#include "blaswrap.h" /* -- translated by f2c (version 19990503). You must link the resulting object file with the libraries: -lf2c -lm (in that order) */ #include "f2c.h" /* Table of constant values */ static doublecomplex c_b1 = {0.,0.}; static doublecomplex c_b2 = {1.,0.}; static integer c__4 = 4; static doublereal c_b17 = 1.; static integer c__3 = 3; static integer c__1 = 1; static logical c_true = TRUE_; static logical c_false = FALSE_; static integer c__2 = 2; /* Subroutine */ int zchkgg_(integer *nsizes, integer *nn, integer *ntypes, logical *dotype, integer *iseed, doublereal *thresh, logical *tstdif, doublereal *thrshn, integer *nounit, doublecomplex *a, integer *lda, doublecomplex *b, doublecomplex *h__, doublecomplex *t, doublecomplex *s1, doublecomplex *s2, doublecomplex *p1, doublecomplex *p2, doublecomplex *u, integer *ldu, doublecomplex *v, doublecomplex *q, doublecomplex *z__, doublecomplex *alpha1, doublecomplex *beta1, doublecomplex *alpha3, doublecomplex *beta3, doublecomplex *evectl, doublecomplex *evectr, doublecomplex *work, integer *lwork, doublereal *rwork, logical *llwork, 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 ZCHKGG: \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 ZCHKGG: \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\002)"; static char fmt_9996[] = "(\002 Matrix types (see ZCHKGG 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: (H is Hessenberg, S " "is Schur, B, \002,\002T, P are triangular,\002,/20x,\002U, V, Q," " and Z are \002,a,\002, l and r are the\002,/20x,\002appropriate" " left and right eigenvectors, resp., a is\002,/20x,\002alpha, b " "is beta, and \002,a,\002 means \002,a,\002.)\002,/\002 1 = | A -" " U H V\002,a,\002 | / ( |A| n ulp ) 2 = | B - U T V\002,a" ",\002 | / ( |B| n ulp )\002,/\002 3 = | I - UU\002,a,\002 | / ( " "n ulp ) 4 = | I - VV\002,a,\002 | / ( n ulp )\002," "/\002 5 = | H - Q S Z\002,a,\002 | / ( |H| n ulp )\002,6x,\0026 " "= | T - Q P Z\002,a,\002 | / ( |T| n ulp )\002,/\002 7 = | I - QQ" "\002,a,\002 | / ( n ulp ) 8 = | I - ZZ\002,a,\002 | " "/ ( n ulp )\002,/\002 9 = max | ( b S - a P )\002,a,\002 l | / c" "onst. 10 = max | ( b H - a T )\002,a,\002 l | / const.\002,/" "\002 11= max | ( b S - a P ) r | / const. 12 = max | ( b H\002," "\002 - a T ) r | / const.\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, evectl_dim1, evectl_offset, evectr_dim1, evectr_offset, h_dim1, h_offset, p1_dim1, p1_offset, p2_dim1, p2_offset, q_dim1, q_offset, s1_dim1, s1_offset, s2_dim1, s2_offset, t_dim1, t_offset, u_dim1, u_offset, v_dim1, v_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 iadd, nmax; static doublereal temp1, temp2; static integer j, n; static logical badnn; static doublereal dumma[4]; static integer iinfo; static doublereal rmagn[4]; static doublecomplex ctemp; static doublereal anorm, bnorm; extern /* Subroutine */ int 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 *); static integer nmats, jsize, nerrs, i1, jtype, ntest, n1; extern /* Subroutine */ int dlabad_(doublereal *, doublereal *), zgeqr2_( integer *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *), zlatm4_(integer *, integer *, integer *, integer *, logical *, doublereal *, doublereal *, doublereal *, integer *, integer *, doublecomplex *, integer *); static integer jc, in; extern doublereal dlamch_(char *); static integer jr; extern /* Subroutine */ int zunm2r_(char *, char *, integer *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *); static doublecomplex cdumma[4]; static doublereal safmin, safmax; static integer ioldsd[4]; extern doublereal zlange_(char *, integer *, integer *, doublecomplex *, integer *, doublereal *); extern /* Subroutine */ int dlasum_(char *, integer *, integer *, integer *), xerbla_(char *, integer *); extern /* Double Complex */ VOID zlarnd_(doublecomplex *, integer *, integer *); extern /* Subroutine */ int zgghrd_(char *, char *, integer *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, integer * ), zlacpy_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *), zlarfg_(integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *), zlaset_(char *, integer *, integer *, doublecomplex *, doublecomplex *, doublecomplex *, integer *), ztgevc_(char *, char *, logical *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, integer *, integer *, doublecomplex *, doublereal *, integer *), zhgeqz_(char *, char *, char *, integer *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, integer *); static doublereal ulpinv; static integer lwkopt, mtypes, ntestt; static doublereal ulp; /* Fortran I/O blocks */ static cilist io___41 = { 0, 0, 0, fmt_9999, 0 }; static cilist io___42 = { 0, 0, 0, fmt_9999, 0 }; static cilist io___43 = { 0, 0, 0, fmt_9999, 0 }; static cilist io___44 = { 0, 0, 0, fmt_9999, 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_9999, 0 }; static cilist io___51 = { 0, 0, 0, fmt_9999, 0 }; static cilist io___52 = { 0, 0, 0, fmt_9999, 0 }; static cilist io___54 = { 0, 0, 0, fmt_9998, 0 }; static cilist io___55 = { 0, 0, 0, fmt_9999, 0 }; static cilist io___56 = { 0, 0, 0, fmt_9998, 0 }; static cilist io___57 = { 0, 0, 0, fmt_9999, 0 }; static cilist io___58 = { 0, 0, 0, fmt_9999, 0 }; static cilist io___59 = { 0, 0, 0, fmt_9998, 0 }; static cilist io___60 = { 0, 0, 0, fmt_9999, 0 }; static cilist io___61 = { 0, 0, 0, fmt_9998, 0 }; static cilist io___64 = { 0, 0, 0, fmt_9997, 0 }; static cilist io___65 = { 0, 0, 0, fmt_9996, 0 }; static cilist io___66 = { 0, 0, 0, fmt_9995, 0 }; static cilist io___67 = { 0, 0, 0, fmt_9994, 0 }; static cilist io___68 = { 0, 0, 0, fmt_9993, 0 }; static cilist io___69 = { 0, 0, 0, fmt_9992, 0 }; static cilist io___70 = { 0, 0, 0, fmt_9991, 0 }; #define a_subscr(a_1,a_2) (a_2)*a_dim1 + a_1 #define a_ref(a_1,a_2) a[a_subscr(a_1,a_2)] #define b_subscr(a_1,a_2) (a_2)*b_dim1 + a_1 #define b_ref(a_1,a_2) b[b_subscr(a_1,a_2)] #define u_subscr(a_1,a_2) (a_2)*u_dim1 + a_1 #define u_ref(a_1,a_2) u[u_subscr(a_1,a_2)] #define v_subscr(a_1,a_2) (a_2)*v_dim1 + a_1 #define v_ref(a_1,a_2) v[v_subscr(a_1,a_2)] #define evectl_subscr(a_1,a_2) (a_2)*evectl_dim1 + a_1 #define evectl_ref(a_1,a_2) evectl[evectl_subscr(a_1,a_2)] #define evectr_subscr(a_1,a_2) (a_2)*evectr_dim1 + a_1 #define evectr_ref(a_1,a_2) evectr[evectr_subscr(a_1,a_2)] /* -- LAPACK test routine (version 3.0) -- Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., Courant Institute, Argonne National Lab, and Rice University September 30, 1994 Purpose ======= ZCHKGG checks the nonsymmetric generalized eigenvalue problem routines. H H H ZGGHRD factors A and B as U H V and U T V , where means conjugate transpose, H is hessenberg, T is triangular and U and V are unitary. H H ZHGEQZ factors H and T as Q S Z and Q P Z , where P and S are 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)=P(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 ZTGEVC computes the matrix L of left eigenvectors and the matrix R of right eigenvectors for the matrix pair ( S, P ). In the description below, l and r are left and right eigenvectors corresponding to the generalized eigenvalues (alpha,beta). When ZCHKGG 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, 13 tests will be performed. The first twelve "test ratios" should be small -- O(1). They will be compared with the threshhold THRESH: H (1) | A - U H V | / ( |A| n ulp ) H (2) | B - U T V | / ( |B| n ulp ) H (3) | I - UU | / ( n ulp ) H (4) | I - VV | / ( n ulp ) H (5) | H - Q S Z | / ( |H| n ulp ) H (6) | T - Q P Z | / ( |T| n ulp ) H (7) | I - QQ | / ( n ulp ) H (8) | I - ZZ | / ( n ulp ) (9) max over all left eigenvalue/-vector pairs (beta/alpha,l) of H | (beta A - alpha B) l | / ( ulp max( |beta A|, |alpha B| ) ) (10) max over all left eigenvalue/-vector pairs (beta/alpha,l') of H | (beta H - alpha T) l' | / ( ulp max( |beta H|, |alpha T| ) ) where the eigenvectors l' are the result of passing Q to DTGEVC and back transforming (JOB='B'). (11) max over all right eigenvalue/-vector pairs (beta/alpha,r) of | (beta A - alpha B) r | / ( ulp max( |beta A|, |alpha B| ) ) (12) max over all right eigenvalue/-vector pairs (beta/alpha,r') of | (beta H - alpha T) r' | / ( ulp max( |beta H|, |alpha T| ) ) where the eigenvectors r' are the result of passing Z to DTGEVC and back transforming (JOB='B'). The last three test ratios will usually be small, but there is no mathematical requirement that they be so. They are therefore compared with THRESH only if TSTDIF is .TRUE. (13) | S(Q,Z computed) - S(Q,Z not computed) | / ( |S| ulp ) (14) | P(Q,Z computed) - P(Q,Z not computed) | / ( |P| ulp ) (15) max( |alpha(Q,Z computed) - alpha(Q,Z not computed)|/|S| , |beta(Q,Z computed) - beta(Q,Z not computed)|/|P| ) / ulp In addition, the normalization of L and R are checked, and compared with the threshhold THRSHN. 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 P*D1, P is a random unitary diagonal matrix (i.e., with random magnitude 1 entries on the diagonal), and D1=diag( 0, 1,..., N-1 ) (i.e., a diagonal matrix with D1(1,1)=0, D1(2,2)=1, ..., D1(N,N)=N-1.) (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=P*diag( 0, 0, 1, ..., N-3, 0 ) and D2=Q*diag( 0, N-3, N-4,..., 1, 0, 0 ), and P and Q are random unitary diagonal matrices. t t (16) U ( J , J ) V where U and V are random unitary matrices. (17) U ( T1, T2 ) V where T1 and T2 are upper triangular matrices with random O(1) entries above the diagonal and diagonal entries diag(T1) = P*( 0, 0, 1, ..., N-3, 0 ) and diag(T2) = Q*( 0, N-3, N-4,..., 1, 0, 0 ) (18) U ( T1, T2 ) V diag(T1) = ( 0, 0, 1, 1, s, ..., s, 0 ) diag(T2) = ( 0, 1, 0, 1,..., 1, 0 ) s = machine precision. (19) U ( T1, T2 ) V 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) U ( T1, T2 ) V diag(T1)=( 0, 0, 1, 1, a, ..., a =s, 0 ) diag(T2) = ( 0, 1, 0, 1, ..., 1, 0, 0 ) (21) U ( T1, T2 ) V 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) U ( big*T1, small*T2 ) V diag(T1) = P*( 0, 0, 1, ..., N-3, 0 ) diag(T2) = ( 0, 1, ..., 1, 0, 0 ) (23) U ( small*T1, big*T2 ) V diag(T1) = P*( 0, 0, 1, ..., N-3, 0 ) diag(T2) = ( 0, 1, ..., 1, 0, 0 ) (24) U ( small*T1, small*T2 ) V diag(T1) = P*( 0, 0, 1, ..., N-3, 0 ) diag(T2) = ( 0, 1, ..., 1, 0, 0 ) (25) U ( big*T1, big*T2 ) V diag(T1) = P*( 0, 0, 1, ..., N-3, 0 ) diag(T2) = ( 0, 1, ..., 1, 0, 0 ) (26) U ( T1, T2 ) V 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, ZCHKGG 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, ZCHKGG 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 ZCHKGG 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. TSTDIF (input) LOGICAL Specifies whether test ratios 13-15 will be computed and compared with THRESH. = .FALSE.: Only test ratios 1-12 will be computed and tested. Ratios 13-15 will be set to zero. = .TRUE.: All the test ratios 1-15 will be computed and tested. 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, H, T, S1, P1, S2, and P2. 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. H (workspace) COMPLEX*16 array, dimension (LDA, max(NN)) The upper Hessenberg matrix computed from A by ZGGHRD. T (workspace) COMPLEX*16 array, dimension (LDA, max(NN)) The upper triangular matrix computed from B by ZGGHRD. S1 (workspace) COMPLEX*16 array, dimension (LDA, max(NN)) The Schur (upper triangular) matrix computed from H by ZHGEQZ when Q and Z are also computed. S2 (workspace) COMPLEX*16 array, dimension (LDA, max(NN)) The Schur (upper triangular) matrix computed from H by ZHGEQZ when Q and Z are not computed. P1 (workspace) COMPLEX*16 array, dimension (LDA, max(NN)) The upper triangular matrix computed from T by ZHGEQZ when Q and Z are also computed. P2 (workspace) COMPLEX*16 array, dimension (LDA, max(NN)) The upper triangular matrix computed from T by ZHGEQZ when Q and Z are not computed. U (workspace) COMPLEX*16 array, dimension (LDU, max(NN)) The (left) unitary matrix computed by ZGGHRD. LDU (input) INTEGER The leading dimension of U, V, Q, Z, EVECTL, and EVEZTR. It must be at least 1 and at least max( NN ). V (workspace) COMPLEX*16 array, dimension (LDU, max(NN)) The (right) unitary matrix computed by ZGGHRD. Q (workspace) COMPLEX*16 array, dimension (LDU, max(NN)) The (left) unitary matrix computed by ZHGEQZ. Z (workspace) COMPLEX*16 array, dimension (LDU, max(NN)) The (left) unitary matrix computed by ZHGEQZ. ALPHA1 (workspace) COMPLEX*16 array, dimension (max(NN)) BETA1 (workspace) COMPLEX*16 array, dimension (max(NN)) The generalized eigenvalues of (A,B) computed by ZHGEQZ when Q, Z, and the full Schur matrices are computed. ALPHA3 (workspace) COMPLEX*16 array, dimension (max(NN)) BETA3 (workspace) COMPLEX*16 array, dimension (max(NN)) The generalized eigenvalues of (A,B) computed by ZHGEQZ when neither Q, Z, nor the Schur matrices are computed. EVECTL (workspace) COMPLEX*16 array, dimension (LDU, max(NN)) The (lower triangular) left eigenvector matrix for the matrices in S1 and P1. EVEZTR (workspace) COMPLEX*16 array, dimension (LDU, max(NN)) The (upper triangular) right eigenvector matrix for the matrices in S1 and P1. WORK (workspace) COMPLEX*16 array, dimension (LWORK) LWORK (input) INTEGER The number of entries in WORK. This must be at least max( 4*N, 2 * N**2, 1 ), for all N=NN(j). RWORK (workspace) DOUBLE PRECISION array, dimension (2*max(NN)) LLWORK (workspace) LOGICAL array, dimension (max(NN)) 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. 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; p2_dim1 = *lda; p2_offset = 1 + p2_dim1 * 1; p2 -= p2_offset; p1_dim1 = *lda; p1_offset = 1 + p1_dim1 * 1; p1 -= p1_offset; s2_dim1 = *lda; s2_offset = 1 + s2_dim1 * 1; s2 -= s2_offset; s1_dim1 = *lda; s1_offset = 1 + s1_dim1 * 1; s1 -= s1_offset; t_dim1 = *lda; t_offset = 1 + t_dim1 * 1; t -= t_offset; h_dim1 = *lda; h_offset = 1 + h_dim1 * 1; h__ -= h_offset; b_dim1 = *lda; b_offset = 1 + b_dim1 * 1; b -= b_offset; a_dim1 = *lda; a_offset = 1 + a_dim1 * 1; a -= a_offset; evectr_dim1 = *ldu; evectr_offset = 1 + evectr_dim1 * 1; evectr -= evectr_offset; evectl_dim1 = *ldu; evectl_offset = 1 + evectl_dim1 * 1; evectl -= evectl_offset; z_dim1 = *ldu; z_offset = 1 + z_dim1 * 1; z__ -= z_offset; q_dim1 = *ldu; q_offset = 1 + q_dim1 * 1; q -= q_offset; v_dim1 = *ldu; v_offset = 1 + v_dim1 * 1; v -= v_offset; u_dim1 = *ldu; u_offset = 1 + u_dim1 * 1; u -= u_offset; --alpha1; --beta1; --alpha3; --beta3; --work; --rwork; --llwork; --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: */ } /* Computing MAX */ i__1 = (nmax << 1) * nmax, i__2 = nmax << 2, i__1 = max(i__1,i__2); lwkopt = max(i__1,1); /* 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 (*ldu <= 1 || *ldu < nmax) { *info = -19; } else if (lwkopt > *lwork) { *info = -30; } if (*info != 0) { i__1 = -(*info); xerbla_("ZCHKGG", &i__1); return 0; } /* Quick return if possible */ if (*nsizes == 0 || *ntypes == 0) { return 0; } safmin = dlamch_("Safe minimum"); ulp = dlamch_("Epsilon") * dlamch_("Base"); 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 L230; } ++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 <= 15; ++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, 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__4, &iseed[1], &a[ a_offset], lda); iadd = kadd[kazero[jtype - 1] - 1]; if (iadd > 0 && iadd <= n) { i__3 = a_subscr(iadd, iadd); 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_b17, &rmagn[ktrian[jtype - 1] * kbmagn[jtype - 1]], &c__4, &iseed[1], &b[ b_offset], lda); iadd = kadd[kbzero[jtype - 1] - 1]; if (iadd != 0) { i__3 = b_subscr(iadd, iadd); 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 U, V as Householder transformations times a diagonal matrix. (Note that ZLARFG makes U(j,j) and V(j,j) real.) */ i__3 = n - 1; for (jc = 1; jc <= i__3; ++jc) { i__4 = n; for (jr = jc; jr <= i__4; ++jr) { i__5 = u_subscr(jr, jc); zlarnd_(&z__1, &c__3, &iseed[1]); u[i__5].r = z__1.r, u[i__5].i = z__1.i; i__5 = v_subscr(jr, jc); zlarnd_(&z__1, &c__3, &iseed[1]); v[i__5].r = z__1.r, v[i__5].i = z__1.i; /* L40: */ } i__4 = n + 1 - jc; zlarfg_(&i__4, &u_ref(jc, jc), &u_ref(jc + 1, jc), & c__1, &work[jc]); i__4 = (n << 1) + jc; i__5 = u_subscr(jc, jc); d__2 = u[i__5].r; d__1 = d_sign(&c_b17, &d__2); work[i__4].r = d__1, work[i__4].i = 0.; i__4 = u_subscr(jc, jc); u[i__4].r = 1., u[i__4].i = 0.; i__4 = n + 1 - jc; zlarfg_(&i__4, &v_ref(jc, jc), &v_ref(jc + 1, jc), & c__1, &work[n + jc]); i__4 = n * 3 + jc; i__5 = v_subscr(jc, jc); d__2 = v[i__5].r; d__1 = d_sign(&c_b17, &d__2); work[i__4].r = d__1, work[i__4].i = 0.; i__4 = v_subscr(jc, jc); v[i__4].r = 1., v[i__4].i = 0.; /* L50: */ } zlarnd_(&z__1, &c__3, &iseed[1]); ctemp.r = z__1.r, ctemp.i = z__1.i; i__3 = u_subscr(n, n); u[i__3].r = 1., u[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 = v_subscr(n, n); v[i__3].r = 1., v[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 = a_subscr(jr, jc); 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 = a_subscr(jr, jc); 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 = b_subscr(jr, jc); 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 = b_subscr(jr, jc); 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, &u[u_offset], ldu, &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, &v[v_offset], ldu, &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, &u[u_offset], ldu, &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, &v[v_offset], ldu, &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 = a_subscr(jr, jc); 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 = b_subscr(jr, jc); 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: */ } } anorm = zlange_("1", &n, &n, &a[a_offset], lda, &rwork[1]); bnorm = zlange_("1", &n, &n, &b[b_offset], lda, &rwork[1]); 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: /* Call ZGEQR2, ZUNM2R, and ZGGHRD to compute H, T, U, and V */ zlacpy_(" ", &n, &n, &a[a_offset], lda, &h__[h_offset], lda); zlacpy_(" ", &n, &n, &b[b_offset], lda, &t[t_offset], lda); ntest = 1; result[1] = ulpinv; zgeqr2_(&n, &n, &t[t_offset], lda, &work[1], &work[n + 1], &iinfo) ; if (iinfo != 0) { io___42.ciunit = *nounit; s_wsfe(&io___42); do_fio(&c__1, "ZGEQR2", (ftnlen)6); do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer)); do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer)); e_wsfe(); *info = abs(iinfo); goto L210; } zunm2r_("L", "C", &n, &n, &n, &t[t_offset], lda, &work[1], &h__[ h_offset], lda, &work[n + 1], &iinfo); if (iinfo != 0) { io___43.ciunit = *nounit; s_wsfe(&io___43); do_fio(&c__1, "ZUNM2R", (ftnlen)6); do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer)); do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer)); e_wsfe(); *info = abs(iinfo); goto L210; } zlaset_("Full", &n, &n, &c_b1, &c_b2, &u[u_offset], ldu); zunm2r_("R", "N", &n, &n, &n, &t[t_offset], lda, &work[1], &u[ u_offset], ldu, &work[n + 1], &iinfo); if (iinfo != 0) { io___44.ciunit = *nounit; s_wsfe(&io___44); do_fio(&c__1, "ZUNM2R", (ftnlen)6); do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer)); do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer)); e_wsfe(); *info = abs(iinfo); goto L210; } zgghrd_("V", "I", &n, &c__1, &n, &h__[h_offset], lda, &t[t_offset] , lda, &u[u_offset], ldu, &v[v_offset], ldu, &iinfo); if (iinfo != 0) { io___45.ciunit = *nounit; s_wsfe(&io___45); do_fio(&c__1, "ZGGHRD", (ftnlen)6); do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer)); do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer)); e_wsfe(); *info = abs(iinfo); goto L210; } ntest = 4; /* Do tests 1--4 */ zget51_(&c__1, &n, &a[a_offset], lda, &h__[h_offset], lda, &u[ u_offset], ldu, &v[v_offset], ldu, &work[1], &rwork[1], & result[1]); zget51_(&c__1, &n, &b[b_offset], lda, &t[t_offset], lda, &u[ u_offset], ldu, &v[v_offset], ldu, &work[1], &rwork[1], & result[2]); zget51_(&c__3, &n, &b[b_offset], lda, &t[t_offset], lda, &u[ u_offset], ldu, &u[u_offset], ldu, &work[1], &rwork[1], & result[3]); zget51_(&c__3, &n, &b[b_offset], lda, &t[t_offset], lda, &v[ v_offset], ldu, &v[v_offset], ldu, &work[1], &rwork[1], & result[4]); /* Call ZHGEQZ to compute S1, P1, S2, P2, Q, and Z, do tests. Compute T1 and UZ Eigenvalues only */ zlacpy_(" ", &n, &n, &h__[h_offset], lda, &s2[s2_offset], lda); zlacpy_(" ", &n, &n, &t[t_offset], lda, &p2[p2_offset], lda); ntest = 5; result[5] = ulpinv; zhgeqz_("E", "N", "N", &n, &c__1, &n, &s2[s2_offset], lda, &p2[ p2_offset], lda, &alpha3[1], &beta3[1], &q[q_offset], ldu, &z__[z_offset], ldu, &work[1], lwork, &rwork[1], &iinfo); if (iinfo != 0) { io___46.ciunit = *nounit; s_wsfe(&io___46); do_fio(&c__1, "ZHGEQZ(E)", (ftnlen)9); do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer)); do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer)); e_wsfe(); *info = abs(iinfo); goto L210; } /* Eigenvalues and Full Schur Form */ zlacpy_(" ", &n, &n, &h__[h_offset], lda, &s2[s2_offset], lda); zlacpy_(" ", &n, &n, &t[t_offset], lda, &p2[p2_offset], lda); zhgeqz_("S", "N", "N", &n, &c__1, &n, &s2[s2_offset], lda, &p2[ p2_offset], lda, &alpha1[1], &beta1[1], &q[q_offset], ldu, &z__[z_offset], ldu, &work[1], lwork, &rwork[1], &iinfo); if (iinfo != 0) { io___47.ciunit = *nounit; s_wsfe(&io___47); do_fio(&c__1, "ZHGEQZ(S)", (ftnlen)9); do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer)); do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer)); e_wsfe(); *info = abs(iinfo); goto L210; } /* Eigenvalues, Schur Form, and Schur Vectors */ zlacpy_(" ", &n, &n, &h__[h_offset], lda, &s1[s1_offset], lda); zlacpy_(" ", &n, &n, &t[t_offset], lda, &p1[p1_offset], lda); zhgeqz_("S", "I", "I", &n, &c__1, &n, &s1[s1_offset], lda, &p1[ p1_offset], lda, &alpha1[1], &beta1[1], &q[q_offset], ldu, &z__[z_offset], ldu, &work[1], lwork, &rwork[1], &iinfo); if (iinfo != 0) { io___48.ciunit = *nounit; s_wsfe(&io___48); do_fio(&c__1, "ZHGEQZ(V)", (ftnlen)9); do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer)); do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer)); e_wsfe(); *info = abs(iinfo); goto L210; } ntest = 8; /* Do Tests 5--8 */ zget51_(&c__1, &n, &h__[h_offset], lda, &s1[s1_offset], lda, &q[ q_offset], ldu, &z__[z_offset], ldu, &work[1], &rwork[1], &result[5]); zget51_(&c__1, &n, &t[t_offset], lda, &p1[p1_offset], lda, &q[ q_offset], ldu, &z__[z_offset], ldu, &work[1], &rwork[1], &result[6]); zget51_(&c__3, &n, &t[t_offset], lda, &p1[p1_offset], lda, &q[ q_offset], ldu, &q[q_offset], ldu, &work[1], &rwork[1], & result[7]); zget51_(&c__3, &n, &t[t_offset], lda, &p1[p1_offset], lda, &z__[ z_offset], ldu, &z__[z_offset], ldu, &work[1], &rwork[1], &result[8]); /* Compute the Left and Right Eigenvectors of (S1,P1) 9: Compute the left eigenvector Matrix without back transforming: */ ntest = 9; result[9] = ulpinv; /* To test "SELECT" option, compute half of the eigenvectors in one call, and half in another */ i1 = n / 2; i__3 = i1; for (j = 1; j <= i__3; ++j) { llwork[j] = TRUE_; /* L120: */ } i__3 = n; for (j = i1 + 1; j <= i__3; ++j) { llwork[j] = FALSE_; /* L130: */ } ztgevc_("L", "S", &llwork[1], &n, &s1[s1_offset], lda, &p1[ p1_offset], lda, &evectl[evectl_offset], ldu, cdumma, ldu, &n, &in, &work[1], &rwork[1], &iinfo); if (iinfo != 0) { io___51.ciunit = *nounit; s_wsfe(&io___51); do_fio(&c__1, "ZTGEVC(L,S1)", (ftnlen)12); 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 L210; } i1 = in; i__3 = i1; for (j = 1; j <= i__3; ++j) { llwork[j] = FALSE_; /* L140: */ } i__3 = n; for (j = i1 + 1; j <= i__3; ++j) { llwork[j] = TRUE_; /* L150: */ } ztgevc_("L", "S", &llwork[1], &n, &s1[s1_offset], lda, &p1[ p1_offset], lda, &evectl_ref(1, i1 + 1), ldu, cdumma, ldu, &n, &in, &work[1], &rwork[1], &iinfo); if (iinfo != 0) { io___52.ciunit = *nounit; s_wsfe(&io___52); do_fio(&c__1, "ZTGEVC(L,S2)", (ftnlen)12); 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 L210; } zget52_(&c_true, &n, &s1[s1_offset], lda, &p1[p1_offset], lda, & evectl[evectl_offset], ldu, &alpha1[1], &beta1[1], &work[ 1], &rwork[1], dumma); result[9] = dumma[0]; if (dumma[1] > *thrshn) { io___54.ciunit = *nounit; s_wsfe(&io___54); do_fio(&c__1, "Left", (ftnlen)4); do_fio(&c__1, "ZTGEVC(HOWMNY=S)", (ftnlen)16); 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(); } /* 10: Compute the left eigenvector Matrix with back transforming: */ ntest = 10; result[10] = ulpinv; zlacpy_("F", &n, &n, &q[q_offset], ldu, &evectl[evectl_offset], ldu); ztgevc_("L", "B", &llwork[1], &n, &s1[s1_offset], lda, &p1[ p1_offset], lda, &evectl[evectl_offset], ldu, cdumma, ldu, &n, &in, &work[1], &rwork[1], &iinfo); if (iinfo != 0) { io___55.ciunit = *nounit; s_wsfe(&io___55); do_fio(&c__1, "ZTGEVC(L,B)", (ftnlen)11); do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer)); do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer)); e_wsfe(); *info = abs(iinfo); goto L210; } zget52_(&c_true, &n, &h__[h_offset], lda, &t[t_offset], lda, & evectl[evectl_offset], ldu, &alpha1[1], &beta1[1], &work[ 1], &rwork[1], dumma); result[10] = dumma[0]; if (dumma[1] > *thrshn) { io___56.ciunit = *nounit; s_wsfe(&io___56); do_fio(&c__1, "Left", (ftnlen)4); do_fio(&c__1, "ZTGEVC(HOWMNY=B)", (ftnlen)16); 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(); } /* 11: Compute the right eigenvector Matrix without back transforming: */ ntest = 11; result[11] = ulpinv; /* To test "SELECT" option, compute half of the eigenvectors in one call, and half in another */ i1 = n / 2; i__3 = i1; for (j = 1; j <= i__3; ++j) { llwork[j] = TRUE_; /* L160: */ } i__3 = n; for (j = i1 + 1; j <= i__3; ++j) { llwork[j] = FALSE_; /* L170: */ } ztgevc_("R", "S", &llwork[1], &n, &s1[s1_offset], lda, &p1[ p1_offset], lda, cdumma, ldu, &evectr[evectr_offset], ldu, &n, &in, &work[1], &rwork[1], &iinfo); if (iinfo != 0) { io___57.ciunit = *nounit; s_wsfe(&io___57); do_fio(&c__1, "ZTGEVC(R,S1)", (ftnlen)12); 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 L210; } i1 = in; i__3 = i1; for (j = 1; j <= i__3; ++j) { llwork[j] = FALSE_; /* L180: */ } i__3 = n; for (j = i1 + 1; j <= i__3; ++j) { llwork[j] = TRUE_; /* L190: */ } ztgevc_("R", "S", &llwork[1], &n, &s1[s1_offset], lda, &p1[ p1_offset], lda, cdumma, ldu, &evectr_ref(1, i1 + 1), ldu, &n, &in, &work[1], &rwork[1], &iinfo); if (iinfo != 0) { io___58.ciunit = *nounit; s_wsfe(&io___58); do_fio(&c__1, "ZTGEVC(R,S2)", (ftnlen)12); 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 L210; } zget52_(&c_false, &n, &s1[s1_offset], lda, &p1[p1_offset], lda, & evectr[evectr_offset], ldu, &alpha1[1], &beta1[1], &work[ 1], &rwork[1], dumma); result[11] = dumma[0]; if (dumma[1] > *thresh) { io___59.ciunit = *nounit; s_wsfe(&io___59); do_fio(&c__1, "Right", (ftnlen)5); do_fio(&c__1, "ZTGEVC(HOWMNY=S)", (ftnlen)16); 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(); } /* 12: Compute the right eigenvector Matrix with back transforming: */ ntest = 12; result[12] = ulpinv; zlacpy_("F", &n, &n, &z__[z_offset], ldu, &evectr[evectr_offset], ldu); ztgevc_("R", "B", &llwork[1], &n, &s1[s1_offset], lda, &p1[ p1_offset], lda, cdumma, ldu, &evectr[evectr_offset], ldu, &n, &in, &work[1], &rwork[1], &iinfo); if (iinfo != 0) { io___60.ciunit = *nounit; s_wsfe(&io___60); do_fio(&c__1, "ZTGEVC(R,B)", (ftnlen)11); do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer)); do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer)); e_wsfe(); *info = abs(iinfo); goto L210; } zget52_(&c_false, &n, &h__[h_offset], lda, &t[t_offset], lda, & evectr[evectr_offset], ldu, &alpha1[1], &beta1[1], &work[ 1], &rwork[1], dumma); result[12] = dumma[0]; if (dumma[1] > *thresh) { io___61.ciunit = *nounit; s_wsfe(&io___61); do_fio(&c__1, "Right", (ftnlen)5); do_fio(&c__1, "ZTGEVC(HOWMNY=B)", (ftnlen)16); 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(); } /* Tests 13--15 are done only on request */ if (*tstdif) { /* Do Tests 13--14 */ zget51_(&c__2, &n, &s1[s1_offset], lda, &s2[s2_offset], lda, & q[q_offset], ldu, &z__[z_offset], ldu, &work[1], & rwork[1], &result[13]); zget51_(&c__2, &n, &p1[p1_offset], lda, &p2[p2_offset], lda, & q[q_offset], ldu, &z__[z_offset], ldu, &work[1], & rwork[1], &result[14]); /* Do Test 15 */ temp1 = 0.; temp2 = 0.; i__3 = n; for (j = 1; j <= i__3; ++j) { /* Computing MAX */ i__4 = j; i__5 = j; z__1.r = alpha1[i__4].r - alpha3[i__5].r, z__1.i = alpha1[ i__4].i - alpha3[i__5].i; d__1 = temp1, d__2 = z_abs(&z__1); temp1 = max(d__1,d__2); /* Computing MAX */ i__4 = j; i__5 = j; z__1.r = beta1[i__4].r - beta3[i__5].r, z__1.i = beta1[ i__4].i - beta3[i__5].i; d__1 = temp2, d__2 = z_abs(&z__1); temp2 = max(d__1,d__2); /* L200: */ } /* Computing MAX */ d__1 = safmin, d__2 = ulp * max(temp1,anorm); temp1 /= max(d__1,d__2); /* Computing MAX */ d__1 = safmin, d__2 = ulp * max(temp2,bnorm); temp2 /= max(d__1,d__2); result[15] = max(temp1,temp2); ntest = 15; } else { result[13] = 0.; result[14] = 0.; result[15] = 0.; ntest = 12; } /* End of Loop -- Check for RESULT(j) > THRESH */ L210: 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___64.ciunit = *nounit; s_wsfe(&io___64); do_fio(&c__1, "ZGG", (ftnlen)3); e_wsfe(); /* Matrix types */ io___65.ciunit = *nounit; s_wsfe(&io___65); e_wsfe(); io___66.ciunit = *nounit; s_wsfe(&io___66); e_wsfe(); io___67.ciunit = *nounit; s_wsfe(&io___67); do_fio(&c__1, "Unitary", (ftnlen)7); e_wsfe(); /* Tests performed */ io___68.ciunit = *nounit; s_wsfe(&io___68); 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 <= 10; ++j) { do_fio(&c__1, "*", (ftnlen)1); } e_wsfe(); } ++nerrs; if (result[jr] < 1e4) { io___69.ciunit = *nounit; s_wsfe(&io___69); 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___70.ciunit = *nounit; s_wsfe(&io___70); 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(); } } /* L220: */ } L230: ; } /* L240: */ } /* Summary */ dlasum_("ZGG", nounit, &nerrs, &ntestt); return 0; /* End of ZCHKGG */ } /* zchkgg_ */ #undef evectr_ref #undef evectr_subscr #undef evectl_ref #undef evectl_subscr #undef v_ref #undef v_subscr #undef u_ref #undef u_subscr #undef b_ref #undef b_subscr #undef a_ref #undef a_subscr