#include "blaswrap.h" /* dget23.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" /* Table of constant values */ static integer c__1 = 1; static integer c__4 = 4; /* Subroutine */ int dget23_(logical *comp, char *balanc, integer *jtype, doublereal *thresh, integer *iseed, integer *nounit, integer *n, doublereal *a, integer *lda, doublereal *h__, doublereal *wr, doublereal *wi, doublereal *wr1, doublereal *wi1, doublereal *vl, integer *ldvl, doublereal *vr, integer *ldvr, doublereal *lre, integer *ldlre, doublereal *rcondv, doublereal *rcndv1, doublereal * rcdvin, doublereal *rconde, doublereal *rcnde1, doublereal *rcdein, doublereal *scale, doublereal *scale1, doublereal *result, doublereal *work, integer *lwork, integer *iwork, integer *info ) { /* Initialized data */ static char sens[1*2] = "N" "V"; /* Format strings */ static char fmt_9998[] = "(\002 DGET23: \002,a,\002 returned INFO=\002,i" "6,\002.\002,/9x,\002N=\002,i6,\002, JTYPE=\002,i6,\002, BALANC = " "\002,a,\002, ISEED=(\002,3(i5,\002,\002),i5,\002)\002)"; static char fmt_9999[] = "(\002 DGET23: \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, lre_dim1, lre_offset, vl_dim1, vl_offset, vr_dim1, vr_offset, i__1, i__2, i__3; doublereal d__1, d__2, d__3, d__4, d__5; /* Builtin functions */ integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void); /* Local variables */ static integer i__, j; static doublereal v; static integer jj, ihi, ilo; static doublereal dum[1], eps, res[2], tol, ulp, vmx; static integer ihi1, ilo1, kmin; static doublereal vmax, tnrm, vrmx, vtst; extern doublereal dnrm2_(integer *, doublereal *, integer *); static logical balok, nobal; extern /* Subroutine */ int dget22_(char *, char *, char *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, doublereal *); static doublereal abnrm; extern logical lsame_(char *, char *); static integer iinfo; static char sense[1]; static integer isens; static doublereal vimin, tolin, vrmin, abnrm1; extern doublereal dlapy2_(doublereal *, doublereal *), dlamch_(char *); extern /* Subroutine */ int dlacpy_(char *, integer *, integer *, doublereal *, integer *, doublereal *, integer *), xerbla_(char *, integer *), dgeevx_(char *, char *, char * , char *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, integer *, doublereal *, integer *, integer *, integer *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, integer *, integer *, integer *); static integer isensm; static doublereal smlnum, ulpinv; /* Fortran I/O blocks */ static cilist io___14 = { 0, 0, 0, fmt_9998, 0 }; static cilist io___15 = { 0, 0, 0, fmt_9999, 0 }; static cilist io___28 = { 0, 0, 0, fmt_9998, 0 }; static cilist io___29 = { 0, 0, 0, fmt_9999, 0 }; static cilist io___30 = { 0, 0, 0, fmt_9998, 0 }; static cilist io___31 = { 0, 0, 0, fmt_9999, 0 }; static cilist io___32 = { 0, 0, 0, fmt_9998, 0 }; static cilist io___33 = { 0, 0, 0, fmt_9999, 0 }; static cilist io___34 = { 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 ======= DGET23 checks the nonsymmetric eigenvalue problem driver SGEEVX. If COMP = .FALSE., the first 8 of the following tests will be performed on the input matrix A, and also test 9 if LWORK is sufficiently large. if COMP is .TRUE. all 11 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) 0 if W(full) = W(partial), 1/ulp otherwise 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) 0 if VR(full) = VR(partial), 1/ulp otherwise 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) 0 if VL(full) = VL(partial), 1/ulp otherwise 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) 0 if RCONDV(full) = RCONDV(partial), 1/ulp otherwise 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. (10) |RCONDV - RCDVIN| / cond(RCONDV) RCONDV is the reciprocal right eigenvector condition number computed by DGEEVX 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 DGEEVX 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 ========= 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 BALANC (input) CHARACTER Describes the balancing option to be tested. = 'N' for no permuting or diagonal scaling = 'P' for permuting but no diagonal scaling = 'S' for no permuting but diagonal scaling = 'B' for permuting and diagonal scaling JTYPE (input) INTEGER Type of input matrix. Used to label output if error occurs. THRESH (input) DOUBLE PRECISION A test will count as "failed" if the "error", computed as described above, exceeds THRESH. Note that the error is scaled to be O(1), so THRESH should be a reasonably small multiple of 1, e.g., 10 or 100. In particular, it should not depend on the precision (single vs. double) or the size of the matrix. It must be at least zero. 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. 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) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (LDA,N) Another copy of the test matrix A, modified by DGEEVX. WR (workspace) DOUBLE PRECISION array, dimension (N) WI (workspace) DOUBLE PRECISION 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. WR1 (workspace) DOUBLE PRECISION array, dimension (N) WI1 (workspace) DOUBLE PRECISION array, dimension (N) Like WR, WI, these arrays contain the eigenvalues of A, but those computed when DGEEVX only computes a partial eigendecomposition, i.e. not the eigenvalues and left and right eigenvectors. VL (workspace) DOUBLE PRECISION array, dimension (LDVL,N) VL holds the computed left eigenvectors. LDVL (input) INTEGER Leading dimension of VL. Must be at least max(1,N). VR (workspace) DOUBLE PRECISION array, dimension (LDVR,N) VR holds the computed right eigenvectors. LDVR (input) INTEGER Leading dimension of VR. Must be at least max(1,N). LRE (workspace) DOUBLE PRECISION array, dimension (LDLRE,N) LRE holds the computed right or left eigenvectors. LDLRE (input) INTEGER Leading dimension of LRE. Must be at least max(1,N). RCONDV (workspace) DOUBLE PRECISION array, dimension (N) RCONDV holds the computed reciprocal condition numbers for eigenvectors. RCNDV1 (workspace) DOUBLE PRECISION array, dimension (N) RCNDV1 holds more computed reciprocal condition numbers for eigenvectors. RCDVIN (input) DOUBLE PRECISION array, dimension (N) When COMP = .TRUE. RCDVIN holds the precomputed reciprocal condition numbers for eigenvectors to be compared with RCONDV. RCONDE (workspace) DOUBLE PRECISION array, dimension (N) RCONDE holds the computed reciprocal condition numbers for eigenvalues. RCNDE1 (workspace) DOUBLE PRECISION array, dimension (N) RCNDE1 holds more computed reciprocal condition numbers for eigenvalues. RCDEIN (input) DOUBLE PRECISION array, dimension (N) When COMP = .TRUE. RCDEIN holds the precomputed reciprocal condition numbers for eigenvalues to be compared with RCONDE. SCALE (workspace) DOUBLE PRECISION array, dimension (N) Holds information describing balancing of matrix. SCALE1 (workspace) DOUBLE PRECISION array, dimension (N) Holds information describing balancing of matrix. RESULT (output) DOUBLE PRECISION array, dimension (11) The values computed by the 11 tests described above. The values are currently limited to 1/ulp, to avoid overflow. WORK (workspace) DOUBLE PRECISION array, dimension (LWORK) LWORK (input) INTEGER The number of entries in WORK. This must be at least 3*N, and 6*N+N**2 if tests 9, 10 or 11 are to be performed. IWORK (workspace) INTEGER array, dimension (2*N) INFO (output) INTEGER If 0, successful exit. If <0, input parameter -INFO had an incorrect value. If >0, DGEEVX returned an error code, the absolute value of which is returned. ===================================================================== Parameter adjustments */ --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; --rcondv; --rcndv1; --rcdvin; --rconde; --rcnde1; --rcdein; --scale; --scale1; --result; --work; --iwork; /* Function Body Check for errors */ nobal = lsame_(balanc, "N"); balok = nobal || lsame_(balanc, "P") || lsame_( balanc, "S") || lsame_(balanc, "B"); *info = 0; if (! balok) { *info = -2; } else if (*thresh < 0.) { *info = -4; } else if (*nounit <= 0) { *info = -6; } else if (*n < 0) { *info = -7; } else if (*lda < 1 || *lda < *n) { *info = -9; } else if (*ldvl < 1 || *ldvl < *n) { *info = -16; } else if (*ldvr < 1 || *ldvr < *n) { *info = -18; } else if (*ldlre < 1 || *ldlre < *n) { *info = -20; } else if (*lwork < *n * 3 || *comp && *lwork < *n * 6 + *n * *n) { *info = -31; } if (*info != 0) { i__1 = -(*info); xerbla_("DGET23", &i__1); return 0; } /* Quick return if nothing to do */ for (i__ = 1; i__ <= 11; ++i__) { result[i__] = -1.; /* L10: */ } if (*n == 0) { return 0; } /* More Important constants */ ulp = dlamch_("Precision"); smlnum = dlamch_("S"); ulpinv = 1. / ulp; /* Compute eigenvalues and eigenvectors, and test them */ if (*lwork >= *n * 6 + *n * *n) { *(unsigned char *)sense = 'B'; isensm = 2; } else { *(unsigned char *)sense = 'E'; isensm = 1; } dlacpy_("F", n, n, &a[a_offset], lda, &h__[h_offset], lda); dgeevx_(balanc, "V", "V", sense, n, &h__[h_offset], lda, &wr[1], &wi[1], & vl[vl_offset], ldvl, &vr[vr_offset], ldvr, &ilo, &ihi, &scale[1], &abnrm, &rconde[1], &rcondv[1], &work[1], lwork, &iwork[1], & iinfo); if (iinfo != 0) { result[1] = ulpinv; if (*jtype != 22) { io___14.ciunit = *nounit; s_wsfe(&io___14); do_fio(&c__1, "DGEEVX1", (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__1, balanc, (ftnlen)1); do_fio(&c__4, (char *)&iseed[1], (ftnlen)sizeof(integer)); e_wsfe(); } else { io___15.ciunit = *nounit; s_wsfe(&io___15); do_fio(&c__1, "DGEEVX1", (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; } /* Do Test (1) */ dget22_("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) */ dget22_("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__1 = *n; for (j = 1; j <= i__1; ++j) { tnrm = 1.; if (wi[j] == 0.) { tnrm = dnrm2_(n, &vr[j * vr_dim1 + 1], &c__1); } else if (wi[j] > 0.) { d__1 = dnrm2_(n, &vr[j * vr_dim1 + 1], &c__1); d__2 = dnrm2_(n, &vr[(j + 1) * vr_dim1 + 1], &c__1); tnrm = dlapy2_(&d__1, &d__2); } /* Computing MAX Computing MIN */ d__4 = ulpinv, d__5 = (d__1 = tnrm - 1., abs(d__1)) / ulp; d__2 = result[3], d__3 = min(d__4,d__5); result[3] = max(d__2,d__3); if (wi[j] > 0.) { vmx = 0.; vrmx = 0.; i__2 = *n; for (jj = 1; jj <= i__2; ++jj) { vtst = dlapy2_(&vr[jj + j * vr_dim1], &vr[jj + (j + 1) * vr_dim1]); if (vtst > vmx) { vmx = vtst; } if (vr[jj + (j + 1) * vr_dim1] == 0. && (d__1 = vr[jj + j * vr_dim1], abs(d__1)) > vrmx) { vrmx = (d__2 = vr[jj + j * vr_dim1], abs(d__2)); } /* L20: */ } if (vrmx / vmx < 1. - ulp * 2.) { result[3] = ulpinv; } } /* L30: */ } /* Do Test (4) */ i__1 = *n; for (j = 1; j <= i__1; ++j) { tnrm = 1.; if (wi[j] == 0.) { tnrm = dnrm2_(n, &vl[j * vl_dim1 + 1], &c__1); } else if (wi[j] > 0.) { d__1 = dnrm2_(n, &vl[j * vl_dim1 + 1], &c__1); d__2 = dnrm2_(n, &vl[(j + 1) * vl_dim1 + 1], &c__1); tnrm = dlapy2_(&d__1, &d__2); } /* Computing MAX Computing MIN */ d__4 = ulpinv, d__5 = (d__1 = tnrm - 1., abs(d__1)) / ulp; d__2 = result[4], d__3 = min(d__4,d__5); result[4] = max(d__2,d__3); if (wi[j] > 0.) { vmx = 0.; vrmx = 0.; i__2 = *n; for (jj = 1; jj <= i__2; ++jj) { vtst = dlapy2_(&vl[jj + j * vl_dim1], &vl[jj + (j + 1) * vl_dim1]); if (vtst > vmx) { vmx = vtst; } if (vl[jj + (j + 1) * vl_dim1] == 0. && (d__1 = vl[jj + j * vl_dim1], abs(d__1)) > vrmx) { vrmx = (d__2 = vl[jj + j * vl_dim1], abs(d__2)); } /* L40: */ } if (vrmx / vmx < 1. - ulp * 2.) { result[4] = ulpinv; } } /* L50: */ } /* Test for all options of computing condition numbers */ i__1 = isensm; for (isens = 1; isens <= i__1; ++isens) { *(unsigned char *)sense = *(unsigned char *)&sens[isens - 1]; /* Compute eigenvalues only, and test them */ dlacpy_("F", n, n, &a[a_offset], lda, &h__[h_offset], lda); dgeevx_(balanc, "N", "N", sense, n, &h__[h_offset], lda, &wr1[1], & wi1[1], dum, &c__1, dum, &c__1, &ilo1, &ihi1, &scale1[1], & abnrm1, &rcnde1[1], &rcndv1[1], &work[1], lwork, &iwork[1], & iinfo); if (iinfo != 0) { result[1] = ulpinv; if (*jtype != 22) { io___28.ciunit = *nounit; s_wsfe(&io___28); do_fio(&c__1, "DGEEVX2", (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__1, balanc, (ftnlen)1); do_fio(&c__4, (char *)&iseed[1], (ftnlen)sizeof(integer)); e_wsfe(); } else { io___29.ciunit = *nounit; s_wsfe(&io___29); do_fio(&c__1, "DGEEVX2", (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 L190; } /* Do Test (5) */ i__2 = *n; for (j = 1; j <= i__2; ++j) { if (wr[j] != wr1[j] || wi[j] != wi1[j]) { result[5] = ulpinv; } /* L60: */ } /* Do Test (8) */ if (! nobal) { i__2 = *n; for (j = 1; j <= i__2; ++j) { if (scale[j] != scale1[j]) { result[8] = ulpinv; } /* L70: */ } if (ilo != ilo1) { result[8] = ulpinv; } if (ihi != ihi1) { result[8] = ulpinv; } if (abnrm != abnrm1) { result[8] = ulpinv; } } /* Do Test (9) */ if (isens == 2 && *n > 1) { i__2 = *n; for (j = 1; j <= i__2; ++j) { if (rcondv[j] != rcndv1[j]) { result[9] = ulpinv; } /* L80: */ } } /* Compute eigenvalues and right eigenvectors, and test them */ dlacpy_("F", n, n, &a[a_offset], lda, &h__[h_offset], lda); dgeevx_(balanc, "N", "V", sense, n, &h__[h_offset], lda, &wr1[1], & wi1[1], dum, &c__1, &lre[lre_offset], ldlre, &ilo1, &ihi1, & scale1[1], &abnrm1, &rcnde1[1], &rcndv1[1], &work[1], lwork, & iwork[1], &iinfo); if (iinfo != 0) { result[1] = ulpinv; if (*jtype != 22) { io___30.ciunit = *nounit; s_wsfe(&io___30); do_fio(&c__1, "DGEEVX3", (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__1, balanc, (ftnlen)1); do_fio(&c__4, (char *)&iseed[1], (ftnlen)sizeof(integer)); e_wsfe(); } else { io___31.ciunit = *nounit; s_wsfe(&io___31); do_fio(&c__1, "DGEEVX3", (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 L190; } /* Do Test (5) again */ i__2 = *n; for (j = 1; j <= i__2; ++j) { if (wr[j] != wr1[j] || wi[j] != wi1[j]) { result[5] = ulpinv; } /* L90: */ } /* Do Test (6) */ i__2 = *n; for (j = 1; j <= i__2; ++j) { i__3 = *n; for (jj = 1; jj <= i__3; ++jj) { if (vr[j + jj * vr_dim1] != lre[j + jj * lre_dim1]) { result[6] = ulpinv; } /* L100: */ } /* L110: */ } /* Do Test (8) again */ if (! nobal) { i__2 = *n; for (j = 1; j <= i__2; ++j) { if (scale[j] != scale1[j]) { result[8] = ulpinv; } /* L120: */ } if (ilo != ilo1) { result[8] = ulpinv; } if (ihi != ihi1) { result[8] = ulpinv; } if (abnrm != abnrm1) { result[8] = ulpinv; } } /* Do Test (9) again */ if (isens == 2 && *n > 1) { i__2 = *n; for (j = 1; j <= i__2; ++j) { if (rcondv[j] != rcndv1[j]) { result[9] = ulpinv; } /* L130: */ } } /* Compute eigenvalues and left eigenvectors, and test them */ dlacpy_("F", n, n, &a[a_offset], lda, &h__[h_offset], lda); dgeevx_(balanc, "V", "N", sense, n, &h__[h_offset], lda, &wr1[1], & wi1[1], &lre[lre_offset], ldlre, dum, &c__1, &ilo1, &ihi1, & scale1[1], &abnrm1, &rcnde1[1], &rcndv1[1], &work[1], lwork, & iwork[1], &iinfo); if (iinfo != 0) { result[1] = ulpinv; if (*jtype != 22) { io___32.ciunit = *nounit; s_wsfe(&io___32); do_fio(&c__1, "DGEEVX4", (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__1, balanc, (ftnlen)1); do_fio(&c__4, (char *)&iseed[1], (ftnlen)sizeof(integer)); e_wsfe(); } else { io___33.ciunit = *nounit; s_wsfe(&io___33); do_fio(&c__1, "DGEEVX4", (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 L190; } /* Do Test (5) again */ i__2 = *n; for (j = 1; j <= i__2; ++j) { if (wr[j] != wr1[j] || wi[j] != wi1[j]) { result[5] = ulpinv; } /* L140: */ } /* Do Test (7) */ i__2 = *n; for (j = 1; j <= i__2; ++j) { i__3 = *n; for (jj = 1; jj <= i__3; ++jj) { if (vl[j + jj * vl_dim1] != lre[j + jj * lre_dim1]) { result[7] = ulpinv; } /* L150: */ } /* L160: */ } /* Do Test (8) again */ if (! nobal) { i__2 = *n; for (j = 1; j <= i__2; ++j) { if (scale[j] != scale1[j]) { result[8] = ulpinv; } /* L170: */ } if (ilo != ilo1) { result[8] = ulpinv; } if (ihi != ihi1) { result[8] = ulpinv; } if (abnrm != abnrm1) { result[8] = ulpinv; } } /* Do Test (9) again */ if (isens == 2 && *n > 1) { i__2 = *n; for (j = 1; j <= i__2; ++j) { if (rcondv[j] != rcndv1[j]) { result[9] = ulpinv; } /* L180: */ } } L190: /* L200: */ ; } /* If COMP, compare condition numbers to precomputed ones */ if (*comp) { dlacpy_("F", n, n, &a[a_offset], lda, &h__[h_offset], lda); dgeevx_("N", "V", "V", "B", n, &h__[h_offset], lda, &wr[1], &wi[1], & vl[vl_offset], ldvl, &vr[vr_offset], ldvr, &ilo, &ihi, &scale[ 1], &abnrm, &rconde[1], &rcondv[1], &work[1], lwork, &iwork[1] , &iinfo); if (iinfo != 0) { result[1] = ulpinv; io___34.ciunit = *nounit; s_wsfe(&io___34); do_fio(&c__1, "DGEEVX5", (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; } /* Sort eigenvalues and condition numbers lexicographically to compare with inputs */ i__1 = *n - 1; for (i__ = 1; i__ <= i__1; ++i__) { kmin = i__; vrmin = wr[i__]; vimin = wi[i__]; i__2 = *n; for (j = i__ + 1; j <= i__2; ++j) { if (wr[j] < vrmin) { kmin = j; vrmin = wr[j]; vimin = wi[j]; } /* L210: */ } wr[kmin] = wr[i__]; wi[kmin] = wi[i__]; wr[i__] = vrmin; wi[i__] = vimin; vrmin = rconde[kmin]; rconde[kmin] = rconde[i__]; rconde[i__] = vrmin; vrmin = rcondv[kmin]; rcondv[kmin] = rcondv[i__]; rcondv[i__] = vrmin; /* L220: */ } /* Compare condition numbers for eigenvectors taking their condition numbers into account */ result[10] = 0.; eps = max(5.9605e-8,ulp); /* Computing MAX */ d__1 = (doublereal) (*n) * eps * abnrm; v = max(d__1,smlnum); if (abnrm == 0.) { v = 1.; } i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { if (v > rcondv[i__] * rconde[i__]) { tol = rcondv[i__]; } else { tol = v / rconde[i__]; } if (v > rcdvin[i__] * rcdein[i__]) { tolin = rcdvin[i__]; } else { tolin = v / rcdein[i__]; } /* Computing MAX */ d__1 = tol, d__2 = smlnum / eps; tol = max(d__1,d__2); /* Computing MAX */ d__1 = tolin, d__2 = smlnum / eps; tolin = max(d__1,d__2); if (eps * (rcdvin[i__] - tolin) > rcondv[i__] + tol) { vmax = 1. / eps; } else if (rcdvin[i__] - tolin > rcondv[i__] + tol) { vmax = (rcdvin[i__] - tolin) / (rcondv[i__] + tol); } else if (rcdvin[i__] + tolin < eps * (rcondv[i__] - tol)) { vmax = 1. / eps; } else if (rcdvin[i__] + tolin < rcondv[i__] - tol) { vmax = (rcondv[i__] - tol) / (rcdvin[i__] + tolin); } else { vmax = 1.; } result[10] = max(result[10],vmax); /* L230: */ } /* Compare condition numbers for eigenvalues taking their condition numbers into account */ result[11] = 0.; i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { if (v > rcondv[i__]) { tol = 1.; } else { tol = v / rcondv[i__]; } if (v > rcdvin[i__]) { tolin = 1.; } else { tolin = v / rcdvin[i__]; } /* Computing MAX */ d__1 = tol, d__2 = smlnum / eps; tol = max(d__1,d__2); /* Computing MAX */ d__1 = tolin, d__2 = smlnum / eps; tolin = max(d__1,d__2); if (eps * (rcdein[i__] - tolin) > rconde[i__] + tol) { vmax = 1. / eps; } else if (rcdein[i__] - tolin > rconde[i__] + tol) { vmax = (rcdein[i__] - tolin) / (rconde[i__] + tol); } else if (rcdein[i__] + tolin < eps * (rconde[i__] - tol)) { vmax = 1. / eps; } else if (rcdein[i__] + tolin < rconde[i__] - tol) { vmax = (rconde[i__] - tol) / (rcdein[i__] + tolin); } else { vmax = 1.; } result[11] = max(result[11],vmax); /* L240: */ } L250: ; } return 0; /* End of DGET23 */ } /* dget23_ */