#include "f2c.h" #include "blaswrap.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_b29 = 1.; static integer c__3 = 3; static integer c__4 = 4; static integer c__0 = 0; /* 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; /* 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 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_ */