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author | shmel1k <shmel1k@ydb.tech> | 2022-09-02 12:44:59 +0300 |
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committer | shmel1k <shmel1k@ydb.tech> | 2022-09-02 12:44:59 +0300 |
commit | 90d450f74722da7859d6f510a869f6c6908fd12f (patch) | |
tree | 538c718dedc76cdfe37ad6d01ff250dd930d9278 /contrib/libs/clapack/dgegv.c | |
parent | 01f64c1ecd0d4ffa9e3a74478335f1745f26cc75 (diff) | |
download | ydb-90d450f74722da7859d6f510a869f6c6908fd12f.tar.gz |
[] add metering mode to CLI
Diffstat (limited to 'contrib/libs/clapack/dgegv.c')
-rw-r--r-- | contrib/libs/clapack/dgegv.c | 842 |
1 files changed, 842 insertions, 0 deletions
diff --git a/contrib/libs/clapack/dgegv.c b/contrib/libs/clapack/dgegv.c new file mode 100644 index 0000000000..8551895e4c --- /dev/null +++ b/contrib/libs/clapack/dgegv.c @@ -0,0 +1,842 @@ +/* dgegv.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" + +/* Table of constant values */ + +static integer c__1 = 1; +static integer c_n1 = -1; +static doublereal c_b27 = 1.; +static doublereal c_b38 = 0.; + +/* Subroutine */ int dgegv_(char *jobvl, char *jobvr, integer *n, doublereal * + a, integer *lda, doublereal *b, integer *ldb, doublereal *alphar, + doublereal *alphai, doublereal *beta, doublereal *vl, integer *ldvl, + doublereal *vr, integer *ldvr, doublereal *work, integer *lwork, + integer *info) +{ + /* System generated locals */ + integer a_dim1, a_offset, b_dim1, b_offset, vl_dim1, vl_offset, vr_dim1, + vr_offset, i__1, i__2; + doublereal d__1, d__2, d__3, d__4; + + /* Local variables */ + integer jc, nb, in, jr, nb1, nb2, nb3, ihi, ilo; + doublereal eps; + logical ilv; + doublereal absb, anrm, bnrm; + integer itau; + doublereal temp; + logical ilvl, ilvr; + integer lopt; + doublereal anrm1, anrm2, bnrm1, bnrm2, absai, scale, absar, sbeta; + extern logical lsame_(char *, char *); + integer ileft, iinfo, icols, iwork, irows; + extern /* Subroutine */ int dggbak_(char *, char *, integer *, integer *, + integer *, doublereal *, doublereal *, integer *, doublereal *, + integer *, integer *), dggbal_(char *, integer *, + doublereal *, integer *, doublereal *, integer *, integer *, + integer *, doublereal *, doublereal *, doublereal *, integer *); + extern doublereal dlamch_(char *), dlange_(char *, integer *, + integer *, doublereal *, integer *, doublereal *); + doublereal salfai; + extern /* Subroutine */ int dgghrd_(char *, char *, integer *, integer *, + integer *, doublereal *, integer *, doublereal *, integer *, + doublereal *, integer *, doublereal *, integer *, integer *), dlascl_(char *, integer *, integer *, doublereal + *, doublereal *, integer *, integer *, doublereal *, integer *, + integer *); + doublereal salfar; + extern /* Subroutine */ int dgeqrf_(integer *, integer *, doublereal *, + integer *, doublereal *, doublereal *, integer *, integer *), + dlacpy_(char *, integer *, integer *, doublereal *, integer *, + doublereal *, integer *); + doublereal safmin; + extern /* Subroutine */ int dlaset_(char *, integer *, integer *, + doublereal *, doublereal *, doublereal *, integer *); + doublereal safmax; + char chtemp[1]; + logical ldumma[1]; + extern /* Subroutine */ int dhgeqz_(char *, char *, char *, integer *, + integer *, integer *, doublereal *, integer *, doublereal *, + integer *, doublereal *, doublereal *, doublereal *, doublereal *, + integer *, doublereal *, integer *, doublereal *, integer *, + integer *), dtgevc_(char *, char *, + logical *, integer *, doublereal *, integer *, doublereal *, + integer *, doublereal *, integer *, doublereal *, integer *, + integer *, integer *, doublereal *, integer *), + xerbla_(char *, integer *); + integer ijobvl, iright; + logical ilimit; + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *); + integer ijobvr; + extern /* Subroutine */ int dorgqr_(integer *, integer *, integer *, + doublereal *, integer *, doublereal *, doublereal *, integer *, + integer *); + doublereal onepls; + integer lwkmin; + extern /* Subroutine */ int dormqr_(char *, char *, integer *, integer *, + integer *, doublereal *, integer *, doublereal *, doublereal *, + integer *, doublereal *, integer *, integer *); + integer lwkopt; + logical lquery; + + +/* -- LAPACK driver routine (version 3.2) -- */ +/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ +/* November 2006 */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* Purpose */ +/* ======= */ + +/* This routine is deprecated and has been replaced by routine DGGEV. */ + +/* DGEGV computes the eigenvalues and, optionally, the left and/or right */ +/* eigenvectors of a real matrix pair (A,B). */ +/* Given two square matrices A and B, */ +/* the generalized nonsymmetric eigenvalue problem (GNEP) is to find the */ +/* eigenvalues lambda and corresponding (non-zero) eigenvectors x such */ +/* that */ + +/* A*x = lambda*B*x. */ + +/* An alternate form is to find the eigenvalues mu and corresponding */ +/* eigenvectors y such that */ + +/* mu*A*y = B*y. */ + +/* These two forms are equivalent with mu = 1/lambda and x = y if */ +/* neither lambda nor mu is zero. In order to deal with the case that */ +/* lambda or mu is zero or small, two values alpha and beta are returned */ +/* for each eigenvalue, such that lambda = alpha/beta and */ +/* mu = beta/alpha. */ + +/* The vectors x and y in the above equations are right eigenvectors of */ +/* the matrix pair (A,B). Vectors u and v satisfying */ + +/* u**H*A = lambda*u**H*B or mu*v**H*A = v**H*B */ + +/* are left eigenvectors of (A,B). */ + +/* Note: this routine performs "full balancing" on A and B -- see */ +/* "Further Details", below. */ + +/* Arguments */ +/* ========= */ + +/* JOBVL (input) CHARACTER*1 */ +/* = 'N': do not compute the left generalized eigenvectors; */ +/* = 'V': compute the left generalized eigenvectors (returned */ +/* in VL). */ + +/* JOBVR (input) CHARACTER*1 */ +/* = 'N': do not compute the right generalized eigenvectors; */ +/* = 'V': compute the right generalized eigenvectors (returned */ +/* in VR). */ + +/* N (input) INTEGER */ +/* The order of the matrices A, B, VL, and VR. N >= 0. */ + +/* A (input/output) DOUBLE PRECISION array, dimension (LDA, N) */ +/* On entry, the matrix A. */ +/* If JOBVL = 'V' or JOBVR = 'V', then on exit A */ +/* contains the real Schur form of A from the generalized Schur */ +/* factorization of the pair (A,B) after balancing. */ +/* If no eigenvectors were computed, then only the diagonal */ +/* blocks from the Schur form will be correct. See DGGHRD and */ +/* DHGEQZ for details. */ + +/* LDA (input) INTEGER */ +/* The leading dimension of A. LDA >= max(1,N). */ + +/* B (input/output) DOUBLE PRECISION array, dimension (LDB, N) */ +/* On entry, the matrix B. */ +/* If JOBVL = 'V' or JOBVR = 'V', then on exit B contains the */ +/* upper triangular matrix obtained from B in the generalized */ +/* Schur factorization of the pair (A,B) after balancing. */ +/* If no eigenvectors were computed, then only those elements of */ +/* B corresponding to the diagonal blocks from the Schur form of */ +/* A will be correct. See DGGHRD and DHGEQZ for details. */ + +/* LDB (input) INTEGER */ +/* The leading dimension of B. LDB >= max(1,N). */ + +/* ALPHAR (output) DOUBLE PRECISION array, dimension (N) */ +/* The real parts of each scalar alpha defining an eigenvalue of */ +/* GNEP. */ + +/* ALPHAI (output) DOUBLE PRECISION array, dimension (N) */ +/* The imaginary parts of each scalar alpha defining an */ +/* eigenvalue of GNEP. If ALPHAI(j) is zero, then the j-th */ +/* eigenvalue is real; if positive, then the j-th and */ +/* (j+1)-st eigenvalues are a complex conjugate pair, with */ +/* ALPHAI(j+1) = -ALPHAI(j). */ + +/* BETA (output) DOUBLE PRECISION array, dimension (N) */ +/* The scalars beta that define the eigenvalues of GNEP. */ + +/* Together, the quantities alpha = (ALPHAR(j),ALPHAI(j)) and */ +/* beta = BETA(j) represent the j-th eigenvalue of the matrix */ +/* pair (A,B), in one of the forms lambda = alpha/beta or */ +/* mu = beta/alpha. Since either lambda or mu may overflow, */ +/* they should not, in general, be computed. */ + +/* VL (output) DOUBLE PRECISION array, dimension (LDVL,N) */ +/* If JOBVL = 'V', the left eigenvectors u(j) are stored */ +/* in the columns of VL, in the same order as their eigenvalues. */ +/* If the j-th eigenvalue is real, then u(j) = VL(:,j). */ +/* If the j-th and (j+1)-st eigenvalues form a complex conjugate */ +/* pair, then */ +/* u(j) = VL(:,j) + i*VL(:,j+1) */ +/* and */ +/* u(j+1) = VL(:,j) - i*VL(:,j+1). */ + +/* Each eigenvector is scaled so that its largest component has */ +/* abs(real part) + abs(imag. part) = 1, except for eigenvectors */ +/* corresponding to an eigenvalue with alpha = beta = 0, which */ +/* are set to zero. */ +/* Not referenced if JOBVL = 'N'. */ + +/* LDVL (input) INTEGER */ +/* The leading dimension of the matrix VL. LDVL >= 1, and */ +/* if JOBVL = 'V', LDVL >= N. */ + +/* VR (output) DOUBLE PRECISION array, dimension (LDVR,N) */ +/* If JOBVR = 'V', the right eigenvectors x(j) are stored */ +/* in the columns of VR, in the same order as their eigenvalues. */ +/* If the j-th eigenvalue is real, then x(j) = VR(:,j). */ +/* If the j-th and (j+1)-st eigenvalues form a complex conjugate */ +/* pair, then */ +/* x(j) = VR(:,j) + i*VR(:,j+1) */ +/* and */ +/* x(j+1) = VR(:,j) - i*VR(:,j+1). */ + +/* Each eigenvector is scaled so that its largest component has */ +/* abs(real part) + abs(imag. part) = 1, except for eigenvalues */ +/* corresponding to an eigenvalue with alpha = beta = 0, which */ +/* are set to zero. */ +/* Not referenced if JOBVR = 'N'. */ + +/* LDVR (input) INTEGER */ +/* The leading dimension of the matrix VR. LDVR >= 1, and */ +/* if JOBVR = 'V', LDVR >= N. */ + +/* WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */ +/* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ + +/* LWORK (input) INTEGER */ +/* The dimension of the array WORK. LWORK >= max(1,8*N). */ +/* For good performance, LWORK must generally be larger. */ +/* To compute the optimal value of LWORK, call ILAENV to get */ +/* blocksizes (for DGEQRF, DORMQR, and DORGQR.) Then compute: */ +/* NB -- MAX of the blocksizes for DGEQRF, DORMQR, and DORGQR; */ +/* The optimal LWORK is: */ +/* 2*N + MAX( 6*N, N*(NB+1) ). */ + +/* If LWORK = -1, then a workspace query is assumed; the routine */ +/* only calculates the optimal size of the WORK array, returns */ +/* this value as the first entry of the WORK array, and no error */ +/* message related to LWORK is issued by XERBLA. */ + +/* INFO (output) INTEGER */ +/* = 0: successful exit */ +/* < 0: if INFO = -i, the i-th argument had an illegal value. */ +/* = 1,...,N: */ +/* The QZ iteration failed. No eigenvectors have been */ +/* calculated, but ALPHAR(j), ALPHAI(j), and BETA(j) */ +/* should be correct for j=INFO+1,...,N. */ +/* > N: errors that usually indicate LAPACK problems: */ +/* =N+1: error return from DGGBAL */ +/* =N+2: error return from DGEQRF */ +/* =N+3: error return from DORMQR */ +/* =N+4: error return from DORGQR */ +/* =N+5: error return from DGGHRD */ +/* =N+6: error return from DHGEQZ (other than failed */ +/* iteration) */ +/* =N+7: error return from DTGEVC */ +/* =N+8: error return from DGGBAK (computing VL) */ +/* =N+9: error return from DGGBAK (computing VR) */ +/* =N+10: error return from DLASCL (various calls) */ + +/* Further Details */ +/* =============== */ + +/* Balancing */ +/* --------- */ + +/* This driver calls DGGBAL to both permute and scale rows and columns */ +/* of A and B. The permutations PL and PR are chosen so that PL*A*PR */ +/* and PL*B*R will be upper triangular except for the diagonal blocks */ +/* A(i:j,i:j) and B(i:j,i:j), with i and j as close together as */ +/* possible. The diagonal scaling matrices DL and DR are chosen so */ +/* that the pair DL*PL*A*PR*DR, DL*PL*B*PR*DR have elements close to */ +/* one (except for the elements that start out zero.) */ + +/* After the eigenvalues and eigenvectors of the balanced matrices */ +/* have been computed, DGGBAK transforms the eigenvectors back to what */ +/* they would have been (in perfect arithmetic) if they had not been */ +/* balanced. */ + +/* Contents of A and B on Exit */ +/* -------- -- - --- - -- ---- */ + +/* If any eigenvectors are computed (either JOBVL='V' or JOBVR='V' or */ +/* both), then on exit the arrays A and B will contain the real Schur */ +/* form[*] of the "balanced" versions of A and B. If no eigenvectors */ +/* are computed, then only the diagonal blocks will be correct. */ + +/* [*] See DHGEQZ, DGEGS, or read the book "Matrix Computations", */ +/* by Golub & van Loan, pub. by Johns Hopkins U. Press. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. Local Arrays .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Decode the input arguments */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + b_dim1 = *ldb; + b_offset = 1 + b_dim1; + b -= b_offset; + --alphar; + --alphai; + --beta; + vl_dim1 = *ldvl; + vl_offset = 1 + vl_dim1; + vl -= vl_offset; + vr_dim1 = *ldvr; + vr_offset = 1 + vr_dim1; + vr -= vr_offset; + --work; + + /* Function Body */ + if (lsame_(jobvl, "N")) { + ijobvl = 1; + ilvl = FALSE_; + } else if (lsame_(jobvl, "V")) { + ijobvl = 2; + ilvl = TRUE_; + } else { + ijobvl = -1; + ilvl = FALSE_; + } + + if (lsame_(jobvr, "N")) { + ijobvr = 1; + ilvr = FALSE_; + } else if (lsame_(jobvr, "V")) { + ijobvr = 2; + ilvr = TRUE_; + } else { + ijobvr = -1; + ilvr = FALSE_; + } + ilv = ilvl || ilvr; + +/* Test the input arguments */ + +/* Computing MAX */ + i__1 = *n << 3; + lwkmin = max(i__1,1); + lwkopt = lwkmin; + work[1] = (doublereal) lwkopt; + lquery = *lwork == -1; + *info = 0; + if (ijobvl <= 0) { + *info = -1; + } else if (ijobvr <= 0) { + *info = -2; + } else if (*n < 0) { + *info = -3; + } else if (*lda < max(1,*n)) { + *info = -5; + } else if (*ldb < max(1,*n)) { + *info = -7; + } else if (*ldvl < 1 || ilvl && *ldvl < *n) { + *info = -12; + } else if (*ldvr < 1 || ilvr && *ldvr < *n) { + *info = -14; + } else if (*lwork < lwkmin && ! lquery) { + *info = -16; + } + + if (*info == 0) { + nb1 = ilaenv_(&c__1, "DGEQRF", " ", n, n, &c_n1, &c_n1); + nb2 = ilaenv_(&c__1, "DORMQR", " ", n, n, n, &c_n1); + nb3 = ilaenv_(&c__1, "DORGQR", " ", n, n, n, &c_n1); +/* Computing MAX */ + i__1 = max(nb1,nb2); + nb = max(i__1,nb3); +/* Computing MAX */ + i__1 = *n * 6, i__2 = *n * (nb + 1); + lopt = (*n << 1) + max(i__1,i__2); + work[1] = (doublereal) lopt; + } + + if (*info != 0) { + i__1 = -(*info); + xerbla_("DGEGV ", &i__1); + return 0; + } else if (lquery) { + return 0; + } + +/* Quick return if possible */ + + if (*n == 0) { + return 0; + } + +/* Get machine constants */ + + eps = dlamch_("E") * dlamch_("B"); + safmin = dlamch_("S"); + safmin += safmin; + safmax = 1. / safmin; + onepls = eps * 4 + 1.; + +/* Scale A */ + + anrm = dlange_("M", n, n, &a[a_offset], lda, &work[1]); + anrm1 = anrm; + anrm2 = 1.; + if (anrm < 1.) { + if (safmax * anrm < 1.) { + anrm1 = safmin; + anrm2 = safmax * anrm; + } + } + + if (anrm > 0.) { + dlascl_("G", &c_n1, &c_n1, &anrm, &c_b27, n, n, &a[a_offset], lda, & + iinfo); + if (iinfo != 0) { + *info = *n + 10; + return 0; + } + } + +/* Scale B */ + + bnrm = dlange_("M", n, n, &b[b_offset], ldb, &work[1]); + bnrm1 = bnrm; + bnrm2 = 1.; + if (bnrm < 1.) { + if (safmax * bnrm < 1.) { + bnrm1 = safmin; + bnrm2 = safmax * bnrm; + } + } + + if (bnrm > 0.) { + dlascl_("G", &c_n1, &c_n1, &bnrm, &c_b27, n, n, &b[b_offset], ldb, & + iinfo); + if (iinfo != 0) { + *info = *n + 10; + return 0; + } + } + +/* Permute the matrix to make it more nearly triangular */ +/* Workspace layout: (8*N words -- "work" requires 6*N words) */ +/* left_permutation, right_permutation, work... */ + + ileft = 1; + iright = *n + 1; + iwork = iright + *n; + dggbal_("P", n, &a[a_offset], lda, &b[b_offset], ldb, &ilo, &ihi, &work[ + ileft], &work[iright], &work[iwork], &iinfo); + if (iinfo != 0) { + *info = *n + 1; + goto L120; + } + +/* Reduce B to triangular form, and initialize VL and/or VR */ +/* Workspace layout: ("work..." must have at least N words) */ +/* left_permutation, right_permutation, tau, work... */ + + irows = ihi + 1 - ilo; + if (ilv) { + icols = *n + 1 - ilo; + } else { + icols = irows; + } + itau = iwork; + iwork = itau + irows; + i__1 = *lwork + 1 - iwork; + dgeqrf_(&irows, &icols, &b[ilo + ilo * b_dim1], ldb, &work[itau], &work[ + iwork], &i__1, &iinfo); + if (iinfo >= 0) { +/* Computing MAX */ + i__1 = lwkopt, i__2 = (integer) work[iwork] + iwork - 1; + lwkopt = max(i__1,i__2); + } + if (iinfo != 0) { + *info = *n + 2; + goto L120; + } + + i__1 = *lwork + 1 - iwork; + dormqr_("L", "T", &irows, &icols, &irows, &b[ilo + ilo * b_dim1], ldb, & + work[itau], &a[ilo + ilo * a_dim1], lda, &work[iwork], &i__1, & + iinfo); + if (iinfo >= 0) { +/* Computing MAX */ + i__1 = lwkopt, i__2 = (integer) work[iwork] + iwork - 1; + lwkopt = max(i__1,i__2); + } + if (iinfo != 0) { + *info = *n + 3; + goto L120; + } + + if (ilvl) { + dlaset_("Full", n, n, &c_b38, &c_b27, &vl[vl_offset], ldvl) + ; + i__1 = irows - 1; + i__2 = irows - 1; + dlacpy_("L", &i__1, &i__2, &b[ilo + 1 + ilo * b_dim1], ldb, &vl[ilo + + 1 + ilo * vl_dim1], ldvl); + i__1 = *lwork + 1 - iwork; + dorgqr_(&irows, &irows, &irows, &vl[ilo + ilo * vl_dim1], ldvl, &work[ + itau], &work[iwork], &i__1, &iinfo); + if (iinfo >= 0) { +/* Computing MAX */ + i__1 = lwkopt, i__2 = (integer) work[iwork] + iwork - 1; + lwkopt = max(i__1,i__2); + } + if (iinfo != 0) { + *info = *n + 4; + goto L120; + } + } + + if (ilvr) { + dlaset_("Full", n, n, &c_b38, &c_b27, &vr[vr_offset], ldvr) + ; + } + +/* Reduce to generalized Hessenberg form */ + + if (ilv) { + +/* Eigenvectors requested -- work on whole matrix. */ + + dgghrd_(jobvl, jobvr, n, &ilo, &ihi, &a[a_offset], lda, &b[b_offset], + ldb, &vl[vl_offset], ldvl, &vr[vr_offset], ldvr, &iinfo); + } else { + dgghrd_("N", "N", &irows, &c__1, &irows, &a[ilo + ilo * a_dim1], lda, + &b[ilo + ilo * b_dim1], ldb, &vl[vl_offset], ldvl, &vr[ + vr_offset], ldvr, &iinfo); + } + if (iinfo != 0) { + *info = *n + 5; + goto L120; + } + +/* Perform QZ algorithm */ +/* Workspace layout: ("work..." must have at least 1 word) */ +/* left_permutation, right_permutation, work... */ + + iwork = itau; + if (ilv) { + *(unsigned char *)chtemp = 'S'; + } else { + *(unsigned char *)chtemp = 'E'; + } + i__1 = *lwork + 1 - iwork; + dhgeqz_(chtemp, jobvl, jobvr, n, &ilo, &ihi, &a[a_offset], lda, &b[ + b_offset], ldb, &alphar[1], &alphai[1], &beta[1], &vl[vl_offset], + ldvl, &vr[vr_offset], ldvr, &work[iwork], &i__1, &iinfo); + if (iinfo >= 0) { +/* Computing MAX */ + i__1 = lwkopt, i__2 = (integer) work[iwork] + iwork - 1; + lwkopt = max(i__1,i__2); + } + if (iinfo != 0) { + if (iinfo > 0 && iinfo <= *n) { + *info = iinfo; + } else if (iinfo > *n && iinfo <= *n << 1) { + *info = iinfo - *n; + } else { + *info = *n + 6; + } + goto L120; + } + + if (ilv) { + +/* Compute Eigenvectors (DTGEVC requires 6*N words of workspace) */ + + if (ilvl) { + if (ilvr) { + *(unsigned char *)chtemp = 'B'; + } else { + *(unsigned char *)chtemp = 'L'; + } + } else { + *(unsigned char *)chtemp = 'R'; + } + + dtgevc_(chtemp, "B", ldumma, n, &a[a_offset], lda, &b[b_offset], ldb, + &vl[vl_offset], ldvl, &vr[vr_offset], ldvr, n, &in, &work[ + iwork], &iinfo); + if (iinfo != 0) { + *info = *n + 7; + goto L120; + } + +/* Undo balancing on VL and VR, rescale */ + + if (ilvl) { + dggbak_("P", "L", n, &ilo, &ihi, &work[ileft], &work[iright], n, & + vl[vl_offset], ldvl, &iinfo); + if (iinfo != 0) { + *info = *n + 8; + goto L120; + } + i__1 = *n; + for (jc = 1; jc <= i__1; ++jc) { + if (alphai[jc] < 0.) { + goto L50; + } + temp = 0.; + if (alphai[jc] == 0.) { + i__2 = *n; + for (jr = 1; jr <= i__2; ++jr) { +/* Computing MAX */ + d__2 = temp, d__3 = (d__1 = vl[jr + jc * vl_dim1], + abs(d__1)); + temp = max(d__2,d__3); +/* L10: */ + } + } else { + i__2 = *n; + for (jr = 1; jr <= i__2; ++jr) { +/* Computing MAX */ + d__3 = temp, d__4 = (d__1 = vl[jr + jc * vl_dim1], + abs(d__1)) + (d__2 = vl[jr + (jc + 1) * + vl_dim1], abs(d__2)); + temp = max(d__3,d__4); +/* L20: */ + } + } + if (temp < safmin) { + goto L50; + } + temp = 1. / temp; + if (alphai[jc] == 0.) { + i__2 = *n; + for (jr = 1; jr <= i__2; ++jr) { + vl[jr + jc * vl_dim1] *= temp; +/* L30: */ + } + } else { + i__2 = *n; + for (jr = 1; jr <= i__2; ++jr) { + vl[jr + jc * vl_dim1] *= temp; + vl[jr + (jc + 1) * vl_dim1] *= temp; +/* L40: */ + } + } +L50: + ; + } + } + if (ilvr) { + dggbak_("P", "R", n, &ilo, &ihi, &work[ileft], &work[iright], n, & + vr[vr_offset], ldvr, &iinfo); + if (iinfo != 0) { + *info = *n + 9; + goto L120; + } + i__1 = *n; + for (jc = 1; jc <= i__1; ++jc) { + if (alphai[jc] < 0.) { + goto L100; + } + temp = 0.; + if (alphai[jc] == 0.) { + i__2 = *n; + for (jr = 1; jr <= i__2; ++jr) { +/* Computing MAX */ + d__2 = temp, d__3 = (d__1 = vr[jr + jc * vr_dim1], + abs(d__1)); + temp = max(d__2,d__3); +/* L60: */ + } + } else { + i__2 = *n; + for (jr = 1; jr <= i__2; ++jr) { +/* Computing MAX */ + d__3 = temp, d__4 = (d__1 = vr[jr + jc * vr_dim1], + abs(d__1)) + (d__2 = vr[jr + (jc + 1) * + vr_dim1], abs(d__2)); + temp = max(d__3,d__4); +/* L70: */ + } + } + if (temp < safmin) { + goto L100; + } + temp = 1. / temp; + if (alphai[jc] == 0.) { + i__2 = *n; + for (jr = 1; jr <= i__2; ++jr) { + vr[jr + jc * vr_dim1] *= temp; +/* L80: */ + } + } else { + i__2 = *n; + for (jr = 1; jr <= i__2; ++jr) { + vr[jr + jc * vr_dim1] *= temp; + vr[jr + (jc + 1) * vr_dim1] *= temp; +/* L90: */ + } + } +L100: + ; + } + } + +/* End of eigenvector calculation */ + + } + +/* Undo scaling in alpha, beta */ + +/* Note: this does not give the alpha and beta for the unscaled */ +/* problem. */ + +/* Un-scaling is limited to avoid underflow in alpha and beta */ +/* if they are significant. */ + + i__1 = *n; + for (jc = 1; jc <= i__1; ++jc) { + absar = (d__1 = alphar[jc], abs(d__1)); + absai = (d__1 = alphai[jc], abs(d__1)); + absb = (d__1 = beta[jc], abs(d__1)); + salfar = anrm * alphar[jc]; + salfai = anrm * alphai[jc]; + sbeta = bnrm * beta[jc]; + ilimit = FALSE_; + scale = 1.; + +/* Check for significant underflow in ALPHAI */ + +/* Computing MAX */ + d__1 = safmin, d__2 = eps * absar, d__1 = max(d__1,d__2), d__2 = eps * + absb; + if (abs(salfai) < safmin && absai >= max(d__1,d__2)) { + ilimit = TRUE_; +/* Computing MAX */ + d__1 = onepls * safmin, d__2 = anrm2 * absai; + scale = onepls * safmin / anrm1 / max(d__1,d__2); + + } else if (salfai == 0.) { + +/* If insignificant underflow in ALPHAI, then make the */ +/* conjugate eigenvalue real. */ + + if (alphai[jc] < 0. && jc > 1) { + alphai[jc - 1] = 0.; + } else if (alphai[jc] > 0. && jc < *n) { + alphai[jc + 1] = 0.; + } + } + +/* Check for significant underflow in ALPHAR */ + +/* Computing MAX */ + d__1 = safmin, d__2 = eps * absai, d__1 = max(d__1,d__2), d__2 = eps * + absb; + if (abs(salfar) < safmin && absar >= max(d__1,d__2)) { + ilimit = TRUE_; +/* Computing MAX */ +/* Computing MAX */ + d__3 = onepls * safmin, d__4 = anrm2 * absar; + d__1 = scale, d__2 = onepls * safmin / anrm1 / max(d__3,d__4); + scale = max(d__1,d__2); + } + +/* Check for significant underflow in BETA */ + +/* Computing MAX */ + d__1 = safmin, d__2 = eps * absar, d__1 = max(d__1,d__2), d__2 = eps * + absai; + if (abs(sbeta) < safmin && absb >= max(d__1,d__2)) { + ilimit = TRUE_; +/* Computing MAX */ +/* Computing MAX */ + d__3 = onepls * safmin, d__4 = bnrm2 * absb; + d__1 = scale, d__2 = onepls * safmin / bnrm1 / max(d__3,d__4); + scale = max(d__1,d__2); + } + +/* Check for possible overflow when limiting scaling */ + + if (ilimit) { +/* Computing MAX */ + d__1 = abs(salfar), d__2 = abs(salfai), d__1 = max(d__1,d__2), + d__2 = abs(sbeta); + temp = scale * safmin * max(d__1,d__2); + if (temp > 1.) { + scale /= temp; + } + if (scale < 1.) { + ilimit = FALSE_; + } + } + +/* Recompute un-scaled ALPHAR, ALPHAI, BETA if necessary. */ + + if (ilimit) { + salfar = scale * alphar[jc] * anrm; + salfai = scale * alphai[jc] * anrm; + sbeta = scale * beta[jc] * bnrm; + } + alphar[jc] = salfar; + alphai[jc] = salfai; + beta[jc] = sbeta; +/* L110: */ + } + +L120: + work[1] = (doublereal) lwkopt; + + return 0; + +/* End of DGEGV */ + +} /* dgegv_ */ |