/* 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 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 zdrvvx_(integer *nsizes, integer *nn, integer *ntypes,
logical *dotype, integer *iseed, doublereal *thresh, integer *niunit,
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 *rcondv, doublereal *rcndv1, doublereal *rcdvin,
doublereal *rconde, doublereal *rcnde1, doublereal *rcdein,
doublereal *scale, doublereal *scale1, doublereal *result,
doublecomplex *work, integer *nwork, doublereal *rwork, 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 };
static char bal[1*4] = "N" "P" "S" "B";
/* Format strings */
static char fmt_9992[] = "(\002 ZDRVVX: \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 Expert Driver\002,/\002 Matrix types ("
"see ZDRVVX 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,/\002"
" 12=Well-cond., random complex \002,\002 \002,\002 17=Il"
"l-cond., large rand. complx \002,/\002 13=Ill-condi\002,\002tion"
"ed, evenly spaced. \002,\002 18=Ill-cond., small rand.\002"
",\002 complx \002)";
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,\002 "
"22=Matrix read from input file\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 = | transpose(A) VL - VL W | / ( n |A| ulp ) \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 what else co"
"mputed,\002,\002 1/ulp otherwise\002,/\002 7 = 0 if VL same no "
"matter what else computed,\002,\002 1/ulp otherwise\002,/\002 8"
" = 0 if RCONDV same no matter what else computed,\002,\002 1/ul"
"p otherwise\002,/\002 9 = 0 if SCALE, ILO, IHI, ABNRM same no ma"
"tter what else\002,\002 computed, 1/ulp otherwise\002,/\002 10 "
"= | RCONDV - RCONDV(precomputed) | / cond(RCONDV),\002,/\002 11 "
"= | RCONDE - RCONDE(precomputed) | / cond(RCONDE),\002)";
static char fmt_9994[] = "(\002 BALANC='\002,a1,\002',N=\002,i4,\002,I"
"WK=\002,i1,\002, seed=\002,4(i4,\002,\002),\002 type \002,i2,"
"\002, test(\002,i2,\002)=\002,g10.3)";
static char fmt_9993[] = "(\002 N=\002,i5,\002, input example =\002,i3"
",\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;
doublecomplex z__1;
/* Local variables */
integer i__, j, n;
doublereal wi, wr;
integer iwk;
doublereal ulp;
integer ibal;
doublereal cond;
integer jcol;
char path[3];
integer nmax;
doublereal unfl, ovfl;
integer isrt;
logical badnn;
integer nfail, imode, iinfo;
doublereal conds, anorm;
extern /* Subroutine */ int zget23_(logical *, integer *, char *, integer
*, doublereal *, integer *, integer *, integer *, doublecomplex *,
integer *, doublecomplex *, doublecomplex *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *, doublecomplex *,
integer *, doublereal *, integer *);
integer jsize, nerrs, itype, jtype, ntest;
doublereal rtulp;
extern /* Subroutine */ int dlabad_(doublereal *, doublereal *);
char balanc[1];
extern doublereal dlamch_(char *);
integer idumma[1];
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 *), zlaset_(char *, integer *, integer *, doublecomplex *,
doublecomplex *, doublecomplex *, integer *);
integer ntestf;
extern /* Subroutine */ int 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;
doublereal rtulpi;
integer mtypes, ntestt;
/* Fortran I/O blocks */
static cilist io___32 = { 0, 0, 0, fmt_9992, 0 };
static cilist io___39 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___40 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___41 = { 0, 0, 0, fmt_9997, 0 };
static cilist io___42 = { 0, 0, 0, fmt_9996, 0 };
static cilist io___43 = { 0, 0, 0, fmt_9995, 0 };
static cilist io___44 = { 0, 0, 0, fmt_9994, 0 };
static cilist io___45 = { 0, 0, 1, 0, 0 };
static cilist io___48 = { 0, 0, 0, 0, 0 };
static cilist io___49 = { 0, 0, 0, 0, 0 };
static cilist io___52 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___53 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___54 = { 0, 0, 0, fmt_9997, 0 };
static cilist io___55 = { 0, 0, 0, fmt_9996, 0 };
static cilist io___56 = { 0, 0, 0, fmt_9995, 0 };
static cilist io___57 = { 0, 0, 0, fmt_9993, 0 };
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZDRVVX checks the nonsymmetric eigenvalue problem expert driver */
/* ZGEEVX. */
/* ZDRVVX uses both test matrices generated randomly depending on */
/* data supplied in the calling sequence, as well as on data */
/* read from an input file and including precomputed condition */
/* numbers to which it compares the ones it computes. */
/* When ZDRVVX is called, a number of matrix "sizes" ("n's") and a */
/* number of matrix "types" are specified in the calling sequence. */
/* For each size ("n") and each type of matrix, one matrix will be */
/* generated and used to test the nonsymmetric eigenroutines. For */
/* each matrix, 9 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) W(full) = W(partial) */
/* 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) VR(full) = VR(partial) */
/* 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) VL(full) = VL(partial) */
/* 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) RCONDV(full) = RCONDV(partial) */
/* 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. */
/* 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 */
/* In addition, an input file will be read from logical unit number */
/* NIUNIT. The file contains matrices along with precomputed */
/* eigenvalues and reciprocal condition numbers for the eigenvalues */
/* and right eigenvectors. For these matrices, in addition to tests */
/* (1) to (9) we will compute the following two tests: */
/* (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 */
/* ========== */
/* NSIZES (input) INTEGER */
/* The number of sizes of matrices to use. NSIZES must be at */
/* least zero. If it is zero, no randomly generated matrices */
/* are tested, but any test matrices read from NIUNIT will be */
/* tested. */
/* 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. NTYPES must be at least */
/* zero. If it is zero, no randomly generated test matrices */
/* are tested, but and test matrices read from NIUNIT will be */
/* tested. 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 ZDRVVX 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. */
/* NIUNIT (input) INTEGER */
/* The FORTRAN unit number for reading in the data file of */
/* problems to solve. */
/* 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,12)) */
/* 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, 12 ). (12 is the */
/* dimension of the largest matrix on the precomputed */
/* input file.) */
/* H (workspace) COMPLEX*16 array, dimension (LDA, max(NN,12)) */
/* Another copy of the test matrix A, modified by ZGEEVX. */
/* W (workspace) COMPLEX*16 array, dimension (max(NN,12)) */
/* Contains the eigenvalues of A. */
/* W1 (workspace) COMPLEX*16 array, dimension (max(NN,12)) */
/* 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, max(NN,12)) */
/* VL holds the computed left eigenvectors. */
/* LDVL (input) INTEGER */
/* Leading dimension of VL. Must be at least max(1,max(NN,12)). */
/* VR (workspace) COMPLEX*16 array, dimension (LDVR, max(NN,12)) */
/* VR holds the computed right eigenvectors. */
/* LDVR (input) INTEGER */
/* Leading dimension of VR. Must be at least max(1,max(NN,12)). */
/* LRE (workspace) COMPLEX*16 array, dimension (LDLRE, max(NN,12)) */
/* LRE holds the computed right or left eigenvectors. */
/* LDLRE (input) INTEGER */
/* Leading dimension of LRE. Must be at least max(1,max(NN,12)) */
/* RESULT (output) DOUBLE PRECISION array, dimension (11) */
/* 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 */
/* max(6*12+2*12**2,6*NN(j)+2*NN(j)**2) = */
/* max( 360 ,6*NN(j)+2*NN(j)**2) for all j. */
/* RWORK (workspace) DOUBLE PRECISION array, dimension (2*max(NN,12)) */
/* INFO (output) INTEGER */
/* If 0, then successful exit. */
/* If <0, then input paramter -INFO is incorrect. */
/* If >0, ZLATMR, CLATMS, CLATME or ZGET23 returned an error */
/* code, and INFO is its absolute value. */
/* ----------------------------------------------------------------------- */
/* Some Local Variables and Parameters: */
/* ---- ----- --------- --- ---------- */
/* ZERO, ONE Real 0 and 1. */
/* MAXTYP The number of types defined. */
/* NMAX Largest value in NN or 12. */
/* 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;
--rcondv;
--rcndv1;
--rcdvin;
--rconde;
--rcnde1;
--rcdein;
--scale;
--scale1;
--result;
--work;
--rwork;
/* Function Body */
/* .. */
/* .. Executable Statements .. */
s_copy(path, "Zomplex precision", (ftnlen)1, (ftnlen)17);
s_copy(path + 1, "VX", (ftnlen)2, (ftnlen)2);
/* Check for errors */
ntestt = 0;
ntestf = 0;
*info = 0;
/* Important constants */
badnn = FALSE_;
/* 7 is the largest dimension in the input file of precomputed */
/* problems */
nmax = 7;
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 = -10;
} else if (*ldvl < 1 || *ldvl < nmax) {
*info = -15;
} else if (*ldvr < 1 || *ldvr < nmax) {
*info = -17;
} else if (*ldlre < 1 || *ldlre < nmax) {
*info = -19;
} else /* if(complicated condition) */ {
/* Computing 2nd power */
i__1 = nmax;
if (nmax * 6 + (i__1 * i__1 << 1) > *nwork) {
*info = -30;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZDRVVX", &i__1);
return 0;
}
/* If nothing to do check on NIUNIT */
if (*nsizes == 0 || *ntypes == 0) {
goto L160;
}
/* 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 L140;
}
/* 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;
a[i__4].r = anorm, a[i__4].i = 0.;
/* L70: */
}
} 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.;
}
/* 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) {
/* Symmetric, 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], "S", &work[1], &c__6, &c_b39,
&c_b2, "T", "N", &work[n + 1], &c__1, &c_b39, &work[(
n << 1) + 1], &c__1, &c_b39, "N", idumma, &c__0, &
c__0, &c_b49, &anorm, "NO", &a[a_offset], lda, idumma,
&iinfo);
} else if (itype == 8) {
/* Symmetric, random eigenvalues */
zlatmr_(&n, &n, "D", &iseed[1], "H", &work[1], &c__6, &c_b39,
&c_b2, "T", "N", &work[n + 1], &c__1, &c_b39, &work[(
n << 1) + 1], &c__1, &c_b39, "N", idumma, &n, &n, &
c_b49, &anorm, "NO", &a[a_offset], lda, idumma, &
iinfo);
} else if (itype == 9) {
/* General, random eigenvalues */
zlatmr_(&n, &n, "D", &iseed[1], "N", &work[1], &c__6, &c_b39,
&c_b2, "T", "N", &work[n + 1], &c__1, &c_b39, &work[(
n << 1) + 1], &c__1, &c_b39, "N", idumma, &n, &n, &
c_b49, &anorm, "NO", &a[a_offset], lda, idumma, &
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_b39,
&c_b2, "T", "N", &work[n + 1], &c__1, &c_b39, &work[(
n << 1) + 1], &c__1, &c_b39, "N", idumma, &n, &c__0, &
c_b49, &anorm, "NO", &a[a_offset], lda, idumma, &
iinfo);
} else {
iinfo = 1;
}
if (iinfo != 0) {
io___32.ciunit = *nounit;
s_wsfe(&io___32);
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 <= 3; ++iwk) {
if (iwk == 1) {
nnwork = n << 1;
} else if (iwk == 2) {
/* Computing 2nd power */
i__3 = n;
nnwork = (n << 1) + i__3 * i__3;
} else {
/* Computing 2nd power */
i__3 = n;
nnwork = n * 6 + (i__3 * i__3 << 1);
}
nnwork = max(nnwork,1);
/* Test for all balancing options */
for (ibal = 1; ibal <= 4; ++ibal) {
*(unsigned char *)balanc = *(unsigned char *)&bal[ibal -
1];
/* Perform tests */
zget23_(&c_false, &c__0, balanc, &jtype, thresh, ioldsd,
nounit, &n, &a[a_offset], lda, &h__[h_offset], &w[
1], &w1[1], &vl[vl_offset], ldvl, &vr[vr_offset],
ldvr, &lre[lre_offset], ldlre, &rcondv[1], &
rcndv1[1], &rcdvin[1], &rconde[1], &rcnde1[1], &
rcdein[1], &scale[1], &scale1[1], &result[1], &
work[1], &nnwork, &rwork[1], info);
/* Check for RESULT(j) > THRESH */
ntest = 0;
nfail = 0;
for (j = 1; j <= 9; ++j) {
if (result[j] >= 0.) {
++ntest;
}
if (result[j] >= *thresh) {
++nfail;
}
/* L100: */
}
if (nfail > 0) {
++ntestf;
}
if (ntestf == 1) {
io___39.ciunit = *nounit;
s_wsfe(&io___39);
do_fio(&c__1, path, (ftnlen)3);
e_wsfe();
io___40.ciunit = *nounit;
s_wsfe(&io___40);
e_wsfe();
io___41.ciunit = *nounit;
s_wsfe(&io___41);
e_wsfe();
io___42.ciunit = *nounit;
s_wsfe(&io___42);
e_wsfe();
io___43.ciunit = *nounit;
s_wsfe(&io___43);
do_fio(&c__1, (char *)&(*thresh), (ftnlen)sizeof(
doublereal));
e_wsfe();
ntestf = 2;
}
for (j = 1; j <= 9; ++j) {
if (result[j] >= *thresh) {
io___44.ciunit = *nounit;
s_wsfe(&io___44);
do_fio(&c__1, balanc, (ftnlen)1);
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();
}
/* L110: */
}
nerrs += nfail;
ntestt += ntest;
/* L120: */
}
/* L130: */
}
L140:
;
}
/* L150: */
}
L160:
/* Read in data from file to check accuracy of condition estimation. */
/* Assume input eigenvalues are sorted lexicographically (increasing */
/* by real part, then decreasing by imaginary part) */
jtype = 0;
L170:
io___45.ciunit = *niunit;
i__1 = s_rsle(&io___45);
if (i__1 != 0) {
goto L220;
}
i__1 = do_lio(&c__3, &c__1, (char *)&n, (ftnlen)sizeof(integer));
if (i__1 != 0) {
goto L220;
}
i__1 = do_lio(&c__3, &c__1, (char *)&isrt, (ftnlen)sizeof(integer));
if (i__1 != 0) {
goto L220;
}
i__1 = e_rsle();
if (i__1 != 0) {
goto L220;
}
/* Read input data until N=0 */
if (n == 0) {
goto L220;
}
++jtype;
iseed[1] = jtype;
i__1 = n;
for (i__ = 1; i__ <= i__1; ++i__) {
io___48.ciunit = *niunit;
s_rsle(&io___48);
i__2 = n;
for (j = 1; j <= i__2; ++j) {
do_lio(&c__7, &c__1, (char *)&a[i__ + j * a_dim1], (ftnlen)sizeof(
doublecomplex));
}
e_rsle();
/* L180: */
}
i__1 = n;
for (i__ = 1; i__ <= i__1; ++i__) {
io___49.ciunit = *niunit;
s_rsle(&io___49);
do_lio(&c__5, &c__1, (char *)&wr, (ftnlen)sizeof(doublereal));
do_lio(&c__5, &c__1, (char *)&wi, (ftnlen)sizeof(doublereal));
do_lio(&c__5, &c__1, (char *)&rcdein[i__], (ftnlen)sizeof(doublereal))
;
do_lio(&c__5, &c__1, (char *)&rcdvin[i__], (ftnlen)sizeof(doublereal))
;
e_rsle();
i__2 = i__;
z__1.r = wr, z__1.i = wi;
w1[i__2].r = z__1.r, w1[i__2].i = z__1.i;
/* L190: */
}
/* Computing 2nd power */
i__2 = n;
i__1 = n * 6 + (i__2 * i__2 << 1);
zget23_(&c_true, &isrt, "N", &c__22, thresh, &iseed[1], nounit, &n, &a[
a_offset], lda, &h__[h_offset], &w[1], &w1[1], &vl[vl_offset],
ldvl, &vr[vr_offset], ldvr, &lre[lre_offset], ldlre, &rcondv[1], &
rcndv1[1], &rcdvin[1], &rconde[1], &rcnde1[1], &rcdein[1], &scale[
1], &scale1[1], &result[1], &work[1], &i__1, &rwork[1], info);
/* Check for RESULT(j) > THRESH */
ntest = 0;
nfail = 0;
for (j = 1; j <= 11; ++j) {
if (result[j] >= 0.) {
++ntest;
}
if (result[j] >= *thresh) {
++nfail;
}
/* L200: */
}
if (nfail > 0) {
++ntestf;
}
if (ntestf == 1) {
io___52.ciunit = *nounit;
s_wsfe(&io___52);
do_fio(&c__1, path, (ftnlen)3);
e_wsfe();
io___53.ciunit = *nounit;
s_wsfe(&io___53);
e_wsfe();
io___54.ciunit = *nounit;
s_wsfe(&io___54);
e_wsfe();
io___55.ciunit = *nounit;
s_wsfe(&io___55);
e_wsfe();
io___56.ciunit = *nounit;
s_wsfe(&io___56);
do_fio(&c__1, (char *)&(*thresh), (ftnlen)sizeof(doublereal));
e_wsfe();
ntestf = 2;
}
for (j = 1; j <= 11; ++j) {
if (result[j] >= *thresh) {
io___57.ciunit = *nounit;
s_wsfe(&io___57);
do_fio(&c__1, (char *)&n, (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();
}
/* L210: */
}
nerrs += nfail;
ntestt += ntest;
goto L170;
L220:
/* Summary */
dlasum_(path, nounit, &nerrs, &ntestt);
return 0;
/* End of ZDRVVX */
} /* zdrvvx_ */
/* Subroutine */ int zchkhb_(integer *nsizes, integer *nn, integer *nwdths,
integer *kk, integer *ntypes, logical *dotype, integer *iseed,
doublereal *thresh, integer *nounit, doublecomplex *a, integer *lda,
doublereal *sd, doublereal *se, doublecomplex *u, integer *ldu,
doublecomplex *work, integer *lwork, doublereal *rwork, doublereal *
result, integer *info)
{
/* Initialized data */
static integer ktype[15] = { 1,2,4,4,4,4,4,5,5,5,5,5,8,8,8 };
static integer kmagn[15] = { 1,1,1,1,1,2,3,1,1,1,2,3,1,2,3 };
static integer kmode[15] = { 0,0,4,3,1,4,4,4,3,1,4,4,0,0,0 };
/* Format strings */
static char fmt_9999[] = "(\002 ZCHKHB: \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[] = "(/1x,a3,\002 -- Complex Hermitian Banded Tridi"
"agonal Reduction Routines\002)";
static char fmt_9997[] = "(\002 Matrix types (see DCHK23 for details):"
" \002)";
static char fmt_9996[] = "(/\002 Special Matrices:\002,/\002 1=Zero mat"
"rix. \002,\002 5=Diagonal: clustered ent"
"ries.\002,/\002 2=Identity matrix. \002,\002"
" 6=Diagonal: large, evenly spaced.\002,/\002 3=Diagonal: evenl"
"y spaced entries. \002,\002 7=Diagonal: small, evenly spaced."
"\002,/\002 4=Diagonal: geometr. spaced entries.\002)";
static char fmt_9995[] = "(\002 Dense \002,a,\002 Banded Matrices:\002,"
"/\002 8=Evenly spaced eigenvals. \002,\002 12=Small,"
" evenly spaced eigenvals.\002,/\002 9=Geometrically spaced eige"
"nvals. \002,\002 13=Matrix with random O(1) entries.\002,"
"/\002 10=Clustered eigenvalues. \002,\002 14=Matrix"
" with large random entries.\002,/\002 11=Large, evenly spaced ei"
"genvals. \002,\002 15=Matrix with small random entries.\002)";
static char fmt_9994[] = "(/\002 Tests performed: (S is Tridiag, U "
"is \002,a,\002,\002,/20x,a,\002 means \002,a,\002.\002,/\002 UPL"
"O='U':\002,/\002 1= | A - U S U\002,a1,\002 | / ( |A| n ulp ) "
" \002,\002 2= | I - U U\002,a1,\002 | / ( n ulp )\002,/\002 U"
"PLO='L':\002,/\002 3= | A - U S U\002,a1,\002 | / ( |A| n ulp )"
" \002,\002 4= | I - U U\002,a1,\002 | / ( n ulp )\002)";
static char fmt_9993[] = "(\002 N=\002,i5,\002, K=\002,i4,\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, u_dim1, u_offset, i__1, i__2, i__3, i__4, i__5,
i__6, i__7;
doublereal d__1;
doublecomplex z__1;
/* Local variables */
integer i__, j, k, n, jc, jr;
doublereal ulp, cond;
integer jcol, kmax, nmax;
doublereal unfl, ovfl, temp1;
logical badnn;
integer imode, iinfo;
extern /* Subroutine */ int zhbt21_(char *, integer *, integer *, integer
*, doublecomplex *, integer *, doublereal *, doublereal *,
doublecomplex *, integer *, doublecomplex *, doublereal *,
doublereal *);
doublereal aninv, anorm;
integer nmats, jsize, nerrs, itype, jtype, ntest;
logical badnnb;
extern doublereal dlamch_(char *);
integer idumma[1];
integer ioldsd[4];
extern /* Subroutine */ int dlasum_(char *, integer *, integer *, integer
*);
integer jwidth;
extern /* Subroutine */ int zhbtrd_(char *, char *, integer *, integer *,
doublecomplex *, integer *, doublereal *, doublereal *,
doublecomplex *, integer *, doublecomplex *, 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, ulpinv;
extern /* Subroutine */ int zlatms_(integer *, integer *, char *, integer
*, char *, doublereal *, integer *, doublereal *, doublereal *,
integer *, integer *, char *, doublecomplex *, integer *,
doublecomplex *, integer *);
integer mtypes, ntestt;
/* Fortran I/O blocks */
static cilist io___36 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___37 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___40 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___41 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___42 = { 0, 0, 0, fmt_9997, 0 };
static cilist io___43 = { 0, 0, 0, fmt_9996, 0 };
static cilist io___44 = { 0, 0, 0, fmt_9995, 0 };
static cilist io___45 = { 0, 0, 0, fmt_9994, 0 };
static cilist io___46 = { 0, 0, 0, fmt_9993, 0 };
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZCHKHB tests the reduction of a Hermitian band matrix to tridiagonal */
/* from, used with the Hermitian eigenvalue problem. */
/* ZHBTRD factors a Hermitian band matrix A as U S U* , where * means */
/* conjugate transpose, S is symmetric tridiagonal, and U is unitary. */
/* ZHBTRD can use either just the lower or just the upper triangle */
/* of A; ZCHKHB checks both cases. */
/* When ZCHKHB is called, a number of matrix "sizes" ("n's"), a number */
/* of bandwidths ("k's"), and a number of matrix "types" are */
/* specified. For each size ("n"), each bandwidth ("k") less than or */
/* equal to "n", and each type of matrix, one matrix will be generated */
/* and used to test the hermitian banded reduction routine. For each */
/* matrix, a number of tests will be performed: */
/* (1) | A - V S V* | / ( |A| n ulp ) computed by ZHBTRD with */
/* UPLO='U' */
/* (2) | I - UU* | / ( n ulp ) */
/* (3) | A - V S V* | / ( |A| n ulp ) computed by ZHBTRD with */
/* UPLO='L' */
/* (4) | I - UU* | / ( n 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 diagonal matrix with evenly spaced entries */
/* 1, ..., ULP and random signs. */
/* (ULP = (first number larger than 1) - 1 ) */
/* (4) A diagonal matrix with geometrically spaced entries */
/* 1, ..., ULP and random signs. */
/* (5) A diagonal matrix with "clustered" entries 1, ULP, ..., ULP */
/* and random signs. */
/* (6) Same as (4), but multiplied by SQRT( overflow threshold ) */
/* (7) Same as (4), but multiplied by SQRT( underflow threshold ) */
/* (8) A matrix of the form U* D U, where U is unitary and */
/* D has evenly spaced entries 1, ..., ULP with random signs */
/* on the diagonal. */
/* (9) A matrix of the form U* D U, where U is unitary and */
/* D has geometrically spaced entries 1, ..., ULP with random */
/* signs on the diagonal. */
/* (10) A matrix of the form U* D U, where U is unitary and */
/* D has "clustered" entries 1, ULP,..., ULP with random */
/* signs on the diagonal. */
/* (11) Same as (8), but multiplied by SQRT( overflow threshold ) */
/* (12) Same as (8), but multiplied by SQRT( underflow threshold ) */
/* (13) Hermitian matrix with random entries chosen from (-1,1). */
/* (14) Same as (13), but multiplied by SQRT( overflow threshold ) */
/* (15) Same as (13), but multiplied by SQRT( underflow threshold ) */
/* Arguments */
/* ========= */
/* NSIZES (input) INTEGER */
/* The number of sizes of matrices to use. If it is zero, */
/* ZCHKHB 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. */
/* NWDTHS (input) INTEGER */
/* The number of bandwidths to use. If it is zero, */
/* ZCHKHB does nothing. It must be at least zero. */
/* KK (input) INTEGER array, dimension (NWDTHS) */
/* An array containing the bandwidths to be used for the band */
/* matrices. The values must be at least zero. */
/* NTYPES (input) INTEGER */
/* The number of elements in DOTYPE. If it is zero, ZCHKHB */
/* 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 ZCHKHB 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 IINFO not equal to 0.) */
/* A (input/workspace) DOUBLE PRECISION array, dimension */
/* (LDA, max(NN)) */
/* Used to hold the matrix whose eigenvalues are to be */
/* computed. */
/* LDA (input) INTEGER */
/* The leading dimension of A. It must be at least 2 (not 1!) */
/* and at least max( KK )+1. */
/* SD (workspace) DOUBLE PRECISION array, dimension (max(NN)) */
/* Used to hold the diagonal of the tridiagonal matrix computed */
/* by ZHBTRD. */
/* SE (workspace) DOUBLE PRECISION array, dimension (max(NN)) */
/* Used to hold the off-diagonal of the tridiagonal matrix */
/* computed by ZHBTRD. */
/* U (workspace) DOUBLE PRECISION array, dimension (LDU, max(NN)) */
/* Used to hold the unitary matrix computed by ZHBTRD. */
/* LDU (input) INTEGER */
/* The leading dimension of U. It must be at least 1 */
/* and at least max( NN ). */
/* WORK (workspace) DOUBLE PRECISION array, dimension (LWORK) */
/* LWORK (input) INTEGER */
/* The number of entries in WORK. This must be at least */
/* max( LDA+1, max(NN)+1 )*max(NN). */
/* RESULT (output) DOUBLE PRECISION array, dimension (4) */
/* The values computed by the tests described above. */
/* The values are currently limited to 1/ulp, to avoid */
/* overflow. */
/* INFO (output) INTEGER */
/* If 0, then everything ran OK. */
/* ----------------------------------------------------------------------- */
/* Some Local Variables and Parameters: */
/* ---- ----- --------- --- ---------- */
/* ZERO, ONE Real 0 and 1. */
/* MAXTYP The number of types defined. */
/* NTEST The number of tests performed, or which can */
/* be performed so far, for the current matrix. */
/* NTESTT The total number of tests performed so far. */
/* NMAX Largest value in NN. */
/* NMATS The number of matrices generated so far. */
/* NERRS The number of tests which have exceeded THRESH */
/* so far. */
/* COND, 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 Square roots of the previous 2 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) ) */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Data statements .. */
/* Parameter adjustments */
--nn;
--kk;
--dotype;
--iseed;
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--sd;
--se;
u_dim1 = *ldu;
u_offset = 1 + u_dim1;
u -= u_offset;
--work;
--rwork;
--result;
/* Function Body */
/* .. */
/* .. Executable Statements .. */
/* Check for errors */
ntestt = 0;
*info = 0;
/* Important constants */
badnn = FALSE_;
nmax = 1;
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: */
}
badnnb = FALSE_;
kmax = 0;
i__1 = *nsizes;
for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
i__2 = kmax, i__3 = kk[j];
kmax = max(i__2,i__3);
if (kk[j] < 0) {
badnnb = TRUE_;
}
/* L20: */
}
/* Computing MIN */
i__1 = nmax - 1;
kmax = min(i__1,kmax);
/* Check for errors */
if (*nsizes < 0) {
*info = -1;
} else if (badnn) {
*info = -2;
} else if (*nwdths < 0) {
*info = -3;
} else if (badnnb) {
*info = -4;
} else if (*ntypes < 0) {
*info = -5;
} else if (*lda < kmax + 1) {
*info = -11;
} else if (*ldu < nmax) {
*info = -15;
} else if ((max(*lda,nmax) + 1) * nmax > *lwork) {
*info = -17;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZCHKHB", &i__1);
return 0;
}
/* Quick return if possible */
if (*nsizes == 0 || *ntypes == 0 || *nwdths == 0) {
return 0;
}
/* More Important constants */
unfl = dlamch_("Safe minimum");
ovfl = 1. / unfl;
ulp = dlamch_("Epsilon") * dlamch_("Base");
ulpinv = 1. / ulp;
rtunfl = sqrt(unfl);
rtovfl = sqrt(ovfl);
/* Loop over sizes, types */
nerrs = 0;
nmats = 0;
i__1 = *nsizes;
for (jsize = 1; jsize <= i__1; ++jsize) {
n = nn[jsize];
aninv = 1. / (doublereal) max(1,n);
i__2 = *nwdths;
for (jwidth = 1; jwidth <= i__2; ++jwidth) {
k = kk[jwidth];
if (k > n) {
goto L180;
}
/* Computing MAX */
/* Computing MIN */
i__5 = n - 1;
i__3 = 0, i__4 = min(i__5,k);
k = max(i__3,i__4);
if (*nsizes != 1) {
mtypes = min(15,*ntypes);
} else {
mtypes = min(16,*ntypes);
}
i__3 = mtypes;
for (jtype = 1; jtype <= i__3; ++jtype) {
if (! dotype[jtype]) {
goto L170;
}
++nmats;
ntest = 0;
for (j = 1; j <= 4; ++j) {
ioldsd[j - 1] = iseed[j];
/* L30: */
}
/* Compute "A". */
/* Store as "Upper"; later, we will copy to other format. */
/* Control parameters: */
/* KMAGN KMODE KTYPE */
/* =1 O(1) clustered 1 zero */
/* =2 large clustered 2 identity */
/* =3 small exponential (none) */
/* =4 arithmetic diagonal, (w/ eigenvalues) */
/* =5 random log hermitian, w/ eigenvalues */
/* =6 random (none) */
/* =7 random diagonal */
/* =8 random hermitian */
/* =9 positive definite */
/* =10 diagonally dominant tridiagonal */
if (mtypes > 15) {
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;
if (jtype <= 15) {
cond = ulpinv;
} else {
cond = ulpinv * aninv / 10.;
}
/* Special Matrices -- Identity & Jordan block */
/* Zero */
if (itype == 1) {
iinfo = 0;
} else if (itype == 2) {
/* Identity */
i__4 = n;
for (jcol = 1; jcol <= i__4; ++jcol) {
i__5 = k + 1 + jcol * a_dim1;
a[i__5].r = anorm, a[i__5].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, "Q", &a[k + 1 +
a_dim1], lda, &work[1], &iinfo);
} else if (itype == 5) {
/* Hermitian, eigenvalues specified */
zlatms_(&n, &n, "S", &iseed[1], "H", &rwork[1], &imode, &
cond, &anorm, &k, &k, "Q", &a[a_offset], lda, &
work[1], &iinfo);
} else if (itype == 7) {
/* Diagonal, random eigenvalues */
zlatmr_(&n, &n, "S", &iseed[1], "H", &work[1], &c__6, &
c_b32, &c_b2, "T", "N", &work[n + 1], &c__1, &
c_b32, &work[(n << 1) + 1], &c__1, &c_b32, "N",
idumma, &c__0, &c__0, &c_b42, &anorm, "Q", &a[k +
1 + a_dim1], lda, idumma, &iinfo);
} else if (itype == 8) {
/* Hermitian, random eigenvalues */
zlatmr_(&n, &n, "S", &iseed[1], "H", &work[1], &c__6, &
c_b32, &c_b2, "T", "N", &work[n + 1], &c__1, &
c_b32, &work[(n << 1) + 1], &c__1, &c_b32, "N",
idumma, &k, &k, &c_b42, &anorm, "Q", &a[a_offset],
lda, idumma, &iinfo);
} else if (itype == 9) {
/* Positive definite, eigenvalues specified. */
zlatms_(&n, &n, "S", &iseed[1], "P", &rwork[1], &imode, &
cond, &anorm, &k, &k, "Q", &a[a_offset], lda, &
work[n + 1], &iinfo);
} else if (itype == 10) {
/* Positive definite tridiagonal, eigenvalues specified. */
if (n > 1) {
k = max(1,k);
}
zlatms_(&n, &n, "S", &iseed[1], "P", &rwork[1], &imode, &
cond, &anorm, &c__1, &c__1, "Q", &a[k + a_dim1],
lda, &work[1], &iinfo);
i__4 = n;
for (i__ = 2; i__ <= i__4; ++i__) {
i__5 = k + 1 + (i__ - 1) * a_dim1;
i__6 = k + 1 + i__ * a_dim1;
z__1.r = a[i__5].r * a[i__6].r - a[i__5].i * a[i__6]
.i, z__1.i = a[i__5].r * a[i__6].i + a[i__5]
.i * a[i__6].r;
temp1 = z_abs(&a[k + i__ * a_dim1]) / sqrt(z_abs(&
z__1));
if (temp1 > .5) {
i__5 = k + i__ * a_dim1;
i__6 = k + 1 + (i__ - 1) * a_dim1;
i__7 = k + 1 + i__ * a_dim1;
z__1.r = a[i__6].r * a[i__7].r - a[i__6].i * a[
i__7].i, z__1.i = a[i__6].r * a[i__7].i +
a[i__6].i * a[i__7].r;
d__1 = sqrt(z_abs(&z__1)) * .5;
a[i__5].r = d__1, a[i__5].i = 0.;
}
/* L90: */
}
} else {
iinfo = 1;
}
if (iinfo != 0) {
io___36.ciunit = *nounit;
s_wsfe(&io___36);
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 ZHBTRD to compute S and U from upper triangle. */
i__4 = k + 1;
zlacpy_(" ", &i__4, &n, &a[a_offset], lda, &work[1], lda);
ntest = 1;
zhbtrd_("V", "U", &n, &k, &work[1], lda, &sd[1], &se[1], &u[
u_offset], ldu, &work[*lda * n + 1], &iinfo);
if (iinfo != 0) {
io___37.ciunit = *nounit;
s_wsfe(&io___37);
do_fio(&c__1, "ZHBTRD(U)", (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) {
return 0;
} else {
result[1] = ulpinv;
goto L150;
}
}
/* Do tests 1 and 2 */
zhbt21_("Upper", &n, &k, &c__1, &a[a_offset], lda, &sd[1], &
se[1], &u[u_offset], ldu, &work[1], &rwork[1], &
result[1]);
/* Convert A from Upper-Triangle-Only storage to */
/* Lower-Triangle-Only storage. */
i__4 = n;
for (jc = 1; jc <= i__4; ++jc) {
/* Computing MIN */
i__6 = k, i__7 = n - jc;
i__5 = min(i__6,i__7);
for (jr = 0; jr <= i__5; ++jr) {
i__6 = jr + 1 + jc * a_dim1;
d_cnjg(&z__1, &a[k + 1 - jr + (jc + jr) * a_dim1]);
a[i__6].r = z__1.r, a[i__6].i = z__1.i;
/* L110: */
}
/* L120: */
}
i__4 = n;
for (jc = n + 1 - k; jc <= i__4; ++jc) {
/* Computing MIN */
i__5 = k, i__6 = n - jc;
i__7 = k;
for (jr = min(i__5,i__6) + 1; jr <= i__7; ++jr) {
i__5 = jr + 1 + jc * a_dim1;
a[i__5].r = 0., a[i__5].i = 0.;
/* L130: */
}
/* L140: */
}
/* Call ZHBTRD to compute S and U from lower triangle */
i__4 = k + 1;
zlacpy_(" ", &i__4, &n, &a[a_offset], lda, &work[1], lda);
ntest = 3;
zhbtrd_("V", "L", &n, &k, &work[1], lda, &sd[1], &se[1], &u[
u_offset], ldu, &work[*lda * n + 1], &iinfo);
if (iinfo != 0) {
io___40.ciunit = *nounit;
s_wsfe(&io___40);
do_fio(&c__1, "ZHBTRD(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) {
return 0;
} else {
result[3] = ulpinv;
goto L150;
}
}
ntest = 4;
/* Do tests 3 and 4 */
zhbt21_("Lower", &n, &k, &c__1, &a[a_offset], lda, &sd[1], &
se[1], &u[u_offset], ldu, &work[1], &rwork[1], &
result[3]);
/* End of Loop -- Check for RESULT(j) > THRESH */
L150:
ntestt += ntest;
/* Print out tests which fail. */
i__4 = ntest;
for (jr = 1; jr <= i__4; ++jr) {
if (result[jr] >= *thresh) {
/* If this is the first test to fail, */
/* print a header to the data file. */
if (nerrs == 0) {
io___41.ciunit = *nounit;
s_wsfe(&io___41);
do_fio(&c__1, "ZHB", (ftnlen)3);
e_wsfe();
io___42.ciunit = *nounit;
s_wsfe(&io___42);
e_wsfe();
io___43.ciunit = *nounit;
s_wsfe(&io___43);
e_wsfe();
io___44.ciunit = *nounit;
s_wsfe(&io___44);
do_fio(&c__1, "Hermitian", (ftnlen)9);
e_wsfe();
io___45.ciunit = *nounit;
s_wsfe(&io___45);
do_fio(&c__1, "unitary", (ftnlen)7);
do_fio(&c__1, "*", (ftnlen)1);
do_fio(&c__1, "conjugate transpose", (ftnlen)19);
for (j = 1; j <= 4; ++j) {
do_fio(&c__1, "*", (ftnlen)1);
}
e_wsfe();
}
++nerrs;
io___46.ciunit = *nounit;
s_wsfe(&io___46);
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&k, (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 *)&jr, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&result[jr], (ftnlen)sizeof(
doublereal));
e_wsfe();
}
/* L160: */
}
L170:
;
}
L180:
;
}
/* L190: */
}
/* Summary */
dlasum_("ZHB", nounit, &nerrs, &ntestt);
return 0;
/* End of ZCHKHB */
} /* zchkhb_ */
/* Subroutine */ int zchkbb_(integer *nsizes, integer *mval, integer *nval,
integer *nwdths, integer *kk, integer *ntypes, logical *dotype,
integer *nrhs, integer *iseed, doublereal *thresh, integer *nounit,
doublecomplex *a, integer *lda, doublecomplex *ab, integer *ldab,
doublereal *bd, doublereal *be, doublecomplex *q, integer *ldq,
doublecomplex *p, integer *ldp, doublecomplex *c__, integer *ldc,
doublecomplex *cc, doublecomplex *work, integer *lwork, doublereal *
rwork, doublereal *result, integer *info)
{
/* Initialized data */
static integer ktype[15] = { 1,2,4,4,4,4,4,6,6,6,6,6,9,9,9 };
static integer kmagn[15] = { 1,1,1,1,1,2,3,1,1,1,2,3,1,2,3 };
static integer kmode[15] = { 0,0,4,3,1,4,4,4,3,1,4,4,0,0,0 };
/* Format strings */
static char fmt_9999[] = "(\002 ZCHKBB: \002,a,\002 returned INFO=\002,i"
"5,\002.\002,/9x,\002M=\002,i5,\002 N=\002,i5,\002 K=\002,i5,\002"
", JTYPE=\002,i5,\002, ISEED=(\002,3(i5,\002,\002),i5,\002)\002)";
static char fmt_9998[] = "(\002 M =\002,i4,\002 N=\002,i4,\002, K=\002,i"
"3,\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, ab_dim1, ab_offset, c_dim1, c_offset, cc_dim1,
cc_offset, p_dim1, p_offset, q_dim1, q_offset, i__1, i__2, i__3,
i__4, i__5, i__6, i__7, i__8, i__9;
/* Builtin functions */
double sqrt(doublereal);
integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void);
/* Local variables */
integer i__, j, k, m, n, kl, jr, ku;
doublereal ulp, cond;
integer jcol, kmax, mmax, nmax;
doublereal unfl, ovfl;
logical badmm, badnn;
integer imode, iinfo;
extern /* Subroutine */ int zbdt01_(integer *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublereal *, doublereal *, doublecomplex *, integer *,
doublecomplex *, doublereal *, doublereal *), zbdt02_(integer *,
integer *, doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, doublereal *,
doublereal *);
doublereal anorm;
integer mnmin, mnmax, nmats, jsize, nerrs, itype, jtype, ntest;
extern /* Subroutine */ int dlahd2_(integer *, char *), zunt01_(
char *, integer *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublereal *, doublereal *);
logical badnnb;
extern doublereal dlamch_(char *);
extern /* Subroutine */ int zgbbrd_(char *, integer *, integer *, integer
*, integer *, integer *, doublecomplex *, integer *, doublereal *,
doublereal *, doublecomplex *, integer *, doublecomplex *,
integer *, doublecomplex *, integer *, doublecomplex *,
doublereal *, integer *);
integer idumma[1];
extern /* Subroutine */ int xerbla_(char *, integer *);
integer ioldsd[4];
extern /* Subroutine */ int dlasum_(char *, integer *, integer *, integer
*);
doublereal amninv;
integer jwidth;
extern /* Subroutine */ int 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, ulpinv;
extern /* Subroutine */ int zlatms_(integer *, integer *, char *, integer
*, char *, doublereal *, integer *, doublereal *, doublereal *,
integer *, integer *, char *, doublecomplex *, integer *,
doublecomplex *, integer *);
integer mtypes, ntestt;
/* Fortran I/O blocks */
static cilist io___41 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___43 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___45 = { 0, 0, 0, fmt_9998, 0 };
/* -- LAPACK test routine (new routine for release 2.0) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZCHKBB tests the reduction of a general complex rectangular band */
/* matrix to real bidiagonal form. */
/* ZGBBRD factors a general band matrix A as Q B P* , where * means */
/* conjugate transpose, B is upper bidiagonal, and Q and P are unitary; */
/* ZGBBRD can also overwrite a given matrix C with Q* C . */
/* For each pair of matrix dimensions (M,N) and each selected matrix */
/* type, an M by N matrix A and an M by NRHS matrix C are generated. */
/* The problem dimensions are as follows */
/* A: M x N */
/* Q: M x M */
/* P: N x N */
/* B: min(M,N) x min(M,N) */
/* C: M x NRHS */
/* For each generated matrix, 4 tests are performed: */
/* (1) | A - Q B PT | / ( |A| max(M,N) ulp ), PT = P' */
/* (2) | I - Q' Q | / ( M ulp ) */
/* (3) | I - PT PT' | / ( N ulp ) */
/* (4) | Y - Q' C | / ( |Y| max(M,NRHS) ulp ), where Y = Q' C. */
/* 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: */
/* The possible matrix types are */
/* (1) The zero matrix. */
/* (2) The identity matrix. */
/* (3) A diagonal matrix with evenly spaced entries */
/* 1, ..., ULP and random signs. */
/* (ULP = (first number larger than 1) - 1 ) */
/* (4) A diagonal matrix with geometrically spaced entries */
/* 1, ..., ULP and random signs. */
/* (5) A diagonal matrix with "clustered" entries 1, ULP, ..., ULP */
/* and random signs. */
/* (6) Same as (3), but multiplied by SQRT( overflow threshold ) */
/* (7) Same as (3), but multiplied by SQRT( underflow threshold ) */
/* (8) A matrix of the form U D V, where U and V are orthogonal and */
/* D has evenly spaced entries 1, ..., ULP with random signs */
/* on the diagonal. */
/* (9) A matrix of the form U D V, where U and V are orthogonal and */
/* D has geometrically spaced entries 1, ..., ULP with random */
/* signs on the diagonal. */
/* (10) A matrix of the form U D V, where U and V are orthogonal and */
/* D has "clustered" entries 1, ULP,..., ULP with random */
/* signs on the diagonal. */
/* (11) Same as (8), but multiplied by SQRT( overflow threshold ) */
/* (12) Same as (8), but multiplied by SQRT( underflow threshold ) */
/* (13) Rectangular matrix with random entries chosen from (-1,1). */
/* (14) Same as (13), but multiplied by SQRT( overflow threshold ) */
/* (15) Same as (13), but multiplied by SQRT( underflow threshold ) */
/* Arguments */
/* ========= */
/* NSIZES (input) INTEGER */
/* The number of values of M and N contained in the vectors */
/* MVAL and NVAL. The matrix sizes are used in pairs (M,N). */
/* If NSIZES is zero, ZCHKBB does nothing. NSIZES must be at */
/* least zero. */
/* MVAL (input) INTEGER array, dimension (NSIZES) */
/* The values of the matrix row dimension M. */
/* NVAL (input) INTEGER array, dimension (NSIZES) */
/* The values of the matrix column dimension N. */
/* NWDTHS (input) INTEGER */
/* The number of bandwidths to use. If it is zero, */
/* ZCHKBB does nothing. It must be at least zero. */
/* KK (input) INTEGER array, dimension (NWDTHS) */
/* An array containing the bandwidths to be used for the band */
/* matrices. The values must be at least zero. */
/* NTYPES (input) INTEGER */
/* The number of elements in DOTYPE. If it is zero, ZCHKBB */
/* 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. */
/* NRHS (input) INTEGER */
/* The number of columns in the "right-hand side" matrix C. */
/* If NRHS = 0, then the operations on the right-hand side will */
/* not be tested. NRHS must be at least 0. */
/* ISEED (input/output) INTEGER array, dimension (4) */
/* On entry ISEED specifies the seed of the random number */
/* generator. The array elements should be between 0 and 4095; */
/* if not they will be reduced mod 4096. Also, ISEED(4) must */
/* be odd. The 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 ZCHKBB 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 IINFO not equal to 0.) */
/* A (input/workspace) DOUBLE PRECISION array, dimension */
/* (LDA, max(NN)) */
/* Used to hold the matrix A. */
/* LDA (input) INTEGER */
/* The leading dimension of A. It must be at least 1 */
/* and at least max( NN ). */
/* AB (workspace) DOUBLE PRECISION array, dimension (LDAB, max(NN)) */
/* Used to hold A in band storage format. */
/* LDAB (input) INTEGER */
/* The leading dimension of AB. It must be at least 2 (not 1!) */
/* and at least max( KK )+1. */
/* BD (workspace) DOUBLE PRECISION array, dimension (max(NN)) */
/* Used to hold the diagonal of the bidiagonal matrix computed */
/* by ZGBBRD. */
/* BE (workspace) DOUBLE PRECISION array, dimension (max(NN)) */
/* Used to hold the off-diagonal of the bidiagonal matrix */
/* computed by ZGBBRD. */
/* Q (workspace) COMPLEX*16 array, dimension (LDQ, max(NN)) */
/* Used to hold the unitary matrix Q computed by ZGBBRD. */
/* LDQ (input) INTEGER */
/* The leading dimension of Q. It must be at least 1 */
/* and at least max( NN ). */
/* P (workspace) COMPLEX*16 array, dimension (LDP, max(NN)) */
/* Used to hold the unitary matrix P computed by ZGBBRD. */
/* LDP (input) INTEGER */
/* The leading dimension of P. It must be at least 1 */
/* and at least max( NN ). */
/* C (workspace) COMPLEX*16 array, dimension (LDC, max(NN)) */
/* Used to hold the matrix C updated by ZGBBRD. */
/* LDC (input) INTEGER */
/* The leading dimension of U. It must be at least 1 */
/* and at least max( NN ). */
/* CC (workspace) COMPLEX*16 array, dimension (LDC, max(NN)) */
/* Used to hold a copy of the matrix C. */
/* WORK (workspace) COMPLEX*16 array, dimension (LWORK) */
/* LWORK (input) INTEGER */
/* The number of entries in WORK. This must be at least */
/* max( LDA+1, max(NN)+1 )*max(NN). */
/* RWORK (workspace) DOUBLE PRECISION array, dimension (max(NN)) */
/* RESULT (output) DOUBLE PRECISION array, dimension (4) */
/* The values computed by the tests described above. */
/* The values are currently limited to 1/ulp, to avoid */
/* overflow. */
/* INFO (output) INTEGER */
/* If 0, then everything ran OK. */
/* ----------------------------------------------------------------------- */
/* Some Local Variables and Parameters: */
/* ---- ----- --------- --- ---------- */
/* ZERO, ONE Real 0 and 1. */
/* MAXTYP The number of types defined. */
/* NTEST The number of tests performed, or which can */
/* be performed so far, for the current matrix. */
/* NTESTT The total number of tests performed so far. */
/* NMAX Largest value in NN. */
/* NMATS The number of matrices generated so far. */
/* NERRS The number of tests which have exceeded THRESH */
/* so far. */
/* COND, 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 Square roots of the previous 2 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) ) */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Data statements .. */
/* Parameter adjustments */
--mval;
--nval;
--kk;
--dotype;
--iseed;
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
ab_dim1 = *ldab;
ab_offset = 1 + ab_dim1;
ab -= ab_offset;
--bd;
--be;
q_dim1 = *ldq;
q_offset = 1 + q_dim1;
q -= q_offset;
p_dim1 = *ldp;
p_offset = 1 + p_dim1;
p -= p_offset;
cc_dim1 = *ldc;
cc_offset = 1 + cc_dim1;
cc -= cc_offset;
c_dim1 = *ldc;
c_offset = 1 + c_dim1;
c__ -= c_offset;
--work;
--rwork;
--result;
/* Function Body */
/* .. */
/* .. Executable Statements .. */
/* Check for errors */
ntestt = 0;
*info = 0;
/* Important constants */
badmm = FALSE_;
badnn = FALSE_;
mmax = 1;
nmax = 1;
mnmax = 1;
i__1 = *nsizes;
for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
i__2 = mmax, i__3 = mval[j];
mmax = max(i__2,i__3);
if (mval[j] < 0) {
badmm = TRUE_;
}
/* Computing MAX */
i__2 = nmax, i__3 = nval[j];
nmax = max(i__2,i__3);
if (nval[j] < 0) {
badnn = TRUE_;
}
/* Computing MAX */
/* Computing MIN */
i__4 = mval[j], i__5 = nval[j];
i__2 = mnmax, i__3 = min(i__4,i__5);
mnmax = max(i__2,i__3);
/* L10: */
}
badnnb = FALSE_;
kmax = 0;
i__1 = *nwdths;
for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
i__2 = kmax, i__3 = kk[j];
kmax = max(i__2,i__3);
if (kk[j] < 0) {
badnnb = TRUE_;
}
/* L20: */
}
/* Check for errors */
if (*nsizes < 0) {
*info = -1;
} else if (badmm) {
*info = -2;
} else if (badnn) {
*info = -3;
} else if (*nwdths < 0) {
*info = -4;
} else if (badnnb) {
*info = -5;
} else if (*ntypes < 0) {
*info = -6;
} else if (*nrhs < 0) {
*info = -8;
} else if (*lda < nmax) {
*info = -13;
} else if (*ldab < (kmax << 1) + 1) {
*info = -15;
} else if (*ldq < nmax) {
*info = -19;
} else if (*ldp < nmax) {
*info = -21;
} else if (*ldc < nmax) {
*info = -23;
} else if ((max(*lda,nmax) + 1) * nmax > *lwork) {
*info = -26;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZCHKBB", &i__1);
return 0;
}
/* Quick return if possible */
if (*nsizes == 0 || *ntypes == 0 || *nwdths == 0) {
return 0;
}
/* More Important constants */
unfl = dlamch_("Safe minimum");
ovfl = 1. / unfl;
ulp = dlamch_("Epsilon") * dlamch_("Base");
ulpinv = 1. / ulp;
rtunfl = sqrt(unfl);
rtovfl = sqrt(ovfl);
/* Loop over sizes, widths, types */
nerrs = 0;
nmats = 0;
i__1 = *nsizes;
for (jsize = 1; jsize <= i__1; ++jsize) {
m = mval[jsize];
n = nval[jsize];
mnmin = min(m,n);
/* Computing MAX */
i__2 = max(1,m);
amninv = 1. / (doublereal) max(i__2,n);
i__2 = *nwdths;
for (jwidth = 1; jwidth <= i__2; ++jwidth) {
k = kk[jwidth];
if (k >= m && k >= n) {
goto L150;
}
/* Computing MAX */
/* Computing MIN */
i__5 = m - 1;
i__3 = 0, i__4 = min(i__5,k);
kl = max(i__3,i__4);
/* Computing MAX */
/* Computing MIN */
i__5 = n - 1;
i__3 = 0, i__4 = min(i__5,k);
ku = max(i__3,i__4);
if (*nsizes != 1) {
mtypes = min(15,*ntypes);
} else {
mtypes = min(16,*ntypes);
}
i__3 = mtypes;
for (jtype = 1; jtype <= i__3; ++jtype) {
if (! dotype[jtype]) {
goto L140;
}
++nmats;
ntest = 0;
for (j = 1; j <= 4; ++j) {
ioldsd[j - 1] = iseed[j];
/* L30: */
}
/* Compute "A". */
/* Control parameters: */
/* KMAGN KMODE KTYPE */
/* =1 O(1) clustered 1 zero */
/* =2 large clustered 2 identity */
/* =3 small exponential (none) */
/* =4 arithmetic diagonal, (w/ singular values) */
/* =5 random log (none) */
/* =6 random nonhermitian, w/ singular values */
/* =7 (none) */
/* =8 (none) */
/* =9 random nonhermitian */
if (mtypes > 15) {
goto L90;
}
itype = ktype[jtype - 1];
imode = kmode[jtype - 1];
/* Compute norm */
switch (kmagn[jtype - 1]) {
case 1: goto L40;
case 2: goto L50;
case 3: goto L60;
}
L40:
anorm = 1.;
goto L70;
L50:
anorm = rtovfl * ulp * amninv;
goto L70;
L60:
anorm = rtunfl * max(m,n) * ulpinv;
goto L70;
L70:
zlaset_("Full", lda, &n, &c_b1, &c_b1, &a[a_offset], lda);
zlaset_("Full", ldab, &n, &c_b1, &c_b1, &ab[ab_offset], ldab);
iinfo = 0;
cond = ulpinv;
/* Special Matrices -- Identity & Jordan block */
/* Zero */
if (itype == 1) {
iinfo = 0;
} else if (itype == 2) {
/* Identity */
i__4 = n;
for (jcol = 1; jcol <= i__4; ++jcol) {
i__5 = jcol + jcol * a_dim1;
a[i__5].r = anorm, a[i__5].i = 0.;
/* L80: */
}
} else if (itype == 4) {
/* Diagonal Matrix, singular values specified */
zlatms_(&m, &n, "S", &iseed[1], "N", &rwork[1], &imode, &
cond, &anorm, &c__0, &c__0, "N", &a[a_offset],
lda, &work[1], &iinfo);
} else if (itype == 6) {
/* Nonhermitian, singular values specified */
zlatms_(&m, &n, "S", &iseed[1], "N", &rwork[1], &imode, &
cond, &anorm, &kl, &ku, "N", &a[a_offset], lda, &
work[1], &iinfo);
} else if (itype == 9) {
/* Nonhermitian, random entries */
zlatmr_(&m, &n, "S", &iseed[1], "N", &work[1], &c__6, &
c_b33, &c_b2, "T", "N", &work[n + 1], &c__1, &
c_b33, &work[(n << 1) + 1], &c__1, &c_b33, "N",
idumma, &kl, &ku, &c_b41, &anorm, "N", &a[
a_offset], lda, idumma, &iinfo);
} else {
iinfo = 1;
}
/* Generate Right-Hand Side */
zlatmr_(&m, nrhs, "S", &iseed[1], "N", &work[1], &c__6, &
c_b33, &c_b2, "T", "N", &work[m + 1], &c__1, &c_b33, &
work[(m << 1) + 1], &c__1, &c_b33, "N", idumma, &m,
nrhs, &c_b41, &c_b33, "NO", &c__[c_offset], ldc,
idumma, &iinfo);
if (iinfo != 0) {
io___41.ciunit = *nounit;
s_wsfe(&io___41);
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:
/* Copy A to band storage. */
i__4 = n;
for (j = 1; j <= i__4; ++j) {
/* Computing MAX */
i__5 = 1, i__6 = j - ku;
/* Computing MIN */
i__8 = m, i__9 = j + kl;
i__7 = min(i__8,i__9);
for (i__ = max(i__5,i__6); i__ <= i__7; ++i__) {
i__5 = ku + 1 + i__ - j + j * ab_dim1;
i__6 = i__ + j * a_dim1;
ab[i__5].r = a[i__6].r, ab[i__5].i = a[i__6].i;
/* L100: */
}
/* L110: */
}
/* Copy C */
zlacpy_("Full", &m, nrhs, &c__[c_offset], ldc, &cc[cc_offset],
ldc);
/* Call ZGBBRD to compute B, Q and P, and to update C. */
zgbbrd_("B", &m, &n, nrhs, &kl, &ku, &ab[ab_offset], ldab, &
bd[1], &be[1], &q[q_offset], ldq, &p[p_offset], ldp, &
cc[cc_offset], ldc, &work[1], &rwork[1], &iinfo);
if (iinfo != 0) {
io___43.ciunit = *nounit;
s_wsfe(&io___43);
do_fio(&c__1, "ZGBBRD", (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);
if (iinfo < 0) {
return 0;
} else {
result[1] = ulpinv;
goto L120;
}
}
/* Test 1: Check the decomposition A := Q * B * P' */
/* 2: Check the orthogonality of Q */
/* 3: Check the orthogonality of P */
/* 4: Check the computation of Q' * C */
zbdt01_(&m, &n, &c_n1, &a[a_offset], lda, &q[q_offset], ldq, &
bd[1], &be[1], &p[p_offset], ldp, &work[1], &rwork[1],
&result[1]);
zunt01_("Columns", &m, &m, &q[q_offset], ldq, &work[1], lwork,
&rwork[1], &result[2]);
zunt01_("Rows", &n, &n, &p[p_offset], ldp, &work[1], lwork, &
rwork[1], &result[3]);
zbdt02_(&m, nrhs, &c__[c_offset], ldc, &cc[cc_offset], ldc, &
q[q_offset], ldq, &work[1], &rwork[1], &result[4]);
/* End of Loop -- Check for RESULT(j) > THRESH */
ntest = 4;
L120:
ntestt += ntest;
/* Print out tests which fail. */
i__4 = ntest;
for (jr = 1; jr <= i__4; ++jr) {
if (result[jr] >= *thresh) {
if (nerrs == 0) {
dlahd2_(nounit, "ZBB");
}
++nerrs;
io___45.ciunit = *nounit;
s_wsfe(&io___45);
do_fio(&c__1, (char *)&m, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&k, (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 *)&jr, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&result[jr], (ftnlen)sizeof(
doublereal));
e_wsfe();
}
/* L130: */
}
L140:
;
}
L150:
;
}
/* L160: */
}
/* Summary */
dlasum_("ZBB", nounit, &nerrs, &ntestt);
return 0;
/* End of ZCHKBB */
} /* zchkbb_ */
