/* Subroutine */ int sdrvsx_(integer *nsizes, integer *nn, integer *ntypes, logical *dotype, integer *iseed, real *thresh, integer *niunit, integer *nounit, real *a, integer *lda, real *h__, real *ht, real *wr, real *wi, real *wrt, real *wit, real *wrtmp, real *witmp, real *vs, integer *ldvs, real *vs1, real *result, real *work, integer *lwork, integer *iwork, logical *bwork, integer *info) { /* Initialized data */ static integer ktype[21] = { 1,2,3,4,4,4,4,4,6,6,6,6,6,6,6,6,6,6,9,9,9 }; static integer kmagn[21] = { 1,1,1,1,1,1,2,3,1,1,1,1,1,1,1,1,2,3,1,2,3 }; static integer kmode[21] = { 0,0,0,4,3,1,4,4,4,3,1,5,4,3,1,5,5,5,4,3,1 }; static integer kconds[21] = { 0,0,0,0,0,0,0,0,1,1,1,1,2,2,2,2,2,2,0,0,0 }; /* Format strings */ static char fmt_9991[] = "(\002 SDRVSX: \002,a,\002 returned INFO=\002,i" "6,\002.\002,/9x,\002N=\002,i6,\002, JTYPE=\002,i6,\002, ISEED=" "(\002,3(i5,\002,\002),i5,\002)\002)"; static char fmt_9999[] = "(/1x,a3,\002 -- Real Schur Form Decomposition " "Expert \002,\002Driver\002,/\002 Matrix types (see SDRVSX for de" "tails):\002)"; static char fmt_9998[] = "(/\002 Special Matrices:\002,/\002 1=Zero mat" "rix. \002,\002 \002,\002 5=Diagonal: geom" "etr. spaced entries.\002,/\002 2=Identity matrix. " " \002,\002 6=Diagona\002,\002l: clustered entries.\002," "/\002 3=Transposed Jordan block. \002,\002 \002,\002 " " 7=Diagonal: large, evenly spaced.\002,/\002 \002,\0024=Diagona" "l: evenly spaced entries. \002,\002 8=Diagonal: s\002,\002ma" "ll, evenly spaced.\002)"; static char fmt_9997[] = "(\002 Dense, Non-Symmetric Matrices:\002,/\002" " 9=Well-cond., ev\002,\002enly spaced eigenvals.\002,\002 14=Il" "l-cond., geomet. spaced e\002,\002igenals.\002,/\002 10=Well-con" "d., geom. spaced eigenvals. \002,\002 15=Ill-conditioned, cluste" "red e.vals.\002,/\002 11=Well-cond\002,\002itioned, clustered e." "vals. \002,\002 16=Ill-cond., random comp\002,\002lex \002,/\002" " 12=Well-cond., random complex \002,\002 \002,\002 17=Il" "l-cond., large rand. complx \002,/\002 13=Ill-condi\002,\002tion" "ed, evenly spaced. \002,\002 18=Ill-cond., small rand.\002" ",\002 complx \002)"; static char fmt_9996[] = "(\002 19=Matrix with random O(1) entries. " " \002,\002 21=Matrix \002,\002with small random entries.\002," "/\002 20=Matrix with large ran\002,\002dom entries. \002,/)"; static char fmt_9995[] = "(\002 Tests performed with test threshold =" "\002,f8.2,/\002 ( A denotes A on input and T denotes A on output)" "\002,//\002 1 = 0 if T in Schur form (no sort), \002,\002 1/ulp" " otherwise\002,/\002 2 = | A - VS T transpose(VS) | / ( n |A| ul" "p ) (no sort)\002,/\002 3 = | I - VS transpose(VS) | / ( n ulp )" " (no sort) \002,/\002 4 = 0 if WR+sqrt(-1)*WI are eigenvalues of" " T (no sort),\002,\002 1/ulp otherwise\002,/\002 5 = 0 if T sam" "e no matter if VS computed (no sort),\002,\002 1/ulp otherwis" "e\002,/\002 6 = 0 if WR, WI same no matter if VS computed (no so" "rt)\002,\002, 1/ulp otherwise\002)"; static char fmt_9994[] = "(\002 7 = 0 if T in Schur form (sort), \002" ",\002 1/ulp otherwise\002,/\002 8 = | A - VS T transpose(VS) | " "/ ( n |A| ulp ) (sort)\002,/\002 9 = | I - VS transpose(VS) | / " "( n ulp ) (sort) \002,/\002 10 = 0 if WR+sqrt(-1)*WI are eigenva" "lues of T (sort),\002,\002 1/ulp otherwise\002,/\002 11 = 0 if " "T same no matter what else computed (sort),\002,\002 1/ulp othe" "rwise\002,/\002 12 = 0 if WR, WI same no matter what else comput" "ed \002,\002(sort), 1/ulp otherwise\002,/\002 13 = 0 if sorting " "succesful, 1/ulp otherwise\002,/\002 14 = 0 if RCONDE same no ma" "tter what else computed,\002,\002 1/ulp otherwise\002,/\002 15 =" " 0 if RCONDv same no matter what else computed,\002,\002 1/ulp o" "therwise\002,/\002 16 = | RCONDE - RCONDE(precomputed) | / cond(" "RCONDE),\002,/\002 17 = | RCONDV - RCONDV(precomputed) | / cond(" "RCONDV),\002)"; static char fmt_9993[] = "(\002 N=\002,i5,\002, IWK=\002,i2,\002, seed" "=\002,4(i4,\002,\002),\002 type \002,i2,\002, test(\002,i2,\002)=" "\002,g10.3)"; static char fmt_9992[] = "(\002 N=\002,i5,\002, input example =\002,i3" ",\002, test(\002,i2,\002)=\002,g10.3)"; /* System generated locals */ integer a_dim1, a_offset, h_dim1, h_offset, ht_dim1, ht_offset, vs_dim1, vs_offset, vs1_dim1, vs1_offset, i__1, i__2, i__3, i__4; /* Builtin functions */ /* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen); double sqrt(doublereal); integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void), s_rsle(cilist *), do_lio(integer *, integer *, char *, ftnlen), e_rsle(void); /* Local variables */ integer i__, j, n, iwk; real ulp, cond; integer jcol; char path[3]; integer nmax; real unfl, ovfl; logical badnn; integer nfail, imode, iinfo; real conds; extern /* Subroutine */ int sget24_(logical *, integer *, real *, integer *, integer *, integer *, real *, integer *, real *, real *, real * , real *, real *, real *, real *, real *, real *, integer *, real *, real *, real *, integer *, integer *, real *, real *, integer * , integer *, logical *, integer *); real anorm; integer islct[20], nslct, jsize, nerrs, itype, jtype, ntest; real rtulp; extern /* Subroutine */ int slabad_(real *, real *); real rcdein; char adumma[1*1]; extern doublereal slamch_(char *); integer idumma[1], ioldsd[4]; extern /* Subroutine */ int xerbla_(char *, integer *); real rcdvin; extern /* Subroutine */ int slatme_(integer *, char *, integer *, real *, integer *, real *, real *, char *, char *, char *, char *, real *, integer *, real *, integer *, integer *, real *, real *, integer *, real *, integer *), slaset_(char *, integer *, integer *, real *, real *, real *, integer *), slatmr_(integer *, integer *, char *, integer *, char *, real *, integer *, real *, real *, char *, char *, real *, integer *, real *, real *, integer *, real *, char *, integer *, integer *, integer *, real *, real *, char *, real *, integer *, integer *, integer *); integer ntestf; extern /* Subroutine */ int slasum_(char *, integer *, integer *, integer *), slatms_(integer *, integer *, char *, integer *, char *, real *, integer *, real *, real *, integer *, integer *, char * , real *, integer *, real *, integer *); real ulpinv; integer nnwork; real rtulpi; integer mtypes, ntestt; /* Fortran I/O blocks */ static cilist io___32 = { 0, 0, 0, fmt_9991, 0 }; static cilist io___41 = { 0, 0, 0, fmt_9999, 0 }; static cilist io___42 = { 0, 0, 0, fmt_9998, 0 }; static cilist io___43 = { 0, 0, 0, fmt_9997, 0 }; static cilist io___44 = { 0, 0, 0, fmt_9996, 0 }; static cilist io___45 = { 0, 0, 0, fmt_9995, 0 }; static cilist io___46 = { 0, 0, 0, fmt_9994, 0 }; static cilist io___47 = { 0, 0, 0, fmt_9993, 0 }; static cilist io___48 = { 0, 0, 1, 0, 0 }; static cilist io___49 = { 0, 0, 0, 0, 0 }; static cilist io___51 = { 0, 0, 0, 0, 0 }; static cilist io___52 = { 0, 0, 0, 0, 0 }; static cilist io___53 = { 0, 0, 0, fmt_9999, 0 }; static cilist io___54 = { 0, 0, 0, fmt_9998, 0 }; static cilist io___55 = { 0, 0, 0, fmt_9997, 0 }; static cilist io___56 = { 0, 0, 0, fmt_9996, 0 }; static cilist io___57 = { 0, 0, 0, fmt_9995, 0 }; static cilist io___58 = { 0, 0, 0, fmt_9994, 0 }; static cilist io___59 = { 0, 0, 0, fmt_9992, 0 }; /* -- LAPACK test routine (version 3.1) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* SDRVSX checks the nonsymmetric eigenvalue (Schur form) problem */ /* expert driver SGEESX. */ /* SDRVSX uses both test matrices generated randomly depending on */ /* data supplied in the calling sequence, as well as on data */ /* read from an input file and including precomputed condition */ /* numbers to which it compares the ones it computes. */ /* When SDRVSX 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, 15 */ /* tests will be performed: */ /* (1) 0 if T is in Schur form, 1/ulp otherwise */ /* (no sorting of eigenvalues) */ /* (2) | A - VS T VS' | / ( n |A| ulp ) */ /* Here VS is the matrix of Schur eigenvectors, and T is in Schur */ /* form (no sorting of eigenvalues). */ /* (3) | I - VS VS' | / ( n ulp ) (no sorting of eigenvalues). */ /* (4) 0 if WR+sqrt(-1)*WI are eigenvalues of T */ /* 1/ulp otherwise */ /* (no sorting of eigenvalues) */ /* (5) 0 if T(with VS) = T(without VS), */ /* 1/ulp otherwise */ /* (no sorting of eigenvalues) */ /* (6) 0 if eigenvalues(with VS) = eigenvalues(without VS), */ /* 1/ulp otherwise */ /* (no sorting of eigenvalues) */ /* (7) 0 if T is in Schur form, 1/ulp otherwise */ /* (with sorting of eigenvalues) */ /* (8) | A - VS T VS' | / ( n |A| ulp ) */ /* Here VS is the matrix of Schur eigenvectors, and T is in Schur */ /* form (with sorting of eigenvalues). */ /* (9) | I - VS VS' | / ( n ulp ) (with sorting of eigenvalues). */ /* (10) 0 if WR+sqrt(-1)*WI are eigenvalues of T */ /* 1/ulp otherwise */ /* If workspace sufficient, also compare WR, WI with and */ /* without reciprocal condition numbers */ /* (with sorting of eigenvalues) */ /* (11) 0 if T(with VS) = T(without VS), */ /* 1/ulp otherwise */ /* If workspace sufficient, also compare T with and without */ /* reciprocal condition numbers */ /* (with sorting of eigenvalues) */ /* (12) 0 if eigenvalues(with VS) = eigenvalues(without VS), */ /* 1/ulp otherwise */ /* If workspace sufficient, also compare VS with and without */ /* reciprocal condition numbers */ /* (with sorting of eigenvalues) */ /* (13) if sorting worked and SDIM is the number of */ /* eigenvalues which were SELECTed */ /* If workspace sufficient, also compare SDIM with and */ /* without reciprocal condition numbers */ /* (14) if RCONDE the same no matter if VS and/or RCONDV computed */ /* (15) if RCONDV the same no matter if VS and/or RCONDE computed */ /* The "sizes" are specified by an array NN(1:NSIZES); the value of */ /* each element NN(j) specifies one size. */ /* The "types" are specified by a logical array DOTYPE( 1:NTYPES ); */ /* if DOTYPE(j) is .TRUE., then matrix type "j" will be generated. */ /* Currently, the list of possible types is: */ /* (1) The zero matrix. */ /* (2) The identity matrix. */ /* (3) A (transposed) Jordan block, with 1's on the diagonal. */ /* (4) A diagonal matrix with evenly spaced entries */ /* 1, ..., ULP and random signs. */ /* (ULP = (first number larger than 1) - 1 ) */ /* (5) A diagonal matrix with geometrically spaced entries */ /* 1, ..., ULP and random signs. */ /* (6) A diagonal matrix with "clustered" entries 1, ULP, ..., ULP */ /* and random signs. */ /* (7) Same as (4), but multiplied by a constant near */ /* the overflow threshold */ /* (8) Same as (4), but multiplied by a constant near */ /* the underflow threshold */ /* (9) A matrix of the form U' T U, where U is orthogonal and */ /* T has evenly spaced entries 1, ..., ULP with random signs */ /* on the diagonal and random O(1) entries in the upper */ /* triangle. */ /* (10) A matrix of the form U' T U, where U is orthogonal and */ /* T has geometrically spaced entries 1, ..., ULP with random */ /* signs on the diagonal and random O(1) entries in the upper */ /* triangle. */ /* (11) A matrix of the form U' T U, where U is orthogonal and */ /* T has "clustered" entries 1, ULP,..., ULP with random */ /* signs on the diagonal and random O(1) entries in the upper */ /* triangle. */ /* (12) A matrix of the form U' T U, where U is orthogonal and */ /* T has real or complex conjugate paired eigenvalues randomly */ /* chosen from ( ULP, 1 ) and random O(1) entries in the upper */ /* triangle. */ /* (13) A matrix of the form X' T X, where X has condition */ /* SQRT( ULP ) and T has evenly spaced entries 1, ..., ULP */ /* with random signs on the diagonal and random O(1) entries */ /* in the upper triangle. */ /* (14) A matrix of the form X' T X, where X has condition */ /* SQRT( ULP ) and T has geometrically spaced entries */ /* 1, ..., ULP with random signs on the diagonal and random */ /* O(1) entries in the upper triangle. */ /* (15) A matrix of the form X' T X, where X has condition */ /* SQRT( ULP ) and T has "clustered" entries 1, ULP,..., ULP */ /* with random signs on the diagonal and random O(1) entries */ /* in the upper triangle. */ /* (16) A matrix of the form X' T X, where X has condition */ /* SQRT( ULP ) and T has real or complex conjugate paired */ /* eigenvalues randomly chosen from ( ULP, 1 ) and random */ /* O(1) entries in the upper triangle. */ /* (17) Same as (16), but multiplied by a constant */ /* near the overflow threshold */ /* (18) Same as (16), but multiplied by a constant */ /* near the underflow threshold */ /* (19) Nonsymmetric matrix with random entries chosen from (-1,1). */ /* If N is at least 4, all entries in first two rows and last */ /* row, and first column and last two columns are zero. */ /* (20) Same as (19), but multiplied by a constant */ /* near the overflow threshold */ /* (21) Same as (19), but multiplied by a constant */ /* near the underflow threshold */ /* In addition, an input file will be read from logical unit number */ /* NIUNIT. The file contains matrices along with precomputed */ /* eigenvalues and reciprocal condition numbers for the eigenvalue */ /* average and right invariant subspace. For these matrices, in */ /* addition to tests (1) to (15) we will compute the following two */ /* tests: */ /* (16) |RCONDE - RCDEIN| / cond(RCONDE) */ /* RCONDE is the reciprocal average eigenvalue condition number */ /* computed by SGEESX and RCDEIN (the precomputed true value) */ /* is supplied as input. cond(RCONDE) is the condition number */ /* of RCONDE, and takes errors in computing RCONDE into account, */ /* so that the resulting quantity should be O(ULP). cond(RCONDE) */ /* is essentially given by norm(A)/RCONDV. */ /* (17) |RCONDV - RCDVIN| / cond(RCONDV) */ /* RCONDV is the reciprocal right invariant subspace condition */ /* number computed by SGEESX and RCDVIN (the precomputed true */ /* value) is supplied as input. cond(RCONDV) is the condition */ /* number of RCONDV, and takes errors in computing RCONDV into */ /* account, so that the resulting quantity should be O(ULP). */ /* cond(RCONDV) is essentially given by norm(A)/RCONDE. */ /* Arguments */ /* ========= */ /* NSIZES (input) INTEGER */ /* The number of sizes of matrices to use. NSIZES must be at */ /* least zero. If it is zero, no randomly generated matrices */ /* are tested, but any test matrices read from NIUNIT will be */ /* tested. */ /* NN (input) INTEGER array, dimension (NSIZES) */ /* An array containing the sizes to be used for the matrices. */ /* Zero values will be skipped. The values must be at least */ /* zero. */ /* NTYPES (input) INTEGER */ /* The number of elements in DOTYPE. NTYPES must be at least */ /* zero. If it is zero, no randomly generated test matrices */ /* are tested, but and test matrices read from NIUNIT will be */ /* tested. If it is MAXTYP+1 and NSIZES is 1, then an */ /* additional type, MAXTYP+1 is defined, which is to use */ /* whatever matrix is in A. This is only useful if */ /* DOTYPE(1:MAXTYP) is .FALSE. and DOTYPE(MAXTYP+1) is .TRUE. . */ /* DOTYPE (input) LOGICAL array, dimension (NTYPES) */ /* If DOTYPE(j) is .TRUE., then for each size in NN a */ /* matrix of that size and of type j will be generated. */ /* If NTYPES is smaller than the maximum number of types */ /* defined (PARAMETER MAXTYP), then types NTYPES+1 through */ /* MAXTYP will not be generated. If NTYPES is larger */ /* than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES) */ /* will be ignored. */ /* ISEED (input/output) INTEGER array, dimension (4) */ /* On entry ISEED specifies the seed of the random number */ /* generator. The array elements should be between 0 and 4095; */ /* if not they will be reduced mod 4096. Also, ISEED(4) must */ /* be odd. The random number generator uses a linear */ /* congruential sequence limited to small integers, and so */ /* should produce machine independent random numbers. The */ /* values of ISEED are changed on exit, and can be used in the */ /* next call to SDRVSX to continue the same random number */ /* sequence. */ /* THRESH (input) REAL */ /* A test will count as "failed" if the "error", computed as */ /* described above, exceeds THRESH. Note that the error */ /* is scaled to be O(1), so THRESH should be a reasonably */ /* small multiple of 1, e.g., 10 or 100. In particular, */ /* it should not depend on the precision (single vs. double) */ /* or the size of the matrix. It must be at least zero. */ /* NIUNIT (input) INTEGER */ /* The FORTRAN unit number for reading in the data file of */ /* problems to solve. */ /* NOUNIT (input) INTEGER */ /* The FORTRAN unit number for printing out error messages */ /* (e.g., if a routine returns INFO not equal to 0.) */ /* A (workspace) REAL array, dimension (LDA, max(NN)) */ /* Used to hold the matrix whose eigenvalues are to be */ /* computed. On exit, A contains the last matrix actually used. */ /* LDA (input) INTEGER */ /* The leading dimension of A, and H. LDA must be at */ /* least 1 and at least max( NN ). */ /* H (workspace) REAL array, dimension (LDA, max(NN)) */ /* Another copy of the test matrix A, modified by SGEESX. */ /* HT (workspace) REAL array, dimension (LDA, max(NN)) */ /* Yet another copy of the test matrix A, modified by SGEESX. */ /* WR (workspace) REAL array, dimension (max(NN)) */ /* WI (workspace) REAL array, dimension (max(NN)) */ /* The real and imaginary parts of the eigenvalues of A. */ /* On exit, WR + WI*i are the eigenvalues of the matrix in A. */ /* WRT (workspace) REAL array, dimension (max(NN)) */ /* WIT (workspace) REAL array, dimension (max(NN)) */ /* Like WR, WI, these arrays contain the eigenvalues of A, */ /* but those computed when SGEESX only computes a partial */ /* eigendecomposition, i.e. not Schur vectors */ /* WRTMP (workspace) REAL array, dimension (max(NN)) */ /* WITMP (workspace) REAL array, dimension (max(NN)) */ /* More temporary storage for eigenvalues. */ /* VS (workspace) REAL array, dimension (LDVS, max(NN)) */ /* VS holds the computed Schur vectors. */ /* LDVS (input) INTEGER */ /* Leading dimension of VS. Must be at least max(1,max(NN)). */ /* VS1 (workspace) REAL array, dimension (LDVS, max(NN)) */ /* VS1 holds another copy of the computed Schur vectors. */ /* RESULT (output) REAL array, dimension (17) */ /* The values computed by the 17 tests described above. */ /* The values are currently limited to 1/ulp, to avoid overflow. */ /* WORK (workspace) REAL array, dimension (LWORK) */ /* LWORK (input) INTEGER */ /* The number of entries in WORK. This must be at least */ /* max(3*NN(j),2*NN(j)**2) for all j. */ /* IWORK (workspace) INTEGER array, dimension (max(NN)*max(NN)) */ /* INFO (output) INTEGER */ /* If 0, successful exit. */ /* <0, input parameter -INFO is incorrect */ /* >0, SLATMR, SLATMS, SLATME or SGET24 returned an error */ /* code and INFO is its absolute value */ /* ----------------------------------------------------------------------- */ /* Some Local Variables and Parameters: */ /* ---- ----- --------- --- ---------- */ /* ZERO, ONE Real 0 and 1. */ /* MAXTYP The number of types defined. */ /* NMAX Largest value in NN. */ /* NERRS The number of tests which have exceeded THRESH */ /* COND, CONDS, */ /* IMODE Values to be passed to the matrix generators. */ /* ANORM Norm of A; passed to matrix generators. */ /* OVFL, UNFL Overflow and underflow thresholds. */ /* ULP, ULPINV Finest relative precision and its inverse. */ /* RTULP, RTULPI Square roots of the previous 4 values. */ /* The following four arrays decode JTYPE: */ /* KTYPE(j) The general type (1-10) for type "j". */ /* KMODE(j) The MODE value to be passed to the matrix */ /* generator for type "j". */ /* KMAGN(j) The order of magnitude ( O(1), */ /* O(overflow^(1/2) ), O(underflow^(1/2) ) */ /* KCONDS(j) Selectw whether CONDS is to be 1 or */ /* 1/sqrt(ulp). (0 means irrelevant.) */ /* ===================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. Local Arrays .. */ /* .. */ /* .. Arrays in Common .. */ /* .. */ /* .. Scalars in Common .. */ /* .. */ /* .. Common blocks .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Data statements .. */ /* Parameter adjustments */ --nn; --dotype; --iseed; ht_dim1 = *lda; ht_offset = 1 + ht_dim1; ht -= ht_offset; h_dim1 = *lda; h_offset = 1 + h_dim1; h__ -= h_offset; a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --wr; --wi; --wrt; --wit; --wrtmp; --witmp; vs1_dim1 = *ldvs; vs1_offset = 1 + vs1_dim1; vs1 -= vs1_offset; vs_dim1 = *ldvs; vs_offset = 1 + vs_dim1; vs -= vs_offset; --result; --work; --iwork; --bwork; /* Function Body */ /* .. */ /* .. Executable Statements .. */ s_copy(path, "Single precision", (ftnlen)1, (ftnlen)16); s_copy(path + 1, "SX", (ftnlen)2, (ftnlen)2); /* Check for errors */ ntestt = 0; ntestf = 0; *info = 0; /* Important constants */ badnn = FALSE_; /* 12 is the largest dimension in the input file of precomputed */ /* problems */ nmax = 12; i__1 = *nsizes; for (j = 1; j <= i__1; ++j) { /* Computing MAX */ i__2 = nmax, i__3 = nn[j]; nmax = max(i__2,i__3); if (nn[j] < 0) { badnn = TRUE_; } /* L10: */ } /* Check for errors */ if (*nsizes < 0) { *info = -1; } else if (badnn) { *info = -2; } else if (*ntypes < 0) { *info = -3; } else if (*thresh < 0.f) { *info = -6; } else if (*niunit <= 0) { *info = -7; } else if (*nounit <= 0) { *info = -8; } else if (*lda < 1 || *lda < nmax) { *info = -10; } else if (*ldvs < 1 || *ldvs < nmax) { *info = -20; } else /* if(complicated condition) */ { /* Computing MAX */ /* Computing 2nd power */ i__3 = nmax; i__1 = nmax * 3, i__2 = i__3 * i__3 << 1; if (max(i__1,i__2) > *lwork) { *info = -24; } } if (*info != 0) { i__1 = -(*info); xerbla_("SDRVSX", &i__1); return 0; } /* If nothing to do check on NIUNIT */ if (*nsizes == 0 || *ntypes == 0) { goto L150; } /* More Important constants */ unfl = slamch_("Safe minimum"); ovfl = 1.f / unfl; slabad_(&unfl, &ovfl); ulp = slamch_("Precision"); ulpinv = 1.f / ulp; rtulp = sqrt(ulp); rtulpi = 1.f / rtulp; /* Loop over sizes, types */ nerrs = 0; i__1 = *nsizes; for (jsize = 1; jsize <= i__1; ++jsize) { n = nn[jsize]; if (*nsizes != 1) { mtypes = min(21,*ntypes); } else { mtypes = min(22,*ntypes); } i__2 = mtypes; for (jtype = 1; jtype <= i__2; ++jtype) { if (! dotype[jtype]) { goto L130; } /* Save ISEED in case of an error. */ for (j = 1; j <= 4; ++j) { ioldsd[j - 1] = iseed[j]; /* L20: */ } /* Compute "A" */ /* Control parameters: */ /* KMAGN KCONDS KMODE KTYPE */ /* =1 O(1) 1 clustered 1 zero */ /* =2 large large clustered 2 identity */ /* =3 small exponential Jordan */ /* =4 arithmetic diagonal, (w/ eigenvalues) */ /* =5 random log symmetric, w/ eigenvalues */ /* =6 random general, w/ eigenvalues */ /* =7 random diagonal */ /* =8 random symmetric */ /* =9 random general */ /* =10 random triangular */ if (mtypes > 21) { goto L90; } itype = ktype[jtype - 1]; imode = kmode[jtype - 1]; /* Compute norm */ switch (kmagn[jtype - 1]) { case 1: goto L30; case 2: goto L40; case 3: goto L50; } L30: anorm = 1.f; goto L60; L40: anorm = ovfl * ulp; goto L60; L50: anorm = unfl * ulpinv; goto L60; L60: slaset_("Full", lda, &n, &c_b18, &c_b18, &a[a_offset], lda); iinfo = 0; cond = ulpinv; /* Special Matrices -- Identity & Jordan block */ /* Zero */ if (itype == 1) { iinfo = 0; } else if (itype == 2) { /* Identity */ i__3 = n; for (jcol = 1; jcol <= i__3; ++jcol) { a[jcol + jcol * a_dim1] = anorm; /* L70: */ } } else if (itype == 3) { /* Jordan Block */ i__3 = n; for (jcol = 1; jcol <= i__3; ++jcol) { a[jcol + jcol * a_dim1] = anorm; if (jcol > 1) { a[jcol + (jcol - 1) * a_dim1] = 1.f; } /* L80: */ } } else if (itype == 4) { /* Diagonal Matrix, [Eigen]values Specified */ slatms_(&n, &n, "S", &iseed[1], "S", &work[1], &imode, &cond, &anorm, &c__0, &c__0, "N", &a[a_offset], lda, &work[n + 1], &iinfo); } else if (itype == 5) { /* Symmetric, eigenvalues specified */ slatms_(&n, &n, "S", &iseed[1], "S", &work[1], &imode, &cond, &anorm, &n, &n, "N", &a[a_offset], lda, &work[n + 1], &iinfo); } else if (itype == 6) { /* General, eigenvalues specified */ if (kconds[jtype - 1] == 1) { conds = 1.f; } else if (kconds[jtype - 1] == 2) { conds = rtulpi; } else { conds = 0.f; } *(unsigned char *)&adumma[0] = ' '; slatme_(&n, "S", &iseed[1], &work[1], &imode, &cond, &c_b32, adumma, "T", "T", "T", &work[n + 1], &c__4, &conds, & n, &n, &anorm, &a[a_offset], lda, &work[(n << 1) + 1], &iinfo); } else if (itype == 7) { /* Diagonal, random eigenvalues */ slatmr_(&n, &n, "S", &iseed[1], "S", &work[1], &c__6, &c_b32, &c_b32, "T", "N", &work[n + 1], &c__1, &c_b32, &work[( n << 1) + 1], &c__1, &c_b32, "N", idumma, &c__0, & c__0, &c_b18, &anorm, "NO", &a[a_offset], lda, &iwork[ 1], &iinfo); } else if (itype == 8) { /* Symmetric, random eigenvalues */ slatmr_(&n, &n, "S", &iseed[1], "S", &work[1], &c__6, &c_b32, &c_b32, "T", "N", &work[n + 1], &c__1, &c_b32, &work[( n << 1) + 1], &c__1, &c_b32, "N", idumma, &n, &n, & c_b18, &anorm, "NO", &a[a_offset], lda, &iwork[1], & iinfo); } else if (itype == 9) { /* General, random eigenvalues */ slatmr_(&n, &n, "S", &iseed[1], "N", &work[1], &c__6, &c_b32, &c_b32, "T", "N", &work[n + 1], &c__1, &c_b32, &work[( n << 1) + 1], &c__1, &c_b32, "N", idumma, &n, &n, & c_b18, &anorm, "NO", &a[a_offset], lda, &iwork[1], & iinfo); if (n >= 4) { slaset_("Full", &c__2, &n, &c_b18, &c_b18, &a[a_offset], lda); i__3 = n - 3; slaset_("Full", &i__3, &c__1, &c_b18, &c_b18, &a[a_dim1 + 3], lda); i__3 = n - 3; slaset_("Full", &i__3, &c__2, &c_b18, &c_b18, &a[(n - 1) * a_dim1 + 3], lda); slaset_("Full", &c__1, &n, &c_b18, &c_b18, &a[n + a_dim1], lda); } } else if (itype == 10) { /* Triangular, random eigenvalues */ slatmr_(&n, &n, "S", &iseed[1], "N", &work[1], &c__6, &c_b32, &c_b32, "T", "N", &work[n + 1], &c__1, &c_b32, &work[( n << 1) + 1], &c__1, &c_b32, "N", idumma, &n, &c__0, & c_b18, &anorm, "NO", &a[a_offset], lda, &iwork[1], & iinfo); } else { iinfo = 1; } if (iinfo != 0) { io___32.ciunit = *nounit; s_wsfe(&io___32); do_fio(&c__1, "Generator", (ftnlen)9); do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer)); do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer)); e_wsfe(); *info = abs(iinfo); return 0; } L90: /* Test for minimal and generous workspace */ for (iwk = 1; iwk <= 2; ++iwk) { if (iwk == 1) { nnwork = n * 3; } else { /* Computing MAX */ i__3 = n * 3, i__4 = (n << 1) * n; nnwork = max(i__3,i__4); } nnwork = max(nnwork,1); sget24_(&c_false, &jtype, thresh, ioldsd, nounit, &n, &a[ a_offset], lda, &h__[h_offset], &ht[ht_offset], &wr[1] , &wi[1], &wrt[1], &wit[1], &wrtmp[1], &witmp[1], &vs[ vs_offset], ldvs, &vs1[vs1_offset], &rcdein, &rcdvin, &nslct, islct, &result[1], &work[1], &nnwork, &iwork[ 1], &bwork[1], info); /* Check for RESULT(j) > THRESH */ ntest = 0; nfail = 0; for (j = 1; j <= 15; ++j) { if (result[j] >= 0.f) { ++ntest; } if (result[j] >= *thresh) { ++nfail; } /* L100: */ } if (nfail > 0) { ++ntestf; } if (ntestf == 1) { io___41.ciunit = *nounit; s_wsfe(&io___41); do_fio(&c__1, path, (ftnlen)3); e_wsfe(); io___42.ciunit = *nounit; s_wsfe(&io___42); e_wsfe(); io___43.ciunit = *nounit; s_wsfe(&io___43); e_wsfe(); io___44.ciunit = *nounit; s_wsfe(&io___44); e_wsfe(); io___45.ciunit = *nounit; s_wsfe(&io___45); do_fio(&c__1, (char *)&(*thresh), (ftnlen)sizeof(real)); e_wsfe(); io___46.ciunit = *nounit; s_wsfe(&io___46); e_wsfe(); ntestf = 2; } for (j = 1; j <= 15; ++j) { if (result[j] >= *thresh) { io___47.ciunit = *nounit; s_wsfe(&io___47); do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&iwk, (ftnlen)sizeof(integer)); do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof( integer)); do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer)) ; do_fio(&c__1, (char *)&j, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&result[j], (ftnlen)sizeof(real) ); e_wsfe(); } /* L110: */ } nerrs += nfail; ntestt += ntest; /* L120: */ } L130: ; } /* L140: */ } L150: /* Read in data from file to check accuracy of condition estimation */ /* Read input data until N=0 */ jtype = 0; L160: io___48.ciunit = *niunit; i__1 = s_rsle(&io___48); if (i__1 != 0) { goto L200; } i__1 = do_lio(&c__3, &c__1, (char *)&n, (ftnlen)sizeof(integer)); if (i__1 != 0) { goto L200; } i__1 = do_lio(&c__3, &c__1, (char *)&nslct, (ftnlen)sizeof(integer)); if (i__1 != 0) { goto L200; } i__1 = e_rsle(); if (i__1 != 0) { goto L200; } if (n == 0) { goto L200; } ++jtype; iseed[1] = jtype; if (nslct > 0) { io___49.ciunit = *niunit; s_rsle(&io___49); i__1 = nslct; for (i__ = 1; i__ <= i__1; ++i__) { do_lio(&c__3, &c__1, (char *)&islct[i__ - 1], (ftnlen)sizeof( integer)); } e_rsle(); } i__1 = n; for (i__ = 1; i__ <= i__1; ++i__) { io___51.ciunit = *niunit; s_rsle(&io___51); i__2 = n; for (j = 1; j <= i__2; ++j) { do_lio(&c__4, &c__1, (char *)&a[i__ + j * a_dim1], (ftnlen)sizeof( real)); } e_rsle(); /* L170: */ } io___52.ciunit = *niunit; s_rsle(&io___52); do_lio(&c__4, &c__1, (char *)&rcdein, (ftnlen)sizeof(real)); do_lio(&c__4, &c__1, (char *)&rcdvin, (ftnlen)sizeof(real)); e_rsle(); sget24_(&c_true, &c__22, thresh, &iseed[1], nounit, &n, &a[a_offset], lda, &h__[h_offset], &ht[ht_offset], &wr[1], &wi[1], &wrt[1], &wit[1], &wrtmp[1], &witmp[1], &vs[vs_offset], ldvs, &vs1[vs1_offset], & rcdein, &rcdvin, &nslct, islct, &result[1], &work[1], lwork, & iwork[1], &bwork[1], info); /* Check for RESULT(j) > THRESH */ ntest = 0; nfail = 0; for (j = 1; j <= 17; ++j) { if (result[j] >= 0.f) { ++ntest; } if (result[j] >= *thresh) { ++nfail; } /* L180: */ } if (nfail > 0) { ++ntestf; } if (ntestf == 1) { io___53.ciunit = *nounit; s_wsfe(&io___53); do_fio(&c__1, path, (ftnlen)3); e_wsfe(); io___54.ciunit = *nounit; s_wsfe(&io___54); e_wsfe(); io___55.ciunit = *nounit; s_wsfe(&io___55); e_wsfe(); io___56.ciunit = *nounit; s_wsfe(&io___56); e_wsfe(); io___57.ciunit = *nounit; s_wsfe(&io___57); do_fio(&c__1, (char *)&(*thresh), (ftnlen)sizeof(real)); e_wsfe(); io___58.ciunit = *nounit; s_wsfe(&io___58); e_wsfe(); ntestf = 2; } for (j = 1; j <= 17; ++j) { if (result[j] >= *thresh) { 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__1, (char *)&j, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&result[j], (ftnlen)sizeof(real)); e_wsfe(); } /* L190: */ } nerrs += nfail; ntestt += ntest; goto L160; L200: /* Summary */ slasum_(path, nounit, &nerrs, &ntestt); return 0; /* End of SDRVSX */ } /* sdrvsx_ */
/* Subroutine */ int sdrvvx_(integer *nsizes, integer *nn, integer *ntypes, logical *dotype, integer *iseed, real *thresh, integer *niunit, integer *nounit, real *a, integer *lda, real *h__, real *wr, real *wi, real *wr1, real *wi1, real *vl, integer *ldvl, real *vr, integer * ldvr, real *lre, integer *ldlre, real *rcondv, real *rcndv1, real * rcdvin, real *rconde, real *rcnde1, real *rcdein, real *scale, real * scale1, real *result, real *work, integer *nwork, integer *iwork, integer *info) { /* Initialized data */ static integer ktype[21] = { 1,2,3,4,4,4,4,4,6,6,6,6,6,6,6,6,6,6,9,9,9 }; static integer kmagn[21] = { 1,1,1,1,1,1,2,3,1,1,1,1,1,1,1,1,2,3,1,2,3 }; static integer kmode[21] = { 0,0,0,4,3,1,4,4,4,3,1,5,4,3,1,5,5,5,4,3,1 }; static integer kconds[21] = { 0,0,0,0,0,0,0,0,1,1,1,1,2,2,2,2,2,2,0,0,0 }; static char bal[1*4] = "N" "P" "S" "B"; /* Format strings */ static char fmt_9992[] = "(\002 SDRVVX: \002,a,\002 returned INFO=\002,i" "6,\002.\002,/9x,\002N=\002,i6,\002, JTYPE=\002,i6,\002, ISEED=" "(\002,3(i5,\002,\002),i5,\002)\002)"; static char fmt_9999[] = "(/1x,a3,\002 -- Real Eigenvalue-Eigenvector De" "composition\002,\002 Expert Driver\002,/\002 Matrix types (see S" "DRVVX for details): \002)"; static char fmt_9998[] = "(/\002 Special Matrices:\002,/\002 1=Zero mat" "rix. \002,\002 \002,\002 5=Diagonal: geom" "etr. spaced entries.\002,/\002 2=Identity matrix. " " \002,\002 6=Diagona\002,\002l: clustered entries.\002," "/\002 3=Transposed Jordan block. \002,\002 \002,\002 " " 7=Diagonal: large, evenly spaced.\002,/\002 \002,\0024=Diagona" "l: evenly spaced entries. \002,\002 8=Diagonal: s\002,\002ma" "ll, evenly spaced.\002)"; static char fmt_9997[] = "(\002 Dense, Non-Symmetric Matrices:\002,/\002" " 9=Well-cond., ev\002,\002enly spaced eigenvals.\002,\002 14=Il" "l-cond., geomet. spaced e\002,\002igenals.\002,/\002 10=Well-con" "d., geom. spaced eigenvals. \002,\002 15=Ill-conditioned, cluste" "red e.vals.\002,/\002 11=Well-cond\002,\002itioned, clustered e." "vals. \002,\002 16=Ill-cond., random comp\002,\002lex \002,/\002" " 12=Well-cond., random complex \002,\002 \002,\002 17=Il" "l-cond., large rand. complx \002,/\002 13=Ill-condi\002,\002tion" "ed, evenly spaced. \002,\002 18=Ill-cond., small rand.\002" ",\002 complx \002)"; static char fmt_9996[] = "(\002 19=Matrix with random O(1) entries. " " \002,\002 21=Matrix \002,\002with small random entries.\002," "/\002 20=Matrix with large ran\002,\002dom entries. \002,\002 " "22=Matrix read from input file\002,/)"; static char fmt_9995[] = "(\002 Tests performed with test threshold =" "\002,f8.2,//\002 1 = | A VR - VR W | / ( n |A| ulp ) \002,/\002 " "2 = | transpose(A) VL - VL W | / ( n |A| ulp ) \002,/\002 3 = | " "|VR(i)| - 1 | / ulp \002,/\002 4 = | |VL(i)| - 1 | / ulp \002," "/\002 5 = 0 if W same no matter if VR or VL computed,\002,\002 1" "/ulp otherwise\002,/\002 6 = 0 if VR same no matter what else co" "mputed,\002,\002 1/ulp otherwise\002,/\002 7 = 0 if VL same no " "matter what else computed,\002,\002 1/ulp otherwise\002,/\002 8" " = 0 if RCONDV same no matter what else computed,\002,\002 1/ul" "p otherwise\002,/\002 9 = 0 if SCALE, ILO, IHI, ABNRM same no ma" "tter what else\002,\002 computed, 1/ulp otherwise\002,/\002 10 " "= | RCONDV - RCONDV(precomputed) | / cond(RCONDV),\002,/\002 11 " "= | RCONDE - RCONDE(precomputed) | / cond(RCONDE),\002)"; static char fmt_9994[] = "(\002 BALANC='\002,a1,\002',N=\002,i4,\002,I" "WK=\002,i1,\002, seed=\002,4(i4,\002,\002),\002 type \002,i2," "\002, test(\002,i2,\002)=\002,g10.3)"; static char fmt_9993[] = "(\002 N=\002,i5,\002, input example =\002,i3" ",\002, test(\002,i2,\002)=\002,g10.3)"; /* System generated locals */ integer a_dim1, a_offset, h_dim1, h_offset, lre_dim1, lre_offset, vl_dim1, vl_offset, vr_dim1, vr_offset, i__1, i__2, i__3; /* Builtin functions Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen); double sqrt(doublereal); integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void), s_rsle(cilist *), do_lio(integer *, integer *, char *, ftnlen), e_rsle(void); /* Local variables */ static integer ibal; static real cond; static integer jcol; static char path[3]; static integer nmax; static real unfl, ovfl; static integer i__, j, n; static logical badnn; static integer nfail, imode, iinfo; static real conds; extern /* Subroutine */ int sget23_(logical *, char *, integer *, real *, integer *, integer *, integer *, real *, integer *, real *, real * , real *, real *, real *, real *, integer *, real *, integer *, real *, integer *, real *, real *, real *, real *, real *, real *, real *, real *, real *, real *, integer *, integer *, integer *); static real anorm; static integer jsize, nerrs, itype, jtype, ntest; static real rtulp; static char balanc[1]; extern /* Subroutine */ int slabad_(real *, real *); static char adumma[1*1]; extern doublereal slamch_(char *); static integer idumma[1]; extern /* Subroutine */ int xerbla_(char *, integer *); static integer ioldsd[4]; extern /* Subroutine */ int slatme_(integer *, char *, integer *, real *, integer *, real *, real *, char *, char *, char *, char *, real *, integer *, real *, integer *, integer *, real *, real *, integer *, real *, integer *), slaset_(char *, integer *, integer *, real *, real *, real *, integer *), slatmr_(integer *, integer *, char *, integer *, char *, real *, integer *, real *, real *, char *, char *, real *, integer *, real *, real *, integer *, real *, char *, integer *, integer *, integer *, real *, real *, char *, real *, integer *, integer *, integer *); static integer ntestf; extern /* Subroutine */ int slasum_(char *, integer *, integer *, integer *), slatms_(integer *, integer *, char *, integer *, char *, real *, integer *, real *, real *, integer *, integer *, char * , real *, integer *, real *, integer *); static real ulpinv; static integer nnwork; static real rtulpi; static integer mtypes, ntestt, iwk; static real ulp; /* Fortran I/O blocks */ static cilist io___33 = { 0, 0, 0, fmt_9992, 0 }; static cilist io___40 = { 0, 0, 0, fmt_9999, 0 }; static cilist io___41 = { 0, 0, 0, fmt_9998, 0 }; static cilist io___42 = { 0, 0, 0, fmt_9997, 0 }; static cilist io___43 = { 0, 0, 0, fmt_9996, 0 }; static cilist io___44 = { 0, 0, 0, fmt_9995, 0 }; static cilist io___45 = { 0, 0, 0, fmt_9994, 0 }; static cilist io___46 = { 0, 0, 1, 0, 0 }; static cilist io___48 = { 0, 0, 0, 0, 0 }; static cilist io___49 = { 0, 0, 0, 0, 0 }; static cilist io___50 = { 0, 0, 0, fmt_9999, 0 }; static cilist io___51 = { 0, 0, 0, fmt_9998, 0 }; static cilist io___52 = { 0, 0, 0, fmt_9997, 0 }; static cilist io___53 = { 0, 0, 0, fmt_9996, 0 }; static cilist io___54 = { 0, 0, 0, fmt_9995, 0 }; static cilist io___55 = { 0, 0, 0, fmt_9993, 0 }; #define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1] /* -- 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 ======= SDRVVX checks the nonsymmetric eigenvalue problem expert driver SGEEVX. SDRVVX uses both test matrices generated randomly depending on data supplied in the calling sequence, as well as on data read from an input file and including precomputed condition numbers to which it compares the ones it computes. When SDRVVX is called, a number of matrix "sizes" ("n's") and a number of matrix "types" are specified in the calling sequence. For each size ("n") and each type of matrix, one matrix will be generated and used to test the nonsymmetric eigenroutines. For each matrix, 9 tests will be performed: (1) | A * VR - VR * W | / ( n |A| ulp ) Here VR is the matrix of unit right eigenvectors. W is a block diagonal matrix, with a 1x1 block for each real eigenvalue and a 2x2 block for each complex conjugate pair. If eigenvalues j and j+1 are a complex conjugate pair, so WR(j) = WR(j+1) = wr and WI(j) = - WI(j+1) = wi, then the 2 x 2 block corresponding to the pair will be: ( wr wi ) ( -wi wr ) Such a block multiplying an n x 2 matrix ( ur ui ) on the right will be the same as multiplying ur + i*ui by wr + i*wi. (2) | A**H * VL - VL * W**H | / ( n |A| ulp ) Here VL is the matrix of unit left eigenvectors, A**H is the conjugate transpose of A, and W is as above. (3) | |VR(i)| - 1 | / ulp and largest component real VR(i) denotes the i-th column of VR. (4) | |VL(i)| - 1 | / ulp and largest component real VL(i) denotes the i-th column of VL. (5) W(full) = W(partial) W(full) denotes the eigenvalues computed when VR, VL, RCONDV and RCONDE are also computed, and W(partial) denotes the eigenvalues computed when only some of VR, VL, RCONDV, and RCONDE are computed. (6) VR(full) = VR(partial) VR(full) denotes the right eigenvectors computed when VL, RCONDV and RCONDE are computed, and VR(partial) denotes the result when only some of VL and RCONDV are computed. (7) VL(full) = VL(partial) VL(full) denotes the left eigenvectors computed when VR, RCONDV and RCONDE are computed, and VL(partial) denotes the result when only some of VR and RCONDV are computed. (8) 0 if SCALE, ILO, IHI, ABNRM (full) = SCALE, ILO, IHI, ABNRM (partial) 1/ulp otherwise SCALE, ILO, IHI and ABNRM describe how the matrix is balanced. (full) is when VR, VL, RCONDE and RCONDV are also computed, and (partial) is when some are not computed. (9) RCONDV(full) = RCONDV(partial) RCONDV(full) denotes the reciprocal condition numbers of the right eigenvectors computed when VR, VL and RCONDE are also computed. RCONDV(partial) denotes the reciprocal condition numbers when only some of VR, VL and RCONDE are computed. The "sizes" are specified by an array NN(1:NSIZES); the value of each element NN(j) specifies one size. The "types" are specified by a logical array DOTYPE( 1:NTYPES ); if DOTYPE(j) is .TRUE., then matrix type "j" will be generated. Currently, the list of possible types is: (1) The zero matrix. (2) The identity matrix. (3) A (transposed) Jordan block, with 1's on the diagonal. (4) A diagonal matrix with evenly spaced entries 1, ..., ULP and random signs. (ULP = (first number larger than 1) - 1 ) (5) A diagonal matrix with geometrically spaced entries 1, ..., ULP and random signs. (6) A diagonal matrix with "clustered" entries 1, ULP, ..., ULP and random signs. (7) Same as (4), but multiplied by a constant near the overflow threshold (8) Same as (4), but multiplied by a constant near the underflow threshold (9) A matrix of the form U' T U, where U is orthogonal and T has evenly spaced entries 1, ..., ULP with random signs on the diagonal and random O(1) entries in the upper triangle. (10) A matrix of the form U' T U, where U is orthogonal and T has geometrically spaced entries 1, ..., ULP with random signs on the diagonal and random O(1) entries in the upper triangle. (11) A matrix of the form U' T U, where U is orthogonal and T has "clustered" entries 1, ULP,..., ULP with random signs on the diagonal and random O(1) entries in the upper triangle. (12) A matrix of the form U' T U, where U is orthogonal and T has real or complex conjugate paired eigenvalues randomly chosen from ( ULP, 1 ) and random O(1) entries in the upper triangle. (13) A matrix of the form X' T X, where X has condition SQRT( ULP ) and T has evenly spaced entries 1, ..., ULP with random signs on the diagonal and random O(1) entries in the upper triangle. (14) A matrix of the form X' T X, where X has condition SQRT( ULP ) and T has geometrically spaced entries 1, ..., ULP with random signs on the diagonal and random O(1) entries in the upper triangle. (15) A matrix of the form X' T X, where X has condition SQRT( ULP ) and T has "clustered" entries 1, ULP,..., ULP with random signs on the diagonal and random O(1) entries in the upper triangle. (16) A matrix of the form X' T X, where X has condition SQRT( ULP ) and T has real or complex conjugate paired eigenvalues randomly chosen from ( ULP, 1 ) and random O(1) entries in the upper triangle. (17) Same as (16), but multiplied by a constant near the overflow threshold (18) Same as (16), but multiplied by a constant near the underflow threshold (19) Nonsymmetric matrix with random entries chosen from (-1,1). If N is at least 4, all entries in first two rows and last row, and first column and last two columns are zero. (20) Same as (19), but multiplied by a constant near the overflow threshold (21) Same as (19), but multiplied by a constant near the underflow threshold In addition, an input file will be read from logical unit number NIUNIT. The file contains matrices along with precomputed eigenvalues and reciprocal condition numbers for the eigenvalues and right eigenvectors. For these matrices, in addition to tests (1) to (9) we will compute the following two tests: (10) |RCONDV - RCDVIN| / cond(RCONDV) RCONDV is the reciprocal right eigenvector condition number computed by SGEEVX and RCDVIN (the precomputed true value) is supplied as input. cond(RCONDV) is the condition number of RCONDV, and takes errors in computing RCONDV into account, so that the resulting quantity should be O(ULP). cond(RCONDV) is essentially given by norm(A)/RCONDE. (11) |RCONDE - RCDEIN| / cond(RCONDE) RCONDE is the reciprocal eigenvalue condition number computed by SGEEVX and RCDEIN (the precomputed true value) is supplied as input. cond(RCONDE) is the condition number of RCONDE, and takes errors in computing RCONDE into account, so that the resulting quantity should be O(ULP). cond(RCONDE) is essentially given by norm(A)/RCONDV. Arguments ========== NSIZES (input) INTEGER The number of sizes of matrices to use. NSIZES must be at least zero. If it is zero, no randomly generated matrices are tested, but any test matrices read from NIUNIT will be tested. NN (input) INTEGER array, dimension (NSIZES) An array containing the sizes to be used for the matrices. Zero values will be skipped. The values must be at least zero. NTYPES (input) INTEGER The number of elements in DOTYPE. NTYPES must be at least zero. If it is zero, no randomly generated test matrices are tested, but and test matrices read from NIUNIT will be tested. If it is MAXTYP+1 and NSIZES is 1, then an additional type, MAXTYP+1 is defined, which is to use whatever matrix is in A. This is only useful if DOTYPE(1:MAXTYP) is .FALSE. and DOTYPE(MAXTYP+1) is .TRUE. . DOTYPE (input) LOGICAL array, dimension (NTYPES) If DOTYPE(j) is .TRUE., then for each size in NN a matrix of that size and of type j will be generated. If NTYPES is smaller than the maximum number of types defined (PARAMETER MAXTYP), then types NTYPES+1 through MAXTYP will not be generated. If NTYPES is larger than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES) will be ignored. ISEED (input/output) INTEGER array, dimension (4) On entry ISEED specifies the seed of the random number generator. The array elements should be between 0 and 4095; if not they will be reduced mod 4096. Also, ISEED(4) must be odd. The random number generator uses a linear congruential sequence limited to small integers, and so should produce machine independent random numbers. The values of ISEED are changed on exit, and can be used in the next call to SDRVVX to continue the same random number sequence. THRESH (input) REAL A test will count as "failed" if the "error", computed as described above, exceeds THRESH. Note that the error is scaled to be O(1), so THRESH should be a reasonably small multiple of 1, e.g., 10 or 100. In particular, it should not depend on the precision (single vs. double) or the size of the matrix. It must be at least zero. NIUNIT (input) INTEGER The FORTRAN unit number for reading in the data file of problems to solve. NOUNIT (input) INTEGER The FORTRAN unit number for printing out error messages (e.g., if a routine returns INFO not equal to 0.) A (workspace) REAL array, dimension (LDA, max(NN,12)) Used to hold the matrix whose eigenvalues are to be computed. On exit, A contains the last matrix actually used. LDA (input) INTEGER The leading dimension of the arrays A and H. LDA >= max(NN,12), since 12 is the dimension of the largest matrix in the precomputed input file. H (workspace) REAL array, dimension (LDA, max(NN,12)) Another copy of the test matrix A, modified by SGEEVX. WR (workspace) REAL array, dimension (max(NN)) WI (workspace) REAL array, dimension (max(NN)) The real and imaginary parts of the eigenvalues of A. On exit, WR + WI*i are the eigenvalues of the matrix in A. WR1 (workspace) REAL array, dimension (max(NN,12)) WI1 (workspace) REAL array, dimension (max(NN,12)) Like WR, WI, these arrays contain the eigenvalues of A, but those computed when SGEEVX only computes a partial eigendecomposition, i.e. not the eigenvalues and left and right eigenvectors. VL (workspace) REAL array, dimension (LDVL, max(NN,12)) VL holds the computed left eigenvectors. LDVL (input) INTEGER Leading dimension of VL. Must be at least max(1,max(NN,12)). VR (workspace) REAL array, dimension (LDVR, max(NN,12)) VR holds the computed right eigenvectors. LDVR (input) INTEGER Leading dimension of VR. Must be at least max(1,max(NN,12)). LRE (workspace) REAL array, dimension (LDLRE, max(NN,12)) LRE holds the computed right or left eigenvectors. LDLRE (input) INTEGER Leading dimension of LRE. Must be at least max(1,max(NN,12)) RCONDV (workspace) REAL array, dimension (N) RCONDV holds the computed reciprocal condition numbers for eigenvectors. RCNDV1 (workspace) REAL array, dimension (N) RCNDV1 holds more computed reciprocal condition numbers for eigenvectors. RCDVIN (workspace) REAL array, dimension (N) When COMP = .TRUE. RCDVIN holds the precomputed reciprocal condition numbers for eigenvectors to be compared with RCONDV. RCONDE (workspace) REAL array, dimension (N) RCONDE holds the computed reciprocal condition numbers for eigenvalues. RCNDE1 (workspace) REAL array, dimension (N) RCNDE1 holds more computed reciprocal condition numbers for eigenvalues. RCDEIN (workspace) REAL array, dimension (N) When COMP = .TRUE. RCDEIN holds the precomputed reciprocal condition numbers for eigenvalues to be compared with RCONDE. RESULT (output) REAL array, dimension (11) The values computed by the seven tests described above. The values are currently limited to 1/ulp, to avoid overflow. WORK (workspace) REAL array, dimension (NWORK) NWORK (input) INTEGER The number of entries in WORK. This must be at least max(6*12+2*12**2,6*NN(j)+2*NN(j)**2) = max( 360 ,6*NN(j)+2*NN(j)**2) for all j. IWORK (workspace) INTEGER array, dimension (2*max(NN,12)) INFO (output) INTEGER If 0, then successful exit. If <0, then input paramter -INFO is incorrect. If >0, SLATMR, SLATMS, SLATME or SGET23 returned an error code, and INFO is its absolute value. ----------------------------------------------------------------------- Some Local Variables and Parameters: ---- ----- --------- --- ---------- ZERO, ONE Real 0 and 1. MAXTYP The number of types defined. NMAX Largest value in NN or 12. NERRS The number of tests which have exceeded THRESH COND, CONDS, IMODE Values to be passed to the matrix generators. ANORM Norm of A; passed to matrix generators. OVFL, UNFL Overflow and underflow thresholds. ULP, ULPINV Finest relative precision and its inverse. RTULP, RTULPI Square roots of the previous 4 values. The following four arrays decode JTYPE: KTYPE(j) The general type (1-10) for type "j". KMODE(j) The MODE value to be passed to the matrix generator for type "j". KMAGN(j) The order of magnitude ( O(1), O(overflow^(1/2) ), O(underflow^(1/2) ) KCONDS(j) Selectw whether CONDS is to be 1 or 1/sqrt(ulp). (0 means irrelevant.) ===================================================================== Parameter adjustments */ --nn; --dotype; --iseed; h_dim1 = *lda; h_offset = 1 + h_dim1 * 1; h__ -= h_offset; a_dim1 = *lda; a_offset = 1 + a_dim1 * 1; a -= a_offset; --wr; --wi; --wr1; --wi1; vl_dim1 = *ldvl; vl_offset = 1 + vl_dim1 * 1; vl -= vl_offset; vr_dim1 = *ldvr; vr_offset = 1 + vr_dim1 * 1; vr -= vr_offset; lre_dim1 = *ldlre; lre_offset = 1 + lre_dim1 * 1; lre -= lre_offset; --rcondv; --rcndv1; --rcdvin; --rconde; --rcnde1; --rcdein; --scale; --scale1; --result; --work; --iwork; /* Function Body */ s_copy(path, "Single precision", (ftnlen)1, (ftnlen)16); s_copy(path + 1, "VX", (ftnlen)2, (ftnlen)2); /* Check for errors */ ntestt = 0; ntestf = 0; *info = 0; /* Important constants */ badnn = FALSE_; /* 12 is the largest dimension in the input file of precomputed problems */ nmax = 12; i__1 = *nsizes; for (j = 1; j <= i__1; ++j) { /* Computing MAX */ i__2 = nmax, i__3 = nn[j]; nmax = max(i__2,i__3); if (nn[j] < 0) { badnn = TRUE_; } /* L10: */ } /* Check for errors */ if (*nsizes < 0) { *info = -1; } else if (badnn) { *info = -2; } else if (*ntypes < 0) { *info = -3; } else if (*thresh < 0.f) { *info = -6; } else if (*lda < 1 || *lda < nmax) { *info = -10; } else if (*ldvl < 1 || *ldvl < nmax) { *info = -17; } else if (*ldvr < 1 || *ldvr < nmax) { *info = -19; } else if (*ldlre < 1 || *ldlre < nmax) { *info = -21; } else /* if(complicated condition) */ { /* Computing 2nd power */ i__1 = nmax; if (nmax * 6 + (i__1 * i__1 << 1) > *nwork) { *info = -32; } } if (*info != 0) { i__1 = -(*info); xerbla_("SDRVVX", &i__1); return 0; } /* If nothing to do check on NIUNIT */ if (*nsizes == 0 || *ntypes == 0) { goto L160; } /* More Important constants */ unfl = slamch_("Safe minimum"); ovfl = 1.f / unfl; slabad_(&unfl, &ovfl); ulp = slamch_("Precision"); ulpinv = 1.f / ulp; rtulp = sqrt(ulp); rtulpi = 1.f / rtulp; /* Loop over sizes, types */ nerrs = 0; i__1 = *nsizes; for (jsize = 1; jsize <= i__1; ++jsize) { n = nn[jsize]; if (*nsizes != 1) { mtypes = min(21,*ntypes); } else { mtypes = min(22,*ntypes); } i__2 = mtypes; for (jtype = 1; jtype <= i__2; ++jtype) { if (! dotype[jtype]) { goto L140; } /* Save ISEED in case of an error. */ for (j = 1; j <= 4; ++j) { ioldsd[j - 1] = iseed[j]; /* L20: */ } /* Compute "A" Control parameters: KMAGN KCONDS KMODE KTYPE =1 O(1) 1 clustered 1 zero =2 large large clustered 2 identity =3 small exponential Jordan =4 arithmetic diagonal, (w/ eigenvalues) =5 random log symmetric, w/ eigenvalues =6 random general, w/ eigenvalues =7 random diagonal =8 random symmetric =9 random general =10 random triangular */ if (mtypes > 21) { goto L90; } itype = ktype[jtype - 1]; imode = kmode[jtype - 1]; /* Compute norm */ switch (kmagn[jtype - 1]) { case 1: goto L30; case 2: goto L40; case 3: goto L50; } L30: anorm = 1.f; goto L60; L40: anorm = ovfl * ulp; goto L60; L50: anorm = unfl * ulpinv; goto L60; L60: slaset_("Full", lda, &n, &c_b18, &c_b18, &a[a_offset], lda); iinfo = 0; cond = ulpinv; /* Special Matrices -- Identity & Jordan block Zero */ if (itype == 1) { iinfo = 0; } else if (itype == 2) { /* Identity */ i__3 = n; for (jcol = 1; jcol <= i__3; ++jcol) { a_ref(jcol, jcol) = anorm; /* L70: */ } } else if (itype == 3) { /* Jordan Block */ i__3 = n; for (jcol = 1; jcol <= i__3; ++jcol) { a_ref(jcol, jcol) = anorm; if (jcol > 1) { a_ref(jcol, jcol - 1) = 1.f; } /* L80: */ } } else if (itype == 4) { /* Diagonal Matrix, [Eigen]values Specified */ slatms_(&n, &n, "S", &iseed[1], "S", &work[1], &imode, &cond, &anorm, &c__0, &c__0, "N", &a[a_offset], lda, &work[n + 1], &iinfo); } else if (itype == 5) { /* Symmetric, eigenvalues specified */ slatms_(&n, &n, "S", &iseed[1], "S", &work[1], &imode, &cond, &anorm, &n, &n, "N", &a[a_offset], lda, &work[n + 1], &iinfo); } else if (itype == 6) { /* General, eigenvalues specified */ if (kconds[jtype - 1] == 1) { conds = 1.f; } else if (kconds[jtype - 1] == 2) { conds = rtulpi; } else { conds = 0.f; } *(unsigned char *)&adumma[0] = ' '; slatme_(&n, "S", &iseed[1], &work[1], &imode, &cond, &c_b32, adumma, "T", "T", "T", &work[n + 1], &c__4, &conds, & n, &n, &anorm, &a[a_offset], lda, &work[(n << 1) + 1], &iinfo); } else if (itype == 7) { /* Diagonal, random eigenvalues */ slatmr_(&n, &n, "S", &iseed[1], "S", &work[1], &c__6, &c_b32, &c_b32, "T", "N", &work[n + 1], &c__1, &c_b32, &work[( n << 1) + 1], &c__1, &c_b32, "N", idumma, &c__0, & c__0, &c_b18, &anorm, "NO", &a[a_offset], lda, &iwork[ 1], &iinfo); } else if (itype == 8) { /* Symmetric, random eigenvalues */ slatmr_(&n, &n, "S", &iseed[1], "S", &work[1], &c__6, &c_b32, &c_b32, "T", "N", &work[n + 1], &c__1, &c_b32, &work[( n << 1) + 1], &c__1, &c_b32, "N", idumma, &n, &n, & c_b18, &anorm, "NO", &a[a_offset], lda, &iwork[1], & iinfo); } else if (itype == 9) { /* General, random eigenvalues */ slatmr_(&n, &n, "S", &iseed[1], "N", &work[1], &c__6, &c_b32, &c_b32, "T", "N", &work[n + 1], &c__1, &c_b32, &work[( n << 1) + 1], &c__1, &c_b32, "N", idumma, &n, &n, & c_b18, &anorm, "NO", &a[a_offset], lda, &iwork[1], & iinfo); if (n >= 4) { slaset_("Full", &c__2, &n, &c_b18, &c_b18, &a[a_offset], lda); i__3 = n - 3; slaset_("Full", &i__3, &c__1, &c_b18, &c_b18, &a_ref(3, 1) , lda); i__3 = n - 3; slaset_("Full", &i__3, &c__2, &c_b18, &c_b18, &a_ref(3, n - 1), lda); slaset_("Full", &c__1, &n, &c_b18, &c_b18, &a_ref(n, 1), lda); } } else if (itype == 10) { /* Triangular, random eigenvalues */ slatmr_(&n, &n, "S", &iseed[1], "N", &work[1], &c__6, &c_b32, &c_b32, "T", "N", &work[n + 1], &c__1, &c_b32, &work[( n << 1) + 1], &c__1, &c_b32, "N", idumma, &n, &c__0, & c_b18, &anorm, "NO", &a[a_offset], lda, &iwork[1], & iinfo); } else { iinfo = 1; } if (iinfo != 0) { io___33.ciunit = *nounit; s_wsfe(&io___33); do_fio(&c__1, "Generator", (ftnlen)9); do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer)); do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer)); e_wsfe(); *info = abs(iinfo); return 0; } L90: /* Test for minimal and generous workspace */ for (iwk = 1; iwk <= 3; ++iwk) { if (iwk == 1) { nnwork = n * 3; } else if (iwk == 2) { /* Computing 2nd power */ i__3 = n; nnwork = n * 6 + i__3 * i__3; } else { /* Computing 2nd power */ i__3 = n; nnwork = n * 6 + (i__3 * i__3 << 1); } nnwork = max(nnwork,1); /* Test for all balancing options */ for (ibal = 1; ibal <= 4; ++ibal) { *(unsigned char *)balanc = *(unsigned char *)&bal[ibal - 1]; /* Perform tests */ sget23_(&c_false, balanc, &jtype, thresh, ioldsd, nounit, &n, &a[a_offset], lda, &h__[h_offset], &wr[1], & wi[1], &wr1[1], &wi1[1], &vl[vl_offset], ldvl, & vr[vr_offset], ldvr, &lre[lre_offset], ldlre, & rcondv[1], &rcndv1[1], &rcdvin[1], &rconde[1], & rcnde1[1], &rcdein[1], &scale[1], &scale1[1], & result[1], &work[1], &nnwork, &iwork[1], info); /* Check for RESULT(j) > THRESH */ ntest = 0; nfail = 0; for (j = 1; j <= 9; ++j) { if (result[j] >= 0.f) { ++ntest; } if (result[j] >= *thresh) { ++nfail; } /* L100: */ } if (nfail > 0) { ++ntestf; } if (ntestf == 1) { io___40.ciunit = *nounit; s_wsfe(&io___40); do_fio(&c__1, path, (ftnlen)3); e_wsfe(); io___41.ciunit = *nounit; s_wsfe(&io___41); e_wsfe(); io___42.ciunit = *nounit; s_wsfe(&io___42); e_wsfe(); io___43.ciunit = *nounit; s_wsfe(&io___43); e_wsfe(); io___44.ciunit = *nounit; s_wsfe(&io___44); do_fio(&c__1, (char *)&(*thresh), (ftnlen)sizeof(real) ); e_wsfe(); ntestf = 2; } for (j = 1; j <= 9; ++j) { if (result[j] >= *thresh) { io___45.ciunit = *nounit; s_wsfe(&io___45); do_fio(&c__1, balanc, (ftnlen)1); do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer)) ; do_fio(&c__1, (char *)&iwk, (ftnlen)sizeof( integer)); do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof( integer)); do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof( integer)); do_fio(&c__1, (char *)&j, (ftnlen)sizeof(integer)) ; do_fio(&c__1, (char *)&result[j], (ftnlen)sizeof( real)); e_wsfe(); } /* L110: */ } nerrs += nfail; ntestt += ntest; /* L120: */ } /* L130: */ } L140: ; } /* L150: */ } L160: /* Read in data from file to check accuracy of condition estimation. Assume input eigenvalues are sorted lexicographically (increasing by real part, then decreasing by imaginary part) */ jtype = 0; L170: io___46.ciunit = *niunit; i__1 = s_rsle(&io___46); if (i__1 != 0) { goto L220; } i__1 = do_lio(&c__3, &c__1, (char *)&n, (ftnlen)sizeof(integer)); if (i__1 != 0) { goto L220; } i__1 = e_rsle(); if (i__1 != 0) { goto L220; } /* Read input data until N=0 */ if (n == 0) { goto L220; } ++jtype; iseed[1] = jtype; i__1 = n; for (i__ = 1; i__ <= i__1; ++i__) { io___48.ciunit = *niunit; s_rsle(&io___48); i__2 = n; for (j = 1; j <= i__2; ++j) { do_lio(&c__4, &c__1, (char *)&a_ref(i__, j), (ftnlen)sizeof(real)) ; } e_rsle(); /* L180: */ } i__1 = n; for (i__ = 1; i__ <= i__1; ++i__) { io___49.ciunit = *niunit; s_rsle(&io___49); do_lio(&c__4, &c__1, (char *)&wr1[i__], (ftnlen)sizeof(real)); do_lio(&c__4, &c__1, (char *)&wi1[i__], (ftnlen)sizeof(real)); do_lio(&c__4, &c__1, (char *)&rcdein[i__], (ftnlen)sizeof(real)); do_lio(&c__4, &c__1, (char *)&rcdvin[i__], (ftnlen)sizeof(real)); e_rsle(); /* L190: */ } /* Computing 2nd power */ i__2 = n; i__1 = n * 6 + (i__2 * i__2 << 1); sget23_(&c_true, "N", &c__22, thresh, &iseed[1], nounit, &n, &a[a_offset], lda, &h__[h_offset], &wr[1], &wi[1], &wr1[1], &wi1[1], &vl[ vl_offset], ldvl, &vr[vr_offset], ldvr, &lre[lre_offset], ldlre, & rcondv[1], &rcndv1[1], &rcdvin[1], &rconde[1], &rcnde1[1], & rcdein[1], &scale[1], &scale1[1], &result[1], &work[1], &i__1, & iwork[1], info); /* Check for RESULT(j) > THRESH */ ntest = 0; nfail = 0; for (j = 1; j <= 11; ++j) { if (result[j] >= 0.f) { ++ntest; } if (result[j] >= *thresh) { ++nfail; } /* L200: */ } if (nfail > 0) { ++ntestf; } if (ntestf == 1) { io___50.ciunit = *nounit; s_wsfe(&io___50); do_fio(&c__1, path, (ftnlen)3); e_wsfe(); io___51.ciunit = *nounit; s_wsfe(&io___51); e_wsfe(); io___52.ciunit = *nounit; s_wsfe(&io___52); e_wsfe(); io___53.ciunit = *nounit; s_wsfe(&io___53); e_wsfe(); io___54.ciunit = *nounit; s_wsfe(&io___54); do_fio(&c__1, (char *)&(*thresh), (ftnlen)sizeof(real)); e_wsfe(); ntestf = 2; } for (j = 1; j <= 11; ++j) { if (result[j] >= *thresh) { io___55.ciunit = *nounit; s_wsfe(&io___55); do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&j, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&result[j], (ftnlen)sizeof(real)); e_wsfe(); } /* L210: */ } nerrs += nfail; ntestt += ntest; goto L170; L220: /* Summary */ slasum_(path, nounit, &nerrs, &ntestt); return 0; /* End of SDRVVX */ } /* sdrvvx_ */
/* Subroutine */ int sdrvev_(integer *nsizes, integer *nn, integer *ntypes, logical *dotype, integer *iseed, real *thresh, integer *nounit, real * a, integer *lda, real *h__, real *wr, real *wi, real *wr1, real *wi1, real *vl, integer *ldvl, real *vr, integer *ldvr, real *lre, integer * ldlre, real *result, real *work, integer *nwork, integer *iwork, integer *info) { /* Initialized data */ static integer ktype[21] = { 1,2,3,4,4,4,4,4,6,6,6,6,6,6,6,6,6,6,9,9,9 }; static integer kmagn[21] = { 1,1,1,1,1,1,2,3,1,1,1,1,1,1,1,1,2,3,1,2,3 }; static integer kmode[21] = { 0,0,0,4,3,1,4,4,4,3,1,5,4,3,1,5,5,5,4,3,1 }; static integer kconds[21] = { 0,0,0,0,0,0,0,0,1,1,1,1,2,2,2,2,2,2,0,0,0 }; /* Format strings */ static char fmt_9993[] = "(\002 SDRVEV: \002,a,\002 returned INFO=\002,i" "6,\002.\002,/9x,\002N=\002,i6,\002, JTYPE=\002,i6,\002, ISEED=" "(\002,3(i5,\002,\002),i5,\002)\002)"; static char fmt_9999[] = "(/1x,a3,\002 -- Real Eigenvalue-Eigenvector De" "composition\002,\002 Driver\002,/\002 Matrix types (see SDRVEV f" "or details): \002)"; static char fmt_9998[] = "(/\002 Special Matrices:\002,/\002 1=Zero mat" "rix. \002,\002 \002,\002 5=Diagonal: geom" "etr. spaced entries.\002,/\002 2=Identity matrix. " " \002,\002 6=Diagona\002,\002l: clustered entries.\002," "/\002 3=Transposed Jordan block. \002,\002 \002,\002 " " 7=Diagonal: large, evenly spaced.\002,/\002 \002,\0024=Diagona" "l: evenly spaced entries. \002,\002 8=Diagonal: s\002,\002ma" "ll, evenly spaced.\002)"; static char fmt_9997[] = "(\002 Dense, Non-Symmetric Matrices:\002,/\002" " 9=Well-cond., ev\002,\002enly spaced eigenvals.\002,\002 14=Il" "l-cond., geomet. spaced e\002,\002igenals.\002,/\002 10=Well-con" "d., geom. spaced eigenvals. \002,\002 15=Ill-conditioned, cluste" "red e.vals.\002,/\002 11=Well-cond\002,\002itioned, clustered e." "vals. \002,\002 16=Ill-cond., random comp\002,\002lex \002,/\002" " 12=Well-cond., random complex \002,6x,\002 \002,\002 17=Ill-c" "ond., large rand. complx \002,/\002 13=Ill-condi\002,\002tioned," " evenly spaced. \002,\002 18=Ill-cond., small rand.\002,\002" " complx \002)"; static char fmt_9996[] = "(\002 19=Matrix with random O(1) entries. " " \002,\002 21=Matrix \002,\002with small random entries.\002," "/\002 20=Matrix with large ran\002,\002dom entries. \002,/)"; static char fmt_9995[] = "(\002 Tests performed with test threshold =" "\002,f8.2,//\002 1 = | A VR - VR W | / ( n |A| ulp ) \002,/\002 " "2 = | transpose(A) VL - VL W | / ( n |A| ulp ) \002,/\002 3 = | " "|VR(i)| - 1 | / ulp \002,/\002 4 = | |VL(i)| - 1 | / ulp \002," "/\002 5 = 0 if W same no matter if VR or VL computed,\002,\002 1" "/ulp otherwise\002,/\002 6 = 0 if VR same no matter if VL comput" "ed,\002,\002 1/ulp otherwise\002,/\002 7 = 0 if VL same no matt" "er if VR computed,\002,\002 1/ulp otherwise\002,/)"; static char fmt_9994[] = "(\002 N=\002,i5,\002, IWK=\002,i2,\002, seed" "=\002,4(i4,\002,\002),\002 type \002,i2,\002, test(\002,i2,\002)=" "\002,g10.3)"; /* System generated locals */ integer a_dim1, a_offset, h_dim1, h_offset, lre_dim1, lre_offset, vl_dim1, vl_offset, vr_dim1, vr_offset, i__1, i__2, i__3, i__4; real r__1, r__2, r__3, r__4, r__5; /* Local variables */ integer j, n, jj; real dum[1], res[2]; integer iwk; real ulp, vmx, cond; integer jcol; char path[3]; integer nmax; real unfl, ovfl, tnrm, vrmx, vtst; extern doublereal snrm2_(integer *, real *, integer *); logical badnn; integer nfail, imode, iinfo; real conds; extern /* Subroutine */ int sget22_(char *, char *, char *, integer *, real *, integer *, real *, integer *, real *, real *, real *, real *), sgeev_(char *, char *, integer *, real *, integer *, real *, real *, real *, integer *, real *, integer *, real *, integer *, integer *); real anorm; integer jsize, nerrs, itype, jtype, ntest; real rtulp; extern doublereal slapy2_(real *, real *); extern /* Subroutine */ int slabad_(real *, real *); char adumma[1*1]; extern doublereal slamch_(char *); integer idumma[1]; integer ioldsd[4]; extern /* Subroutine */ int slatme_(integer *, char *, integer *, real *, integer *, real *, real *, char *, char *, char *, char *, real *, integer *, real *, integer *, integer *, real *, real *, integer *, real *, integer *), slacpy_(char *, integer *, integer *, real *, integer *, real *, integer *), slaset_(char *, integer *, integer *, real *, real *, real *, integer *), slatmr_(integer *, integer *, char *, integer *, char *, real *, integer *, real *, real *, char *, char *, real *, integer *, real *, real *, integer *, real *, char *, integer *, integer *, integer *, real *, real *, char *, real *, integer *, integer *, integer *); integer ntestf; extern /* Subroutine */ int slasum_(char *, integer *, integer *, integer *), slatms_(integer *, integer *, char *, integer *, char *, real *, integer *, real *, real *, integer *, integer *, char * , real *, integer *, real *, integer *); real ulpinv; integer nnwork; real rtulpi; integer mtypes, ntestt; /* Fortran I/O blocks */ static cilist io___32 = { 0, 0, 0, fmt_9993, 0 }; static cilist io___35 = { 0, 0, 0, fmt_9993, 0 }; static cilist io___43 = { 0, 0, 0, fmt_9993, 0 }; static cilist io___44 = { 0, 0, 0, fmt_9993, 0 }; static cilist io___45 = { 0, 0, 0, fmt_9993, 0 }; static cilist io___48 = { 0, 0, 0, fmt_9999, 0 }; static cilist io___49 = { 0, 0, 0, fmt_9998, 0 }; static cilist io___50 = { 0, 0, 0, fmt_9997, 0 }; static cilist io___51 = { 0, 0, 0, fmt_9996, 0 }; static cilist io___52 = { 0, 0, 0, fmt_9995, 0 }; static cilist io___53 = { 0, 0, 0, fmt_9994, 0 }; /* -- LAPACK test routine (version 3.1) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* SDRVEV checks the nonsymmetric eigenvalue problem driver SGEEV. */ /* When SDRVEV is called, a number of matrix "sizes" ("n's") and a */ /* number of matrix "types" are specified. For each size ("n") */ /* and each type of matrix, one matrix will be generated and used */ /* to test the nonsymmetric eigenroutines. For each matrix, 7 */ /* tests will be performed: */ /* (1) | A * VR - VR * W | / ( n |A| ulp ) */ /* Here VR is the matrix of unit right eigenvectors. */ /* W is a block diagonal matrix, with a 1x1 block for each */ /* real eigenvalue and a 2x2 block for each complex conjugate */ /* pair. If eigenvalues j and j+1 are a complex conjugate pair, */ /* so WR(j) = WR(j+1) = wr and WI(j) = - WI(j+1) = wi, then the */ /* 2 x 2 block corresponding to the pair will be: */ /* ( wr wi ) */ /* ( -wi wr ) */ /* Such a block multiplying an n x 2 matrix ( ur ui ) on the */ /* right will be the same as multiplying ur + i*ui by wr + i*wi. */ /* (2) | A**H * VL - VL * W**H | / ( n |A| ulp ) */ /* Here VL is the matrix of unit left eigenvectors, A**H is the */ /* conjugate transpose of A, and W is as above. */ /* (3) | |VR(i)| - 1 | / ulp and whether largest component real */ /* VR(i) denotes the i-th column of VR. */ /* (4) | |VL(i)| - 1 | / ulp and whether largest component real */ /* VL(i) denotes the i-th column of VL. */ /* (5) W(full) = W(partial) */ /* W(full) denotes the eigenvalues computed when both VR and VL */ /* are also computed, and W(partial) denotes the eigenvalues */ /* computed when only W, only W and VR, or only W and VL are */ /* computed. */ /* (6) VR(full) = VR(partial) */ /* VR(full) denotes the right eigenvectors computed when both VR */ /* and VL are computed, and VR(partial) denotes the result */ /* when only VR is computed. */ /* (7) VL(full) = VL(partial) */ /* VL(full) denotes the left eigenvectors computed when both VR */ /* and VL are also computed, and VL(partial) denotes the result */ /* when only VL is computed. */ /* The "sizes" are specified by an array NN(1:NSIZES); the value of */ /* each element NN(j) specifies one size. */ /* The "types" are specified by a logical array DOTYPE( 1:NTYPES ); */ /* if DOTYPE(j) is .TRUE., then matrix type "j" will be generated. */ /* Currently, the list of possible types is: */ /* (1) The zero matrix. */ /* (2) The identity matrix. */ /* (3) A (transposed) Jordan block, with 1's on the diagonal. */ /* (4) A diagonal matrix with evenly spaced entries */ /* 1, ..., ULP and random signs. */ /* (ULP = (first number larger than 1) - 1 ) */ /* (5) A diagonal matrix with geometrically spaced entries */ /* 1, ..., ULP and random signs. */ /* (6) A diagonal matrix with "clustered" entries 1, ULP, ..., ULP */ /* and random signs. */ /* (7) Same as (4), but multiplied by a constant near */ /* the overflow threshold */ /* (8) Same as (4), but multiplied by a constant near */ /* the underflow threshold */ /* (9) A matrix of the form U' T U, where U is orthogonal and */ /* T has evenly spaced entries 1, ..., ULP with random signs */ /* on the diagonal and random O(1) entries in the upper */ /* triangle. */ /* (10) A matrix of the form U' T U, where U is orthogonal and */ /* T has geometrically spaced entries 1, ..., ULP with random */ /* signs on the diagonal and random O(1) entries in the upper */ /* triangle. */ /* (11) A matrix of the form U' T U, where U is orthogonal and */ /* T has "clustered" entries 1, ULP,..., ULP with random */ /* signs on the diagonal and random O(1) entries in the upper */ /* triangle. */ /* (12) A matrix of the form U' T U, where U is orthogonal and */ /* T has real or complex conjugate paired eigenvalues randomly */ /* chosen from ( ULP, 1 ) and random O(1) entries in the upper */ /* triangle. */ /* (13) A matrix of the form X' T X, where X has condition */ /* SQRT( ULP ) and T has evenly spaced entries 1, ..., ULP */ /* with random signs on the diagonal and random O(1) entries */ /* in the upper triangle. */ /* (14) A matrix of the form X' T X, where X has condition */ /* SQRT( ULP ) and T has geometrically spaced entries */ /* 1, ..., ULP with random signs on the diagonal and random */ /* O(1) entries in the upper triangle. */ /* (15) A matrix of the form X' T X, where X has condition */ /* SQRT( ULP ) and T has "clustered" entries 1, ULP,..., ULP */ /* with random signs on the diagonal and random O(1) entries */ /* in the upper triangle. */ /* (16) A matrix of the form X' T X, where X has condition */ /* SQRT( ULP ) and T has real or complex conjugate paired */ /* eigenvalues randomly chosen from ( ULP, 1 ) and random */ /* O(1) entries in the upper triangle. */ /* (17) Same as (16), but multiplied by a constant */ /* near the overflow threshold */ /* (18) Same as (16), but multiplied by a constant */ /* near the underflow threshold */ /* (19) Nonsymmetric matrix with random entries chosen from (-1,1). */ /* If N is at least 4, all entries in first two rows and last */ /* row, and first column and last two columns are zero. */ /* (20) Same as (19), but multiplied by a constant */ /* near the overflow threshold */ /* (21) Same as (19), but multiplied by a constant */ /* near the underflow threshold */ /* Arguments */ /* ========== */ /* NSIZES (input) INTEGER */ /* The number of sizes of matrices to use. If it is zero, */ /* SDRVEV 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, SDRVEV */ /* 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 SDRVEV to continue the same random number */ /* sequence. */ /* THRESH (input) REAL */ /* A test will count as "failed" if the "error", computed as */ /* described above, exceeds THRESH. Note that the error */ /* is scaled to be O(1), so THRESH should be a reasonably */ /* small multiple of 1, e.g., 10 or 100. In particular, */ /* it should not depend on the precision (single vs. double) */ /* or the size of the matrix. It must be at least zero. */ /* NOUNIT (input) INTEGER */ /* The FORTRAN unit number for printing out error messages */ /* (e.g., if a routine returns INFO not equal to 0.) */ /* A (workspace) REAL array, dimension (LDA, max(NN)) */ /* Used to hold the matrix whose eigenvalues are to be */ /* computed. On exit, A contains the last matrix actually used. */ /* LDA (input) INTEGER */ /* The leading dimension of A, and H. LDA must be at */ /* least 1 and at least max(NN). */ /* H (workspace) REAL array, dimension (LDA, max(NN)) */ /* Another copy of the test matrix A, modified by SGEEV. */ /* WR (workspace) REAL array, dimension (max(NN)) */ /* WI (workspace) REAL array, dimension (max(NN)) */ /* The real and imaginary parts of the eigenvalues of A. */ /* On exit, WR + WI*i are the eigenvalues of the matrix in A. */ /* WR1 (workspace) REAL array, dimension (max(NN)) */ /* WI1 (workspace) REAL array, dimension (max(NN)) */ /* Like WR, WI, these arrays contain the eigenvalues of A, */ /* but those computed when SGEEV only computes a partial */ /* eigendecomposition, i.e. not the eigenvalues and left */ /* and right eigenvectors. */ /* VL (workspace) REAL array, dimension (LDVL, max(NN)) */ /* VL holds the computed left eigenvectors. */ /* LDVL (input) INTEGER */ /* Leading dimension of VL. Must be at least max(1,max(NN)). */ /* VR (workspace) REAL array, dimension (LDVR, max(NN)) */ /* VR holds the computed right eigenvectors. */ /* LDVR (input) INTEGER */ /* Leading dimension of VR. Must be at least max(1,max(NN)). */ /* LRE (workspace) REAL array, dimension (LDLRE,max(NN)) */ /* LRE holds the computed right or left eigenvectors. */ /* LDLRE (input) INTEGER */ /* Leading dimension of LRE. Must be at least max(1,max(NN)). */ /* RESULT (output) REAL array, dimension (7) */ /* The values computed by the seven tests described above. */ /* The values are currently limited to 1/ulp, to avoid overflow. */ /* WORK (workspace) REAL array, dimension (NWORK) */ /* NWORK (input) INTEGER */ /* The number of entries in WORK. This must be at least */ /* 5*NN(j)+2*NN(j)**2 for all j. */ /* IWORK (workspace) INTEGER array, dimension (max(NN)) */ /* INFO (output) INTEGER */ /* If 0, then everything ran OK. */ /* -1: NSIZES < 0 */ /* -2: Some NN(j) < 0 */ /* -3: NTYPES < 0 */ /* -6: THRESH < 0 */ /* -9: LDA < 1 or LDA < NMAX, where NMAX is max( NN(j) ). */ /* -16: LDVL < 1 or LDVL < NMAX, where NMAX is max( NN(j) ). */ /* -18: LDVR < 1 or LDVR < NMAX, where NMAX is max( NN(j) ). */ /* -20: LDLRE < 1 or LDLRE < NMAX, where NMAX is max( NN(j) ). */ /* -23: NWORK too small. */ /* If SLATMR, SLATMS, SLATME or SGEEV returns an error code, */ /* the absolute value of it is returned. */ /* ----------------------------------------------------------------------- */ /* Some Local Variables and Parameters: */ /* ---- ----- --------- --- ---------- */ /* ZERO, ONE Real 0 and 1. */ /* MAXTYP The number of types defined. */ /* NMAX Largest value in NN. */ /* NERRS The number of tests which have exceeded THRESH */ /* COND, CONDS, */ /* IMODE Values to be passed to the matrix generators. */ /* ANORM Norm of A; passed to matrix generators. */ /* OVFL, UNFL Overflow and underflow thresholds. */ /* ULP, ULPINV Finest relative precision and its inverse. */ /* RTULP, RTULPI Square roots of the previous 4 values. */ /* The following four arrays decode JTYPE: */ /* KTYPE(j) The general type (1-10) for type "j". */ /* KMODE(j) The MODE value to be passed to the matrix */ /* generator for type "j". */ /* KMAGN(j) The order of magnitude ( O(1), */ /* O(overflow^(1/2) ), O(underflow^(1/2) ) */ /* KCONDS(j) Selectw whether CONDS is to be 1 or */ /* 1/sqrt(ulp). (0 means irrelevant.) */ /* ===================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. Local Arrays .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Data statements .. */ /* Parameter adjustments */ --nn; --dotype; --iseed; h_dim1 = *lda; h_offset = 1 + h_dim1; h__ -= h_offset; a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --wr; --wi; --wr1; --wi1; vl_dim1 = *ldvl; vl_offset = 1 + vl_dim1; vl -= vl_offset; vr_dim1 = *ldvr; vr_offset = 1 + vr_dim1; vr -= vr_offset; lre_dim1 = *ldlre; lre_offset = 1 + lre_dim1; lre -= lre_offset; --result; --work; --iwork; /* Function Body */ /* .. */ /* .. Executable Statements .. */ s_copy(path, "Single precision", (ftnlen)1, (ftnlen)16); s_copy(path + 1, "EV", (ftnlen)2, (ftnlen)2); /* Check for errors */ ntestt = 0; ntestf = 0; *info = 0; /* Important constants */ badnn = FALSE_; nmax = 0; i__1 = *nsizes; for (j = 1; j <= i__1; ++j) { /* Computing MAX */ i__2 = nmax, i__3 = nn[j]; nmax = max(i__2,i__3); if (nn[j] < 0) { badnn = TRUE_; } /* L10: */ } /* Check for errors */ if (*nsizes < 0) { *info = -1; } else if (badnn) { *info = -2; } else if (*ntypes < 0) { *info = -3; } else if (*thresh < 0.f) { *info = -6; } else if (*nounit <= 0) { *info = -7; } else if (*lda < 1 || *lda < nmax) { *info = -9; } else if (*ldvl < 1 || *ldvl < nmax) { *info = -16; } else if (*ldvr < 1 || *ldvr < nmax) { *info = -18; } else if (*ldlre < 1 || *ldlre < nmax) { *info = -20; } else /* if(complicated condition) */ { /* Computing 2nd power */ i__1 = nmax; if (nmax * 5 + (i__1 * i__1 << 1) > *nwork) { *info = -23; } } if (*info != 0) { i__1 = -(*info); xerbla_("SDRVEV", &i__1); return 0; } /* Quick return if nothing to do */ if (*nsizes == 0 || *ntypes == 0) { return 0; } /* More Important constants */ unfl = slamch_("Safe minimum"); ovfl = 1.f / unfl; slabad_(&unfl, &ovfl); ulp = slamch_("Precision"); ulpinv = 1.f / ulp; rtulp = sqrt(ulp); rtulpi = 1.f / rtulp; /* Loop over sizes, types */ nerrs = 0; i__1 = *nsizes; for (jsize = 1; jsize <= i__1; ++jsize) { n = nn[jsize]; if (*nsizes != 1) { mtypes = min(21,*ntypes); } else { mtypes = min(22,*ntypes); } i__2 = mtypes; for (jtype = 1; jtype <= i__2; ++jtype) { if (! dotype[jtype]) { goto L260; } /* Save ISEED in case of an error. */ for (j = 1; j <= 4; ++j) { ioldsd[j - 1] = iseed[j]; /* L20: */ } /* Compute "A" */ /* Control parameters: */ /* KMAGN KCONDS KMODE KTYPE */ /* =1 O(1) 1 clustered 1 zero */ /* =2 large large clustered 2 identity */ /* =3 small exponential Jordan */ /* =4 arithmetic diagonal, (w/ eigenvalues) */ /* =5 random log symmetric, w/ eigenvalues */ /* =6 random general, w/ eigenvalues */ /* =7 random diagonal */ /* =8 random symmetric */ /* =9 random general */ /* =10 random triangular */ if (mtypes > 21) { goto L90; } itype = ktype[jtype - 1]; imode = kmode[jtype - 1]; /* Compute norm */ switch (kmagn[jtype - 1]) { case 1: goto L30; case 2: goto L40; case 3: goto L50; } L30: anorm = 1.f; goto L60; L40: anorm = ovfl * ulp; goto L60; L50: anorm = unfl * ulpinv; goto L60; L60: slaset_("Full", lda, &n, &c_b17, &c_b17, &a[a_offset], lda); iinfo = 0; cond = ulpinv; /* Special Matrices -- Identity & Jordan block */ /* Zero */ if (itype == 1) { iinfo = 0; } else if (itype == 2) { /* Identity */ i__3 = n; for (jcol = 1; jcol <= i__3; ++jcol) { a[jcol + jcol * a_dim1] = anorm; /* L70: */ } } else if (itype == 3) { /* Jordan Block */ i__3 = n; for (jcol = 1; jcol <= i__3; ++jcol) { a[jcol + jcol * a_dim1] = anorm; if (jcol > 1) { a[jcol + (jcol - 1) * a_dim1] = 1.f; } /* L80: */ } } else if (itype == 4) { /* Diagonal Matrix, [Eigen]values Specified */ slatms_(&n, &n, "S", &iseed[1], "S", &work[1], &imode, &cond, &anorm, &c__0, &c__0, "N", &a[a_offset], lda, &work[n + 1], &iinfo); } else if (itype == 5) { /* Symmetric, eigenvalues specified */ slatms_(&n, &n, "S", &iseed[1], "S", &work[1], &imode, &cond, &anorm, &n, &n, "N", &a[a_offset], lda, &work[n + 1], &iinfo); } else if (itype == 6) { /* General, eigenvalues specified */ if (kconds[jtype - 1] == 1) { conds = 1.f; } else if (kconds[jtype - 1] == 2) { conds = rtulpi; } else { conds = 0.f; } *(unsigned char *)&adumma[0] = ' '; slatme_(&n, "S", &iseed[1], &work[1], &imode, &cond, &c_b31, adumma, "T", "T", "T", &work[n + 1], &c__4, &conds, & n, &n, &anorm, &a[a_offset], lda, &work[(n << 1) + 1], &iinfo); } else if (itype == 7) { /* Diagonal, random eigenvalues */ slatmr_(&n, &n, "S", &iseed[1], "S", &work[1], &c__6, &c_b31, &c_b31, "T", "N", &work[n + 1], &c__1, &c_b31, &work[( n << 1) + 1], &c__1, &c_b31, "N", idumma, &c__0, & c__0, &c_b17, &anorm, "NO", &a[a_offset], lda, &iwork[ 1], &iinfo); } else if (itype == 8) { /* Symmetric, random eigenvalues */ slatmr_(&n, &n, "S", &iseed[1], "S", &work[1], &c__6, &c_b31, &c_b31, "T", "N", &work[n + 1], &c__1, &c_b31, &work[( n << 1) + 1], &c__1, &c_b31, "N", idumma, &n, &n, & c_b17, &anorm, "NO", &a[a_offset], lda, &iwork[1], & iinfo); } else if (itype == 9) { /* General, random eigenvalues */ slatmr_(&n, &n, "S", &iseed[1], "N", &work[1], &c__6, &c_b31, &c_b31, "T", "N", &work[n + 1], &c__1, &c_b31, &work[( n << 1) + 1], &c__1, &c_b31, "N", idumma, &n, &n, & c_b17, &anorm, "NO", &a[a_offset], lda, &iwork[1], & iinfo); if (n >= 4) { slaset_("Full", &c__2, &n, &c_b17, &c_b17, &a[a_offset], lda); i__3 = n - 3; slaset_("Full", &i__3, &c__1, &c_b17, &c_b17, &a[a_dim1 + 3], lda); i__3 = n - 3; slaset_("Full", &i__3, &c__2, &c_b17, &c_b17, &a[(n - 1) * a_dim1 + 3], lda); slaset_("Full", &c__1, &n, &c_b17, &c_b17, &a[n + a_dim1], lda); } } else if (itype == 10) { /* Triangular, random eigenvalues */ slatmr_(&n, &n, "S", &iseed[1], "N", &work[1], &c__6, &c_b31, &c_b31, "T", "N", &work[n + 1], &c__1, &c_b31, &work[( n << 1) + 1], &c__1, &c_b31, "N", idumma, &n, &c__0, & c_b17, &anorm, "NO", &a[a_offset], lda, &iwork[1], & iinfo); } else { iinfo = 1; } if (iinfo != 0) { io___32.ciunit = *nounit; s_wsfe(&io___32); do_fio(&c__1, "Generator", (ftnlen)9); do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer)); do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer)); e_wsfe(); *info = abs(iinfo); return 0; } L90: /* Test for minimal and generous workspace */ for (iwk = 1; iwk <= 2; ++iwk) { if (iwk == 1) { nnwork = n << 2; } else { /* Computing 2nd power */ i__3 = n; nnwork = n * 5 + (i__3 * i__3 << 1); } nnwork = max(nnwork,1); /* Initialize RESULT */ for (j = 1; j <= 7; ++j) { result[j] = -1.f; /* L100: */ } /* Compute eigenvalues and eigenvectors, and test them */ slacpy_("F", &n, &n, &a[a_offset], lda, &h__[h_offset], lda); sgeev_("V", "V", &n, &h__[h_offset], lda, &wr[1], &wi[1], &vl[ vl_offset], ldvl, &vr[vr_offset], ldvr, &work[1], & nnwork, &iinfo); if (iinfo != 0) { result[1] = ulpinv; io___35.ciunit = *nounit; s_wsfe(&io___35); do_fio(&c__1, "SGEEV1", (ftnlen)6); do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer)); do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer)) ; e_wsfe(); *info = abs(iinfo); goto L220; } /* Do Test (1) */ sget22_("N", "N", "N", &n, &a[a_offset], lda, &vr[vr_offset], ldvr, &wr[1], &wi[1], &work[1], res); result[1] = res[0]; /* Do Test (2) */ sget22_("T", "N", "T", &n, &a[a_offset], lda, &vl[vl_offset], ldvl, &wr[1], &wi[1], &work[1], res); result[2] = res[0]; /* Do Test (3) */ i__3 = n; for (j = 1; j <= i__3; ++j) { tnrm = 1.f; if (wi[j] == 0.f) { tnrm = snrm2_(&n, &vr[j * vr_dim1 + 1], &c__1); } else if (wi[j] > 0.f) { r__1 = snrm2_(&n, &vr[j * vr_dim1 + 1], &c__1); r__2 = snrm2_(&n, &vr[(j + 1) * vr_dim1 + 1], &c__1); tnrm = slapy2_(&r__1, &r__2); } /* Computing MAX */ /* Computing MIN */ r__4 = ulpinv, r__5 = (r__1 = tnrm - 1.f, dabs(r__1)) / ulp; r__2 = result[3], r__3 = dmin(r__4,r__5); result[3] = dmax(r__2,r__3); if (wi[j] > 0.f) { vmx = 0.f; vrmx = 0.f; i__4 = n; for (jj = 1; jj <= i__4; ++jj) { vtst = slapy2_(&vr[jj + j * vr_dim1], &vr[jj + (j + 1) * vr_dim1]); if (vtst > vmx) { vmx = vtst; } if (vr[jj + (j + 1) * vr_dim1] == 0.f && (r__1 = vr[jj + j * vr_dim1], dabs(r__1)) > vrmx) { vrmx = (r__2 = vr[jj + j * vr_dim1], dabs( r__2)); } /* L110: */ } if (vrmx / vmx < 1.f - ulp * 2.f) { result[3] = ulpinv; } } /* L120: */ } /* Do Test (4) */ i__3 = n; for (j = 1; j <= i__3; ++j) { tnrm = 1.f; if (wi[j] == 0.f) { tnrm = snrm2_(&n, &vl[j * vl_dim1 + 1], &c__1); } else if (wi[j] > 0.f) { r__1 = snrm2_(&n, &vl[j * vl_dim1 + 1], &c__1); r__2 = snrm2_(&n, &vl[(j + 1) * vl_dim1 + 1], &c__1); tnrm = slapy2_(&r__1, &r__2); } /* Computing MAX */ /* Computing MIN */ r__4 = ulpinv, r__5 = (r__1 = tnrm - 1.f, dabs(r__1)) / ulp; r__2 = result[4], r__3 = dmin(r__4,r__5); result[4] = dmax(r__2,r__3); if (wi[j] > 0.f) { vmx = 0.f; vrmx = 0.f; i__4 = n; for (jj = 1; jj <= i__4; ++jj) { vtst = slapy2_(&vl[jj + j * vl_dim1], &vl[jj + (j + 1) * vl_dim1]); if (vtst > vmx) { vmx = vtst; } if (vl[jj + (j + 1) * vl_dim1] == 0.f && (r__1 = vl[jj + j * vl_dim1], dabs(r__1)) > vrmx) { vrmx = (r__2 = vl[jj + j * vl_dim1], dabs( r__2)); } /* L130: */ } if (vrmx / vmx < 1.f - ulp * 2.f) { result[4] = ulpinv; } } /* L140: */ } /* Compute eigenvalues only, and test them */ slacpy_("F", &n, &n, &a[a_offset], lda, &h__[h_offset], lda); sgeev_("N", "N", &n, &h__[h_offset], lda, &wr1[1], &wi1[1], dum, &c__1, dum, &c__1, &work[1], &nnwork, &iinfo); if (iinfo != 0) { result[1] = ulpinv; io___43.ciunit = *nounit; s_wsfe(&io___43); do_fio(&c__1, "SGEEV2", (ftnlen)6); do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer)); do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer)) ; e_wsfe(); *info = abs(iinfo); goto L220; } /* Do Test (5) */ i__3 = n; for (j = 1; j <= i__3; ++j) { if (wr[j] != wr1[j] || wi[j] != wi1[j]) { result[5] = ulpinv; } /* L150: */ } /* Compute eigenvalues and right eigenvectors, and test them */ slacpy_("F", &n, &n, &a[a_offset], lda, &h__[h_offset], lda); sgeev_("N", "V", &n, &h__[h_offset], lda, &wr1[1], &wi1[1], dum, &c__1, &lre[lre_offset], ldlre, &work[1], & nnwork, &iinfo); if (iinfo != 0) { result[1] = ulpinv; io___44.ciunit = *nounit; s_wsfe(&io___44); do_fio(&c__1, "SGEEV3", (ftnlen)6); do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer)); do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer)) ; e_wsfe(); *info = abs(iinfo); goto L220; } /* Do Test (5) again */ i__3 = n; for (j = 1; j <= i__3; ++j) { if (wr[j] != wr1[j] || wi[j] != wi1[j]) { result[5] = ulpinv; } /* L160: */ } /* Do Test (6) */ i__3 = n; for (j = 1; j <= i__3; ++j) { i__4 = n; for (jj = 1; jj <= i__4; ++jj) { if (vr[j + jj * vr_dim1] != lre[j + jj * lre_dim1]) { result[6] = ulpinv; } /* L170: */ } /* L180: */ } /* Compute eigenvalues and left eigenvectors, and test them */ slacpy_("F", &n, &n, &a[a_offset], lda, &h__[h_offset], lda); sgeev_("V", "N", &n, &h__[h_offset], lda, &wr1[1], &wi1[1], & lre[lre_offset], ldlre, dum, &c__1, &work[1], &nnwork, &iinfo); if (iinfo != 0) { result[1] = ulpinv; io___45.ciunit = *nounit; s_wsfe(&io___45); do_fio(&c__1, "SGEEV4", (ftnlen)6); do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer)); do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer)) ; e_wsfe(); *info = abs(iinfo); goto L220; } /* Do Test (5) again */ i__3 = n; for (j = 1; j <= i__3; ++j) { if (wr[j] != wr1[j] || wi[j] != wi1[j]) { result[5] = ulpinv; } /* L190: */ } /* Do Test (7) */ i__3 = n; for (j = 1; j <= i__3; ++j) { i__4 = n; for (jj = 1; jj <= i__4; ++jj) { if (vl[j + jj * vl_dim1] != lre[j + jj * lre_dim1]) { result[7] = ulpinv; } /* L200: */ } /* L210: */ } /* End of Loop -- Check for RESULT(j) > THRESH */ L220: ntest = 0; nfail = 0; for (j = 1; j <= 7; ++j) { if (result[j] >= 0.f) { ++ntest; } if (result[j] >= *thresh) { ++nfail; } /* L230: */ } if (nfail > 0) { ++ntestf; } if (ntestf == 1) { io___48.ciunit = *nounit; s_wsfe(&io___48); do_fio(&c__1, path, (ftnlen)3); e_wsfe(); io___49.ciunit = *nounit; s_wsfe(&io___49); e_wsfe(); io___50.ciunit = *nounit; s_wsfe(&io___50); e_wsfe(); io___51.ciunit = *nounit; s_wsfe(&io___51); e_wsfe(); io___52.ciunit = *nounit; s_wsfe(&io___52); do_fio(&c__1, (char *)&(*thresh), (ftnlen)sizeof(real)); e_wsfe(); ntestf = 2; } for (j = 1; j <= 7; ++j) { if (result[j] >= *thresh) { io___53.ciunit = *nounit; s_wsfe(&io___53); do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&iwk, (ftnlen)sizeof(integer)); do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof( integer)); do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer)) ; do_fio(&c__1, (char *)&j, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&result[j], (ftnlen)sizeof(real) ); e_wsfe(); } /* L240: */ } nerrs += nfail; ntestt += ntest; /* L250: */ } L260: ; } /* L270: */ } /* Summary */ slasum_(path, nounit, &nerrs, &ntestt); return 0; /* End of SDRVEV */ } /* sdrvev_ */