#include "blaswrap.h" /* zdrgev.f -- translated by f2c (version 20061008). You must link the resulting object file with libf2c: on Microsoft Windows system, link with libf2c.lib; on Linux or Unix systems, link with .../path/to/libf2c.a -lm or, if you install libf2c.a in a standard place, with -lf2c -lm -- in that order, at the end of the command line, as in cc *.o -lf2c -lm Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., http://www.netlib.org/f2c/libf2c.zip */ #include "f2c.h" /* Table of constant values */ static doublecomplex c_b1 = {0.,0.}; static integer c__1 = 1; static integer c_n1 = -1; static integer c__2 = 2; static doublereal c_b28 = 1.; static integer c__3 = 3; static integer c__4 = 4; static logical c_true = TRUE_; static logical c_false = FALSE_; static integer c__0 = 0; /* Subroutine */ int zdrgev_(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 *qe, integer *ldqe, doublecomplex *alpha, doublecomplex *beta, doublecomplex *alpha1, doublecomplex *beta1, 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 ZDRGEV: \002,a,\002 returned INFO=\002,i" "6,\002.\002,/3x,\002N=\002,i6,\002, JTYPE=\002,i6,\002, ISEED=" "(\002,3(i5,\002,\002),i5,\002)\002)"; static char fmt_9998[] = "(\002 ZDRGEV: \002,a,\002 Eigenvectors from" " \002,a,\002 incorrectly \002,\002normalized.\002,/\002 Bits of " "error=\002,0p,g10.3,\002,\002,3x,\002N=\002,i4,\002, JTYPE=\002," "i3,\002, ISEED=(\002,3(i4,\002,\002),i5,\002)\002)"; static char fmt_9997[] = "(/1x,a3,\002 -- Complex Generalized eigenvalue" " problem \002,\002driver\002)"; static char fmt_9996[] = "(\002 Matrix types (see ZDRGEV 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: \002,/\002 1 = max " "| ( b A - a B )'*l | / const.,\002,/\002 2 = | |VR(i)| - 1 | / u" "lp,\002,/\002 3 = max | ( b A - a B )*r | / const.\002,/\002 4 =" " | |VL(i)| - 1 | / ulp,\002,/\002 5 = 0 if W same no matter if r" " or l computed,\002,/\002 6 = 0 if l same no matter if l compute" "d,\002,/\002 7 = 0 if r same no matter if r computed,\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,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, qe_dim1, qe_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; doublereal d__1, d__2; doublecomplex z__1, z__2, z__3; /* 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); /* Local variables */ static integer i__, j, n, n1, jc, nb, in, jr; static doublereal ulp; static integer iadd, ierr, nmax; static logical badnn; static doublereal rmagn[4]; static doublecomplex ctemp; extern /* Subroutine */ int zget52_(logical *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer * , doublecomplex *, doublecomplex *, doublecomplex *, doublereal *, doublereal *); static integer nmats, jsize; extern /* Subroutine */ int zggev_(char *, char *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, integer *); static integer nerrs, jtype; 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 *); static doublereal safmin, safmax; static integer ioldsd[4]; extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, ftnlen, ftnlen); 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 *); static integer minwrk, maxwrk; static doublereal ulpinv; static integer mtypes, ntestt; /* Fortran I/O blocks */ static cilist io___40 = { 0, 0, 0, fmt_9999, 0 }; static cilist io___42 = { 0, 0, 0, fmt_9999, 0 }; static cilist io___43 = { 0, 0, 0, fmt_9998, 0 }; static cilist io___44 = { 0, 0, 0, fmt_9998, 0 }; static cilist io___45 = { 0, 0, 0, fmt_9999, 0 }; static cilist io___46 = { 0, 0, 0, fmt_9999, 0 }; static cilist io___47 = { 0, 0, 0, fmt_9999, 0 }; static cilist io___48 = { 0, 0, 0, fmt_9997, 0 }; static cilist io___49 = { 0, 0, 0, fmt_9996, 0 }; static cilist io___50 = { 0, 0, 0, fmt_9995, 0 }; static cilist io___51 = { 0, 0, 0, fmt_9994, 0 }; static cilist io___52 = { 0, 0, 0, fmt_9993, 0 }; static cilist io___53 = { 0, 0, 0, fmt_9992, 0 }; static cilist io___54 = { 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 Purpose ======= ZDRGEV checks the nonsymmetric generalized eigenvalue problem driver routine ZGGEV. ZGGEV computes for a pair of n-by-n nonsymmetric matrices (A,B) the generalized eigenvalues and, optionally, the left and right eigenvectors. A generalized eigenvalue for a pair of matrices (A,B) is a scalar w or a ratio alpha/beta = w, such that A - w*B is singular. It is usually represented as the pair (alpha,beta), as there is reasonalbe interpretation for beta=0, and even for both being zero. A right generalized eigenvector corresponding to a generalized eigenvalue w for a pair of matrices (A,B) is a vector r such that (A - wB) * r = 0. A left generalized eigenvector is a vector l such that l**H * (A - wB) = 0, where l**H is the conjugate-transpose of l. When ZDRGEV 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 tests will be performed and compared with the threshhold THRESH. Results from ZGGEV: (1) max over all left eigenvalue/-vector pairs (alpha/beta,l) of | VL**H * (beta A - alpha B) |/( ulp max(|beta A|, |alpha B|) ) where VL**H is the conjugate-transpose of VL. (2) | |VL(i)| - 1 | / ulp and whether largest component real VL(i) denotes the i-th column of VL. (3) max over all left eigenvalue/-vector pairs (alpha/beta,r) of | (beta A - alpha B) * VR | / ( ulp max(|beta A|, |alpha B|) ) (4) | |VR(i)| - 1 | / ulp and whether largest component real VR(i) denotes the i-th column of VR. (5) W(full) = W(partial) W(full) denotes the eigenvalues computed when both l and r are also computed, and W(partial) denotes the eigenvalues computed when only W, only W and r, or only W and l are computed. (6) VL(full) = VL(partial) VL(full) denotes the left eigenvectors computed when both l and r are computed, and VL(partial) denotes the result when only l is computed. (7) VR(full) = VR(partial) VR(full) denotes the right eigenvectors computed when both l and r are also computed, and VR(partial) denotes the result when only l is computed. 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, ZDRGES 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, ZDRGEV 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 ZDRGES to continue the same random number sequence. THRESH (input) DOUBLE PRECISION A test will count as "failed" if the "error", computed as described above, exceeds THRESH. Note that the error is scaled to be O(1), so THRESH should be a reasonably small multiple of 1, e.g., 10 or 100. In particular, it should not depend on the precision (single vs. double) or the size of the matrix. It must be at least zero. NOUNIT (input) INTEGER The FORTRAN unit number for printing out error messages (e.g., if a routine returns IERR 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 ZGGEV. 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 ZGGEV. Q (workspace) COMPLEX*16 array, dimension (LDQ, max(NN)) The (left) eigenvectors matrix computed by ZGGEV. 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 ZGGEV. QE (workspace) COMPLEX*16 array, dimension( LDQ, max(NN) ) QE holds the computed right or left eigenvectors. LDQE (input) INTEGER The leading dimension of QE. LDQE >= max(1,max(NN)). ALPHA (workspace) COMPLEX*16 array, dimension (max(NN)) BETA (workspace) COMPLEX*16 array, dimension (max(NN)) The generalized eigenvalues of (A,B) computed by ZGGEV. ( ALPHAR(k)+ALPHAI(k)*i ) / BETA(k) is the k-th generalized eigenvalue of A and B. ALPHA1 (workspace) COMPLEX*16 array, dimension (max(NN)) BETA1 (workspace) COMPLEX*16 array, dimension (max(NN)) Like ALPHAR, ALPHAI, BETA, these arrays contain the eigenvalues of A and B, but those computed when ZGGEV only computes a partial eigendecomposition, i.e. not the eigenvalues and left and right eigenvectors. WORK (workspace) COMPLEX*16 array, dimension (LWORK) LWORK (input) INTEGER The number of entries in WORK. LWORK >= N*(N+1) RWORK (workspace) DOUBLE PRECISION array, dimension (8*N) Real workspace. RESULT (output) DOUBLE PRECISION array, dimension (2) 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. ===================================================================== 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; qe_dim1 = *ldqe; qe_offset = 1 + qe_dim1; qe -= qe_offset; --alpha; --beta; --alpha1; --beta1; --work; --rwork; --result; /* Function Body 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; } else if (*ldqe <= 1 || *ldqe < nmax) { *info = -17; } /* 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 * (nmax + 1); /* Computing MAX */ i__1 = 1, i__2 = ilaenv_(&c__1, "ZGEQRF", " ", &nmax, &nmax, &c_n1, & c_n1, (ftnlen)6, (ftnlen)1), i__1 = max(i__1,i__2), i__2 = ilaenv_(&c__1, "ZUNMQR", "LC", &nmax, &nmax, &nmax, &c_n1, ( ftnlen)6, (ftnlen)2), i__1 = max(i__1,i__2), i__2 = ilaenv_(& c__1, "ZUNGQR", " ", &nmax, &nmax, &nmax, &c_n1, (ftnlen)6, ( ftnlen)1); nb = max(i__1,i__2); /* Computing MAX */ i__1 = nmax << 1, i__2 = nmax * (nb + 1), i__1 = max(i__1,i__2), i__2 = nmax * (nmax + 1); maxwrk = max(i__1,i__2); work[1].r = (doublereal) maxwrk, work[1].i = 0.; } if (*lwork < minwrk) { *info = -23; } if (*info != 0) { i__1 = -(*info); xerbla_("ZDRGEV", &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 L210; } ++nmats; /* Save ISEED in case of an error. */ for (j = 1; j <= 4; ++j) { ioldsd[j - 1] = iseed[j]; /* L20: */ } /* 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 L100; } ierr = 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_b28, &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; /* L30: */ } 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_b28, &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_b28, &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.; /* L40: */ } 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; /* L50: */ } /* L60: */ } 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], &ierr); if (ierr != 0) { goto L90; } 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], &ierr); if (ierr != 0) { goto L90; } 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], &ierr); if (ierr != 0) { goto L90; } 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], &ierr); if (ierr != 0) { goto L90; } } } 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; /* L70: */ } /* L80: */ } } L90: if (ierr != 0) { io___40.ciunit = *nounit; s_wsfe(&io___40); do_fio(&c__1, "Generator", (ftnlen)9); do_fio(&c__1, (char *)&ierr, (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(ierr); return 0; } L100: for (i__ = 1; i__ <= 7; ++i__) { result[i__] = -1.; /* L110: */ } /* Call ZGGEV to compute eigenvalues and eigenvectors. */ zlacpy_(" ", &n, &n, &a[a_offset], lda, &s[s_offset], lda); zlacpy_(" ", &n, &n, &b[b_offset], lda, &t[t_offset], lda); zggev_("V", "V", &n, &s[s_offset], lda, &t[t_offset], lda, &alpha[ 1], &beta[1], &q[q_offset], ldq, &z__[z_offset], ldq, & work[1], lwork, &rwork[1], &ierr); if (ierr != 0 && ierr != n + 1) { result[1] = ulpinv; io___42.ciunit = *nounit; s_wsfe(&io___42); do_fio(&c__1, "ZGGEV1", (ftnlen)6); do_fio(&c__1, (char *)&ierr, (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(ierr); goto L190; } /* Do the tests (1) and (2) */ zget52_(&c_true, &n, &a[a_offset], lda, &b[b_offset], lda, &q[ q_offset], ldq, &alpha[1], &beta[1], &work[1], &rwork[1], &result[1]); if (result[2] > *thresh) { io___43.ciunit = *nounit; s_wsfe(&io___43); do_fio(&c__1, "Left", (ftnlen)4); do_fio(&c__1, "ZGGEV1", (ftnlen)6); do_fio(&c__1, (char *)&result[2], (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(); } /* Do the tests (3) and (4) */ zget52_(&c_false, &n, &a[a_offset], lda, &b[b_offset], lda, &z__[ z_offset], ldq, &alpha[1], &beta[1], &work[1], &rwork[1], &result[3]); if (result[4] > *thresh) { io___44.ciunit = *nounit; s_wsfe(&io___44); do_fio(&c__1, "Right", (ftnlen)5); do_fio(&c__1, "ZGGEV1", (ftnlen)6); do_fio(&c__1, (char *)&result[4], (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(); } /* Do test (5) */ zlacpy_(" ", &n, &n, &a[a_offset], lda, &s[s_offset], lda); zlacpy_(" ", &n, &n, &b[b_offset], lda, &t[t_offset], lda); zggev_("N", "N", &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], &ierr); if (ierr != 0 && ierr != n + 1) { result[1] = ulpinv; io___45.ciunit = *nounit; s_wsfe(&io___45); do_fio(&c__1, "ZGGEV2", (ftnlen)6); do_fio(&c__1, (char *)&ierr, (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(ierr); goto L190; } i__3 = n; for (j = 1; j <= i__3; ++j) { i__4 = j; i__5 = j; i__6 = j; i__7 = j; if (alpha[i__4].r != alpha1[i__5].r || alpha[i__4].i != alpha1[i__5].i || (beta[i__6].r != beta1[i__7].r || beta[i__6].i != beta1[i__7].i)) { result[5] = ulpinv; } /* L120: */ } /* Do test (6): Compute eigenvalues and left eigenvectors, and test them */ zlacpy_(" ", &n, &n, &a[a_offset], lda, &s[s_offset], lda); zlacpy_(" ", &n, &n, &b[b_offset], lda, &t[t_offset], lda); zggev_("V", "N", &n, &s[s_offset], lda, &t[t_offset], lda, & alpha1[1], &beta1[1], &qe[qe_offset], ldqe, &z__[z_offset] , ldq, &work[1], lwork, &rwork[1], &ierr); if (ierr != 0 && ierr != n + 1) { result[1] = ulpinv; io___46.ciunit = *nounit; s_wsfe(&io___46); do_fio(&c__1, "ZGGEV3", (ftnlen)6); do_fio(&c__1, (char *)&ierr, (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(ierr); goto L190; } i__3 = n; for (j = 1; j <= i__3; ++j) { i__4 = j; i__5 = j; i__6 = j; i__7 = j; if (alpha[i__4].r != alpha1[i__5].r || alpha[i__4].i != alpha1[i__5].i || (beta[i__6].r != beta1[i__7].r || beta[i__6].i != beta1[i__7].i)) { result[6] = ulpinv; } /* L130: */ } i__3 = n; for (j = 1; j <= i__3; ++j) { i__4 = n; for (jc = 1; jc <= i__4; ++jc) { i__5 = j + jc * q_dim1; i__6 = j + jc * qe_dim1; if (q[i__5].r != qe[i__6].r || q[i__5].i != qe[i__6].i) { result[6] = ulpinv; } /* L140: */ } /* L150: */ } /* Do test (7): Compute eigenvalues and right eigenvectors, and test them */ zlacpy_(" ", &n, &n, &a[a_offset], lda, &s[s_offset], lda); zlacpy_(" ", &n, &n, &b[b_offset], lda, &t[t_offset], lda); zggev_("N", "V", &n, &s[s_offset], lda, &t[t_offset], lda, & alpha1[1], &beta1[1], &q[q_offset], ldq, &qe[qe_offset], ldqe, &work[1], lwork, &rwork[1], &ierr); if (ierr != 0 && ierr != n + 1) { result[1] = ulpinv; io___47.ciunit = *nounit; s_wsfe(&io___47); do_fio(&c__1, "ZGGEV4", (ftnlen)6); do_fio(&c__1, (char *)&ierr, (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(ierr); goto L190; } i__3 = n; for (j = 1; j <= i__3; ++j) { i__4 = j; i__5 = j; i__6 = j; i__7 = j; if (alpha[i__4].r != alpha1[i__5].r || alpha[i__4].i != alpha1[i__5].i || (beta[i__6].r != beta1[i__7].r || beta[i__6].i != beta1[i__7].i)) { result[7] = ulpinv; } /* L160: */ } i__3 = n; for (j = 1; j <= i__3; ++j) { i__4 = n; for (jc = 1; jc <= i__4; ++jc) { i__5 = j + jc * z_dim1; i__6 = j + jc * qe_dim1; if (z__[i__5].r != qe[i__6].r || z__[i__5].i != qe[i__6] .i) { result[7] = ulpinv; } /* L170: */ } /* L180: */ } /* End of Loop -- Check for RESULT(j) > THRESH */ L190: ntestt += 7; /* Print out tests which fail. */ for (jr = 1; jr <= 7; ++jr) { if (result[jr] >= *thresh) { /* If this is the first test to fail, print a header to the data file. */ if (nerrs == 0) { io___48.ciunit = *nounit; s_wsfe(&io___48); do_fio(&c__1, "ZGV", (ftnlen)3); e_wsfe(); /* Matrix types */ io___49.ciunit = *nounit; s_wsfe(&io___49); e_wsfe(); io___50.ciunit = *nounit; s_wsfe(&io___50); e_wsfe(); io___51.ciunit = *nounit; s_wsfe(&io___51); do_fio(&c__1, "Orthogonal", (ftnlen)10); e_wsfe(); /* Tests performed */ io___52.ciunit = *nounit; s_wsfe(&io___52); e_wsfe(); } ++nerrs; if (result[jr] < 1e4) { io___53.ciunit = *nounit; s_wsfe(&io___53); 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___54.ciunit = *nounit; s_wsfe(&io___54); 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(); } } /* L200: */ } L210: ; } /* L220: */ } /* Summary */ alasvm_("ZGV", nounit, &nerrs, &ntestt, &c__0); work[1].r = (doublereal) maxwrk, work[1].i = 0.; return 0; /* End of ZDRGEV */ } /* zdrgev_ */