int
mad_mat_div (const num_t x[], const num_t y[], num_t r[], ssz_t m, ssz_t n, ssz_t p, num_t rcond)
{
CHKXYR;
int info=0;
const int nm=m, nn=n, np=p;
mad_alloc_tmp(num_t, a, n*p);
mad_vec_copy(y, a, n*p);
// square system (y is square, n == p), use LU decomposition
if (n == p) {
int ipiv[n];
mad_vec_copy(x, r, m*p);
dgesv_(&np, &nm, a, &np, ipiv, r, &np, &info);
if (!info) return mad_free_tmp(a), n;
}
// non-square system or singular square system, use QR or LQ factorization
num_t sz;
int rank, ldb=MAX(nn,np), lwork=-1; // query for optimal size
int JPVT[nn]; memset(JPVT, 0, sizeof JPVT);
mad_alloc_tmp(num_t, rr, ldb*nm);
mad_mat_copy(x, rr, m, p, p, ldb); // input strided copy [M x NRHS]
dgelsy_(&np, &nn, &nm, a, &np, rr, &ldb, JPVT, &rcond, &rank, &sz, &lwork, &info); // query
mad_alloc_tmp(num_t, wk, lwork=sz);
dgelsy_(&np, &nn, &nm, a, &np, rr, &ldb, JPVT, &rcond, &rank, wk, &lwork, &info); // compute
mad_mat_copy(rr, r, m, n, ldb, n); // output strided copy [N x NRHS]
mad_free_tmp(wk); mad_free_tmp(rr); mad_free_tmp(a);
if (info < 0) error("invalid input argument");
if (info > 0) error("unexpect lapack error");
return rank;
}
void dgelsy_driver(double *A, double *b, double *x, int m, int n, int nrhs) {
if (m < n) {
printf("Error: driver now only works when m >= n\n");
return;
} else {
double *Atmp = malloc(sizeof(double) * m * n);
double *btmp = malloc(sizeof(double) * m * nrhs);
int lda = m;
int ldb = m;
int *jpvt = calloc(sizeof(int), n);
double rcond = -1.0;
int rank; /* Output */
int lwork = -1;
double *work = malloc(sizeof(double) * 1);
int info;
int i, j;
/* Go from row- to column-major */
for (i = 0; i < m; i++)
for (j = 0; j < n; j++)
Atmp[j * m + i] = A[i * n + j];
for (i = 0; i < m; i++)
for (j = 0; j < nrhs; j++)
btmp[j * m + i] = b[i * nrhs + j];
/* Query to find a good size for the work array */
dgelsy_(&m, &n, &nrhs, Atmp, &lda, btmp, &ldb, jpvt,
&rcond, &rank, work, &lwork, &info);
lwork = (int) work[0];
/* printf("Work size: %d\n", lwork); */
free(work);
work = malloc(sizeof(double) * lwork);
/* Make the FORTRAN call */
dgelsy_(&m, &n, &nrhs, Atmp, &lda, btmp, &ldb, jpvt,
&rcond, &rank, work, &lwork, &info);
if (info != 0)
printf("Error [%d] in call to dgelsy\n", info);
/* Go from column- to row-major */
for (i = 0; i < n; i++)
for (j = 0; j < nrhs; j++)
x[i * nrhs + j] = btmp[j * m + i];
free(Atmp);
free(btmp);
free(work);
free(jpvt);
}
}
DLLEXPORT MKL_INT d_qr_solve(MKL_INT m, MKL_INT n, MKL_INT bn, double a[], double b[], double x[], double work[], MKL_INT len)
{
MKL_INT info = 0;
MKL_INT* jpvt = new MKL_INT[n];
MKL_INT rank = 0;
double cond = -1.0;
double* clone_a = new double[m*n];
std::memcpy(clone_a, a, m*n*sizeof(double));
double* clone_b = new double[m*bn];
std::memcpy(clone_b, b, m*bn*sizeof(double));
dgelsy_(&m, &n, &bn, clone_a, &m, clone_b, &m, jpvt, &cond, &rank, work, &len, &info);
for (MKL_INT i = 0; i < n; ++i)
{
for (MKL_INT j = 0; j < bn; ++j)
{
x[j * n + i] = clone_b[j * m + i];
}
}
delete[] jpvt;
delete[] clone_a;
delete[] clone_b;
return info;
}
int ccdl::LeastSquaresFit
( int const nobs, int const nparam,
double const * A_obs_by_param,
double * x_param,
double const * b_obs,
double relative_accuracy_of_the_obs )
{
// min (xt.At-bt).(A.x-b)
std::vector<double> A( A_obs_by_param, A_obs_by_param + nparam*nobs );
int nmax = std::max( nparam, nobs );
std::vector<double> X( nmax, 0. );
std::copy( b_obs, b_obs + nobs, X.data() );
std::vector<int> jpvt( nparam, 0 );
int LWORK = -1;
int INFO = 0;
double twork = 0;
int rank = 0;
int nrhs=1;
dgelsy_( &nobs, &nparam, &nrhs,
A.data(), &nobs, X.data(), &nmax,
jpvt.data(), &relative_accuracy_of_the_obs, &rank,
&twork, &LWORK, &INFO );
if ( INFO == 0 )
{
LWORK = twork+1;
std::vector<double> WORK( LWORK, 0. );
#ifdef PDBG
std::printf("dgelsy_\n");
#endif
dgelsy_( &nobs, &nparam, &nrhs,
A.data(), &nobs, X.data(), &nmax,
jpvt.data(), &relative_accuracy_of_the_obs, &rank,
WORK.data(), &LWORK, &INFO );
#ifdef PDBG
std::printf("return %i\n",INFO);
#endif
std::copy( X.data(), X.data() + nparam, x_param );
}
else
{
std::fill( x_param, x_param + nparam, 0. );
};
return INFO;
}
void u8rdivma ( uint8 * in1, int lines1, int columns1,
uint8 * in2, int lines2, int columns2,
uint8 * out){
char cNorm = 0;
int iExit = 0;
/*temporary variables*/
int iWork = 0;
int iInfo = 0;
int iMax = 0;
uint8 dblRcond = 0;
uint8 dblEps = 0;
uint8 dblAnorm = 0;
uint8 *pAf = NULL;
uint8 *pAt = NULL;
uint8 *pBt = NULL;
uint8 *pDwork = NULL;
int *pRank = NULL;
int *pIpiv = NULL;
int *pJpvt = NULL;
int *pIwork = NULL;
iWork = max(4 * columns2, max(min(lines2, columns2) + 3 * lines2 + 1, 2 * min(lines2, columns2) + lines1));
/* Array allocations*/
pAf = (uint8*)malloc(sizeof(uint8) * (unsigned int)columns2 * (unsigned int)lines2);
pAt = (uint8*)malloc(sizeof(uint8) * (unsigned int)columns2 *(unsigned int) lines2);
pBt = (uint8*)malloc(sizeof(uint8) * (unsigned int)max(lines2,columns2) * (unsigned int)lines1);
pRank = (int*)malloc(sizeof(int));
pIpiv = (int*)malloc(sizeof(int) * (unsigned int)columns2);
pJpvt = (int*)malloc(sizeof(int) * (unsigned int)lines2);
pIwork = (int*)malloc(sizeof(int) * (unsigned int)columns2);
cNorm = '1';
pDwork = (uint8*)malloc(sizeof(uint8) * (unsigned int)iWork);
dblEps = getRelativeMachinePrecision() ;
dblAnorm = dlange_(&cNorm, &lines2, &columns1, in2, &lines2, pDwork);
/*tranpose A and B*/
dtransposea(in2, lines2, columns2, pAt);
dtransposea(in1, lines1, columns2, pBt);
if(lines2 == columns2)
{
cNorm = 'F';
dlacpy_(&cNorm, &columns2, &columns2, pAt, &columns2, pAf, &columns2);
dgetrf_(&columns2, &columns2, pAf, &columns2, pIpiv, &iInfo);
if(iInfo == 0)
{
cNorm = '1';
dgecon_(&cNorm, &columns2, pAf, &columns2, &dblAnorm, &dblRcond, pDwork, pIwork, &iInfo);
if(dblRcond > sqrt(dblEps))
{
cNorm = 'N';
dgetrs_(&cNorm, &columns2, &lines1, pAf, &columns2, pIpiv, pBt, &columns2, &iInfo);
dtransposea(pBt, columns2, lines1, out);
iExit = 1;
}
}
}
if(iExit == 0)
{
dblRcond = sqrt(dblEps);
cNorm = 'F';
iMax = max(lines2, columns2);
memset(pJpvt, 0x00, (unsigned int)sizeof(int) * (unsigned int)lines2);
dgelsy_(&columns2, &lines2, &lines1, pAt, &columns2, pBt, &iMax,
pJpvt, &dblRcond, &pRank[0], pDwork, &iWork, &iInfo);
if(iInfo == 0)
{
/* TransposeRealMatrix(pBt, lines1, lines2, out, Max(lines1,columns1), lines2);*/
/*Mega caca de la mort qui tue des ours a mains nues
mais je ne sais pas comment le rendre "beau" :(*/
{
int i,j,ij,ji;
for(j = 0 ; j < lines2 ; j++)
{
for(i = 0 ; i < lines1 ; i++)
{
ij = i + j * lines1;
ji = j + i * max(lines2, columns2);
out[ij] = pBt[ji];
}
}
}
}
}
free(pAf);
free(pAt);
free(pBt);
free(pRank);
free(pIpiv);
free(pJpvt);
free(pIwork);
free(pDwork);
}
/** Calculate least squares baseline solution from a set of double difference
* carrier phase observations and carrier phase ambiguities.
*
* Given the double difference carrier phase measurement equation:
*
* \f[
* \nabla \Delta \phi_i = N_i +
* \frac{1}{\lambda} (\mathbf{e}_i - \mathbf{e}_r) \cdot \mathbf{b} +
* \epsilon
* \f]
*
* where \f$ \nabla \Delta \phi_i \f$ is the double differenced carrier phase
* between satellite \f$i\f$ and reference satellite \f$r\f$, \f$N_i \in
* \mathbb{R}\f$ is the corresponding integer ambiguity, \f$\mathbf{e}_i\f$ is
* the unit vector to the \f$i\f$th satellite and \f$\mathbf{b}\f$ is the
* baseline vector between the rover and reference station.
*
* If there are 3 or more double difference carrier phase observations then the
* baseline can be estimated using a least squares solution:
*
* \f[
* \tilde{\mathbf{b}} = \underset{\mathbf{b}}{\mathrm{argmin}}
* \left\|
* \frac{1}{\lambda} \mathbf{DE}_i \cdot \mathbf{b} -
* \nabla \Delta \phi_i + N_i
* \right\|_{\mathcal{l}_2}
* \f]
*
* where:
*
* \f[
* \mathbf{DE}_i = \mathbf{e}_i - \mathbf{e}_r
* \f]
*
* \note This function takes real valued carrier phase ambiguities. For integer
* valued ambiguities, see lesq_solution_int().
*
* \param num_dds_u8 Number of double difference observations
* \param dd_obs Double differenced carrier phase observations in cycles,
* length `num_dds`
* \param N Carrier phase ambiguity vector, length `num_dds`
* \param DE Double differenced matrix of unit vectors to the satellites,
* length `3 * num_dds`
* \param b The output baseline in meters.
* \param resid The output least squares residuals in cycles.
* \return 0 on success,
* -1 if there were insufficient observations to calculate the
* baseline (the solution was under-constrained),
* -2 if an error occurred
*/
s8 lesq_solution_float(u8 num_dds_u8, const double *dd_obs, const double *N,
const double *DE, double b[3], double *resid)
{
assert(dd_obs != NULL);
assert(N != NULL);
assert(DE != NULL);
assert(b != NULL);
if (num_dds_u8 < 3) {
return -1;
}
assert(num_dds_u8 < MAX_CHANNELS);
for(int i = 0; i < num_dds_u8 * 3; i++) {
assert(isfinite(DE[i]));
}
integer num_dds = num_dds_u8;
double DET[num_dds * 3];
matrix_transpose(num_dds, 3, DE, DET);
double phase_ranges[MAX(num_dds,3)];
for (u8 i=0; i< num_dds; i++) {
phase_ranges[i] = dd_obs[i] - N[i];
}
s32 ldb = (s32) MAX(num_dds,3);
integer jpvt[3] = {0, 0, 0};
double rcond = 1e-12;
s32 rank;
s32 info;
s32 three = 3;
s32 one = 1;
/* From LAPACK DGELSY documentation:
* The unblocked strategy requires that:
* LWORK >= MAX( MN+3*N+1, 2*MN+NRHS )
* where MN = MIN( M, N )
*
* Therefore:
* M >= 3, N = 3, NRHS = 1
* MN = 3
* LWORK >= 13
*/
s32 lwork = 13;
double work[lwork];
/* DGELSY solves:
* argmin || A.x - B ||
* under the l2 norm, where
* A <- DE
* B <- phase_ranges = dd_obs - N
* M <- num_dds
* N <- 3
* NRHS <- 1
*
* the baseline result x is returned in the first 3 elements of phase_ranges.
*/
dgelsy_(&num_dds, &three, &one, /* M, N, NRHS. */
DET, &num_dds, /* A, LDA. */
phase_ranges, &ldb, /* B, LDB. */
jpvt, &rcond, /* JPVT, RCOND. */
&rank, /* RANK. */
work, &lwork, /* WORK, LWORK. */
&info); /* INFO. */
if (info != 0) {
log_error("dgelsy returned error %"PRId32"", info);
return -2;
}
assert(num_dds == num_dds_u8);
b[0] = phase_ranges[0] * GPS_L1_LAMBDA_NO_VAC;
b[1] = phase_ranges[1] * GPS_L1_LAMBDA_NO_VAC;
b[2] = phase_ranges[2] * GPS_L1_LAMBDA_NO_VAC;
if (resid) {
/* Calculate Least Squares Residuals */
/* resid <= dd_obs - N
* alpha <= - 1.0 / GPS_L1_LAMBDA_NO_VAC
* beta <= 1.0
* resid <= beta * resid + alpha * (DE . b)
*/
for (u8 i=0; i<num_dds; i++) {
resid[i] = dd_obs[i] - N[i];
}
cblas_dgemv(
CblasRowMajor, CblasNoTrans, num_dds, 3,
-1.0 / GPS_L1_LAMBDA_NO_VAC, DE, 3, b, 1,
1.0, resid, 1
);
}
return 0;
}
/* Subroutine */ int derrls_(char *path, integer *nunit)
{
/* Builtin functions */
integer s_wsle(cilist *), e_wsle(void);
/* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
/* Local variables */
doublereal a[4] /* was [2][2] */, b[4] /* was [2][2] */, s[2], w[2];
char c2[2];
integer ip[2], info, irnk;
extern /* Subroutine */ int dgels_(char *, integer *, integer *, integer *
, doublereal *, integer *, doublereal *, integer *, doublereal *,
integer *, integer *);
doublereal rcond;
extern /* Subroutine */ int alaesm_(char *, logical *, integer *),
dgelsd_(integer *, integer *, integer *, doublereal *, integer *,
doublereal *, integer *, doublereal *, doublereal *, integer *,
doublereal *, integer *, integer *, integer *);
extern logical lsamen_(integer *, char *, char *);
extern /* Subroutine */ int dgelss_(integer *, integer *, integer *,
doublereal *, integer *, doublereal *, integer *, doublereal *,
doublereal *, integer *, doublereal *, integer *, integer *),
chkxer_(char *, integer *, integer *, logical *, logical *), dgelsx_(integer *, integer *, integer *, doublereal *,
integer *, doublereal *, integer *, integer *, doublereal *,
integer *, doublereal *, integer *), dgelsy_(integer *, integer *,
integer *, doublereal *, integer *, doublereal *, integer *,
integer *, doublereal *, integer *, doublereal *, integer *,
integer *);
/* Fortran I/O blocks */
static cilist io___1 = { 0, 0, 0, 0, 0 };
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DERRLS tests the error exits for the DOUBLE PRECISION least squares */
/* driver routines (DGELS, SGELSS, SGELSX, SGELSY, SGELSD). */
/* 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 .. */
/* .. */
/* .. 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);
a[0] = 1.;
a[2] = 2.;
a[3] = 3.;
a[1] = 4.;
infoc_1.ok = TRUE_;
if (lsamen_(&c__2, c2, "LS")) {
/* Test error exits for the least squares driver routines. */
/* DGELS */
s_copy(srnamc_1.srnamt, "DGELS ", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
dgels_("/", &c__0, &c__0, &c__0, a, &c__1, b, &c__1, w, &c__1, &info);
chkxer_("DGELS ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
dgels_("N", &c_n1, &c__0, &c__0, a, &c__1, b, &c__1, w, &c__1, &info);
chkxer_("DGELS ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
dgels_("N", &c__0, &c_n1, &c__0, a, &c__1, b, &c__1, w, &c__1, &info);
chkxer_("DGELS ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
dgels_("N", &c__0, &c__0, &c_n1, a, &c__1, b, &c__1, w, &c__1, &info);
chkxer_("DGELS ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
dgels_("N", &c__2, &c__0, &c__0, a, &c__1, b, &c__2, w, &c__2, &info);
chkxer_("DGELS ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
dgels_("N", &c__2, &c__0, &c__0, a, &c__2, b, &c__1, w, &c__2, &info);
chkxer_("DGELS ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
dgels_("N", &c__1, &c__1, &c__0, a, &c__1, b, &c__1, w, &c__1, &info);
chkxer_("DGELS ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* DGELSS */
s_copy(srnamc_1.srnamt, "DGELSS", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
dgelss_(&c_n1, &c__0, &c__0, a, &c__1, b, &c__1, s, &rcond, &irnk, w,
&c__1, &info);
chkxer_("DGELSS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
dgelss_(&c__0, &c_n1, &c__0, a, &c__1, b, &c__1, s, &rcond, &irnk, w,
&c__1, &info);
chkxer_("DGELSS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
dgelss_(&c__0, &c__0, &c_n1, a, &c__1, b, &c__1, s, &rcond, &irnk, w,
&c__1, &info);
chkxer_("DGELSS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
dgelss_(&c__2, &c__0, &c__0, a, &c__1, b, &c__2, s, &rcond, &irnk, w,
&c__2, &info);
chkxer_("DGELSS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
dgelss_(&c__2, &c__0, &c__0, a, &c__2, b, &c__1, s, &rcond, &irnk, w,
&c__2, &info);
chkxer_("DGELSS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* DGELSX */
s_copy(srnamc_1.srnamt, "DGELSX", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
dgelsx_(&c_n1, &c__0, &c__0, a, &c__1, b, &c__1, ip, &rcond, &irnk, w,
&info);
chkxer_("DGELSX", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
dgelsx_(&c__0, &c_n1, &c__0, a, &c__1, b, &c__1, ip, &rcond, &irnk, w,
&info);
chkxer_("DGELSX", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
dgelsx_(&c__0, &c__0, &c_n1, a, &c__1, b, &c__1, ip, &rcond, &irnk, w,
&info);
chkxer_("DGELSX", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
dgelsx_(&c__2, &c__0, &c__0, a, &c__1, b, &c__2, ip, &rcond, &irnk, w,
&info);
chkxer_("DGELSX", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
dgelsx_(&c__2, &c__0, &c__0, a, &c__2, b, &c__1, ip, &rcond, &irnk, w,
&info);
chkxer_("DGELSX", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* DGELSY */
s_copy(srnamc_1.srnamt, "DGELSY", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
dgelsy_(&c_n1, &c__0, &c__0, a, &c__1, b, &c__1, ip, &rcond, &irnk, w,
&c__10, &info);
chkxer_("DGELSY", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
dgelsy_(&c__0, &c_n1, &c__0, a, &c__1, b, &c__1, ip, &rcond, &irnk, w,
&c__10, &info);
chkxer_("DGELSY", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
dgelsy_(&c__0, &c__0, &c_n1, a, &c__1, b, &c__1, ip, &rcond, &irnk, w,
&c__10, &info);
chkxer_("DGELSY", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
dgelsy_(&c__2, &c__0, &c__0, a, &c__1, b, &c__2, ip, &rcond, &irnk, w,
&c__10, &info);
chkxer_("DGELSY", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
dgelsy_(&c__2, &c__0, &c__0, a, &c__2, b, &c__1, ip, &rcond, &irnk, w,
&c__10, &info);
chkxer_("DGELSY", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 12;
dgelsy_(&c__2, &c__2, &c__1, a, &c__2, b, &c__2, ip, &rcond, &irnk, w,
&c__1, &info);
chkxer_("DGELSY", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* DGELSD */
s_copy(srnamc_1.srnamt, "DGELSD", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
dgelsd_(&c_n1, &c__0, &c__0, a, &c__1, b, &c__1, s, &rcond, &irnk, w,
&c__10, ip, &info);
chkxer_("DGELSD", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
dgelsd_(&c__0, &c_n1, &c__0, a, &c__1, b, &c__1, s, &rcond, &irnk, w,
&c__10, ip, &info);
chkxer_("DGELSD", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
dgelsd_(&c__0, &c__0, &c_n1, a, &c__1, b, &c__1, s, &rcond, &irnk, w,
&c__10, ip, &info);
chkxer_("DGELSD", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
dgelsd_(&c__2, &c__0, &c__0, a, &c__1, b, &c__2, s, &rcond, &irnk, w,
&c__10, ip, &info);
chkxer_("DGELSD", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
dgelsd_(&c__2, &c__0, &c__0, a, &c__2, b, &c__1, s, &rcond, &irnk, w,
&c__10, ip, &info);
chkxer_("DGELSD", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 12;
dgelsd_(&c__2, &c__2, &c__1, a, &c__2, b, &c__2, s, &rcond, &irnk, w,
&c__1, ip, &info);
chkxer_("DGELSD", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
}
/* Print a summary line. */
alaesm_(path, &infoc_1.ok, &infoc_1.nout);
return 0;
/* End of DERRLS */
} /* derrls_ */
/* Subroutine */ int ddrvls_(logical *dotype, integer *nm, integer *mval,
integer *nn, integer *nval, integer *nns, integer *nsval, integer *
nnb, integer *nbval, integer *nxval, doublereal *thresh, logical *
tsterr, doublereal *a, doublereal *copya, doublereal *b, doublereal *
copyb, doublereal *c__, doublereal *s, doublereal *copys, doublereal *
work, integer *iwork, integer *nout)
{
/* Initialized data */
static integer iseedy[4] = { 1988,1989,1990,1991 };
/* Format strings */
static char fmt_9999[] = "(\002 TRANS='\002,a1,\002', M=\002,i5,\002, N"
"=\002,i5,\002, NRHS=\002,i4,\002, NB=\002,i4,\002, type\002,i2"
",\002, test(\002,i2,\002)=\002,g12.5)";
static char fmt_9998[] = "(\002 M=\002,i5,\002, N=\002,i5,\002, NRHS="
"\002,i4,\002, NB=\002,i4,\002, type\002,i2,\002, test(\002,i2"
",\002)=\002,g12.5)";
/* System generated locals */
integer i__1, i__2, i__3, i__4, i__5, i__6;
doublereal d__1, d__2;
/* Builtin functions
Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
double sqrt(doublereal), log(doublereal);
integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void);
/* Local variables */
static integer info;
static char path[3];
static integer rank, nrhs, nlvl, nrun, i__, j, k;
extern /* Subroutine */ int alahd_(integer *, char *);
static integer m, n;
extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *,
integer *);
static integer nfail, iseed[4];
extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *,
integer *, doublereal *, doublereal *, integer *, doublereal *,
integer *, doublereal *, doublereal *, integer *);
static integer crank;
extern /* Subroutine */ int dgels_(char *, integer *, integer *, integer *
, doublereal *, integer *, doublereal *, integer *, doublereal *,
integer *, integer *);
static integer irank;
static doublereal rcond;
extern doublereal dasum_(integer *, doublereal *, integer *);
static integer itran, mnmin, ncols;
static doublereal norma, normb;
extern doublereal dqrt12_(integer *, integer *, doublereal *, integer *,
doublereal *, doublereal *, integer *), dqrt14_(char *, integer *,
integer *, integer *, doublereal *, integer *, doublereal *,
integer *, doublereal *, integer *), dqrt17_(char *,
integer *, integer *, integer *, integer *, doublereal *, integer
*, doublereal *, integer *, doublereal *, integer *, doublereal *,
doublereal *, integer *);
extern /* Subroutine */ int daxpy_(integer *, doublereal *, doublereal *,
integer *, doublereal *, integer *);
static char trans[1];
static integer nerrs, itype;
extern /* Subroutine */ int dqrt13_(integer *, integer *, integer *,
doublereal *, integer *, doublereal *, integer *);
static integer lwork;
extern /* Subroutine */ int dqrt15_(integer *, integer *, integer *,
integer *, integer *, doublereal *, integer *, doublereal *,
integer *, doublereal *, integer *, doublereal *, doublereal *,
integer *, doublereal *, integer *), dqrt16_(char *, integer *,
integer *, integer *, doublereal *, integer *, doublereal *,
integer *, doublereal *, integer *, doublereal *, doublereal *);
static integer nrows, lwlsy, nb, im, in;
extern doublereal dlamch_(char *);
extern /* Subroutine */ int alaerh_(char *, char *, integer *, integer *,
char *, integer *, integer *, integer *, integer *, integer *,
integer *, integer *, integer *, integer *);
static integer iscale;
extern /* Subroutine */ int dgelsd_(integer *, integer *, integer *,
doublereal *, integer *, doublereal *, integer *, doublereal *,
doublereal *, integer *, doublereal *, integer *, integer *,
integer *), dlacpy_(char *, integer *, integer *, doublereal *,
integer *, doublereal *, integer *), dgelss_(integer *,
integer *, integer *, doublereal *, integer *, doublereal *,
integer *, doublereal *, doublereal *, integer *, doublereal *,
integer *, integer *), alasvm_(char *, integer *, integer *,
integer *, integer *), dgelsx_(integer *, integer *,
integer *, doublereal *, integer *, doublereal *, integer *,
integer *, doublereal *, integer *, doublereal *, integer *),
dgelsy_(integer *, integer *, integer *, doublereal *, integer *,
doublereal *, integer *, integer *, doublereal *, integer *,
doublereal *, integer *, integer *), dlarnv_(integer *, integer *,
integer *, doublereal *), derrls_(char *, integer *),
xlaenv_(integer *, integer *);
static integer ldwork;
static doublereal result[18];
static integer lda, ldb, inb;
static doublereal eps;
static integer ins;
/* Fortran I/O blocks */
static cilist io___35 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___40 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___42 = { 0, 0, 0, fmt_9998, 0 };
/* -- LAPACK test routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
January 3, 2000
Purpose
=======
DDRVLS tests the least squares driver routines DGELS, DGELSS, DGELSX,
DGELSY and DGELSD.
Arguments
=========
DOTYPE (input) LOGICAL array, dimension (NTYPES)
The matrix types to be used for testing. Matrices of type j
(for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
.TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
The matrix of type j is generated as follows:
j=1: A = U*D*V where U and V are random orthogonal matrices
and D has random entries (> 0.1) taken from a uniform
distribution (0,1). A is full rank.
j=2: The same of 1, but A is scaled up.
j=3: The same of 1, but A is scaled down.
j=4: A = U*D*V where U and V are random orthogonal matrices
and D has 3*min(M,N)/4 random entries (> 0.1) taken
from a uniform distribution (0,1) and the remaining
entries set to 0. A is rank-deficient.
j=5: The same of 4, but A is scaled up.
j=6: The same of 5, but A is scaled down.
NM (input) INTEGER
The number of values of M contained in the vector MVAL.
MVAL (input) INTEGER array, dimension (NM)
The values of the matrix row dimension M.
NN (input) INTEGER
The number of values of N contained in the vector NVAL.
NVAL (input) INTEGER array, dimension (NN)
The values of the matrix column dimension N.
NNS (input) INTEGER
The number of values of NRHS contained in the vector NSVAL.
NSVAL (input) INTEGER array, dimension (NNS)
The values of the number of right hand sides NRHS.
NNB (input) INTEGER
The number of values of NB and NX contained in the
vectors NBVAL and NXVAL. The blocking parameters are used
in pairs (NB,NX).
NBVAL (input) INTEGER array, dimension (NNB)
The values of the blocksize NB.
NXVAL (input) INTEGER array, dimension (NNB)
The values of the crossover point NX.
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.
TSTERR (input) LOGICAL
Flag that indicates whether error exits are to be tested.
A (workspace) DOUBLE PRECISION array, dimension (MMAX*NMAX)
where MMAX is the maximum value of M in MVAL and NMAX is the
maximum value of N in NVAL.
COPYA (workspace) DOUBLE PRECISION array, dimension (MMAX*NMAX)
B (workspace) DOUBLE PRECISION array, dimension (MMAX*NSMAX)
where MMAX is the maximum value of M in MVAL and NSMAX is the
maximum value of NRHS in NSVAL.
COPYB (workspace) DOUBLE PRECISION array, dimension (MMAX*NSMAX)
C (workspace) DOUBLE PRECISION array, dimension (MMAX*NSMAX)
S (workspace) DOUBLE PRECISION array, dimension
(min(MMAX,NMAX))
COPYS (workspace) DOUBLE PRECISION array, dimension
(min(MMAX,NMAX))
WORK (workspace) DOUBLE PRECISION array,
dimension (MMAX*NMAX + 4*NMAX + MMAX).
IWORK (workspace) INTEGER array, dimension (15*NMAX)
NOUT (input) INTEGER
The unit number for output.
=====================================================================
Parameter adjustments */
--iwork;
--work;
--copys;
--s;
--c__;
--copyb;
--b;
--copya;
--a;
--nxval;
--nbval;
--nsval;
--nval;
--mval;
--dotype;
/* Function Body
Initialize constants and the random number seed. */
s_copy(path, "Double precision", (ftnlen)1, (ftnlen)16);
s_copy(path + 1, "LS", (ftnlen)2, (ftnlen)2);
nrun = 0;
nfail = 0;
nerrs = 0;
for (i__ = 1; i__ <= 4; ++i__) {
iseed[i__ - 1] = iseedy[i__ - 1];
/* L10: */
}
eps = dlamch_("Epsilon");
/* Threshold for rank estimation */
rcond = sqrt(eps) - (sqrt(eps) - eps) / 2;
/* Test the error exits */
if (*tsterr) {
derrls_(path, nout);
}
/* Print the header if NM = 0 or NN = 0 and THRESH = 0. */
if ((*nm == 0 || *nn == 0) && *thresh == 0.) {
alahd_(nout, path);
}
infoc_1.infot = 0;
xlaenv_(&c__2, &c__2);
xlaenv_(&c__9, &c__25);
i__1 = *nm;
for (im = 1; im <= i__1; ++im) {
m = mval[im];
lda = max(1,m);
i__2 = *nn;
for (in = 1; in <= i__2; ++in) {
n = nval[in];
mnmin = min(m,n);
/* Computing MAX */
i__3 = max(1,m);
ldb = max(i__3,n);
i__3 = *nns;
for (ins = 1; ins <= i__3; ++ins) {
nrhs = nsval[ins];
/* Computing MAX
Computing MAX */
d__1 = 1., d__2 = (doublereal) mnmin;
i__4 = (integer) (log(max(d__1,d__2) / 26.) / log(2.)) + 1;
nlvl = max(i__4,0);
/* Computing MAX */
i__4 = 1, i__5 = (m + nrhs) * (n + 2), i__4 = max(i__4,i__5),
i__5 = (n + nrhs) * (m + 2), i__4 = max(i__4,i__5),
i__5 = m * n + (mnmin << 2) + max(m,n), i__4 = max(
i__4,i__5), i__5 = mnmin * 12 + mnmin * 50 + (mnmin <<
3) * nlvl + mnmin * nrhs + 676;
lwork = max(i__4,i__5);
for (irank = 1; irank <= 2; ++irank) {
for (iscale = 1; iscale <= 3; ++iscale) {
itype = (irank - 1) * 3 + iscale;
if (! dotype[itype]) {
goto L110;
}
if (irank == 1) {
/* Test DGELS
Generate a matrix of scaling type ISCALE */
dqrt13_(&iscale, &m, &n, ©a[1], &lda, &norma,
iseed);
i__4 = *nnb;
for (inb = 1; inb <= i__4; ++inb) {
nb = nbval[inb];
xlaenv_(&c__1, &nb);
xlaenv_(&c__3, &nxval[inb]);
for (itran = 1; itran <= 2; ++itran) {
if (itran == 1) {
*(unsigned char *)trans = 'N';
nrows = m;
ncols = n;
} else {
*(unsigned char *)trans = 'T';
nrows = n;
ncols = m;
}
ldwork = max(1,ncols);
/* Set up a consistent rhs */
if (ncols > 0) {
i__5 = ncols * nrhs;
dlarnv_(&c__2, iseed, &i__5, &work[1])
;
i__5 = ncols * nrhs;
d__1 = 1. / (doublereal) ncols;
dscal_(&i__5, &d__1, &work[1], &c__1);
}
dgemm_(trans, "No transpose", &nrows, &
nrhs, &ncols, &c_b24, ©a[1], &
lda, &work[1], &ldwork, &c_b25, &
b[1], &ldb)
;
dlacpy_("Full", &nrows, &nrhs, &b[1], &
ldb, ©b[1], &ldb);
/* Solve LS or overdetermined system */
if (m > 0 && n > 0) {
dlacpy_("Full", &m, &n, ©a[1], &
lda, &a[1], &lda);
dlacpy_("Full", &nrows, &nrhs, ©b[
1], &ldb, &b[1], &ldb);
}
s_copy(srnamc_1.srnamt, "DGELS ", (ftnlen)
6, (ftnlen)6);
dgels_(trans, &m, &n, &nrhs, &a[1], &lda,
&b[1], &ldb, &work[1], &lwork, &
info);
if (info != 0) {
alaerh_(path, "DGELS ", &info, &c__0,
trans, &m, &n, &nrhs, &c_n1, &
nb, &itype, &nfail, &nerrs,
nout);
}
/* Check correctness of results */
ldwork = max(1,nrows);
if (nrows > 0 && nrhs > 0) {
dlacpy_("Full", &nrows, &nrhs, ©b[
1], &ldb, &c__[1], &ldb);
}
dqrt16_(trans, &m, &n, &nrhs, ©a[1], &
lda, &b[1], &ldb, &c__[1], &ldb, &
work[1], result);
if (itran == 1 && m >= n || itran == 2 &&
m < n) {
/* Solving LS system */
result[1] = dqrt17_(trans, &c__1, &m,
&n, &nrhs, ©a[1], &lda, &
b[1], &ldb, ©b[1], &ldb, &
c__[1], &work[1], &lwork);
} else {
/* Solving overdetermined system */
result[1] = dqrt14_(trans, &m, &n, &
nrhs, ©a[1], &lda, &b[1],
&ldb, &work[1], &lwork);
}
/* Print information about the tests that
did not pass the threshold. */
for (k = 1; k <= 2; ++k) {
if (result[k - 1] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
alahd_(nout, path);
}
io___35.ciunit = *nout;
s_wsfe(&io___35);
do_fio(&c__1, trans, (ftnlen)1);
do_fio(&c__1, (char *)&m, (ftnlen)
sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)
sizeof(integer));
do_fio(&c__1, (char *)&nrhs, (
ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&nb, (
ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&itype, (
ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&k, (ftnlen)
sizeof(integer));
do_fio(&c__1, (char *)&result[k -
1], (ftnlen)sizeof(
doublereal));
e_wsfe();
++nfail;
}
/* L20: */
}
nrun += 2;
/* L30: */
}
/* L40: */
}
}
/* Generate a matrix of scaling type ISCALE and rank
type IRANK. */
dqrt15_(&iscale, &irank, &m, &n, &nrhs, ©a[1], &
lda, ©b[1], &ldb, ©s[1], &rank, &
norma, &normb, iseed, &work[1], &lwork);
/* workspace used: MAX(M+MIN(M,N),NRHS*MIN(M,N),2*N+M)
Initialize vector IWORK. */
i__4 = n;
for (j = 1; j <= i__4; ++j) {
iwork[j] = 0;
/* L50: */
}
ldwork = max(1,m);
/* Test DGELSX
DGELSX: Compute the minimum-norm solution X
to min( norm( A * X - B ) ) using a complete
orthogonal factorization. */
dlacpy_("Full", &m, &n, ©a[1], &lda, &a[1], &lda);
dlacpy_("Full", &m, &nrhs, ©b[1], &ldb, &b[1], &
ldb);
s_copy(srnamc_1.srnamt, "DGELSX", (ftnlen)6, (ftnlen)
6);
dgelsx_(&m, &n, &nrhs, &a[1], &lda, &b[1], &ldb, &
iwork[1], &rcond, &crank, &work[1], &info);
if (info != 0) {
alaerh_(path, "DGELSX", &info, &c__0, " ", &m, &n,
&nrhs, &c_n1, &nb, &itype, &nfail, &
nerrs, nout);
}
/* workspace used: MAX( MNMIN+3*N, 2*MNMIN+NRHS )
Test 3: Compute relative error in svd
workspace: M*N + 4*MIN(M,N) + MAX(M,N) */
result[2] = dqrt12_(&crank, &crank, &a[1], &lda, &
copys[1], &work[1], &lwork);
/* Test 4: Compute error in solution
workspace: M*NRHS + M */
dlacpy_("Full", &m, &nrhs, ©b[1], &ldb, &work[1],
&ldwork);
dqrt16_("No transpose", &m, &n, &nrhs, ©a[1], &
lda, &b[1], &ldb, &work[1], &ldwork, &work[m *
nrhs + 1], &result[3]);
/* Test 5: Check norm of r'*A
workspace: NRHS*(M+N) */
result[4] = 0.;
if (m > crank) {
result[4] = dqrt17_("No transpose", &c__1, &m, &n,
&nrhs, ©a[1], &lda, &b[1], &ldb, &
copyb[1], &ldb, &c__[1], &work[1], &lwork);
}
/* Test 6: Check if x is in the rowspace of A
workspace: (M+NRHS)*(N+2) */
result[5] = 0.;
if (n > crank) {
result[5] = dqrt14_("No transpose", &m, &n, &nrhs,
©a[1], &lda, &b[1], &ldb, &work[1], &
lwork);
}
/* Print information about the tests that did not
pass the threshold. */
for (k = 3; k <= 6; ++k) {
if (result[k - 1] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
alahd_(nout, path);
}
io___40.ciunit = *nout;
s_wsfe(&io___40);
do_fio(&c__1, (char *)&m, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&nrhs, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&nb, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&itype, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&k, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&result[k - 1], (ftnlen)
sizeof(doublereal));
e_wsfe();
++nfail;
}
/* L60: */
}
nrun += 4;
/* Loop for testing different block sizes. */
i__4 = *nnb;
for (inb = 1; inb <= i__4; ++inb) {
nb = nbval[inb];
xlaenv_(&c__1, &nb);
xlaenv_(&c__3, &nxval[inb]);
/* Test DGELSY
DGELSY: Compute the minimum-norm solution X
to min( norm( A * X - B ) )
using the rank-revealing orthogonal
factorization.
Initialize vector IWORK. */
i__5 = n;
for (j = 1; j <= i__5; ++j) {
iwork[j] = 0;
/* L70: */
}
/* Set LWLSY to the adequate value.
Computing MAX */
i__5 = 1, i__6 = mnmin + (n << 1) + nb * (n + 1),
i__5 = max(i__5,i__6), i__6 = (mnmin << 1)
+ nb * nrhs;
lwlsy = max(i__5,i__6);
dlacpy_("Full", &m, &n, ©a[1], &lda, &a[1], &
lda);
dlacpy_("Full", &m, &nrhs, ©b[1], &ldb, &b[1],
&ldb);
s_copy(srnamc_1.srnamt, "DGELSY", (ftnlen)6, (
ftnlen)6);
dgelsy_(&m, &n, &nrhs, &a[1], &lda, &b[1], &ldb, &
iwork[1], &rcond, &crank, &work[1], &
lwlsy, &info);
if (info != 0) {
alaerh_(path, "DGELSY", &info, &c__0, " ", &m,
&n, &nrhs, &c_n1, &nb, &itype, &
nfail, &nerrs, nout);
}
/* Test 7: Compute relative error in svd
workspace: M*N + 4*MIN(M,N) + MAX(M,N) */
result[6] = dqrt12_(&crank, &crank, &a[1], &lda, &
copys[1], &work[1], &lwork);
/* Test 8: Compute error in solution
workspace: M*NRHS + M */
dlacpy_("Full", &m, &nrhs, ©b[1], &ldb, &work[
1], &ldwork);
dqrt16_("No transpose", &m, &n, &nrhs, ©a[1],
&lda, &b[1], &ldb, &work[1], &ldwork, &
work[m * nrhs + 1], &result[7]);
/* Test 9: Check norm of r'*A
workspace: NRHS*(M+N) */
result[8] = 0.;
if (m > crank) {
result[8] = dqrt17_("No transpose", &c__1, &m,
&n, &nrhs, ©a[1], &lda, &b[1], &
ldb, ©b[1], &ldb, &c__[1], &work[
1], &lwork);
}
/* Test 10: Check if x is in the rowspace of A
workspace: (M+NRHS)*(N+2) */
result[9] = 0.;
if (n > crank) {
result[9] = dqrt14_("No transpose", &m, &n, &
nrhs, ©a[1], &lda, &b[1], &ldb, &
work[1], &lwork);
}
/* Test DGELSS
DGELSS: Compute the minimum-norm solution X
to min( norm( A * X - B ) )
using the SVD. */
dlacpy_("Full", &m, &n, ©a[1], &lda, &a[1], &
lda);
dlacpy_("Full", &m, &nrhs, ©b[1], &ldb, &b[1],
&ldb);
s_copy(srnamc_1.srnamt, "DGELSS", (ftnlen)6, (
ftnlen)6);
dgelss_(&m, &n, &nrhs, &a[1], &lda, &b[1], &ldb, &
s[1], &rcond, &crank, &work[1], &lwork, &
info);
if (info != 0) {
alaerh_(path, "DGELSS", &info, &c__0, " ", &m,
&n, &nrhs, &c_n1, &nb, &itype, &
nfail, &nerrs, nout);
}
/* workspace used: 3*min(m,n) +
max(2*min(m,n),nrhs,max(m,n))
Test 11: Compute relative error in svd */
if (rank > 0) {
daxpy_(&mnmin, &c_b92, ©s[1], &c__1, &s[1]
, &c__1);
result[10] = dasum_(&mnmin, &s[1], &c__1) /
dasum_(&mnmin, ©s[1], &c__1) / (
eps * (doublereal) mnmin);
} else {
result[10] = 0.;
}
/* Test 12: Compute error in solution */
dlacpy_("Full", &m, &nrhs, ©b[1], &ldb, &work[
1], &ldwork);
dqrt16_("No transpose", &m, &n, &nrhs, ©a[1],
&lda, &b[1], &ldb, &work[1], &ldwork, &
work[m * nrhs + 1], &result[11]);
/* Test 13: Check norm of r'*A */
result[12] = 0.;
if (m > crank) {
result[12] = dqrt17_("No transpose", &c__1, &
m, &n, &nrhs, ©a[1], &lda, &b[1],
&ldb, ©b[1], &ldb, &c__[1], &work[
1], &lwork);
}
/* Test 14: Check if x is in the rowspace of A */
result[13] = 0.;
if (n > crank) {
result[13] = dqrt14_("No transpose", &m, &n, &
nrhs, ©a[1], &lda, &b[1], &ldb, &
work[1], &lwork);
}
/* Test DGELSD
DGELSD: Compute the minimum-norm solution X
to min( norm( A * X - B ) ) using a
divide and conquer SVD.
Initialize vector IWORK. */
i__5 = n;
for (j = 1; j <= i__5; ++j) {
iwork[j] = 0;
/* L80: */
}
dlacpy_("Full", &m, &n, ©a[1], &lda, &a[1], &
lda);
dlacpy_("Full", &m, &nrhs, ©b[1], &ldb, &b[1],
&ldb);
s_copy(srnamc_1.srnamt, "DGELSD", (ftnlen)6, (
ftnlen)6);
dgelsd_(&m, &n, &nrhs, &a[1], &lda, &b[1], &ldb, &
s[1], &rcond, &crank, &work[1], &lwork, &
iwork[1], &info);
if (info != 0) {
alaerh_(path, "DGELSD", &info, &c__0, " ", &m,
&n, &nrhs, &c_n1, &nb, &itype, &
nfail, &nerrs, nout);
}
/* Test 15: Compute relative error in svd */
if (rank > 0) {
daxpy_(&mnmin, &c_b92, ©s[1], &c__1, &s[1]
, &c__1);
result[14] = dasum_(&mnmin, &s[1], &c__1) /
dasum_(&mnmin, ©s[1], &c__1) / (
eps * (doublereal) mnmin);
} else {
result[14] = 0.;
}
/* Test 16: Compute error in solution */
dlacpy_("Full", &m, &nrhs, ©b[1], &ldb, &work[
1], &ldwork);
dqrt16_("No transpose", &m, &n, &nrhs, ©a[1],
&lda, &b[1], &ldb, &work[1], &ldwork, &
work[m * nrhs + 1], &result[15]);
/* Test 17: Check norm of r'*A */
result[16] = 0.;
if (m > crank) {
result[16] = dqrt17_("No transpose", &c__1, &
m, &n, &nrhs, ©a[1], &lda, &b[1],
&ldb, ©b[1], &ldb, &c__[1], &work[
1], &lwork);
}
/* Test 18: Check if x is in the rowspace of A */
result[17] = 0.;
if (n > crank) {
result[17] = dqrt14_("No transpose", &m, &n, &
nrhs, ©a[1], &lda, &b[1], &ldb, &
work[1], &lwork);
}
/* Print information about the tests that did not
pass the threshold. */
for (k = 7; k <= 18; ++k) {
if (result[k - 1] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
alahd_(nout, path);
}
io___42.ciunit = *nout;
s_wsfe(&io___42);
do_fio(&c__1, (char *)&m, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&nrhs, (ftnlen)
sizeof(integer));
do_fio(&c__1, (char *)&nb, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&itype, (ftnlen)
sizeof(integer));
do_fio(&c__1, (char *)&k, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&result[k - 1], (
ftnlen)sizeof(doublereal));
e_wsfe();
++nfail;
}
/* L90: */
}
nrun += 12;
/* L100: */
}
L110:
;
}
/* L120: */
}
/* L130: */
}
/* L140: */
}
/* L150: */
}
/* Print a summary of the results. */
alasvm_(path, nout, &nfail, &nrun, &nerrs);
return 0;
/* End of DDRVLS */
} /* ddrvls_ */