#include "blaswrap.h" /* sget24.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" /* Common Block Declarations */ struct { integer selopt, seldim; logical selval[20]; real selwr[20], selwi[20]; } sslct_; #define sslct_1 sslct_ /* Table of constant values */ static integer c__1 = 1; static integer c__4 = 4; static real c_b35 = 1.f; static real c_b41 = 0.f; static real c_b44 = -1.f; /* Subroutine */ int sget24_(logical *comp, integer *jtype, real *thresh, integer *iseed, integer *nounit, integer *n, 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 *rcdein, real *rcdvin, integer *nslct, integer *islct, real *result, real * work, integer *lwork, integer *iwork, logical *bwork, integer *info) { /* Format strings */ static char fmt_9998[] = "(\002 SGET24: \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[] = "(\002 SGET24: \002,a,\002 returned INFO=\002,i" "6,\002.\002,/9x,\002N=\002,i6,\002, INPUT EXAMPLE NUMBER = \002," "i4)"; /* 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; real r__1, r__2, r__3, r__4; /* Builtin functions */ integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void); double r_sign(real *, real *), sqrt(doublereal); /* Local variables */ static integer i__, j; static real v, eps, tol, tmp, ulp; static integer sdim, kmin, itmp, ipnt[20], rsub; static char sort[1]; static integer sdim1, iinfo; extern /* Subroutine */ int sgemm_(char *, char *, integer *, integer *, integer *, real *, real *, integer *, real *, integer *, real *, real *, integer *); static real anorm, vimin, tolin; extern /* Subroutine */ int sort01_(char *, integer *, integer *, real *, integer *, real *, integer *, real *); static real vrmin; static integer isort; static real wnorm; extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *, integer *); static real rcnde1, rcndv1; extern doublereal slamch_(char *), slange_(char *, integer *, integer *, real *, integer *, real *); static real rconde; extern /* Subroutine */ int xerbla_(char *, integer *); static integer knteig; static real rcondv; extern /* Subroutine */ int slacpy_(char *, integer *, integer *, real *, integer *, real *, integer *); extern logical sslect_(real *, real *); extern /* Subroutine */ int sgeesx_(char *, char *, L_fp, char *, integer *, real *, integer *, integer *, real *, real *, real *, integer * , real *, real *, real *, integer *, integer *, integer *, logical *, integer *); static integer liwork; static real smlnum, ulpinv; /* Fortran I/O blocks */ static cilist io___13 = { 0, 0, 0, fmt_9998, 0 }; static cilist io___14 = { 0, 0, 0, fmt_9999, 0 }; static cilist io___19 = { 0, 0, 0, fmt_9998, 0 }; static cilist io___20 = { 0, 0, 0, fmt_9999, 0 }; static cilist io___23 = { 0, 0, 0, fmt_9998, 0 }; static cilist io___24 = { 0, 0, 0, fmt_9999, 0 }; static cilist io___27 = { 0, 0, 0, fmt_9998, 0 }; static cilist io___28 = { 0, 0, 0, fmt_9999, 0 }; static cilist io___29 = { 0, 0, 0, fmt_9998, 0 }; static cilist io___30 = { 0, 0, 0, fmt_9999, 0 }; static cilist io___31 = { 0, 0, 0, fmt_9998, 0 }; static cilist io___32 = { 0, 0, 0, fmt_9999, 0 }; static cilist io___33 = { 0, 0, 0, fmt_9998, 0 }; static cilist io___34 = { 0, 0, 0, fmt_9999, 0 }; static cilist io___35 = { 0, 0, 0, fmt_9998, 0 }; static cilist io___36 = { 0, 0, 0, fmt_9999, 0 }; static cilist io___43 = { 0, 0, 0, fmt_9999, 0 }; /* -- LAPACK test routine (version 3.1) -- Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. November 2006 Purpose ======= SGET24 checks the nonsymmetric eigenvalue (Schur form) problem expert driver SGEESX. If COMP = .FALSE., the first 13 of the following tests will be be performed on the input matrix A, and also tests 14 and 15 if LWORK is sufficiently large. If COMP = .TRUE., all 17 test 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 (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 ========= COMP (input) LOGICAL COMP describes which input tests to perform: = .FALSE. if the computed condition numbers are not to be tested against RCDVIN and RCDEIN = .TRUE. if they are to be compared JTYPE (input) INTEGER Type of input matrix. Used to label output if error occurs. ISEED (input) INTEGER array, dimension (4) If COMP = .FALSE., the random number generator seed used to produce matrix. If COMP = .TRUE., ISEED(1) = the number of the example. Used to label output if error occurs. 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.) N (input) INTEGER The dimension of A. N must be at least 0. A (input/output) REAL array, dimension (LDA, N) Used to hold the matrix whose eigenvalues are to be computed. LDA (input) INTEGER The leading dimension of A, and H. LDA must be at least 1 and at least N. H (workspace) REAL array, dimension (LDA, N) Another copy of the test matrix A, modified by SGEESX. HT (workspace) REAL array, dimension (LDA, N) Yet another copy of the test matrix A, modified by SGEESX. WR (workspace) REAL array, dimension (N) WI (workspace) REAL array, dimension (N) 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 (N) WIT (workspace) REAL array, dimension (N) 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 (N) WITMP (workspace) REAL array, dimension (N) Like WR, WI, these arrays contain the eigenvalues of A, but sorted by increasing real part. VS (workspace) REAL array, dimension (LDVS, N) VS holds the computed Schur vectors. LDVS (input) INTEGER Leading dimension of VS. Must be at least max(1, N). VS1 (workspace) REAL array, dimension (LDVS, N) VS1 holds another copy of the computed Schur vectors. RCDEIN (input) REAL When COMP = .TRUE. RCDEIN holds the precomputed reciprocal condition number for the average of selected eigenvalues. RCDVIN (input) REAL When COMP = .TRUE. RCDVIN holds the precomputed reciprocal condition number for the selected right invariant subspace. NSLCT (input) INTEGER When COMP = .TRUE. the number of selected eigenvalues corresponding to the precomputed values RCDEIN and RCDVIN. ISLCT (input) INTEGER array, dimension (NSLCT) When COMP = .TRUE. ISLCT selects the eigenvalues of the input matrix corresponding to the precomputed values RCDEIN and RCDVIN. For I=1, ... ,NSLCT, if ISLCT(I) = J, then the eigenvalue with the J-th largest real part is selected. Not referenced if COMP = .FALSE. 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 to be passed to SGEESX. This must be at least 3*N, and N+N**2 if tests 14--16 are to be performed. IWORK (workspace) INTEGER array, dimension (N*N) BWORK (workspace) LOGICAL array, dimension (N) INFO (output) INTEGER If 0, successful exit. If <0, input parameter -INFO had an incorrect value. If >0, SGEESX returned an error code, the absolute value of which is returned. ===================================================================== Check for errors Parameter adjustments */ --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; --islct; --result; --work; --iwork; --bwork; /* Function Body */ *info = 0; if (*thresh < 0.f) { *info = -3; } else if (*nounit <= 0) { *info = -5; } else if (*n < 0) { *info = -6; } else if (*lda < 1 || *lda < *n) { *info = -8; } else if (*ldvs < 1 || *ldvs < *n) { *info = -18; } else if (*lwork < *n * 3) { *info = -26; } if (*info != 0) { i__1 = -(*info); xerbla_("SGET24", &i__1); return 0; } /* Quick return if nothing to do */ for (i__ = 1; i__ <= 17; ++i__) { result[i__] = -1.f; /* L10: */ } if (*n == 0) { return 0; } /* Important constants */ smlnum = slamch_("Safe minimum"); ulp = slamch_("Precision"); ulpinv = 1.f / ulp; /* Perform tests (1)-(13) */ sslct_1.selopt = 0; liwork = *n * *n; for (isort = 0; isort <= 1; ++isort) { if (isort == 0) { *(unsigned char *)sort = 'N'; rsub = 0; } else { *(unsigned char *)sort = 'S'; rsub = 6; } /* Compute Schur form and Schur vectors, and test them */ slacpy_("F", n, n, &a[a_offset], lda, &h__[h_offset], lda); sgeesx_("V", sort, (L_fp)sslect_, "N", n, &h__[h_offset], lda, &sdim, &wr[1], &wi[1], &vs[vs_offset], ldvs, &rconde, &rcondv, &work[ 1], lwork, &iwork[1], &liwork, &bwork[1], &iinfo); if (iinfo != 0 && iinfo != *n + 2) { result[rsub + 1] = ulpinv; if (*jtype != 22) { io___13.ciunit = *nounit; s_wsfe(&io___13); do_fio(&c__1, "SGEESX1", (ftnlen)7); 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 *)&iseed[1], (ftnlen)sizeof(integer)); e_wsfe(); } else { io___14.ciunit = *nounit; s_wsfe(&io___14); do_fio(&c__1, "SGEESX1", (ftnlen)7); do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&(*n), (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&iseed[1], (ftnlen)sizeof(integer)); e_wsfe(); } *info = abs(iinfo); return 0; } if (isort == 0) { scopy_(n, &wr[1], &c__1, &wrtmp[1], &c__1); scopy_(n, &wi[1], &c__1, &witmp[1], &c__1); } /* Do Test (1) or Test (7) */ result[rsub + 1] = 0.f; i__1 = *n - 2; for (j = 1; j <= i__1; ++j) { i__2 = *n; for (i__ = j + 2; i__ <= i__2; ++i__) { if (h__[i__ + j * h_dim1] != 0.f) { result[rsub + 1] = ulpinv; } /* L20: */ } /* L30: */ } i__1 = *n - 2; for (i__ = 1; i__ <= i__1; ++i__) { if (h__[i__ + 1 + i__ * h_dim1] != 0.f && h__[i__ + 2 + (i__ + 1) * h_dim1] != 0.f) { result[rsub + 1] = ulpinv; } /* L40: */ } i__1 = *n - 1; for (i__ = 1; i__ <= i__1; ++i__) { if (h__[i__ + 1 + i__ * h_dim1] != 0.f) { if (h__[i__ + i__ * h_dim1] != h__[i__ + 1 + (i__ + 1) * h_dim1] || h__[i__ + (i__ + 1) * h_dim1] == 0.f || r_sign(&c_b35, &h__[i__ + 1 + i__ * h_dim1]) == r_sign(&c_b35, &h__[i__ + (i__ + 1) * h_dim1])) { result[rsub + 1] = ulpinv; } } /* L50: */ } /* Test (2) or (8): Compute norm(A - Q*H*Q') / (norm(A) * N * ULP) Copy A to VS1, used as workspace */ slacpy_(" ", n, n, &a[a_offset], lda, &vs1[vs1_offset], ldvs); /* Compute Q*H and store in HT. */ sgemm_("No transpose", "No transpose", n, n, n, &c_b35, &vs[vs_offset] , ldvs, &h__[h_offset], lda, &c_b41, &ht[ht_offset], lda); /* Compute A - Q*H*Q' */ sgemm_("No transpose", "Transpose", n, n, n, &c_b44, &ht[ht_offset], lda, &vs[vs_offset], ldvs, &c_b35, &vs1[vs1_offset], ldvs); /* Computing MAX */ r__1 = slange_("1", n, n, &a[a_offset], lda, &work[1]); anorm = dmax(r__1,smlnum); wnorm = slange_("1", n, n, &vs1[vs1_offset], ldvs, &work[1]); if (anorm > wnorm) { result[rsub + 2] = wnorm / anorm / (*n * ulp); } else { if (anorm < 1.f) { /* Computing MIN */ r__1 = wnorm, r__2 = *n * anorm; result[rsub + 2] = dmin(r__1,r__2) / anorm / (*n * ulp); } else { /* Computing MIN */ r__1 = wnorm / anorm, r__2 = (real) (*n); result[rsub + 2] = dmin(r__1,r__2) / (*n * ulp); } } /* Test (3) or (9): Compute norm( I - Q'*Q ) / ( N * ULP ) */ sort01_("Columns", n, n, &vs[vs_offset], ldvs, &work[1], lwork, & result[rsub + 3]); /* Do Test (4) or Test (10) */ result[rsub + 4] = 0.f; i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { if (h__[i__ + i__ * h_dim1] != wr[i__]) { result[rsub + 4] = ulpinv; } /* L60: */ } if (*n > 1) { if (h__[h_dim1 + 2] == 0.f && wi[1] != 0.f) { result[rsub + 4] = ulpinv; } if (h__[*n + (*n - 1) * h_dim1] == 0.f && wi[*n] != 0.f) { result[rsub + 4] = ulpinv; } } i__1 = *n - 1; for (i__ = 1; i__ <= i__1; ++i__) { if (h__[i__ + 1 + i__ * h_dim1] != 0.f) { tmp = sqrt((r__1 = h__[i__ + 1 + i__ * h_dim1], dabs(r__1))) * sqrt((r__2 = h__[i__ + (i__ + 1) * h_dim1], dabs( r__2))); /* Computing MAX Computing MAX */ r__4 = ulp * tmp; r__2 = result[rsub + 4], r__3 = (r__1 = wi[i__] - tmp, dabs( r__1)) / dmax(r__4,smlnum); result[rsub + 4] = dmax(r__2,r__3); /* Computing MAX Computing MAX */ r__4 = ulp * tmp; r__2 = result[rsub + 4], r__3 = (r__1 = wi[i__ + 1] + tmp, dabs(r__1)) / dmax(r__4,smlnum); result[rsub + 4] = dmax(r__2,r__3); } else if (i__ > 1) { if (h__[i__ + 1 + i__ * h_dim1] == 0.f && h__[i__ + (i__ - 1) * h_dim1] == 0.f && wi[i__] != 0.f) { result[rsub + 4] = ulpinv; } } /* L70: */ } /* Do Test (5) or Test (11) */ slacpy_("F", n, n, &a[a_offset], lda, &ht[ht_offset], lda); sgeesx_("N", sort, (L_fp)sslect_, "N", n, &ht[ht_offset], lda, &sdim, &wrt[1], &wit[1], &vs[vs_offset], ldvs, &rconde, &rcondv, & work[1], lwork, &iwork[1], &liwork, &bwork[1], &iinfo); if (iinfo != 0 && iinfo != *n + 2) { result[rsub + 5] = ulpinv; if (*jtype != 22) { io___19.ciunit = *nounit; s_wsfe(&io___19); do_fio(&c__1, "SGEESX2", (ftnlen)7); 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 *)&iseed[1], (ftnlen)sizeof(integer)); e_wsfe(); } else { io___20.ciunit = *nounit; s_wsfe(&io___20); do_fio(&c__1, "SGEESX2", (ftnlen)7); do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&(*n), (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&iseed[1], (ftnlen)sizeof(integer)); e_wsfe(); } *info = abs(iinfo); goto L250; } result[rsub + 5] = 0.f; i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *n; for (i__ = 1; i__ <= i__2; ++i__) { if (h__[i__ + j * h_dim1] != ht[i__ + j * ht_dim1]) { result[rsub + 5] = ulpinv; } /* L80: */ } /* L90: */ } /* Do Test (6) or Test (12) */ result[rsub + 6] = 0.f; i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { if (wr[i__] != wrt[i__] || wi[i__] != wit[i__]) { result[rsub + 6] = ulpinv; } /* L100: */ } /* Do Test (13) */ if (isort == 1) { result[13] = 0.f; knteig = 0; i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { r__1 = -wi[i__]; if (sslect_(&wr[i__], &wi[i__]) || sslect_(&wr[i__], &r__1)) { ++knteig; } if (i__ < *n) { r__1 = -wi[i__ + 1]; r__2 = -wi[i__]; if ((sslect_(&wr[i__ + 1], &wi[i__ + 1]) || sslect_(&wr[ i__ + 1], &r__1)) && ! (sslect_(&wr[i__], &wi[i__] ) || sslect_(&wr[i__], &r__2)) && iinfo != *n + 2) { result[13] = ulpinv; } } /* L110: */ } if (sdim != knteig) { result[13] = ulpinv; } } /* L120: */ } /* If there is enough workspace, perform tests (14) and (15) as well as (10) through (13) */ if (*lwork >= *n + *n * *n / 2) { /* Compute both RCONDE and RCONDV with VS */ *(unsigned char *)sort = 'S'; result[14] = 0.f; result[15] = 0.f; slacpy_("F", n, n, &a[a_offset], lda, &ht[ht_offset], lda); sgeesx_("V", sort, (L_fp)sslect_, "B", n, &ht[ht_offset], lda, &sdim1, &wrt[1], &wit[1], &vs1[vs1_offset], ldvs, &rconde, &rcondv, & work[1], lwork, &iwork[1], &liwork, &bwork[1], &iinfo); if (iinfo != 0 && iinfo != *n + 2) { result[14] = ulpinv; result[15] = ulpinv; if (*jtype != 22) { io___23.ciunit = *nounit; s_wsfe(&io___23); do_fio(&c__1, "SGEESX3", (ftnlen)7); 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 *)&iseed[1], (ftnlen)sizeof(integer)); e_wsfe(); } else { io___24.ciunit = *nounit; s_wsfe(&io___24); do_fio(&c__1, "SGEESX3", (ftnlen)7); do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&(*n), (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&iseed[1], (ftnlen)sizeof(integer)); e_wsfe(); } *info = abs(iinfo); goto L250; } /* Perform tests (10), (11), (12), and (13) */ i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { if (wr[i__] != wrt[i__] || wi[i__] != wit[i__]) { result[10] = ulpinv; } i__2 = *n; for (j = 1; j <= i__2; ++j) { if (h__[i__ + j * h_dim1] != ht[i__ + j * ht_dim1]) { result[11] = ulpinv; } if (vs[i__ + j * vs_dim1] != vs1[i__ + j * vs1_dim1]) { result[12] = ulpinv; } /* L130: */ } /* L140: */ } if (sdim != sdim1) { result[13] = ulpinv; } /* Compute both RCONDE and RCONDV without VS, and compare */ slacpy_("F", n, n, &a[a_offset], lda, &ht[ht_offset], lda); sgeesx_("N", sort, (L_fp)sslect_, "B", n, &ht[ht_offset], lda, &sdim1, &wrt[1], &wit[1], &vs1[vs1_offset], ldvs, &rcnde1, &rcndv1, & work[1], lwork, &iwork[1], &liwork, &bwork[1], &iinfo); if (iinfo != 0 && iinfo != *n + 2) { result[14] = ulpinv; result[15] = ulpinv; if (*jtype != 22) { io___27.ciunit = *nounit; s_wsfe(&io___27); do_fio(&c__1, "SGEESX4", (ftnlen)7); 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 *)&iseed[1], (ftnlen)sizeof(integer)); e_wsfe(); } else { io___28.ciunit = *nounit; s_wsfe(&io___28); do_fio(&c__1, "SGEESX4", (ftnlen)7); do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&(*n), (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&iseed[1], (ftnlen)sizeof(integer)); e_wsfe(); } *info = abs(iinfo); goto L250; } /* Perform tests (14) and (15) */ if (rcnde1 != rconde) { result[14] = ulpinv; } if (rcndv1 != rcondv) { result[15] = ulpinv; } /* Perform tests (10), (11), (12), and (13) */ i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { if (wr[i__] != wrt[i__] || wi[i__] != wit[i__]) { result[10] = ulpinv; } i__2 = *n; for (j = 1; j <= i__2; ++j) { if (h__[i__ + j * h_dim1] != ht[i__ + j * ht_dim1]) { result[11] = ulpinv; } if (vs[i__ + j * vs_dim1] != vs1[i__ + j * vs1_dim1]) { result[12] = ulpinv; } /* L150: */ } /* L160: */ } if (sdim != sdim1) { result[13] = ulpinv; } /* Compute RCONDE with VS, and compare */ slacpy_("F", n, n, &a[a_offset], lda, &ht[ht_offset], lda); sgeesx_("V", sort, (L_fp)sslect_, "E", n, &ht[ht_offset], lda, &sdim1, &wrt[1], &wit[1], &vs1[vs1_offset], ldvs, &rcnde1, &rcndv1, & work[1], lwork, &iwork[1], &liwork, &bwork[1], &iinfo); if (iinfo != 0 && iinfo != *n + 2) { result[14] = ulpinv; if (*jtype != 22) { io___29.ciunit = *nounit; s_wsfe(&io___29); do_fio(&c__1, "SGEESX5", (ftnlen)7); 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 *)&iseed[1], (ftnlen)sizeof(integer)); e_wsfe(); } else { io___30.ciunit = *nounit; s_wsfe(&io___30); do_fio(&c__1, "SGEESX5", (ftnlen)7); do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&(*n), (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&iseed[1], (ftnlen)sizeof(integer)); e_wsfe(); } *info = abs(iinfo); goto L250; } /* Perform test (14) */ if (rcnde1 != rconde) { result[14] = ulpinv; } /* Perform tests (10), (11), (12), and (13) */ i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { if (wr[i__] != wrt[i__] || wi[i__] != wit[i__]) { result[10] = ulpinv; } i__2 = *n; for (j = 1; j <= i__2; ++j) { if (h__[i__ + j * h_dim1] != ht[i__ + j * ht_dim1]) { result[11] = ulpinv; } if (vs[i__ + j * vs_dim1] != vs1[i__ + j * vs1_dim1]) { result[12] = ulpinv; } /* L170: */ } /* L180: */ } if (sdim != sdim1) { result[13] = ulpinv; } /* Compute RCONDE without VS, and compare */ slacpy_("F", n, n, &a[a_offset], lda, &ht[ht_offset], lda); sgeesx_("N", sort, (L_fp)sslect_, "E", n, &ht[ht_offset], lda, &sdim1, &wrt[1], &wit[1], &vs1[vs1_offset], ldvs, &rcnde1, &rcndv1, & work[1], lwork, &iwork[1], &liwork, &bwork[1], &iinfo); if (iinfo != 0 && iinfo != *n + 2) { result[14] = ulpinv; if (*jtype != 22) { io___31.ciunit = *nounit; s_wsfe(&io___31); do_fio(&c__1, "SGEESX6", (ftnlen)7); 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 *)&iseed[1], (ftnlen)sizeof(integer)); e_wsfe(); } else { io___32.ciunit = *nounit; s_wsfe(&io___32); do_fio(&c__1, "SGEESX6", (ftnlen)7); do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&(*n), (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&iseed[1], (ftnlen)sizeof(integer)); e_wsfe(); } *info = abs(iinfo); goto L250; } /* Perform test (14) */ if (rcnde1 != rconde) { result[14] = ulpinv; } /* Perform tests (10), (11), (12), and (13) */ i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { if (wr[i__] != wrt[i__] || wi[i__] != wit[i__]) { result[10] = ulpinv; } i__2 = *n; for (j = 1; j <= i__2; ++j) { if (h__[i__ + j * h_dim1] != ht[i__ + j * ht_dim1]) { result[11] = ulpinv; } if (vs[i__ + j * vs_dim1] != vs1[i__ + j * vs1_dim1]) { result[12] = ulpinv; } /* L190: */ } /* L200: */ } if (sdim != sdim1) { result[13] = ulpinv; } /* Compute RCONDV with VS, and compare */ slacpy_("F", n, n, &a[a_offset], lda, &ht[ht_offset], lda); sgeesx_("V", sort, (L_fp)sslect_, "V", n, &ht[ht_offset], lda, &sdim1, &wrt[1], &wit[1], &vs1[vs1_offset], ldvs, &rcnde1, &rcndv1, & work[1], lwork, &iwork[1], &liwork, &bwork[1], &iinfo); if (iinfo != 0 && iinfo != *n + 2) { result[15] = ulpinv; if (*jtype != 22) { io___33.ciunit = *nounit; s_wsfe(&io___33); do_fio(&c__1, "SGEESX7", (ftnlen)7); 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 *)&iseed[1], (ftnlen)sizeof(integer)); e_wsfe(); } else { io___34.ciunit = *nounit; s_wsfe(&io___34); do_fio(&c__1, "SGEESX7", (ftnlen)7); do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&(*n), (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&iseed[1], (ftnlen)sizeof(integer)); e_wsfe(); } *info = abs(iinfo); goto L250; } /* Perform test (15) */ if (rcndv1 != rcondv) { result[15] = ulpinv; } /* Perform tests (10), (11), (12), and (13) */ i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { if (wr[i__] != wrt[i__] || wi[i__] != wit[i__]) { result[10] = ulpinv; } i__2 = *n; for (j = 1; j <= i__2; ++j) { if (h__[i__ + j * h_dim1] != ht[i__ + j * ht_dim1]) { result[11] = ulpinv; } if (vs[i__ + j * vs_dim1] != vs1[i__ + j * vs1_dim1]) { result[12] = ulpinv; } /* L210: */ } /* L220: */ } if (sdim != sdim1) { result[13] = ulpinv; } /* Compute RCONDV without VS, and compare */ slacpy_("F", n, n, &a[a_offset], lda, &ht[ht_offset], lda); sgeesx_("N", sort, (L_fp)sslect_, "V", n, &ht[ht_offset], lda, &sdim1, &wrt[1], &wit[1], &vs1[vs1_offset], ldvs, &rcnde1, &rcndv1, & work[1], lwork, &iwork[1], &liwork, &bwork[1], &iinfo); if (iinfo != 0 && iinfo != *n + 2) { result[15] = ulpinv; if (*jtype != 22) { io___35.ciunit = *nounit; s_wsfe(&io___35); do_fio(&c__1, "SGEESX8", (ftnlen)7); 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 *)&iseed[1], (ftnlen)sizeof(integer)); e_wsfe(); } else { io___36.ciunit = *nounit; s_wsfe(&io___36); do_fio(&c__1, "SGEESX8", (ftnlen)7); do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&(*n), (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&iseed[1], (ftnlen)sizeof(integer)); e_wsfe(); } *info = abs(iinfo); goto L250; } /* Perform test (15) */ if (rcndv1 != rcondv) { result[15] = ulpinv; } /* Perform tests (10), (11), (12), and (13) */ i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { if (wr[i__] != wrt[i__] || wi[i__] != wit[i__]) { result[10] = ulpinv; } i__2 = *n; for (j = 1; j <= i__2; ++j) { if (h__[i__ + j * h_dim1] != ht[i__ + j * ht_dim1]) { result[11] = ulpinv; } if (vs[i__ + j * vs_dim1] != vs1[i__ + j * vs1_dim1]) { result[12] = ulpinv; } /* L230: */ } /* L240: */ } if (sdim != sdim1) { result[13] = ulpinv; } } L250: /* If there are precomputed reciprocal condition numbers, compare computed values with them. */ if (*comp) { /* First set up SELOPT, SELDIM, SELVAL, SELWR, and SELWI so that the logical function SSLECT selects the eigenvalues specified by NSLCT and ISLCT. */ sslct_1.seldim = *n; sslct_1.selopt = 1; eps = dmax(ulp,5.9605e-8f); i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { ipnt[i__ - 1] = i__; sslct_1.selval[i__ - 1] = FALSE_; sslct_1.selwr[i__ - 1] = wrtmp[i__]; sslct_1.selwi[i__ - 1] = witmp[i__]; /* L260: */ } i__1 = *n - 1; for (i__ = 1; i__ <= i__1; ++i__) { kmin = i__; vrmin = wrtmp[i__]; vimin = witmp[i__]; i__2 = *n; for (j = i__ + 1; j <= i__2; ++j) { if (wrtmp[j] < vrmin) { kmin = j; vrmin = wrtmp[j]; vimin = witmp[j]; } /* L270: */ } wrtmp[kmin] = wrtmp[i__]; witmp[kmin] = witmp[i__]; wrtmp[i__] = vrmin; witmp[i__] = vimin; itmp = ipnt[i__ - 1]; ipnt[i__ - 1] = ipnt[kmin - 1]; ipnt[kmin - 1] = itmp; /* L280: */ } i__1 = *nslct; for (i__ = 1; i__ <= i__1; ++i__) { sslct_1.selval[ipnt[islct[i__] - 1] - 1] = TRUE_; /* L290: */ } /* Compute condition numbers */ slacpy_("F", n, n, &a[a_offset], lda, &ht[ht_offset], lda); sgeesx_("N", "S", (L_fp)sslect_, "B", n, &ht[ht_offset], lda, &sdim1, &wrt[1], &wit[1], &vs1[vs1_offset], ldvs, &rconde, &rcondv, & work[1], lwork, &iwork[1], &liwork, &bwork[1], &iinfo); if (iinfo != 0 && iinfo != *n + 2) { result[16] = ulpinv; result[17] = ulpinv; io___43.ciunit = *nounit; s_wsfe(&io___43); do_fio(&c__1, "SGEESX9", (ftnlen)7); do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&(*n), (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&iseed[1], (ftnlen)sizeof(integer)); e_wsfe(); *info = abs(iinfo); goto L300; } /* Compare condition number for average of selected eigenvalues taking its condition number into account */ anorm = slange_("1", n, n, &a[a_offset], lda, &work[1]); /* Computing MAX */ r__1 = (real) (*n) * eps * anorm; v = dmax(r__1,smlnum); if (anorm == 0.f) { v = 1.f; } if (v > rcondv) { tol = 1.f; } else { tol = v / rcondv; } if (v > *rcdvin) { tolin = 1.f; } else { tolin = v / *rcdvin; } /* Computing MAX */ r__1 = tol, r__2 = smlnum / eps; tol = dmax(r__1,r__2); /* Computing MAX */ r__1 = tolin, r__2 = smlnum / eps; tolin = dmax(r__1,r__2); if (eps * (*rcdein - tolin) > rconde + tol) { result[16] = ulpinv; } else if (*rcdein - tolin > rconde + tol) { result[16] = (*rcdein - tolin) / (rconde + tol); } else if (*rcdein + tolin < eps * (rconde - tol)) { result[16] = ulpinv; } else if (*rcdein + tolin < rconde - tol) { result[16] = (rconde - tol) / (*rcdein + tolin); } else { result[16] = 1.f; } /* Compare condition numbers for right invariant subspace taking its condition number into account */ if (v > rcondv * rconde) { tol = rcondv; } else { tol = v / rconde; } if (v > *rcdvin * *rcdein) { tolin = *rcdvin; } else { tolin = v / *rcdein; } /* Computing MAX */ r__1 = tol, r__2 = smlnum / eps; tol = dmax(r__1,r__2); /* Computing MAX */ r__1 = tolin, r__2 = smlnum / eps; tolin = dmax(r__1,r__2); if (eps * (*rcdvin - tolin) > rcondv + tol) { result[17] = ulpinv; } else if (*rcdvin - tolin > rcondv + tol) { result[17] = (*rcdvin - tolin) / (rcondv + tol); } else if (*rcdvin + tolin < eps * (rcondv - tol)) { result[17] = ulpinv; } else if (*rcdvin + tolin < rcondv - tol) { result[17] = (rcondv - tol) / (*rcdvin + tolin); } else { result[17] = 1.f; } L300: ; } return 0; /* End of SGET24 */ } /* sget24_ */