/* sdrgsx.f -- translated by f2c (version 20061008). You must link the resulting object file with libf2c: on Microsoft Windows system, link with libf2c.lib; on Linux or Unix systems, link with .../path/to/libf2c.a -lm or, if you install libf2c.a in a standard place, with -lf2c -lm -- in that order, at the end of the command line, as in cc *.o -lf2c -lm Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., http://www.netlib.org/f2c/libf2c.zip */ #include "f2c.h" #include "blaswrap.h" /* Common Block Declarations */ struct { integer m, n, mplusn, k; logical fs; } mn_; #define mn_1 mn_ /* Table of constant values */ static integer c__1 = 1; static integer c__0 = 0; static integer c_n1 = -1; static real c_b26 = 0.f; static integer c__3 = 3; static integer c__4 = 4; /* Subroutine */ int sdrgsx_(integer *nsize, integer *ncmax, real *thresh, integer *nin, integer *nout, real *a, integer *lda, real *b, real *ai, real *bi, real *z__, real *q, real *alphar, real *alphai, real *beta, real *c__, integer *ldc, real *s, real *work, integer *lwork, integer *iwork, integer *liwork, logical *bwork, integer *info) { /* Format strings */ static char fmt_9999[] = "(\002 SDRGSX: \002,a,\002 returned INFO=\002,i" "6,\002.\002,/9x,\002N=\002,i6,\002, JTYPE=\002,i6,\002)\002)"; static char fmt_9997[] = "(\002 SDRGSX: SGET53 returned INFO=\002,i1," "\002 for eigenvalue \002,i6,\002.\002,/9x,\002N=\002,i6,\002, JT" "YPE=\002,i6,\002)\002)"; static char fmt_9996[] = "(\002 SDRGSX: S not in Schur form at eigenvalu" "e \002,i6,\002.\002,/9x,\002N=\002,i6,\002, JTYPE=\002,i6,\002" ")\002)"; static char fmt_9995[] = "(/1x,a3,\002 -- Real Expert Generalized Schur " "form\002,\002 problem driver\002)"; static char fmt_9993[] = "(\002 Matrix types: \002,/\002 1: A is a blo" "ck diagonal matrix of Jordan blocks \002,\002and B is the identi" "ty \002,/\002 matrix, \002,/\002 2: A and B are upper tri" "angular matrices, \002,/\002 3: A and B are as type 2, but eac" "h second diagonal \002,\002block in A_11 and \002,/\002 eac" "h third diaongal block in A_22 are 2x2 blocks,\002,/\002 4: A " "and B are block diagonal matrices, \002,/\002 5: (A,B) has pot" "entially close or common \002,\002eigenvalues.\002,/)"; static char fmt_9992[] = "(/\002 Tests performed: (S is Schur, T is tri" "angular, \002,\002Q and Z are \002,a,\002,\002,/19x,\002 a is al" "pha, b is beta, and \002,a,\002 means \002,a,\002.)\002,/\002 1" " = | A - Q S Z\002,a,\002 | / ( |A| n ulp ) 2 = | B - Q T " "Z\002,a,\002 | / ( |B| n ulp )\002,/\002 3 = | I - QQ\002,a," "\002 | / ( n ulp ) 4 = | I - ZZ\002,a,\002 | / ( n u" "lp )\002,/\002 5 = 1/ULP if A is not in \002,\002Schur form " "S\002,/\002 6 = difference between (alpha,beta)\002,\002 and di" "agonals of (S,T)\002,/\002 7 = 1/ULP if SDIM is not the correc" "t number of \002,\002selected eigenvalues\002,/\002 8 = 1/ULP " "if DIFEST/DIFTRU > 10*THRESH or \002,\002DIFTRU/DIFEST > 10*THRE" "SH\002,/\002 9 = 1/ULP if DIFEST <> 0 or DIFTRU > ULP*norm(A,B" ") \002,\002when reordering fails\002,/\002 10 = 1/ULP if PLEST/" "PLTRU > THRESH or \002,\002PLTRU/PLEST > THRESH\002,/\002 ( T" "est 10 is only for input examples )\002,/)"; static char fmt_9991[] = "(\002 Matrix order=\002,i2,\002, type=\002,i2" ",\002, a=\002,e10.4,\002, order(A_11)=\002,i2,\002, result \002," "i2,\002 is \002,0p,f8.2)"; static char fmt_9990[] = "(\002 Matrix order=\002,i2,\002, type=\002,i2" ",\002, a=\002,e10.4,\002, order(A_11)=\002,i2,\002, result \002," "i2,\002 is \002,0p,e10.4)"; static char fmt_9998[] = "(\002 SDRGSX: \002,a,\002 returned INFO=\002,i" "6,\002.\002,/9x,\002N=\002,i6,\002, Input Example #\002,i2,\002" ")\002)"; static char fmt_9994[] = "(\002Input Example\002)"; static char fmt_9989[] = "(\002 Input example #\002,i2,\002, matrix orde" "r=\002,i4,\002,\002,\002 result \002,i2,\002 is\002,0p,f8.2)"; static char fmt_9988[] = "(\002 Input example #\002,i2,\002, matrix orde" "r=\002,i4,\002,\002,\002 result \002,i2,\002 is\002,1p,e10.3)"; /* System generated locals */ integer a_dim1, a_offset, ai_dim1, ai_offset, b_dim1, b_offset, bi_dim1, bi_offset, c_dim1, c_offset, q_dim1, q_offset, z_dim1, z_offset, i__1, i__2, i__3, i__4; real r__1, r__2, r__3, r__4, r__5, r__6, r__7, r__8, r__9, r__10; /* Builtin functions */ 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, i1, mm; real pl[2]; integer mn2, qba, qbb; real ulp, temp1, temp2, abnrm; integer ifunc, iinfo, linfo; extern /* Subroutine */ int sget51_(integer *, integer *, real *, integer *, real *, integer *, real *, integer *, real *, integer *, real * , real *), sget53_(real *, integer *, real *, integer *, real *, real *, real *, real *, integer *); char sense[1]; integer nerrs, ntest; real pltru; extern /* Subroutine */ int slakf2_(integer *, integer *, real *, integer *, real *, real *, real *, real *, integer *), slatm5_(integer *, integer *, integer *, real *, integer *, real *, integer *, real * , integer *, real *, integer *, real *, integer *, real *, integer *, real *, integer *, real *, integer *, real *, integer * , integer *); real thrsh2; logical ilabad; extern /* Subroutine */ int slabad_(real *, real *); integer bdspac; extern doublereal slamch_(char *), slange_(char *, integer *, integer *, real *, integer *, real *); extern /* Subroutine */ int xerbla_(char *, integer *); real difest[2]; extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *); real bignum; extern /* Subroutine */ int alasvm_(char *, integer *, integer *, integer *, integer *); real weight; extern /* Subroutine */ int sgesvd_(char *, char *, integer *, integer *, real *, integer *, real *, real *, integer *, real *, integer *, real *, integer *, integer *), slacpy_(char *, integer *, integer *, real *, integer *, real *, integer *); real diftru; extern /* Subroutine */ int slaset_(char *, integer *, integer *, real *, real *, real *, integer *), sggesx_(char *, char *, char * , L_fp, char *, integer *, real *, integer *, real *, integer *, integer *, real *, real *, real *, real *, integer *, real *, integer *, real *, real *, real *, integer *, integer *, integer * , logical *, integer *); integer minwrk, maxwrk; real smlnum, ulpinv; integer nptknt; real result[10]; extern logical slctsx_(); integer ntestt, prtype; /* Fortran I/O blocks */ static cilist io___22 = { 0, 0, 0, fmt_9999, 0 }; static cilist io___31 = { 0, 0, 0, fmt_9997, 0 }; static cilist io___32 = { 0, 0, 0, fmt_9996, 0 }; static cilist io___35 = { 0, 0, 0, fmt_9995, 0 }; static cilist io___36 = { 0, 0, 0, fmt_9993, 0 }; static cilist io___37 = { 0, 0, 0, fmt_9992, 0 }; static cilist io___39 = { 0, 0, 0, fmt_9991, 0 }; static cilist io___40 = { 0, 0, 0, fmt_9990, 0 }; static cilist io___42 = { 0, 0, 1, 0, 0 }; static cilist io___43 = { 0, 0, 1, 0, 0 }; static cilist io___44 = { 0, 0, 0, 0, 0 }; static cilist io___45 = { 0, 0, 0, 0, 0 }; static cilist io___46 = { 0, 0, 0, 0, 0 }; static cilist io___48 = { 0, 0, 0, fmt_9998, 0 }; static cilist io___49 = { 0, 0, 0, fmt_9997, 0 }; static cilist io___50 = { 0, 0, 0, fmt_9996, 0 }; static cilist io___51 = { 0, 0, 0, fmt_9995, 0 }; static cilist io___52 = { 0, 0, 0, fmt_9994, 0 }; static cilist io___53 = { 0, 0, 0, fmt_9992, 0 }; static cilist io___54 = { 0, 0, 0, fmt_9989, 0 }; static cilist io___55 = { 0, 0, 0, fmt_9988, 0 }; /* -- LAPACK test routine (version 3.1) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* SDRGSX checks the nonsymmetric generalized eigenvalue (Schur form) */ /* problem expert driver SGGESX. */ /* SGGESX factors A and B as Q S Z' and Q T Z', where ' means */ /* transpose, T is upper triangular, S is in generalized Schur form */ /* (block upper triangular, with 1x1 and 2x2 blocks on the diagonal, */ /* the 2x2 blocks corresponding to complex conjugate pairs of */ /* generalized eigenvalues), and Q and Z are orthogonal. It also */ /* computes the generalized eigenvalues (alpha(1),beta(1)), ..., */ /* (alpha(n),beta(n)). Thus, w(j) = alpha(j)/beta(j) is a root of the */ /* characteristic equation */ /* det( A - w(j) B ) = 0 */ /* Optionally it also reorders the eigenvalues so that a selected */ /* cluster of eigenvalues appears in the leading diagonal block of the */ /* Schur forms; computes a reciprocal condition number for the average */ /* of the selected eigenvalues; and computes a reciprocal condition */ /* number for the right and left deflating subspaces corresponding to */ /* the selected eigenvalues. */ /* When SDRGSX is called with NSIZE > 0, five (5) types of built-in */ /* matrix pairs are used to test the routine SGGESX. */ /* When SDRGSX is called with NSIZE = 0, it reads in test matrix data */ /* to test SGGESX. */ /* For each matrix pair, the following tests will be performed and */ /* compared with the threshhold THRESH except for the tests (7) and (9): */ /* (1) | A - Q S Z' | / ( |A| n ulp ) */ /* (2) | B - Q T Z' | / ( |B| n ulp ) */ /* (3) | I - QQ' | / ( n ulp ) */ /* (4) | I - ZZ' | / ( n ulp ) */ /* (5) if A is in Schur form (i.e. quasi-triangular form) */ /* (6) maximum over j of D(j) where: */ /* if alpha(j) is real: */ /* |alpha(j) - S(j,j)| |beta(j) - T(j,j)| */ /* D(j) = ------------------------ + ----------------------- */ /* max(|alpha(j)|,|S(j,j)|) max(|beta(j)|,|T(j,j)|) */ /* if alpha(j) is complex: */ /* | det( s S - w T ) | */ /* D(j) = --------------------------------------------------- */ /* ulp max( s norm(S), |w| norm(T) )*norm( s S - w T ) */ /* and S and T are here the 2 x 2 diagonal blocks of S and T */ /* corresponding to the j-th and j+1-th eigenvalues. */ /* (7) if sorting worked and SDIM is the number of eigenvalues */ /* which were selected. */ /* (8) the estimated value DIF does not differ from the true values of */ /* Difu and Difl more than a factor 10*THRESH. If the estimate DIF */ /* equals zero the corresponding true values of Difu and Difl */ /* should be less than EPS*norm(A, B). If the true value of Difu */ /* and Difl equal zero, the estimate DIF should be less than */ /* EPS*norm(A, B). */ /* (9) If INFO = N+3 is returned by SGGESX, the reordering "failed" */ /* and we check that DIF = PL = PR = 0 and that the true value of */ /* Difu and Difl is < EPS*norm(A, B). We count the events when */ /* INFO=N+3. */ /* For read-in test matrices, the above tests are run except that the */ /* exact value for DIF (and PL) is input data. Additionally, there is */ /* one more test run for read-in test matrices: */ /* (10) the estimated value PL does not differ from the true value of */ /* PLTRU more than a factor THRESH. If the estimate PL equals */ /* zero the corresponding true value of PLTRU should be less than */ /* EPS*norm(A, B). If the true value of PLTRU equal zero, the */ /* estimate PL should be less than EPS*norm(A, B). */ /* Note that for the built-in tests, a total of 10*NSIZE*(NSIZE-1) */ /* matrix pairs are generated and tested. NSIZE should be kept small. */ /* SVD (routine SGESVD) is used for computing the true value of DIF_u */ /* and DIF_l when testing the built-in test problems. */ /* Built-in Test Matrices */ /* ====================== */ /* All built-in test matrices are the 2 by 2 block of triangular */ /* matrices */ /* A = [ A11 A12 ] and B = [ B11 B12 ] */ /* [ A22 ] [ B22 ] */ /* where for different type of A11 and A22 are given as the following. */ /* A12 and B12 are chosen so that the generalized Sylvester equation */ /* A11*R - L*A22 = -A12 */ /* B11*R - L*B22 = -B12 */ /* have prescribed solution R and L. */ /* Type 1: A11 = J_m(1,-1) and A_22 = J_k(1-a,1). */ /* B11 = I_m, B22 = I_k */ /* where J_k(a,b) is the k-by-k Jordan block with ``a'' on */ /* diagonal and ``b'' on superdiagonal. */ /* Type 2: A11 = (a_ij) = ( 2(.5-sin(i)) ) and */ /* B11 = (b_ij) = ( 2(.5-sin(ij)) ) for i=1,...,m, j=i,...,m */ /* A22 = (a_ij) = ( 2(.5-sin(i+j)) ) and */ /* B22 = (b_ij) = ( 2(.5-sin(ij)) ) for i=m+1,...,k, j=i,...,k */ /* Type 3: A11, A22 and B11, B22 are chosen as for Type 2, but each */ /* second diagonal block in A_11 and each third diagonal block */ /* in A_22 are made as 2 by 2 blocks. */ /* Type 4: A11 = ( 20(.5 - sin(ij)) ) and B22 = ( 2(.5 - sin(i+j)) ) */ /* for i=1,...,m, j=1,...,m and */ /* A22 = ( 20(.5 - sin(i+j)) ) and B22 = ( 2(.5 - sin(ij)) ) */ /* for i=m+1,...,k, j=m+1,...,k */ /* Type 5: (A,B) and have potentially close or common eigenvalues and */ /* very large departure from block diagonality A_11 is chosen */ /* as the m x m leading submatrix of A_1: */ /* | 1 b | */ /* | -b 1 | */ /* | 1+d b | */ /* | -b 1+d | */ /* A_1 = | d 1 | */ /* | -1 d | */ /* | -d 1 | */ /* | -1 -d | */ /* | 1 | */ /* and A_22 is chosen as the k x k leading submatrix of A_2: */ /* | -1 b | */ /* | -b -1 | */ /* | 1-d b | */ /* | -b 1-d | */ /* A_2 = | d 1+b | */ /* | -1-b d | */ /* | -d 1+b | */ /* | -1+b -d | */ /* | 1-d | */ /* and matrix B are chosen as identity matrices (see SLATM5). */ /* Arguments */ /* ========= */ /* NSIZE (input) INTEGER */ /* The maximum size of the matrices to use. NSIZE >= 0. */ /* If NSIZE = 0, no built-in tests matrices are used, but */ /* read-in test matrices are used to test SGGESX. */ /* NCMAX (input) INTEGER */ /* Maximum allowable NMAX for generating Kroneker matrix */ /* in call to SLAKF2 */ /* 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. THRESH >= 0. */ /* NIN (input) INTEGER */ /* The FORTRAN unit number for reading in the data file of */ /* problems to solve. */ /* NOUT (input) INTEGER */ /* The FORTRAN unit number for printing out error messages */ /* (e.g., if a routine returns IINFO not equal to 0.) */ /* A (workspace) REAL array, dimension (LDA, NSIZE) */ /* Used to store the matrix whose eigenvalues are to be */ /* computed. On exit, A contains the last matrix actually used. */ /* LDA (input) INTEGER */ /* The leading dimension of A, B, AI, BI, Z and Q, */ /* LDA >= max( 1, NSIZE ). For the read-in test, */ /* LDA >= max( 1, N ), N is the size of the test matrices. */ /* B (workspace) REAL array, dimension (LDA, NSIZE) */ /* Used to store the matrix whose eigenvalues are to be */ /* computed. On exit, B contains the last matrix actually used. */ /* AI (workspace) REAL array, dimension (LDA, NSIZE) */ /* Copy of A, modified by SGGESX. */ /* BI (workspace) REAL array, dimension (LDA, NSIZE) */ /* Copy of B, modified by SGGESX. */ /* Z (workspace) REAL array, dimension (LDA, NSIZE) */ /* Z holds the left Schur vectors computed by SGGESX. */ /* Q (workspace) REAL array, dimension (LDA, NSIZE) */ /* Q holds the right Schur vectors computed by SGGESX. */ /* ALPHAR (workspace) REAL array, dimension (NSIZE) */ /* ALPHAI (workspace) REAL array, dimension (NSIZE) */ /* BETA (workspace) REAL array, dimension (NSIZE) */ /* On exit, (ALPHAR + ALPHAI*i)/BETA are the eigenvalues. */ /* C (workspace) REAL array, dimension (LDC, LDC) */ /* Store the matrix generated by subroutine SLAKF2, this is the */ /* matrix formed by Kronecker products used for estimating */ /* DIF. */ /* LDC (input) INTEGER */ /* The leading dimension of C. LDC >= max(1, LDA*LDA/2 ). */ /* S (workspace) REAL array, dimension (LDC) */ /* Singular values of C */ /* WORK (workspace) REAL array, dimension (LWORK) */ /* LWORK (input) INTEGER */ /* The dimension of the array WORK. */ /* LWORK >= MAX( 5*NSIZE*NSIZE/2 - 2, 10*(NSIZE+1) ) */ /* IWORK (workspace) INTEGER array, dimension (LIWORK) */ /* LIWORK (input) INTEGER */ /* The dimension of the array IWORK. LIWORK >= NSIZE + 6. */ /* BWORK (workspace) LOGICAL array, dimension (LDA) */ /* INFO (output) INTEGER */ /* = 0: successful exit */ /* < 0: if INFO = -i, the i-th argument had an illegal value. */ /* > 0: A routine returned an error code. */ /* ===================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. Local Arrays .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Scalars in Common .. */ /* .. */ /* .. Common blocks .. */ /* .. */ /* .. Executable Statements .. */ /* Check for errors */ /* Parameter adjustments */ q_dim1 = *lda; q_offset = 1 + q_dim1; q -= q_offset; z_dim1 = *lda; z_offset = 1 + z_dim1; z__ -= z_offset; bi_dim1 = *lda; bi_offset = 1 + bi_dim1; bi -= bi_offset; ai_dim1 = *lda; ai_offset = 1 + ai_dim1; ai -= ai_offset; b_dim1 = *lda; b_offset = 1 + b_dim1; b -= b_offset; a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --alphar; --alphai; --beta; c_dim1 = *ldc; c_offset = 1 + c_dim1; c__ -= c_offset; --s; --work; --iwork; --bwork; /* Function Body */ if (*nsize < 0) { *info = -1; } else if (*thresh < 0.f) { *info = -2; } else if (*nin <= 0) { *info = -3; } else if (*nout <= 0) { *info = -4; } else if (*lda < 1 || *lda < *nsize) { *info = -6; } else if (*ldc < 1 || *ldc < *nsize * *nsize / 2) { *info = -17; } else if (*liwork < *nsize + 6) { *info = -21; } /* Compute workspace */ /* (Note: Comments in the code beginning "Workspace:" describe the */ /* minimal amount of workspace needed at that point in the code, */ /* as well as the preferred amount for good performance. */ /* NB refers to the optimal block size for the immediately */ /* following subroutine, as returned by ILAENV.) */ minwrk = 1; if (*info == 0 && *lwork >= 1) { /* MINWRK = MAX( 10*( NSIZE+1 ), 5*NSIZE*NSIZE / 2-2 ) */ /* Computing MAX */ i__1 = (*nsize + 1) * 10, i__2 = *nsize * 5 * *nsize / 2; minwrk = max(i__1,i__2); /* workspace for sggesx */ maxwrk = (*nsize + 1) * 9 + *nsize * ilaenv_(&c__1, "SGEQRF", " ", nsize, &c__1, nsize, &c__0); /* Computing MAX */ i__1 = maxwrk, i__2 = (*nsize + 1) * 9 + *nsize * ilaenv_(&c__1, "SORGQR", " ", nsize, &c__1, nsize, &c_n1); maxwrk = max(i__1,i__2); /* workspace for sgesvd */ bdspac = *nsize * 5 * *nsize / 2; /* Computing MAX */ i__3 = *nsize * *nsize / 2; i__4 = *nsize * *nsize / 2; i__1 = maxwrk, i__2 = *nsize * 3 * *nsize / 2 + *nsize * *nsize * ilaenv_(&c__1, "SGEBRD", " ", &i__3, &i__4, &c_n1, &c_n1); maxwrk = max(i__1,i__2); maxwrk = max(maxwrk,bdspac); maxwrk = max(maxwrk,minwrk); work[1] = (real) maxwrk; } if (*lwork < minwrk) { *info = -19; } if (*info != 0) { i__1 = -(*info); xerbla_("SDRGSX", &i__1); return 0; } /* Important constants */ ulp = slamch_("P"); ulpinv = 1.f / ulp; smlnum = slamch_("S") / ulp; bignum = 1.f / smlnum; slabad_(&smlnum, &bignum); thrsh2 = *thresh * 10.f; ntestt = 0; nerrs = 0; /* Go to the tests for read-in matrix pairs */ ifunc = 0; if (*nsize == 0) { goto L70; } /* Test the built-in matrix pairs. */ /* Loop over different functions (IFUNC) of SGGESX, types (PRTYPE) */ /* of test matrices, different size (M+N) */ prtype = 0; qba = 3; qbb = 4; weight = sqrt(ulp); for (ifunc = 0; ifunc <= 3; ++ifunc) { for (prtype = 1; prtype <= 5; ++prtype) { i__1 = *nsize - 1; for (mn_1.m = 1; mn_1.m <= i__1; ++mn_1.m) { i__2 = *nsize - mn_1.m; for (mn_1.n = 1; mn_1.n <= i__2; ++mn_1.n) { weight = 1.f / weight; mn_1.mplusn = mn_1.m + mn_1.n; /* Generate test matrices */ mn_1.fs = TRUE_; mn_1.k = 0; slaset_("Full", &mn_1.mplusn, &mn_1.mplusn, &c_b26, & c_b26, &ai[ai_offset], lda); slaset_("Full", &mn_1.mplusn, &mn_1.mplusn, &c_b26, & c_b26, &bi[bi_offset], lda); slatm5_(&prtype, &mn_1.m, &mn_1.n, &ai[ai_offset], lda, & ai[mn_1.m + 1 + (mn_1.m + 1) * ai_dim1], lda, &ai[ (mn_1.m + 1) * ai_dim1 + 1], lda, &bi[bi_offset], lda, &bi[mn_1.m + 1 + (mn_1.m + 1) * bi_dim1], lda, &bi[(mn_1.m + 1) * bi_dim1 + 1], lda, &q[ q_offset], lda, &z__[z_offset], lda, &weight, & qba, &qbb); /* Compute the Schur factorization and swapping the */ /* m-by-m (1,1)-blocks with n-by-n (2,2)-blocks. */ /* Swapping is accomplished via the function SLCTSX */ /* which is supplied below. */ if (ifunc == 0) { *(unsigned char *)sense = 'N'; } else if (ifunc == 1) { *(unsigned char *)sense = 'E'; } else if (ifunc == 2) { *(unsigned char *)sense = 'V'; } else if (ifunc == 3) { *(unsigned char *)sense = 'B'; } slacpy_("Full", &mn_1.mplusn, &mn_1.mplusn, &ai[ai_offset] , lda, &a[a_offset], lda); slacpy_("Full", &mn_1.mplusn, &mn_1.mplusn, &bi[bi_offset] , lda, &b[b_offset], lda); sggesx_("V", "V", "S", (L_fp)slctsx_, sense, &mn_1.mplusn, &ai[ai_offset], lda, &bi[bi_offset], lda, &mm, & alphar[1], &alphai[1], &beta[1], &q[q_offset], lda, &z__[z_offset], lda, pl, difest, &work[1], lwork, &iwork[1], liwork, &bwork[1], &linfo); if (linfo != 0 && linfo != mn_1.mplusn + 2) { result[0] = ulpinv; io___22.ciunit = *nout; s_wsfe(&io___22); do_fio(&c__1, "SGGESX", (ftnlen)6); do_fio(&c__1, (char *)&linfo, (ftnlen)sizeof(integer)) ; do_fio(&c__1, (char *)&mn_1.mplusn, (ftnlen)sizeof( integer)); do_fio(&c__1, (char *)&prtype, (ftnlen)sizeof(integer) ); e_wsfe(); *info = linfo; goto L30; } /* Compute the norm(A, B) */ slacpy_("Full", &mn_1.mplusn, &mn_1.mplusn, &ai[ai_offset] , lda, &work[1], &mn_1.mplusn); slacpy_("Full", &mn_1.mplusn, &mn_1.mplusn, &bi[bi_offset] , lda, &work[mn_1.mplusn * mn_1.mplusn + 1], & mn_1.mplusn); i__3 = mn_1.mplusn << 1; abnrm = slange_("Fro", &mn_1.mplusn, &i__3, &work[1], & mn_1.mplusn, &work[1]); /* Do tests (1) to (4) */ sget51_(&c__1, &mn_1.mplusn, &a[a_offset], lda, &ai[ ai_offset], lda, &q[q_offset], lda, &z__[z_offset] , lda, &work[1], result); sget51_(&c__1, &mn_1.mplusn, &b[b_offset], lda, &bi[ bi_offset], lda, &q[q_offset], lda, &z__[z_offset] , lda, &work[1], &result[1]); sget51_(&c__3, &mn_1.mplusn, &b[b_offset], lda, &bi[ bi_offset], lda, &q[q_offset], lda, &q[q_offset], lda, &work[1], &result[2]); sget51_(&c__3, &mn_1.mplusn, &b[b_offset], lda, &bi[ bi_offset], lda, &z__[z_offset], lda, &z__[ z_offset], lda, &work[1], &result[3]); ntest = 4; /* Do tests (5) and (6): check Schur form of A and */ /* compare eigenvalues with diagonals. */ temp1 = 0.f; result[4] = 0.f; result[5] = 0.f; i__3 = mn_1.mplusn; for (j = 1; j <= i__3; ++j) { ilabad = FALSE_; if (alphai[j] == 0.f) { /* Computing MAX */ r__7 = smlnum, r__8 = (r__2 = alphar[j], dabs( r__2)), r__7 = max(r__7,r__8), r__8 = ( r__3 = ai[j + j * ai_dim1], dabs(r__3)); /* Computing MAX */ r__9 = smlnum, r__10 = (r__5 = beta[j], dabs(r__5) ), r__9 = max(r__9,r__10), r__10 = (r__6 = bi[j + j * bi_dim1], dabs(r__6)); temp2 = ((r__1 = alphar[j] - ai[j + j * ai_dim1], dabs(r__1)) / dmax(r__7,r__8) + (r__4 = beta[j] - bi[j + j * bi_dim1], dabs(r__4)) / dmax(r__9,r__10)) / ulp; if (j < mn_1.mplusn) { if (ai[j + 1 + j * ai_dim1] != 0.f) { ilabad = TRUE_; result[4] = ulpinv; } } if (j > 1) { if (ai[j + (j - 1) * ai_dim1] != 0.f) { ilabad = TRUE_; result[4] = ulpinv; } } } else { if (alphai[j] > 0.f) { i1 = j; } else { i1 = j - 1; } if (i1 <= 0 || i1 >= mn_1.mplusn) { ilabad = TRUE_; } else if (i1 < mn_1.mplusn - 1) { if (ai[i1 + 2 + (i1 + 1) * ai_dim1] != 0.f) { ilabad = TRUE_; result[4] = ulpinv; } } else if (i1 > 1) { if (ai[i1 + (i1 - 1) * ai_dim1] != 0.f) { ilabad = TRUE_; result[4] = ulpinv; } } if (! ilabad) { sget53_(&ai[i1 + i1 * ai_dim1], lda, &bi[i1 + i1 * bi_dim1], lda, &beta[j], &alphar[ j], &alphai[j], &temp2, &iinfo); if (iinfo >= 3) { io___31.ciunit = *nout; s_wsfe(&io___31); do_fio(&c__1, (char *)&iinfo, (ftnlen) sizeof(integer)); do_fio(&c__1, (char *)&j, (ftnlen)sizeof( integer)); do_fio(&c__1, (char *)&mn_1.mplusn, ( ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&prtype, (ftnlen) sizeof(integer)); e_wsfe(); *info = abs(iinfo); } } else { temp2 = ulpinv; } } temp1 = dmax(temp1,temp2); if (ilabad) { io___32.ciunit = *nout; s_wsfe(&io___32); do_fio(&c__1, (char *)&j, (ftnlen)sizeof(integer)) ; do_fio(&c__1, (char *)&mn_1.mplusn, (ftnlen) sizeof(integer)); do_fio(&c__1, (char *)&prtype, (ftnlen)sizeof( integer)); e_wsfe(); } /* L10: */ } result[5] = temp1; ntest += 2; /* Test (7) (if sorting worked) */ result[6] = 0.f; if (linfo == mn_1.mplusn + 3) { result[6] = ulpinv; } else if (mm != mn_1.n) { result[6] = ulpinv; } ++ntest; /* Test (8): compare the estimated value DIF and its */ /* value. first, compute the exact DIF. */ result[7] = 0.f; mn2 = mm * (mn_1.mplusn - mm) << 1; if (ifunc >= 2 && mn2 <= *ncmax * *ncmax) { /* Note: for either following two causes, there are */ /* almost same number of test cases fail the test. */ i__3 = mn_1.mplusn - mm; slakf2_(&mm, &i__3, &ai[ai_offset], lda, &ai[mm + 1 + (mm + 1) * ai_dim1], &bi[bi_offset], &bi[mm + 1 + (mm + 1) * bi_dim1], &c__[c_offset], ldc); i__3 = *lwork - 2; sgesvd_("N", "N", &mn2, &mn2, &c__[c_offset], ldc, &s[ 1], &work[1], &c__1, &work[2], &c__1, &work[3] , &i__3, info); diftru = s[mn2]; if (difest[1] == 0.f) { if (diftru > abnrm * ulp) { result[7] = ulpinv; } } else if (diftru == 0.f) { if (difest[1] > abnrm * ulp) { result[7] = ulpinv; } } else if (diftru > thrsh2 * difest[1] || diftru * thrsh2 < difest[1]) { /* Computing MAX */ r__1 = diftru / difest[1], r__2 = difest[1] / diftru; result[7] = dmax(r__1,r__2); } ++ntest; } /* Test (9) */ result[8] = 0.f; if (linfo == mn_1.mplusn + 2) { if (diftru > abnrm * ulp) { result[8] = ulpinv; } if (ifunc > 1 && difest[1] != 0.f) { result[8] = ulpinv; } if (ifunc == 1 && pl[0] != 0.f) { result[8] = ulpinv; } ++ntest; } ntestt += ntest; /* Print out tests which fail. */ for (j = 1; j <= 9; ++j) { if (result[j - 1] >= *thresh) { /* If this is the first test to fail, */ /* print a header to the data file. */ if (nerrs == 0) { io___35.ciunit = *nout; s_wsfe(&io___35); do_fio(&c__1, "SGX", (ftnlen)3); e_wsfe(); /* Matrix types */ io___36.ciunit = *nout; s_wsfe(&io___36); e_wsfe(); /* Tests performed */ io___37.ciunit = *nout; s_wsfe(&io___37); do_fio(&c__1, "orthogonal", (ftnlen)10); do_fio(&c__1, "'", (ftnlen)1); do_fio(&c__1, "transpose", (ftnlen)9); for (i__ = 1; i__ <= 4; ++i__) { do_fio(&c__1, "'", (ftnlen)1); } e_wsfe(); } ++nerrs; if (result[j - 1] < 1e4f) { io___39.ciunit = *nout; s_wsfe(&io___39); do_fio(&c__1, (char *)&mn_1.mplusn, (ftnlen) sizeof(integer)); do_fio(&c__1, (char *)&prtype, (ftnlen)sizeof( integer)); do_fio(&c__1, (char *)&weight, (ftnlen)sizeof( real)); do_fio(&c__1, (char *)&mn_1.m, (ftnlen)sizeof( integer)); do_fio(&c__1, (char *)&j, (ftnlen)sizeof( integer)); do_fio(&c__1, (char *)&result[j - 1], (ftnlen) sizeof(real)); e_wsfe(); } else { io___40.ciunit = *nout; s_wsfe(&io___40); do_fio(&c__1, (char *)&mn_1.mplusn, (ftnlen) sizeof(integer)); do_fio(&c__1, (char *)&prtype, (ftnlen)sizeof( integer)); do_fio(&c__1, (char *)&weight, (ftnlen)sizeof( real)); do_fio(&c__1, (char *)&mn_1.m, (ftnlen)sizeof( integer)); do_fio(&c__1, (char *)&j, (ftnlen)sizeof( integer)); do_fio(&c__1, (char *)&result[j - 1], (ftnlen) sizeof(real)); e_wsfe(); } } /* L20: */ } L30: ; } /* L40: */ } /* L50: */ } /* L60: */ } goto L150; L70: /* Read in data from file to check accuracy of condition estimation */ /* Read input data until N=0 */ nptknt = 0; L80: io___42.ciunit = *nin; i__1 = s_rsle(&io___42); if (i__1 != 0) { goto L140; } i__1 = do_lio(&c__3, &c__1, (char *)&mn_1.mplusn, (ftnlen)sizeof(integer)) ; if (i__1 != 0) { goto L140; } i__1 = e_rsle(); if (i__1 != 0) { goto L140; } if (mn_1.mplusn == 0) { goto L140; } io___43.ciunit = *nin; i__1 = s_rsle(&io___43); if (i__1 != 0) { goto L140; } i__1 = do_lio(&c__3, &c__1, (char *)&mn_1.n, (ftnlen)sizeof(integer)); if (i__1 != 0) { goto L140; } i__1 = e_rsle(); if (i__1 != 0) { goto L140; } i__1 = mn_1.mplusn; for (i__ = 1; i__ <= i__1; ++i__) { io___44.ciunit = *nin; s_rsle(&io___44); i__2 = mn_1.mplusn; for (j = 1; j <= i__2; ++j) { do_lio(&c__4, &c__1, (char *)&ai[i__ + j * ai_dim1], (ftnlen) sizeof(real)); } e_rsle(); /* L90: */ } i__1 = mn_1.mplusn; for (i__ = 1; i__ <= i__1; ++i__) { io___45.ciunit = *nin; s_rsle(&io___45); i__2 = mn_1.mplusn; for (j = 1; j <= i__2; ++j) { do_lio(&c__4, &c__1, (char *)&bi[i__ + j * bi_dim1], (ftnlen) sizeof(real)); } e_rsle(); /* L100: */ } io___46.ciunit = *nin; s_rsle(&io___46); do_lio(&c__4, &c__1, (char *)&pltru, (ftnlen)sizeof(real)); do_lio(&c__4, &c__1, (char *)&diftru, (ftnlen)sizeof(real)); e_rsle(); ++nptknt; mn_1.fs = TRUE_; mn_1.k = 0; mn_1.m = mn_1.mplusn - mn_1.n; slacpy_("Full", &mn_1.mplusn, &mn_1.mplusn, &ai[ai_offset], lda, &a[ a_offset], lda); slacpy_("Full", &mn_1.mplusn, &mn_1.mplusn, &bi[bi_offset], lda, &b[ b_offset], lda); /* Compute the Schur factorization while swaping the */ /* m-by-m (1,1)-blocks with n-by-n (2,2)-blocks. */ sggesx_("V", "V", "S", (L_fp)slctsx_, "B", &mn_1.mplusn, &ai[ai_offset], lda, &bi[bi_offset], lda, &mm, &alphar[1], &alphai[1], &beta[1], & q[q_offset], lda, &z__[z_offset], lda, pl, difest, &work[1], lwork, &iwork[1], liwork, &bwork[1], &linfo); if (linfo != 0 && linfo != mn_1.mplusn + 2) { result[0] = ulpinv; io___48.ciunit = *nout; s_wsfe(&io___48); do_fio(&c__1, "SGGESX", (ftnlen)6); do_fio(&c__1, (char *)&linfo, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&mn_1.mplusn, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&nptknt, (ftnlen)sizeof(integer)); e_wsfe(); goto L130; } /* Compute the norm(A, B) */ /* (should this be norm of (A,B) or (AI,BI)?) */ slacpy_("Full", &mn_1.mplusn, &mn_1.mplusn, &ai[ai_offset], lda, &work[1], &mn_1.mplusn); slacpy_("Full", &mn_1.mplusn, &mn_1.mplusn, &bi[bi_offset], lda, &work[ mn_1.mplusn * mn_1.mplusn + 1], &mn_1.mplusn); i__1 = mn_1.mplusn << 1; abnrm = slange_("Fro", &mn_1.mplusn, &i__1, &work[1], &mn_1.mplusn, &work[ 1]); /* Do tests (1) to (4) */ sget51_(&c__1, &mn_1.mplusn, &a[a_offset], lda, &ai[ai_offset], lda, &q[ q_offset], lda, &z__[z_offset], lda, &work[1], result); sget51_(&c__1, &mn_1.mplusn, &b[b_offset], lda, &bi[bi_offset], lda, &q[ q_offset], lda, &z__[z_offset], lda, &work[1], &result[1]); sget51_(&c__3, &mn_1.mplusn, &b[b_offset], lda, &bi[bi_offset], lda, &q[ q_offset], lda, &q[q_offset], lda, &work[1], &result[2]); sget51_(&c__3, &mn_1.mplusn, &b[b_offset], lda, &bi[bi_offset], lda, &z__[ z_offset], lda, &z__[z_offset], lda, &work[1], &result[3]); /* Do tests (5) and (6): check Schur form of A and compare */ /* eigenvalues with diagonals. */ ntest = 6; temp1 = 0.f; result[4] = 0.f; result[5] = 0.f; i__1 = mn_1.mplusn; for (j = 1; j <= i__1; ++j) { ilabad = FALSE_; if (alphai[j] == 0.f) { /* Computing MAX */ r__7 = smlnum, r__8 = (r__2 = alphar[j], dabs(r__2)), r__7 = max( r__7,r__8), r__8 = (r__3 = ai[j + j * ai_dim1], dabs(r__3) ); /* Computing MAX */ r__9 = smlnum, r__10 = (r__5 = beta[j], dabs(r__5)), r__9 = max( r__9,r__10), r__10 = (r__6 = bi[j + j * bi_dim1], dabs( r__6)); temp2 = ((r__1 = alphar[j] - ai[j + j * ai_dim1], dabs(r__1)) / dmax(r__7,r__8) + (r__4 = beta[j] - bi[j + j * bi_dim1], dabs(r__4)) / dmax(r__9,r__10)) / ulp; if (j < mn_1.mplusn) { if (ai[j + 1 + j * ai_dim1] != 0.f) { ilabad = TRUE_; result[4] = ulpinv; } } if (j > 1) { if (ai[j + (j - 1) * ai_dim1] != 0.f) { ilabad = TRUE_; result[4] = ulpinv; } } } else { if (alphai[j] > 0.f) { i1 = j; } else { i1 = j - 1; } if (i1 <= 0 || i1 >= mn_1.mplusn) { ilabad = TRUE_; } else if (i1 < mn_1.mplusn - 1) { if (ai[i1 + 2 + (i1 + 1) * ai_dim1] != 0.f) { ilabad = TRUE_; result[4] = ulpinv; } } else if (i1 > 1) { if (ai[i1 + (i1 - 1) * ai_dim1] != 0.f) { ilabad = TRUE_; result[4] = ulpinv; } } if (! ilabad) { sget53_(&ai[i1 + i1 * ai_dim1], lda, &bi[i1 + i1 * bi_dim1], lda, &beta[j], &alphar[j], &alphai[j], &temp2, &iinfo) ; if (iinfo >= 3) { io___49.ciunit = *nout; s_wsfe(&io___49); do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&j, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&mn_1.mplusn, (ftnlen)sizeof( integer)); do_fio(&c__1, (char *)&nptknt, (ftnlen)sizeof(integer)); e_wsfe(); *info = abs(iinfo); } } else { temp2 = ulpinv; } } temp1 = dmax(temp1,temp2); if (ilabad) { io___50.ciunit = *nout; s_wsfe(&io___50); do_fio(&c__1, (char *)&j, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&mn_1.mplusn, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&nptknt, (ftnlen)sizeof(integer)); e_wsfe(); } /* L110: */ } result[5] = temp1; /* Test (7) (if sorting worked) <--------- need to be checked. */ ntest = 7; result[6] = 0.f; if (linfo == mn_1.mplusn + 3) { result[6] = ulpinv; } /* Test (8): compare the estimated value of DIF and its true value. */ ntest = 8; result[7] = 0.f; if (difest[1] == 0.f) { if (diftru > abnrm * ulp) { result[7] = ulpinv; } } else if (diftru == 0.f) { if (difest[1] > abnrm * ulp) { result[7] = ulpinv; } } else if (diftru > thrsh2 * difest[1] || diftru * thrsh2 < difest[1]) { /* Computing MAX */ r__1 = diftru / difest[1], r__2 = difest[1] / diftru; result[7] = dmax(r__1,r__2); } /* Test (9) */ ntest = 9; result[8] = 0.f; if (linfo == mn_1.mplusn + 2) { if (diftru > abnrm * ulp) { result[8] = ulpinv; } if (ifunc > 1 && difest[1] != 0.f) { result[8] = ulpinv; } if (ifunc == 1 && pl[0] != 0.f) { result[8] = ulpinv; } } /* Test (10): compare the estimated value of PL and it true value. */ ntest = 10; result[9] = 0.f; if (pl[0] == 0.f) { if (pltru > abnrm * ulp) { result[9] = ulpinv; } } else if (pltru == 0.f) { if (pl[0] > abnrm * ulp) { result[9] = ulpinv; } } else if (pltru > *thresh * pl[0] || pltru * *thresh < pl[0]) { result[9] = ulpinv; } ntestt += ntest; /* Print out tests which fail. */ i__1 = ntest; for (j = 1; j <= i__1; ++j) { if (result[j - 1] >= *thresh) { /* If this is the first test to fail, */ /* print a header to the data file. */ if (nerrs == 0) { io___51.ciunit = *nout; s_wsfe(&io___51); do_fio(&c__1, "SGX", (ftnlen)3); e_wsfe(); /* Matrix types */ io___52.ciunit = *nout; s_wsfe(&io___52); e_wsfe(); /* Tests performed */ io___53.ciunit = *nout; s_wsfe(&io___53); do_fio(&c__1, "orthogonal", (ftnlen)10); do_fio(&c__1, "'", (ftnlen)1); do_fio(&c__1, "transpose", (ftnlen)9); for (i__ = 1; i__ <= 4; ++i__) { do_fio(&c__1, "'", (ftnlen)1); } e_wsfe(); } ++nerrs; if (result[j - 1] < 1e4f) { io___54.ciunit = *nout; s_wsfe(&io___54); do_fio(&c__1, (char *)&nptknt, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&mn_1.mplusn, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&j, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&result[j - 1], (ftnlen)sizeof(real)); e_wsfe(); } else { io___55.ciunit = *nout; s_wsfe(&io___55); do_fio(&c__1, (char *)&nptknt, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&mn_1.mplusn, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&j, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&result[j - 1], (ftnlen)sizeof(real)); e_wsfe(); } } /* L120: */ } L130: goto L80; L140: L150: /* Summary */ alasvm_("SGX", nout, &nerrs, &ntestt, &c__0); work[1] = (real) maxwrk; return 0; /* End of SDRGSX */ } /* sdrgsx_ */