative */
result[17] = 0.;
i__3 = mnmin - 1;
for (i__ = 1; i__ <= i__3; ++i__) {
if (s1[i__] < s1[i__ + 1]) {
result[17] = ulpinv;
}
if (s1[i__] < 0.) {
result[17] = ulpinv;
}
/* L150: */
}
if (mnmin >= 1) {
if (s1[mnmin] < 0.) {
result[17] = ulpinv;
}
}
/* Test 19: Compare DBDSQR with and without singular vectors */
temp2 = 0.;
i__3 = mnmin;
for (j = 1; j <= i__3; ++j) {
/* Computing MAX */
/* Computing MAX */
d__4 = abs(s1[1]), d__5 = abs(s2[1]);
d__2 = sqrt(unfl) * max(s1[1],1.), d__3 = ulp * max(d__4,d__5)
;
temp1 = (d__1 = s1[j] - s2[j], abs(d__1)) / max(d__2,d__3);
temp2 = max(temp1,temp2);
/* L160: */
}
result[18] = temp2;
/* End of Loop -- Check for RESULT(j) > THRESH */
L170:
for (j = 1; j <= 19; ++j) {
if (result[j - 1] >= *thresh) {
if (nfail == 0) {
dlahd2_(nout, path);
}
io___53.ciunit = *nout;
s_wsfe(&io___53);
do_fio(&c__1, (char *)&m, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer))
;
do_fio(&c__1, (char *)&j, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&result[j - 1], (ftnlen)sizeof(
doublereal));
e_wsfe();
++nfail;
}
/* L180: */
}
if (! bidiag) {
ntest += 19;
} else {
ntest += 5;
}
L190:
;
}
/* L200: */
}
/* Summary */
alasum_(path, nout, &nfail, &ntest, &c__0);
return 0;
/* End of DCHKBD */
} /* dchkbd_ */
/* Subroutine */ int dgelsd_(integer *m, integer *n, integer *nrhs,
doublereal *a, integer *lda, doublereal *b, integer *ldb, doublereal *
s, doublereal *rcond, integer *rank, doublereal *work, integer *lwork,
integer *iwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3, i__4;
/* Builtin functions */
double log(doublereal);
/* Local variables */
static doublereal anrm, bnrm;
static integer itau, nlvl, iascl, ibscl;
static doublereal sfmin;
static integer minmn, maxmn, itaup, itauq, mnthr, nwork;
extern /* Subroutine */ int dlabad_(doublereal *, doublereal *);
static integer ie, il;
extern /* Subroutine */ int dgebrd_(integer *, integer *, doublereal *,
integer *, doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *, integer *, integer *);
extern doublereal dlamch_(char *);
static integer mm;
extern doublereal dlange_(char *, integer *, integer *, doublereal *,
integer *, doublereal *);
extern /* Subroutine */ int dgelqf_(integer *, integer *, doublereal *,
integer *, doublereal *, doublereal *, integer *, integer *),
dlalsd_(char *, integer *, integer *, integer *, doublereal *,
doublereal *, doublereal *, integer *, doublereal *, integer *,
doublereal *, integer *, integer *), dlascl_(char *,
integer *, integer *, doublereal *, doublereal *, integer *,
integer *, doublereal *, integer *, integer *), dgeqrf_(
integer *, integer *, doublereal *, integer *, doublereal *,
doublereal *, integer *, integer *), dlacpy_(char *, integer *,
integer *, doublereal *, integer *, doublereal *, integer *), dlaset_(char *, integer *, integer *, doublereal *,
doublereal *, doublereal *, integer *), xerbla_(char *,
integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
static doublereal bignum;
extern /* Subroutine */ int dormbr_(char *, char *, char *, integer *,
integer *, integer *, doublereal *, integer *, doublereal *,
doublereal *, integer *, doublereal *, integer *, integer *);
static integer wlalsd;
extern /* Subroutine */ int dormlq_(char *, char *, integer *, integer *,
integer *, doublereal *, integer *, doublereal *, doublereal *,
integer *, doublereal *, integer *, integer *);
static integer ldwork;
extern /* Subroutine */ int dormqr_(char *, char *, integer *, integer *,
integer *, doublereal *, integer *, doublereal *, doublereal *,
integer *, doublereal *, integer *, integer *);
static integer minwrk, maxwrk;
static doublereal smlnum;
static logical lquery;
static integer smlsiz;
static doublereal eps;
#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]
#define b_ref(a_1,a_2) b[(a_2)*b_dim1 + a_1]
/* -- LAPACK driver routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
October 31, 1999
Purpose
=======
DGELSD computes the minimum-norm solution to a real linear least
squares problem:
minimize 2-norm(| b - A*x |)
using the singular value decomposition (SVD) of A. A is an M-by-N
matrix which may be rank-deficient.
Several right hand side vectors b and solution vectors x can be
handled in a single call; they are stored as the columns of the
M-by-NRHS right hand side matrix B and the N-by-NRHS solution
matrix X.
The problem is solved in three steps:
(1) Reduce the coefficient matrix A to bidiagonal form with
Householder transformations, reducing the original problem
into a "bidiagonal least squares problem" (BLS)
(2) Solve the BLS using a divide and conquer approach.
(3) Apply back all the Householder tranformations to solve
the original least squares problem.
The effective rank of A is determined by treating as zero those
singular values which are less than RCOND times the largest singular
value.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard
digit in add/subtract, or on those binary machines without guard
digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
Cray-2. It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.
Arguments
=========
M (input) INTEGER
The number of rows of A. M >= 0.
N (input) INTEGER
The number of columns of A. N >= 0.
NRHS (input) INTEGER
The number of right hand sides, i.e., the number of columns
of the matrices B and X. NRHS >= 0.
A (input) DOUBLE PRECISION array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, A has been destroyed.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
On entry, the M-by-NRHS right hand side matrix B.
On exit, B is overwritten by the N-by-NRHS solution
matrix X. If m >= n and RANK = n, the residual
sum-of-squares for the solution in the i-th column is given
by the sum of squares of elements n+1:m in that column.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,max(M,N)).
S (output) DOUBLE PRECISION array, dimension (min(M,N))
The singular values of A in decreasing order.
The condition number of A in the 2-norm = S(1)/S(min(m,n)).
RCOND (input) DOUBLE PRECISION
RCOND is used to determine the effective rank of A.
Singular values S(i) <= RCOND*S(1) are treated as zero.
If RCOND < 0, machine precision is used instead.
RANK (output) INTEGER
The effective rank of A, i.e., the number of singular values
which are greater than RCOND*S(1).
WORK (workspace/output) DOUBLE PRECISION array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. LWORK must be at least 1.
The exact minimum amount of workspace needed depends on M,
N and NRHS. As long as LWORK is at least
12*N + 2*N*SMLSIZ + 8*N*NLVL + N*NRHS + (SMLSIZ+1)**2,
if M is greater than or equal to N or
12*M + 2*M*SMLSIZ + 8*M*NLVL + M*NRHS + (SMLSIZ+1)**2,
if M is less than N, the code will execute correctly.
SMLSIZ is returned by ILAENV and is equal to the maximum
size of the subproblems at the bottom of the computation
tree (usually about 25), and
NLVL = MAX( 0, INT( LOG_2( MIN( M,N )/(SMLSIZ+1) ) ) + 1 )
For good performance, LWORK should generally be larger.
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
IWORK (workspace) INTEGER array, dimension (LIWORK)
LIWORK >= 3 * MINMN * NLVL + 11 * MINMN,
where MINMN = MIN( M,N ).
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.
> 0: the algorithm for computing the SVD failed to converge;
if INFO = i, i off-diagonal elements of an intermediate
bidiagonal form did not converge to zero.
Further Details
===============
Based on contributions by
Ming Gu and Ren-Cang Li, Computer Science Division, University of
California at Berkeley, USA
Osni Marques, LBNL/NERSC, USA
=====================================================================
Test the input arguments.
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;
--s;
--work;
--iwork;
/* Function Body */
*info = 0;
minmn = min(*m,*n);
maxmn = max(*m,*n);
mnthr = ilaenv_(&c__6, "DGELSD", " ", m, n, nrhs, &c_n1, (ftnlen)6, (
ftnlen)1);
lquery = *lwork == -1;
if (*m < 0) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*nrhs < 0) {
*info = -3;
} else if (*lda < max(1,*m)) {
*info = -5;
} else if (*ldb < max(1,maxmn)) {
*info = -7;
}
smlsiz = ilaenv_(&c__9, "DGELSD", " ", &c__0, &c__0, &c__0, &c__0, (
ftnlen)6, (ftnlen)1);
/* Compute workspace.
(Note: Comments in the code beginning "Workspace:" describe the
minimal amount of workspace needed at that point in the code,
as well as the preferred amount for good performance.
NB refers to the optimal block size for the immediately
following subroutine, as returned by ILAENV.) */
minwrk = 1;
minmn = max(1,minmn);
/* Computing MAX */
i__1 = (integer) (log((doublereal) minmn / (doublereal) (smlsiz + 1)) /
log(2.)) + 1;
nlvl = max(i__1,0);
if (*info == 0) {
maxwrk = 0;
mm = *m;
if (*m >= *n && *m >= mnthr) {
/* Path 1a - overdetermined, with many more rows than columns. */
mm = *n;
/* Computing MAX */
i__1 = maxwrk, i__2 = *n + *n * ilaenv_(&c__1, "DGEQRF", " ", m,
n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = *n + *nrhs * ilaenv_(&c__1, "DORMQR", "LT",
m, nrhs, n, &c_n1, (ftnlen)6, (ftnlen)2);
maxwrk = max(i__1,i__2);
}
if (*m >= *n) {
/* Path 1 - overdetermined or exactly determined.
Computing MAX */
i__1 = maxwrk, i__2 = *n * 3 + (mm + *n) * ilaenv_(&c__1, "DGEBRD"
, " ", &mm, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = *n * 3 + *nrhs * ilaenv_(&c__1, "DORMBR",
"QLT", &mm, nrhs, n, &c_n1, (ftnlen)6, (ftnlen)3);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = *n * 3 + (*n - 1) * ilaenv_(&c__1, "DORMBR",
"PLN", n, nrhs, n, &c_n1, (ftnlen)6, (ftnlen)3);
maxwrk = max(i__1,i__2);
/* Computing 2nd power */
i__1 = smlsiz + 1;
wlalsd = *n * 9 + (*n << 1) * smlsiz + (*n << 3) * nlvl + *n * *
nrhs + i__1 * i__1;
/* Computing MAX */
i__1 = maxwrk, i__2 = *n * 3 + wlalsd;
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = *n * 3 + mm, i__2 = *n * 3 + *nrhs, i__1 = max(i__1,i__2),
i__2 = *n * 3 + wlalsd;
minwrk = max(i__1,i__2);
}
if (*n > *m) {
/* Computing 2nd power */
i__1 = smlsiz + 1;
wlalsd = *m * 9 + (*m << 1) * smlsiz + (*m << 3) * nlvl + *m * *
nrhs + i__1 * i__1;
if (*n >= mnthr) {
/* Path 2a - underdetermined, with many more columns
than rows. */
maxwrk = *m + *m * ilaenv_(&c__1, "DGELQF", " ", m, n, &c_n1,
&c_n1, (ftnlen)6, (ftnlen)1);
/* Computing MAX */
i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + (*m << 1) *
ilaenv_(&c__1, "DGEBRD", " ", m, m, &c_n1, &c_n1, (
ftnlen)6, (ftnlen)1);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + *nrhs * ilaenv_(&
c__1, "DORMBR", "QLT", m, nrhs, m, &c_n1, (ftnlen)6, (
ftnlen)3);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + (*m - 1) *
ilaenv_(&c__1, "DORMBR", "PLN", m, nrhs, m, &c_n1, (
ftnlen)6, (ftnlen)3);
maxwrk = max(i__1,i__2);
if (*nrhs > 1) {
/* Computing MAX */
i__1 = maxwrk, i__2 = *m * *m + *m + *m * *nrhs;
maxwrk = max(i__1,i__2);
} else {
/* Computing MAX */
i__1 = maxwrk, i__2 = *m * *m + (*m << 1);
maxwrk = max(i__1,i__2);
}
/* Computing MAX */
i__1 = maxwrk, i__2 = *m + *nrhs * ilaenv_(&c__1, "DORMLQ",
"LT", n, nrhs, m, &c_n1, (ftnlen)6, (ftnlen)2);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + wlalsd;
maxwrk = max(i__1,i__2);
} else {
/* Path 2 - remaining underdetermined cases. */
maxwrk = *m * 3 + (*n + *m) * ilaenv_(&c__1, "DGEBRD", " ", m,
n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1);
/* Computing MAX */
i__1 = maxwrk, i__2 = *m * 3 + *nrhs * ilaenv_(&c__1, "DORMBR"
, "QLT", m, nrhs, n, &c_n1, (ftnlen)6, (ftnlen)3);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = *m * 3 + *m * ilaenv_(&c__1, "DORMBR",
"PLN", n, nrhs, m, &c_n1, (ftnlen)6, (ftnlen)3);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = *m * 3 + wlalsd;
maxwrk = max(i__1,i__2);
}
/* Computing MAX */
i__1 = *m * 3 + *nrhs, i__2 = *m * 3 + *m, i__1 = max(i__1,i__2),
i__2 = *m * 3 + wlalsd;
minwrk = max(i__1,i__2);
}
minwrk = min(minwrk,maxwrk);
work[1] = (doublereal) maxwrk;
if (*lwork < minwrk && ! lquery) {
*info = -12;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("DGELSD", &i__1);
return 0;
} else if (lquery) {
goto L10;
}
/* Quick return if possible. */
if (*m == 0 || *n == 0) {
*rank = 0;
return 0;
}
/* Get machine parameters. */
eps = dlamch_("P");
sfmin = dlamch_("S");
smlnum = sfmin / eps;
bignum = 1. / smlnum;
dlabad_(&smlnum, &bignum);
/* Scale A if max entry outside range [SMLNUM,BIGNUM]. */
anrm = dlange_("M", m, n, &a[a_offset], lda, &work[1]);
iascl = 0;
if (anrm > 0. && anrm < smlnum) {
/* Scale matrix norm up to SMLNUM. */
dlascl_("G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda,
info);
iascl = 1;
} else if (anrm > bignum) {
/* Scale matrix norm down to BIGNUM. */
dlascl_("G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda,
info);
iascl = 2;
} else if (anrm == 0.) {
/* Matrix all zero. Return zero solution. */
i__1 = max(*m,*n);
dlaset_("F", &i__1, nrhs, &c_b82, &c_b82, &b[b_offset], ldb);
dlaset_("F", &minmn, &c__1, &c_b82, &c_b82, &s[1], &c__1);
*rank = 0;
goto L10;
}
/* Scale B if max entry outside range [SMLNUM,BIGNUM]. */
bnrm = dlange_("M", m, nrhs, &b[b_offset], ldb, &work[1]);
ibscl = 0;
if (bnrm > 0. && bnrm < smlnum) {
/* Scale matrix norm up to SMLNUM. */
dlascl_("G", &c__0, &c__0, &bnrm, &smlnum, m, nrhs, &b[b_offset], ldb,
info);
ibscl = 1;
} else if (bnrm > bignum) {
/* Scale matrix norm down to BIGNUM. */
dlascl_("G", &c__0, &c__0, &bnrm, &bignum, m, nrhs, &b[b_offset], ldb,
info);
ibscl = 2;
}
/* If M < N make sure certain entries of B are zero. */
if (*m < *n) {
i__1 = *n - *m;
dlaset_("F", &i__1, nrhs, &c_b82, &c_b82, &b_ref(*m + 1, 1), ldb);
}
/* Overdetermined case. */
if (*m >= *n) {
/* Path 1 - overdetermined or exactly determined. */
mm = *m;
if (*m >= mnthr) {
/* Path 1a - overdetermined, with many more rows than columns. */
mm = *n;
itau = 1;
nwork = itau + *n;
/* Compute A=Q*R.
(Workspace: need 2*N, prefer N+N*NB) */
i__1 = *lwork - nwork + 1;
dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &i__1,
info);
/* Multiply B by transpose(Q).
(Workspace: need N+NRHS, prefer N+NRHS*NB) */
i__1 = *lwork - nwork + 1;
dormqr_("L", "T", m, nrhs, n, &a[a_offset], lda, &work[itau], &b[
b_offset], ldb, &work[nwork], &i__1, info);
/* Zero out below R. */
if (*n > 1) {
i__1 = *n - 1;
i__2 = *n - 1;
dlaset_("L", &i__1, &i__2, &c_b82, &c_b82, &a_ref(2, 1), lda);
}
}
ie = 1;
itauq = ie + *n;
itaup = itauq + *n;
nwork = itaup + *n;
/* Bidiagonalize R in A.
(Workspace: need 3*N+MM, prefer 3*N+(MM+N)*NB) */
i__1 = *lwork - nwork + 1;
dgebrd_(&mm, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], &
work[itaup], &work[nwork], &i__1, info);
/* Multiply B by transpose of left bidiagonalizing vectors of R.
(Workspace: need 3*N+NRHS, prefer 3*N+NRHS*NB) */
i__1 = *lwork - nwork + 1;
dormbr_("Q", "L", "T", &mm, nrhs, n, &a[a_offset], lda, &work[itauq],
&b[b_offset], ldb, &work[nwork], &i__1, info);
/* Solve the bidiagonal least squares problem. */
dlalsd_("U", &smlsiz, n, nrhs, &s[1], &work[ie], &b[b_offset], ldb,
rcond, rank, &work[nwork], &iwork[1], info);
if (*info != 0) {
goto L10;
}
/* Multiply B by right bidiagonalizing vectors of R. */
i__1 = *lwork - nwork + 1;
dormbr_("P", "L", "N", n, nrhs, n, &a[a_offset], lda, &work[itaup], &
b[b_offset], ldb, &work[nwork], &i__1, info);
} else /* if(complicated condition) */ {
/* Computing MAX */
i__1 = *m, i__2 = (*m << 1) - 4, i__1 = max(i__1,i__2), i__1 = max(
i__1,*nrhs), i__2 = *n - *m * 3;
if (*n >= mnthr && *lwork >= (*m << 2) + *m * *m + max(i__1,i__2)) {
/* Path 2a - underdetermined, with many more columns than rows
and sufficient workspace for an efficient algorithm. */
ldwork = *m;
/* Computing MAX
Computing MAX */
i__3 = *m, i__4 = (*m << 1) - 4, i__3 = max(i__3,i__4), i__3 =
max(i__3,*nrhs), i__4 = *n - *m * 3;
i__1 = (*m << 2) + *m * *lda + max(i__3,i__4), i__2 = *m * *lda +
*m + *m * *nrhs;
if (*lwork >= max(i__1,i__2)) {
ldwork = *lda;
}
itau = 1;
nwork = *m + 1;
/* Compute A=L*Q.
(Workspace: need 2*M, prefer M+M*NB) */
i__1 = *lwork - nwork + 1;
dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &i__1,
info);
il = nwork;
/* Copy L to WORK(IL), zeroing out above its diagonal. */
dlacpy_("L", m, m, &a[a_offset], lda, &work[il], &ldwork);
i__1 = *m - 1;
i__2 = *m - 1;
dlaset_("U", &i__1, &i__2, &c_b82, &c_b82, &work[il + ldwork], &
ldwork);
ie = il + ldwork * *m;
itauq = ie + *m;
itaup = itauq + *m;
nwork = itaup + *m;
/* Bidiagonalize L in WORK(IL).
(Workspace: need M*M+5*M, prefer M*M+4*M+2*M*NB) */
i__1 = *lwork - nwork + 1;
dgebrd_(m, m, &work[il], &ldwork, &s[1], &work[ie], &work[itauq],
&work[itaup], &work[nwork], &i__1, info);
/* Multiply B by transpose of left bidiagonalizing vectors of L.
(Workspace: need M*M+4*M+NRHS, prefer M*M+4*M+NRHS*NB) */
i__1 = *lwork - nwork + 1;
dormbr_("Q", "L", "T", m, nrhs, m, &work[il], &ldwork, &work[
itauq], &b[b_offset], ldb, &work[nwork], &i__1, info);
/* Solve the bidiagonal least squares problem. */
dlalsd_("U", &smlsiz, m, nrhs, &s[1], &work[ie], &b[b_offset],
ldb, rcond, rank, &work[nwork], &iwork[1], info);
if (*info != 0) {
goto L10;
}
/* Multiply B by right bidiagonalizing vectors of L. */
i__1 = *lwork - nwork + 1;
dormbr_("P", "L", "N", m, nrhs, m, &work[il], &ldwork, &work[
itaup], &b[b_offset], ldb, &work[nwork], &i__1, info);
/* Zero out below first M rows of B. */
i__1 = *n - *m;
dlaset_("F", &i__1, nrhs, &c_b82, &c_b82, &b_ref(*m + 1, 1), ldb);
nwork = itau + *m;
/* Multiply transpose(Q) by B.
(Workspace: need M+NRHS, prefer M+NRHS*NB) */
i__1 = *lwork - nwork + 1;
dormlq_("L", "T", n, nrhs, m, &a[a_offset], lda, &work[itau], &b[
b_offset], ldb, &work[nwork], &i__1, info);
} else {
/* Path 2 - remaining underdetermined cases. */
ie = 1;
itauq = ie + *m;
itaup = itauq + *m;
nwork = itaup + *m;
/* Bidiagonalize A.
(Workspace: need 3*M+N, prefer 3*M+(M+N)*NB) */
i__1 = *lwork - nwork + 1;
dgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], &
work[itaup], &work[nwork], &i__1, info);
/* Multiply B by transpose of left bidiagonalizing vectors.
(Workspace: need 3*M+NRHS, prefer 3*M+NRHS*NB) */
i__1 = *lwork - nwork + 1;
dormbr_("Q", "L", "T", m, nrhs, n, &a[a_offset], lda, &work[itauq]
, &b[b_offset], ldb, &work[nwork], &i__1, info);
/* Solve the bidiagonal least squares problem. */
dlalsd_("L", &smlsiz, m, nrhs, &s[1], &work[ie], &b[b_offset],
ldb, rcond, rank, &work[nwork], &iwork[1], info);
if (*info != 0) {
goto L10;
}
/* Multiply B by right bidiagonalizing vectors of A. */
i__1 = *lwork - nwork + 1;
dormbr_("P", "L", "N", n, nrhs, m, &a[a_offset], lda, &work[itaup]
, &b[b_offset], ldb, &work[nwork], &i__1, info);
}
}
/* Undo scaling. */
if (iascl == 1) {
dlascl_("G", &c__0, &c__0, &anrm, &smlnum, n, nrhs, &b[b_offset], ldb,
info);
dlascl_("G", &c__0, &c__0, &smlnum, &anrm, &minmn, &c__1, &s[1], &
minmn, info);
} else if (iascl == 2) {
dlascl_("G", &c__0, &c__0, &anrm, &bignum, n, nrhs, &b[b_offset], ldb,
info);
dlascl_("G", &c__0, &c__0, &bignum, &anrm, &minmn, &c__1, &s[1], &
minmn, info);
}
if (ibscl == 1) {
dlascl_("G", &c__0, &c__0, &smlnum, &bnrm, n, nrhs, &b[b_offset], ldb,
info);
} else if (ibscl == 2) {
dlascl_("G", &c__0, &c__0, &bignum, &bnrm, n, nrhs, &b[b_offset], ldb,
info);
}
L10:
work[1] = (doublereal) maxwrk;
return 0;
/* End of DGELSD */
} /* dgelsd_ */
/* Subroutine */ int dgelss_(integer *m, integer *n, integer *nrhs,
doublereal *a, integer *lda, doublereal *b, integer *ldb, doublereal *
s, doublereal *rcond, integer *rank, doublereal *work, integer *lwork,
integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3, i__4;
doublereal d__1;
/* Local variables */
static doublereal anrm, bnrm;
static integer itau;
static doublereal vdum[1];
static integer i__;
extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *,
integer *, doublereal *, doublereal *, integer *, doublereal *,
integer *, doublereal *, doublereal *, integer *);
static integer iascl, ibscl;
extern /* Subroutine */ int dgemv_(char *, integer *, integer *,
doublereal *, doublereal *, integer *, doublereal *, integer *,
doublereal *, doublereal *, integer *), drscl_(integer *,
doublereal *, doublereal *, integer *);
static integer chunk;
static doublereal sfmin;
static integer minmn;
extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *,
doublereal *, integer *);
static integer maxmn, itaup, itauq, mnthr, iwork;
extern /* Subroutine */ int dlabad_(doublereal *, doublereal *);
static integer bl, ie, il;
extern /* Subroutine */ int dgebrd_(integer *, integer *, doublereal *,
integer *, doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *, integer *, integer *);
extern doublereal dlamch_(char *);
static integer mm;
extern doublereal dlange_(char *, integer *, integer *, doublereal *,
integer *, doublereal *);
static integer bdspac;
extern /* Subroutine */ int dgelqf_(integer *, integer *, doublereal *,
integer *, doublereal *, doublereal *, integer *, integer *),
dlascl_(char *, integer *, integer *, doublereal *, doublereal *,
integer *, integer *, doublereal *, integer *, integer *),
dgeqrf_(integer *, integer *, doublereal *, integer *,
doublereal *, doublereal *, integer *, integer *), dlacpy_(char *,
integer *, integer *, doublereal *, integer *, doublereal *,
integer *), dlaset_(char *, integer *, integer *,
doublereal *, doublereal *, doublereal *, integer *),
xerbla_(char *, integer *), dbdsqr_(char *, integer *,
integer *, integer *, integer *, doublereal *, doublereal *,
doublereal *, integer *, doublereal *, integer *, doublereal *,
integer *, doublereal *, integer *), dorgbr_(char *,
integer *, integer *, integer *, doublereal *, integer *,
doublereal *, doublereal *, integer *, integer *);
static doublereal bignum;
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
extern /* Subroutine */ int dormbr_(char *, char *, char *, integer *,
integer *, integer *, doublereal *, integer *, doublereal *,
doublereal *, integer *, doublereal *, integer *, integer *), dormlq_(char *, char *, integer *,
integer *, integer *, doublereal *, integer *, doublereal *,
doublereal *, integer *, doublereal *, integer *, integer *);
static integer ldwork;
extern /* Subroutine */ int dormqr_(char *, char *, integer *, integer *,
integer *, doublereal *, integer *, doublereal *, doublereal *,
integer *, doublereal *, integer *, integer *);
static integer minwrk, maxwrk;
static doublereal smlnum;
static logical lquery;
static doublereal eps, thr;
#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]
#define b_ref(a_1,a_2) b[(a_2)*b_dim1 + a_1]
/* -- LAPACK driver routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
October 31, 1999
Purpose
=======
DGELSS computes the minimum norm solution to a real linear least
squares problem:
Minimize 2-norm(| b - A*x |).
using the singular value decomposition (SVD) of A. A is an M-by-N
matrix which may be rank-deficient.
Several right hand side vectors b and solution vectors x can be
handled in a single call; they are stored as the columns of the
M-by-NRHS right hand side matrix B and the N-by-NRHS solution matrix
X.
The effective rank of A is determined by treating as zero those
singular values which are less than RCOND times the largest singular
value.
Arguments
=========
M (input) INTEGER
The number of rows of the matrix A. M >= 0.
N (input) INTEGER
The number of columns of the matrix A. N >= 0.
NRHS (input) INTEGER
The number of right hand sides, i.e., the number of columns
of the matrices B and X. NRHS >= 0.
A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, the first min(m,n) rows of A are overwritten with
its right singular vectors, stored rowwise.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
On entry, the M-by-NRHS right hand side matrix B.
On exit, B is overwritten by the N-by-NRHS solution
matrix X. If m >= n and RANK = n, the residual
sum-of-squares for the solution in the i-th column is given
by the sum of squares of elements n+1:m in that column.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,max(M,N)).
S (output) DOUBLE PRECISION array, dimension (min(M,N))
The singular values of A in decreasing order.
The condition number of A in the 2-norm = S(1)/S(min(m,n)).
RCOND (input) DOUBLE PRECISION
RCOND is used to determine the effective rank of A.
Singular values S(i) <= RCOND*S(1) are treated as zero.
If RCOND < 0, machine precision is used instead.
RANK (output) INTEGER
The effective rank of A, i.e., the number of singular values
which are greater than RCOND*S(1).
WORK (workspace/output) DOUBLE PRECISION array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. LWORK >= 1, and also:
LWORK >= 3*min(M,N) + max( 2*min(M,N), max(M,N), NRHS )
For good performance, LWORK should generally be larger.
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.
> 0: the algorithm for computing the SVD failed to converge;
if INFO = i, i off-diagonal elements of an intermediate
bidiagonal form did not converge to zero.
=====================================================================
Test the input arguments
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;
--s;
--work;
/* Function Body */
*info = 0;
minmn = min(*m,*n);
maxmn = max(*m,*n);
mnthr = ilaenv_(&c__6, "DGELSS", " ", m, n, nrhs, &c_n1, (ftnlen)6, (
ftnlen)1);
lquery = *lwork == -1;
if (*m < 0) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*nrhs < 0) {
*info = -3;
} else if (*lda < max(1,*m)) {
*info = -5;
} else if (*ldb < max(1,maxmn)) {
*info = -7;
}
/* Compute workspace
(Note: Comments in the code beginning "Workspace:" describe the
minimal amount of workspace needed at that point in the code,
as well as the preferred amount for good performance.
NB refers to the optimal block size for the immediately
following subroutine, as returned by ILAENV.) */
minwrk = 1;
if (*info == 0 && (*lwork >= 1 || lquery)) {
maxwrk = 0;
mm = *m;
if (*m >= *n && *m >= mnthr) {
/* Path 1a - overdetermined, with many more rows than columns */
mm = *n;
/* Computing MAX */
i__1 = maxwrk, i__2 = *n + *n * ilaenv_(&c__1, "DGEQRF", " ", m,
n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = *n + *nrhs * ilaenv_(&c__1, "DORMQR", "LT",
m, nrhs, n, &c_n1, (ftnlen)6, (ftnlen)2);
maxwrk = max(i__1,i__2);
}
if (*m >= *n) {
/* Path 1 - overdetermined or exactly determined
Compute workspace needed for DBDSQR
Computing MAX */
i__1 = 1, i__2 = *n * 5;
bdspac = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = *n * 3 + (mm + *n) * ilaenv_(&c__1, "DGEBRD"
, " ", &mm, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = *n * 3 + *nrhs * ilaenv_(&c__1, "DORMBR",
"QLT", &mm, nrhs, n, &c_n1, (ftnlen)6, (ftnlen)3);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = *n * 3 + (*n - 1) * ilaenv_(&c__1, "DORGBR",
"P", n, n, n, &c_n1, (ftnlen)6, (ftnlen)1);
maxwrk = max(i__1,i__2);
maxwrk = max(maxwrk,bdspac);
/* Computing MAX */
i__1 = maxwrk, i__2 = *n * *nrhs;
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = *n * 3 + mm, i__2 = *n * 3 + *nrhs, i__1 = max(i__1,i__2);
minwrk = max(i__1,bdspac);
maxwrk = max(minwrk,maxwrk);
}
if (*n > *m) {
/* Compute workspace needed for DBDSQR
Computing MAX */
i__1 = 1, i__2 = *m * 5;
bdspac = max(i__1,i__2);
/* Computing MAX */
i__1 = *m * 3 + *nrhs, i__2 = *m * 3 + *n, i__1 = max(i__1,i__2);
minwrk = max(i__1,bdspac);
if (*n >= mnthr) {
/* Path 2a - underdetermined, with many more columns
than rows */
maxwrk = *m + *m * ilaenv_(&c__1, "DGELQF", " ", m, n, &c_n1,
&c_n1, (ftnlen)6, (ftnlen)1);
/* Computing MAX */
i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + (*m << 1) *
ilaenv_(&c__1, "DGEBRD", " ", m, m, &c_n1, &c_n1, (
ftnlen)6, (ftnlen)1);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + *nrhs * ilaenv_(&
c__1, "DORMBR", "QLT", m, nrhs, m, &c_n1, (ftnlen)6, (
ftnlen)3);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + (*m - 1) *
ilaenv_(&c__1, "DORGBR", "P", m, m, m, &c_n1, (ftnlen)
6, (ftnlen)1);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = *m * *m + *m + bdspac;
maxwrk = max(i__1,i__2);
if (*nrhs > 1) {
/* Computing MAX */
i__1 = maxwrk, i__2 = *m * *m + *m + *m * *nrhs;
maxwrk = max(i__1,i__2);
} else {
/* Computing MAX */
i__1 = maxwrk, i__2 = *m * *m + (*m << 1);
maxwrk = max(i__1,i__2);
}
/* Computing MAX */
i__1 = maxwrk, i__2 = *m + *nrhs * ilaenv_(&c__1, "DORMLQ",
"LT", n, nrhs, m, &c_n1, (ftnlen)6, (ftnlen)2);
maxwrk = max(i__1,i__2);
} else {
/* Path 2 - underdetermined */
maxwrk = *m * 3 + (*n + *m) * ilaenv_(&c__1, "DGEBRD", " ", m,
n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1);
/* Computing MAX */
i__1 = maxwrk, i__2 = *m * 3 + *nrhs * ilaenv_(&c__1, "DORMBR"
, "QLT", m, nrhs, m, &c_n1, (ftnlen)6, (ftnlen)3);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = *m * 3 + *m * ilaenv_(&c__1, "DORGBR",
"P", m, n, m, &c_n1, (ftnlen)6, (ftnlen)1);
maxwrk = max(i__1,i__2);
maxwrk = max(maxwrk,bdspac);
/* Computing MAX */
i__1 = maxwrk, i__2 = *n * *nrhs;
maxwrk = max(i__1,i__2);
}
}
maxwrk = max(minwrk,maxwrk);
work[1] = (doublereal) maxwrk;
}
minwrk = max(minwrk,1);
if (*lwork < minwrk && ! lquery) {
*info = -12;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("DGELSS", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*m == 0 || *n == 0) {
*rank = 0;
return 0;
}
/* Get machine parameters */
eps = dlamch_("P");
sfmin = dlamch_("S");
smlnum = sfmin / eps;
bignum = 1. / smlnum;
dlabad_(&smlnum, &bignum);
/* Scale A if max element outside range [SMLNUM,BIGNUM] */
anrm = dlange_("M", m, n, &a[a_offset], lda, &work[1]);
iascl = 0;
if (anrm > 0. && anrm < smlnum) {
/* Scale matrix norm up to SMLNUM */
dlascl_("G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda,
info);
iascl = 1;
} else if (anrm > bignum) {
/* Scale matrix norm down to BIGNUM */
dlascl_("G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda,
info);
iascl = 2;
} else if (anrm == 0.) {
/* Matrix all zero. Return zero solution. */
i__1 = max(*m,*n);
dlaset_("F", &i__1, nrhs, &c_b74, &c_b74, &b[b_offset], ldb);
dlaset_("F", &minmn, &c__1, &c_b74, &c_b74, &s[1], &c__1);
*rank = 0;
goto L70;
}
/* Scale B if max element outside range [SMLNUM,BIGNUM] */
bnrm = dlange_("M", m, nrhs, &b[b_offset], ldb, &work[1]);
ibscl = 0;
if (bnrm > 0. && bnrm < smlnum) {
/* Scale matrix norm up to SMLNUM */
dlascl_("G", &c__0, &c__0, &bnrm, &smlnum, m, nrhs, &b[b_offset], ldb,
info);
ibscl = 1;
} else if (bnrm > bignum) {
/* Scale matrix norm down to BIGNUM */
dlascl_("G", &c__0, &c__0, &bnrm, &bignum, m, nrhs, &b[b_offset], ldb,
info);
ibscl = 2;
}
/* Overdetermined case */
if (*m >= *n) {
/* Path 1 - overdetermined or exactly determined */
mm = *m;
if (*m >= mnthr) {
/* Path 1a - overdetermined, with many more rows than columns */
mm = *n;
itau = 1;
iwork = itau + *n;
/* Compute A=Q*R
(Workspace: need 2*N, prefer N+N*NB) */
i__1 = *lwork - iwork + 1;
dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__1,
info);
/* Multiply B by transpose(Q)
(Workspace: need N+NRHS, prefer N+NRHS*NB) */
i__1 = *lwork - iwork + 1;
dormqr_("L", "T", m, nrhs, n, &a[a_offset], lda, &work[itau], &b[
b_offset], ldb, &work[iwork], &i__1, info);
/* Zero out below R */
if (*n > 1) {
i__1 = *n - 1;
i__2 = *n - 1;
dlaset_("L", &i__1, &i__2, &c_b74, &c_b74, &a_ref(2, 1), lda);
}
}
ie = 1;
itauq = ie + *n;
itaup = itauq + *n;
iwork = itaup + *n;
/* Bidiagonalize R in A
(Workspace: need 3*N+MM, prefer 3*N+(MM+N)*NB) */
i__1 = *lwork - iwork + 1;
dgebrd_(&mm, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], &
work[itaup], &work[iwork], &i__1, info);
/* Multiply B by transpose of left bidiagonalizing vectors of R
(Workspace: need 3*N+NRHS, prefer 3*N+NRHS*NB) */
i__1 = *lwork - iwork + 1;
dormbr_("Q", "L", "T", &mm, nrhs, n, &a[a_offset], lda, &work[itauq],
&b[b_offset], ldb, &work[iwork], &i__1, info);
/* Generate right bidiagonalizing vectors of R in A
(Workspace: need 4*N-1, prefer 3*N+(N-1)*NB) */
i__1 = *lwork - iwork + 1;
dorgbr_("P", n, n, n, &a[a_offset], lda, &work[itaup], &work[iwork], &
i__1, info);
iwork = ie + *n;
/* Perform bidiagonal QR iteration
multiply B by transpose of left singular vectors
compute right singular vectors in A
(Workspace: need BDSPAC) */
dbdsqr_("U", n, n, &c__0, nrhs, &s[1], &work[ie], &a[a_offset], lda,
vdum, &c__1, &b[b_offset], ldb, &work[iwork], info)
;
if (*info != 0) {
goto L70;
}
/* Multiply B by reciprocals of singular values
Computing MAX */
d__1 = *rcond * s[1];
thr = max(d__1,sfmin);
if (*rcond < 0.) {
/* Computing MAX */
d__1 = eps * s[1];
thr = max(d__1,sfmin);
}
*rank = 0;
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
if (s[i__] > thr) {
drscl_(nrhs, &s[i__], &b_ref(i__, 1), ldb);
++(*rank);
} else {
dlaset_("F", &c__1, nrhs, &c_b74, &c_b74, &b_ref(i__, 1), ldb);
}
/* L10: */
}
/* Multiply B by right singular vectors
(Workspace: need N, prefer N*NRHS) */
if (*lwork >= *ldb * *nrhs && *nrhs > 1) {
dgemm_("T", "N", n, nrhs, n, &c_b108, &a[a_offset], lda, &b[
b_offset], ldb, &c_b74, &work[1], ldb);
dlacpy_("G", n, nrhs, &work[1], ldb, &b[b_offset], ldb)
;
} else if (*nrhs > 1) {
chunk = *lwork / *n;
i__1 = *nrhs;
i__2 = chunk;
for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
/* Computing MIN */
i__3 = *nrhs - i__ + 1;
bl = min(i__3,chunk);
dgemm_("T", "N", n, &bl, n, &c_b108, &a[a_offset], lda, &
b_ref(1, i__), ldb, &c_b74, &work[1], n);
dlacpy_("G", n, &bl, &work[1], n, &b_ref(1, i__), ldb);
/* L20: */
}
} else {
dgemv_("T", n, n, &c_b108, &a[a_offset], lda, &b[b_offset], &c__1,
&c_b74, &work[1], &c__1);
dcopy_(n, &work[1], &c__1, &b[b_offset], &c__1);
}
} else /* if(complicated condition) */ {
/* Computing MAX */
i__2 = *m, i__1 = (*m << 1) - 4, i__2 = max(i__2,i__1), i__2 = max(
i__2,*nrhs), i__1 = *n - *m * 3;
if (*n >= mnthr && *lwork >= (*m << 2) + *m * *m + max(i__2,i__1)) {
/* Path 2a - underdetermined, with many more columns than rows
and sufficient workspace for an efficient algorithm */
ldwork = *m;
/* Computing MAX
Computing MAX */
i__3 = *m, i__4 = (*m << 1) - 4, i__3 = max(i__3,i__4), i__3 =
max(i__3,*nrhs), i__4 = *n - *m * 3;
i__2 = (*m << 2) + *m * *lda + max(i__3,i__4), i__1 = *m * *lda +
*m + *m * *nrhs;
if (*lwork >= max(i__2,i__1)) {
ldwork = *lda;
}
itau = 1;
iwork = *m + 1;
/* Compute A=L*Q
(Workspace: need 2*M, prefer M+M*NB) */
i__2 = *lwork - iwork + 1;
dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__2,
info);
il = iwork;
/* Copy L to WORK(IL), zeroing out above it */
dlacpy_("L", m, m, &a[a_offset], lda, &work[il], &ldwork);
i__2 = *m - 1;
i__1 = *m - 1;
dlaset_("U", &i__2, &i__1, &c_b74, &c_b74, &work[il + ldwork], &
ldwork);
ie = il + ldwork * *m;
itauq = ie + *m;
itaup = itauq + *m;
iwork = itaup + *m;
/* Bidiagonalize L in WORK(IL)
(Workspace: need M*M+5*M, prefer M*M+4*M+2*M*NB) */
i__2 = *lwork - iwork + 1;
dgebrd_(m, m, &work[il], &ldwork, &s[1], &work[ie], &work[itauq],
&work[itaup], &work[iwork], &i__2, info);
/* Multiply B by transpose of left bidiagonalizing vectors of L
(Workspace: need M*M+4*M+NRHS, prefer M*M+4*M+NRHS*NB) */
i__2 = *lwork - iwork + 1;
dormbr_("Q", "L", "T", m, nrhs, m, &work[il], &ldwork, &work[
itauq], &b[b_offset], ldb, &work[iwork], &i__2, info);
/* Generate right bidiagonalizing vectors of R in WORK(IL)
(Workspace: need M*M+5*M-1, prefer M*M+4*M+(M-1)*NB) */
i__2 = *lwork - iwork + 1;
dorgbr_("P", m, m, m, &work[il], &ldwork, &work[itaup], &work[
iwork], &i__2, info);
iwork = ie + *m;
/* Perform bidiagonal QR iteration,
computing right singular vectors of L in WORK(IL) and
multiplying B by transpose of left singular vectors
(Workspace: need M*M+M+BDSPAC) */
dbdsqr_("U", m, m, &c__0, nrhs, &s[1], &work[ie], &work[il], &
ldwork, &a[a_offset], lda, &b[b_offset], ldb, &work[iwork]
, info);
if (*info != 0) {
goto L70;
}
/* Multiply B by reciprocals of singular values
Computing MAX */
d__1 = *rcond * s[1];
thr = max(d__1,sfmin);
if (*rcond < 0.) {
/* Computing MAX */
d__1 = eps * s[1];
thr = max(d__1,sfmin);
}
*rank = 0;
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
if (s[i__] > thr) {
drscl_(nrhs, &s[i__], &b_ref(i__, 1), ldb);
++(*rank);
} else {
dlaset_("F", &c__1, nrhs, &c_b74, &c_b74, &b_ref(i__, 1),
ldb);
}
/* L30: */
}
iwork = ie;
/* Multiply B by right singular vectors of L in WORK(IL)
(Workspace: need M*M+2*M, prefer M*M+M+M*NRHS) */
if (*lwork >= *ldb * *nrhs + iwork - 1 && *nrhs > 1) {
dgemm_("T", "N", m, nrhs, m, &c_b108, &work[il], &ldwork, &b[
b_offset], ldb, &c_b74, &work[iwork], ldb);
dlacpy_("G", m, nrhs, &work[iwork], ldb, &b[b_offset], ldb);
} else if (*nrhs > 1) {
chunk = (*lwork - iwork + 1) / *m;
i__2 = *nrhs;
i__1 = chunk;
for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ +=
i__1) {
/* Computing MIN */
i__3 = *nrhs - i__ + 1;
bl = min(i__3,chunk);
dgemm_("T", "N", m, &bl, m, &c_b108, &work[il], &ldwork, &
b_ref(1, i__), ldb, &c_b74, &work[iwork], n);
dlacpy_("G", m, &bl, &work[iwork], n, &b_ref(1, i__), ldb);
/* L40: */
}
} else {
dgemv_("T", m, m, &c_b108, &work[il], &ldwork, &b_ref(1, 1), &
c__1, &c_b74, &work[iwork], &c__1);
dcopy_(m, &work[iwork], &c__1, &b_ref(1, 1), &c__1);
}
/* Zero out below first M rows of B */
i__1 = *n - *m;
dlaset_("F", &i__1, nrhs, &c_b74, &c_b74, &b_ref(*m + 1, 1), ldb);
iwork = itau + *m;
/* Multiply transpose(Q) by B
(Workspace: need M+NRHS, prefer M+NRHS*NB) */
i__1 = *lwork - iwork + 1;
dormlq_("L", "T", n, nrhs, m, &a[a_offset], lda, &work[itau], &b[
b_offset], ldb, &work[iwork], &i__1, info);
} else {
/* Path 2 - remaining underdetermined cases */
ie = 1;
itauq = ie + *m;
itaup = itauq + *m;
iwork = itaup + *m;
/* Bidiagonalize A
(Workspace: need 3*M+N, prefer 3*M+(M+N)*NB) */
i__1 = *lwork - iwork + 1;
dgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], &
work[itaup], &work[iwork], &i__1, info);
/* Multiply B by transpose of left bidiagonalizing vectors
(Workspace: need 3*M+NRHS, prefer 3*M+NRHS*NB) */
i__1 = *lwork - iwork + 1;
dormbr_("Q", "L", "T", m, nrhs, n, &a[a_offset], lda, &work[itauq]
, &b[b_offset], ldb, &work[iwork], &i__1, info);
/* Generate right bidiagonalizing vectors in A
(Workspace: need 4*M, prefer 3*M+M*NB) */
i__1 = *lwork - iwork + 1;
dorgbr_("P", m, n, m, &a[a_offset], lda, &work[itaup], &work[
iwork], &i__1, info);
iwork = ie + *m;
/* Perform bidiagonal QR iteration,
computing right singular vectors of A in A and
multiplying B by transpose of left singular vectors
(Workspace: need BDSPAC) */
dbdsqr_("L", m, n, &c__0, nrhs, &s[1], &work[ie], &a[a_offset],
lda, vdum, &c__1, &b[b_offset], ldb, &work[iwork], info);
if (*info != 0) {
goto L70;
}
/* Multiply B by reciprocals of singular values
Computing MAX */
d__1 = *rcond * s[1];
thr = max(d__1,sfmin);
if (*rcond < 0.) {
/* Computing MAX */
d__1 = eps * s[1];
thr = max(d__1,sfmin);
}
*rank = 0;
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
if (s[i__] > thr) {
drscl_(nrhs, &s[i__], &b_ref(i__, 1), ldb);
++(*rank);
} else {
dlaset_("F", &c__1, nrhs, &c_b74, &c_b74, &b_ref(i__, 1),
ldb);
}
/* L50: */
}
/* Multiply B by right singular vectors of A
(Workspace: need N, prefer N*NRHS) */
if (*lwork >= *ldb * *nrhs && *nrhs > 1) {
dgemm_("T", "N", n, nrhs, m, &c_b108, &a[a_offset], lda, &b[
b_offset], ldb, &c_b74, &work[1], ldb);
dlacpy_("F", n, nrhs, &work[1], ldb, &b[b_offset], ldb);
} else if (*nrhs > 1) {
chunk = *lwork / *n;
i__1 = *nrhs;
i__2 = chunk;
for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ +=
i__2) {
/* Computing MIN */
i__3 = *nrhs - i__ + 1;
bl = min(i__3,chunk);
dgemm_("T", "N", n, &bl, m, &c_b108, &a[a_offset], lda, &
b_ref(1, i__), ldb, &c_b74, &work[1], n);
dlacpy_("F", n, &bl, &work[1], n, &b_ref(1, i__), ldb);
/* L60: */
}
} else {
dgemv_("T", m, n, &c_b108, &a[a_offset], lda, &b[b_offset], &
c__1, &c_b74, &work[1], &c__1);
dcopy_(n, &work[1], &c__1, &b[b_offset], &c__1);
}
}
}
/* Undo scaling */
if (iascl == 1) {
dlascl_("G", &c__0, &c__0, &anrm, &smlnum, n, nrhs, &b[b_offset], ldb,
info);
dlascl_("G", &c__0, &c__0, &smlnum, &anrm, &minmn, &c__1, &s[1], &
minmn, info);
} else if (iascl == 2) {
dlascl_("G", &c__0, &c__0, &anrm, &bignum, n, nrhs, &b[b_offset], ldb,
info);
dlascl_("G", &c__0, &c__0, &bignum, &anrm, &minmn, &c__1, &s[1], &
minmn, info);
}
if (ibscl == 1) {
dlascl_("G", &c__0, &c__0, &smlnum, &bnrm, n, nrhs, &b[b_offset], ldb,
info);
} else if (ibscl == 2) {
dlascl_("G", &c__0, &c__0, &bignum, &bnrm, n, nrhs, &b[b_offset], ldb,
info);
}
L70:
work[1] = (doublereal) maxwrk;
return 0;
/* End of DGELSS */
} /* dgelss_ */
