/* Subroutine */ int zdrvev_(integer *nsizes, integer *nn, integer *ntypes,
logical *dotype, integer *iseed, doublereal *thresh, integer *nounit,
doublecomplex *a, integer *lda, doublecomplex *h__, doublecomplex *w,
doublecomplex *w1, doublecomplex *vl, integer *ldvl, doublecomplex *
vr, integer *ldvr, doublecomplex *lre, integer *ldlre, doublereal *
result, doublecomplex *work, integer *nwork, doublereal *rwork,
integer *iwork, integer *info)
{
/* Initialized data */
static integer ktype[21] = { 1,2,3,4,4,4,4,4,6,6,6,6,6,6,6,6,6,6,9,9,9 };
static integer kmagn[21] = { 1,1,1,1,1,1,2,3,1,1,1,1,1,1,1,1,2,3,1,2,3 };
static integer kmode[21] = { 0,0,0,4,3,1,4,4,4,3,1,5,4,3,1,5,5,5,4,3,1 };
static integer kconds[21] = { 0,0,0,0,0,0,0,0,1,1,1,1,2,2,2,2,2,2,0,0,0 };
/* Format strings */
static char fmt_9993[] = "(\002 ZDRVEV: \002,a,\002 returned INFO=\002,i"
"6,\002.\002,/9x,\002N=\002,i6,\002, JTYPE=\002,i6,\002, ISEED="
"(\002,3(i5,\002,\002),i5,\002)\002)";
static char fmt_9999[] = "(/1x,a3,\002 -- Complex Eigenvalue-Eigenvect"
"or \002,\002Decomposition Driver\002,/\002 Matrix types (see ZDR"
"VEV for details): \002)";
static char fmt_9998[] = "(/\002 Special Matrices:\002,/\002 1=Zero mat"
"rix. \002,\002 \002,\002 5=Diagonal: geom"
"etr. spaced entries.\002,/\002 2=Identity matrix. "
" \002,\002 6=Diagona\002,\002l: clustered entries.\002,"
"/\002 3=Transposed Jordan block. \002,\002 \002,\002 "
" 7=Diagonal: large, evenly spaced.\002,/\002 \002,\0024=Diagona"
"l: evenly spaced entries. \002,\002 8=Diagonal: s\002,\002ma"
"ll, evenly spaced.\002)";
static char fmt_9997[] = "(\002 Dense, Non-Symmetric Matrices:\002,/\002"
" 9=Well-cond., ev\002,\002enly spaced eigenvals.\002,\002 14=Il"
"l-cond., geomet. spaced e\002,\002igenals.\002,/\002 10=Well-con"
"d., geom. spaced eigenvals. \002,\002 15=Ill-conditioned, cluste"
"red e.vals.\002,/\002 11=Well-cond\002,\002itioned, clustered e."
"vals. \002,\002 16=Ill-cond., random comp\002,\002lex \002,a6,"
"/\002 12=Well-cond., random complex \002,a6,\002 \002,\002 17="
"Ill-cond., large rand. complx \002,a4,/\002 13=Ill-condi\002,"
"\002tioned, evenly spaced. \002,\002 18=Ill-cond., small ran"
"d.\002,\002 complx \002,a4)";
static char fmt_9996[] = "(\002 19=Matrix with random O(1) entries. "
" \002,\002 21=Matrix \002,\002with small random entries.\002,"
"/\002 20=Matrix with large ran\002,\002dom entries. \002,/)";
static char fmt_9995[] = "(\002 Tests performed with test threshold ="
"\002,f8.2,//\002 1 = | A VR - VR W | / ( n |A| ulp ) \002,/\002 "
"2 = | conj-trans(A) VL - VL conj-trans(W) | /\002,\002 ( n |A| u"
"lp ) \002,/\002 3 = | |VR(i)| - 1 | / ulp \002,/\002 4 = | |VL(i"
")| - 1 | / ulp \002,/\002 5 = 0 if W same no matter if VR or VL "
"computed,\002,\002 1/ulp otherwise\002,/\002 6 = 0 if VR same no"
" matter if VL computed,\002,\002 1/ulp otherwise\002,/\002 7 = "
"0 if VL same no matter if VR computed,\002,\002 1/ulp otherwis"
"e\002,/)";
static char fmt_9994[] = "(\002 N=\002,i5,\002, IWK=\002,i2,\002, seed"
"=\002,4(i4,\002,\002),\002 type \002,i2,\002, test(\002,i2,\002)="
"\002,g10.3)";
/* System generated locals */
integer a_dim1, a_offset, h_dim1, h_offset, lre_dim1, lre_offset, vl_dim1,
vl_offset, vr_dim1, vr_offset, i__1, i__2, i__3, i__4, i__5,
i__6;
doublereal d__1, d__2, d__3, d__4, d__5;
doublecomplex z__1;
/* Builtin functions */
/* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
double sqrt(doublereal);
integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void);
double z_abs(doublecomplex *), d_imag(doublecomplex *);
/* Local variables */
integer j, n, jj;
doublecomplex dum[1];
doublereal res[2];
integer iwk;
doublereal ulp, vmx, cond;
integer jcol;
char path[3];
integer nmax;
doublereal unfl, ovfl, tnrm, vrmx, vtst;
logical badnn;
integer nfail, imode, iinfo;
doublereal conds, anorm;
extern /* Subroutine */ int zget22_(char *, char *, char *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, doublecomplex *, doublereal *, doublereal *), zgeev_(char *, char *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *, doublecomplex *, integer *, doublecomplex *, integer *,
doublereal *, integer *);
integer jsize, nerrs, itype, jtype, ntest;
doublereal rtulp;
extern /* Subroutine */ int dlabad_(doublereal *, doublereal *);
extern doublereal dznrm2_(integer *, doublecomplex *, integer *), dlamch_(
char *);
integer idumma[1];
extern /* Subroutine */ int xerbla_(char *, integer *);
integer ioldsd[4];
extern /* Subroutine */ int dlasum_(char *, integer *, integer *, integer
*), zlatme_(integer *, char *, integer *, doublecomplex *,
integer *, doublereal *, doublecomplex *, char *, char *, char *,
char *, doublereal *, integer *, doublereal *, integer *,
integer *, doublereal *, doublecomplex *, integer *,
doublecomplex *, integer *), zlacpy_(char *, integer *, integer *, doublecomplex *,
integer *, doublecomplex *, integer *);
integer ntestf;
extern /* Subroutine */ int zlaset_(char *, integer *, integer *,
doublecomplex *, doublecomplex *, doublecomplex *, integer *), zlatmr_(integer *, integer *, char *, integer *, char *,
doublecomplex *, integer *, doublereal *, doublecomplex *, char *,
char *, doublecomplex *, integer *, doublereal *, doublecomplex *
, integer *, doublereal *, char *, integer *, integer *, integer *
, doublereal *, doublereal *, char *, doublecomplex *, integer *,
integer *, integer *), zlatms_(integer *, integer *, char *, integer *, char *,
doublereal *, integer *, doublereal *, doublereal *, integer *,
integer *, char *, doublecomplex *, integer *, doublecomplex *,
integer *);
doublereal ulpinv;
integer nnwork, mtypes, ntestt;
doublereal rtulpi;
/* Fortran I/O blocks */
static cilist io___31 = { 0, 0, 0, fmt_9993, 0 };
static cilist io___34 = { 0, 0, 0, fmt_9993, 0 };
static cilist io___42 = { 0, 0, 0, fmt_9993, 0 };
static cilist io___43 = { 0, 0, 0, fmt_9993, 0 };
static cilist io___44 = { 0, 0, 0, fmt_9993, 0 };
static cilist io___47 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___48 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___49 = { 0, 0, 0, fmt_9997, 0 };
static cilist io___50 = { 0, 0, 0, fmt_9996, 0 };
static cilist io___51 = { 0, 0, 0, fmt_9995, 0 };
static cilist io___52 = { 0, 0, 0, fmt_9994, 0 };
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZDRVEV checks the nonsymmetric eigenvalue problem driver ZGEEV. */
/* When ZDRVEV is called, a number of matrix "sizes" ("n's") and a */
/* number of matrix "types" are specified. For each size ("n") */
/* and each type of matrix, one matrix will be generated and used */
/* to test the nonsymmetric eigenroutines. For each matrix, 7 */
/* tests will be performed: */
/* (1) | A * VR - VR * W | / ( n |A| ulp ) */
/* Here VR is the matrix of unit right eigenvectors. */
/* W is a diagonal matrix with diagonal entries W(j). */
/* (2) | A**H * VL - VL * W**H | / ( n |A| ulp ) */
/* Here VL is the matrix of unit left eigenvectors, A**H is the */
/* conjugate-transpose of A, and W is as above. */
/* (3) | |VR(i)| - 1 | / ulp and whether largest component real */
/* VR(i) denotes the i-th column of VR. */
/* (4) | |VL(i)| - 1 | / ulp and whether largest component real */
/* VL(i) denotes the i-th column of VL. */
/* (5) W(full) = W(partial) */
/* W(full) denotes the eigenvalues computed when both VR and VL */
/* are also computed, and W(partial) denotes the eigenvalues */
/* computed when only W, only W and VR, or only W and VL are */
/* computed. */
/* (6) VR(full) = VR(partial) */
/* VR(full) denotes the right eigenvectors computed when both VR */
/* and VL are computed, and VR(partial) denotes the result */
/* when only VR is computed. */
/* (7) VL(full) = VL(partial) */
/* VL(full) denotes the left eigenvectors computed when both VR */
/* and VL are also computed, and VL(partial) denotes the result */
/* when only VL is computed. */
/* The "sizes" are specified by an array NN(1:NSIZES); the value of */
/* each element NN(j) specifies one size. */
/* The "types" are specified by a logical array DOTYPE( 1:NTYPES ); */
/* if DOTYPE(j) is .TRUE., then matrix type "j" will be generated. */
/* Currently, the list of possible types is: */
/* (1) The zero matrix. */
/* (2) The identity matrix. */
/* (3) A (transposed) Jordan block, with 1's on the diagonal. */
/* (4) A diagonal matrix with evenly spaced entries */
/* 1, ..., ULP and random complex angles. */
/* (ULP = (first number larger than 1) - 1 ) */
/* (5) A diagonal matrix with geometrically spaced entries */
/* 1, ..., ULP and random complex angles. */
/* (6) A diagonal matrix with "clustered" entries 1, ULP, ..., ULP */
/* and random complex angles. */
/* (7) Same as (4), but multiplied by a constant near */
/* the overflow threshold */
/* (8) Same as (4), but multiplied by a constant near */
/* the underflow threshold */
/* (9) A matrix of the form U' T U, where U is unitary and */
/* T has evenly spaced entries 1, ..., ULP with random complex */
/* angles on the diagonal and random O(1) entries in the upper */
/* triangle. */
/* (10) A matrix of the form U' T U, where U is unitary and */
/* T has geometrically spaced entries 1, ..., ULP with random */
/* complex angles on the diagonal and random O(1) entries in */
/* the upper triangle. */
/* (11) A matrix of the form U' T U, where U is unitary and */
/* T has "clustered" entries 1, ULP,..., ULP with random */
/* complex angles on the diagonal and random O(1) entries in */
/* the upper triangle. */
/* (12) A matrix of the form U' T U, where U is unitary and */
/* T has complex eigenvalues randomly chosen from */
/* ULP < |z| < 1 and random O(1) entries in the upper */
/* triangle. */
/* (13) A matrix of the form X' T X, where X has condition */
/* SQRT( ULP ) and T has evenly spaced entries 1, ..., ULP */
/* with random complex angles on the diagonal and random O(1) */
/* entries in the upper triangle. */
/* (14) A matrix of the form X' T X, where X has condition */
/* SQRT( ULP ) and T has geometrically spaced entries */
/* 1, ..., ULP with random complex angles on the diagonal */
/* and random O(1) entries in the upper triangle. */
/* (15) A matrix of the form X' T X, where X has condition */
/* SQRT( ULP ) and T has "clustered" entries 1, ULP,..., ULP */
/* with random complex angles on the diagonal and random O(1) */
/* entries in the upper triangle. */
/* (16) A matrix of the form X' T X, where X has condition */
/* SQRT( ULP ) and T has complex eigenvalues randomly chosen */
/* from ULP < |z| < 1 and random O(1) entries in the upper */
/* triangle. */
/* (17) Same as (16), but multiplied by a constant */
/* near the overflow threshold */
/* (18) Same as (16), but multiplied by a constant */
/* near the underflow threshold */
/* (19) Nonsymmetric matrix with random entries chosen from |z| < 1 */
/* If N is at least 4, all entries in first two rows and last */
/* row, and first column and last two columns are zero. */
/* (20) Same as (19), but multiplied by a constant */
/* near the overflow threshold */
/* (21) Same as (19), but multiplied by a constant */
/* near the underflow threshold */
/* Arguments */
/* ========== */
/* NSIZES (input) INTEGER */
/* The number of sizes of matrices to use. If it is zero, */
/* ZDRVEV does nothing. It must be at least zero. */
/* NN (input) INTEGER array, dimension (NSIZES) */
/* An array containing the sizes to be used for the matrices. */
/* Zero values will be skipped. The values must be at least */
/* zero. */
/* NTYPES (input) INTEGER */
/* The number of elements in DOTYPE. If it is zero, ZDRVEV */
/* does nothing. It must be at least zero. If it is MAXTYP+1 */
/* and NSIZES is 1, then an additional type, MAXTYP+1 is */
/* defined, which is to use whatever matrix is in A. This */
/* is only useful if DOTYPE(1:MAXTYP) is .FALSE. and */
/* DOTYPE(MAXTYP+1) is .TRUE. . */
/* DOTYPE (input) LOGICAL array, dimension (NTYPES) */
/* If DOTYPE(j) is .TRUE., then for each size in NN a */
/* matrix of that size and of type j will be generated. */
/* If NTYPES is smaller than the maximum number of types */
/* defined (PARAMETER MAXTYP), then types NTYPES+1 through */
/* MAXTYP will not be generated. If NTYPES is larger */
/* than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES) */
/* will be ignored. */
/* ISEED (input/output) INTEGER array, dimension (4) */
/* On entry ISEED specifies the seed of the random number */
/* generator. The array elements should be between 0 and 4095; */
/* if not they will be reduced mod 4096. Also, ISEED(4) must */
/* be odd. The random number generator uses a linear */
/* congruential sequence limited to small integers, and so */
/* should produce machine independent random numbers. The */
/* values of ISEED are changed on exit, and can be used in the */
/* next call to ZDRVEV to continue the same random number */
/* sequence. */
/* 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. It must be at least zero. */
/* NOUNIT (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, max(NN)) */
/* Used to hold 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, and H. LDA must be at */
/* least 1 and at least max(NN). */
/* H (workspace) COMPLEX*16 array, dimension (LDA, max(NN)) */
/* Another copy of the test matrix A, modified by ZGEEV. */
/* W (workspace) COMPLEX*16 array, dimension (max(NN)) */
/* The eigenvalues of A. On exit, W are the eigenvalues of */
/* the matrix in A. */
/* W1 (workspace) COMPLEX*16 array, dimension (max(NN)) */
/* Like W, this array contains the eigenvalues of A, */
/* but those computed when ZGEEV only computes a partial */
/* eigendecomposition, i.e. not the eigenvalues and left */
/* and right eigenvectors. */
/* VL (workspace) COMPLEX*16 array, dimension (LDVL, max(NN)) */
/* VL holds the computed left eigenvectors. */
/* LDVL (input) INTEGER */
/* Leading dimension of VL. Must be at least max(1,max(NN)). */
/* VR (workspace) COMPLEX*16 array, dimension (LDVR, max(NN)) */
/* VR holds the computed right eigenvectors. */
/* LDVR (input) INTEGER */
/* Leading dimension of VR. Must be at least max(1,max(NN)). */
/* LRE (workspace) COMPLEX*16 array, dimension (LDLRE, max(NN)) */
/* LRE holds the computed right or left eigenvectors. */
/* LDLRE (input) INTEGER */
/* Leading dimension of LRE. Must be at least max(1,max(NN)). */
/* RESULT (output) DOUBLE PRECISION array, dimension (7) */
/* The values computed by the seven tests described above. */
/* The values are currently limited to 1/ulp, to avoid */
/* overflow. */
/* WORK (workspace) COMPLEX*16 array, dimension (NWORK) */
/* NWORK (input) INTEGER */
/* The number of entries in WORK. This must be at least */
/* 5*NN(j)+2*NN(j)**2 for all j. */
/* RWORK (workspace) DOUBLE PRECISION array, dimension (2*max(NN)) */
/* IWORK (workspace) INTEGER array, dimension (max(NN)) */
/* INFO (output) INTEGER */
/* If 0, then everything ran OK. */
/* -1: NSIZES < 0 */
/* -2: Some NN(j) < 0 */
/* -3: NTYPES < 0 */
/* -6: THRESH < 0 */
/* -9: LDA < 1 or LDA < NMAX, where NMAX is max( NN(j) ). */
/* -14: LDVL < 1 or LDVL < NMAX, where NMAX is max( NN(j) ). */
/* -16: LDVR < 1 or LDVR < NMAX, where NMAX is max( NN(j) ). */
/* -18: LDLRE < 1 or LDLRE < NMAX, where NMAX is max( NN(j) ). */
/* -21: NWORK too small. */
/* If ZLATMR, CLATMS, CLATME or ZGEEV returns an error code, */
/* the absolute value of it is returned. */
/* ----------------------------------------------------------------------- */
/* Some Local Variables and Parameters: */
/* ---- ----- --------- --- ---------- */
/* ZERO, ONE Real 0 and 1. */
/* MAXTYP The number of types defined. */
/* NMAX Largest value in NN. */
/* NERRS The number of tests which have exceeded THRESH */
/* COND, CONDS, */
/* IMODE Values to be passed to the matrix generators. */
/* ANORM Norm of A; passed to matrix generators. */
/* OVFL, UNFL Overflow and underflow thresholds. */
/* ULP, ULPINV Finest relative precision and its inverse. */
/* RTULP, RTULPI Square roots of the previous 4 values. */
/* The following four arrays decode JTYPE: */
/* KTYPE(j) The general type (1-10) for type "j". */
/* KMODE(j) The MODE value to be passed to the matrix */
/* generator for type "j". */
/* KMAGN(j) The order of magnitude ( O(1), */
/* O(overflow^(1/2) ), O(underflow^(1/2) ) */
/* KCONDS(j) Selectw whether CONDS is to be 1 or */
/* 1/sqrt(ulp). (0 means irrelevant.) */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Data statements .. */
/* Parameter adjustments */
--nn;
--dotype;
--iseed;
h_dim1 = *lda;
h_offset = 1 + h_dim1;
h__ -= h_offset;
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--w;
--w1;
vl_dim1 = *ldvl;
vl_offset = 1 + vl_dim1;
vl -= vl_offset;
vr_dim1 = *ldvr;
vr_offset = 1 + vr_dim1;
vr -= vr_offset;
lre_dim1 = *ldlre;
lre_offset = 1 + lre_dim1;
lre -= lre_offset;
--result;
--work;
--rwork;
--iwork;
/* Function Body */
/* .. */
/* .. Executable Statements .. */
s_copy(path, "Zomplex precision", (ftnlen)1, (ftnlen)17);
s_copy(path + 1, "EV", (ftnlen)2, (ftnlen)2);
/* Check for errors */
ntestt = 0;
ntestf = 0;
*info = 0;
/* Important constants */
badnn = FALSE_;
nmax = 0;
i__1 = *nsizes;
for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
i__2 = nmax, i__3 = nn[j];
nmax = max(i__2,i__3);
if (nn[j] < 0) {
badnn = TRUE_;
}
/* L10: */
}
/* Check for errors */
if (*nsizes < 0) {
*info = -1;
} else if (badnn) {
*info = -2;
} else if (*ntypes < 0) {
*info = -3;
} else if (*thresh < 0.) {
*info = -6;
} else if (*nounit <= 0) {
*info = -7;
} else if (*lda < 1 || *lda < nmax) {
*info = -9;
} else if (*ldvl < 1 || *ldvl < nmax) {
*info = -14;
} else if (*ldvr < 1 || *ldvr < nmax) {
*info = -16;
} else if (*ldlre < 1 || *ldlre < nmax) {
*info = -28;
} else /* if(complicated condition) */ {
/* Computing 2nd power */
i__1 = nmax;
if (nmax * 5 + (i__1 * i__1 << 1) > *nwork) {
*info = -21;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZDRVEV", &i__1);
return 0;
}
/* Quick return if nothing to do */
if (*nsizes == 0 || *ntypes == 0) {
return 0;
}
/* More Important constants */
unfl = dlamch_("Safe minimum");
ovfl = 1. / unfl;
dlabad_(&unfl, &ovfl);
ulp = dlamch_("Precision");
ulpinv = 1. / ulp;
rtulp = sqrt(ulp);
rtulpi = 1. / rtulp;
/* Loop over sizes, types */
nerrs = 0;
i__1 = *nsizes;
for (jsize = 1; jsize <= i__1; ++jsize) {
n = nn[jsize];
if (*nsizes != 1) {
mtypes = min(21,*ntypes);
} else {
mtypes = min(22,*ntypes);
}
i__2 = mtypes;
for (jtype = 1; jtype <= i__2; ++jtype) {
if (! dotype[jtype]) {
goto L260;
}
/* Save ISEED in case of an error. */
for (j = 1; j <= 4; ++j) {
ioldsd[j - 1] = iseed[j];
/* L20: */
}
/* Compute "A" */
/* Control parameters: */
/* KMAGN KCONDS KMODE KTYPE */
/* =1 O(1) 1 clustered 1 zero */
/* =2 large large clustered 2 identity */
/* =3 small exponential Jordan */
/* =4 arithmetic diagonal, (w/ eigenvalues) */
/* =5 random log symmetric, w/ eigenvalues */
/* =6 random general, w/ eigenvalues */
/* =7 random diagonal */
/* =8 random symmetric */
/* =9 random general */
/* =10 random triangular */
if (mtypes > 21) {
goto L90;
}
itype = ktype[jtype - 1];
imode = kmode[jtype - 1];
/* Compute norm */
switch (kmagn[jtype - 1]) {
case 1: goto L30;
case 2: goto L40;
case 3: goto L50;
}
L30:
anorm = 1.;
goto L60;
L40:
anorm = ovfl * ulp;
goto L60;
L50:
anorm = unfl * ulpinv;
goto L60;
L60:
zlaset_("Full", lda, &n, &c_b1, &c_b1, &a[a_offset], lda);
iinfo = 0;
cond = ulpinv;
/* Special Matrices -- Identity & Jordan block */
/* Zero */
if (itype == 1) {
iinfo = 0;
} else if (itype == 2) {
/* Identity */
i__3 = n;
for (jcol = 1; jcol <= i__3; ++jcol) {
i__4 = jcol + jcol * a_dim1;
z__1.r = anorm, z__1.i = 0.;
a[i__4].r = z__1.r, a[i__4].i = z__1.i;
/* L70: */
}
} else if (itype == 3) {
/* Jordan Block */
i__3 = n;
for (jcol = 1; jcol <= i__3; ++jcol) {
i__4 = jcol + jcol * a_dim1;
z__1.r = anorm, z__1.i = 0.;
a[i__4].r = z__1.r, a[i__4].i = z__1.i;
if (jcol > 1) {
i__4 = jcol + (jcol - 1) * a_dim1;
a[i__4].r = 1., a[i__4].i = 0.;
}
/* L80: */
}
} else if (itype == 4) {
/* Diagonal Matrix, [Eigen]values Specified */
zlatms_(&n, &n, "S", &iseed[1], "H", &rwork[1], &imode, &cond,
&anorm, &c__0, &c__0, "N", &a[a_offset], lda, &work[
n + 1], &iinfo);
} else if (itype == 5) {
/* Hermitian, eigenvalues specified */
zlatms_(&n, &n, "S", &iseed[1], "H", &rwork[1], &imode, &cond,
&anorm, &n, &n, "N", &a[a_offset], lda, &work[n + 1],
&iinfo);
} else if (itype == 6) {
/* General, eigenvalues specified */
if (kconds[jtype - 1] == 1) {
conds = 1.;
} else if (kconds[jtype - 1] == 2) {
conds = rtulpi;
} else {
conds = 0.;
}
zlatme_(&n, "D", &iseed[1], &work[1], &imode, &cond, &c_b2,
" ", "T", "T", "T", &rwork[1], &c__4, &conds, &n, &n,
&anorm, &a[a_offset], lda, &work[(n << 1) + 1], &
iinfo);
} else if (itype == 7) {
/* Diagonal, random eigenvalues */
zlatmr_(&n, &n, "D", &iseed[1], "N", &work[1], &c__6, &c_b38,
&c_b2, "T", "N", &work[n + 1], &c__1, &c_b38, &work[(
n << 1) + 1], &c__1, &c_b38, "N", idumma, &c__0, &
c__0, &c_b48, &anorm, "NO", &a[a_offset], lda, &iwork[
1], &iinfo);
} else if (itype == 8) {
/* Symmetric, random eigenvalues */
zlatmr_(&n, &n, "D", &iseed[1], "H", &work[1], &c__6, &c_b38,
&c_b2, "T", "N", &work[n + 1], &c__1, &c_b38, &work[(
n << 1) + 1], &c__1, &c_b38, "N", idumma, &n, &n, &
c_b48, &anorm, "NO", &a[a_offset], lda, &iwork[1], &
iinfo);
} else if (itype == 9) {
/* General, random eigenvalues */
zlatmr_(&n, &n, "D", &iseed[1], "N", &work[1], &c__6, &c_b38,
&c_b2, "T", "N", &work[n + 1], &c__1, &c_b38, &work[(
n << 1) + 1], &c__1, &c_b38, "N", idumma, &n, &n, &
c_b48, &anorm, "NO", &a[a_offset], lda, &iwork[1], &
iinfo);
if (n >= 4) {
zlaset_("Full", &c__2, &n, &c_b1, &c_b1, &a[a_offset],
lda);
i__3 = n - 3;
zlaset_("Full", &i__3, &c__1, &c_b1, &c_b1, &a[a_dim1 + 3]
, lda);
i__3 = n - 3;
zlaset_("Full", &i__3, &c__2, &c_b1, &c_b1, &a[(n - 1) *
a_dim1 + 3], lda);
zlaset_("Full", &c__1, &n, &c_b1, &c_b1, &a[n + a_dim1],
lda);
}
} else if (itype == 10) {
/* Triangular, random eigenvalues */
zlatmr_(&n, &n, "D", &iseed[1], "N", &work[1], &c__6, &c_b38,
&c_b2, "T", "N", &work[n + 1], &c__1, &c_b38, &work[(
n << 1) + 1], &c__1, &c_b38, "N", idumma, &n, &c__0, &
c_b48, &anorm, "NO", &a[a_offset], lda, &iwork[1], &
iinfo);
} else {
iinfo = 1;
}
if (iinfo != 0) {
io___31.ciunit = *nounit;
s_wsfe(&io___31);
do_fio(&c__1, "Generator", (ftnlen)9);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
*info = abs(iinfo);
return 0;
}
L90:
/* Test for minimal and generous workspace */
for (iwk = 1; iwk <= 2; ++iwk) {
if (iwk == 1) {
nnwork = n << 1;
} else {
/* Computing 2nd power */
i__3 = n;
nnwork = n * 5 + (i__3 * i__3 << 1);
}
nnwork = max(nnwork,1);
/* Initialize RESULT */
for (j = 1; j <= 7; ++j) {
result[j] = -1.;
/* L100: */
}
/* Compute eigenvalues and eigenvectors, and test them */
zlacpy_("F", &n, &n, &a[a_offset], lda, &h__[h_offset], lda);
zgeev_("V", "V", &n, &h__[h_offset], lda, &w[1], &vl[
vl_offset], ldvl, &vr[vr_offset], ldvr, &work[1], &
nnwork, &rwork[1], &iinfo);
if (iinfo != 0) {
result[1] = ulpinv;
io___34.ciunit = *nounit;
s_wsfe(&io___34);
do_fio(&c__1, "ZGEEV1", (ftnlen)6);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer))
;
e_wsfe();
*info = abs(iinfo);
goto L220;
}
/* Do Test (1) */
zget22_("N", "N", "N", &n, &a[a_offset], lda, &vr[vr_offset],
ldvr, &w[1], &work[1], &rwork[1], res);
result[1] = res[0];
/* Do Test (2) */
zget22_("C", "N", "C", &n, &a[a_offset], lda, &vl[vl_offset],
ldvl, &w[1], &work[1], &rwork[1], res);
result[2] = res[0];
/* Do Test (3) */
i__3 = n;
for (j = 1; j <= i__3; ++j) {
tnrm = dznrm2_(&n, &vr[j * vr_dim1 + 1], &c__1);
/* Computing MAX */
/* Computing MIN */
d__4 = ulpinv, d__5 = (d__1 = tnrm - 1., abs(d__1)) / ulp;
d__2 = result[3], d__3 = min(d__4,d__5);
result[3] = max(d__2,d__3);
vmx = 0.;
vrmx = 0.;
i__4 = n;
for (jj = 1; jj <= i__4; ++jj) {
vtst = z_abs(&vr[jj + j * vr_dim1]);
if (vtst > vmx) {
vmx = vtst;
}
i__5 = jj + j * vr_dim1;
if (d_imag(&vr[jj + j * vr_dim1]) == 0. && (d__1 = vr[
i__5].r, abs(d__1)) > vrmx) {
i__6 = jj + j * vr_dim1;
vrmx = (d__2 = vr[i__6].r, abs(d__2));
}
/* L110: */
}
if (vrmx / vmx < 1. - ulp * 2.) {
result[3] = ulpinv;
}
/* L120: */
}
/* Do Test (4) */
i__3 = n;
for (j = 1; j <= i__3; ++j) {
tnrm = dznrm2_(&n, &vl[j * vl_dim1 + 1], &c__1);
/* Computing MAX */
/* Computing MIN */
d__4 = ulpinv, d__5 = (d__1 = tnrm - 1., abs(d__1)) / ulp;
d__2 = result[4], d__3 = min(d__4,d__5);
result[4] = max(d__2,d__3);
vmx = 0.;
vrmx = 0.;
i__4 = n;
for (jj = 1; jj <= i__4; ++jj) {
vtst = z_abs(&vl[jj + j * vl_dim1]);
if (vtst > vmx) {
vmx = vtst;
}
i__5 = jj + j * vl_dim1;
if (d_imag(&vl[jj + j * vl_dim1]) == 0. && (d__1 = vl[
i__5].r, abs(d__1)) > vrmx) {
i__6 = jj + j * vl_dim1;
vrmx = (d__2 = vl[i__6].r, abs(d__2));
}
/* L130: */
}
if (vrmx / vmx < 1. - ulp * 2.) {
result[4] = ulpinv;
}
/* L140: */
}
/* Compute eigenvalues only, and test them */
zlacpy_("F", &n, &n, &a[a_offset], lda, &h__[h_offset], lda);
zgeev_("N", "N", &n, &h__[h_offset], lda, &w1[1], dum, &c__1,
dum, &c__1, &work[1], &nnwork, &rwork[1], &iinfo);
if (iinfo != 0) {
result[1] = ulpinv;
io___42.ciunit = *nounit;
s_wsfe(&io___42);
do_fio(&c__1, "ZGEEV2", (ftnlen)6);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer))
;
e_wsfe();
*info = abs(iinfo);
goto L220;
}
/* Do Test (5) */
i__3 = n;
for (j = 1; j <= i__3; ++j) {
i__4 = j;
i__5 = j;
if (w[i__4].r != w1[i__5].r || w[i__4].i != w1[i__5].i) {
result[5] = ulpinv;
}
/* L150: */
}
/* Compute eigenvalues and right eigenvectors, and test them */
zlacpy_("F", &n, &n, &a[a_offset], lda, &h__[h_offset], lda);
zgeev_("N", "V", &n, &h__[h_offset], lda, &w1[1], dum, &c__1,
&lre[lre_offset], ldlre, &work[1], &nnwork, &rwork[1],
&iinfo);
if (iinfo != 0) {
result[1] = ulpinv;
io___43.ciunit = *nounit;
s_wsfe(&io___43);
do_fio(&c__1, "ZGEEV3", (ftnlen)6);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer))
;
e_wsfe();
*info = abs(iinfo);
goto L220;
}
/* Do Test (5) again */
i__3 = n;
for (j = 1; j <= i__3; ++j) {
i__4 = j;
i__5 = j;
if (w[i__4].r != w1[i__5].r || w[i__4].i != w1[i__5].i) {
result[5] = ulpinv;
}
/* L160: */
}
/* Do Test (6) */
i__3 = n;
for (j = 1; j <= i__3; ++j) {
i__4 = n;
for (jj = 1; jj <= i__4; ++jj) {
i__5 = j + jj * vr_dim1;
i__6 = j + jj * lre_dim1;
if (vr[i__5].r != lre[i__6].r || vr[i__5].i != lre[
i__6].i) {
result[6] = ulpinv;
}
/* L170: */
}
/* L180: */
}
/* Compute eigenvalues and left eigenvectors, and test them */
zlacpy_("F", &n, &n, &a[a_offset], lda, &h__[h_offset], lda);
zgeev_("V", "N", &n, &h__[h_offset], lda, &w1[1], &lre[
lre_offset], ldlre, dum, &c__1, &work[1], &nnwork, &
rwork[1], &iinfo);
if (iinfo != 0) {
result[1] = ulpinv;
io___44.ciunit = *nounit;
s_wsfe(&io___44);
do_fio(&c__1, "ZGEEV4", (ftnlen)6);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer))
;
e_wsfe();
*info = abs(iinfo);
goto L220;
}
/* Do Test (5) again */
i__3 = n;
for (j = 1; j <= i__3; ++j) {
i__4 = j;
i__5 = j;
if (w[i__4].r != w1[i__5].r || w[i__4].i != w1[i__5].i) {
result[5] = ulpinv;
}
/* L190: */
}
/* Do Test (7) */
i__3 = n;
for (j = 1; j <= i__3; ++j) {
i__4 = n;
for (jj = 1; jj <= i__4; ++jj) {
i__5 = j + jj * vl_dim1;
i__6 = j + jj * lre_dim1;
if (vl[i__5].r != lre[i__6].r || vl[i__5].i != lre[
i__6].i) {
result[7] = ulpinv;
}
/* L200: */
}
/* L210: */
}
/* End of Loop -- Check for RESULT(j) > THRESH */
L220:
ntest = 0;
nfail = 0;
for (j = 1; j <= 7; ++j) {
if (result[j] >= 0.) {
++ntest;
}
if (result[j] >= *thresh) {
++nfail;
}
/* L230: */
}
if (nfail > 0) {
++ntestf;
}
if (ntestf == 1) {
io___47.ciunit = *nounit;
s_wsfe(&io___47);
do_fio(&c__1, path, (ftnlen)3);
e_wsfe();
io___48.ciunit = *nounit;
s_wsfe(&io___48);
e_wsfe();
io___49.ciunit = *nounit;
s_wsfe(&io___49);
e_wsfe();
io___50.ciunit = *nounit;
s_wsfe(&io___50);
e_wsfe();
io___51.ciunit = *nounit;
s_wsfe(&io___51);
do_fio(&c__1, (char *)&(*thresh), (ftnlen)sizeof(
doublereal));
e_wsfe();
ntestf = 2;
}
for (j = 1; j <= 7; ++j) {
if (result[j] >= *thresh) {
io___52.ciunit = *nounit;
s_wsfe(&io___52);
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&iwk, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer))
;
do_fio(&c__1, (char *)&j, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&result[j], (ftnlen)sizeof(
doublereal));
e_wsfe();
}
/* L240: */
}
nerrs += nfail;
ntestt += ntest;
/* L250: */
}
L260:
;
}
/* L270: */
}
/* Summary */
dlasum_(path, nounit, &nerrs, &ntestt);
return 0;
/* End of ZDRVEV */
} /* zdrvev_ */
/* Subroutine */ int zchkhs_(integer *nsizes, integer *nn, integer *ntypes,
logical *dotype, integer *iseed, doublereal *thresh, integer *nounit,
doublecomplex *a, integer *lda, doublecomplex *h__, doublecomplex *t1,
doublecomplex *t2, doublecomplex *u, integer *ldu, doublecomplex *
z__, doublecomplex *uz, doublecomplex *w1, doublecomplex *w3,
doublecomplex *evectl, doublecomplex *evectr, doublecomplex *evecty,
doublecomplex *evectx, doublecomplex *uu, doublecomplex *tau,
doublecomplex *work, integer *nwork, doublereal *rwork, integer *
iwork, logical *select, doublereal *result, integer *info)
{
/* Initialized data */
static integer ktype[21] = { 1,2,3,4,4,4,4,4,6,6,6,6,6,6,6,6,6,6,9,9,9 };
static integer kmagn[21] = { 1,1,1,1,1,1,2,3,1,1,1,1,1,1,1,1,2,3,1,2,3 };
static integer kmode[21] = { 0,0,0,4,3,1,4,4,4,3,1,5,4,3,1,5,5,5,4,3,1 };
static integer kconds[21] = { 0,0,0,0,0,0,0,0,1,1,1,1,2,2,2,2,2,2,0,0,0 };
/* Format strings */
static char fmt_9999[] = "(\002 ZCHKHS: \002,a,\002 returned INFO=\002,i"
"6,\002.\002,/9x,\002N=\002,i6,\002, JTYPE=\002,i6,\002, ISEED="
"(\002,3(i5,\002,\002),i5,\002)\002)";
static char fmt_9998[] = "(\002 ZCHKHS: \002,a,\002 Eigenvectors from"
" \002,a,\002 incorrectly \002,\002normalized.\002,/\002 Bits of "
"error=\002,0p,g10.3,\002,\002,9x,\002N=\002,i6,\002, JTYPE=\002,"
"i6,\002, ISEED=(\002,3(i5,\002,\002),i5,\002)\002)";
static char fmt_9997[] = "(\002 ZCHKHS: Selected \002,a,\002 Eigenvector"
"s from \002,a,\002 do not match other eigenvectors \002,9x,\002N="
"\002,i6,\002, JTYPE=\002,i6,\002, ISEED=(\002,3(i5,\002,\002),i5,"
"\002)\002)";
/* System generated locals */
integer a_dim1, a_offset, evectl_dim1, evectl_offset, evectr_dim1,
evectr_offset, evectx_dim1, evectx_offset, evecty_dim1,
evecty_offset, h_dim1, h_offset, t1_dim1, t1_offset, t2_dim1,
t2_offset, u_dim1, u_offset, uu_dim1, uu_offset, uz_dim1,
uz_offset, z_dim1, z_offset, i__1, i__2, i__3, i__4, i__5, i__6;
doublereal d__1, d__2;
doublecomplex z__1;
/* Builtin functions */
double sqrt(doublereal);
integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void);
double z_abs(doublecomplex *);
/* Local variables */
integer i__, j, k, n, n1, jj, in, ihi, ilo;
doublereal ulp, cond;
integer jcol, nmax;
doublereal unfl, ovfl, temp1, temp2;
logical badnn, match;
integer imode;
doublereal dumma[4];
integer iinfo;
doublereal conds;
extern /* Subroutine */ int zget10_(integer *, integer *, doublecomplex *,
integer *, doublecomplex *, integer *, doublecomplex *,
doublereal *, doublereal *);
doublereal aninv, anorm;
extern /* Subroutine */ int zget22_(char *, char *, char *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, doublecomplex *, doublereal *, doublereal *), zgemm_(char *, char *, integer *,
integer *, integer *, doublecomplex *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *);
integer nmats, jsize, nerrs, itype, jtype, ntest;
extern /* Subroutine */ int zhst01_(integer *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublereal *, doublereal *), zcopy_(integer *, doublecomplex *,
integer *, doublecomplex *, integer *);
doublereal rtulp;
extern /* Subroutine */ int dlabad_(doublereal *, doublereal *);
extern doublereal dlamch_(char *);
doublecomplex cdumma[4];
integer idumma[1];
extern /* Subroutine */ int dlafts_(char *, integer *, integer *, integer
*, integer *, doublereal *, integer *, doublereal *, integer *,
integer *);
integer ioldsd[4];
extern /* Subroutine */ int xerbla_(char *, integer *), zgehrd_(
integer *, integer *, integer *, doublecomplex *, integer *,
doublecomplex *, doublecomplex *, integer *, integer *), dlasum_(
char *, integer *, integer *, integer *), zlatme_(integer
*, char *, integer *, doublecomplex *, integer *, doublereal *,
doublecomplex *, char *, char *, char *, char *, doublereal *,
integer *, doublereal *, integer *, integer *, doublereal *,
doublecomplex *, integer *, doublecomplex *, integer *), zhsein_(char *, char *, char *,
logical *, integer *, doublecomplex *, integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *, integer *
, integer *, doublecomplex *, doublereal *, integer *, integer *,
integer *), zlacpy_(char *, integer *,
integer *, doublecomplex *, integer *, doublecomplex *, integer *), zlaset_(char *, integer *, integer *, doublecomplex *,
doublecomplex *, doublecomplex *, integer *), zlatmr_(
integer *, integer *, char *, integer *, char *, doublecomplex *,
integer *, doublereal *, doublecomplex *, char *, char *,
doublecomplex *, integer *, doublereal *, doublecomplex *,
integer *, doublereal *, char *, integer *, integer *, integer *,
doublereal *, doublereal *, char *, doublecomplex *, integer *,
integer *, integer *);
doublereal rtunfl, rtovfl, rtulpi, ulpinv;
integer mtypes, ntestt;
extern /* Subroutine */ int zhseqr_(char *, char *, integer *, integer *,
integer *, doublecomplex *, integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *, integer *), zlatms_(integer *, integer *, char *, integer *,
char *, doublereal *, integer *, doublereal *, doublereal *,
integer *, integer *, char *, doublecomplex *, integer *,
doublecomplex *, integer *), ztrevc_(char
*, char *, logical *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *, integer *,
integer *, doublecomplex *, doublereal *, integer *), zunghr_(integer *, integer *, integer *, doublecomplex *,
integer *, doublecomplex *, doublecomplex *, integer *, integer *
), zunmhr_(char *, char *, integer *, integer *, integer *,
integer *, doublecomplex *, integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *, integer *);
/* Fortran I/O blocks */
static cilist io___35 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___38 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___40 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___41 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___42 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___47 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___49 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___50 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___54 = { 0, 0, 0, fmt_9997, 0 };
static cilist io___55 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___56 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___57 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___58 = { 0, 0, 0, fmt_9997, 0 };
static cilist io___59 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___60 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___61 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___62 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___63 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___64 = { 0, 0, 0, fmt_9999, 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 */
/* ======= */
/* ZCHKHS checks the nonsymmetric eigenvalue problem routines. */
/* ZGEHRD factors A as U H U' , where ' means conjugate */
/* transpose, H is hessenberg, and U is unitary. */
/* ZUNGHR generates the unitary matrix U. */
/* ZUNMHR multiplies a matrix by the unitary matrix U. */
/* ZHSEQR factors H as Z T Z' , where Z is unitary and T */
/* is upper triangular. It also computes the eigenvalues, */
/* w(1), ..., w(n); we define a diagonal matrix W whose */
/* (diagonal) entries are the eigenvalues. */
/* ZTREVC computes the left eigenvector matrix L and the */
/* right eigenvector matrix R for the matrix T. The */
/* columns of L are the complex conjugates of the left */
/* eigenvectors of T. The columns of R are the right */
/* eigenvectors of T. L is lower triangular, and R is */
/* upper triangular. */
/* ZHSEIN computes the left eigenvector matrix Y and the */
/* right eigenvector matrix X for the matrix H. The */
/* columns of Y are the complex conjugates of the left */
/* eigenvectors of H. The columns of X are the right */
/* eigenvectors of H. Y is lower triangular, and X is */
/* upper triangular. */
/* When ZCHKHS is called, a number of matrix "sizes" ("n's") and a */
/* number of matrix "types" are specified. For each size ("n") */
/* and each type of matrix, one matrix will be generated and used */
/* to test the nonsymmetric eigenroutines. For each matrix, 14 */
/* tests will be performed: */
/* (1) | A - U H U**H | / ( |A| n ulp ) */
/* (2) | I - UU**H | / ( n ulp ) */
/* (3) | H - Z T Z**H | / ( |H| n ulp ) */
/* (4) | I - ZZ**H | / ( n ulp ) */
/* (5) | A - UZ H (UZ)**H | / ( |A| n ulp ) */
/* (6) | I - UZ (UZ)**H | / ( n ulp ) */
/* (7) | T(Z computed) - T(Z not computed) | / ( |T| ulp ) */
/* (8) | W(Z computed) - W(Z not computed) | / ( |W| ulp ) */
/* (9) | TR - RW | / ( |T| |R| ulp ) */
/* (10) | L**H T - W**H L | / ( |T| |L| ulp ) */
/* (11) | HX - XW | / ( |H| |X| ulp ) */
/* (12) | Y**H H - W**H Y | / ( |H| |Y| ulp ) */
/* (13) | AX - XW | / ( |A| |X| ulp ) */
/* (14) | Y**H A - W**H Y | / ( |A| |Y| ulp ) */
/* The "sizes" are specified by an array NN(1:NSIZES); the value of */
/* each element NN(j) specifies one size. */
/* The "types" are specified by a logical array DOTYPE( 1:NTYPES ); */
/* if DOTYPE(j) is .TRUE., then matrix type "j" will be generated. */
/* Currently, the list of possible types is: */
/* (1) The zero matrix. */
/* (2) The identity matrix. */
/* (3) A (transposed) Jordan block, with 1's on the diagonal. */
/* (4) A diagonal matrix with evenly spaced entries */
/* 1, ..., ULP and random complex angles. */
/* (ULP = (first number larger than 1) - 1 ) */
/* (5) A diagonal matrix with geometrically spaced entries */
/* 1, ..., ULP and random complex angles. */
/* (6) A diagonal matrix with "clustered" entries 1, ULP, ..., ULP */
/* and random complex angles. */
/* (7) Same as (4), but multiplied by SQRT( overflow threshold ) */
/* (8) Same as (4), but multiplied by SQRT( underflow threshold ) */
/* (9) A matrix of the form U' T U, where U is unitary and */
/* T has evenly spaced entries 1, ..., ULP with random complex */
/* angles on the diagonal and random O(1) entries in the upper */
/* triangle. */
/* (10) A matrix of the form U' T U, where U is unitary and */
/* T has geometrically spaced entries 1, ..., ULP with random */
/* complex angles on the diagonal and random O(1) entries in */
/* the upper triangle. */
/* (11) A matrix of the form U' T U, where U is unitary and */
/* T has "clustered" entries 1, ULP,..., ULP with random */
/* complex angles on the diagonal and random O(1) entries in */
/* the upper triangle. */
/* (12) A matrix of the form U' T U, where U is unitary and */
/* T has complex eigenvalues randomly chosen from */
/* ULP < |z| < 1 and random O(1) entries in the upper */
/* triangle. */
/* (13) A matrix of the form X' T X, where X has condition */
/* SQRT( ULP ) and T has evenly spaced entries 1, ..., ULP */
/* with random complex angles on the diagonal and random O(1) */
/* entries in the upper triangle. */
/* (14) A matrix of the form X' T X, where X has condition */
/* SQRT( ULP ) and T has geometrically spaced entries */
/* 1, ..., ULP with random complex angles on the diagonal */
/* and random O(1) entries in the upper triangle. */
/* (15) A matrix of the form X' T X, where X has condition */
/* SQRT( ULP ) and T has "clustered" entries 1, ULP,..., ULP */
/* with random complex angles on the diagonal and random O(1) */
/* entries in the upper triangle. */
/* (16) A matrix of the form X' T X, where X has condition */
/* SQRT( ULP ) and T has complex eigenvalues randomly chosen */
/* from ULP < |z| < 1 and random O(1) entries in the upper */
/* triangle. */
/* (17) Same as (16), but multiplied by SQRT( overflow threshold ) */
/* (18) Same as (16), but multiplied by SQRT( underflow threshold ) */
/* (19) Nonsymmetric matrix with random entries chosen from |z| < 1 */
/* (20) Same as (19), but multiplied by SQRT( overflow threshold ) */
/* (21) Same as (19), but multiplied by SQRT( underflow threshold ) */
/* Arguments */
/* ========== */
/* NSIZES - INTEGER */
/* The number of sizes of matrices to use. If it is zero, */
/* ZCHKHS does nothing. It must be at least zero. */
/* Not modified. */
/* NN - INTEGER array, dimension (NSIZES) */
/* An array containing the sizes to be used for the matrices. */
/* Zero values will be skipped. The values must be at least */
/* zero. */
/* Not modified. */
/* NTYPES - INTEGER */
/* The number of elements in DOTYPE. If it is zero, ZCHKHS */
/* does nothing. It must be at least zero. If it is MAXTYP+1 */
/* and NSIZES is 1, then an additional type, MAXTYP+1 is */
/* defined, which is to use whatever matrix is in A. This */
/* is only useful if DOTYPE(1:MAXTYP) is .FALSE. and */
/* DOTYPE(MAXTYP+1) is .TRUE. . */
/* Not modified. */
/* DOTYPE - LOGICAL array, dimension (NTYPES) */
/* If DOTYPE(j) is .TRUE., then for each size in NN a */
/* matrix of that size and of type j will be generated. */
/* If NTYPES is smaller than the maximum number of types */
/* defined (PARAMETER MAXTYP), then types NTYPES+1 through */
/* MAXTYP will not be generated. If NTYPES is larger */
/* than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES) */
/* will be ignored. */
/* Not modified. */
/* ISEED - INTEGER array, dimension (4) */
/* On entry ISEED specifies the seed of the random number */
/* generator. The array elements should be between 0 and 4095; */
/* if not they will be reduced mod 4096. Also, ISEED(4) must */
/* be odd. The random number generator uses a linear */
/* congruential sequence limited to small integers, and so */
/* should produce machine independent random numbers. The */
/* values of ISEED are changed on exit, and can be used in the */
/* next call to ZCHKHS to continue the same random number */
/* sequence. */
/* Modified. */
/* THRESH - 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. It must be at least zero. */
/* Not modified. */
/* NOUNIT - INTEGER */
/* The FORTRAN unit number for printing out error messages */
/* (e.g., if a routine returns IINFO not equal to 0.) */
/* Not modified. */
/* A - COMPLEX*16 array, dimension (LDA,max(NN)) */
/* Used to hold the matrix whose eigenvalues are to be */
/* computed. On exit, A contains the last matrix actually */
/* used. */
/* Modified. */
/* LDA - INTEGER */
/* The leading dimension of A, H, T1 and T2. It must be at */
/* least 1 and at least max( NN ). */
/* Not modified. */
/* H - COMPLEX*16 array, dimension (LDA,max(NN)) */
/* The upper hessenberg matrix computed by ZGEHRD. On exit, */
/* H contains the Hessenberg form of the matrix in A. */
/* Modified. */
/* T1 - COMPLEX*16 array, dimension (LDA,max(NN)) */
/* The Schur (="quasi-triangular") matrix computed by ZHSEQR */
/* if Z is computed. On exit, T1 contains the Schur form of */
/* the matrix in A. */
/* Modified. */
/* T2 - COMPLEX*16 array, dimension (LDA,max(NN)) */
/* The Schur matrix computed by ZHSEQR when Z is not computed. */
/* This should be identical to T1. */
/* Modified. */
/* LDU - INTEGER */
/* The leading dimension of U, Z, UZ and UU. It must be at */
/* least 1 and at least max( NN ). */
/* Not modified. */
/* U - COMPLEX*16 array, dimension (LDU,max(NN)) */
/* The unitary matrix computed by ZGEHRD. */
/* Modified. */
/* Z - COMPLEX*16 array, dimension (LDU,max(NN)) */
/* The unitary matrix computed by ZHSEQR. */
/* Modified. */
/* UZ - COMPLEX*16 array, dimension (LDU,max(NN)) */
/* The product of U times Z. */
/* Modified. */
/* W1 - COMPLEX*16 array, dimension (max(NN)) */
/* The eigenvalues of A, as computed by a full Schur */
/* decomposition H = Z T Z'. On exit, W1 contains the */
/* eigenvalues of the matrix in A. */
/* Modified. */
/* W3 - COMPLEX*16 array, dimension (max(NN)) */
/* The eigenvalues of A, as computed by a partial Schur */
/* decomposition (Z not computed, T only computed as much */
/* as is necessary for determining eigenvalues). On exit, */
/* W3 contains the eigenvalues of the matrix in A, possibly */
/* perturbed by ZHSEIN. */
/* Modified. */
/* EVECTL - COMPLEX*16 array, dimension (LDU,max(NN)) */
/* The conjugate transpose of the (upper triangular) left */
/* eigenvector matrix for the matrix in T1. */
/* Modified. */
/* EVEZTR - COMPLEX*16 array, dimension (LDU,max(NN)) */
/* The (upper triangular) right eigenvector matrix for the */
/* matrix in T1. */
/* Modified. */
/* EVECTY - COMPLEX*16 array, dimension (LDU,max(NN)) */
/* The conjugate transpose of the left eigenvector matrix */
/* for the matrix in H. */
/* Modified. */
/* EVECTX - COMPLEX*16 array, dimension (LDU,max(NN)) */
/* The right eigenvector matrix for the matrix in H. */
/* Modified. */
/* UU - COMPLEX*16 array, dimension (LDU,max(NN)) */
/* Details of the unitary matrix computed by ZGEHRD. */
/* Modified. */
/* TAU - COMPLEX*16 array, dimension (max(NN)) */
/* Further details of the unitary matrix computed by ZGEHRD. */
/* Modified. */
/* WORK - COMPLEX*16 array, dimension (NWORK) */
/* Workspace. */
/* Modified. */
/* NWORK - INTEGER */
/* The number of entries in WORK. NWORK >= 4*NN(j)*NN(j) + 2. */
/* RWORK - DOUBLE PRECISION array, dimension (max(NN)) */
/* Workspace. Could be equivalenced to IWORK, but not SELECT. */
/* Modified. */
/* IWORK - INTEGER array, dimension (max(NN)) */
/* Workspace. */
/* Modified. */
/* SELECT - LOGICAL array, dimension (max(NN)) */
/* Workspace. Could be equivalenced to IWORK, but not RWORK. */
/* Modified. */
/* RESULT - DOUBLE PRECISION array, dimension (14) */
/* The values computed by the fourteen tests described above. */
/* The values are currently limited to 1/ulp, to avoid */
/* overflow. */
/* Modified. */
/* INFO - INTEGER */
/* If 0, then everything ran OK. */
/* -1: NSIZES < 0 */
/* -2: Some NN(j) < 0 */
/* -3: NTYPES < 0 */
/* -6: THRESH < 0 */
/* -9: LDA < 1 or LDA < NMAX, where NMAX is max( NN(j) ). */
/* -14: LDU < 1 or LDU < NMAX. */
/* -26: NWORK too small. */
/* If ZLATMR, CLATMS, or CLATME returns an error code, the */
/* absolute value of it is returned. */
/* If 1, then ZHSEQR could not find all the shifts. */
/* If 2, then the EISPACK code (for small blocks) failed. */
/* If >2, then 30*N iterations were not enough to find an */
/* eigenvalue or to decompose the problem. */
/* Modified. */
/* ----------------------------------------------------------------------- */
/* Some Local Variables and Parameters: */
/* ---- ----- --------- --- ---------- */
/* ZERO, ONE Real 0 and 1. */
/* MAXTYP The number of types defined. */
/* MTEST The number of tests defined: care must be taken */
/* that (1) the size of RESULT, (2) the number of */
/* tests actually performed, and (3) MTEST agree. */
/* NTEST The number of tests performed on this matrix */
/* so far. This should be less than MTEST, and */
/* equal to it by the last test. It will be less */
/* if any of the routines being tested indicates */
/* that it could not compute the matrices that */
/* would be tested. */
/* NMAX Largest value in NN. */
/* NMATS The number of matrices generated so far. */
/* NERRS The number of tests which have exceeded THRESH */
/* so far (computed by DLAFTS). */
/* COND, CONDS, */
/* IMODE Values to be passed to the matrix generators. */
/* ANORM Norm of A; passed to matrix generators. */
/* OVFL, UNFL Overflow and underflow thresholds. */
/* ULP, ULPINV Finest relative precision and its inverse. */
/* RTOVFL, RTUNFL, */
/* RTULP, RTULPI Square roots of the previous 4 values. */
/* The following four arrays decode JTYPE: */
/* KTYPE(j) The general type (1-10) for type "j". */
/* KMODE(j) The MODE value to be passed to the matrix */
/* generator for type "j". */
/* KMAGN(j) The order of magnitude ( O(1), */
/* O(overflow^(1/2) ), O(underflow^(1/2) ) */
/* KCONDS(j) Selects whether CONDS is to be 1 or */
/* 1/sqrt(ulp). (0 means irrelevant.) */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Data statements .. */
/* Parameter adjustments */
--nn;
--dotype;
--iseed;
t2_dim1 = *lda;
t2_offset = 1 + t2_dim1;
t2 -= t2_offset;
t1_dim1 = *lda;
t1_offset = 1 + t1_dim1;
t1 -= t1_offset;
h_dim1 = *lda;
h_offset = 1 + h_dim1;
h__ -= h_offset;
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
uu_dim1 = *ldu;
uu_offset = 1 + uu_dim1;
uu -= uu_offset;
evectx_dim1 = *ldu;
evectx_offset = 1 + evectx_dim1;
evectx -= evectx_offset;
evecty_dim1 = *ldu;
evecty_offset = 1 + evecty_dim1;
evecty -= evecty_offset;
evectr_dim1 = *ldu;
evectr_offset = 1 + evectr_dim1;
evectr -= evectr_offset;
evectl_dim1 = *ldu;
evectl_offset = 1 + evectl_dim1;
evectl -= evectl_offset;
uz_dim1 = *ldu;
uz_offset = 1 + uz_dim1;
uz -= uz_offset;
z_dim1 = *ldu;
z_offset = 1 + z_dim1;
z__ -= z_offset;
u_dim1 = *ldu;
u_offset = 1 + u_dim1;
u -= u_offset;
--w1;
--w3;
--tau;
--work;
--rwork;
--iwork;
--select;
--result;
/* Function Body */
/* .. */
/* .. Executable Statements .. */
/* Check for errors */
ntestt = 0;
*info = 0;
badnn = FALSE_;
nmax = 0;
i__1 = *nsizes;
for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
i__2 = nmax, i__3 = nn[j];
nmax = max(i__2,i__3);
if (nn[j] < 0) {
badnn = TRUE_;
}
/* L10: */
}
/* Check for errors */
if (*nsizes < 0) {
*info = -1;
} else if (badnn) {
*info = -2;
} else if (*ntypes < 0) {
*info = -3;
} else if (*thresh < 0.) {
*info = -6;
} else if (*lda <= 1 || *lda < nmax) {
*info = -9;
} else if (*ldu <= 1 || *ldu < nmax) {
*info = -14;
} else if ((nmax << 2) * nmax + 2 > *nwork) {
*info = -26;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZCHKHS", &i__1);
return 0;
}
/* Quick return if possible */
if (*nsizes == 0 || *ntypes == 0) {
return 0;
}
/* More important constants */
unfl = dlamch_("Safe minimum");
ovfl = dlamch_("Overflow");
dlabad_(&unfl, &ovfl);
ulp = dlamch_("Epsilon") * dlamch_("Base");
ulpinv = 1. / ulp;
rtunfl = sqrt(unfl);
rtovfl = sqrt(ovfl);
rtulp = sqrt(ulp);
rtulpi = 1. / rtulp;
/* Loop over sizes, types */
nerrs = 0;
nmats = 0;
i__1 = *nsizes;
for (jsize = 1; jsize <= i__1; ++jsize) {
n = nn[jsize];
n1 = max(1,n);
aninv = 1. / (doublereal) n1;
if (*nsizes != 1) {
mtypes = min(21,*ntypes);
} else {
mtypes = min(22,*ntypes);
}
i__2 = mtypes;
for (jtype = 1; jtype <= i__2; ++jtype) {
if (! dotype[jtype]) {
goto L250;
}
++nmats;
ntest = 0;
/* Save ISEED in case of an error. */
for (j = 1; j <= 4; ++j) {
ioldsd[j - 1] = iseed[j];
/* L20: */
}
/* Initialize RESULT */
for (j = 1; j <= 14; ++j) {
result[j] = 0.;
/* L30: */
}
/* Compute "A" */
/* Control parameters: */
/* KMAGN KCONDS KMODE KTYPE */
/* =1 O(1) 1 clustered 1 zero */
/* =2 large large clustered 2 identity */
/* =3 small exponential Jordan */
/* =4 arithmetic diagonal, (w/ eigenvalues) */
/* =5 random log hermitian, w/ eigenvalues */
/* =6 random general, w/ eigenvalues */
/* =7 random diagonal */
/* =8 random hermitian */
/* =9 random general */
/* =10 random triangular */
if (mtypes > 21) {
goto L100;
}
itype = ktype[jtype - 1];
imode = kmode[jtype - 1];
/* Compute norm */
switch (kmagn[jtype - 1]) {
case 1: goto L40;
case 2: goto L50;
case 3: goto L60;
}
L40:
anorm = 1.;
goto L70;
L50:
anorm = rtovfl * ulp * aninv;
goto L70;
L60:
anorm = rtunfl * n * ulpinv;
goto L70;
L70:
zlaset_("Full", lda, &n, &c_b1, &c_b1, &a[a_offset], lda);
iinfo = 0;
cond = ulpinv;
/* Special Matrices */
if (itype == 1) {
/* Zero */
iinfo = 0;
} else if (itype == 2) {
/* Identity */
i__3 = n;
for (jcol = 1; jcol <= i__3; ++jcol) {
i__4 = jcol + jcol * a_dim1;
a[i__4].r = anorm, a[i__4].i = 0.;
/* L80: */
}
} else if (itype == 3) {
/* Jordan Block */
i__3 = n;
for (jcol = 1; jcol <= i__3; ++jcol) {
i__4 = jcol + jcol * a_dim1;
a[i__4].r = anorm, a[i__4].i = 0.;
if (jcol > 1) {
i__4 = jcol + (jcol - 1) * a_dim1;
a[i__4].r = 1., a[i__4].i = 0.;
}
/* L90: */
}
} else if (itype == 4) {
/* Diagonal Matrix, [Eigen]values Specified */
zlatmr_(&n, &n, "D", &iseed[1], "N", &work[1], &imode, &cond,
&c_b2, "T", "N", &work[n + 1], &c__1, &c_b27, &work[(
n << 1) + 1], &c__1, &c_b27, "N", idumma, &c__0, &
c__0, &c_b33, &anorm, "NO", &a[a_offset], lda, &iwork[
1], &iinfo);
} else if (itype == 5) {
/* Hermitian, eigenvalues specified */
zlatms_(&n, &n, "D", &iseed[1], "H", &rwork[1], &imode, &cond,
&anorm, &n, &n, "N", &a[a_offset], lda, &work[1], &
iinfo);
} else if (itype == 6) {
/* General, eigenvalues specified */
if (kconds[jtype - 1] == 1) {
conds = 1.;
} else if (kconds[jtype - 1] == 2) {
conds = rtulpi;
} else {
conds = 0.;
}
zlatme_(&n, "D", &iseed[1], &work[1], &imode, &cond, &c_b2,
" ", "T", "T", "T", &rwork[1], &c__4, &conds, &n, &n,
&anorm, &a[a_offset], lda, &work[n + 1], &iinfo);
} else if (itype == 7) {
/* Diagonal, random eigenvalues */
zlatmr_(&n, &n, "D", &iseed[1], "N", &work[1], &c__6, &c_b27,
&c_b2, "T", "N", &work[n + 1], &c__1, &c_b27, &work[(
n << 1) + 1], &c__1, &c_b27, "N", idumma, &c__0, &
c__0, &c_b33, &anorm, "NO", &a[a_offset], lda, &iwork[
1], &iinfo);
} else if (itype == 8) {
/* Hermitian, random eigenvalues */
zlatmr_(&n, &n, "D", &iseed[1], "H", &work[1], &c__6, &c_b27,
&c_b2, "T", "N", &work[n + 1], &c__1, &c_b27, &work[(
n << 1) + 1], &c__1, &c_b27, "N", idumma, &n, &n, &
c_b33, &anorm, "NO", &a[a_offset], lda, &iwork[1], &
iinfo);
} else if (itype == 9) {
/* General, random eigenvalues */
zlatmr_(&n, &n, "D", &iseed[1], "N", &work[1], &c__6, &c_b27,
&c_b2, "T", "N", &work[n + 1], &c__1, &c_b27, &work[(
n << 1) + 1], &c__1, &c_b27, "N", idumma, &n, &n, &
c_b33, &anorm, "NO", &a[a_offset], lda, &iwork[1], &
iinfo);
} else if (itype == 10) {
/* Triangular, random eigenvalues */
zlatmr_(&n, &n, "D", &iseed[1], "N", &work[1], &c__6, &c_b27,
&c_b2, "T", "N", &work[n + 1], &c__1, &c_b27, &work[(
n << 1) + 1], &c__1, &c_b27, "N", idumma, &n, &c__0, &
c_b33, &anorm, "NO", &a[a_offset], lda, &iwork[1], &
iinfo);
} else {
iinfo = 1;
}
if (iinfo != 0) {
io___35.ciunit = *nounit;
s_wsfe(&io___35);
do_fio(&c__1, "Generator", (ftnlen)9);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
*info = abs(iinfo);
return 0;
}
L100:
/* Call ZGEHRD to compute H and U, do tests. */
zlacpy_(" ", &n, &n, &a[a_offset], lda, &h__[h_offset], lda);
ntest = 1;
ilo = 1;
ihi = n;
i__3 = *nwork - n;
zgehrd_(&n, &ilo, &ihi, &h__[h_offset], lda, &work[1], &work[n +
1], &i__3, &iinfo);
if (iinfo != 0) {
result[1] = ulpinv;
io___38.ciunit = *nounit;
s_wsfe(&io___38);
do_fio(&c__1, "ZGEHRD", (ftnlen)6);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
*info = abs(iinfo);
goto L240;
}
i__3 = n - 1;
for (j = 1; j <= i__3; ++j) {
i__4 = j + 1 + j * uu_dim1;
uu[i__4].r = 0., uu[i__4].i = 0.;
i__4 = n;
for (i__ = j + 2; i__ <= i__4; ++i__) {
i__5 = i__ + j * u_dim1;
i__6 = i__ + j * h_dim1;
u[i__5].r = h__[i__6].r, u[i__5].i = h__[i__6].i;
i__5 = i__ + j * uu_dim1;
i__6 = i__ + j * h_dim1;
uu[i__5].r = h__[i__6].r, uu[i__5].i = h__[i__6].i;
i__5 = i__ + j * h_dim1;
h__[i__5].r = 0., h__[i__5].i = 0.;
/* L110: */
}
/* L120: */
}
i__3 = n - 1;
zcopy_(&i__3, &work[1], &c__1, &tau[1], &c__1);
i__3 = *nwork - n;
zunghr_(&n, &ilo, &ihi, &u[u_offset], ldu, &work[1], &work[n + 1],
&i__3, &iinfo);
ntest = 2;
zhst01_(&n, &ilo, &ihi, &a[a_offset], lda, &h__[h_offset], lda, &
u[u_offset], ldu, &work[1], nwork, &rwork[1], &result[1]);
/* Call ZHSEQR to compute T1, T2 and Z, do tests. */
/* Eigenvalues only (W3) */
zlacpy_(" ", &n, &n, &h__[h_offset], lda, &t2[t2_offset], lda);
ntest = 3;
result[3] = ulpinv;
zhseqr_("E", "N", &n, &ilo, &ihi, &t2[t2_offset], lda, &w3[1], &
uz[uz_offset], ldu, &work[1], nwork, &iinfo);
if (iinfo != 0) {
io___40.ciunit = *nounit;
s_wsfe(&io___40);
do_fio(&c__1, "ZHSEQR(E)", (ftnlen)9);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
if (iinfo <= n + 2) {
*info = abs(iinfo);
goto L240;
}
}
/* Eigenvalues (W1) and Full Schur Form (T2) */
zlacpy_(" ", &n, &n, &h__[h_offset], lda, &t2[t2_offset], lda);
zhseqr_("S", "N", &n, &ilo, &ihi, &t2[t2_offset], lda, &w1[1], &
uz[uz_offset], ldu, &work[1], nwork, &iinfo);
if (iinfo != 0 && iinfo <= n + 2) {
io___41.ciunit = *nounit;
s_wsfe(&io___41);
do_fio(&c__1, "ZHSEQR(S)", (ftnlen)9);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
*info = abs(iinfo);
goto L240;
}
/* Eigenvalues (W1), Schur Form (T1), and Schur Vectors (UZ) */
zlacpy_(" ", &n, &n, &h__[h_offset], lda, &t1[t1_offset], lda);
zlacpy_(" ", &n, &n, &u[u_offset], ldu, &uz[uz_offset], ldu);
zhseqr_("S", "V", &n, &ilo, &ihi, &t1[t1_offset], lda, &w1[1], &
uz[uz_offset], ldu, &work[1], nwork, &iinfo);
if (iinfo != 0 && iinfo <= n + 2) {
io___42.ciunit = *nounit;
s_wsfe(&io___42);
do_fio(&c__1, "ZHSEQR(V)", (ftnlen)9);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
*info = abs(iinfo);
goto L240;
}
/* Compute Z = U' UZ */
zgemm_("C", "N", &n, &n, &n, &c_b2, &u[u_offset], ldu, &uz[
uz_offset], ldu, &c_b1, &z__[z_offset], ldu);
ntest = 8;
/* Do Tests 3: | H - Z T Z' | / ( |H| n ulp ) */
/* and 4: | I - Z Z' | / ( n ulp ) */
zhst01_(&n, &ilo, &ihi, &h__[h_offset], lda, &t1[t1_offset], lda,
&z__[z_offset], ldu, &work[1], nwork, &rwork[1], &result[
3]);
/* Do Tests 5: | A - UZ T (UZ)' | / ( |A| n ulp ) */
/* and 6: | I - UZ (UZ)' | / ( n ulp ) */
zhst01_(&n, &ilo, &ihi, &a[a_offset], lda, &t1[t1_offset], lda, &
uz[uz_offset], ldu, &work[1], nwork, &rwork[1], &result[5]
);
/* Do Test 7: | T2 - T1 | / ( |T| n ulp ) */
zget10_(&n, &n, &t2[t2_offset], lda, &t1[t1_offset], lda, &work[1]
, &rwork[1], &result[7]);
/* Do Test 8: | W3 - W1 | / ( max(|W1|,|W3|) ulp ) */
temp1 = 0.;
temp2 = 0.;
i__3 = n;
for (j = 1; j <= i__3; ++j) {
/* Computing MAX */
d__1 = temp1, d__2 = z_abs(&w1[j]), d__1 = max(d__1,d__2),
d__2 = z_abs(&w3[j]);
temp1 = max(d__1,d__2);
/* Computing MAX */
i__4 = j;
i__5 = j;
z__1.r = w1[i__4].r - w3[i__5].r, z__1.i = w1[i__4].i - w3[
i__5].i;
d__1 = temp2, d__2 = z_abs(&z__1);
temp2 = max(d__1,d__2);
/* L130: */
}
/* Computing MAX */
d__1 = unfl, d__2 = ulp * max(temp1,temp2);
result[8] = temp2 / max(d__1,d__2);
/* Compute the Left and Right Eigenvectors of T */
/* Compute the Right eigenvector Matrix: */
ntest = 9;
result[9] = ulpinv;
/* Select every other eigenvector */
i__3 = n;
for (j = 1; j <= i__3; ++j) {
select[j] = FALSE_;
/* L140: */
}
i__3 = n;
for (j = 1; j <= i__3; j += 2) {
select[j] = TRUE_;
/* L150: */
}
ztrevc_("Right", "All", &select[1], &n, &t1[t1_offset], lda,
cdumma, ldu, &evectr[evectr_offset], ldu, &n, &in, &work[
1], &rwork[1], &iinfo);
if (iinfo != 0) {
io___47.ciunit = *nounit;
s_wsfe(&io___47);
do_fio(&c__1, "ZTREVC(R,A)", (ftnlen)11);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
*info = abs(iinfo);
goto L240;
}
/* Test 9: | TR - RW | / ( |T| |R| ulp ) */
zget22_("N", "N", "N", &n, &t1[t1_offset], lda, &evectr[
evectr_offset], ldu, &w1[1], &work[1], &rwork[1], dumma);
result[9] = dumma[0];
if (dumma[1] > *thresh) {
io___49.ciunit = *nounit;
s_wsfe(&io___49);
do_fio(&c__1, "Right", (ftnlen)5);
do_fio(&c__1, "ZTREVC", (ftnlen)6);
do_fio(&c__1, (char *)&dumma[1], (ftnlen)sizeof(doublereal));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
}
/* Compute selected right eigenvectors and confirm that */
/* they agree with previous right eigenvectors */
ztrevc_("Right", "Some", &select[1], &n, &t1[t1_offset], lda,
cdumma, ldu, &evectl[evectl_offset], ldu, &n, &in, &work[
1], &rwork[1], &iinfo);
if (iinfo != 0) {
io___50.ciunit = *nounit;
s_wsfe(&io___50);
do_fio(&c__1, "ZTREVC(R,S)", (ftnlen)11);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
*info = abs(iinfo);
goto L240;
}
k = 1;
match = TRUE_;
i__3 = n;
for (j = 1; j <= i__3; ++j) {
if (select[j]) {
i__4 = n;
for (jj = 1; jj <= i__4; ++jj) {
i__5 = jj + j * evectr_dim1;
i__6 = jj + k * evectl_dim1;
if (evectr[i__5].r != evectl[i__6].r || evectr[i__5]
.i != evectl[i__6].i) {
match = FALSE_;
goto L180;
}
/* L160: */
}
++k;
}
/* L170: */
}
L180:
if (! match) {
io___54.ciunit = *nounit;
s_wsfe(&io___54);
do_fio(&c__1, "Right", (ftnlen)5);
do_fio(&c__1, "ZTREVC", (ftnlen)6);
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
}
/* Compute the Left eigenvector Matrix: */
ntest = 10;
result[10] = ulpinv;
ztrevc_("Left", "All", &select[1], &n, &t1[t1_offset], lda, &
evectl[evectl_offset], ldu, cdumma, ldu, &n, &in, &work[1]
, &rwork[1], &iinfo);
if (iinfo != 0) {
io___55.ciunit = *nounit;
s_wsfe(&io___55);
do_fio(&c__1, "ZTREVC(L,A)", (ftnlen)11);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
*info = abs(iinfo);
goto L240;
}
/* Test 10: | LT - WL | / ( |T| |L| ulp ) */
zget22_("C", "N", "C", &n, &t1[t1_offset], lda, &evectl[
evectl_offset], ldu, &w1[1], &work[1], &rwork[1], &dumma[
2]);
result[10] = dumma[2];
if (dumma[3] > *thresh) {
io___56.ciunit = *nounit;
s_wsfe(&io___56);
do_fio(&c__1, "Left", (ftnlen)4);
do_fio(&c__1, "ZTREVC", (ftnlen)6);
do_fio(&c__1, (char *)&dumma[3], (ftnlen)sizeof(doublereal));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
}
/* Compute selected left eigenvectors and confirm that */
/* they agree with previous left eigenvectors */
ztrevc_("Left", "Some", &select[1], &n, &t1[t1_offset], lda, &
evectr[evectr_offset], ldu, cdumma, ldu, &n, &in, &work[1]
, &rwork[1], &iinfo);
if (iinfo != 0) {
io___57.ciunit = *nounit;
s_wsfe(&io___57);
do_fio(&c__1, "ZTREVC(L,S)", (ftnlen)11);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
*info = abs(iinfo);
goto L240;
}
k = 1;
match = TRUE_;
i__3 = n;
for (j = 1; j <= i__3; ++j) {
if (select[j]) {
i__4 = n;
for (jj = 1; jj <= i__4; ++jj) {
i__5 = jj + j * evectl_dim1;
i__6 = jj + k * evectr_dim1;
if (evectl[i__5].r != evectr[i__6].r || evectl[i__5]
.i != evectr[i__6].i) {
match = FALSE_;
goto L210;
}
/* L190: */
}
++k;
}
/* L200: */
}
L210:
if (! match) {
io___58.ciunit = *nounit;
s_wsfe(&io___58);
do_fio(&c__1, "Left", (ftnlen)4);
do_fio(&c__1, "ZTREVC", (ftnlen)6);
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
}
/* Call ZHSEIN for Right eigenvectors of H, do test 11 */
ntest = 11;
result[11] = ulpinv;
i__3 = n;
for (j = 1; j <= i__3; ++j) {
select[j] = TRUE_;
/* L220: */
}
zhsein_("Right", "Qr", "Ninitv", &select[1], &n, &h__[h_offset],
lda, &w3[1], cdumma, ldu, &evectx[evectx_offset], ldu, &
n1, &in, &work[1], &rwork[1], &iwork[1], &iwork[1], &
iinfo);
if (iinfo != 0) {
io___59.ciunit = *nounit;
s_wsfe(&io___59);
do_fio(&c__1, "ZHSEIN(R)", (ftnlen)9);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
*info = abs(iinfo);
if (iinfo < 0) {
goto L240;
}
} else {
/* Test 11: | HX - XW | / ( |H| |X| ulp ) */
/* (from inverse iteration) */
zget22_("N", "N", "N", &n, &h__[h_offset], lda, &evectx[
evectx_offset], ldu, &w3[1], &work[1], &rwork[1],
dumma);
if (dumma[0] < ulpinv) {
result[11] = dumma[0] * aninv;
}
if (dumma[1] > *thresh) {
io___60.ciunit = *nounit;
s_wsfe(&io___60);
do_fio(&c__1, "Right", (ftnlen)5);
do_fio(&c__1, "ZHSEIN", (ftnlen)6);
do_fio(&c__1, (char *)&dumma[1], (ftnlen)sizeof(
doublereal));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer))
;
e_wsfe();
}
}
/* Call ZHSEIN for Left eigenvectors of H, do test 12 */
ntest = 12;
result[12] = ulpinv;
i__3 = n;
for (j = 1; j <= i__3; ++j) {
select[j] = TRUE_;
/* L230: */
}
zhsein_("Left", "Qr", "Ninitv", &select[1], &n, &h__[h_offset],
lda, &w3[1], &evecty[evecty_offset], ldu, cdumma, ldu, &
n1, &in, &work[1], &rwork[1], &iwork[1], &iwork[1], &
iinfo);
if (iinfo != 0) {
io___61.ciunit = *nounit;
s_wsfe(&io___61);
do_fio(&c__1, "ZHSEIN(L)", (ftnlen)9);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
*info = abs(iinfo);
if (iinfo < 0) {
goto L240;
}
} else {
/* Test 12: | YH - WY | / ( |H| |Y| ulp ) */
/* (from inverse iteration) */
zget22_("C", "N", "C", &n, &h__[h_offset], lda, &evecty[
evecty_offset], ldu, &w3[1], &work[1], &rwork[1], &
dumma[2]);
if (dumma[2] < ulpinv) {
result[12] = dumma[2] * aninv;
}
if (dumma[3] > *thresh) {
io___62.ciunit = *nounit;
s_wsfe(&io___62);
do_fio(&c__1, "Left", (ftnlen)4);
do_fio(&c__1, "ZHSEIN", (ftnlen)6);
do_fio(&c__1, (char *)&dumma[3], (ftnlen)sizeof(
doublereal));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer))
;
e_wsfe();
}
}
/* Call ZUNMHR for Right eigenvectors of A, do test 13 */
ntest = 13;
result[13] = ulpinv;
zunmhr_("Left", "No transpose", &n, &n, &ilo, &ihi, &uu[uu_offset]
, ldu, &tau[1], &evectx[evectx_offset], ldu, &work[1],
nwork, &iinfo);
if (iinfo != 0) {
io___63.ciunit = *nounit;
s_wsfe(&io___63);
do_fio(&c__1, "ZUNMHR(L)", (ftnlen)9);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
*info = abs(iinfo);
if (iinfo < 0) {
goto L240;
}
} else {
/* Test 13: | AX - XW | / ( |A| |X| ulp ) */
/* (from inverse iteration) */
zget22_("N", "N", "N", &n, &a[a_offset], lda, &evectx[
evectx_offset], ldu, &w3[1], &work[1], &rwork[1],
dumma);
if (dumma[0] < ulpinv) {
result[13] = dumma[0] * aninv;
}
}
/* Call ZUNMHR for Left eigenvectors of A, do test 14 */
ntest = 14;
result[14] = ulpinv;
zunmhr_("Left", "No transpose", &n, &n, &ilo, &ihi, &uu[uu_offset]
, ldu, &tau[1], &evecty[evecty_offset], ldu, &work[1],
nwork, &iinfo);
if (iinfo != 0) {
io___64.ciunit = *nounit;
s_wsfe(&io___64);
do_fio(&c__1, "ZUNMHR(L)", (ftnlen)9);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
*info = abs(iinfo);
if (iinfo < 0) {
goto L240;
}
} else {
/* Test 14: | YA - WY | / ( |A| |Y| ulp ) */
/* (from inverse iteration) */
zget22_("C", "N", "C", &n, &a[a_offset], lda, &evecty[
evecty_offset], ldu, &w3[1], &work[1], &rwork[1], &
dumma[2]);
if (dumma[2] < ulpinv) {
result[14] = dumma[2] * aninv;
}
}
/* End of Loop -- Check for RESULT(j) > THRESH */
L240:
ntestt += ntest;
dlafts_("ZHS", &n, &n, &jtype, &ntest, &result[1], ioldsd, thresh,
nounit, &nerrs);
L250:
;
}
/* L260: */
}
/* Summary */
dlasum_("ZHS", nounit, &nerrs, &ntestt);
return 0;
/* End of ZCHKHS */
} /* zchkhs_ */
/* Subroutine */ int zget23_(logical *comp, integer *isrt, char *balanc,
integer *jtype, doublereal *thresh, integer *iseed, integer *nounit,
integer *n, doublecomplex *a, integer *lda, doublecomplex *h__,
doublecomplex *w, doublecomplex *w1, doublecomplex *vl, integer *ldvl,
doublecomplex *vr, integer *ldvr, doublecomplex *lre, integer *ldlre,
doublereal *rcondv, doublereal *rcndv1, doublereal *rcdvin,
doublereal *rconde, doublereal *rcnde1, doublereal *rcdein,
doublereal *scale, doublereal *scale1, doublereal *result,
doublecomplex *work, integer *lwork, doublereal *rwork, integer *info)
{
/* Initialized data */
static char sens[1*2] = "N" "V";
/* Format strings */
static char fmt_9998[] = "(\002 ZGET23: \002,a,\002 returned INFO=\002,i"
"6,\002.\002,/9x,\002N=\002,i6,\002, JTYPE=\002,i6,\002, BALANC = "
"\002,a,\002, ISEED=(\002,3(i5,\002,\002),i5,\002)\002)";
static char fmt_9999[] = "(\002 ZGET23: \002,a,\002 returned INFO=\002,i"
"6,\002.\002,/9x,\002N=\002,i6,\002, INPUT EXAMPLE NUMBER = \002,"
"i4)";
/* System generated locals */
integer a_dim1, a_offset, h_dim1, h_offset, lre_dim1, lre_offset, vl_dim1,
vl_offset, vr_dim1, vr_offset, i__1, i__2, i__3, i__4, i__5;
doublereal d__1, d__2, d__3, d__4, d__5;
/* Builtin functions */
integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void);
double z_abs(doublecomplex *), d_imag(doublecomplex *);
/* Local variables */
static doublecomplex cdum[1];
static integer kmin;
static doublecomplex ctmp;
static doublereal vmax, tnrm, vrmx, vtst;
static integer i__, j;
static doublereal v;
static logical balok, nobal;
static doublereal abnrm;
extern logical lsame_(char *, char *);
static integer iinfo;
static char sense[1];
extern /* Subroutine */ int zget22_(char *, char *, char *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, doublecomplex *, doublereal *, doublereal *);
static integer isens;
static doublereal tolin, abnrm1;
extern doublereal dznrm2_(integer *, doublecomplex *, integer *);
static integer jj;
extern doublereal dlamch_(char *);
extern /* Subroutine */ int xerbla_(char *, integer *);
static integer isensm;
static doublereal vricmp;
extern /* Subroutine */ int zlacpy_(char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *);
static doublereal vrimin;
extern /* Subroutine */ int zgeevx_(char *, char *, char *, char *,
integer *, doublecomplex *, integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *, integer *,
integer *, doublereal *, doublereal *, doublereal *, doublereal *
, doublecomplex *, integer *, doublereal *, integer *);
static doublereal smlnum, ulpinv;
static integer ihi, ilo;
static doublereal eps, res[2], tol, ulp, vmx;
static integer ihi1, ilo1;
/* Fortran I/O blocks */
static cilist io___14 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___15 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___28 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___29 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___30 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___31 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___32 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___33 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___34 = { 0, 0, 0, fmt_9999, 0 };
#define vl_subscr(a_1,a_2) (a_2)*vl_dim1 + a_1
#define vl_ref(a_1,a_2) vl[vl_subscr(a_1,a_2)]
#define vr_subscr(a_1,a_2) (a_2)*vr_dim1 + a_1
#define vr_ref(a_1,a_2) vr[vr_subscr(a_1,a_2)]
#define lre_subscr(a_1,a_2) (a_2)*lre_dim1 + a_1
#define lre_ref(a_1,a_2) lre[lre_subscr(a_1,a_2)]
/* -- LAPACK test routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
September 30, 1994
Purpose
=======
ZGET23 checks the nonsymmetric eigenvalue problem driver CGEEVX.
If COMP = .FALSE., the first 8 of the following tests will be
performed on the input matrix A, and also test 9 if LWORK is
sufficiently large.
if COMP is .TRUE. all 11 tests will be performed.
(1) | A * VR - VR * W | / ( n |A| ulp )
Here VR is the matrix of unit right eigenvectors.
W is a diagonal matrix with diagonal entries W(j).
(2) | A**H * VL - VL * W**H | / ( n |A| ulp )
Here VL is the matrix of unit left eigenvectors, A**H is the
conjugate transpose of A, and W is as above.
(3) | |VR(i)| - 1 | / ulp and largest component real
VR(i) denotes the i-th column of VR.
(4) | |VL(i)| - 1 | / ulp and largest component real
VL(i) denotes the i-th column of VL.
(5) 0 if W(full) = W(partial), 1/ulp otherwise
W(full) denotes the eigenvalues computed when VR, VL, RCONDV
and RCONDE are also computed, and W(partial) denotes the
eigenvalues computed when only some of VR, VL, RCONDV, and
RCONDE are computed.
(6) 0 if VR(full) = VR(partial), 1/ulp otherwise
VR(full) denotes the right eigenvectors computed when VL, RCONDV
and RCONDE are computed, and VR(partial) denotes the result
when only some of VL and RCONDV are computed.
(7) 0 if VL(full) = VL(partial), 1/ulp otherwise
VL(full) denotes the left eigenvectors computed when VR, RCONDV
and RCONDE are computed, and VL(partial) denotes the result
when only some of VR and RCONDV are computed.
(8) 0 if SCALE, ILO, IHI, ABNRM (full) =
SCALE, ILO, IHI, ABNRM (partial)
1/ulp otherwise
SCALE, ILO, IHI and ABNRM describe how the matrix is balanced.
(full) is when VR, VL, RCONDE and RCONDV are also computed, and
(partial) is when some are not computed.
(9) 0 if RCONDV(full) = RCONDV(partial), 1/ulp otherwise
RCONDV(full) denotes the reciprocal condition numbers of the
right eigenvectors computed when VR, VL and RCONDE are also
computed. RCONDV(partial) denotes the reciprocal condition
numbers when only some of VR, VL and RCONDE are computed.
(10) |RCONDV - RCDVIN| / cond(RCONDV)
RCONDV is the reciprocal right eigenvector condition number
computed by ZGEEVX and RCDVIN (the precomputed true value)
is supplied as input. cond(RCONDV) is the condition number of
RCONDV, and takes errors in computing RCONDV into account, so
that the resulting quantity should be O(ULP). cond(RCONDV) is
essentially given by norm(A)/RCONDE.
(11) |RCONDE - RCDEIN| / cond(RCONDE)
RCONDE is the reciprocal eigenvalue condition number
computed by ZGEEVX and RCDEIN (the precomputed true value)
is supplied as input. cond(RCONDE) is the condition number
of RCONDE, and takes errors in computing RCONDE into account,
so that the resulting quantity should be O(ULP). cond(RCONDE)
is essentially given by norm(A)/RCONDV.
Arguments
=========
COMP (input) LOGICAL
COMP describes which input tests to perform:
= .FALSE. if the computed condition numbers are not to
be tested against RCDVIN and RCDEIN
= .TRUE. if they are to be compared
ISRT (input) INTEGER
If COMP = .TRUE., ISRT indicates in how the eigenvalues
corresponding to values in RCDVIN and RCDEIN are ordered:
= 0 means the eigenvalues are sorted by
increasing real part
= 1 means the eigenvalues are sorted by
increasing imaginary part
If COMP = .FALSE., ISRT is not referenced.
BALANC (input) CHARACTER
Describes the balancing option to be tested.
= 'N' for no permuting or diagonal scaling
= 'P' for permuting but no diagonal scaling
= 'S' for no permuting but diagonal scaling
= 'B' for permuting and diagonal scaling
JTYPE (input) INTEGER
Type of input matrix. Used to label output if error occurs.
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. It must be at least zero.
ISEED (input) INTEGER array, dimension (4)
If COMP = .FALSE., the random number generator seed
used to produce matrix.
If COMP = .TRUE., ISEED(1) = the number of the example.
Used to label output if error occurs.
NOUNIT (input) INTEGER
The FORTRAN unit number for printing out error messages
(e.g., if a routine returns INFO not equal to 0.)
N (input) INTEGER
The dimension of A. N must be at least 0.
A (input/output) COMPLEX*16 array, dimension (LDA,N)
Used to hold the matrix whose eigenvalues are to be
computed.
LDA (input) INTEGER
The leading dimension of A, and H. LDA must be at
least 1 and at least N.
H (workspace) COMPLEX*16 array, dimension (LDA,N)
Another copy of the test matrix A, modified by ZGEEVX.
W (workspace) COMPLEX*16 array, dimension (N)
Contains the eigenvalues of A.
W1 (workspace) COMPLEX*16 array, dimension (N)
Like W, this array contains the eigenvalues of A,
but those computed when ZGEEVX only computes a partial
eigendecomposition, i.e. not the eigenvalues and left
and right eigenvectors.
VL (workspace) COMPLEX*16 array, dimension (LDVL,N)
VL holds the computed left eigenvectors.
LDVL (input) INTEGER
Leading dimension of VL. Must be at least max(1,N).
VR (workspace) COMPLEX*16 array, dimension (LDVR,N)
VR holds the computed right eigenvectors.
LDVR (input) INTEGER
Leading dimension of VR. Must be at least max(1,N).
LRE (workspace) COMPLEX*16 array, dimension (LDLRE,N)
LRE holds the computed right or left eigenvectors.
LDLRE (input) INTEGER
Leading dimension of LRE. Must be at least max(1,N).
RCONDV (workspace) DOUBLE PRECISION array, dimension (N)
RCONDV holds the computed reciprocal condition numbers
for eigenvectors.
RCNDV1 (workspace) DOUBLE PRECISION array, dimension (N)
RCNDV1 holds more computed reciprocal condition numbers
for eigenvectors.
RCDVIN (input) DOUBLE PRECISION array, dimension (N)
When COMP = .TRUE. RCDVIN holds the precomputed reciprocal
condition numbers for eigenvectors to be compared with
RCONDV.
RCONDE (workspace) DOUBLE PRECISION array, dimension (N)
RCONDE holds the computed reciprocal condition numbers
for eigenvalues.
RCNDE1 (workspace) DOUBLE PRECISION array, dimension (N)
RCNDE1 holds more computed reciprocal condition numbers
for eigenvalues.
RCDEIN (input) DOUBLE PRECISION array, dimension (N)
When COMP = .TRUE. RCDEIN holds the precomputed reciprocal
condition numbers for eigenvalues to be compared with
RCONDE.
SCALE (workspace) DOUBLE PRECISION array, dimension (N)
Holds information describing balancing of matrix.
SCALE1 (workspace) DOUBLE PRECISION array, dimension (N)
Holds information describing balancing of matrix.
RESULT (output) DOUBLE PRECISION array, dimension (11)
The values computed by the 11 tests described above.
The values are currently limited to 1/ulp, to avoid
overflow.
WORK (workspace) COMPLEX*16 array, dimension (LWORK)
LWORK (input) INTEGER
The number of entries in WORK. This must be at least
2*N, and 2*N+N**2 if tests 9, 10 or 11 are to be performed.
RWORK (workspace) DOUBLE PRECISION array, dimension (2*N)
INFO (output) INTEGER
If 0, successful exit.
If <0, input parameter -INFO had an incorrect value.
If >0, ZGEEVX returned an error code, the absolute
value of which is returned.
=====================================================================
Parameter adjustments */
--iseed;
h_dim1 = *lda;
h_offset = 1 + h_dim1 * 1;
h__ -= h_offset;
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--w;
--w1;
vl_dim1 = *ldvl;
vl_offset = 1 + vl_dim1 * 1;
vl -= vl_offset;
vr_dim1 = *ldvr;
vr_offset = 1 + vr_dim1 * 1;
vr -= vr_offset;
lre_dim1 = *ldlre;
lre_offset = 1 + lre_dim1 * 1;
lre -= lre_offset;
--rcondv;
--rcndv1;
--rcdvin;
--rconde;
--rcnde1;
--rcdein;
--scale;
--scale1;
--result;
--work;
--rwork;
/* Function Body
Check for errors */
nobal = lsame_(balanc, "N");
balok = nobal || lsame_(balanc, "P") || lsame_(
balanc, "S") || lsame_(balanc, "B");
*info = 0;
if (*isrt != 0 && *isrt != 1) {
*info = -2;
} else if (! balok) {
*info = -3;
} else if (*thresh < 0.) {
*info = -5;
} else if (*nounit <= 0) {
*info = -7;
} else if (*n < 0) {
*info = -8;
} else if (*lda < 1 || *lda < *n) {
*info = -10;
} else if (*ldvl < 1 || *ldvl < *n) {
*info = -15;
} else if (*ldvr < 1 || *ldvr < *n) {
*info = -17;
} else if (*ldlre < 1 || *ldlre < *n) {
*info = -19;
} else if (*lwork < *n << 1 || *comp && *lwork < (*n << 1) + *n * *n) {
*info = -30;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZGET23", &i__1);
return 0;
}
/* Quick return if nothing to do */
for (i__ = 1; i__ <= 11; ++i__) {
result[i__] = -1.;
/* L10: */
}
if (*n == 0) {
return 0;
}
/* More Important constants */
ulp = dlamch_("Precision");
smlnum = dlamch_("S");
ulpinv = 1. / ulp;
/* Compute eigenvalues and eigenvectors, and test them */
if (*lwork >= (*n << 1) + *n * *n) {
*(unsigned char *)sense = 'B';
isensm = 2;
} else {
*(unsigned char *)sense = 'E';
isensm = 1;
}
zlacpy_("F", n, n, &a[a_offset], lda, &h__[h_offset], lda);
zgeevx_(balanc, "V", "V", sense, n, &h__[h_offset], lda, &w[1], &vl[
vl_offset], ldvl, &vr[vr_offset], ldvr, &ilo, &ihi, &scale[1], &
abnrm, &rconde[1], &rcondv[1], &work[1], lwork, &rwork[1], &iinfo);
if (iinfo != 0) {
result[1] = ulpinv;
if (*jtype != 22) {
io___14.ciunit = *nounit;
s_wsfe(&io___14);
do_fio(&c__1, "ZGEEVX1", (ftnlen)7);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&(*n), (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&(*jtype), (ftnlen)sizeof(integer));
do_fio(&c__1, balanc, (ftnlen)1);
do_fio(&c__4, (char *)&iseed[1], (ftnlen)sizeof(integer));
e_wsfe();
} else {
io___15.ciunit = *nounit;
s_wsfe(&io___15);
do_fio(&c__1, "ZGEEVX1", (ftnlen)7);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&(*n), (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&iseed[1], (ftnlen)sizeof(integer));
e_wsfe();
}
*info = abs(iinfo);
return 0;
}
/* Do Test (1) */
zget22_("N", "N", "N", n, &a[a_offset], lda, &vr[vr_offset], ldvr, &w[1],
&work[1], &rwork[1], res);
result[1] = res[0];
/* Do Test (2) */
zget22_("C", "N", "C", n, &a[a_offset], lda, &vl[vl_offset], ldvl, &w[1],
&work[1], &rwork[1], res);
result[2] = res[0];
/* Do Test (3) */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
tnrm = dznrm2_(n, &vr_ref(1, j), &c__1);
/* Computing MAX
Computing MIN */
d__4 = ulpinv, d__5 = (d__1 = tnrm - 1., abs(d__1)) / ulp;
d__2 = result[3], d__3 = min(d__4,d__5);
result[3] = max(d__2,d__3);
vmx = 0.;
vrmx = 0.;
i__2 = *n;
for (jj = 1; jj <= i__2; ++jj) {
vtst = z_abs(&vr_ref(jj, j));
if (vtst > vmx) {
vmx = vtst;
}
i__3 = vr_subscr(jj, j);
if (d_imag(&vr_ref(jj, j)) == 0. && (d__1 = vr[i__3].r, abs(d__1))
> vrmx) {
i__4 = vr_subscr(jj, j);
vrmx = (d__2 = vr[i__4].r, abs(d__2));
}
/* L20: */
}
if (vrmx / vmx < 1. - ulp * 2.) {
result[3] = ulpinv;
}
/* L30: */
}
/* Do Test (4) */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
tnrm = dznrm2_(n, &vl_ref(1, j), &c__1);
/* Computing MAX
Computing MIN */
d__4 = ulpinv, d__5 = (d__1 = tnrm - 1., abs(d__1)) / ulp;
d__2 = result[4], d__3 = min(d__4,d__5);
result[4] = max(d__2,d__3);
vmx = 0.;
vrmx = 0.;
i__2 = *n;
for (jj = 1; jj <= i__2; ++jj) {
vtst = z_abs(&vl_ref(jj, j));
if (vtst > vmx) {
vmx = vtst;
}
i__3 = vl_subscr(jj, j);
if (d_imag(&vl_ref(jj, j)) == 0. && (d__1 = vl[i__3].r, abs(d__1))
> vrmx) {
i__4 = vl_subscr(jj, j);
vrmx = (d__2 = vl[i__4].r, abs(d__2));
}
/* L40: */
}
if (vrmx / vmx < 1. - ulp * 2.) {
result[4] = ulpinv;
}
/* L50: */
}
/* Test for all options of computing condition numbers */
i__1 = isensm;
for (isens = 1; isens <= i__1; ++isens) {
*(unsigned char *)sense = *(unsigned char *)&sens[isens - 1];
/* Compute eigenvalues only, and test them */
zlacpy_("F", n, n, &a[a_offset], lda, &h__[h_offset], lda);
zgeevx_(balanc, "N", "N", sense, n, &h__[h_offset], lda, &w1[1], cdum,
&c__1, cdum, &c__1, &ilo1, &ihi1, &scale1[1], &abnrm1, &
rcnde1[1], &rcndv1[1], &work[1], lwork, &rwork[1], &iinfo);
if (iinfo != 0) {
result[1] = ulpinv;
if (*jtype != 22) {
io___28.ciunit = *nounit;
s_wsfe(&io___28);
do_fio(&c__1, "ZGEEVX2", (ftnlen)7);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&(*n), (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&(*jtype), (ftnlen)sizeof(integer));
do_fio(&c__1, balanc, (ftnlen)1);
do_fio(&c__4, (char *)&iseed[1], (ftnlen)sizeof(integer));
e_wsfe();
} else {
io___29.ciunit = *nounit;
s_wsfe(&io___29);
do_fio(&c__1, "ZGEEVX2", (ftnlen)7);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&(*n), (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&iseed[1], (ftnlen)sizeof(integer));
e_wsfe();
}
*info = abs(iinfo);
goto L190;
}
/* Do Test (5) */
i__2 = *n;
for (j = 1; j <= i__2; ++j) {
i__3 = j;
i__4 = j;
if (w[i__3].r != w1[i__4].r || w[i__3].i != w1[i__4].i) {
result[5] = ulpinv;
}
/* L60: */
}
/* Do Test (8) */
if (! nobal) {
i__2 = *n;
for (j = 1; j <= i__2; ++j) {
if (scale[j] != scale1[j]) {
result[8] = ulpinv;
}
/* L70: */
}
if (ilo != ilo1) {
result[8] = ulpinv;
}
if (ihi != ihi1) {
result[8] = ulpinv;
}
if (abnrm != abnrm1) {
result[8] = ulpinv;
}
}
/* Do Test (9) */
if (isens == 2 && *n > 1) {
i__2 = *n;
for (j = 1; j <= i__2; ++j) {
if (rcondv[j] != rcndv1[j]) {
result[9] = ulpinv;
}
/* L80: */
}
}
/* Compute eigenvalues and right eigenvectors, and test them */
zlacpy_("F", n, n, &a[a_offset], lda, &h__[h_offset], lda);
zgeevx_(balanc, "N", "V", sense, n, &h__[h_offset], lda, &w1[1], cdum,
&c__1, &lre[lre_offset], ldlre, &ilo1, &ihi1, &scale1[1], &
abnrm1, &rcnde1[1], &rcndv1[1], &work[1], lwork, &rwork[1], &
iinfo);
if (iinfo != 0) {
result[1] = ulpinv;
if (*jtype != 22) {
io___30.ciunit = *nounit;
s_wsfe(&io___30);
do_fio(&c__1, "ZGEEVX3", (ftnlen)7);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&(*n), (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&(*jtype), (ftnlen)sizeof(integer));
do_fio(&c__1, balanc, (ftnlen)1);
do_fio(&c__4, (char *)&iseed[1], (ftnlen)sizeof(integer));
e_wsfe();
} else {
io___31.ciunit = *nounit;
s_wsfe(&io___31);
do_fio(&c__1, "ZGEEVX3", (ftnlen)7);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&(*n), (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&iseed[1], (ftnlen)sizeof(integer));
e_wsfe();
}
*info = abs(iinfo);
goto L190;
}
/* Do Test (5) again */
i__2 = *n;
for (j = 1; j <= i__2; ++j) {
i__3 = j;
i__4 = j;
if (w[i__3].r != w1[i__4].r || w[i__3].i != w1[i__4].i) {
result[5] = ulpinv;
}
/* L90: */
}
/* Do Test (6) */
i__2 = *n;
for (j = 1; j <= i__2; ++j) {
i__3 = *n;
for (jj = 1; jj <= i__3; ++jj) {
i__4 = vr_subscr(j, jj);
i__5 = lre_subscr(j, jj);
if (vr[i__4].r != lre[i__5].r || vr[i__4].i != lre[i__5].i) {
result[6] = ulpinv;
}
/* L100: */
}
/* L110: */
}
/* Do Test (8) again */
if (! nobal) {
i__2 = *n;
for (j = 1; j <= i__2; ++j) {
if (scale[j] != scale1[j]) {
result[8] = ulpinv;
}
/* L120: */
}
if (ilo != ilo1) {
result[8] = ulpinv;
}
if (ihi != ihi1) {
result[8] = ulpinv;
}
if (abnrm != abnrm1) {
result[8] = ulpinv;
}
}
/* Do Test (9) again */
if (isens == 2 && *n > 1) {
i__2 = *n;
for (j = 1; j <= i__2; ++j) {
if (rcondv[j] != rcndv1[j]) {
result[9] = ulpinv;
}
/* L130: */
}
}
/* Compute eigenvalues and left eigenvectors, and test them */
zlacpy_("F", n, n, &a[a_offset], lda, &h__[h_offset], lda);
zgeevx_(balanc, "V", "N", sense, n, &h__[h_offset], lda, &w1[1], &lre[
lre_offset], ldlre, cdum, &c__1, &ilo1, &ihi1, &scale1[1], &
abnrm1, &rcnde1[1], &rcndv1[1], &work[1], lwork, &rwork[1], &
iinfo);
if (iinfo != 0) {
result[1] = ulpinv;
if (*jtype != 22) {
io___32.ciunit = *nounit;
s_wsfe(&io___32);
do_fio(&c__1, "ZGEEVX4", (ftnlen)7);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&(*n), (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&(*jtype), (ftnlen)sizeof(integer));
do_fio(&c__1, balanc, (ftnlen)1);
do_fio(&c__4, (char *)&iseed[1], (ftnlen)sizeof(integer));
e_wsfe();
} else {
io___33.ciunit = *nounit;
s_wsfe(&io___33);
do_fio(&c__1, "ZGEEVX4", (ftnlen)7);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&(*n), (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&iseed[1], (ftnlen)sizeof(integer));
e_wsfe();
}
*info = abs(iinfo);
goto L190;
}
/* Do Test (5) again */
i__2 = *n;
for (j = 1; j <= i__2; ++j) {
i__3 = j;
i__4 = j;
if (w[i__3].r != w1[i__4].r || w[i__3].i != w1[i__4].i) {
result[5] = ulpinv;
}
/* L140: */
}
/* Do Test (7) */
i__2 = *n;
for (j = 1; j <= i__2; ++j) {
i__3 = *n;
for (jj = 1; jj <= i__3; ++jj) {
i__4 = vl_subscr(j, jj);
i__5 = lre_subscr(j, jj);
if (vl[i__4].r != lre[i__5].r || vl[i__4].i != lre[i__5].i) {
result[7] = ulpinv;
}
/* L150: */
}
/* L160: */
}
/* Do Test (8) again */
if (! nobal) {
i__2 = *n;
for (j = 1; j <= i__2; ++j) {
if (scale[j] != scale1[j]) {
result[8] = ulpinv;
}
/* L170: */
}
if (ilo != ilo1) {
result[8] = ulpinv;
}
if (ihi != ihi1) {
result[8] = ulpinv;
}
if (abnrm != abnrm1) {
result[8] = ulpinv;
}
}
/* Do Test (9) again */
if (isens == 2 && *n > 1) {
i__2 = *n;
for (j = 1; j <= i__2; ++j) {
if (rcondv[j] != rcndv1[j]) {
result[9] = ulpinv;
}
/* L180: */
}
}
L190:
/* L200: */
;
}
/* If COMP, compare condition numbers to precomputed ones */
if (*comp) {
zlacpy_("F", n, n, &a[a_offset], lda, &h__[h_offset], lda);
zgeevx_("N", "V", "V", "B", n, &h__[h_offset], lda, &w[1], &vl[
vl_offset], ldvl, &vr[vr_offset], ldvr, &ilo, &ihi, &scale[1],
&abnrm, &rconde[1], &rcondv[1], &work[1], lwork, &rwork[1], &
iinfo);
if (iinfo != 0) {
result[1] = ulpinv;
io___34.ciunit = *nounit;
s_wsfe(&io___34);
do_fio(&c__1, "ZGEEVX5", (ftnlen)7);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&(*n), (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&iseed[1], (ftnlen)sizeof(integer));
e_wsfe();
*info = abs(iinfo);
goto L250;
}
/* Sort eigenvalues and condition numbers lexicographically
to compare with inputs */
i__1 = *n - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
kmin = i__;
if (*isrt == 0) {
i__2 = i__;
vrimin = w[i__2].r;
} else {
vrimin = d_imag(&w[i__]);
}
i__2 = *n;
for (j = i__ + 1; j <= i__2; ++j) {
if (*isrt == 0) {
i__3 = j;
vricmp = w[i__3].r;
} else {
vricmp = d_imag(&w[j]);
}
if (vricmp < vrimin) {
kmin = j;
vrimin = vricmp;
}
/* L210: */
}
i__2 = kmin;
ctmp.r = w[i__2].r, ctmp.i = w[i__2].i;
i__2 = kmin;
i__3 = i__;
w[i__2].r = w[i__3].r, w[i__2].i = w[i__3].i;
i__2 = i__;
w[i__2].r = ctmp.r, w[i__2].i = ctmp.i;
vrimin = rconde[kmin];
rconde[kmin] = rconde[i__];
rconde[i__] = vrimin;
vrimin = rcondv[kmin];
rcondv[kmin] = rcondv[i__];
rcondv[i__] = vrimin;
/* L220: */
}
/* Compare condition numbers for eigenvectors
taking their condition numbers into account */
result[10] = 0.;
eps = max(5.9605e-8,ulp);
/* Computing MAX */
d__1 = (doublereal) (*n) * eps * abnrm;
v = max(d__1,smlnum);
if (abnrm == 0.) {
v = 1.;
}
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
if (v > rcondv[i__] * rconde[i__]) {
tol = rcondv[i__];
} else {
tol = v / rconde[i__];
}
if (v > rcdvin[i__] * rcdein[i__]) {
tolin = rcdvin[i__];
} else {
tolin = v / rcdein[i__];
}
/* Computing MAX */
d__1 = tol, d__2 = smlnum / eps;
tol = max(d__1,d__2);
/* Computing MAX */
d__1 = tolin, d__2 = smlnum / eps;
tolin = max(d__1,d__2);
if (eps * (rcdvin[i__] - tolin) > rcondv[i__] + tol) {
vmax = 1. / eps;
} else if (rcdvin[i__] - tolin > rcondv[i__] + tol) {
vmax = (rcdvin[i__] - tolin) / (rcondv[i__] + tol);
} else if (rcdvin[i__] + tolin < eps * (rcondv[i__] - tol)) {
vmax = 1. / eps;
} else if (rcdvin[i__] + tolin < rcondv[i__] - tol) {
vmax = (rcondv[i__] - tol) / (rcdvin[i__] + tolin);
} else {
vmax = 1.;
}
result[10] = max(result[10],vmax);
/* L230: */
}
/* Compare condition numbers for eigenvalues
taking their condition numbers into account */
result[11] = 0.;
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
if (v > rcondv[i__]) {
tol = 1.;
} else {
tol = v / rcondv[i__];
}
if (v > rcdvin[i__]) {
tolin = 1.;
} else {
tolin = v / rcdvin[i__];
}
/* Computing MAX */
d__1 = tol, d__2 = smlnum / eps;
tol = max(d__1,d__2);
/* Computing MAX */
d__1 = tolin, d__2 = smlnum / eps;
tolin = max(d__1,d__2);
if (eps * (rcdein[i__] - tolin) > rconde[i__] + tol) {
vmax = 1. / eps;
} else if (rcdein[i__] - tolin > rconde[i__] + tol) {
vmax = (rcdein[i__] - tolin) / (rconde[i__] + tol);
} else if (rcdein[i__] + tolin < eps * (rconde[i__] - tol)) {
vmax = 1. / eps;
} else if (rcdein[i__] + tolin < rconde[i__] - tol) {
vmax = (rconde[i__] - tol) / (rcdein[i__] + tolin);
} else {
vmax = 1.;
}
result[11] = max(result[11],vmax);
/* L240: */
}
L250:
;
}
return 0;
/* End of ZGET23 */
} /* zget23_ */
