/* Subroutine */ int zdrvgg_(integer *nsizes, integer *nn, integer *ntypes,
logical *dotype, integer *iseed, doublereal *thresh, doublereal *
thrshn, integer *nounit, doublecomplex *a, integer *lda,
doublecomplex *b, doublecomplex *s, doublecomplex *t, doublecomplex *
s2, doublecomplex *t2, doublecomplex *q, integer *ldq, doublecomplex *
z__, doublecomplex *alpha1, doublecomplex *beta1, doublecomplex *
alpha2, doublecomplex *beta2, doublecomplex *vl, doublecomplex *vr,
doublecomplex *work, integer *lwork, doublereal *rwork, doublereal *
result, integer *info)
{
/* Initialized data */
static integer kclass[26] = { 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,
2,2,2,3 };
static integer kbmagn[26] = { 1,1,1,1,1,1,1,1,3,2,3,2,2,3,1,1,1,1,1,1,1,3,
2,3,2,1 };
static integer ktrian[26] = { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,
1,1,1,1 };
static logical lasign[26] = { FALSE_,FALSE_,FALSE_,FALSE_,FALSE_,FALSE_,
TRUE_,FALSE_,TRUE_,TRUE_,FALSE_,FALSE_,TRUE_,TRUE_,TRUE_,FALSE_,
TRUE_,FALSE_,FALSE_,FALSE_,TRUE_,TRUE_,TRUE_,TRUE_,TRUE_,FALSE_ };
static logical lbsign[26] = { FALSE_,FALSE_,FALSE_,FALSE_,FALSE_,FALSE_,
FALSE_,TRUE_,FALSE_,FALSE_,TRUE_,TRUE_,FALSE_,FALSE_,TRUE_,FALSE_,
TRUE_,FALSE_,FALSE_,FALSE_,FALSE_,FALSE_,FALSE_,FALSE_,FALSE_,
FALSE_ };
static integer kz1[6] = { 0,1,2,1,3,3 };
static integer kz2[6] = { 0,0,1,2,1,1 };
static integer kadd[6] = { 0,0,0,0,3,2 };
static integer katype[26] = { 0,1,0,1,2,3,4,1,4,4,1,1,4,4,4,2,4,5,8,7,9,4,
4,4,4,0 };
static integer kbtype[26] = { 0,0,1,1,2,-3,1,4,1,1,4,4,1,1,-4,2,-4,8,8,8,
8,8,8,8,8,0 };
static integer kazero[26] = { 1,1,1,1,1,1,2,1,2,2,1,1,2,2,3,1,3,5,5,5,5,3,
3,3,3,1 };
static integer kbzero[26] = { 1,1,1,1,1,1,1,2,1,1,2,2,1,1,4,1,4,6,6,6,6,4,
4,4,4,1 };
static integer kamagn[26] = { 1,1,1,1,1,1,1,1,2,3,2,3,2,3,1,1,1,1,1,1,1,2,
3,3,2,1 };
/* Format strings */
static char fmt_9999[] = "(\002 ZDRVGG: \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 ZDRVGG: \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[] = "(/1x,a3,\002 -- Complex Generalized eigenvalue"
" problem driver\002)";
static char fmt_9996[] = "(\002 Matrix types (see ZDRVGG for details):"
" \002)";
static char fmt_9995[] = "(\002 Special Matrices:\002,23x,\002(J'=transp"
"osed Jordan block)\002,/\002 1=(0,0) 2=(I,0) 3=(0,I) 4=(I,I"
") 5=(J',J') \002,\0026=(diag(J',I), diag(I,J'))\002,/\002 Diag"
"onal Matrices: ( \002,\002D=diag(0,1,2,...) )\002,/\002 7=(D,"
"I) 9=(large*D, small*I\002,\002) 11=(large*I, small*D) 13=(l"
"arge*D, large*I)\002,/\002 8=(I,D) 10=(small*D, large*I) 12="
"(small*I, large*D) \002,\002 14=(small*D, small*I)\002,/\002 15"
"=(D, reversed D)\002)";
static char fmt_9994[] = "(\002 Matrices Rotated by Random \002,a,\002 M"
"atrices U, V:\002,/\002 16=Transposed Jordan Blocks "
" 19=geometric \002,\002alpha, beta=0,1\002,/\002 17=arithm. alp"
"ha&beta \002,\002 20=arithmetic alpha, beta=0,"
"1\002,/\002 18=clustered \002,\002alpha, beta=0,1 21"
"=random alpha, beta=0,1\002,/\002 Large & Small Matrices:\002,"
"/\002 22=(large, small) \002,\00223=(small,large) 24=(smal"
"l,small) 25=(large,large)\002,/\002 26=random O(1) matrices"
".\002)";
static char fmt_9993[] = "(/\002 Tests performed: (S is Schur, T is tri"
"angular, \002,\002Q and Z are \002,a,\002,\002,/20x,\002l and r "
"are the appropriate left and right\002,/19x,\002eigenvectors, re"
"sp., a is alpha, b is beta, and\002,/19x,a,\002 means \002,a,"
"\002.)\002,/\002 1 = | A - Q S Z\002,a,\002 | / ( |A| n ulp ) "
" 2 = | B - Q T Z\002,a,\002 | / ( |B| n ulp )\002,/\002 3 = | "
"I - QQ\002,a,\002 | / ( n ulp ) 4 = | I - ZZ\002,a"
",\002 | / ( n ulp )\002,/\002 5 = difference between (alpha,beta"
") and diagonals of\002,\002 (S,T)\002,/\002 6 = max | ( b A - a "
"B )\002,a,\002 l | / const. 7 = max | ( b A - a B ) r | / cons"
"t.\002,/1x)";
static char fmt_9992[] = "(\002 Matrix order=\002,i5,\002, type=\002,i2"
",\002, seed=\002,4(i4,\002,\002),\002 result \002,i3,\002 is\002"
",0p,f8.2)";
static char fmt_9991[] = "(\002 Matrix order=\002,i5,\002, type=\002,i2"
",\002, seed=\002,4(i4,\002,\002),\002 result \002,i3,\002 is\002"
",1p,d10.3)";
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, q_dim1, q_offset, s_dim1,
s_offset, s2_dim1, s2_offset, t_dim1, t_offset, t2_dim1,
t2_offset, vl_dim1, vl_offset, vr_dim1, vr_offset, z_dim1,
z_offset, i__1, i__2, i__3, i__4, i__5, i__6, i__7, i__8, i__9,
i__10, i__11;
doublereal d__1, d__2, d__3, d__4, d__5, d__6, d__7, d__8, d__9, d__10,
d__11, d__12, d__13, d__14, d__15, d__16;
doublecomplex z__1, z__2, z__3, z__4;
/* Builtin functions */
double d_sign(doublereal *, doublereal *), z_abs(doublecomplex *);
void d_cnjg(doublecomplex *, doublecomplex *);
integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void);
double d_imag(doublecomplex *);
/* Local variables */
integer j, n, i1, n1, jc, nb, in, jr, ns, nbz;
doublereal ulp;
integer iadd, nmax;
doublereal temp1, temp2;
logical badnn;
doublereal dumma[4];
integer iinfo;
doublereal rmagn[4];
doublecomplex ctemp;
extern /* Subroutine */ int zgegs_(char *, char *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, doublecomplex *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublereal *, integer *), zget51_(integer *,
integer *, doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, doublereal *, doublereal *), zget52_(logical *,
integer *, doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
doublecomplex *, doublereal *, doublereal *);
integer nmats, jsize;
extern /* Subroutine */ int zgegv_(char *, char *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, doublecomplex *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublereal *, integer *);
integer nerrs, jtype, ntest;
extern /* Subroutine */ int dlabad_(doublereal *, doublereal *), zlatm4_(
integer *, integer *, integer *, integer *, logical *, doublereal
*, doublereal *, doublereal *, integer *, integer *,
doublecomplex *, integer *);
extern doublereal dlamch_(char *);
extern /* Subroutine */ int zunm2r_(char *, char *, integer *, integer *,
integer *, doublecomplex *, integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *);
doublereal safmin, safmax;
integer ioldsd[4];
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *);
extern /* Subroutine */ int alasvm_(char *, integer *, integer *, integer
*, integer *), xerbla_(char *, integer *),
zlarfg_(integer *, doublecomplex *, doublecomplex *, integer *,
doublecomplex *);
extern /* Double Complex */ VOID zlarnd_(doublecomplex *, integer *,
integer *);
extern /* Subroutine */ int zlacpy_(char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *),
zlaset_(char *, integer *, integer *, doublecomplex *,
doublecomplex *, doublecomplex *, integer *);
doublereal ulpinv;
integer lwkopt, mtypes, ntestt;
/* Fortran I/O blocks */
static cilist io___43 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___44 = { 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_9998, 0 };
static cilist io___51 = { 0, 0, 0, fmt_9997, 0 };
static cilist io___52 = { 0, 0, 0, fmt_9996, 0 };
static cilist io___53 = { 0, 0, 0, fmt_9995, 0 };
static cilist io___54 = { 0, 0, 0, fmt_9994, 0 };
static cilist io___55 = { 0, 0, 0, fmt_9993, 0 };
static cilist io___56 = { 0, 0, 0, fmt_9992, 0 };
static cilist io___57 = { 0, 0, 0, fmt_9991, 0 };
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* Purpose */
/* ======= */
/* ZDRVGG checks the nonsymmetric generalized eigenvalue driver */
/* routines. */
/* T T T */
/* ZGEGS factors A and B as Q S Z and Q T Z , where means */
/* transpose, T is upper triangular, S is in generalized Schur form */
/* (upper triangular), and Q and Z are unitary. It also */
/* computes the generalized eigenvalues (alpha(1),beta(1)), ..., */
/* (alpha(n),beta(n)), where alpha(j)=S(j,j) and beta(j)=T(j,j) -- */
/* thus, w(j) = alpha(j)/beta(j) is a root of the generalized */
/* eigenvalue problem */
/* det( A - w(j) B ) = 0 */
/* and m(j) = beta(j)/alpha(j) is a root of the essentially equivalent */
/* problem */
/* det( m(j) A - B ) = 0 */
/* ZGEGV computes the generalized eigenvalues (alpha(1),beta(1)), ..., */
/* (alpha(n),beta(n)), the matrix L whose columns contain the */
/* generalized left eigenvectors l, and the matrix R whose columns */
/* contain the generalized right eigenvectors r for the pair (A,B). */
/* When ZDRVGG 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 and compared with the threshhold THRESH: */
/* Results from ZGEGS: */
/* H */
/* (1) | A - Q S Z | / ( |A| n ulp ) */
/* H */
/* (2) | B - Q T Z | / ( |B| n ulp ) */
/* H */
/* (3) | I - QQ | / ( n ulp ) */
/* H */
/* (4) | I - ZZ | / ( n ulp ) */
/* (5) maximum over j of D(j) where: */
/* |alpha(j) - S(j,j)| |beta(j) - T(j,j)| */
/* D(j) = ------------------------ + ----------------------- */
/* max(|alpha(j)|,|S(j,j)|) max(|beta(j)|,|T(j,j)|) */
/* Results from ZGEGV: */
/* (6) max over all left eigenvalue/-vector pairs (beta/alpha,l) of */
/* | l**H * (beta A - alpha B) | / ( ulp max( |beta A|, |alpha B| ) ) */
/* where l**H is the conjugate tranpose of l. */
/* (7) max over all right eigenvalue/-vector pairs (beta/alpha,r) of */
/* | (beta A - alpha B) r | / ( ulp max( |beta A|, |alpha B| ) ) */
/* Test Matrices */
/* ---- -------- */
/* The sizes of the test matrices 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) ( 0, 0 ) (a pair of zero matrices) */
/* (2) ( I, 0 ) (an identity and a zero matrix) */
/* (3) ( 0, I ) (an identity and a zero matrix) */
/* (4) ( I, I ) (a pair of identity matrices) */
/* t t */
/* (5) ( J , J ) (a pair of transposed Jordan blocks) */
/* t ( I 0 ) */
/* (6) ( X, Y ) where X = ( J 0 ) and Y = ( t ) */
/* ( 0 I ) ( 0 J ) */
/* and I is a k x k identity and J a (k+1)x(k+1) */
/* Jordan block; k=(N-1)/2 */
/* (7) ( D, I ) where D is diag( 0, 1,..., N-1 ) (a diagonal */
/* matrix with those diagonal entries.) */
/* (8) ( I, D ) */
/* (9) ( big*D, small*I ) where "big" is near overflow and small=1/big */
/* (10) ( small*D, big*I ) */
/* (11) ( big*I, small*D ) */
/* (12) ( small*I, big*D ) */
/* (13) ( big*D, big*I ) */
/* (14) ( small*D, small*I ) */
/* (15) ( D1, D2 ) where D1 is diag( 0, 0, 1, ..., N-3, 0 ) and */
/* D2 is diag( 0, N-3, N-4,..., 1, 0, 0 ) */
/* t t */
/* (16) Q ( J , J ) Z where Q and Z are random unitary matrices. */
/* (17) Q ( T1, T2 ) Z where T1 and T2 are upper triangular matrices */
/* with random O(1) entries above the diagonal */
/* and diagonal entries diag(T1) = */
/* ( 0, 0, 1, ..., N-3, 0 ) and diag(T2) = */
/* ( 0, N-3, N-4,..., 1, 0, 0 ) */
/* (18) Q ( T1, T2 ) Z diag(T1) = ( 0, 0, 1, 1, s, ..., s, 0 ) */
/* diag(T2) = ( 0, 1, 0, 1,..., 1, 0 ) */
/* s = machine precision. */
/* (19) Q ( T1, T2 ) Z diag(T1)=( 0,0,1,1, 1-d, ..., 1-(N-5)*d=s, 0 ) */
/* diag(T2) = ( 0, 1, 0, 1, ..., 1, 0 ) */
/* N-5 */
/* (20) Q ( T1, T2 ) Z diag(T1)=( 0, 0, 1, 1, a, ..., a =s, 0 ) */
/* diag(T2) = ( 0, 1, 0, 1, ..., 1, 0, 0 ) */
/* (21) Q ( T1, T2 ) Z diag(T1)=( 0, 0, 1, r1, r2, ..., r(N-4), 0 ) */
/* diag(T2) = ( 0, 1, 0, 1, ..., 1, 0, 0 ) */
/* where r1,..., r(N-4) are random. */
/* (22) Q ( big*T1, small*T2 ) Z diag(T1) = ( 0, 0, 1, ..., N-3, 0 ) */
/* diag(T2) = ( 0, 1, ..., 1, 0, 0 ) */
/* (23) Q ( small*T1, big*T2 ) Z diag(T1) = ( 0, 0, 1, ..., N-3, 0 ) */
/* diag(T2) = ( 0, 1, ..., 1, 0, 0 ) */
/* (24) Q ( small*T1, small*T2 ) Z diag(T1) = ( 0, 0, 1, ..., N-3, 0 ) */
/* diag(T2) = ( 0, 1, ..., 1, 0, 0 ) */
/* (25) Q ( big*T1, big*T2 ) Z diag(T1) = ( 0, 0, 1, ..., N-3, 0 ) */
/* diag(T2) = ( 0, 1, ..., 1, 0, 0 ) */
/* (26) Q ( T1, T2 ) Z where T1 and T2 are random upper-triangular */
/* matrices. */
/* Arguments */
/* ========= */
/* NSIZES (input) INTEGER */
/* The number of sizes of matrices to use. If it is zero, */
/* ZDRVGG 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, ZDRVGG */
/* 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 ZDRVGG 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. */
/* THRSHN (input) DOUBLE PRECISION */
/* Threshhold for reporting eigenvector normalization error. */
/* If the normalization of any eigenvector differs from 1 by */
/* more than THRSHN*ulp, then a special error message will be */
/* printed. (This is handled separately from the other tests, */
/* since only a compiler or programming error should cause an */
/* error message, at least if THRSHN is at least 5--10.) */
/* 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) COMPLEX*16 array, dimension (LDA, max(NN)) */
/* Used to hold the original A matrix. Used as input only */
/* if NTYPES=MAXTYP+1, DOTYPE(1:MAXTYP)=.FALSE., and */
/* DOTYPE(MAXTYP+1)=.TRUE. */
/* LDA (input) INTEGER */
/* The leading dimension of A, B, S, T, S2, and T2. */
/* It must be at least 1 and at least max( NN ). */
/* B (input/workspace) COMPLEX*16 array, dimension (LDA, max(NN)) */
/* Used to hold the original B matrix. Used as input only */
/* if NTYPES=MAXTYP+1, DOTYPE(1:MAXTYP)=.FALSE., and */
/* DOTYPE(MAXTYP+1)=.TRUE. */
/* S (workspace) COMPLEX*16 array, dimension (LDA, max(NN)) */
/* The upper triangular matrix computed from A by ZGEGS. */
/* T (workspace) COMPLEX*16 array, dimension (LDA, max(NN)) */
/* The upper triangular matrix computed from B by ZGEGS. */
/* S2 (workspace) COMPLEX*16 array, dimension (LDA, max(NN)) */
/* The matrix computed from A by ZGEGV. This will be the */
/* Schur (upper triangular) form of some matrix related to A, */
/* but will not, in general, be the same as S. */
/* T2 (workspace) COMPLEX*16 array, dimension (LDA, max(NN)) */
/* The matrix computed from B by ZGEGV. This will be the */
/* Schur form of some matrix related to B, but will not, in */
/* general, be the same as T. */
/* Q (workspace) COMPLEX*16 array, dimension (LDQ, max(NN)) */
/* The (left) unitary matrix computed by ZGEGS. */
/* LDQ (input) INTEGER */
/* The leading dimension of Q, Z, VL, and VR. It must */
/* be at least 1 and at least max( NN ). */
/* Z (workspace) COMPLEX*16 array, dimension (LDQ, max(NN)) */
/* The (right) unitary matrix computed by ZGEGS. */
/* ALPHA1 (workspace) COMPLEX*16 array, dimension (max(NN)) */
/* BETA1 (workspace) COMPLEX*16 array, dimension (max(NN)) */
/* The generalized eigenvalues of (A,B) computed by ZGEGS. */
/* ALPHA1(k) / BETA1(k) is the k-th generalized eigenvalue of */
/* the matrices in A and B. */
/* ALPHA2 (workspace) COMPLEX*16 array, dimension (max(NN)) */
/* BETA2 (workspace) COMPLEX*16 array, dimension (max(NN)) */
/* The generalized eigenvalues of (A,B) computed by ZGEGV. */
/* ALPHA2(k) / BETA2(k) is the k-th generalized eigenvalue of */
/* the matrices in A and B. */
/* VL (workspace) COMPLEX*16 array, dimension (LDQ, max(NN)) */
/* The (lower triangular) left eigenvector matrix for the */
/* matrices in A and B. */
/* VR (workspace) COMPLEX*16 array, dimension (LDQ, max(NN)) */
/* The (upper triangular) right eigenvector matrix for the */
/* matrices in A and B. */
/* WORK (workspace) COMPLEX*16 array, dimension (LWORK) */
/* LWORK (input) INTEGER */
/* The number of entries in WORK. This must be at least */
/* MAX( 2*N, N*(NB+1), (k+1)*(2*k+N+1) ), where "k" is the */
/* sum of the blocksize and number-of-shifts for ZHGEQZ, and */
/* NB is the greatest of the blocksizes for ZGEQRF, ZUNMQR, */
/* and ZUNGQR. (The blocksizes and the number-of-shifts are */
/* retrieved through calls to ILAENV.) */
/* RWORK (workspace) DOUBLE PRECISION array, dimension (8*N) */
/* RESULT (output) DOUBLE PRECISION array, dimension (7) */
/* The values computed by the tests described above. */
/* The values are currently limited to 1/ulp, to avoid */
/* overflow. */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value. */
/* > 0: A routine returned an error code. INFO is the */
/* absolute value of the INFO value returned. */
/* ===================================================================== */
/* .. */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Statement Functions .. */
/* .. */
/* .. Statement Function definitions .. */
/* .. */
/* .. Data statements .. */
/* Parameter adjustments */
--nn;
--dotype;
--iseed;
t2_dim1 = *lda;
t2_offset = 1 + t2_dim1;
t2 -= t2_offset;
s2_dim1 = *lda;
s2_offset = 1 + s2_dim1;
s2 -= s2_offset;
t_dim1 = *lda;
t_offset = 1 + t_dim1;
t -= t_offset;
s_dim1 = *lda;
s_offset = 1 + s_dim1;
s -= s_offset;
b_dim1 = *lda;
b_offset = 1 + b_dim1;
b -= b_offset;
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
vr_dim1 = *ldq;
vr_offset = 1 + vr_dim1;
vr -= vr_offset;
vl_dim1 = *ldq;
vl_offset = 1 + vl_dim1;
vl -= vl_offset;
z_dim1 = *ldq;
z_offset = 1 + z_dim1;
z__ -= z_offset;
q_dim1 = *ldq;
q_offset = 1 + q_dim1;
q -= q_offset;
--alpha1;
--beta1;
--alpha2;
--beta2;
--work;
--rwork;
--result;
/* Function Body */
/* .. */
/* .. Executable Statements .. */
/* Check for errors */
*info = 0;
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: */
}
/* Maximum blocksize and shift -- we assume that blocksize and number */
/* of shifts are monotone increasing functions of N. */
/* Computing MAX */
i__1 = 1, i__2 = ilaenv_(&c__1, "ZGEQRF", " ", &nmax, &nmax, &c_n1, &c_n1), i__1 = max(i__1,i__2), i__2 = ilaenv_(&
c__1, "ZUNMQR", "LC", &nmax, &nmax, &nmax, &c_n1), i__1 = max(i__1,i__2), i__2 = ilaenv_(&c__1, "ZUNGQR",
" ", &nmax, &nmax, &nmax, &c_n1);
nb = max(i__1,i__2);
nbz = ilaenv_(&c__1, "ZHGEQZ", "SII", &nmax, &c__1, &nmax, &c__0);
ns = ilaenv_(&c__4, "ZHGEQZ", "SII", &nmax, &c__1, &nmax, &c__0);
i1 = nbz + ns;
/* Computing MAX */
i__1 = nmax << 1, i__2 = nmax * (nb + 1), i__1 = max(i__1,i__2), i__2 = ((
i1 << 1) + nmax + 1) * (i1 + 1);
lwkopt = max(i__1,i__2);
/* 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 (*ldq <= 1 || *ldq < nmax) {
*info = -19;
} else if (lwkopt > *lwork) {
*info = -30;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZDRVGG", &i__1);
return 0;
}
/* Quick return if possible */
if (*nsizes == 0 || *ntypes == 0) {
return 0;
}
ulp = dlamch_("Precision");
safmin = dlamch_("Safe minimum");
safmin /= ulp;
safmax = 1. / safmin;
dlabad_(&safmin, &safmax);
ulpinv = 1. / ulp;
/* The values RMAGN(2:3) depend on N, see below. */
rmagn[0] = 0.;
rmagn[1] = 1.;
/* Loop over sizes, types */
ntestt = 0;
nerrs = 0;
nmats = 0;
i__1 = *nsizes;
for (jsize = 1; jsize <= i__1; ++jsize) {
n = nn[jsize];
n1 = max(1,n);
rmagn[2] = safmax * ulp / (doublereal) n1;
rmagn[3] = safmin * ulpinv * n1;
if (*nsizes != 1) {
mtypes = min(26,*ntypes);
} else {
mtypes = min(27,*ntypes);
}
i__2 = mtypes;
for (jtype = 1; jtype <= i__2; ++jtype) {
if (! dotype[jtype]) {
goto L150;
}
++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 <= 7; ++j) {
result[j] = 0.;
/* L30: */
}
/* Compute A and B */
/* Description of control parameters: */
/* KZLASS: =1 means w/o rotation, =2 means w/ rotation, */
/* =3 means random. */
/* KATYPE: the "type" to be passed to ZLATM4 for computing A. */
/* KAZERO: the pattern of zeros on the diagonal for A: */
/* =1: ( xxx ), =2: (0, xxx ) =3: ( 0, 0, xxx, 0 ), */
/* =4: ( 0, xxx, 0, 0 ), =5: ( 0, 0, 1, xxx, 0 ), */
/* =6: ( 0, 1, 0, xxx, 0 ). (xxx means a string of */
/* non-zero entries.) */
/* KAMAGN: the magnitude of the matrix: =0: zero, =1: O(1), */
/* =2: large, =3: small. */
/* LASIGN: .TRUE. if the diagonal elements of A are to be */
/* multiplied by a random magnitude 1 number. */
/* KBTYPE, KBZERO, KBMAGN, IBSIGN: the same, but for B. */
/* KTRIAN: =0: don't fill in the upper triangle, =1: do. */
/* KZ1, KZ2, KADD: used to implement KAZERO and KBZERO. */
/* RMAGN: used to implement KAMAGN and KBMAGN. */
if (mtypes > 26) {
goto L110;
}
iinfo = 0;
if (kclass[jtype - 1] < 3) {
/* Generate A (w/o rotation) */
if ((i__3 = katype[jtype - 1], abs(i__3)) == 3) {
in = ((n - 1) / 2 << 1) + 1;
if (in != n) {
zlaset_("Full", &n, &n, &c_b1, &c_b1, &a[a_offset],
lda);
}
} else {
in = n;
}
zlatm4_(&katype[jtype - 1], &in, &kz1[kazero[jtype - 1] - 1],
&kz2[kazero[jtype - 1] - 1], &lasign[jtype - 1], &
rmagn[kamagn[jtype - 1]], &ulp, &rmagn[ktrian[jtype -
1] * kamagn[jtype - 1]], &c__2, &iseed[1], &a[
a_offset], lda);
iadd = kadd[kazero[jtype - 1] - 1];
if (iadd > 0 && iadd <= n) {
i__3 = iadd + iadd * a_dim1;
i__4 = kamagn[jtype - 1];
a[i__3].r = rmagn[i__4], a[i__3].i = 0.;
}
/* Generate B (w/o rotation) */
if ((i__3 = kbtype[jtype - 1], abs(i__3)) == 3) {
in = ((n - 1) / 2 << 1) + 1;
if (in != n) {
zlaset_("Full", &n, &n, &c_b1, &c_b1, &b[b_offset],
lda);
}
} else {
in = n;
}
zlatm4_(&kbtype[jtype - 1], &in, &kz1[kbzero[jtype - 1] - 1],
&kz2[kbzero[jtype - 1] - 1], &lbsign[jtype - 1], &
rmagn[kbmagn[jtype - 1]], &c_b39, &rmagn[ktrian[jtype
- 1] * kbmagn[jtype - 1]], &c__2, &iseed[1], &b[
b_offset], lda);
iadd = kadd[kbzero[jtype - 1] - 1];
if (iadd != 0 && iadd <= n) {
i__3 = iadd + iadd * b_dim1;
i__4 = kbmagn[jtype - 1];
b[i__3].r = rmagn[i__4], b[i__3].i = 0.;
}
if (kclass[jtype - 1] == 2 && n > 0) {
/* Include rotations */
/* Generate Q, Z as Householder transformations times */
/* a diagonal matrix. */
i__3 = n - 1;
for (jc = 1; jc <= i__3; ++jc) {
i__4 = n;
for (jr = jc; jr <= i__4; ++jr) {
i__5 = jr + jc * q_dim1;
zlarnd_(&z__1, &c__3, &iseed[1]);
q[i__5].r = z__1.r, q[i__5].i = z__1.i;
i__5 = jr + jc * z_dim1;
zlarnd_(&z__1, &c__3, &iseed[1]);
z__[i__5].r = z__1.r, z__[i__5].i = z__1.i;
/* L40: */
}
i__4 = n + 1 - jc;
zlarfg_(&i__4, &q[jc + jc * q_dim1], &q[jc + 1 + jc *
q_dim1], &c__1, &work[jc]);
i__4 = (n << 1) + jc;
i__5 = jc + jc * q_dim1;
d__2 = q[i__5].r;
d__1 = d_sign(&c_b39, &d__2);
work[i__4].r = d__1, work[i__4].i = 0.;
i__4 = jc + jc * q_dim1;
q[i__4].r = 1., q[i__4].i = 0.;
i__4 = n + 1 - jc;
zlarfg_(&i__4, &z__[jc + jc * z_dim1], &z__[jc + 1 +
jc * z_dim1], &c__1, &work[n + jc]);
i__4 = n * 3 + jc;
i__5 = jc + jc * z_dim1;
d__2 = z__[i__5].r;
d__1 = d_sign(&c_b39, &d__2);
work[i__4].r = d__1, work[i__4].i = 0.;
i__4 = jc + jc * z_dim1;
z__[i__4].r = 1., z__[i__4].i = 0.;
/* L50: */
}
zlarnd_(&z__1, &c__3, &iseed[1]);
ctemp.r = z__1.r, ctemp.i = z__1.i;
i__3 = n + n * q_dim1;
q[i__3].r = 1., q[i__3].i = 0.;
i__3 = n;
work[i__3].r = 0., work[i__3].i = 0.;
i__3 = n * 3;
d__1 = z_abs(&ctemp);
z__1.r = ctemp.r / d__1, z__1.i = ctemp.i / d__1;
work[i__3].r = z__1.r, work[i__3].i = z__1.i;
zlarnd_(&z__1, &c__3, &iseed[1]);
ctemp.r = z__1.r, ctemp.i = z__1.i;
i__3 = n + n * z_dim1;
z__[i__3].r = 1., z__[i__3].i = 0.;
i__3 = n << 1;
work[i__3].r = 0., work[i__3].i = 0.;
i__3 = n << 2;
d__1 = z_abs(&ctemp);
z__1.r = ctemp.r / d__1, z__1.i = ctemp.i / d__1;
work[i__3].r = z__1.r, work[i__3].i = z__1.i;
/* Apply the diagonal matrices */
i__3 = n;
for (jc = 1; jc <= i__3; ++jc) {
i__4 = n;
for (jr = 1; jr <= i__4; ++jr) {
i__5 = jr + jc * a_dim1;
i__6 = (n << 1) + jr;
d_cnjg(&z__3, &work[n * 3 + jc]);
z__2.r = work[i__6].r * z__3.r - work[i__6].i *
z__3.i, z__2.i = work[i__6].r * z__3.i +
work[i__6].i * z__3.r;
i__7 = jr + jc * a_dim1;
z__1.r = z__2.r * a[i__7].r - z__2.i * a[i__7].i,
z__1.i = z__2.r * a[i__7].i + z__2.i * a[
i__7].r;
a[i__5].r = z__1.r, a[i__5].i = z__1.i;
i__5 = jr + jc * b_dim1;
i__6 = (n << 1) + jr;
d_cnjg(&z__3, &work[n * 3 + jc]);
z__2.r = work[i__6].r * z__3.r - work[i__6].i *
z__3.i, z__2.i = work[i__6].r * z__3.i +
work[i__6].i * z__3.r;
i__7 = jr + jc * b_dim1;
z__1.r = z__2.r * b[i__7].r - z__2.i * b[i__7].i,
z__1.i = z__2.r * b[i__7].i + z__2.i * b[
i__7].r;
b[i__5].r = z__1.r, b[i__5].i = z__1.i;
/* L60: */
}
/* L70: */
}
i__3 = n - 1;
zunm2r_("L", "N", &n, &n, &i__3, &q[q_offset], ldq, &work[
1], &a[a_offset], lda, &work[(n << 1) + 1], &
iinfo);
if (iinfo != 0) {
goto L100;
}
i__3 = n - 1;
zunm2r_("R", "C", &n, &n, &i__3, &z__[z_offset], ldq, &
work[n + 1], &a[a_offset], lda, &work[(n << 1) +
1], &iinfo);
if (iinfo != 0) {
goto L100;
}
i__3 = n - 1;
zunm2r_("L", "N", &n, &n, &i__3, &q[q_offset], ldq, &work[
1], &b[b_offset], lda, &work[(n << 1) + 1], &
iinfo);
if (iinfo != 0) {
goto L100;
}
i__3 = n - 1;
zunm2r_("R", "C", &n, &n, &i__3, &z__[z_offset], ldq, &
work[n + 1], &b[b_offset], lda, &work[(n << 1) +
1], &iinfo);
if (iinfo != 0) {
goto L100;
}
}
} else {
/* Random matrices */
i__3 = n;
for (jc = 1; jc <= i__3; ++jc) {
i__4 = n;
for (jr = 1; jr <= i__4; ++jr) {
i__5 = jr + jc * a_dim1;
i__6 = kamagn[jtype - 1];
zlarnd_(&z__2, &c__4, &iseed[1]);
z__1.r = rmagn[i__6] * z__2.r, z__1.i = rmagn[i__6] *
z__2.i;
a[i__5].r = z__1.r, a[i__5].i = z__1.i;
i__5 = jr + jc * b_dim1;
i__6 = kbmagn[jtype - 1];
zlarnd_(&z__2, &c__4, &iseed[1]);
z__1.r = rmagn[i__6] * z__2.r, z__1.i = rmagn[i__6] *
z__2.i;
b[i__5].r = z__1.r, b[i__5].i = z__1.i;
/* L80: */
}
/* L90: */
}
}
L100:
if (iinfo != 0) {
io___43.ciunit = *nounit;
s_wsfe(&io___43);
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;
}
L110:
/* Call ZGEGS to compute H, T, Q, Z, alpha, and beta. */
zlacpy_(" ", &n, &n, &a[a_offset], lda, &s[s_offset], lda);
zlacpy_(" ", &n, &n, &b[b_offset], lda, &t[t_offset], lda);
ntest = 1;
result[1] = ulpinv;
zgegs_("V", "V", &n, &s[s_offset], lda, &t[t_offset], lda, &
alpha1[1], &beta1[1], &q[q_offset], ldq, &z__[z_offset],
ldq, &work[1], lwork, &rwork[1], &iinfo);
if (iinfo != 0) {
io___44.ciunit = *nounit;
s_wsfe(&io___44);
do_fio(&c__1, "ZGEGS", (ftnlen)5);
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 L130;
}
ntest = 4;
/* Do tests 1--4 */
zget51_(&c__1, &n, &a[a_offset], lda, &s[s_offset], lda, &q[
q_offset], ldq, &z__[z_offset], ldq, &work[1], &rwork[1],
&result[1]);
zget51_(&c__1, &n, &b[b_offset], lda, &t[t_offset], lda, &q[
q_offset], ldq, &z__[z_offset], ldq, &work[1], &rwork[1],
&result[2]);
zget51_(&c__3, &n, &b[b_offset], lda, &t[t_offset], lda, &q[
q_offset], ldq, &q[q_offset], ldq, &work[1], &rwork[1], &
result[3]);
zget51_(&c__3, &n, &b[b_offset], lda, &t[t_offset], lda, &z__[
z_offset], ldq, &z__[z_offset], ldq, &work[1], &rwork[1],
&result[4]);
/* Do test 5: compare eigenvalues with diagonals. */
temp1 = 0.;
i__3 = n;
for (j = 1; j <= i__3; ++j) {
i__4 = j;
i__5 = j + j * s_dim1;
z__2.r = alpha1[i__4].r - s[i__5].r, z__2.i = alpha1[i__4].i
- s[i__5].i;
z__1.r = z__2.r, z__1.i = z__2.i;
i__6 = j;
i__7 = j + j * t_dim1;
z__4.r = beta1[i__6].r - t[i__7].r, z__4.i = beta1[i__6].i -
t[i__7].i;
z__3.r = z__4.r, z__3.i = z__4.i;
/* Computing MAX */
i__8 = j;
i__9 = j + j * s_dim1;
d__13 = safmin, d__14 = (d__1 = alpha1[i__8].r, abs(d__1)) + (
d__2 = d_imag(&alpha1[j]), abs(d__2)), d__13 = max(
d__13,d__14), d__14 = (d__3 = s[i__9].r, abs(d__3)) +
(d__4 = d_imag(&s[j + j * s_dim1]), abs(d__4));
/* Computing MAX */
i__10 = j;
i__11 = j + j * t_dim1;
d__15 = safmin, d__16 = (d__5 = beta1[i__10].r, abs(d__5)) + (
d__6 = d_imag(&beta1[j]), abs(d__6)), d__15 = max(
d__15,d__16), d__16 = (d__7 = t[i__11].r, abs(d__7))
+ (d__8 = d_imag(&t[j + j * t_dim1]), abs(d__8));
temp2 = (((d__9 = z__1.r, abs(d__9)) + (d__10 = d_imag(&z__1),
abs(d__10))) / max(d__13,d__14) + ((d__11 = z__3.r,
abs(d__11)) + (d__12 = d_imag(&z__3), abs(d__12))) /
max(d__15,d__16)) / ulp;
temp1 = max(temp1,temp2);
/* L120: */
}
result[5] = temp1;
/* Call ZGEGV to compute S2, T2, VL, and VR, do tests. */
/* Eigenvalues and Eigenvectors */
zlacpy_(" ", &n, &n, &a[a_offset], lda, &s2[s2_offset], lda);
zlacpy_(" ", &n, &n, &b[b_offset], lda, &t2[t2_offset], lda);
ntest = 6;
result[6] = ulpinv;
zgegv_("V", "V", &n, &s2[s2_offset], lda, &t2[t2_offset], lda, &
alpha2[1], &beta2[1], &vl[vl_offset], ldq, &vr[vr_offset],
ldq, &work[1], lwork, &rwork[1], &iinfo);
if (iinfo != 0) {
io___47.ciunit = *nounit;
s_wsfe(&io___47);
do_fio(&c__1, "ZGEGV", (ftnlen)5);
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 L130;
}
ntest = 7;
/* Do Tests 6 and 7 */
zget52_(&c_true, &n, &a[a_offset], lda, &b[b_offset], lda, &vl[
vl_offset], ldq, &alpha2[1], &beta2[1], &work[1], &rwork[
1], dumma);
result[6] = dumma[0];
if (dumma[1] > *thrshn) {
io___49.ciunit = *nounit;
s_wsfe(&io___49);
do_fio(&c__1, "Left", (ftnlen)4);
do_fio(&c__1, "ZGEGV", (ftnlen)5);
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();
}
zget52_(&c_false, &n, &a[a_offset], lda, &b[b_offset], lda, &vr[
vr_offset], ldq, &alpha2[1], &beta2[1], &work[1], &rwork[
1], dumma);
result[7] = dumma[0];
if (dumma[1] > *thresh) {
io___50.ciunit = *nounit;
s_wsfe(&io___50);
do_fio(&c__1, "Right", (ftnlen)5);
do_fio(&c__1, "ZGEGV", (ftnlen)5);
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();
}
/* End of Loop -- Check for RESULT(j) > THRESH */
L130:
ntestt += ntest;
/* Print out tests which fail. */
i__3 = ntest;
for (jr = 1; jr <= i__3; ++jr) {
if (result[jr] >= *thresh) {
/* If this is the first test to fail, */
/* print a header to the data file. */
if (nerrs == 0) {
io___51.ciunit = *nounit;
s_wsfe(&io___51);
do_fio(&c__1, "ZGG", (ftnlen)3);
e_wsfe();
/* Matrix types */
io___52.ciunit = *nounit;
s_wsfe(&io___52);
e_wsfe();
io___53.ciunit = *nounit;
s_wsfe(&io___53);
e_wsfe();
io___54.ciunit = *nounit;
s_wsfe(&io___54);
do_fio(&c__1, "Unitary", (ftnlen)7);
e_wsfe();
/* Tests performed */
io___55.ciunit = *nounit;
s_wsfe(&io___55);
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 <= 5; ++j) {
do_fio(&c__1, "*", (ftnlen)1);
}
e_wsfe();
}
++nerrs;
if (result[jr] < 1e4) {
io___56.ciunit = *nounit;
s_wsfe(&io___56);
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer))
;
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&jr, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&result[jr], (ftnlen)sizeof(
doublereal));
e_wsfe();
} else {
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__4, (char *)&ioldsd[0], (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&jr, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&result[jr], (ftnlen)sizeof(
doublereal));
e_wsfe();
}
}
/* L140: */
}
L150:
;
}
/* L160: */
}
/* Summary */
alasvm_("ZGG", nounit, &nerrs, &ntestt, &c__0);
return 0;
/* End of ZDRVGG */
} /* zdrvgg_ */
/* Subroutine */ int zdrges_(integer *nsizes, integer *nn, integer *ntypes,
logical *dotype, integer *iseed, doublereal *thresh, integer *nounit,
doublecomplex *a, integer *lda, doublecomplex *b, doublecomplex *s,
doublecomplex *t, doublecomplex *q, integer *ldq, doublecomplex *z__,
doublecomplex *alpha, doublecomplex *beta, doublecomplex *work,
integer *lwork, doublereal *rwork, doublereal *result, logical *bwork,
integer *info)
{
/* Initialized data */
static integer kclass[26] = { 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,
2,2,2,3 };
static integer kbmagn[26] = { 1,1,1,1,1,1,1,1,3,2,3,2,2,3,1,1,1,1,1,1,1,3,
2,3,2,1 };
static integer ktrian[26] = { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,
1,1,1,1 };
static logical lasign[26] = { FALSE_,FALSE_,FALSE_,FALSE_,FALSE_,FALSE_,
TRUE_,FALSE_,TRUE_,TRUE_,FALSE_,FALSE_,TRUE_,TRUE_,TRUE_,FALSE_,
TRUE_,FALSE_,FALSE_,FALSE_,TRUE_,TRUE_,TRUE_,TRUE_,TRUE_,FALSE_ };
static logical lbsign[26] = { FALSE_,FALSE_,FALSE_,FALSE_,FALSE_,FALSE_,
FALSE_,TRUE_,FALSE_,FALSE_,TRUE_,TRUE_,FALSE_,FALSE_,TRUE_,FALSE_,
TRUE_,FALSE_,FALSE_,FALSE_,FALSE_,FALSE_,FALSE_,FALSE_,FALSE_,
FALSE_ };
static integer kz1[6] = { 0,1,2,1,3,3 };
static integer kz2[6] = { 0,0,1,2,1,1 };
static integer kadd[6] = { 0,0,0,0,3,2 };
static integer katype[26] = { 0,1,0,1,2,3,4,1,4,4,1,1,4,4,4,2,4,5,8,7,9,4,
4,4,4,0 };
static integer kbtype[26] = { 0,0,1,1,2,-3,1,4,1,1,4,4,1,1,-4,2,-4,8,8,8,
8,8,8,8,8,0 };
static integer kazero[26] = { 1,1,1,1,1,1,2,1,2,2,1,1,2,2,3,1,3,5,5,5,5,3,
3,3,3,1 };
static integer kbzero[26] = { 1,1,1,1,1,1,1,2,1,1,2,2,1,1,4,1,4,6,6,6,6,4,
4,4,4,1 };
static integer kamagn[26] = { 1,1,1,1,1,1,1,1,2,3,2,3,2,3,1,1,1,1,1,1,1,2,
3,3,2,1 };
/* Format strings */
static char fmt_9999[] = "(\002 ZDRGES: \002,a,\002 returned INFO=\002,i"
"6,\002.\002,/9x,\002N=\002,i6,\002, JTYPE=\002,i6,\002, ISEED="
"(\002,4(i4,\002,\002),i5,\002)\002)";
static char fmt_9998[] = "(\002 ZDRGES: S not in Schur form at eigenvalu"
"e \002,i6,\002.\002,/9x,\002N=\002,i6,\002, JTYPE=\002,i6,\002, "
"ISEED=(\002,3(i5,\002,\002),i5,\002)\002)";
static char fmt_9997[] = "(/1x,a3,\002 -- Complex Generalized Schur from"
" problem \002,\002driver\002)";
static char fmt_9996[] = "(\002 Matrix types (see ZDRGES for details):"
" \002)";
static char fmt_9995[] = "(\002 Special Matrices:\002,23x,\002(J'=transp"
"osed Jordan block)\002,/\002 1=(0,0) 2=(I,0) 3=(0,I) 4=(I,I"
") 5=(J',J') \002,\0026=(diag(J',I), diag(I,J'))\002,/\002 Diag"
"onal Matrices: ( \002,\002D=diag(0,1,2,...) )\002,/\002 7=(D,"
"I) 9=(large*D, small*I\002,\002) 11=(large*I, small*D) 13=(l"
"arge*D, large*I)\002,/\002 8=(I,D) 10=(small*D, large*I) 12="
"(small*I, large*D) \002,\002 14=(small*D, small*I)\002,/\002 15"
"=(D, reversed D)\002)";
static char fmt_9994[] = "(\002 Matrices Rotated by Random \002,a,\002 M"
"atrices U, V:\002,/\002 16=Transposed Jordan Blocks "
" 19=geometric \002,\002alpha, beta=0,1\002,/\002 17=arithm. alp"
"ha&beta \002,\002 20=arithmetic alpha, beta=0,"
"1\002,/\002 18=clustered \002,\002alpha, beta=0,1 21"
"=random alpha, beta=0,1\002,/\002 Large & Small Matrices:\002,"
"/\002 22=(large, small) \002,\00223=(small,large) 24=(smal"
"l,small) 25=(large,large)\002,/\002 26=random O(1) matrices"
".\002)";
static char fmt_9993[] = "(/\002 Tests performed: (S is Schur, T is tri"
"angular, \002,\002Q and Z are \002,a,\002,\002,/19x,\002l and r "
"are the appropriate left and right\002,/19x,\002eigenvectors, re"
"sp., a is alpha, b is beta, and\002,/19x,a,\002 means \002,a,"
"\002.)\002,/\002 Without ordering: \002,/\002 1 = | A - Q S "
"Z\002,a,\002 | / ( |A| n ulp ) 2 = | B - Q T Z\002,a,\002 |"
" / ( |B| n ulp )\002,/\002 3 = | I - QQ\002,a,\002 | / ( n ulp "
") 4 = | I - ZZ\002,a,\002 | / ( n ulp )\002,/\002 5"
" = A is in Schur form S\002,/\002 6 = difference between (alpha"
",beta)\002,\002 and diagonals of (S,T)\002,/\002 With ordering:"
" \002,/\002 7 = | (A,B) - Q (S,T) Z\002,a,\002 | / ( |(A,B)| n "
"ulp )\002,/\002 8 = | I - QQ\002,a,\002 | / ( n ulp ) "
" 9 = | I - ZZ\002,a,\002 | / ( n ulp )\002,/\002 10 = A is in "
"Schur form S\002,/\002 11 = difference between (alpha,beta) and "
"diagonals\002,\002 of (S,T)\002,/\002 12 = SDIM is the correct n"
"umber of \002,\002selected eigenvalues\002,/)";
static char fmt_9992[] = "(\002 Matrix order=\002,i5,\002, type=\002,i2"
",\002, seed=\002,4(i4,\002,\002),\002 result \002,i2,\002 is\002"
",0p,f8.2)";
static char fmt_9991[] = "(\002 Matrix order=\002,i5,\002, type=\002,i2"
",\002, seed=\002,4(i4,\002,\002),\002 result \002,i2,\002 is\002"
",1p,d10.3)";
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, q_dim1, q_offset, s_dim1,
s_offset, t_dim1, t_offset, z_dim1, z_offset, i__1, i__2, i__3,
i__4, i__5, i__6, i__7, i__8, i__9, i__10, i__11;
doublereal d__1, d__2, d__3, d__4, d__5, d__6, d__7, d__8, d__9, d__10,
d__11, d__12, d__13, d__14, d__15, d__16;
doublecomplex z__1, z__2, z__3, z__4;
/* Local variables */
integer i__, j, n, n1, jc, nb, in, jr;
doublereal ulp;
integer iadd, sdim, nmax, rsub;
char sort[1];
doublereal temp1, temp2;
logical badnn;
integer iinfo;
doublereal rmagn[4];
doublecomplex ctemp;
extern /* Subroutine */ int zget51_(integer *, integer *, doublecomplex *,
integer *, doublecomplex *, integer *, doublecomplex *, integer *
, doublecomplex *, integer *, doublecomplex *, doublereal *,
doublereal *), zgges_(char *, char *, char *, L_fp, integer *,
doublecomplex *, integer *, doublecomplex *, integer *, integer *,
doublecomplex *, doublecomplex *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublereal *, logical *, integer *);
integer nmats, jsize;
extern /* Subroutine */ int zget54_(integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, doublereal *);
integer nerrs, jtype, ntest, isort;
extern /* Subroutine */ int dlabad_(doublereal *, doublereal *), zlatm4_(
integer *, integer *, integer *, integer *, logical *, doublereal
*, doublereal *, doublereal *, integer *, integer *,
doublecomplex *, integer *);
logical ilabad;
extern doublereal dlamch_(char *);
extern /* Subroutine */ int zunm2r_(char *, char *, integer *, integer *,
integer *, doublecomplex *, integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *);
doublereal safmin, safmax;
integer knteig, ioldsd[4];
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *);
extern /* Subroutine */ int alasvm_(char *, integer *, integer *, integer
*, integer *), xerbla_(char *, integer *),
zlarfg_(integer *, doublecomplex *, doublecomplex *, integer *,
doublecomplex *);
extern /* Double Complex */ void zlarnd_(doublecomplex *, integer *,
integer *);
extern /* Subroutine */ int zlacpy_(char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *),
zlaset_(char *, integer *, integer *, doublecomplex *,
doublecomplex *, doublecomplex *, integer *);
extern logical zlctes_(doublecomplex *, doublecomplex *);
integer minwrk, maxwrk;
doublereal ulpinv;
integer mtypes, ntestt;
/* Fortran I/O blocks */
static cilist io___41 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___47 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___51 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___53 = { 0, 0, 0, fmt_9997, 0 };
static cilist io___54 = { 0, 0, 0, fmt_9996, 0 };
static cilist io___55 = { 0, 0, 0, fmt_9995, 0 };
static cilist io___56 = { 0, 0, 0, fmt_9994, 0 };
static cilist io___57 = { 0, 0, 0, fmt_9993, 0 };
static cilist io___58 = { 0, 0, 0, fmt_9992, 0 };
static cilist io___59 = { 0, 0, 0, fmt_9991, 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 */
/* ======= */
/* ZDRGES checks the nonsymmetric generalized eigenvalue (Schur form) */
/* problem driver ZGGES. */
/* ZGGES factors A and B as Q*S*Z' and Q*T*Z' , where ' means conjugate */
/* transpose, S and T are upper triangular (i.e., in generalized Schur */
/* form), and Q and Z are unitary. It also computes the generalized */
/* eigenvalues (alpha(j),beta(j)), j=1,...,n. Thus, */
/* w(j) = alpha(j)/beta(j) is a root of the characteristic equation */
/* det( A - w(j) B ) = 0 */
/* Optionally it also reorder the eigenvalues so that a selected */
/* cluster of eigenvalues appears in the leading diagonal block of the */
/* Schur forms. */
/* When ZDRGES 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, a pair of matrices (A, B) will be generated */
/* and used for testing. For each matrix pair, the following 13 tests */
/* will be performed and compared with the threshhold THRESH except */
/* the tests (5), (11) and (13). */
/* (1) | A - Q S Z' | / ( |A| n ulp ) (no sorting of eigenvalues) */
/* (2) | B - Q T Z' | / ( |B| n ulp ) (no sorting of eigenvalues) */
/* (3) | I - QQ' | / ( n ulp ) (no sorting of eigenvalues) */
/* (4) | I - ZZ' | / ( n ulp ) (no sorting of eigenvalues) */
/* (5) if A is in Schur form (i.e. triangular form) (no sorting of */
/* eigenvalues) */
/* (6) if eigenvalues = diagonal elements of the Schur form (S, T), */
/* i.e., test the maximum over j of D(j) where: */
/* |alpha(j) - S(j,j)| |beta(j) - T(j,j)| */
/* D(j) = ------------------------ + ----------------------- */
/* max(|alpha(j)|,|S(j,j)|) max(|beta(j)|,|T(j,j)|) */
/* (no sorting of eigenvalues) */
/* (7) | (A,B) - Q (S,T) Z' | / ( |(A,B)| n ulp ) */
/* (with sorting of eigenvalues). */
/* (8) | I - QQ' | / ( n ulp ) (with sorting of eigenvalues). */
/* (9) | I - ZZ' | / ( n ulp ) (with sorting of eigenvalues). */
/* (10) if A is in Schur form (i.e. quasi-triangular form) */
/* (with sorting of eigenvalues). */
/* (11) if eigenvalues = diagonal elements of the Schur form (S, T), */
/* i.e. test the maximum over j of D(j) where: */
/* |alpha(j) - S(j,j)| |beta(j) - T(j,j)| */
/* D(j) = ------------------------ + ----------------------- */
/* max(|alpha(j)|,|S(j,j)|) max(|beta(j)|,|T(j,j)|) */
/* (with sorting of eigenvalues). */
/* (12) if sorting worked and SDIM is the number of eigenvalues */
/* which were CELECTed. */
/* Test Matrices */
/* ============= */
/* The sizes of the test matrices 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) ( 0, 0 ) (a pair of zero matrices) */
/* (2) ( I, 0 ) (an identity and a zero matrix) */
/* (3) ( 0, I ) (an identity and a zero matrix) */
/* (4) ( I, I ) (a pair of identity matrices) */
/* t t */
/* (5) ( J , J ) (a pair of transposed Jordan blocks) */
/* t ( I 0 ) */
/* (6) ( X, Y ) where X = ( J 0 ) and Y = ( t ) */
/* ( 0 I ) ( 0 J ) */
/* and I is a k x k identity and J a (k+1)x(k+1) */
/* Jordan block; k=(N-1)/2 */
/* (7) ( D, I ) where D is diag( 0, 1,..., N-1 ) (a diagonal */
/* matrix with those diagonal entries.) */
/* (8) ( I, D ) */
/* (9) ( big*D, small*I ) where "big" is near overflow and small=1/big */
/* (10) ( small*D, big*I ) */
/* (11) ( big*I, small*D ) */
/* (12) ( small*I, big*D ) */
/* (13) ( big*D, big*I ) */
/* (14) ( small*D, small*I ) */
/* (15) ( D1, D2 ) where D1 is diag( 0, 0, 1, ..., N-3, 0 ) and */
/* D2 is diag( 0, N-3, N-4,..., 1, 0, 0 ) */
/* t t */
/* (16) Q ( J , J ) Z where Q and Z are random orthogonal matrices. */
/* (17) Q ( T1, T2 ) Z where T1 and T2 are upper triangular matrices */
/* with random O(1) entries above the diagonal */
/* and diagonal entries diag(T1) = */
/* ( 0, 0, 1, ..., N-3, 0 ) and diag(T2) = */
/* ( 0, N-3, N-4,..., 1, 0, 0 ) */
/* (18) Q ( T1, T2 ) Z diag(T1) = ( 0, 0, 1, 1, s, ..., s, 0 ) */
/* diag(T2) = ( 0, 1, 0, 1,..., 1, 0 ) */
/* s = machine precision. */
/* (19) Q ( T1, T2 ) Z diag(T1)=( 0,0,1,1, 1-d, ..., 1-(N-5)*d=s, 0 ) */
/* diag(T2) = ( 0, 1, 0, 1, ..., 1, 0 ) */
/* N-5 */
/* (20) Q ( T1, T2 ) Z diag(T1)=( 0, 0, 1, 1, a, ..., a =s, 0 ) */
/* diag(T2) = ( 0, 1, 0, 1, ..., 1, 0, 0 ) */
/* (21) Q ( T1, T2 ) Z diag(T1)=( 0, 0, 1, r1, r2, ..., r(N-4), 0 ) */
/* diag(T2) = ( 0, 1, 0, 1, ..., 1, 0, 0 ) */
/* where r1,..., r(N-4) are random. */
/* (22) Q ( big*T1, small*T2 ) Z diag(T1) = ( 0, 0, 1, ..., N-3, 0 ) */
/* diag(T2) = ( 0, 1, ..., 1, 0, 0 ) */
/* (23) Q ( small*T1, big*T2 ) Z diag(T1) = ( 0, 0, 1, ..., N-3, 0 ) */
/* diag(T2) = ( 0, 1, ..., 1, 0, 0 ) */
/* (24) Q ( small*T1, small*T2 ) Z diag(T1) = ( 0, 0, 1, ..., N-3, 0 ) */
/* diag(T2) = ( 0, 1, ..., 1, 0, 0 ) */
/* (25) Q ( big*T1, big*T2 ) Z diag(T1) = ( 0, 0, 1, ..., N-3, 0 ) */
/* diag(T2) = ( 0, 1, ..., 1, 0, 0 ) */
/* (26) Q ( T1, T2 ) Z where T1 and T2 are random upper-triangular */
/* matrices. */
/* Arguments */
/* ========= */
/* NSIZES (input) INTEGER */
/* The number of sizes of matrices to use. If it is zero, */
/* DDRGES does nothing. NSIZES >= 0. */
/* NN (input) INTEGER array, dimension (NSIZES) */
/* An array containing the sizes to be used for the matrices. */
/* Zero values will be skipped. NN >= 0. */
/* NTYPES (input) INTEGER */
/* The number of elements in DOTYPE. If it is zero, DDRGES */
/* 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 on input. */
/* 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 DDRGES 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. THRESH >= 0. */
/* 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) COMPLEX*16 array, dimension(LDA, max(NN)) */
/* Used to hold the original A matrix. Used as input only */
/* if NTYPES=MAXTYP+1, DOTYPE(1:MAXTYP)=.FALSE., and */
/* DOTYPE(MAXTYP+1)=.TRUE. */
/* LDA (input) INTEGER */
/* The leading dimension of A, B, S, and T. */
/* It must be at least 1 and at least max( NN ). */
/* B (input/workspace) COMPLEX*16 array, dimension(LDA, max(NN)) */
/* Used to hold the original B matrix. Used as input only */
/* if NTYPES=MAXTYP+1, DOTYPE(1:MAXTYP)=.FALSE., and */
/* DOTYPE(MAXTYP+1)=.TRUE. */
/* S (workspace) COMPLEX*16 array, dimension (LDA, max(NN)) */
/* The Schur form matrix computed from A by ZGGES. On exit, S */
/* contains the Schur form matrix corresponding to the matrix */
/* in A. */
/* T (workspace) COMPLEX*16 array, dimension (LDA, max(NN)) */
/* The upper triangular matrix computed from B by ZGGES. */
/* Q (workspace) COMPLEX*16 array, dimension (LDQ, max(NN)) */
/* The (left) orthogonal matrix computed by ZGGES. */
/* LDQ (input) INTEGER */
/* The leading dimension of Q and Z. It must */
/* be at least 1 and at least max( NN ). */
/* Z (workspace) COMPLEX*16 array, dimension( LDQ, max(NN) ) */
/* The (right) orthogonal matrix computed by ZGGES. */
/* ALPHA (workspace) COMPLEX*16 array, dimension (max(NN)) */
/* BETA (workspace) COMPLEX*16 array, dimension (max(NN)) */
/* The generalized eigenvalues of (A,B) computed by ZGGES. */
/* ALPHA(k) / BETA(k) is the k-th generalized eigenvalue of A */
/* and B. */
/* WORK (workspace) COMPLEX*16 array, dimension (LWORK) */
/* LWORK (input) INTEGER */
/* The dimension of the array WORK. LWORK >= 3*N*N. */
/* RWORK (workspace) DOUBLE PRECISION array, dimension ( 8*N ) */
/* Real workspace. */
/* RESULT (output) DOUBLE PRECISION array, dimension (15) */
/* The values computed by the tests described above. */
/* The values are currently limited to 1/ulp, to avoid overflow. */
/* BWORK (workspace) LOGICAL array, dimension (N) */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value. */
/* > 0: A routine returned an error code. INFO is the */
/* absolute value of the INFO value returned. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Statement Functions .. */
/* .. */
/* .. Statement Function definitions .. */
/* .. */
/* .. Data statements .. */
/* Parameter adjustments */
--nn;
--dotype;
--iseed;
t_dim1 = *lda;
t_offset = 1 + t_dim1;
t -= t_offset;
s_dim1 = *lda;
s_offset = 1 + s_dim1;
s -= s_offset;
b_dim1 = *lda;
b_offset = 1 + b_dim1;
b -= b_offset;
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
z_dim1 = *ldq;
z_offset = 1 + z_dim1;
z__ -= z_offset;
q_dim1 = *ldq;
q_offset = 1 + q_dim1;
q -= q_offset;
--alpha;
--beta;
--work;
--rwork;
--result;
--bwork;
/* Function Body */
/* .. */
/* .. Executable Statements .. */
/* Check for errors */
*info = 0;
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: */
}
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 (*ldq <= 1 || *ldq < nmax) {
*info = -14;
}
/* Compute workspace */
/* (Note: Comments in the code beginning "Workspace:" describe the */
/* minimal amount of workspace needed at that point in the code, */
/* as well as the preferred amount for good performance. */
/* NB refers to the optimal block size for the immediately */
/* following subroutine, as returned by ILAENV. */
minwrk = 1;
if (*info == 0 && *lwork >= 1) {
minwrk = nmax * 3 * nmax;
/* Computing MAX */
i__1 = 1, i__2 = ilaenv_(&c__1, "ZGEQRF", " ", &nmax, &nmax, &c_n1, &
c_n1), i__1 = max(i__1,i__2), i__2 =
ilaenv_(&c__1, "ZUNMQR", "LC", &nmax, &nmax, &nmax, &c_n1), i__1 = max(i__1,i__2), i__2 = ilaenv_(&
c__1, "ZUNGQR", " ", &nmax, &nmax, &nmax, &c_n1);
nb = max(i__1,i__2);
/* Computing MAX */
i__1 = nmax + nmax * nb, i__2 = nmax * 3 * nmax;
maxwrk = max(i__1,i__2);
work[1].r = (doublereal) maxwrk, work[1].i = 0.;
}
if (*lwork < minwrk) {
*info = -19;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZDRGES", &i__1);
return 0;
}
/* Quick return if possible */
if (*nsizes == 0 || *ntypes == 0) {
return 0;
}
ulp = dlamch_("Precision");
safmin = dlamch_("Safe minimum");
safmin /= ulp;
safmax = 1. / safmin;
dlabad_(&safmin, &safmax);
ulpinv = 1. / ulp;
/* The values RMAGN(2:3) depend on N, see below. */
rmagn[0] = 0.;
rmagn[1] = 1.;
/* Loop over matrix sizes */
ntestt = 0;
nerrs = 0;
nmats = 0;
i__1 = *nsizes;
for (jsize = 1; jsize <= i__1; ++jsize) {
n = nn[jsize];
n1 = max(1,n);
rmagn[2] = safmax * ulp / (doublereal) n1;
rmagn[3] = safmin * ulpinv * (doublereal) n1;
if (*nsizes != 1) {
mtypes = min(26,*ntypes);
} else {
mtypes = min(27,*ntypes);
}
/* Loop over matrix types */
i__2 = mtypes;
for (jtype = 1; jtype <= i__2; ++jtype) {
if (! dotype[jtype]) {
goto L180;
}
++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 <= 13; ++j) {
result[j] = 0.;
/* L30: */
}
/* Generate test matrices A and B */
/* Description of control parameters: */
/* KZLASS: =1 means w/o rotation, =2 means w/ rotation, */
/* =3 means random. */
/* KATYPE: the "type" to be passed to ZLATM4 for computing A. */
/* KAZERO: the pattern of zeros on the diagonal for A: */
/* =1: ( xxx ), =2: (0, xxx ) =3: ( 0, 0, xxx, 0 ), */
/* =4: ( 0, xxx, 0, 0 ), =5: ( 0, 0, 1, xxx, 0 ), */
/* =6: ( 0, 1, 0, xxx, 0 ). (xxx means a string of */
/* non-zero entries.) */
/* KAMAGN: the magnitude of the matrix: =0: zero, =1: O(1), */
/* =2: large, =3: small. */
/* LASIGN: .TRUE. if the diagonal elements of A are to be */
/* multiplied by a random magnitude 1 number. */
/* KBTYPE, KBZERO, KBMAGN, LBSIGN: the same, but for B. */
/* KTRIAN: =0: don't fill in the upper triangle, =1: do. */
/* KZ1, KZ2, KADD: used to implement KAZERO and KBZERO. */
/* RMAGN: used to implement KAMAGN and KBMAGN. */
if (mtypes > 26) {
goto L110;
}
iinfo = 0;
if (kclass[jtype - 1] < 3) {
/* Generate A (w/o rotation) */
if ((i__3 = katype[jtype - 1], abs(i__3)) == 3) {
in = ((n - 1) / 2 << 1) + 1;
if (in != n) {
zlaset_("Full", &n, &n, &c_b1, &c_b1, &a[a_offset],
lda);
}
} else {
in = n;
}
zlatm4_(&katype[jtype - 1], &in, &kz1[kazero[jtype - 1] - 1],
&kz2[kazero[jtype - 1] - 1], &lasign[jtype - 1], &
rmagn[kamagn[jtype - 1]], &ulp, &rmagn[ktrian[jtype -
1] * kamagn[jtype - 1]], &c__2, &iseed[1], &a[
a_offset], lda);
iadd = kadd[kazero[jtype - 1] - 1];
if (iadd > 0 && iadd <= n) {
i__3 = iadd + iadd * a_dim1;
i__4 = kamagn[jtype - 1];
a[i__3].r = rmagn[i__4], a[i__3].i = 0.;
}
/* Generate B (w/o rotation) */
if ((i__3 = kbtype[jtype - 1], abs(i__3)) == 3) {
in = ((n - 1) / 2 << 1) + 1;
if (in != n) {
zlaset_("Full", &n, &n, &c_b1, &c_b1, &b[b_offset],
lda);
}
} else {
in = n;
}
zlatm4_(&kbtype[jtype - 1], &in, &kz1[kbzero[jtype - 1] - 1],
&kz2[kbzero[jtype - 1] - 1], &lbsign[jtype - 1], &
rmagn[kbmagn[jtype - 1]], &c_b29, &rmagn[ktrian[jtype
- 1] * kbmagn[jtype - 1]], &c__2, &iseed[1], &b[
b_offset], lda);
iadd = kadd[kbzero[jtype - 1] - 1];
if (iadd != 0 && iadd <= n) {
i__3 = iadd + iadd * b_dim1;
i__4 = kbmagn[jtype - 1];
b[i__3].r = rmagn[i__4], b[i__3].i = 0.;
}
if (kclass[jtype - 1] == 2 && n > 0) {
/* Include rotations */
/* Generate Q, Z as Householder transformations times */
/* a diagonal matrix. */
i__3 = n - 1;
for (jc = 1; jc <= i__3; ++jc) {
i__4 = n;
for (jr = jc; jr <= i__4; ++jr) {
i__5 = jr + jc * q_dim1;
zlarnd_(&z__1, &c__3, &iseed[1]);
q[i__5].r = z__1.r, q[i__5].i = z__1.i;
i__5 = jr + jc * z_dim1;
zlarnd_(&z__1, &c__3, &iseed[1]);
z__[i__5].r = z__1.r, z__[i__5].i = z__1.i;
/* L40: */
}
i__4 = n + 1 - jc;
zlarfg_(&i__4, &q[jc + jc * q_dim1], &q[jc + 1 + jc *
q_dim1], &c__1, &work[jc]);
i__4 = (n << 1) + jc;
i__5 = jc + jc * q_dim1;
d__2 = q[i__5].r;
d__1 = d_sign(&c_b29, &d__2);
work[i__4].r = d__1, work[i__4].i = 0.;
i__4 = jc + jc * q_dim1;
q[i__4].r = 1., q[i__4].i = 0.;
i__4 = n + 1 - jc;
zlarfg_(&i__4, &z__[jc + jc * z_dim1], &z__[jc + 1 +
jc * z_dim1], &c__1, &work[n + jc]);
i__4 = n * 3 + jc;
i__5 = jc + jc * z_dim1;
d__2 = z__[i__5].r;
d__1 = d_sign(&c_b29, &d__2);
work[i__4].r = d__1, work[i__4].i = 0.;
i__4 = jc + jc * z_dim1;
z__[i__4].r = 1., z__[i__4].i = 0.;
/* L50: */
}
zlarnd_(&z__1, &c__3, &iseed[1]);
ctemp.r = z__1.r, ctemp.i = z__1.i;
i__3 = n + n * q_dim1;
q[i__3].r = 1., q[i__3].i = 0.;
i__3 = n;
work[i__3].r = 0., work[i__3].i = 0.;
i__3 = n * 3;
d__1 = z_abs(&ctemp);
z__1.r = ctemp.r / d__1, z__1.i = ctemp.i / d__1;
work[i__3].r = z__1.r, work[i__3].i = z__1.i;
zlarnd_(&z__1, &c__3, &iseed[1]);
ctemp.r = z__1.r, ctemp.i = z__1.i;
i__3 = n + n * z_dim1;
z__[i__3].r = 1., z__[i__3].i = 0.;
i__3 = n << 1;
work[i__3].r = 0., work[i__3].i = 0.;
i__3 = n << 2;
d__1 = z_abs(&ctemp);
z__1.r = ctemp.r / d__1, z__1.i = ctemp.i / d__1;
work[i__3].r = z__1.r, work[i__3].i = z__1.i;
/* Apply the diagonal matrices */
i__3 = n;
for (jc = 1; jc <= i__3; ++jc) {
i__4 = n;
for (jr = 1; jr <= i__4; ++jr) {
i__5 = jr + jc * a_dim1;
i__6 = (n << 1) + jr;
d_cnjg(&z__3, &work[n * 3 + jc]);
z__2.r = work[i__6].r * z__3.r - work[i__6].i *
z__3.i, z__2.i = work[i__6].r * z__3.i +
work[i__6].i * z__3.r;
i__7 = jr + jc * a_dim1;
z__1.r = z__2.r * a[i__7].r - z__2.i * a[i__7].i,
z__1.i = z__2.r * a[i__7].i + z__2.i * a[
i__7].r;
a[i__5].r = z__1.r, a[i__5].i = z__1.i;
i__5 = jr + jc * b_dim1;
i__6 = (n << 1) + jr;
d_cnjg(&z__3, &work[n * 3 + jc]);
z__2.r = work[i__6].r * z__3.r - work[i__6].i *
z__3.i, z__2.i = work[i__6].r * z__3.i +
work[i__6].i * z__3.r;
i__7 = jr + jc * b_dim1;
z__1.r = z__2.r * b[i__7].r - z__2.i * b[i__7].i,
z__1.i = z__2.r * b[i__7].i + z__2.i * b[
i__7].r;
b[i__5].r = z__1.r, b[i__5].i = z__1.i;
/* L60: */
}
/* L70: */
}
i__3 = n - 1;
zunm2r_("L", "N", &n, &n, &i__3, &q[q_offset], ldq, &work[
1], &a[a_offset], lda, &work[(n << 1) + 1], &
iinfo);
if (iinfo != 0) {
goto L100;
}
i__3 = n - 1;
zunm2r_("R", "C", &n, &n, &i__3, &z__[z_offset], ldq, &
work[n + 1], &a[a_offset], lda, &work[(n << 1) +
1], &iinfo);
if (iinfo != 0) {
goto L100;
}
i__3 = n - 1;
zunm2r_("L", "N", &n, &n, &i__3, &q[q_offset], ldq, &work[
1], &b[b_offset], lda, &work[(n << 1) + 1], &
iinfo);
if (iinfo != 0) {
goto L100;
}
i__3 = n - 1;
zunm2r_("R", "C", &n, &n, &i__3, &z__[z_offset], ldq, &
work[n + 1], &b[b_offset], lda, &work[(n << 1) +
1], &iinfo);
if (iinfo != 0) {
goto L100;
}
}
} else {
/* Random matrices */
i__3 = n;
for (jc = 1; jc <= i__3; ++jc) {
i__4 = n;
for (jr = 1; jr <= i__4; ++jr) {
i__5 = jr + jc * a_dim1;
i__6 = kamagn[jtype - 1];
zlarnd_(&z__2, &c__4, &iseed[1]);
z__1.r = rmagn[i__6] * z__2.r, z__1.i = rmagn[i__6] *
z__2.i;
a[i__5].r = z__1.r, a[i__5].i = z__1.i;
i__5 = jr + jc * b_dim1;
i__6 = kbmagn[jtype - 1];
zlarnd_(&z__2, &c__4, &iseed[1]);
z__1.r = rmagn[i__6] * z__2.r, z__1.i = rmagn[i__6] *
z__2.i;
b[i__5].r = z__1.r, b[i__5].i = z__1.i;
/* L80: */
}
/* L90: */
}
}
L100:
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;
}
L110:
for (i__ = 1; i__ <= 13; ++i__) {
result[i__] = -1.;
/* L120: */
}
/* Test with and without sorting of eigenvalues */
for (isort = 0; isort <= 1; ++isort) {
if (isort == 0) {
*(unsigned char *)sort = 'N';
rsub = 0;
} else {
*(unsigned char *)sort = 'S';
rsub = 5;
}
/* Call ZGGES to compute H, T, Q, Z, alpha, and beta. */
zlacpy_("Full", &n, &n, &a[a_offset], lda, &s[s_offset], lda);
zlacpy_("Full", &n, &n, &b[b_offset], lda, &t[t_offset], lda);
ntest = rsub + 1 + isort;
result[rsub + 1 + isort] = ulpinv;
zgges_("V", "V", sort, (L_fp)zlctes_, &n, &s[s_offset], lda, &
t[t_offset], lda, &sdim, &alpha[1], &beta[1], &q[
q_offset], ldq, &z__[z_offset], ldq, &work[1], lwork,
&rwork[1], &bwork[1], &iinfo);
if (iinfo != 0 && iinfo != n + 2) {
result[rsub + 1 + isort] = ulpinv;
io___47.ciunit = *nounit;
s_wsfe(&io___47);
do_fio(&c__1, "ZGGES", (ftnlen)5);
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 L160;
}
ntest = rsub + 4;
/* Do tests 1--4 (or tests 7--9 when reordering ) */
if (isort == 0) {
zget51_(&c__1, &n, &a[a_offset], lda, &s[s_offset], lda, &
q[q_offset], ldq, &z__[z_offset], ldq, &work[1], &
rwork[1], &result[1]);
zget51_(&c__1, &n, &b[b_offset], lda, &t[t_offset], lda, &
q[q_offset], ldq, &z__[z_offset], ldq, &work[1], &
rwork[1], &result[2]);
} else {
zget54_(&n, &a[a_offset], lda, &b[b_offset], lda, &s[
s_offset], lda, &t[t_offset], lda, &q[q_offset],
ldq, &z__[z_offset], ldq, &work[1], &result[rsub
+ 2]);
}
zget51_(&c__3, &n, &b[b_offset], lda, &t[t_offset], lda, &q[
q_offset], ldq, &q[q_offset], ldq, &work[1], &rwork[1]
, &result[rsub + 3]);
zget51_(&c__3, &n, &b[b_offset], lda, &t[t_offset], lda, &z__[
z_offset], ldq, &z__[z_offset], ldq, &work[1], &rwork[
1], &result[rsub + 4]);
/* Do test 5 and 6 (or Tests 10 and 11 when reordering): */
/* check Schur form of A and compare eigenvalues with */
/* diagonals. */
ntest = rsub + 6;
temp1 = 0.;
i__3 = n;
for (j = 1; j <= i__3; ++j) {
ilabad = FALSE_;
i__4 = j;
i__5 = j + j * s_dim1;
z__2.r = alpha[i__4].r - s[i__5].r, z__2.i = alpha[i__4]
.i - s[i__5].i;
z__1.r = z__2.r, z__1.i = z__2.i;
i__6 = j;
i__7 = j + j * t_dim1;
z__4.r = beta[i__6].r - t[i__7].r, z__4.i = beta[i__6].i
- t[i__7].i;
z__3.r = z__4.r, z__3.i = z__4.i;
/* Computing MAX */
i__8 = j;
i__9 = j + j * s_dim1;
d__13 = safmin, d__14 = (d__1 = alpha[i__8].r, abs(d__1))
+ (d__2 = d_imag(&alpha[j]), abs(d__2)), d__13 =
max(d__13,d__14), d__14 = (d__3 = s[i__9].r, abs(
d__3)) + (d__4 = d_imag(&s[j + j * s_dim1]), abs(
d__4));
/* Computing MAX */
i__10 = j;
i__11 = j + j * t_dim1;
d__15 = safmin, d__16 = (d__5 = beta[i__10].r, abs(d__5))
+ (d__6 = d_imag(&beta[j]), abs(d__6)), d__15 =
max(d__15,d__16), d__16 = (d__7 = t[i__11].r, abs(
d__7)) + (d__8 = d_imag(&t[j + j * t_dim1]), abs(
d__8));
temp2 = (((d__9 = z__1.r, abs(d__9)) + (d__10 = d_imag(&
z__1), abs(d__10))) / max(d__13,d__14) + ((d__11 =
z__3.r, abs(d__11)) + (d__12 = d_imag(&z__3),
abs(d__12))) / max(d__15,d__16)) / ulp;
if (j < n) {
i__4 = j + 1 + j * s_dim1;
if (s[i__4].r != 0. || s[i__4].i != 0.) {
ilabad = TRUE_;
result[rsub + 5] = ulpinv;
}
}
if (j > 1) {
i__4 = j + (j - 1) * s_dim1;
if (s[i__4].r != 0. || s[i__4].i != 0.) {
ilabad = TRUE_;
result[rsub + 5] = ulpinv;
}
}
temp1 = max(temp1,temp2);
if (ilabad) {
io___51.ciunit = *nounit;
s_wsfe(&io___51);
do_fio(&c__1, (char *)&j, (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();
}
/* L130: */
}
result[rsub + 6] = temp1;
if (isort >= 1) {
/* Do test 12 */
ntest = 12;
result[12] = 0.;
knteig = 0;
i__3 = n;
for (i__ = 1; i__ <= i__3; ++i__) {
if (zlctes_(&alpha[i__], &beta[i__])) {
++knteig;
}
/* L140: */
}
if (sdim != knteig) {
result[13] = ulpinv;
}
}
/* L150: */
}
/* End of Loop -- Check for RESULT(j) > THRESH */
L160:
ntestt += ntest;
/* Print out tests which fail. */
i__3 = ntest;
for (jr = 1; jr <= i__3; ++jr) {
if (result[jr] >= *thresh) {
/* If this is the first test to fail, */
/* print a header to the data file. */
if (nerrs == 0) {
io___53.ciunit = *nounit;
s_wsfe(&io___53);
do_fio(&c__1, "ZGS", (ftnlen)3);
e_wsfe();
/* Matrix types */
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, "Unitary", (ftnlen)7);
e_wsfe();
/* Tests performed */
io___57.ciunit = *nounit;
s_wsfe(&io___57);
do_fio(&c__1, "unitary", (ftnlen)7);
do_fio(&c__1, "'", (ftnlen)1);
do_fio(&c__1, "transpose", (ftnlen)9);
for (j = 1; j <= 8; ++j) {
do_fio(&c__1, "'", (ftnlen)1);
}
e_wsfe();
}
++nerrs;
if (result[jr] < 1e4) {
io___58.ciunit = *nounit;
s_wsfe(&io___58);
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer))
;
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&jr, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&result[jr], (ftnlen)sizeof(
doublereal));
e_wsfe();
} else {
io___59.ciunit = *nounit;
s_wsfe(&io___59);
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer))
;
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&jr, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&result[jr], (ftnlen)sizeof(
doublereal));
e_wsfe();
}
}
/* L170: */
}
L180:
;
}
/* L190: */
}
/* Summary */
alasvm_("ZGS", nounit, &nerrs, &ntestt, &c__0);
work[1].r = (doublereal) maxwrk, work[1].i = 0.;
return 0;
/* End of ZDRGES */
} /* zdrges_ */
/* Subroutine */ int zdrgsx_(integer *nsize, integer *ncmax, doublereal *
thresh, integer *nin, integer *nout, doublecomplex *a, integer *lda,
doublecomplex *b, doublecomplex *ai, doublecomplex *bi, doublecomplex
*z__, doublecomplex *q, doublecomplex *alpha, doublecomplex *beta,
doublecomplex *c__, integer *ldc, doublereal *s, doublecomplex *work,
integer *lwork, doublereal *rwork, integer *iwork, integer *liwork,
logical *bwork, integer *info)
{
/* Format strings */
static char fmt_9999[] = "(\002 ZDRGSX: \002,a,\002 returned INFO=\002,i"
"6,\002.\002,/9x,\002N=\002,i6,\002, JTYPE=\002,i6,\002)\002)";
static char fmt_9997[] = "(\002 ZDRGSX: S not in Schur form at eigenvalu"
"e \002,i6,\002.\002,/9x,\002N=\002,i6,\002, JTYPE=\002,i6,\002"
")\002)";
static char fmt_9996[] = "(/1x,a3,\002 -- Complex Expert Generalized Sch"
"ur form\002,\002 problem driver\002)";
static char fmt_9994[] = "(\002 Matrix types: \002,/\002 1: A is a blo"
"ck diagonal matrix of Jordan blocks \002,\002and B is the identi"
"ty \002,/\002 matrix, \002,/\002 2: A and B are upper tri"
"angular matrices, \002,/\002 3: A and B are as type 2, but eac"
"h second diagonal \002,\002block in A_11 and \002,/\002 eac"
"h third diaongal block in A_22 are 2x2 blocks,\002,/\002 4: A "
"and B are block diagonal matrices, \002,/\002 5: (A,B) has pot"
"entially close or common \002,\002eigenvalues.\002,/)";
static char fmt_9993[] = "(/\002 Tests performed: (S is Schur, T is tri"
"angular, \002,\002Q and Z are \002,a,\002,\002,/19x,\002 a is al"
"pha, b is beta, and \002,a,\002 means \002,a,\002.)\002,/\002 1"
" = | A - Q S Z\002,a,\002 | / ( |A| n ulp ) 2 = | B - Q T "
"Z\002,a,\002 | / ( |B| n ulp )\002,/\002 3 = | I - QQ\002,a,"
"\002 | / ( n ulp ) 4 = | I - ZZ\002,a,\002 | / ( n u"
"lp )\002,/\002 5 = 1/ULP if A is not in \002,\002Schur form "
"S\002,/\002 6 = difference between (alpha,beta)\002,\002 and di"
"agonals of (S,T)\002,/\002 7 = 1/ULP if SDIM is not the correc"
"t number of \002,\002selected eigenvalues\002,/\002 8 = 1/ULP "
"if DIFEST/DIFTRU > 10*THRESH or \002,\002DIFTRU/DIFEST > 10*THRE"
"SH\002,/\002 9 = 1/ULP if DIFEST <> 0 or DIFTRU > ULP*norm(A,B"
") \002,\002when reordering fails\002,/\002 10 = 1/ULP if PLEST/"
"PLTRU > THRESH or \002,\002PLTRU/PLEST > THRESH\002,/\002 ( T"
"est 10 is only for input examples )\002,/)";
static char fmt_9992[] = "(\002 Matrix order=\002,i2,\002, type=\002,i2"
",\002, a=\002,d10.4,\002, order(A_11)=\002,i2,\002, result \002,"
"i2,\002 is \002,0p,f8.2)";
static char fmt_9991[] = "(\002 Matrix order=\002,i2,\002, type=\002,i2"
",\002, a=\002,d10.4,\002, order(A_11)=\002,i2,\002, result \002,"
"i2,\002 is \002,0p,d10.4)";
static char fmt_9998[] = "(\002 ZDRGSX: \002,a,\002 returned INFO=\002,i"
"6,\002.\002,/9x,\002N=\002,i6,\002, Input Example #\002,i2,\002"
")\002)";
static char fmt_9995[] = "(\002Input Example\002)";
static char fmt_9990[] = "(\002 Input example #\002,i2,\002, matrix orde"
"r=\002,i4,\002,\002,\002 result \002,i2,\002 is\002,0p,f8.2)";
static char fmt_9989[] = "(\002 Input example #\002,i2,\002, matrix orde"
"r=\002,i4,\002,\002,\002 result \002,i2,\002 is\002,1p,d10.3)";
/* System generated locals */
integer a_dim1, a_offset, ai_dim1, ai_offset, b_dim1, b_offset, bi_dim1,
bi_offset, c_dim1, c_offset, q_dim1, q_offset, z_dim1, z_offset,
i__1, i__2, i__3, i__4, i__5, i__6, i__7, i__8, i__9, i__10,
i__11;
doublereal d__1, d__2, d__3, d__4, d__5, d__6, d__7, d__8, d__9, d__10,
d__11, d__12, d__13, d__14, d__15, d__16;
doublecomplex z__1, z__2, z__3, z__4;
/* Builtin functions */
double sqrt(doublereal);
integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void);
double d_imag(doublecomplex *);
integer s_rsle(cilist *), do_lio(integer *, integer *, char *, ftnlen),
e_rsle(void);
/* Local variables */
integer i__, j, mm;
doublereal pl[2];
integer mn2, qba, qbb;
doublereal ulp, temp1, temp2, abnrm;
integer ifunc, linfo;
char sense[1];
extern /* Subroutine */ int zget51_(integer *, integer *, doublecomplex *,
integer *, doublecomplex *, integer *, doublecomplex *, integer *
, doublecomplex *, integer *, doublecomplex *, doublereal *,
doublereal *);
integer nerrs, ntest;
doublereal pltru;
extern /* Subroutine */ int zlakf2_(integer *, integer *, doublecomplex *,
integer *, doublecomplex *, doublecomplex *, doublecomplex *,
doublecomplex *, integer *), dlabad_(doublereal *, doublereal *);
doublereal thrsh2;
logical ilabad;
extern /* Subroutine */ int zlatm5_(integer *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublereal *, integer *, integer *);
extern doublereal dlamch_(char *);
integer bdspac;
extern /* Subroutine */ int xerbla_(char *, integer *);
doublereal difest[2];
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *);
extern doublereal zlange_(char *, integer *, integer *, doublecomplex *,
integer *, doublereal *);
doublereal bignum;
extern /* Subroutine */ int alasvm_(char *, integer *, integer *, integer
*, integer *);
doublereal weight, diftru;
extern /* Subroutine */ int zgesvd_(char *, char *, integer *, integer *,
doublecomplex *, integer *, doublereal *, doublecomplex *,
integer *, doublecomplex *, integer *, doublecomplex *, integer *,
doublereal *, integer *), zlacpy_(char *,
integer *, integer *, doublecomplex *, integer *, doublecomplex *,
integer *), zlaset_(char *, integer *, integer *,
doublecomplex *, doublecomplex *, doublecomplex *, integer *);
integer minwrk, maxwrk;
extern /* Subroutine */ int zggesx_(char *, char *, char *, L_fp, char *,
integer *, doublecomplex *, integer *, doublecomplex *, integer *,
integer *, doublecomplex *, doublecomplex *, doublecomplex *,
integer *, doublecomplex *, integer *, doublereal *, doublereal *,
doublecomplex *, integer *, doublereal *, integer *, integer *,
logical *, integer *);
doublereal smlnum, ulpinv;
integer nptknt;
doublereal result[10];
integer ntestt, prtype;
extern logical zlctsx_();
/* Fortran I/O blocks */
static cilist io___22 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___29 = { 0, 0, 0, fmt_9997, 0 };
static cilist io___32 = { 0, 0, 0, fmt_9996, 0 };
static cilist io___33 = { 0, 0, 0, fmt_9994, 0 };
static cilist io___34 = { 0, 0, 0, fmt_9993, 0 };
static cilist io___36 = { 0, 0, 0, fmt_9992, 0 };
static cilist io___37 = { 0, 0, 0, fmt_9991, 0 };
static cilist io___39 = { 0, 0, 1, 0, 0 };
static cilist io___40 = { 0, 0, 1, 0, 0 };
static cilist io___41 = { 0, 0, 0, 0, 0 };
static cilist io___42 = { 0, 0, 0, 0, 0 };
static cilist io___43 = { 0, 0, 0, 0, 0 };
static cilist io___45 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___46 = { 0, 0, 0, fmt_9997, 0 };
static cilist io___47 = { 0, 0, 0, fmt_9996, 0 };
static cilist io___48 = { 0, 0, 0, fmt_9995, 0 };
static cilist io___49 = { 0, 0, 0, fmt_9993, 0 };
static cilist io___50 = { 0, 0, 0, fmt_9990, 0 };
static cilist io___51 = { 0, 0, 0, fmt_9989, 0 };
/* -- LAPACK test routine (version 3.1.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* February 2007 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZDRGSX checks the nonsymmetric generalized eigenvalue (Schur form) */
/* problem expert driver ZGGESX. */
/* ZGGES factors A and B as Q*S*Z' and Q*T*Z' , where ' means conjugate */
/* transpose, S and T are upper triangular (i.e., in generalized Schur */
/* form), and Q and Z are unitary. It also computes the generalized */
/* eigenvalues (alpha(j),beta(j)), j=1,...,n. Thus, */
/* w(j) = alpha(j)/beta(j) is a root of the characteristic equation */
/* det( A - w(j) B ) = 0 */
/* Optionally it also reorders the eigenvalues so that a selected */
/* cluster of eigenvalues appears in the leading diagonal block of the */
/* Schur forms; computes a reciprocal condition number for the average */
/* of the selected eigenvalues; and computes a reciprocal condition */
/* number for the right and left deflating subspaces corresponding to */
/* the selected eigenvalues. */
/* When ZDRGSX is called with NSIZE > 0, five (5) types of built-in */
/* matrix pairs are used to test the routine ZGGESX. */
/* When ZDRGSX is called with NSIZE = 0, it reads in test matrix data */
/* to test ZGGESX. */
/* (need more details on what kind of read-in data are needed). */
/* For each matrix pair, the following tests will be performed and */
/* compared with the threshhold THRESH except for the tests (7) and (9): */
/* (1) | A - Q S Z' | / ( |A| n ulp ) */
/* (2) | B - Q T Z' | / ( |B| n ulp ) */
/* (3) | I - QQ' | / ( n ulp ) */
/* (4) | I - ZZ' | / ( n ulp ) */
/* (5) if A is in Schur form (i.e. triangular form) */
/* (6) maximum over j of D(j) where: */
/* |alpha(j) - S(j,j)| |beta(j) - T(j,j)| */
/* D(j) = ------------------------ + ----------------------- */
/* max(|alpha(j)|,|S(j,j)|) max(|beta(j)|,|T(j,j)|) */
/* (7) if sorting worked and SDIM is the number of eigenvalues */
/* which were selected. */
/* (8) the estimated value DIF does not differ from the true values of */
/* Difu and Difl more than a factor 10*THRESH. If the estimate DIF */
/* equals zero the corresponding true values of Difu and Difl */
/* should be less than EPS*norm(A, B). If the true value of Difu */
/* and Difl equal zero, the estimate DIF should be less than */
/* EPS*norm(A, B). */
/* (9) If INFO = N+3 is returned by ZGGESX, the reordering "failed" */
/* and we check that DIF = PL = PR = 0 and that the true value of */
/* Difu and Difl is < EPS*norm(A, B). We count the events when */
/* INFO=N+3. */
/* For read-in test matrices, the same tests are run except that the */
/* exact value for DIF (and PL) is input data. Additionally, there is */
/* one more test run for read-in test matrices: */
/* (10) the estimated value PL does not differ from the true value of */
/* PLTRU more than a factor THRESH. If the estimate PL equals */
/* zero the corresponding true value of PLTRU should be less than */
/* EPS*norm(A, B). If the true value of PLTRU equal zero, the */
/* estimate PL should be less than EPS*norm(A, B). */
/* Note that for the built-in tests, a total of 10*NSIZE*(NSIZE-1) */
/* matrix pairs are generated and tested. NSIZE should be kept small. */
/* SVD (routine ZGESVD) is used for computing the true value of DIF_u */
/* and DIF_l when testing the built-in test problems. */
/* Built-in Test Matrices */
/* ====================== */
/* All built-in test matrices are the 2 by 2 block of triangular */
/* matrices */
/* A = [ A11 A12 ] and B = [ B11 B12 ] */
/* [ A22 ] [ B22 ] */
/* where for different type of A11 and A22 are given as the following. */
/* A12 and B12 are chosen so that the generalized Sylvester equation */
/* A11*R - L*A22 = -A12 */
/* B11*R - L*B22 = -B12 */
/* have prescribed solution R and L. */
/* Type 1: A11 = J_m(1,-1) and A_22 = J_k(1-a,1). */
/* B11 = I_m, B22 = I_k */
/* where J_k(a,b) is the k-by-k Jordan block with ``a'' on */
/* diagonal and ``b'' on superdiagonal. */
/* Type 2: A11 = (a_ij) = ( 2(.5-sin(i)) ) and */
/* B11 = (b_ij) = ( 2(.5-sin(ij)) ) for i=1,...,m, j=i,...,m */
/* A22 = (a_ij) = ( 2(.5-sin(i+j)) ) and */
/* B22 = (b_ij) = ( 2(.5-sin(ij)) ) for i=m+1,...,k, j=i,...,k */
/* Type 3: A11, A22 and B11, B22 are chosen as for Type 2, but each */
/* second diagonal block in A_11 and each third diagonal block */
/* in A_22 are made as 2 by 2 blocks. */
/* Type 4: A11 = ( 20(.5 - sin(ij)) ) and B22 = ( 2(.5 - sin(i+j)) ) */
/* for i=1,...,m, j=1,...,m and */
/* A22 = ( 20(.5 - sin(i+j)) ) and B22 = ( 2(.5 - sin(ij)) ) */
/* for i=m+1,...,k, j=m+1,...,k */
/* Type 5: (A,B) and have potentially close or common eigenvalues and */
/* very large departure from block diagonality A_11 is chosen */
/* as the m x m leading submatrix of A_1: */
/* | 1 b | */
/* | -b 1 | */
/* | 1+d b | */
/* | -b 1+d | */
/* A_1 = | d 1 | */
/* | -1 d | */
/* | -d 1 | */
/* | -1 -d | */
/* | 1 | */
/* and A_22 is chosen as the k x k leading submatrix of A_2: */
/* | -1 b | */
/* | -b -1 | */
/* | 1-d b | */
/* | -b 1-d | */
/* A_2 = | d 1+b | */
/* | -1-b d | */
/* | -d 1+b | */
/* | -1+b -d | */
/* | 1-d | */
/* and matrix B are chosen as identity matrices (see DLATM5). */
/* Arguments */
/* ========= */
/* NSIZE (input) INTEGER */
/* The maximum size of the matrices to use. NSIZE >= 0. */
/* If NSIZE = 0, no built-in tests matrices are used, but */
/* read-in test matrices are used to test DGGESX. */
/* NCMAX (input) INTEGER */
/* Maximum allowable NMAX for generating Kroneker matrix */
/* in call to ZLAKF2 */
/* THRESH (input) DOUBLE PRECISION */
/* A test will count as "failed" if the "error", computed as */
/* described above, exceeds THRESH. Note that the error */
/* is scaled to be O(1), so THRESH should be a reasonably */
/* small multiple of 1, e.g., 10 or 100. In particular, */
/* it should not depend on the precision (single vs. double) */
/* or the size of the matrix. THRESH >= 0. */
/* NIN (input) INTEGER */
/* The FORTRAN unit number for reading in the data file of */
/* problems to solve. */
/* NOUT (input) INTEGER */
/* The FORTRAN unit number for printing out error messages */
/* (e.g., if a routine returns INFO not equal to 0.) */
/* A (workspace) COMPLEX*16 array, dimension (LDA, NSIZE) */
/* Used to store the matrix whose eigenvalues are to be */
/* computed. On exit, A contains the last matrix actually used. */
/* LDA (input) INTEGER */
/* The leading dimension of A, B, AI, BI, Z and Q, */
/* LDA >= max( 1, NSIZE ). For the read-in test, */
/* LDA >= max( 1, N ), N is the size of the test matrices. */
/* B (workspace) COMPLEX*16 array, dimension (LDA, NSIZE) */
/* Used to store the matrix whose eigenvalues are to be */
/* computed. On exit, B contains the last matrix actually used. */
/* AI (workspace) COMPLEX*16 array, dimension (LDA, NSIZE) */
/* Copy of A, modified by ZGGESX. */
/* BI (workspace) COMPLEX*16 array, dimension (LDA, NSIZE) */
/* Copy of B, modified by ZGGESX. */
/* Z (workspace) COMPLEX*16 array, dimension (LDA, NSIZE) */
/* Z holds the left Schur vectors computed by ZGGESX. */
/* Q (workspace) COMPLEX*16 array, dimension (LDA, NSIZE) */
/* Q holds the right Schur vectors computed by ZGGESX. */
/* ALPHA (workspace) COMPLEX*16 array, dimension (NSIZE) */
/* BETA (workspace) COMPLEX*16 array, dimension (NSIZE) */
/* On exit, ALPHA/BETA are the eigenvalues. */
/* C (workspace) COMPLEX*16 array, dimension (LDC, LDC) */
/* Store the matrix generated by subroutine ZLAKF2, this is the */
/* matrix formed by Kronecker products used for estimating */
/* DIF. */
/* LDC (input) INTEGER */
/* The leading dimension of C. LDC >= max(1, LDA*LDA/2 ). */
/* S (workspace) DOUBLE PRECISION array, dimension (LDC) */
/* Singular values of C */
/* WORK (workspace) COMPLEX*16 array, dimension (LWORK) */
/* LWORK (input) INTEGER */
/* The dimension of the array WORK. LWORK >= 3*NSIZE*NSIZE/2 */
/* RWORK (workspace) DOUBLE PRECISION array, */
/* dimension (5*NSIZE*NSIZE/2 - 4) */
/* IWORK (workspace) INTEGER array, dimension (LIWORK) */
/* LIWORK (input) INTEGER */
/* The dimension of the array IWORK. LIWORK >= NSIZE + 2. */
/* BWORK (workspace) LOGICAL array, dimension (NSIZE) */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value. */
/* > 0: A routine returned an error code. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Scalars in Common .. */
/* .. */
/* .. Common blocks .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Statement Functions .. */
/* .. */
/* .. Statement Function definitions .. */
/* .. */
/* .. Executable Statements .. */
/* Check for errors */
/* Parameter adjustments */
q_dim1 = *lda;
q_offset = 1 + q_dim1;
q -= q_offset;
z_dim1 = *lda;
z_offset = 1 + z_dim1;
z__ -= z_offset;
bi_dim1 = *lda;
bi_offset = 1 + bi_dim1;
bi -= bi_offset;
ai_dim1 = *lda;
ai_offset = 1 + ai_dim1;
ai -= ai_offset;
b_dim1 = *lda;
b_offset = 1 + b_dim1;
b -= b_offset;
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--alpha;
--beta;
c_dim1 = *ldc;
c_offset = 1 + c_dim1;
c__ -= c_offset;
--s;
--work;
--rwork;
--iwork;
--bwork;
/* Function Body */
*info = 0;
if (*nsize < 0) {
*info = -1;
} else if (*thresh < 0.) {
*info = -2;
} else if (*nin <= 0) {
*info = -3;
} else if (*nout <= 0) {
*info = -4;
} else if (*lda < 1 || *lda < *nsize) {
*info = -6;
} else if (*ldc < 1 || *ldc < *nsize * *nsize / 2) {
*info = -15;
} else if (*liwork < *nsize + 2) {
*info = -21;
}
/* Compute workspace */
/* (Note: Comments in the code beginning "Workspace:" describe the */
/* minimal amount of workspace needed at that point in the code, */
/* as well as the preferred amount for good performance. */
/* NB refers to the optimal block size for the immediately */
/* following subroutine, as returned by ILAENV.) */
minwrk = 1;
if (*info == 0 && *lwork >= 1) {
minwrk = *nsize * 3 * *nsize / 2;
/* workspace for cggesx */
maxwrk = *nsize * (ilaenv_(&c__1, "ZGEQRF", " ", nsize, &c__1, nsize,
&c__0) + 1);
/* Computing MAX */
i__1 = maxwrk, i__2 = *nsize * (ilaenv_(&c__1, "ZUNGQR", " ", nsize, &
c__1, nsize, &c_n1) + 1);
maxwrk = max(i__1,i__2);
/* workspace for zgesvd */
bdspac = *nsize * 3 * *nsize / 2;
/* Computing MAX */
i__3 = *nsize * *nsize / 2;
i__4 = *nsize * *nsize / 2;
i__1 = maxwrk, i__2 = *nsize * *nsize * (ilaenv_(&c__1, "ZGEBRD",
" ", &i__3, &i__4, &c_n1, &c_n1) + 1);
maxwrk = max(i__1,i__2);
maxwrk = max(maxwrk,bdspac);
maxwrk = max(maxwrk,minwrk);
work[1].r = (doublereal) maxwrk, work[1].i = 0.;
}
if (*lwork < minwrk) {
*info = -18;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZDRGSX", &i__1);
return 0;
}
/* Important constants */
ulp = dlamch_("P");
ulpinv = 1. / ulp;
smlnum = dlamch_("S") / ulp;
bignum = 1. / smlnum;
dlabad_(&smlnum, &bignum);
thrsh2 = *thresh * 10.;
ntestt = 0;
nerrs = 0;
/* Go to the tests for read-in matrix pairs */
ifunc = 0;
if (*nsize == 0) {
goto L70;
}
/* Test the built-in matrix pairs. */
/* Loop over different functions (IFUNC) of ZGGESX, types (PRTYPE) */
/* of test matrices, different size (M+N) */
prtype = 0;
qba = 3;
qbb = 4;
weight = sqrt(ulp);
for (ifunc = 0; ifunc <= 3; ++ifunc) {
for (prtype = 1; prtype <= 5; ++prtype) {
i__1 = *nsize - 1;
for (mn_1.m = 1; mn_1.m <= i__1; ++mn_1.m) {
i__2 = *nsize - mn_1.m;
for (mn_1.n = 1; mn_1.n <= i__2; ++mn_1.n) {
weight = 1. / weight;
mn_1.mplusn = mn_1.m + mn_1.n;
/* Generate test matrices */
mn_1.fs = TRUE_;
mn_1.k = 0;
zlaset_("Full", &mn_1.mplusn, &mn_1.mplusn, &c_b1, &c_b1,
&ai[ai_offset], lda);
zlaset_("Full", &mn_1.mplusn, &mn_1.mplusn, &c_b1, &c_b1,
&bi[bi_offset], lda);
zlatm5_(&prtype, &mn_1.m, &mn_1.n, &ai[ai_offset], lda, &
ai[mn_1.m + 1 + (mn_1.m + 1) * ai_dim1], lda, &ai[
(mn_1.m + 1) * ai_dim1 + 1], lda, &bi[bi_offset],
lda, &bi[mn_1.m + 1 + (mn_1.m + 1) * bi_dim1],
lda, &bi[(mn_1.m + 1) * bi_dim1 + 1], lda, &q[
q_offset], lda, &z__[z_offset], lda, &weight, &
qba, &qbb);
/* Compute the Schur factorization and swapping the */
/* m-by-m (1,1)-blocks with n-by-n (2,2)-blocks. */
/* Swapping is accomplished via the function ZLCTSX */
/* which is supplied below. */
if (ifunc == 0) {
*(unsigned char *)sense = 'N';
} else if (ifunc == 1) {
*(unsigned char *)sense = 'E';
} else if (ifunc == 2) {
*(unsigned char *)sense = 'V';
} else if (ifunc == 3) {
*(unsigned char *)sense = 'B';
}
zlacpy_("Full", &mn_1.mplusn, &mn_1.mplusn, &ai[ai_offset]
, lda, &a[a_offset], lda);
zlacpy_("Full", &mn_1.mplusn, &mn_1.mplusn, &bi[bi_offset]
, lda, &b[b_offset], lda);
zggesx_("V", "V", "S", (L_fp)zlctsx_, sense, &mn_1.mplusn,
&ai[ai_offset], lda, &bi[bi_offset], lda, &mm, &
alpha[1], &beta[1], &q[q_offset], lda, &z__[
z_offset], lda, pl, difest, &work[1], lwork, &
rwork[1], &iwork[1], liwork, &bwork[1], &linfo);
if (linfo != 0 && linfo != mn_1.mplusn + 2) {
result[0] = ulpinv;
io___22.ciunit = *nout;
s_wsfe(&io___22);
do_fio(&c__1, "ZGGESX", (ftnlen)6);
do_fio(&c__1, (char *)&linfo, (ftnlen)sizeof(integer))
;
do_fio(&c__1, (char *)&mn_1.mplusn, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&prtype, (ftnlen)sizeof(integer)
);
e_wsfe();
*info = linfo;
goto L30;
}
/* Compute the norm(A, B) */
zlacpy_("Full", &mn_1.mplusn, &mn_1.mplusn, &ai[ai_offset]
, lda, &work[1], &mn_1.mplusn);
zlacpy_("Full", &mn_1.mplusn, &mn_1.mplusn, &bi[bi_offset]
, lda, &work[mn_1.mplusn * mn_1.mplusn + 1], &
mn_1.mplusn);
i__3 = mn_1.mplusn << 1;
abnrm = zlange_("Fro", &mn_1.mplusn, &i__3, &work[1], &
mn_1.mplusn, &rwork[1]);
/* Do tests (1) to (4) */
result[1] = 0.;
zget51_(&c__1, &mn_1.mplusn, &a[a_offset], lda, &ai[
ai_offset], lda, &q[q_offset], lda, &z__[z_offset]
, lda, &work[1], &rwork[1], result);
zget51_(&c__1, &mn_1.mplusn, &b[b_offset], lda, &bi[
bi_offset], lda, &q[q_offset], lda, &z__[z_offset]
, lda, &work[1], &rwork[1], &result[1]);
zget51_(&c__3, &mn_1.mplusn, &b[b_offset], lda, &bi[
bi_offset], lda, &q[q_offset], lda, &q[q_offset],
lda, &work[1], &rwork[1], &result[2]);
zget51_(&c__3, &mn_1.mplusn, &b[b_offset], lda, &bi[
bi_offset], lda, &z__[z_offset], lda, &z__[
z_offset], lda, &work[1], &rwork[1], &result[3]);
ntest = 4;
/* Do tests (5) and (6): check Schur form of A and */
/* compare eigenvalues with diagonals. */
temp1 = 0.;
result[4] = 0.;
result[5] = 0.;
i__3 = mn_1.mplusn;
for (j = 1; j <= i__3; ++j) {
ilabad = FALSE_;
i__4 = j;
i__5 = j + j * ai_dim1;
z__2.r = alpha[i__4].r - ai[i__5].r, z__2.i = alpha[
i__4].i - ai[i__5].i;
z__1.r = z__2.r, z__1.i = z__2.i;
i__6 = j;
i__7 = j + j * bi_dim1;
z__4.r = beta[i__6].r - bi[i__7].r, z__4.i = beta[
i__6].i - bi[i__7].i;
z__3.r = z__4.r, z__3.i = z__4.i;
/* Computing MAX */
i__8 = j;
i__9 = j + j * ai_dim1;
d__13 = smlnum, d__14 = (d__1 = alpha[i__8].r, abs(
d__1)) + (d__2 = d_imag(&alpha[j]), abs(d__2))
, d__13 = max(d__13,d__14), d__14 = (d__3 =
ai[i__9].r, abs(d__3)) + (d__4 = d_imag(&ai[j
+ j * ai_dim1]), abs(d__4));
/* Computing MAX */
i__10 = j;
i__11 = j + j * bi_dim1;
d__15 = smlnum, d__16 = (d__5 = beta[i__10].r, abs(
d__5)) + (d__6 = d_imag(&beta[j]), abs(d__6)),
d__15 = max(d__15,d__16), d__16 = (d__7 = bi[
i__11].r, abs(d__7)) + (d__8 = d_imag(&bi[j +
j * bi_dim1]), abs(d__8));
temp2 = (((d__9 = z__1.r, abs(d__9)) + (d__10 =
d_imag(&z__1), abs(d__10))) / max(d__13,d__14)
+ ((d__11 = z__3.r, abs(d__11)) + (d__12 =
d_imag(&z__3), abs(d__12))) / max(d__15,d__16)
) / ulp;
if (j < mn_1.mplusn) {
i__4 = j + 1 + j * ai_dim1;
if (ai[i__4].r != 0. || ai[i__4].i != 0.) {
ilabad = TRUE_;
result[4] = ulpinv;
}
}
if (j > 1) {
i__4 = j + (j - 1) * ai_dim1;
if (ai[i__4].r != 0. || ai[i__4].i != 0.) {
ilabad = TRUE_;
result[4] = ulpinv;
}
}
temp1 = max(temp1,temp2);
if (ilabad) {
io___29.ciunit = *nout;
s_wsfe(&io___29);
do_fio(&c__1, (char *)&j, (ftnlen)sizeof(integer))
;
do_fio(&c__1, (char *)&mn_1.mplusn, (ftnlen)
sizeof(integer));
do_fio(&c__1, (char *)&prtype, (ftnlen)sizeof(
integer));
e_wsfe();
}
/* L10: */
}
result[5] = temp1;
ntest += 2;
/* Test (7) (if sorting worked) */
result[6] = 0.;
if (linfo == mn_1.mplusn + 3) {
result[6] = ulpinv;
} else if (mm != mn_1.n) {
result[6] = ulpinv;
}
++ntest;
/* Test (8): compare the estimated value DIF and its */
/* value. first, compute the exact DIF. */
result[7] = 0.;
mn2 = mm * (mn_1.mplusn - mm) << 1;
if (ifunc >= 2 && mn2 <= *ncmax * *ncmax) {
/* Note: for either following two cases, there are */
/* almost same number of test cases fail the test. */
i__3 = mn_1.mplusn - mm;
zlakf2_(&mm, &i__3, &ai[ai_offset], lda, &ai[mm + 1 +
(mm + 1) * ai_dim1], &bi[bi_offset], &bi[mm +
1 + (mm + 1) * bi_dim1], &c__[c_offset], ldc);
i__3 = *lwork - 2;
zgesvd_("N", "N", &mn2, &mn2, &c__[c_offset], ldc, &s[
1], &work[1], &c__1, &work[2], &c__1, &work[3]
, &i__3, &rwork[1], info);
diftru = s[mn2];
if (difest[1] == 0.) {
if (diftru > abnrm * ulp) {
result[7] = ulpinv;
}
} else if (diftru == 0.) {
if (difest[1] > abnrm * ulp) {
result[7] = ulpinv;
}
} else if (diftru > thrsh2 * difest[1] || diftru *
thrsh2 < difest[1]) {
/* Computing MAX */
d__1 = diftru / difest[1], d__2 = difest[1] /
diftru;
result[7] = max(d__1,d__2);
}
++ntest;
}
/* Test (9) */
result[8] = 0.;
if (linfo == mn_1.mplusn + 2) {
if (diftru > abnrm * ulp) {
result[8] = ulpinv;
}
if (ifunc > 1 && difest[1] != 0.) {
result[8] = ulpinv;
}
if (ifunc == 1 && pl[0] != 0.) {
result[8] = ulpinv;
}
++ntest;
}
ntestt += ntest;
/* Print out tests which fail. */
for (j = 1; j <= 9; ++j) {
if (result[j - 1] >= *thresh) {
/* If this is the first test to fail, */
/* print a header to the data file. */
if (nerrs == 0) {
io___32.ciunit = *nout;
s_wsfe(&io___32);
do_fio(&c__1, "CGX", (ftnlen)3);
e_wsfe();
/* Matrix types */
io___33.ciunit = *nout;
s_wsfe(&io___33);
e_wsfe();
/* Tests performed */
io___34.ciunit = *nout;
s_wsfe(&io___34);
do_fio(&c__1, "unitary", (ftnlen)7);
do_fio(&c__1, "'", (ftnlen)1);
do_fio(&c__1, "transpose", (ftnlen)9);
for (i__ = 1; i__ <= 4; ++i__) {
do_fio(&c__1, "'", (ftnlen)1);
}
e_wsfe();
}
++nerrs;
if (result[j - 1] < 1e4) {
io___36.ciunit = *nout;
s_wsfe(&io___36);
do_fio(&c__1, (char *)&mn_1.mplusn, (ftnlen)
sizeof(integer));
do_fio(&c__1, (char *)&prtype, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&weight, (ftnlen)sizeof(
doublereal));
do_fio(&c__1, (char *)&mn_1.m, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&j, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&result[j - 1], (ftnlen)
sizeof(doublereal));
e_wsfe();
} else {
io___37.ciunit = *nout;
s_wsfe(&io___37);
do_fio(&c__1, (char *)&mn_1.mplusn, (ftnlen)
sizeof(integer));
do_fio(&c__1, (char *)&prtype, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&weight, (ftnlen)sizeof(
doublereal));
do_fio(&c__1, (char *)&mn_1.m, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&j, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&result[j - 1], (ftnlen)
sizeof(doublereal));
e_wsfe();
}
}
/* L20: */
}
L30:
;
}
/* L40: */
}
/* L50: */
}
/* L60: */
}
goto L150;
L70:
/* Read in data from file to check accuracy of condition estimation */
/* Read input data until N=0 */
nptknt = 0;
L80:
io___39.ciunit = *nin;
i__1 = s_rsle(&io___39);
if (i__1 != 0) {
goto L140;
}
i__1 = do_lio(&c__3, &c__1, (char *)&mn_1.mplusn, (ftnlen)sizeof(integer))
;
if (i__1 != 0) {
goto L140;
}
i__1 = e_rsle();
if (i__1 != 0) {
goto L140;
}
if (mn_1.mplusn == 0) {
goto L140;
}
io___40.ciunit = *nin;
i__1 = s_rsle(&io___40);
if (i__1 != 0) {
goto L140;
}
i__1 = do_lio(&c__3, &c__1, (char *)&mn_1.n, (ftnlen)sizeof(integer));
if (i__1 != 0) {
goto L140;
}
i__1 = e_rsle();
if (i__1 != 0) {
goto L140;
}
i__1 = mn_1.mplusn;
for (i__ = 1; i__ <= i__1; ++i__) {
io___41.ciunit = *nin;
s_rsle(&io___41);
i__2 = mn_1.mplusn;
for (j = 1; j <= i__2; ++j) {
do_lio(&c__7, &c__1, (char *)&ai[i__ + j * ai_dim1], (ftnlen)
sizeof(doublecomplex));
}
e_rsle();
/* L90: */
}
i__1 = mn_1.mplusn;
for (i__ = 1; i__ <= i__1; ++i__) {
io___42.ciunit = *nin;
s_rsle(&io___42);
i__2 = mn_1.mplusn;
for (j = 1; j <= i__2; ++j) {
do_lio(&c__7, &c__1, (char *)&bi[i__ + j * bi_dim1], (ftnlen)
sizeof(doublecomplex));
}
e_rsle();
/* L100: */
}
io___43.ciunit = *nin;
s_rsle(&io___43);
do_lio(&c__5, &c__1, (char *)&pltru, (ftnlen)sizeof(doublereal));
do_lio(&c__5, &c__1, (char *)&diftru, (ftnlen)sizeof(doublereal));
e_rsle();
++nptknt;
mn_1.fs = TRUE_;
mn_1.k = 0;
mn_1.m = mn_1.mplusn - mn_1.n;
zlacpy_("Full", &mn_1.mplusn, &mn_1.mplusn, &ai[ai_offset], lda, &a[
a_offset], lda);
zlacpy_("Full", &mn_1.mplusn, &mn_1.mplusn, &bi[bi_offset], lda, &b[
b_offset], lda);
/* Compute the Schur factorization while swaping the */
/* m-by-m (1,1)-blocks with n-by-n (2,2)-blocks. */
zggesx_("V", "V", "S", (L_fp)zlctsx_, "B", &mn_1.mplusn, &ai[ai_offset],
lda, &bi[bi_offset], lda, &mm, &alpha[1], &beta[1], &q[q_offset],
lda, &z__[z_offset], lda, pl, difest, &work[1], lwork, &rwork[1],
&iwork[1], liwork, &bwork[1], &linfo);
if (linfo != 0 && linfo != mn_1.mplusn + 2) {
result[0] = ulpinv;
io___45.ciunit = *nout;
s_wsfe(&io___45);
do_fio(&c__1, "ZGGESX", (ftnlen)6);
do_fio(&c__1, (char *)&linfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&mn_1.mplusn, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&nptknt, (ftnlen)sizeof(integer));
e_wsfe();
goto L130;
}
/* Compute the norm(A, B) */
/* (should this be norm of (A,B) or (AI,BI)?) */
zlacpy_("Full", &mn_1.mplusn, &mn_1.mplusn, &ai[ai_offset], lda, &work[1],
&mn_1.mplusn);
zlacpy_("Full", &mn_1.mplusn, &mn_1.mplusn, &bi[bi_offset], lda, &work[
mn_1.mplusn * mn_1.mplusn + 1], &mn_1.mplusn);
i__1 = mn_1.mplusn << 1;
abnrm = zlange_("Fro", &mn_1.mplusn, &i__1, &work[1], &mn_1.mplusn, &
rwork[1]);
/* Do tests (1) to (4) */
zget51_(&c__1, &mn_1.mplusn, &a[a_offset], lda, &ai[ai_offset], lda, &q[
q_offset], lda, &z__[z_offset], lda, &work[1], &rwork[1], result);
zget51_(&c__1, &mn_1.mplusn, &b[b_offset], lda, &bi[bi_offset], lda, &q[
q_offset], lda, &z__[z_offset], lda, &work[1], &rwork[1], &result[
1]);
zget51_(&c__3, &mn_1.mplusn, &b[b_offset], lda, &bi[bi_offset], lda, &q[
q_offset], lda, &q[q_offset], lda, &work[1], &rwork[1], &result[2]
);
zget51_(&c__3, &mn_1.mplusn, &b[b_offset], lda, &bi[bi_offset], lda, &z__[
z_offset], lda, &z__[z_offset], lda, &work[1], &rwork[1], &result[
3]);
/* Do tests (5) and (6): check Schur form of A and compare */
/* eigenvalues with diagonals. */
ntest = 6;
temp1 = 0.;
result[4] = 0.;
result[5] = 0.;
i__1 = mn_1.mplusn;
for (j = 1; j <= i__1; ++j) {
ilabad = FALSE_;
i__2 = j;
i__3 = j + j * ai_dim1;
z__2.r = alpha[i__2].r - ai[i__3].r, z__2.i = alpha[i__2].i - ai[i__3]
.i;
z__1.r = z__2.r, z__1.i = z__2.i;
i__4 = j;
i__5 = j + j * bi_dim1;
z__4.r = beta[i__4].r - bi[i__5].r, z__4.i = beta[i__4].i - bi[i__5]
.i;
z__3.r = z__4.r, z__3.i = z__4.i;
/* Computing MAX */
i__6 = j;
i__7 = j + j * ai_dim1;
d__13 = smlnum, d__14 = (d__1 = alpha[i__6].r, abs(d__1)) + (d__2 =
d_imag(&alpha[j]), abs(d__2)), d__13 = max(d__13,d__14),
d__14 = (d__3 = ai[i__7].r, abs(d__3)) + (d__4 = d_imag(&ai[j
+ j * ai_dim1]), abs(d__4));
/* Computing MAX */
i__8 = j;
i__9 = j + j * bi_dim1;
d__15 = smlnum, d__16 = (d__5 = beta[i__8].r, abs(d__5)) + (d__6 =
d_imag(&beta[j]), abs(d__6)), d__15 = max(d__15,d__16), d__16
= (d__7 = bi[i__9].r, abs(d__7)) + (d__8 = d_imag(&bi[j + j *
bi_dim1]), abs(d__8));
temp2 = (((d__9 = z__1.r, abs(d__9)) + (d__10 = d_imag(&z__1), abs(
d__10))) / max(d__13,d__14) + ((d__11 = z__3.r, abs(d__11)) +
(d__12 = d_imag(&z__3), abs(d__12))) / max(d__15,d__16)) /
ulp;
if (j < mn_1.mplusn) {
i__2 = j + 1 + j * ai_dim1;
if (ai[i__2].r != 0. || ai[i__2].i != 0.) {
ilabad = TRUE_;
result[4] = ulpinv;
}
}
if (j > 1) {
i__2 = j + (j - 1) * ai_dim1;
if (ai[i__2].r != 0. || ai[i__2].i != 0.) {
ilabad = TRUE_;
result[4] = ulpinv;
}
}
temp1 = max(temp1,temp2);
if (ilabad) {
io___46.ciunit = *nout;
s_wsfe(&io___46);
do_fio(&c__1, (char *)&j, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&mn_1.mplusn, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&nptknt, (ftnlen)sizeof(integer));
e_wsfe();
}
/* L110: */
}
result[5] = temp1;
/* Test (7) (if sorting worked) <--------- need to be checked. */
ntest = 7;
result[6] = 0.;
if (linfo == mn_1.mplusn + 3) {
result[6] = ulpinv;
}
/* Test (8): compare the estimated value of DIF and its true value. */
ntest = 8;
result[7] = 0.;
if (difest[1] == 0.) {
if (diftru > abnrm * ulp) {
result[7] = ulpinv;
}
} else if (diftru == 0.) {
if (difest[1] > abnrm * ulp) {
result[7] = ulpinv;
}
} else if (diftru > thrsh2 * difest[1] || diftru * thrsh2 < difest[1]) {
/* Computing MAX */
d__1 = diftru / difest[1], d__2 = difest[1] / diftru;
result[7] = max(d__1,d__2);
}
/* Test (9) */
ntest = 9;
result[8] = 0.;
if (linfo == mn_1.mplusn + 2) {
if (diftru > abnrm * ulp) {
result[8] = ulpinv;
}
if (ifunc > 1 && difest[1] != 0.) {
result[8] = ulpinv;
}
if (ifunc == 1 && pl[0] != 0.) {
result[8] = ulpinv;
}
}
/* Test (10): compare the estimated value of PL and it true value. */
ntest = 10;
result[9] = 0.;
if (pl[0] == 0.) {
if (pltru > abnrm * ulp) {
result[9] = ulpinv;
}
} else if (pltru == 0.) {
if (pl[0] > abnrm * ulp) {
result[9] = ulpinv;
}
} else if (pltru > *thresh * pl[0] || pltru * *thresh < pl[0]) {
result[9] = ulpinv;
}
ntestt += ntest;
/* Print out tests which fail. */
i__1 = ntest;
for (j = 1; j <= i__1; ++j) {
if (result[j - 1] >= *thresh) {
/* If this is the first test to fail, */
/* print a header to the data file. */
if (nerrs == 0) {
io___47.ciunit = *nout;
s_wsfe(&io___47);
do_fio(&c__1, "CGX", (ftnlen)3);
e_wsfe();
/* Matrix types */
io___48.ciunit = *nout;
s_wsfe(&io___48);
e_wsfe();
/* Tests performed */
io___49.ciunit = *nout;
s_wsfe(&io___49);
do_fio(&c__1, "unitary", (ftnlen)7);
do_fio(&c__1, "'", (ftnlen)1);
do_fio(&c__1, "transpose", (ftnlen)9);
for (i__ = 1; i__ <= 4; ++i__) {
do_fio(&c__1, "'", (ftnlen)1);
}
e_wsfe();
}
++nerrs;
if (result[j - 1] < 1e4) {
io___50.ciunit = *nout;
s_wsfe(&io___50);
do_fio(&c__1, (char *)&nptknt, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&mn_1.mplusn, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&j, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&result[j - 1], (ftnlen)sizeof(
doublereal));
e_wsfe();
} else {
io___51.ciunit = *nout;
s_wsfe(&io___51);
do_fio(&c__1, (char *)&nptknt, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&mn_1.mplusn, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&j, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&result[j - 1], (ftnlen)sizeof(
doublereal));
e_wsfe();
}
}
/* L120: */
}
L130:
goto L80;
L140:
L150:
/* Summary */
alasvm_("CGX", nout, &nerrs, &ntestt, &c__0);
work[1].r = (doublereal) maxwrk, work[1].i = 0.;
return 0;
/* End of ZDRGSX */
} /* zdrgsx_ */
