void matrix::svd(matrix& U, diagMatrix& S, matrix& Vdag) const
{ static StopWatch watch("matrix::svd");
watch.start();
//Initialize input and outputs:
matrix A = *this; //destructible copy
int M = A.nRows();
int N = A.nCols();
U.init(M,M);
Vdag.init(N,N);
S.resize(std::min(M,N));
//Initialize temporaries:
char jobz = 'A'; //full SVD (return complete unitary matrices)
int lwork = 2*(M*N + M + N);
std::vector<complex> work(lwork);
std::vector<double> rwork(S.nRows() * std::max(5*S.nRows()+7, 2*(M+N)+1));
std::vector<int> iwork(8*S.nRows());
//Call LAPACK and check errors:
int info=0;
zgesdd_(&jobz, &M, &N, A.data(), &M, S.data(), U.data(), &M, Vdag.data(), &N,
work.data(), &lwork, rwork.data(), iwork.data(), &info);
if(info>0) //convergence failure; try the slower stabler version
{ int info=0;
matrix A = *this; //destructible copy
zgesvd_(&jobz, &jobz, &M, &N, A.data(), &M, S.data(), U.data(), &M, Vdag.data(), &N,
work.data(), &lwork, rwork.data(), &info);
if(info<0) { logPrintf("Argument# %d to LAPACK SVD routine ZGESVD is invalid.\n", -info); stackTraceExit(1); }
if(info>0) { logPrintf("Error code %d in LAPACK SVD routine ZGESVD.\n", info); stackTraceExit(1); }
}
if(info<0) { logPrintf("Argument# %d to LAPACK SVD routine ZGESDD is invalid.\n", -info); stackTraceExit(1); }
watch.stop();
}
DLLEXPORT MKL_INT z_svd_factor(bool compute_vectors, MKL_INT m, MKL_INT n, MKL_Complex16 a[], MKL_Complex16 s[], MKL_Complex16 u[], MKL_Complex16 v[], MKL_Complex16 work[], MKL_INT len)
{
MKL_INT info = 0;
MKL_INT dim_s = std::min(m,n);
double* rwork = new double[5 * std::min(m, n)];
double* s_local = new double[dim_s];
char job = compute_vectors ? 'A' : 'N';
zgesvd_(&job, &job, &m, &n, a, &m, s_local, u, &m, v, &n, work, &len, rwork, &info);
for(MKL_INT index = 0; index < dim_s; ++index){
MKL_Complex16 value = {s_local[index], 0.0f};
s[index] = value;
}
delete[] rwork;
delete[] s_local;
return info;
}
DLLEXPORT int z_svd_factor(bool compute_vectors, int m, int n, doublecomplex a[], doublecomplex s[], doublecomplex u[], doublecomplex v[], doublecomplex work[], int len)
{
int info = 0;
int dim_s = min(m,n);
double* rwork = new double[5 * min(m, n)];
double* s_local = new double[dim_s];
char job = compute_vectors ? 'A' : 'N';
zgesvd_(&job, &job, &m, &n, a, &m, s_local, u, &m, v, &n, work, &len, rwork, &info);
for(int index = 0; index < dim_s; ++index){
doublecomplex value = {s_local[index], 0.0f};
s[index] = value;
}
delete[] rwork;
delete[] s_local;
return info;
}
/* Subroutine */ int zlatm6_(integer *type__, integer *n, doublecomplex *a,
integer *lda, doublecomplex *b, doublecomplex *x, integer *ldx,
doublecomplex *y, integer *ldy, doublecomplex *alpha, doublecomplex *
beta, doublecomplex *wx, doublecomplex *wy, doublereal *s, doublereal
*dif)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, x_dim1, x_offset, y_dim1,
y_offset, i__1, i__2, i__3;
doublereal d__1, d__2;
doublecomplex z__1, z__2, z__3, z__4;
/* Builtin functions */
void d_cnjg(doublecomplex *, doublecomplex *);
double z_abs(doublecomplex *), sqrt(doublereal);
/* Local variables */
integer i__, j;
doublecomplex z__[64] /* was [8][8] */;
integer info;
doublecomplex work[26];
doublereal rwork[50];
extern /* Subroutine */ int zlakf2_(integer *, integer *, doublecomplex *,
integer *, doublecomplex *, doublecomplex *, doublecomplex *,
doublecomplex *, integer *), zgesvd_(char *, char *, integer *,
integer *, doublecomplex *, integer *, doublereal *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublereal *, integer *), zlacpy_(char *, integer *, integer *, doublecomplex *,
integer *, doublecomplex *, integer *);
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZLATM6 generates test matrices for the generalized eigenvalue */
/* problem, their corresponding right and left eigenvector matrices, */
/* and also reciprocal condition numbers for all eigenvalues and */
/* the reciprocal condition numbers of eigenvectors corresponding to */
/* the 1th and 5th eigenvalues. */
/* Test Matrices */
/* ============= */
/* Two kinds of test matrix pairs */
/* (A, B) = inverse(YH) * (Da, Db) * inverse(X) */
/* are used in the tests: */
/* Type 1: */
/* Da = 1+a 0 0 0 0 Db = 1 0 0 0 0 */
/* 0 2+a 0 0 0 0 1 0 0 0 */
/* 0 0 3+a 0 0 0 0 1 0 0 */
/* 0 0 0 4+a 0 0 0 0 1 0 */
/* 0 0 0 0 5+a , 0 0 0 0 1 */
/* and Type 2: */
/* Da = 1+i 0 0 0 0 Db = 1 0 0 0 0 */
/* 0 1-i 0 0 0 0 1 0 0 0 */
/* 0 0 1 0 0 0 0 1 0 0 */
/* 0 0 0 (1+a)+(1+b)i 0 0 0 0 1 0 */
/* 0 0 0 0 (1+a)-(1+b)i, 0 0 0 0 1 . */
/* In both cases the same inverse(YH) and inverse(X) are used to compute */
/* (A, B), giving the exact eigenvectors to (A,B) as (YH, X): */
/* YH: = 1 0 -y y -y X = 1 0 -x -x x */
/* 0 1 -y y -y 0 1 x -x -x */
/* 0 0 1 0 0 0 0 1 0 0 */
/* 0 0 0 1 0 0 0 0 1 0 */
/* 0 0 0 0 1, 0 0 0 0 1 , where */
/* a, b, x and y will have all values independently of each other. */
/* Arguments */
/* ========= */
/* TYPE (input) INTEGER */
/* Specifies the problem type (see futher details). */
/* N (input) INTEGER */
/* Size of the matrices A and B. */
/* A (output) COMPLEX*16 array, dimension (LDA, N). */
/* On exit A N-by-N is initialized according to TYPE. */
/* LDA (input) INTEGER */
/* The leading dimension of A and of B. */
/* B (output) COMPLEX*16 array, dimension (LDA, N). */
/* On exit B N-by-N is initialized according to TYPE. */
/* X (output) COMPLEX*16 array, dimension (LDX, N). */
/* On exit X is the N-by-N matrix of right eigenvectors. */
/* LDX (input) INTEGER */
/* The leading dimension of X. */
/* Y (output) COMPLEX*16 array, dimension (LDY, N). */
/* On exit Y is the N-by-N matrix of left eigenvectors. */
/* LDY (input) INTEGER */
/* The leading dimension of Y. */
/* ALPHA (input) COMPLEX*16 */
/* BETA (input) COMPLEX*16 */
/* Weighting constants for matrix A. */
/* WX (input) COMPLEX*16 */
/* Constant for right eigenvector matrix. */
/* WY (input) COMPLEX*16 */
/* Constant for left eigenvector matrix. */
/* S (output) DOUBLE PRECISION array, dimension (N) */
/* S(i) is the reciprocal condition number for eigenvalue i. */
/* DIF (output) DOUBLE PRECISION array, dimension (N) */
/* DIF(i) is the reciprocal condition number for eigenvector i. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Executable Statements .. */
/* Generate test problem ... */
/* (Da, Db) ... */
/* Parameter adjustments */
b_dim1 = *lda;
b_offset = 1 + b_dim1;
b -= b_offset;
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
x_dim1 = *ldx;
x_offset = 1 + x_dim1;
x -= x_offset;
y_dim1 = *ldy;
y_offset = 1 + y_dim1;
y -= y_offset;
--s;
--dif;
/* Function Body */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = *n;
for (j = 1; j <= i__2; ++j) {
if (i__ == j) {
i__3 = i__ + i__ * a_dim1;
z__2.r = (doublereal) i__, z__2.i = 0.;
z__1.r = z__2.r + alpha->r, z__1.i = z__2.i + alpha->i;
a[i__3].r = z__1.r, a[i__3].i = z__1.i;
i__3 = i__ + i__ * b_dim1;
b[i__3].r = 1., b[i__3].i = 0.;
} else {
i__3 = i__ + j * a_dim1;
a[i__3].r = 0., a[i__3].i = 0.;
i__3 = i__ + j * b_dim1;
b[i__3].r = 0., b[i__3].i = 0.;
}
/* L10: */
}
/* L20: */
}
if (*type__ == 2) {
i__1 = a_dim1 + 1;
a[i__1].r = 1., a[i__1].i = 1.;
i__1 = (a_dim1 << 1) + 2;
d_cnjg(&z__1, &a[a_dim1 + 1]);
a[i__1].r = z__1.r, a[i__1].i = z__1.i;
i__1 = a_dim1 * 3 + 3;
a[i__1].r = 1., a[i__1].i = 0.;
i__1 = (a_dim1 << 2) + 4;
z__2.r = alpha->r + 1., z__2.i = alpha->i + 0.;
d__1 = z__2.r;
z__3.r = beta->r + 1., z__3.i = beta->i + 0.;
d__2 = z__3.r;
z__1.r = d__1, z__1.i = d__2;
a[i__1].r = z__1.r, a[i__1].i = z__1.i;
i__1 = a_dim1 * 5 + 5;
d_cnjg(&z__1, &a[(a_dim1 << 2) + 4]);
a[i__1].r = z__1.r, a[i__1].i = z__1.i;
}
/* Form X and Y */
zlacpy_("F", n, n, &b[b_offset], lda, &y[y_offset], ldy);
i__1 = y_dim1 + 3;
d_cnjg(&z__2, wy);
z__1.r = -z__2.r, z__1.i = -z__2.i;
y[i__1].r = z__1.r, y[i__1].i = z__1.i;
i__1 = y_dim1 + 4;
d_cnjg(&z__1, wy);
y[i__1].r = z__1.r, y[i__1].i = z__1.i;
i__1 = y_dim1 + 5;
d_cnjg(&z__2, wy);
z__1.r = -z__2.r, z__1.i = -z__2.i;
y[i__1].r = z__1.r, y[i__1].i = z__1.i;
i__1 = (y_dim1 << 1) + 3;
d_cnjg(&z__2, wy);
z__1.r = -z__2.r, z__1.i = -z__2.i;
y[i__1].r = z__1.r, y[i__1].i = z__1.i;
i__1 = (y_dim1 << 1) + 4;
d_cnjg(&z__1, wy);
y[i__1].r = z__1.r, y[i__1].i = z__1.i;
i__1 = (y_dim1 << 1) + 5;
d_cnjg(&z__2, wy);
z__1.r = -z__2.r, z__1.i = -z__2.i;
y[i__1].r = z__1.r, y[i__1].i = z__1.i;
zlacpy_("F", n, n, &b[b_offset], lda, &x[x_offset], ldx);
i__1 = x_dim1 * 3 + 1;
z__1.r = -wx->r, z__1.i = -wx->i;
x[i__1].r = z__1.r, x[i__1].i = z__1.i;
i__1 = (x_dim1 << 2) + 1;
z__1.r = -wx->r, z__1.i = -wx->i;
x[i__1].r = z__1.r, x[i__1].i = z__1.i;
i__1 = x_dim1 * 5 + 1;
x[i__1].r = wx->r, x[i__1].i = wx->i;
i__1 = x_dim1 * 3 + 2;
x[i__1].r = wx->r, x[i__1].i = wx->i;
i__1 = (x_dim1 << 2) + 2;
z__1.r = -wx->r, z__1.i = -wx->i;
x[i__1].r = z__1.r, x[i__1].i = z__1.i;
i__1 = x_dim1 * 5 + 2;
z__1.r = -wx->r, z__1.i = -wx->i;
x[i__1].r = z__1.r, x[i__1].i = z__1.i;
/* Form (A, B) */
i__1 = b_dim1 * 3 + 1;
z__1.r = wx->r + wy->r, z__1.i = wx->i + wy->i;
b[i__1].r = z__1.r, b[i__1].i = z__1.i;
i__1 = b_dim1 * 3 + 2;
z__2.r = -wx->r, z__2.i = -wx->i;
z__1.r = z__2.r + wy->r, z__1.i = z__2.i + wy->i;
b[i__1].r = z__1.r, b[i__1].i = z__1.i;
i__1 = (b_dim1 << 2) + 1;
z__1.r = wx->r - wy->r, z__1.i = wx->i - wy->i;
b[i__1].r = z__1.r, b[i__1].i = z__1.i;
i__1 = (b_dim1 << 2) + 2;
z__1.r = wx->r - wy->r, z__1.i = wx->i - wy->i;
b[i__1].r = z__1.r, b[i__1].i = z__1.i;
i__1 = b_dim1 * 5 + 1;
z__2.r = -wx->r, z__2.i = -wx->i;
z__1.r = z__2.r + wy->r, z__1.i = z__2.i + wy->i;
b[i__1].r = z__1.r, b[i__1].i = z__1.i;
i__1 = b_dim1 * 5 + 2;
z__1.r = wx->r + wy->r, z__1.i = wx->i + wy->i;
b[i__1].r = z__1.r, b[i__1].i = z__1.i;
i__1 = a_dim1 * 3 + 1;
i__2 = a_dim1 + 1;
z__2.r = wx->r * a[i__2].r - wx->i * a[i__2].i, z__2.i = wx->r * a[i__2]
.i + wx->i * a[i__2].r;
i__3 = a_dim1 * 3 + 3;
z__3.r = wy->r * a[i__3].r - wy->i * a[i__3].i, z__3.i = wy->r * a[i__3]
.i + wy->i * a[i__3].r;
z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
a[i__1].r = z__1.r, a[i__1].i = z__1.i;
i__1 = a_dim1 * 3 + 2;
z__3.r = -wx->r, z__3.i = -wx->i;
i__2 = (a_dim1 << 1) + 2;
z__2.r = z__3.r * a[i__2].r - z__3.i * a[i__2].i, z__2.i = z__3.r * a[
i__2].i + z__3.i * a[i__2].r;
i__3 = a_dim1 * 3 + 3;
z__4.r = wy->r * a[i__3].r - wy->i * a[i__3].i, z__4.i = wy->r * a[i__3]
.i + wy->i * a[i__3].r;
z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i;
a[i__1].r = z__1.r, a[i__1].i = z__1.i;
i__1 = (a_dim1 << 2) + 1;
i__2 = a_dim1 + 1;
z__2.r = wx->r * a[i__2].r - wx->i * a[i__2].i, z__2.i = wx->r * a[i__2]
.i + wx->i * a[i__2].r;
i__3 = (a_dim1 << 2) + 4;
z__3.r = wy->r * a[i__3].r - wy->i * a[i__3].i, z__3.i = wy->r * a[i__3]
.i + wy->i * a[i__3].r;
z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - z__3.i;
a[i__1].r = z__1.r, a[i__1].i = z__1.i;
i__1 = (a_dim1 << 2) + 2;
i__2 = (a_dim1 << 1) + 2;
z__2.r = wx->r * a[i__2].r - wx->i * a[i__2].i, z__2.i = wx->r * a[i__2]
.i + wx->i * a[i__2].r;
i__3 = (a_dim1 << 2) + 4;
z__3.r = wy->r * a[i__3].r - wy->i * a[i__3].i, z__3.i = wy->r * a[i__3]
.i + wy->i * a[i__3].r;
z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - z__3.i;
a[i__1].r = z__1.r, a[i__1].i = z__1.i;
i__1 = a_dim1 * 5 + 1;
z__3.r = -wx->r, z__3.i = -wx->i;
i__2 = a_dim1 + 1;
z__2.r = z__3.r * a[i__2].r - z__3.i * a[i__2].i, z__2.i = z__3.r * a[
i__2].i + z__3.i * a[i__2].r;
i__3 = a_dim1 * 5 + 5;
z__4.r = wy->r * a[i__3].r - wy->i * a[i__3].i, z__4.i = wy->r * a[i__3]
.i + wy->i * a[i__3].r;
z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i;
a[i__1].r = z__1.r, a[i__1].i = z__1.i;
i__1 = a_dim1 * 5 + 2;
i__2 = (a_dim1 << 1) + 2;
z__2.r = wx->r * a[i__2].r - wx->i * a[i__2].i, z__2.i = wx->r * a[i__2]
.i + wx->i * a[i__2].r;
i__3 = a_dim1 * 5 + 5;
z__3.r = wy->r * a[i__3].r - wy->i * a[i__3].i, z__3.i = wy->r * a[i__3]
.i + wy->i * a[i__3].r;
z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
a[i__1].r = z__1.r, a[i__1].i = z__1.i;
/* Compute condition numbers */
s[1] = 1. / sqrt((z_abs(wy) * 3. * z_abs(wy) + 1.) / (z_abs(&a[a_dim1 + 1]
) * z_abs(&a[a_dim1 + 1]) + 1.));
s[2] = 1. / sqrt((z_abs(wy) * 3. * z_abs(wy) + 1.) / (z_abs(&a[(a_dim1 <<
1) + 2]) * z_abs(&a[(a_dim1 << 1) + 2]) + 1.));
s[3] = 1. / sqrt((z_abs(wx) * 2. * z_abs(wx) + 1.) / (z_abs(&a[a_dim1 * 3
+ 3]) * z_abs(&a[a_dim1 * 3 + 3]) + 1.));
s[4] = 1. / sqrt((z_abs(wx) * 2. * z_abs(wx) + 1.) / (z_abs(&a[(a_dim1 <<
2) + 4]) * z_abs(&a[(a_dim1 << 2) + 4]) + 1.));
s[5] = 1. / sqrt((z_abs(wx) * 2. * z_abs(wx) + 1.) / (z_abs(&a[a_dim1 * 5
+ 5]) * z_abs(&a[a_dim1 * 5 + 5]) + 1.));
zlakf2_(&c__1, &c__4, &a[a_offset], lda, &a[(a_dim1 << 1) + 2], &b[
b_offset], &b[(b_dim1 << 1) + 2], z__, &c__8);
zgesvd_("N", "N", &c__8, &c__8, z__, &c__8, rwork, work, &c__1, &work[1],
&c__1, &work[2], &c__24, &rwork[8], &info);
dif[1] = rwork[7];
zlakf2_(&c__4, &c__1, &a[a_offset], lda, &a[a_dim1 * 5 + 5], &b[b_offset],
&b[b_dim1 * 5 + 5], z__, &c__8);
zgesvd_("N", "N", &c__8, &c__8, z__, &c__8, rwork, work, &c__1, &work[1],
&c__1, &work[2], &c__24, &rwork[8], &info);
dif[5] = rwork[7];
return 0;
/* End of ZLATM6 */
} /* zlatm6_ */
/* Subroutine */ int zerred_(char *path, integer *nunit)
{
/* Format strings */
static char fmt_9999[] = "(1x,a,\002 passed the tests of the error exits"
" (\002,i3,\002 tests done)\002)";
static char fmt_9998[] = "(\002 *** \002,a,\002 failed the tests of the "
"error exits ***\002)";
/* System generated locals */
integer i__1;
/* Builtin functions */
integer s_wsle(cilist *), e_wsle(void);
/* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
integer s_wsfe(cilist *), i_len_trim(char *, ftnlen), do_fio(integer *,
char *, ftnlen), e_wsfe(void);
/* Local variables */
doublecomplex a[16] /* was [4][4] */;
logical b[4];
integer i__, j;
doublereal s[4];
doublecomplex u[16] /* was [4][4] */, w[16], x[4];
char c2[2];
doublereal r1[4], r2[4];
integer iw[16], nt;
doublecomplex vl[16] /* was [4][4] */, vr[16] /* was [4][4]
*/;
doublereal rw[20];
doublecomplex vt[16] /* was [4][4] */;
integer ihi, ilo, info, sdim;
doublereal abnrm;
extern /* Subroutine */ int zgees_(char *, char *, L_fp, integer *,
doublecomplex *, integer *, integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublereal *, logical *, integer *), zgeev_(char *
, char *, integer *, doublecomplex *, integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublereal *, integer *);
extern logical lsamen_(integer *, char *, char *);
extern /* Subroutine */ int zgesdd_(char *, integer *, integer *,
doublecomplex *, integer *, doublereal *, doublecomplex *,
integer *, doublecomplex *, integer *, doublecomplex *, integer *,
doublereal *, integer *, integer *), chkxer_(char *,
integer *, integer *, logical *, logical *), zgesvd_(char
*, char *, integer *, integer *, doublecomplex *, integer *,
doublereal *, doublecomplex *, integer *, doublecomplex *,
integer *, doublecomplex *, integer *, doublereal *, integer *);
extern logical zslect_();
extern /* Subroutine */ int zgeesx_(char *, char *, L_fp, char *, integer
*, doublecomplex *, integer *, integer *, doublecomplex *,
doublecomplex *, integer *, doublereal *, doublereal *,
doublecomplex *, integer *, doublereal *, logical *, integer *), zgeevx_(char *, char *, char *, char *,
integer *, doublecomplex *, integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *, integer *,
integer *, doublereal *, doublereal *, doublereal *, doublereal *
, doublecomplex *, integer *, doublereal *, integer *);
/* Fortran I/O blocks */
static cilist io___1 = { 0, 0, 0, 0, 0 };
static cilist io___23 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___24 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___26 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___27 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___28 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___29 = { 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 */
/* ======= */
/* ZERRED tests the error exits for the eigenvalue driver routines for */
/* DOUBLE PRECISION matrices: */
/* PATH driver description */
/* ---- ------ ----------- */
/* ZEV ZGEEV find eigenvalues/eigenvectors for nonsymmetric A */
/* ZES ZGEES find eigenvalues/Schur form for nonsymmetric A */
/* ZVX ZGEEVX ZGEEV + balancing and condition estimation */
/* ZSX ZGEESX ZGEES + balancing and condition estimation */
/* ZBD ZGESVD compute SVD of an M-by-N matrix A */
/* ZGESDD compute SVD of an M-by-N matrix A(by divide and */
/* conquer) */
/* 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 Subroutines .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Arrays in Common .. */
/* .. */
/* .. 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);
/* Initialize A */
for (j = 1; j <= 4; ++j) {
for (i__ = 1; i__ <= 4; ++i__) {
i__1 = i__ + (j << 2) - 5;
a[i__1].r = 0., a[i__1].i = 0.;
/* L10: */
}
/* L20: */
}
for (i__ = 1; i__ <= 4; ++i__) {
i__1 = i__ + (i__ << 2) - 5;
a[i__1].r = 1., a[i__1].i = 0.;
/* L30: */
}
infoc_1.ok = TRUE_;
nt = 0;
if (lsamen_(&c__2, c2, "EV")) {
/* Test ZGEEV */
s_copy(srnamc_1.srnamt, "ZGEEV ", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
zgeev_("X", "N", &c__0, a, &c__1, x, vl, &c__1, vr, &c__1, w, &c__1,
rw, &info);
chkxer_("ZGEEV ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zgeev_("N", "X", &c__0, a, &c__1, x, vl, &c__1, vr, &c__1, w, &c__1,
rw, &info);
chkxer_("ZGEEV ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
zgeev_("N", "N", &c_n1, a, &c__1, x, vl, &c__1, vr, &c__1, w, &c__1,
rw, &info);
chkxer_("ZGEEV ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
zgeev_("N", "N", &c__2, a, &c__1, x, vl, &c__1, vr, &c__1, w, &c__4,
rw, &info);
chkxer_("ZGEEV ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
zgeev_("V", "N", &c__2, a, &c__2, x, vl, &c__1, vr, &c__1, w, &c__4,
rw, &info);
chkxer_("ZGEEV ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
zgeev_("N", "V", &c__2, a, &c__2, x, vl, &c__1, vr, &c__1, w, &c__4,
rw, &info);
chkxer_("ZGEEV ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 12;
zgeev_("V", "V", &c__1, a, &c__1, x, vl, &c__1, vr, &c__1, w, &c__1,
rw, &info);
chkxer_("ZGEEV ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
nt += 7;
} else if (lsamen_(&c__2, c2, "ES")) {
/* Test ZGEES */
s_copy(srnamc_1.srnamt, "ZGEES ", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
zgees_("X", "N", (L_fp)zslect_, &c__0, a, &c__1, &sdim, x, vl, &c__1,
w, &c__1, rw, b, &info);
chkxer_("ZGEES ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zgees_("N", "X", (L_fp)zslect_, &c__0, a, &c__1, &sdim, x, vl, &c__1,
w, &c__1, rw, b, &info);
chkxer_("ZGEES ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
zgees_("N", "S", (L_fp)zslect_, &c_n1, a, &c__1, &sdim, x, vl, &c__1,
w, &c__1, rw, b, &info);
chkxer_("ZGEES ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
zgees_("N", "S", (L_fp)zslect_, &c__2, a, &c__1, &sdim, x, vl, &c__1,
w, &c__4, rw, b, &info);
chkxer_("ZGEES ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
zgees_("V", "S", (L_fp)zslect_, &c__2, a, &c__2, &sdim, x, vl, &c__1,
w, &c__4, rw, b, &info);
chkxer_("ZGEES ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 12;
zgees_("N", "S", (L_fp)zslect_, &c__1, a, &c__1, &sdim, x, vl, &c__1,
w, &c__1, rw, b, &info);
chkxer_("ZGEES ", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
nt += 6;
} else if (lsamen_(&c__2, c2, "VX")) {
/* Test ZGEEVX */
s_copy(srnamc_1.srnamt, "ZGEEVX", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
zgeevx_("X", "N", "N", "N", &c__0, a, &c__1, x, vl, &c__1, vr, &c__1,
&ilo, &ihi, s, &abnrm, r1, r2, w, &c__1, rw, &info);
chkxer_("ZGEEVX", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zgeevx_("N", "X", "N", "N", &c__0, a, &c__1, x, vl, &c__1, vr, &c__1,
&ilo, &ihi, s, &abnrm, r1, r2, w, &c__1, rw, &info);
chkxer_("ZGEEVX", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
zgeevx_("N", "N", "X", "N", &c__0, a, &c__1, x, vl, &c__1, vr, &c__1,
&ilo, &ihi, s, &abnrm, r1, r2, w, &c__1, rw, &info);
chkxer_("ZGEEVX", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
zgeevx_("N", "N", "N", "X", &c__0, a, &c__1, x, vl, &c__1, vr, &c__1,
&ilo, &ihi, s, &abnrm, r1, r2, w, &c__1, rw, &info);
chkxer_("ZGEEVX", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
zgeevx_("N", "N", "N", "N", &c_n1, a, &c__1, x, vl, &c__1, vr, &c__1,
&ilo, &ihi, s, &abnrm, r1, r2, w, &c__1, rw, &info);
chkxer_("ZGEEVX", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
zgeevx_("N", "N", "N", "N", &c__2, a, &c__1, x, vl, &c__1, vr, &c__1,
&ilo, &ihi, s, &abnrm, r1, r2, w, &c__4, rw, &info);
chkxer_("ZGEEVX", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
zgeevx_("N", "V", "N", "N", &c__2, a, &c__2, x, vl, &c__1, vr, &c__1,
&ilo, &ihi, s, &abnrm, r1, r2, w, &c__4, rw, &info);
chkxer_("ZGEEVX", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 12;
zgeevx_("N", "N", "V", "N", &c__2, a, &c__2, x, vl, &c__1, vr, &c__1,
&ilo, &ihi, s, &abnrm, r1, r2, w, &c__4, rw, &info);
chkxer_("ZGEEVX", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 20;
zgeevx_("N", "N", "N", "N", &c__1, a, &c__1, x, vl, &c__1, vr, &c__1,
&ilo, &ihi, s, &abnrm, r1, r2, w, &c__1, rw, &info);
chkxer_("ZGEEVX", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 20;
zgeevx_("N", "N", "V", "V", &c__1, a, &c__1, x, vl, &c__1, vr, &c__1,
&ilo, &ihi, s, &abnrm, r1, r2, w, &c__2, rw, &info);
chkxer_("ZGEEVX", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
nt += 10;
} else if (lsamen_(&c__2, c2, "SX")) {
/* Test ZGEESX */
s_copy(srnamc_1.srnamt, "ZGEESX", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
zgeesx_("X", "N", (L_fp)zslect_, "N", &c__0, a, &c__1, &sdim, x, vl, &
c__1, r1, r2, w, &c__1, rw, b, &info);
chkxer_("ZGEESX", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zgeesx_("N", "X", (L_fp)zslect_, "N", &c__0, a, &c__1, &sdim, x, vl, &
c__1, r1, r2, w, &c__1, rw, b, &info);
chkxer_("ZGEESX", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
zgeesx_("N", "N", (L_fp)zslect_, "X", &c__0, a, &c__1, &sdim, x, vl, &
c__1, r1, r2, w, &c__1, rw, b, &info);
chkxer_("ZGEESX", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
zgeesx_("N", "N", (L_fp)zslect_, "N", &c_n1, a, &c__1, &sdim, x, vl, &
c__1, r1, r2, w, &c__1, rw, b, &info);
chkxer_("ZGEESX", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
zgeesx_("N", "N", (L_fp)zslect_, "N", &c__2, a, &c__1, &sdim, x, vl, &
c__1, r1, r2, w, &c__4, rw, b, &info);
chkxer_("ZGEESX", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 11;
zgeesx_("V", "N", (L_fp)zslect_, "N", &c__2, a, &c__2, &sdim, x, vl, &
c__1, r1, r2, w, &c__4, rw, b, &info);
chkxer_("ZGEESX", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 15;
zgeesx_("N", "N", (L_fp)zslect_, "N", &c__1, a, &c__1, &sdim, x, vl, &
c__1, r1, r2, w, &c__1, rw, b, &info);
chkxer_("ZGEESX", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
nt += 7;
} else if (lsamen_(&c__2, c2, "BD")) {
/* Test ZGESVD */
s_copy(srnamc_1.srnamt, "ZGESVD", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
zgesvd_("X", "N", &c__0, &c__0, a, &c__1, s, u, &c__1, vt, &c__1, w, &
c__1, rw, &info);
chkxer_("ZGESVD", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zgesvd_("N", "X", &c__0, &c__0, a, &c__1, s, u, &c__1, vt, &c__1, w, &
c__1, rw, &info);
chkxer_("ZGESVD", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zgesvd_("O", "O", &c__0, &c__0, a, &c__1, s, u, &c__1, vt, &c__1, w, &
c__1, rw, &info);
chkxer_("ZGESVD", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
zgesvd_("N", "N", &c_n1, &c__0, a, &c__1, s, u, &c__1, vt, &c__1, w, &
c__1, rw, &info);
chkxer_("ZGESVD", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
zgesvd_("N", "N", &c__0, &c_n1, a, &c__1, s, u, &c__1, vt, &c__1, w, &
c__1, rw, &info);
chkxer_("ZGESVD", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
zgesvd_("N", "N", &c__2, &c__1, a, &c__1, s, u, &c__1, vt, &c__1, w, &
c__5, rw, &info);
chkxer_("ZGESVD", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 9;
zgesvd_("A", "N", &c__2, &c__1, a, &c__2, s, u, &c__1, vt, &c__1, w, &
c__5, rw, &info);
chkxer_("ZGESVD", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 11;
zgesvd_("N", "A", &c__1, &c__2, a, &c__1, s, u, &c__1, vt, &c__1, w, &
c__5, rw, &info);
chkxer_("ZGESVD", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
nt += 8;
if (infoc_1.ok) {
io___23.ciunit = infoc_1.nout;
s_wsfe(&io___23);
do_fio(&c__1, srnamc_1.srnamt, i_len_trim(srnamc_1.srnamt, (
ftnlen)32));
do_fio(&c__1, (char *)&nt, (ftnlen)sizeof(integer));
e_wsfe();
} else {
io___24.ciunit = infoc_1.nout;
s_wsfe(&io___24);
e_wsfe();
}
/* Test ZGESDD */
s_copy(srnamc_1.srnamt, "ZGESDD", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
zgesdd_("X", &c__0, &c__0, a, &c__1, s, u, &c__1, vt, &c__1, w, &c__1,
rw, iw, &info);
chkxer_("ZGESDD", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zgesdd_("N", &c_n1, &c__0, a, &c__1, s, u, &c__1, vt, &c__1, w, &c__1,
rw, iw, &info);
chkxer_("ZGESDD", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
zgesdd_("N", &c__0, &c_n1, a, &c__1, s, u, &c__1, vt, &c__1, w, &c__1,
rw, iw, &info);
chkxer_("ZGESDD", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
zgesdd_("N", &c__2, &c__1, a, &c__1, s, u, &c__1, vt, &c__1, w, &c__5,
rw, iw, &info);
chkxer_("ZGESDD", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
zgesdd_("A", &c__2, &c__1, a, &c__2, s, u, &c__1, vt, &c__1, w, &c__5,
rw, iw, &info);
chkxer_("ZGESDD", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
zgesdd_("A", &c__1, &c__2, a, &c__1, s, u, &c__1, vt, &c__1, w, &c__5,
rw, iw, &info);
chkxer_("ZGESDD", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
nt += -2;
if (infoc_1.ok) {
io___26.ciunit = infoc_1.nout;
s_wsfe(&io___26);
do_fio(&c__1, srnamc_1.srnamt, i_len_trim(srnamc_1.srnamt, (
ftnlen)32));
do_fio(&c__1, (char *)&nt, (ftnlen)sizeof(integer));
e_wsfe();
} else {
io___27.ciunit = infoc_1.nout;
s_wsfe(&io___27);
e_wsfe();
}
}
/* Print a summary line. */
if (! lsamen_(&c__2, c2, "BD")) {
if (infoc_1.ok) {
io___28.ciunit = infoc_1.nout;
s_wsfe(&io___28);
do_fio(&c__1, srnamc_1.srnamt, i_len_trim(srnamc_1.srnamt, (
ftnlen)32));
do_fio(&c__1, (char *)&nt, (ftnlen)sizeof(integer));
e_wsfe();
} else {
io___29.ciunit = infoc_1.nout;
s_wsfe(&io___29);
e_wsfe();
}
}
return 0;
/* End of ZERRED */
} /* zerred_ */
/* Subroutine */ int zdrgsx_(integer *nsize, integer *ncmax, doublereal *
thresh, integer *nin, integer *nout, doublecomplex *a, integer *lda,
doublecomplex *b, doublecomplex *ai, doublecomplex *bi, doublecomplex
*z__, doublecomplex *q, doublecomplex *alpha, doublecomplex *beta,
doublecomplex *c__, integer *ldc, doublereal *s, doublecomplex *work,
integer *lwork, doublereal *rwork, integer *iwork, integer *liwork,
logical *bwork, integer *info)
{
/* Format strings */
static char fmt_9999[] = "(\002 ZDRGSX: \002,a,\002 returned INFO=\002,i"
"6,\002.\002,/9x,\002N=\002,i6,\002, JTYPE=\002,i6,\002)\002)";
static char fmt_9997[] = "(\002 ZDRGSX: S not in Schur form at eigenvalu"
"e \002,i6,\002.\002,/9x,\002N=\002,i6,\002, JTYPE=\002,i6,\002"
")\002)";
static char fmt_9996[] = "(/1x,a3,\002 -- Complex Expert Generalized Sch"
"ur form\002,\002 problem driver\002)";
static char fmt_9994[] = "(\002 Matrix types: \002,/\002 1: A is a blo"
"ck diagonal matrix of Jordan blocks \002,\002and B is the identi"
"ty \002,/\002 matrix, \002,/\002 2: A and B are upper tri"
"angular matrices, \002,/\002 3: A and B are as type 2, but eac"
"h second diagonal \002,\002block in A_11 and \002,/\002 eac"
"h third diaongal block in A_22 are 2x2 blocks,\002,/\002 4: A "
"and B are block diagonal matrices, \002,/\002 5: (A,B) has pot"
"entially close or common \002,\002eigenvalues.\002,/)";
static char fmt_9993[] = "(/\002 Tests performed: (S is Schur, T is tri"
"angular, \002,\002Q and Z are \002,a,\002,\002,/19x,\002 a is al"
"pha, b is beta, and \002,a,\002 means \002,a,\002.)\002,/\002 1"
" = | A - Q S Z\002,a,\002 | / ( |A| n ulp ) 2 = | B - Q T "
"Z\002,a,\002 | / ( |B| n ulp )\002,/\002 3 = | I - QQ\002,a,"
"\002 | / ( n ulp ) 4 = | I - ZZ\002,a,\002 | / ( n u"
"lp )\002,/\002 5 = 1/ULP if A is not in \002,\002Schur form "
"S\002,/\002 6 = difference between (alpha,beta)\002,\002 and di"
"agonals of (S,T)\002,/\002 7 = 1/ULP if SDIM is not the correc"
"t number of \002,\002selected eigenvalues\002,/\002 8 = 1/ULP "
"if DIFEST/DIFTRU > 10*THRESH or \002,\002DIFTRU/DIFEST > 10*THRE"
"SH\002,/\002 9 = 1/ULP if DIFEST <> 0 or DIFTRU > ULP*norm(A,B"
") \002,\002when reordering fails\002,/\002 10 = 1/ULP if PLEST/"
"PLTRU > THRESH or \002,\002PLTRU/PLEST > THRESH\002,/\002 ( T"
"est 10 is only for input examples )\002,/)";
static char fmt_9992[] = "(\002 Matrix order=\002,i2,\002, type=\002,i2"
",\002, a=\002,d10.4,\002, order(A_11)=\002,i2,\002, result \002,"
"i2,\002 is \002,0p,f8.2)";
static char fmt_9991[] = "(\002 Matrix order=\002,i2,\002, type=\002,i2"
",\002, a=\002,d10.4,\002, order(A_11)=\002,i2,\002, result \002,"
"i2,\002 is \002,0p,d10.4)";
static char fmt_9998[] = "(\002 ZDRGSX: \002,a,\002 returned INFO=\002,i"
"6,\002.\002,/9x,\002N=\002,i6,\002, Input Example #\002,i2,\002"
")\002)";
static char fmt_9995[] = "(\002Input Example\002)";
static char fmt_9990[] = "(\002 Input example #\002,i2,\002, matrix orde"
"r=\002,i4,\002,\002,\002 result \002,i2,\002 is\002,0p,f8.2)";
static char fmt_9989[] = "(\002 Input example #\002,i2,\002, matrix orde"
"r=\002,i4,\002,\002,\002 result \002,i2,\002 is\002,1p,d10.3)";
/* System generated locals */
integer a_dim1, a_offset, ai_dim1, ai_offset, b_dim1, b_offset, bi_dim1,
bi_offset, c_dim1, c_offset, q_dim1, q_offset, z_dim1, z_offset,
i__1, i__2, i__3, i__4, i__5, i__6, i__7, i__8, i__9, i__10,
i__11;
doublereal d__1, d__2, d__3, d__4, d__5, d__6, d__7, d__8, d__9, d__10,
d__11, d__12, d__13, d__14, d__15, d__16;
doublecomplex z__1, z__2, z__3, z__4;
/* Builtin functions */
double sqrt(doublereal);
integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void);
double d_imag(doublecomplex *);
integer s_rsle(cilist *), do_lio(integer *, integer *, char *, ftnlen),
e_rsle(void);
/* Local variables */
integer i__, j, mm;
doublereal pl[2];
integer mn2, qba, qbb;
doublereal ulp, temp1, temp2, abnrm;
integer ifunc, linfo;
char sense[1];
extern /* Subroutine */ int zget51_(integer *, integer *, doublecomplex *,
integer *, doublecomplex *, integer *, doublecomplex *, integer *
, doublecomplex *, integer *, doublecomplex *, doublereal *,
doublereal *);
integer nerrs, ntest;
doublereal pltru;
extern /* Subroutine */ int zlakf2_(integer *, integer *, doublecomplex *,
integer *, doublecomplex *, doublecomplex *, doublecomplex *,
doublecomplex *, integer *), dlabad_(doublereal *, doublereal *);
doublereal thrsh2;
logical ilabad;
extern /* Subroutine */ int zlatm5_(integer *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublereal *, integer *, integer *);
extern doublereal dlamch_(char *);
integer bdspac;
extern /* Subroutine */ int xerbla_(char *, integer *);
doublereal difest[2];
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *);
extern doublereal zlange_(char *, integer *, integer *, doublecomplex *,
integer *, doublereal *);
doublereal bignum;
extern /* Subroutine */ int alasvm_(char *, integer *, integer *, integer
*, integer *);
doublereal weight, diftru;
extern /* Subroutine */ int zgesvd_(char *, char *, integer *, integer *,
doublecomplex *, integer *, doublereal *, doublecomplex *,
integer *, doublecomplex *, integer *, doublecomplex *, integer *,
doublereal *, integer *), zlacpy_(char *,
integer *, integer *, doublecomplex *, integer *, doublecomplex *,
integer *), zlaset_(char *, integer *, integer *,
doublecomplex *, doublecomplex *, doublecomplex *, integer *);
integer minwrk, maxwrk;
extern /* Subroutine */ int zggesx_(char *, char *, char *, L_fp, char *,
integer *, doublecomplex *, integer *, doublecomplex *, integer *,
integer *, doublecomplex *, doublecomplex *, doublecomplex *,
integer *, doublecomplex *, integer *, doublereal *, doublereal *,
doublecomplex *, integer *, doublereal *, integer *, integer *,
logical *, integer *);
doublereal smlnum, ulpinv;
integer nptknt;
doublereal result[10];
integer ntestt, prtype;
extern logical zlctsx_();
/* Fortran I/O blocks */
static cilist io___22 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___29 = { 0, 0, 0, fmt_9997, 0 };
static cilist io___32 = { 0, 0, 0, fmt_9996, 0 };
static cilist io___33 = { 0, 0, 0, fmt_9994, 0 };
static cilist io___34 = { 0, 0, 0, fmt_9993, 0 };
static cilist io___36 = { 0, 0, 0, fmt_9992, 0 };
static cilist io___37 = { 0, 0, 0, fmt_9991, 0 };
static cilist io___39 = { 0, 0, 1, 0, 0 };
static cilist io___40 = { 0, 0, 1, 0, 0 };
static cilist io___41 = { 0, 0, 0, 0, 0 };
static cilist io___42 = { 0, 0, 0, 0, 0 };
static cilist io___43 = { 0, 0, 0, 0, 0 };
static cilist io___45 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___46 = { 0, 0, 0, fmt_9997, 0 };
static cilist io___47 = { 0, 0, 0, fmt_9996, 0 };
static cilist io___48 = { 0, 0, 0, fmt_9995, 0 };
static cilist io___49 = { 0, 0, 0, fmt_9993, 0 };
static cilist io___50 = { 0, 0, 0, fmt_9990, 0 };
static cilist io___51 = { 0, 0, 0, fmt_9989, 0 };
/* -- LAPACK test routine (version 3.1.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* February 2007 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZDRGSX checks the nonsymmetric generalized eigenvalue (Schur form) */
/* problem expert driver ZGGESX. */
/* ZGGES factors A and B as Q*S*Z' and Q*T*Z' , where ' means conjugate */
/* transpose, S and T are upper triangular (i.e., in generalized Schur */
/* form), and Q and Z are unitary. It also computes the generalized */
/* eigenvalues (alpha(j),beta(j)), j=1,...,n. Thus, */
/* w(j) = alpha(j)/beta(j) is a root of the characteristic equation */
/* det( A - w(j) B ) = 0 */
/* Optionally it also reorders the eigenvalues so that a selected */
/* cluster of eigenvalues appears in the leading diagonal block of the */
/* Schur forms; computes a reciprocal condition number for the average */
/* of the selected eigenvalues; and computes a reciprocal condition */
/* number for the right and left deflating subspaces corresponding to */
/* the selected eigenvalues. */
/* When ZDRGSX is called with NSIZE > 0, five (5) types of built-in */
/* matrix pairs are used to test the routine ZGGESX. */
/* When ZDRGSX is called with NSIZE = 0, it reads in test matrix data */
/* to test ZGGESX. */
/* (need more details on what kind of read-in data are needed). */
/* For each matrix pair, the following tests will be performed and */
/* compared with the threshhold THRESH except for the tests (7) and (9): */
/* (1) | A - Q S Z' | / ( |A| n ulp ) */
/* (2) | B - Q T Z' | / ( |B| n ulp ) */
/* (3) | I - QQ' | / ( n ulp ) */
/* (4) | I - ZZ' | / ( n ulp ) */
/* (5) if A is in Schur form (i.e. triangular form) */
/* (6) maximum over j of D(j) where: */
/* |alpha(j) - S(j,j)| |beta(j) - T(j,j)| */
/* D(j) = ------------------------ + ----------------------- */
/* max(|alpha(j)|,|S(j,j)|) max(|beta(j)|,|T(j,j)|) */
/* (7) if sorting worked and SDIM is the number of eigenvalues */
/* which were selected. */
/* (8) the estimated value DIF does not differ from the true values of */
/* Difu and Difl more than a factor 10*THRESH. If the estimate DIF */
/* equals zero the corresponding true values of Difu and Difl */
/* should be less than EPS*norm(A, B). If the true value of Difu */
/* and Difl equal zero, the estimate DIF should be less than */
/* EPS*norm(A, B). */
/* (9) If INFO = N+3 is returned by ZGGESX, the reordering "failed" */
/* and we check that DIF = PL = PR = 0 and that the true value of */
/* Difu and Difl is < EPS*norm(A, B). We count the events when */
/* INFO=N+3. */
/* For read-in test matrices, the same tests are run except that the */
/* exact value for DIF (and PL) is input data. Additionally, there is */
/* one more test run for read-in test matrices: */
/* (10) the estimated value PL does not differ from the true value of */
/* PLTRU more than a factor THRESH. If the estimate PL equals */
/* zero the corresponding true value of PLTRU should be less than */
/* EPS*norm(A, B). If the true value of PLTRU equal zero, the */
/* estimate PL should be less than EPS*norm(A, B). */
/* Note that for the built-in tests, a total of 10*NSIZE*(NSIZE-1) */
/* matrix pairs are generated and tested. NSIZE should be kept small. */
/* SVD (routine ZGESVD) is used for computing the true value of DIF_u */
/* and DIF_l when testing the built-in test problems. */
/* Built-in Test Matrices */
/* ====================== */
/* All built-in test matrices are the 2 by 2 block of triangular */
/* matrices */
/* A = [ A11 A12 ] and B = [ B11 B12 ] */
/* [ A22 ] [ B22 ] */
/* where for different type of A11 and A22 are given as the following. */
/* A12 and B12 are chosen so that the generalized Sylvester equation */
/* A11*R - L*A22 = -A12 */
/* B11*R - L*B22 = -B12 */
/* have prescribed solution R and L. */
/* Type 1: A11 = J_m(1,-1) and A_22 = J_k(1-a,1). */
/* B11 = I_m, B22 = I_k */
/* where J_k(a,b) is the k-by-k Jordan block with ``a'' on */
/* diagonal and ``b'' on superdiagonal. */
/* Type 2: A11 = (a_ij) = ( 2(.5-sin(i)) ) and */
/* B11 = (b_ij) = ( 2(.5-sin(ij)) ) for i=1,...,m, j=i,...,m */
/* A22 = (a_ij) = ( 2(.5-sin(i+j)) ) and */
/* B22 = (b_ij) = ( 2(.5-sin(ij)) ) for i=m+1,...,k, j=i,...,k */
/* Type 3: A11, A22 and B11, B22 are chosen as for Type 2, but each */
/* second diagonal block in A_11 and each third diagonal block */
/* in A_22 are made as 2 by 2 blocks. */
/* Type 4: A11 = ( 20(.5 - sin(ij)) ) and B22 = ( 2(.5 - sin(i+j)) ) */
/* for i=1,...,m, j=1,...,m and */
/* A22 = ( 20(.5 - sin(i+j)) ) and B22 = ( 2(.5 - sin(ij)) ) */
/* for i=m+1,...,k, j=m+1,...,k */
/* Type 5: (A,B) and have potentially close or common eigenvalues and */
/* very large departure from block diagonality A_11 is chosen */
/* as the m x m leading submatrix of A_1: */
/* | 1 b | */
/* | -b 1 | */
/* | 1+d b | */
/* | -b 1+d | */
/* A_1 = | d 1 | */
/* | -1 d | */
/* | -d 1 | */
/* | -1 -d | */
/* | 1 | */
/* and A_22 is chosen as the k x k leading submatrix of A_2: */
/* | -1 b | */
/* | -b -1 | */
/* | 1-d b | */
/* | -b 1-d | */
/* A_2 = | d 1+b | */
/* | -1-b d | */
/* | -d 1+b | */
/* | -1+b -d | */
/* | 1-d | */
/* and matrix B are chosen as identity matrices (see DLATM5). */
/* Arguments */
/* ========= */
/* NSIZE (input) INTEGER */
/* The maximum size of the matrices to use. NSIZE >= 0. */
/* If NSIZE = 0, no built-in tests matrices are used, but */
/* read-in test matrices are used to test DGGESX. */
/* NCMAX (input) INTEGER */
/* Maximum allowable NMAX for generating Kroneker matrix */
/* in call to ZLAKF2 */
/* THRESH (input) DOUBLE PRECISION */
/* A test will count as "failed" if the "error", computed as */
/* described above, exceeds THRESH. Note that the error */
/* is scaled to be O(1), so THRESH should be a reasonably */
/* small multiple of 1, e.g., 10 or 100. In particular, */
/* it should not depend on the precision (single vs. double) */
/* or the size of the matrix. THRESH >= 0. */
/* NIN (input) INTEGER */
/* The FORTRAN unit number for reading in the data file of */
/* problems to solve. */
/* NOUT (input) INTEGER */
/* The FORTRAN unit number for printing out error messages */
/* (e.g., if a routine returns INFO not equal to 0.) */
/* A (workspace) COMPLEX*16 array, dimension (LDA, NSIZE) */
/* Used to store the matrix whose eigenvalues are to be */
/* computed. On exit, A contains the last matrix actually used. */
/* LDA (input) INTEGER */
/* The leading dimension of A, B, AI, BI, Z and Q, */
/* LDA >= max( 1, NSIZE ). For the read-in test, */
/* LDA >= max( 1, N ), N is the size of the test matrices. */
/* B (workspace) COMPLEX*16 array, dimension (LDA, NSIZE) */
/* Used to store the matrix whose eigenvalues are to be */
/* computed. On exit, B contains the last matrix actually used. */
/* AI (workspace) COMPLEX*16 array, dimension (LDA, NSIZE) */
/* Copy of A, modified by ZGGESX. */
/* BI (workspace) COMPLEX*16 array, dimension (LDA, NSIZE) */
/* Copy of B, modified by ZGGESX. */
/* Z (workspace) COMPLEX*16 array, dimension (LDA, NSIZE) */
/* Z holds the left Schur vectors computed by ZGGESX. */
/* Q (workspace) COMPLEX*16 array, dimension (LDA, NSIZE) */
/* Q holds the right Schur vectors computed by ZGGESX. */
/* ALPHA (workspace) COMPLEX*16 array, dimension (NSIZE) */
/* BETA (workspace) COMPLEX*16 array, dimension (NSIZE) */
/* On exit, ALPHA/BETA are the eigenvalues. */
/* C (workspace) COMPLEX*16 array, dimension (LDC, LDC) */
/* Store the matrix generated by subroutine ZLAKF2, this is the */
/* matrix formed by Kronecker products used for estimating */
/* DIF. */
/* LDC (input) INTEGER */
/* The leading dimension of C. LDC >= max(1, LDA*LDA/2 ). */
/* S (workspace) DOUBLE PRECISION array, dimension (LDC) */
/* Singular values of C */
/* WORK (workspace) COMPLEX*16 array, dimension (LWORK) */
/* LWORK (input) INTEGER */
/* The dimension of the array WORK. LWORK >= 3*NSIZE*NSIZE/2 */
/* RWORK (workspace) DOUBLE PRECISION array, */
/* dimension (5*NSIZE*NSIZE/2 - 4) */
/* IWORK (workspace) INTEGER array, dimension (LIWORK) */
/* LIWORK (input) INTEGER */
/* The dimension of the array IWORK. LIWORK >= NSIZE + 2. */
/* BWORK (workspace) LOGICAL array, dimension (NSIZE) */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value. */
/* > 0: A routine returned an error code. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Scalars in Common .. */
/* .. */
/* .. Common blocks .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Statement Functions .. */
/* .. */
/* .. Statement Function definitions .. */
/* .. */
/* .. Executable Statements .. */
/* Check for errors */
/* Parameter adjustments */
q_dim1 = *lda;
q_offset = 1 + q_dim1;
q -= q_offset;
z_dim1 = *lda;
z_offset = 1 + z_dim1;
z__ -= z_offset;
bi_dim1 = *lda;
bi_offset = 1 + bi_dim1;
bi -= bi_offset;
ai_dim1 = *lda;
ai_offset = 1 + ai_dim1;
ai -= ai_offset;
b_dim1 = *lda;
b_offset = 1 + b_dim1;
b -= b_offset;
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--alpha;
--beta;
c_dim1 = *ldc;
c_offset = 1 + c_dim1;
c__ -= c_offset;
--s;
--work;
--rwork;
--iwork;
--bwork;
/* Function Body */
*info = 0;
if (*nsize < 0) {
*info = -1;
} else if (*thresh < 0.) {
*info = -2;
} else if (*nin <= 0) {
*info = -3;
} else if (*nout <= 0) {
*info = -4;
} else if (*lda < 1 || *lda < *nsize) {
*info = -6;
} else if (*ldc < 1 || *ldc < *nsize * *nsize / 2) {
*info = -15;
} else if (*liwork < *nsize + 2) {
*info = -21;
}
/* 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) {
minwrk = *nsize * 3 * *nsize / 2;
/* workspace for cggesx */
maxwrk = *nsize * (ilaenv_(&c__1, "ZGEQRF", " ", nsize, &c__1, nsize,
&c__0) + 1);
/* Computing MAX */
i__1 = maxwrk, i__2 = *nsize * (ilaenv_(&c__1, "ZUNGQR", " ", nsize, &
c__1, nsize, &c_n1) + 1);
maxwrk = max(i__1,i__2);
/* workspace for zgesvd */
bdspac = *nsize * 3 * *nsize / 2;
/* Computing MAX */
i__3 = *nsize * *nsize / 2;
i__4 = *nsize * *nsize / 2;
i__1 = maxwrk, i__2 = *nsize * *nsize * (ilaenv_(&c__1, "ZGEBRD",
" ", &i__3, &i__4, &c_n1, &c_n1) + 1);
maxwrk = max(i__1,i__2);
maxwrk = max(maxwrk,bdspac);
maxwrk = max(maxwrk,minwrk);
work[1].r = (doublereal) maxwrk, work[1].i = 0.;
}
if (*lwork < minwrk) {
*info = -18;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZDRGSX", &i__1);
return 0;
}
/* Important constants */
ulp = dlamch_("P");
ulpinv = 1. / ulp;
smlnum = dlamch_("S") / ulp;
bignum = 1. / smlnum;
dlabad_(&smlnum, &bignum);
thrsh2 = *thresh * 10.;
ntestt = 0;
nerrs = 0;
/* Go to the tests for read-in matrix pairs */
ifunc = 0;
if (*nsize == 0) {
goto L70;
}
/* Test the built-in matrix pairs. */
/* Loop over different functions (IFUNC) of ZGGESX, types (PRTYPE) */
/* of test matrices, different size (M+N) */
prtype = 0;
qba = 3;
qbb = 4;
weight = sqrt(ulp);
for (ifunc = 0; ifunc <= 3; ++ifunc) {
for (prtype = 1; prtype <= 5; ++prtype) {
i__1 = *nsize - 1;
for (mn_1.m = 1; mn_1.m <= i__1; ++mn_1.m) {
i__2 = *nsize - mn_1.m;
for (mn_1.n = 1; mn_1.n <= i__2; ++mn_1.n) {
weight = 1. / weight;
mn_1.mplusn = mn_1.m + mn_1.n;
/* Generate test matrices */
mn_1.fs = TRUE_;
mn_1.k = 0;
zlaset_("Full", &mn_1.mplusn, &mn_1.mplusn, &c_b1, &c_b1,
&ai[ai_offset], lda);
zlaset_("Full", &mn_1.mplusn, &mn_1.mplusn, &c_b1, &c_b1,
&bi[bi_offset], lda);
zlatm5_(&prtype, &mn_1.m, &mn_1.n, &ai[ai_offset], lda, &
ai[mn_1.m + 1 + (mn_1.m + 1) * ai_dim1], lda, &ai[
(mn_1.m + 1) * ai_dim1 + 1], lda, &bi[bi_offset],
lda, &bi[mn_1.m + 1 + (mn_1.m + 1) * bi_dim1],
lda, &bi[(mn_1.m + 1) * bi_dim1 + 1], lda, &q[
q_offset], lda, &z__[z_offset], lda, &weight, &
qba, &qbb);
/* Compute the Schur factorization and swapping the */
/* m-by-m (1,1)-blocks with n-by-n (2,2)-blocks. */
/* Swapping is accomplished via the function ZLCTSX */
/* which is supplied below. */
if (ifunc == 0) {
*(unsigned char *)sense = 'N';
} else if (ifunc == 1) {
*(unsigned char *)sense = 'E';
} else if (ifunc == 2) {
*(unsigned char *)sense = 'V';
} else if (ifunc == 3) {
*(unsigned char *)sense = 'B';
}
zlacpy_("Full", &mn_1.mplusn, &mn_1.mplusn, &ai[ai_offset]
, lda, &a[a_offset], lda);
zlacpy_("Full", &mn_1.mplusn, &mn_1.mplusn, &bi[bi_offset]
, lda, &b[b_offset], lda);
zggesx_("V", "V", "S", (L_fp)zlctsx_, sense, &mn_1.mplusn,
&ai[ai_offset], lda, &bi[bi_offset], lda, &mm, &
alpha[1], &beta[1], &q[q_offset], lda, &z__[
z_offset], lda, pl, difest, &work[1], lwork, &
rwork[1], &iwork[1], liwork, &bwork[1], &linfo);
if (linfo != 0 && linfo != mn_1.mplusn + 2) {
result[0] = ulpinv;
io___22.ciunit = *nout;
s_wsfe(&io___22);
do_fio(&c__1, "ZGGESX", (ftnlen)6);
do_fio(&c__1, (char *)&linfo, (ftnlen)sizeof(integer))
;
do_fio(&c__1, (char *)&mn_1.mplusn, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&prtype, (ftnlen)sizeof(integer)
);
e_wsfe();
*info = linfo;
goto L30;
}
/* Compute the norm(A, B) */
zlacpy_("Full", &mn_1.mplusn, &mn_1.mplusn, &ai[ai_offset]
, lda, &work[1], &mn_1.mplusn);
zlacpy_("Full", &mn_1.mplusn, &mn_1.mplusn, &bi[bi_offset]
, lda, &work[mn_1.mplusn * mn_1.mplusn + 1], &
mn_1.mplusn);
i__3 = mn_1.mplusn << 1;
abnrm = zlange_("Fro", &mn_1.mplusn, &i__3, &work[1], &
mn_1.mplusn, &rwork[1]);
/* Do tests (1) to (4) */
result[1] = 0.;
zget51_(&c__1, &mn_1.mplusn, &a[a_offset], lda, &ai[
ai_offset], lda, &q[q_offset], lda, &z__[z_offset]
, lda, &work[1], &rwork[1], result);
zget51_(&c__1, &mn_1.mplusn, &b[b_offset], lda, &bi[
bi_offset], lda, &q[q_offset], lda, &z__[z_offset]
, lda, &work[1], &rwork[1], &result[1]);
zget51_(&c__3, &mn_1.mplusn, &b[b_offset], lda, &bi[
bi_offset], lda, &q[q_offset], lda, &q[q_offset],
lda, &work[1], &rwork[1], &result[2]);
zget51_(&c__3, &mn_1.mplusn, &b[b_offset], lda, &bi[
bi_offset], lda, &z__[z_offset], lda, &z__[
z_offset], lda, &work[1], &rwork[1], &result[3]);
ntest = 4;
/* Do tests (5) and (6): check Schur form of A and */
/* compare eigenvalues with diagonals. */
temp1 = 0.;
result[4] = 0.;
result[5] = 0.;
i__3 = mn_1.mplusn;
for (j = 1; j <= i__3; ++j) {
ilabad = FALSE_;
i__4 = j;
i__5 = j + j * ai_dim1;
z__2.r = alpha[i__4].r - ai[i__5].r, z__2.i = alpha[
i__4].i - ai[i__5].i;
z__1.r = z__2.r, z__1.i = z__2.i;
i__6 = j;
i__7 = j + j * bi_dim1;
z__4.r = beta[i__6].r - bi[i__7].r, z__4.i = beta[
i__6].i - bi[i__7].i;
z__3.r = z__4.r, z__3.i = z__4.i;
/* Computing MAX */
i__8 = j;
i__9 = j + j * ai_dim1;
d__13 = smlnum, d__14 = (d__1 = alpha[i__8].r, abs(
d__1)) + (d__2 = d_imag(&alpha[j]), abs(d__2))
, d__13 = max(d__13,d__14), d__14 = (d__3 =
ai[i__9].r, abs(d__3)) + (d__4 = d_imag(&ai[j
+ j * ai_dim1]), abs(d__4));
/* Computing MAX */
i__10 = j;
i__11 = j + j * bi_dim1;
d__15 = smlnum, d__16 = (d__5 = beta[i__10].r, abs(
d__5)) + (d__6 = d_imag(&beta[j]), abs(d__6)),
d__15 = max(d__15,d__16), d__16 = (d__7 = bi[
i__11].r, abs(d__7)) + (d__8 = d_imag(&bi[j +
j * bi_dim1]), abs(d__8));
temp2 = (((d__9 = z__1.r, abs(d__9)) + (d__10 =
d_imag(&z__1), abs(d__10))) / max(d__13,d__14)
+ ((d__11 = z__3.r, abs(d__11)) + (d__12 =
d_imag(&z__3), abs(d__12))) / max(d__15,d__16)
) / ulp;
if (j < mn_1.mplusn) {
i__4 = j + 1 + j * ai_dim1;
if (ai[i__4].r != 0. || ai[i__4].i != 0.) {
ilabad = TRUE_;
result[4] = ulpinv;
}
}
if (j > 1) {
i__4 = j + (j - 1) * ai_dim1;
if (ai[i__4].r != 0. || ai[i__4].i != 0.) {
ilabad = TRUE_;
result[4] = ulpinv;
}
}
temp1 = max(temp1,temp2);
if (ilabad) {
io___29.ciunit = *nout;
s_wsfe(&io___29);
do_fio(&c__1, (char *)&j, (ftnlen)sizeof(integer))
;
do_fio(&c__1, (char *)&mn_1.mplusn, (ftnlen)
sizeof(integer));
do_fio(&c__1, (char *)&prtype, (ftnlen)sizeof(
integer));
e_wsfe();
}
/* L10: */
}
result[5] = temp1;
ntest += 2;
/* Test (7) (if sorting worked) */
result[6] = 0.;
if (linfo == mn_1.mplusn + 3) {
result[6] = ulpinv;
} else if (mm != mn_1.n) {
result[6] = ulpinv;
}
++ntest;
/* Test (8): compare the estimated value DIF and its */
/* value. first, compute the exact DIF. */
result[7] = 0.;
mn2 = mm * (mn_1.mplusn - mm) << 1;
if (ifunc >= 2 && mn2 <= *ncmax * *ncmax) {
/* Note: for either following two cases, there are */
/* almost same number of test cases fail the test. */
i__3 = mn_1.mplusn - mm;
zlakf2_(&mm, &i__3, &ai[ai_offset], lda, &ai[mm + 1 +
(mm + 1) * ai_dim1], &bi[bi_offset], &bi[mm +
1 + (mm + 1) * bi_dim1], &c__[c_offset], ldc);
i__3 = *lwork - 2;
zgesvd_("N", "N", &mn2, &mn2, &c__[c_offset], ldc, &s[
1], &work[1], &c__1, &work[2], &c__1, &work[3]
, &i__3, &rwork[1], info);
diftru = s[mn2];
if (difest[1] == 0.) {
if (diftru > abnrm * ulp) {
result[7] = ulpinv;
}
} else if (diftru == 0.) {
if (difest[1] > abnrm * ulp) {
result[7] = ulpinv;
}
} else if (diftru > thrsh2 * difest[1] || diftru *
thrsh2 < difest[1]) {
/* Computing MAX */
d__1 = diftru / difest[1], d__2 = difest[1] /
diftru;
result[7] = max(d__1,d__2);
}
++ntest;
}
/* Test (9) */
result[8] = 0.;
if (linfo == mn_1.mplusn + 2) {
if (diftru > abnrm * ulp) {
result[8] = ulpinv;
}
if (ifunc > 1 && difest[1] != 0.) {
result[8] = ulpinv;
}
if (ifunc == 1 && pl[0] != 0.) {
result[8] = ulpinv;
}
++ntest;
}
ntestt += ntest;
/* Print out tests which fail. */
for (j = 1; j <= 9; ++j) {
if (result[j - 1] >= *thresh) {
/* If this is the first test to fail, */
/* print a header to the data file. */
if (nerrs == 0) {
io___32.ciunit = *nout;
s_wsfe(&io___32);
do_fio(&c__1, "CGX", (ftnlen)3);
e_wsfe();
/* Matrix types */
io___33.ciunit = *nout;
s_wsfe(&io___33);
e_wsfe();
/* Tests performed */
io___34.ciunit = *nout;
s_wsfe(&io___34);
do_fio(&c__1, "unitary", (ftnlen)7);
do_fio(&c__1, "'", (ftnlen)1);
do_fio(&c__1, "transpose", (ftnlen)9);
for (i__ = 1; i__ <= 4; ++i__) {
do_fio(&c__1, "'", (ftnlen)1);
}
e_wsfe();
}
++nerrs;
if (result[j - 1] < 1e4) {
io___36.ciunit = *nout;
s_wsfe(&io___36);
do_fio(&c__1, (char *)&mn_1.mplusn, (ftnlen)
sizeof(integer));
do_fio(&c__1, (char *)&prtype, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&weight, (ftnlen)sizeof(
doublereal));
do_fio(&c__1, (char *)&mn_1.m, (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();
} else {
io___37.ciunit = *nout;
s_wsfe(&io___37);
do_fio(&c__1, (char *)&mn_1.mplusn, (ftnlen)
sizeof(integer));
do_fio(&c__1, (char *)&prtype, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&weight, (ftnlen)sizeof(
doublereal));
do_fio(&c__1, (char *)&mn_1.m, (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();
}
}
/* L20: */
}
L30:
;
}
/* L40: */
}
/* L50: */
}
/* L60: */
}
goto L150;
L70:
/* Read in data from file to check accuracy of condition estimation */
/* Read input data until N=0 */
nptknt = 0;
L80:
io___39.ciunit = *nin;
i__1 = s_rsle(&io___39);
if (i__1 != 0) {
goto L140;
}
i__1 = do_lio(&c__3, &c__1, (char *)&mn_1.mplusn, (ftnlen)sizeof(integer))
;
if (i__1 != 0) {
goto L140;
}
i__1 = e_rsle();
if (i__1 != 0) {
goto L140;
}
if (mn_1.mplusn == 0) {
goto L140;
}
io___40.ciunit = *nin;
i__1 = s_rsle(&io___40);
if (i__1 != 0) {
goto L140;
}
i__1 = do_lio(&c__3, &c__1, (char *)&mn_1.n, (ftnlen)sizeof(integer));
if (i__1 != 0) {
goto L140;
}
i__1 = e_rsle();
if (i__1 != 0) {
goto L140;
}
i__1 = mn_1.mplusn;
for (i__ = 1; i__ <= i__1; ++i__) {
io___41.ciunit = *nin;
s_rsle(&io___41);
i__2 = mn_1.mplusn;
for (j = 1; j <= i__2; ++j) {
do_lio(&c__7, &c__1, (char *)&ai[i__ + j * ai_dim1], (ftnlen)
sizeof(doublecomplex));
}
e_rsle();
/* L90: */
}
i__1 = mn_1.mplusn;
for (i__ = 1; i__ <= i__1; ++i__) {
io___42.ciunit = *nin;
s_rsle(&io___42);
i__2 = mn_1.mplusn;
for (j = 1; j <= i__2; ++j) {
do_lio(&c__7, &c__1, (char *)&bi[i__ + j * bi_dim1], (ftnlen)
sizeof(doublecomplex));
}
e_rsle();
/* L100: */
}
io___43.ciunit = *nin;
s_rsle(&io___43);
do_lio(&c__5, &c__1, (char *)&pltru, (ftnlen)sizeof(doublereal));
do_lio(&c__5, &c__1, (char *)&diftru, (ftnlen)sizeof(doublereal));
e_rsle();
++nptknt;
mn_1.fs = TRUE_;
mn_1.k = 0;
mn_1.m = mn_1.mplusn - mn_1.n;
zlacpy_("Full", &mn_1.mplusn, &mn_1.mplusn, &ai[ai_offset], lda, &a[
a_offset], lda);
zlacpy_("Full", &mn_1.mplusn, &mn_1.mplusn, &bi[bi_offset], lda, &b[
b_offset], lda);
/* Compute the Schur factorization while swaping the */
/* m-by-m (1,1)-blocks with n-by-n (2,2)-blocks. */
zggesx_("V", "V", "S", (L_fp)zlctsx_, "B", &mn_1.mplusn, &ai[ai_offset],
lda, &bi[bi_offset], lda, &mm, &alpha[1], &beta[1], &q[q_offset],
lda, &z__[z_offset], lda, pl, difest, &work[1], lwork, &rwork[1],
&iwork[1], liwork, &bwork[1], &linfo);
if (linfo != 0 && linfo != mn_1.mplusn + 2) {
result[0] = ulpinv;
io___45.ciunit = *nout;
s_wsfe(&io___45);
do_fio(&c__1, "ZGGESX", (ftnlen)6);
do_fio(&c__1, (char *)&linfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&mn_1.mplusn, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&nptknt, (ftnlen)sizeof(integer));
e_wsfe();
goto L130;
}
/* Compute the norm(A, B) */
/* (should this be norm of (A,B) or (AI,BI)?) */
zlacpy_("Full", &mn_1.mplusn, &mn_1.mplusn, &ai[ai_offset], lda, &work[1],
&mn_1.mplusn);
zlacpy_("Full", &mn_1.mplusn, &mn_1.mplusn, &bi[bi_offset], lda, &work[
mn_1.mplusn * mn_1.mplusn + 1], &mn_1.mplusn);
i__1 = mn_1.mplusn << 1;
abnrm = zlange_("Fro", &mn_1.mplusn, &i__1, &work[1], &mn_1.mplusn, &
rwork[1]);
/* Do tests (1) to (4) */
zget51_(&c__1, &mn_1.mplusn, &a[a_offset], lda, &ai[ai_offset], lda, &q[
q_offset], lda, &z__[z_offset], lda, &work[1], &rwork[1], result);
zget51_(&c__1, &mn_1.mplusn, &b[b_offset], lda, &bi[bi_offset], lda, &q[
q_offset], lda, &z__[z_offset], lda, &work[1], &rwork[1], &result[
1]);
zget51_(&c__3, &mn_1.mplusn, &b[b_offset], lda, &bi[bi_offset], lda, &q[
q_offset], lda, &q[q_offset], lda, &work[1], &rwork[1], &result[2]
);
zget51_(&c__3, &mn_1.mplusn, &b[b_offset], lda, &bi[bi_offset], lda, &z__[
z_offset], lda, &z__[z_offset], lda, &work[1], &rwork[1], &result[
3]);
/* Do tests (5) and (6): check Schur form of A and compare */
/* eigenvalues with diagonals. */
ntest = 6;
temp1 = 0.;
result[4] = 0.;
result[5] = 0.;
i__1 = mn_1.mplusn;
for (j = 1; j <= i__1; ++j) {
ilabad = FALSE_;
i__2 = j;
i__3 = j + j * ai_dim1;
z__2.r = alpha[i__2].r - ai[i__3].r, z__2.i = alpha[i__2].i - ai[i__3]
.i;
z__1.r = z__2.r, z__1.i = z__2.i;
i__4 = j;
i__5 = j + j * bi_dim1;
z__4.r = beta[i__4].r - bi[i__5].r, z__4.i = beta[i__4].i - bi[i__5]
.i;
z__3.r = z__4.r, z__3.i = z__4.i;
/* Computing MAX */
i__6 = j;
i__7 = j + j * ai_dim1;
d__13 = smlnum, d__14 = (d__1 = alpha[i__6].r, abs(d__1)) + (d__2 =
d_imag(&alpha[j]), abs(d__2)), d__13 = max(d__13,d__14),
d__14 = (d__3 = ai[i__7].r, abs(d__3)) + (d__4 = d_imag(&ai[j
+ j * ai_dim1]), abs(d__4));
/* Computing MAX */
i__8 = j;
i__9 = j + j * bi_dim1;
d__15 = smlnum, d__16 = (d__5 = beta[i__8].r, abs(d__5)) + (d__6 =
d_imag(&beta[j]), abs(d__6)), d__15 = max(d__15,d__16), d__16
= (d__7 = bi[i__9].r, abs(d__7)) + (d__8 = d_imag(&bi[j + j *
bi_dim1]), abs(d__8));
temp2 = (((d__9 = z__1.r, abs(d__9)) + (d__10 = d_imag(&z__1), abs(
d__10))) / max(d__13,d__14) + ((d__11 = z__3.r, abs(d__11)) +
(d__12 = d_imag(&z__3), abs(d__12))) / max(d__15,d__16)) /
ulp;
if (j < mn_1.mplusn) {
i__2 = j + 1 + j * ai_dim1;
if (ai[i__2].r != 0. || ai[i__2].i != 0.) {
ilabad = TRUE_;
result[4] = ulpinv;
}
}
if (j > 1) {
i__2 = j + (j - 1) * ai_dim1;
if (ai[i__2].r != 0. || ai[i__2].i != 0.) {
ilabad = TRUE_;
result[4] = ulpinv;
}
}
temp1 = max(temp1,temp2);
if (ilabad) {
io___46.ciunit = *nout;
s_wsfe(&io___46);
do_fio(&c__1, (char *)&j, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&mn_1.mplusn, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&nptknt, (ftnlen)sizeof(integer));
e_wsfe();
}
/* L110: */
}
result[5] = temp1;
/* Test (7) (if sorting worked) <--------- need to be checked. */
ntest = 7;
result[6] = 0.;
if (linfo == mn_1.mplusn + 3) {
result[6] = ulpinv;
}
/* Test (8): compare the estimated value of DIF and its true value. */
ntest = 8;
result[7] = 0.;
if (difest[1] == 0.) {
if (diftru > abnrm * ulp) {
result[7] = ulpinv;
}
} else if (diftru == 0.) {
if (difest[1] > abnrm * ulp) {
result[7] = ulpinv;
}
} else if (diftru > thrsh2 * difest[1] || diftru * thrsh2 < difest[1]) {
/* Computing MAX */
d__1 = diftru / difest[1], d__2 = difest[1] / diftru;
result[7] = max(d__1,d__2);
}
/* Test (9) */
ntest = 9;
result[8] = 0.;
if (linfo == mn_1.mplusn + 2) {
if (diftru > abnrm * ulp) {
result[8] = ulpinv;
}
if (ifunc > 1 && difest[1] != 0.) {
result[8] = ulpinv;
}
if (ifunc == 1 && pl[0] != 0.) {
result[8] = ulpinv;
}
}
/* Test (10): compare the estimated value of PL and it true value. */
ntest = 10;
result[9] = 0.;
if (pl[0] == 0.) {
if (pltru > abnrm * ulp) {
result[9] = ulpinv;
}
} else if (pltru == 0.) {
if (pl[0] > abnrm * ulp) {
result[9] = ulpinv;
}
} else if (pltru > *thresh * pl[0] || pltru * *thresh < pl[0]) {
result[9] = ulpinv;
}
ntestt += ntest;
/* Print out tests which fail. */
i__1 = ntest;
for (j = 1; j <= i__1; ++j) {
if (result[j - 1] >= *thresh) {
/* If this is the first test to fail, */
/* print a header to the data file. */
if (nerrs == 0) {
io___47.ciunit = *nout;
s_wsfe(&io___47);
do_fio(&c__1, "CGX", (ftnlen)3);
e_wsfe();
/* Matrix types */
io___48.ciunit = *nout;
s_wsfe(&io___48);
e_wsfe();
/* Tests performed */
io___49.ciunit = *nout;
s_wsfe(&io___49);
do_fio(&c__1, "unitary", (ftnlen)7);
do_fio(&c__1, "'", (ftnlen)1);
do_fio(&c__1, "transpose", (ftnlen)9);
for (i__ = 1; i__ <= 4; ++i__) {
do_fio(&c__1, "'", (ftnlen)1);
}
e_wsfe();
}
++nerrs;
if (result[j - 1] < 1e4) {
io___50.ciunit = *nout;
s_wsfe(&io___50);
do_fio(&c__1, (char *)&nptknt, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&mn_1.mplusn, (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();
} else {
io___51.ciunit = *nout;
s_wsfe(&io___51);
do_fio(&c__1, (char *)&nptknt, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&mn_1.mplusn, (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();
}
}
/* L120: */
}
L130:
goto L80;
L140:
L150:
/* Summary */
alasvm_("CGX", nout, &nerrs, &ntestt, &c__0);
work[1].r = (doublereal) maxwrk, work[1].i = 0.;
return 0;
/* End of ZDRGSX */
} /* zdrgsx_ */
int Pseudoinverse(
size_t m, size_t n,
const doublecomplex *A, size_t lda,
doublecomplex *P, size_t ldp
){
integer info;
CMat Acopy(Eigen::Map<const CMat,Eigen::Unaligned,Eigen::OuterStride<> >(A, m, n, Eigen::OuterStride<>(lda)));
Eigen::Map<CMat,Eigen::Unaligned,Eigen::OuterStride<> > mP(P, n, m, Eigen::OuterStride<>(ldp));
if(m >= n){ // tall case
RVec S(n);
CMat VH(n,n);
doublecomplex dum;
integer lwork = -1;
RVec rwork(5*n);
zgesvd_(
"O","A", m,n, Acopy.data(), Acopy.outerStride(),
S.data(), NULL, m, VH.data(), VH.outerStride(),
&dum, lwork, rwork.data(), &info
);
lwork = (integer)dum.real();
CVec work(lwork);
zgesvd_(
"O","A", m,n, Acopy.data(), Acopy.outerStride(),
S.data(), NULL, m, VH.data(), VH.outerStride(),
work.data(), lwork, rwork.data(), &info
);
mP = Acopy.adjoint();
{
double threshold = 2 * std::numeric_limits<double>::epsilon() * S[0];
for(size_t i = 0; i < n; ++i){
if(S[i] < threshold){
break;
}
S[i] = 1./S[i];
}
}
mP = VH.adjoint() * S.asDiagonal() * mP;
}else{ // wide case
RVec S(m);
CMat U(m,m);
doublecomplex dum;
integer lwork = -1;
RVec rwork(5*m);
zgesvd_(
"A","O", m,n, Acopy.data(), Acopy.outerStride(),
S.data(), U.data(), U.outerStride(), NULL, m,
&dum, lwork, rwork.data(), &info
);
lwork = (integer)dum.real();
CVec work(lwork);
zgesvd_(
"A","O", m,n, Acopy.data(), Acopy.outerStride(),
S.data(), U.data(), U.outerStride(), NULL, m,
work.data(), lwork, rwork.data(), &info
);
mP = Acopy.adjoint();
{
double threshold = 2 * std::numeric_limits<double>::epsilon() * S[0];
for(size_t i = 0; i < m; ++i){
if(S[i] < threshold){
break;
}
S[i] = 1./S[i];
}
}
mP = mP * S.asDiagonal() * U.adjoint();
}
return info;
}