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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/dtgevc.c | |
parent | 01f64c1ecd0d4ffa9e3a74478335f1745f26cc75 (diff) | |
download | ydb-90d450f74722da7859d6f510a869f6c6908fd12f.tar.gz |
[] add metering mode to CLI
Diffstat (limited to 'contrib/libs/clapack/dtgevc.c')
-rw-r--r-- | contrib/libs/clapack/dtgevc.c | 1418 |
1 files changed, 1418 insertions, 0 deletions
diff --git a/contrib/libs/clapack/dtgevc.c b/contrib/libs/clapack/dtgevc.c new file mode 100644 index 0000000000..e411ffcb0b --- /dev/null +++ b/contrib/libs/clapack/dtgevc.c @@ -0,0 +1,1418 @@ +/* dtgevc.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 logical c_true = TRUE_; +static integer c__2 = 2; +static doublereal c_b34 = 1.; +static integer c__1 = 1; +static doublereal c_b36 = 0.; +static logical c_false = FALSE_; + +/* Subroutine */ int dtgevc_(char *side, char *howmny, logical *select, + integer *n, doublereal *s, integer *lds, doublereal *p, integer *ldp, + doublereal *vl, integer *ldvl, doublereal *vr, integer *ldvr, integer + *mm, integer *m, doublereal *work, integer *info) +{ + /* System generated locals */ + integer p_dim1, p_offset, s_dim1, s_offset, vl_dim1, vl_offset, vr_dim1, + vr_offset, i__1, i__2, i__3, i__4, i__5; + doublereal d__1, d__2, d__3, d__4, d__5, d__6; + + /* Local variables */ + integer i__, j, ja, jc, je, na, im, jr, jw, nw; + doublereal big; + logical lsa, lsb; + doublereal ulp, sum[4] /* was [2][2] */; + integer ibeg, ieig, iend; + doublereal dmin__, temp, xmax, sump[4] /* was [2][2] */, sums[4] + /* was [2][2] */; + extern /* Subroutine */ int dlag2_(doublereal *, integer *, doublereal *, + integer *, doublereal *, doublereal *, doublereal *, doublereal *, + doublereal *, doublereal *); + doublereal cim2a, cim2b, cre2a, cre2b, temp2, bdiag[2], acoef, scale; + logical ilall; + integer iside; + doublereal sbeta; + extern logical lsame_(char *, char *); + extern /* Subroutine */ int dgemv_(char *, integer *, integer *, + doublereal *, doublereal *, integer *, doublereal *, integer *, + doublereal *, doublereal *, integer *); + logical il2by2; + integer iinfo; + doublereal small; + logical compl; + doublereal anorm, bnorm; + logical compr; + extern /* Subroutine */ int dlaln2_(logical *, integer *, integer *, + doublereal *, doublereal *, doublereal *, integer *, doublereal *, + doublereal *, doublereal *, integer *, doublereal *, doublereal * +, doublereal *, integer *, doublereal *, doublereal *, integer *); + doublereal temp2i; + extern /* Subroutine */ int dlabad_(doublereal *, doublereal *); + doublereal temp2r; + logical ilabad, ilbbad; + doublereal acoefa, bcoefa, cimaga, cimagb; + logical ilback; + doublereal bcoefi, ascale, bscale, creala, crealb; + extern doublereal dlamch_(char *); + doublereal bcoefr, salfar, safmin; + extern /* Subroutine */ int dlacpy_(char *, integer *, integer *, + doublereal *, integer *, doublereal *, integer *); + doublereal xscale, bignum; + extern /* Subroutine */ int xerbla_(char *, integer *); + logical ilcomp, ilcplx; + integer ihwmny; + + +/* -- LAPACK routine (version 3.2) -- */ +/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ +/* November 2006 */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + + +/* Purpose */ +/* ======= */ + +/* DTGEVC computes some or all of the right and/or left eigenvectors of */ +/* a pair of real matrices (S,P), where S is a quasi-triangular matrix */ +/* and P is upper triangular. Matrix pairs of this type are produced by */ +/* the generalized Schur factorization of a matrix pair (A,B): */ + +/* A = Q*S*Z**T, B = Q*P*Z**T */ + +/* as computed by DGGHRD + DHGEQZ. */ + +/* The right eigenvector x and the left eigenvector y of (S,P) */ +/* corresponding to an eigenvalue w are defined by: */ + +/* S*x = w*P*x, (y**H)*S = w*(y**H)*P, */ + +/* where y**H denotes the conjugate tranpose of y. */ +/* The eigenvalues are not input to this routine, but are computed */ +/* directly from the diagonal blocks of S and P. */ + +/* This routine returns the matrices X and/or Y of right and left */ +/* eigenvectors of (S,P), or the products Z*X and/or Q*Y, */ +/* where Z and Q are input matrices. */ +/* If Q and Z are the orthogonal factors from the generalized Schur */ +/* factorization of a matrix pair (A,B), then Z*X and Q*Y */ +/* are the matrices of right and left eigenvectors of (A,B). */ + +/* Arguments */ +/* ========= */ + +/* SIDE (input) CHARACTER*1 */ +/* = 'R': compute right eigenvectors only; */ +/* = 'L': compute left eigenvectors only; */ +/* = 'B': compute both right and left eigenvectors. */ + +/* HOWMNY (input) CHARACTER*1 */ +/* = 'A': compute all right and/or left eigenvectors; */ +/* = 'B': compute all right and/or left eigenvectors, */ +/* backtransformed by the matrices in VR and/or VL; */ +/* = 'S': compute selected right and/or left eigenvectors, */ +/* specified by the logical array SELECT. */ + +/* SELECT (input) LOGICAL array, dimension (N) */ +/* If HOWMNY='S', SELECT specifies the eigenvectors to be */ +/* computed. If w(j) is a real eigenvalue, the corresponding */ +/* real eigenvector is computed if SELECT(j) is .TRUE.. */ +/* If w(j) and w(j+1) are the real and imaginary parts of a */ +/* complex eigenvalue, the corresponding complex eigenvector */ +/* is computed if either SELECT(j) or SELECT(j+1) is .TRUE., */ +/* and on exit SELECT(j) is set to .TRUE. and SELECT(j+1) is */ +/* set to .FALSE.. */ +/* Not referenced if HOWMNY = 'A' or 'B'. */ + +/* N (input) INTEGER */ +/* The order of the matrices S and P. N >= 0. */ + +/* S (input) DOUBLE PRECISION array, dimension (LDS,N) */ +/* The upper quasi-triangular matrix S from a generalized Schur */ +/* factorization, as computed by DHGEQZ. */ + +/* LDS (input) INTEGER */ +/* The leading dimension of array S. LDS >= max(1,N). */ + +/* P (input) DOUBLE PRECISION array, dimension (LDP,N) */ +/* The upper triangular matrix P from a generalized Schur */ +/* factorization, as computed by DHGEQZ. */ +/* 2-by-2 diagonal blocks of P corresponding to 2-by-2 blocks */ +/* of S must be in positive diagonal form. */ + +/* LDP (input) INTEGER */ +/* The leading dimension of array P. LDP >= max(1,N). */ + +/* VL (input/output) DOUBLE PRECISION array, dimension (LDVL,MM) */ +/* On entry, if SIDE = 'L' or 'B' and HOWMNY = 'B', VL must */ +/* contain an N-by-N matrix Q (usually the orthogonal matrix Q */ +/* of left Schur vectors returned by DHGEQZ). */ +/* On exit, if SIDE = 'L' or 'B', VL contains: */ +/* if HOWMNY = 'A', the matrix Y of left eigenvectors of (S,P); */ +/* if HOWMNY = 'B', the matrix Q*Y; */ +/* if HOWMNY = 'S', the left eigenvectors of (S,P) specified by */ +/* SELECT, stored consecutively in the columns of */ +/* VL, in the same order as their eigenvalues. */ + +/* A complex eigenvector corresponding to a complex eigenvalue */ +/* is stored in two consecutive columns, the first holding the */ +/* real part, and the second the imaginary part. */ + +/* Not referenced if SIDE = 'R'. */ + +/* LDVL (input) INTEGER */ +/* The leading dimension of array VL. LDVL >= 1, and if */ +/* SIDE = 'L' or 'B', LDVL >= N. */ + +/* VR (input/output) DOUBLE PRECISION array, dimension (LDVR,MM) */ +/* On entry, if SIDE = 'R' or 'B' and HOWMNY = 'B', VR must */ +/* contain an N-by-N matrix Z (usually the orthogonal matrix Z */ +/* of right Schur vectors returned by DHGEQZ). */ + +/* On exit, if SIDE = 'R' or 'B', VR contains: */ +/* if HOWMNY = 'A', the matrix X of right eigenvectors of (S,P); */ +/* if HOWMNY = 'B' or 'b', the matrix Z*X; */ +/* if HOWMNY = 'S' or 's', the right eigenvectors of (S,P) */ +/* specified by SELECT, stored consecutively in the */ +/* columns of VR, in the same order as their */ +/* eigenvalues. */ + +/* A complex eigenvector corresponding to a complex eigenvalue */ +/* is stored in two consecutive columns, the first holding the */ +/* real part and the second the imaginary part. */ + +/* Not referenced if SIDE = 'L'. */ + +/* LDVR (input) INTEGER */ +/* The leading dimension of the array VR. LDVR >= 1, and if */ +/* SIDE = 'R' or 'B', LDVR >= N. */ + +/* MM (input) INTEGER */ +/* The number of columns in the arrays VL and/or VR. MM >= M. */ + +/* M (output) INTEGER */ +/* The number of columns in the arrays VL and/or VR actually */ +/* used to store the eigenvectors. If HOWMNY = 'A' or 'B', M */ +/* is set to N. Each selected real eigenvector occupies one */ +/* column and each selected complex eigenvector occupies two */ +/* columns. */ + +/* WORK (workspace) DOUBLE PRECISION array, dimension (6*N) */ + +/* INFO (output) INTEGER */ +/* = 0: successful exit. */ +/* < 0: if INFO = -i, the i-th argument had an illegal value. */ +/* > 0: the 2-by-2 block (INFO:INFO+1) does not have a complex */ +/* eigenvalue. */ + +/* Further Details */ +/* =============== */ + +/* Allocation of workspace: */ +/* ---------- -- --------- */ + +/* WORK( j ) = 1-norm of j-th column of A, above the diagonal */ +/* WORK( N+j ) = 1-norm of j-th column of B, above the diagonal */ +/* WORK( 2*N+1:3*N ) = real part of eigenvector */ +/* WORK( 3*N+1:4*N ) = imaginary part of eigenvector */ +/* WORK( 4*N+1:5*N ) = real part of back-transformed eigenvector */ +/* WORK( 5*N+1:6*N ) = imaginary part of back-transformed eigenvector */ + +/* Rowwise vs. columnwise solution methods: */ +/* ------- -- ---------- -------- ------- */ + +/* Finding a generalized eigenvector consists basically of solving the */ +/* singular triangular system */ + +/* (A - w B) x = 0 (for right) or: (A - w B)**H y = 0 (for left) */ + +/* Consider finding the i-th right eigenvector (assume all eigenvalues */ +/* are real). The equation to be solved is: */ +/* n i */ +/* 0 = sum C(j,k) v(k) = sum C(j,k) v(k) for j = i,. . .,1 */ +/* k=j k=j */ + +/* where C = (A - w B) (The components v(i+1:n) are 0.) */ + +/* The "rowwise" method is: */ + +/* (1) v(i) := 1 */ +/* for j = i-1,. . .,1: */ +/* i */ +/* (2) compute s = - sum C(j,k) v(k) and */ +/* k=j+1 */ + +/* (3) v(j) := s / C(j,j) */ + +/* Step 2 is sometimes called the "dot product" step, since it is an */ +/* inner product between the j-th row and the portion of the eigenvector */ +/* that has been computed so far. */ + +/* The "columnwise" method consists basically in doing the sums */ +/* for all the rows in parallel. As each v(j) is computed, the */ +/* contribution of v(j) times the j-th column of C is added to the */ +/* partial sums. Since FORTRAN arrays are stored columnwise, this has */ +/* the advantage that at each step, the elements of C that are accessed */ +/* are adjacent to one another, whereas with the rowwise method, the */ +/* elements accessed at a step are spaced LDS (and LDP) words apart. */ + +/* When finding left eigenvectors, the matrix in question is the */ +/* transpose of the one in storage, so the rowwise method then */ +/* actually accesses columns of A and B at each step, and so is the */ +/* preferred method. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. Local Arrays .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Decode and Test the input parameters */ + + /* Parameter adjustments */ + --select; + s_dim1 = *lds; + s_offset = 1 + s_dim1; + s -= s_offset; + p_dim1 = *ldp; + p_offset = 1 + p_dim1; + p -= p_offset; + 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_(howmny, "A")) { + ihwmny = 1; + ilall = TRUE_; + ilback = FALSE_; + } else if (lsame_(howmny, "S")) { + ihwmny = 2; + ilall = FALSE_; + ilback = FALSE_; + } else if (lsame_(howmny, "B")) { + ihwmny = 3; + ilall = TRUE_; + ilback = TRUE_; + } else { + ihwmny = -1; + ilall = TRUE_; + } + + if (lsame_(side, "R")) { + iside = 1; + compl = FALSE_; + compr = TRUE_; + } else if (lsame_(side, "L")) { + iside = 2; + compl = TRUE_; + compr = FALSE_; + } else if (lsame_(side, "B")) { + iside = 3; + compl = TRUE_; + compr = TRUE_; + } else { + iside = -1; + } + + *info = 0; + if (iside < 0) { + *info = -1; + } else if (ihwmny < 0) { + *info = -2; + } else if (*n < 0) { + *info = -4; + } else if (*lds < max(1,*n)) { + *info = -6; + } else if (*ldp < max(1,*n)) { + *info = -8; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_("DTGEVC", &i__1); + return 0; + } + +/* Count the number of eigenvectors to be computed */ + + if (! ilall) { + im = 0; + ilcplx = FALSE_; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (ilcplx) { + ilcplx = FALSE_; + goto L10; + } + if (j < *n) { + if (s[j + 1 + j * s_dim1] != 0.) { + ilcplx = TRUE_; + } + } + if (ilcplx) { + if (select[j] || select[j + 1]) { + im += 2; + } + } else { + if (select[j]) { + ++im; + } + } +L10: + ; + } + } else { + im = *n; + } + +/* Check 2-by-2 diagonal blocks of A, B */ + + ilabad = FALSE_; + ilbbad = FALSE_; + i__1 = *n - 1; + for (j = 1; j <= i__1; ++j) { + if (s[j + 1 + j * s_dim1] != 0.) { + if (p[j + j * p_dim1] == 0. || p[j + 1 + (j + 1) * p_dim1] == 0. + || p[j + (j + 1) * p_dim1] != 0.) { + ilbbad = TRUE_; + } + if (j < *n - 1) { + if (s[j + 2 + (j + 1) * s_dim1] != 0.) { + ilabad = TRUE_; + } + } + } +/* L20: */ + } + + if (ilabad) { + *info = -5; + } else if (ilbbad) { + *info = -7; + } else if (compl && *ldvl < *n || *ldvl < 1) { + *info = -10; + } else if (compr && *ldvr < *n || *ldvr < 1) { + *info = -12; + } else if (*mm < im) { + *info = -13; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_("DTGEVC", &i__1); + return 0; + } + +/* Quick return if possible */ + + *m = im; + if (*n == 0) { + return 0; + } + +/* Machine Constants */ + + safmin = dlamch_("Safe minimum"); + big = 1. / safmin; + dlabad_(&safmin, &big); + ulp = dlamch_("Epsilon") * dlamch_("Base"); + small = safmin * *n / ulp; + big = 1. / small; + bignum = 1. / (safmin * *n); + +/* Compute the 1-norm of each column of the strictly upper triangular */ +/* part (i.e., excluding all elements belonging to the diagonal */ +/* blocks) of A and B to check for possible overflow in the */ +/* triangular solver. */ + + anorm = (d__1 = s[s_dim1 + 1], abs(d__1)); + if (*n > 1) { + anorm += (d__1 = s[s_dim1 + 2], abs(d__1)); + } + bnorm = (d__1 = p[p_dim1 + 1], abs(d__1)); + work[1] = 0.; + work[*n + 1] = 0.; + + i__1 = *n; + for (j = 2; j <= i__1; ++j) { + temp = 0.; + temp2 = 0.; + if (s[j + (j - 1) * s_dim1] == 0.) { + iend = j - 1; + } else { + iend = j - 2; + } + i__2 = iend; + for (i__ = 1; i__ <= i__2; ++i__) { + temp += (d__1 = s[i__ + j * s_dim1], abs(d__1)); + temp2 += (d__1 = p[i__ + j * p_dim1], abs(d__1)); +/* L30: */ + } + work[j] = temp; + work[*n + j] = temp2; +/* Computing MIN */ + i__3 = j + 1; + i__2 = min(i__3,*n); + for (i__ = iend + 1; i__ <= i__2; ++i__) { + temp += (d__1 = s[i__ + j * s_dim1], abs(d__1)); + temp2 += (d__1 = p[i__ + j * p_dim1], abs(d__1)); +/* L40: */ + } + anorm = max(anorm,temp); + bnorm = max(bnorm,temp2); +/* L50: */ + } + + ascale = 1. / max(anorm,safmin); + bscale = 1. / max(bnorm,safmin); + +/* Left eigenvectors */ + + if (compl) { + ieig = 0; + +/* Main loop over eigenvalues */ + + ilcplx = FALSE_; + i__1 = *n; + for (je = 1; je <= i__1; ++je) { + +/* Skip this iteration if (a) HOWMNY='S' and SELECT=.FALSE., or */ +/* (b) this would be the second of a complex pair. */ +/* Check for complex eigenvalue, so as to be sure of which */ +/* entry(-ies) of SELECT to look at. */ + + if (ilcplx) { + ilcplx = FALSE_; + goto L220; + } + nw = 1; + if (je < *n) { + if (s[je + 1 + je * s_dim1] != 0.) { + ilcplx = TRUE_; + nw = 2; + } + } + if (ilall) { + ilcomp = TRUE_; + } else if (ilcplx) { + ilcomp = select[je] || select[je + 1]; + } else { + ilcomp = select[je]; + } + if (! ilcomp) { + goto L220; + } + +/* Decide if (a) singular pencil, (b) real eigenvalue, or */ +/* (c) complex eigenvalue. */ + + if (! ilcplx) { + if ((d__1 = s[je + je * s_dim1], abs(d__1)) <= safmin && ( + d__2 = p[je + je * p_dim1], abs(d__2)) <= safmin) { + +/* Singular matrix pencil -- return unit eigenvector */ + + ++ieig; + i__2 = *n; + for (jr = 1; jr <= i__2; ++jr) { + vl[jr + ieig * vl_dim1] = 0.; +/* L60: */ + } + vl[ieig + ieig * vl_dim1] = 1.; + goto L220; + } + } + +/* Clear vector */ + + i__2 = nw * *n; + for (jr = 1; jr <= i__2; ++jr) { + work[(*n << 1) + jr] = 0.; +/* L70: */ + } +/* T */ +/* Compute coefficients in ( a A - b B ) y = 0 */ +/* a is ACOEF */ +/* b is BCOEFR + i*BCOEFI */ + + if (! ilcplx) { + +/* Real eigenvalue */ + +/* Computing MAX */ + d__3 = (d__1 = s[je + je * s_dim1], abs(d__1)) * ascale, d__4 + = (d__2 = p[je + je * p_dim1], abs(d__2)) * bscale, + d__3 = max(d__3,d__4); + temp = 1. / max(d__3,safmin); + salfar = temp * s[je + je * s_dim1] * ascale; + sbeta = temp * p[je + je * p_dim1] * bscale; + acoef = sbeta * ascale; + bcoefr = salfar * bscale; + bcoefi = 0.; + +/* Scale to avoid underflow */ + + scale = 1.; + lsa = abs(sbeta) >= safmin && abs(acoef) < small; + lsb = abs(salfar) >= safmin && abs(bcoefr) < small; + if (lsa) { + scale = small / abs(sbeta) * min(anorm,big); + } + if (lsb) { +/* Computing MAX */ + d__1 = scale, d__2 = small / abs(salfar) * min(bnorm,big); + scale = max(d__1,d__2); + } + if (lsa || lsb) { +/* Computing MIN */ +/* Computing MAX */ + d__3 = 1., d__4 = abs(acoef), d__3 = max(d__3,d__4), d__4 + = abs(bcoefr); + d__1 = scale, d__2 = 1. / (safmin * max(d__3,d__4)); + scale = min(d__1,d__2); + if (lsa) { + acoef = ascale * (scale * sbeta); + } else { + acoef = scale * acoef; + } + if (lsb) { + bcoefr = bscale * (scale * salfar); + } else { + bcoefr = scale * bcoefr; + } + } + acoefa = abs(acoef); + bcoefa = abs(bcoefr); + +/* First component is 1 */ + + work[(*n << 1) + je] = 1.; + xmax = 1.; + } else { + +/* Complex eigenvalue */ + + d__1 = safmin * 100.; + dlag2_(&s[je + je * s_dim1], lds, &p[je + je * p_dim1], ldp, & + d__1, &acoef, &temp, &bcoefr, &temp2, &bcoefi); + bcoefi = -bcoefi; + if (bcoefi == 0.) { + *info = je; + return 0; + } + +/* Scale to avoid over/underflow */ + + acoefa = abs(acoef); + bcoefa = abs(bcoefr) + abs(bcoefi); + scale = 1.; + if (acoefa * ulp < safmin && acoefa >= safmin) { + scale = safmin / ulp / acoefa; + } + if (bcoefa * ulp < safmin && bcoefa >= safmin) { +/* Computing MAX */ + d__1 = scale, d__2 = safmin / ulp / bcoefa; + scale = max(d__1,d__2); + } + if (safmin * acoefa > ascale) { + scale = ascale / (safmin * acoefa); + } + if (safmin * bcoefa > bscale) { +/* Computing MIN */ + d__1 = scale, d__2 = bscale / (safmin * bcoefa); + scale = min(d__1,d__2); + } + if (scale != 1.) { + acoef = scale * acoef; + acoefa = abs(acoef); + bcoefr = scale * bcoefr; + bcoefi = scale * bcoefi; + bcoefa = abs(bcoefr) + abs(bcoefi); + } + +/* Compute first two components of eigenvector */ + + temp = acoef * s[je + 1 + je * s_dim1]; + temp2r = acoef * s[je + je * s_dim1] - bcoefr * p[je + je * + p_dim1]; + temp2i = -bcoefi * p[je + je * p_dim1]; + if (abs(temp) > abs(temp2r) + abs(temp2i)) { + work[(*n << 1) + je] = 1.; + work[*n * 3 + je] = 0.; + work[(*n << 1) + je + 1] = -temp2r / temp; + work[*n * 3 + je + 1] = -temp2i / temp; + } else { + work[(*n << 1) + je + 1] = 1.; + work[*n * 3 + je + 1] = 0.; + temp = acoef * s[je + (je + 1) * s_dim1]; + work[(*n << 1) + je] = (bcoefr * p[je + 1 + (je + 1) * + p_dim1] - acoef * s[je + 1 + (je + 1) * s_dim1]) / + temp; + work[*n * 3 + je] = bcoefi * p[je + 1 + (je + 1) * p_dim1] + / temp; + } +/* Computing MAX */ + d__5 = (d__1 = work[(*n << 1) + je], abs(d__1)) + (d__2 = + work[*n * 3 + je], abs(d__2)), d__6 = (d__3 = work[(* + n << 1) + je + 1], abs(d__3)) + (d__4 = work[*n * 3 + + je + 1], abs(d__4)); + xmax = max(d__5,d__6); + } + +/* Computing MAX */ + d__1 = ulp * acoefa * anorm, d__2 = ulp * bcoefa * bnorm, d__1 = + max(d__1,d__2); + dmin__ = max(d__1,safmin); + +/* T */ +/* Triangular solve of (a A - b B) y = 0 */ + +/* T */ +/* (rowwise in (a A - b B) , or columnwise in (a A - b B) ) */ + + il2by2 = FALSE_; + + i__2 = *n; + for (j = je + nw; j <= i__2; ++j) { + if (il2by2) { + il2by2 = FALSE_; + goto L160; + } + + na = 1; + bdiag[0] = p[j + j * p_dim1]; + if (j < *n) { + if (s[j + 1 + j * s_dim1] != 0.) { + il2by2 = TRUE_; + bdiag[1] = p[j + 1 + (j + 1) * p_dim1]; + na = 2; + } + } + +/* Check whether scaling is necessary for dot products */ + + xscale = 1. / max(1.,xmax); +/* Computing MAX */ + d__1 = work[j], d__2 = work[*n + j], d__1 = max(d__1,d__2), + d__2 = acoefa * work[j] + bcoefa * work[*n + j]; + temp = max(d__1,d__2); + if (il2by2) { +/* Computing MAX */ + d__1 = temp, d__2 = work[j + 1], d__1 = max(d__1,d__2), + d__2 = work[*n + j + 1], d__1 = max(d__1,d__2), + d__2 = acoefa * work[j + 1] + bcoefa * work[*n + + j + 1]; + temp = max(d__1,d__2); + } + if (temp > bignum * xscale) { + i__3 = nw - 1; + for (jw = 0; jw <= i__3; ++jw) { + i__4 = j - 1; + for (jr = je; jr <= i__4; ++jr) { + work[(jw + 2) * *n + jr] = xscale * work[(jw + 2) + * *n + jr]; +/* L80: */ + } +/* L90: */ + } + xmax *= xscale; + } + +/* Compute dot products */ + +/* j-1 */ +/* SUM = sum conjg( a*S(k,j) - b*P(k,j) )*x(k) */ +/* k=je */ + +/* To reduce the op count, this is done as */ + +/* _ j-1 _ j-1 */ +/* a*conjg( sum S(k,j)*x(k) ) - b*conjg( sum P(k,j)*x(k) ) */ +/* k=je k=je */ + +/* which may cause underflow problems if A or B are close */ +/* to underflow. (E.g., less than SMALL.) */ + + +/* A series of compiler directives to defeat vectorization */ +/* for the next loop */ + +/* $PL$ CMCHAR=' ' */ +/* DIR$ NEXTSCALAR */ +/* $DIR SCALAR */ +/* DIR$ NEXT SCALAR */ +/* VD$L NOVECTOR */ +/* DEC$ NOVECTOR */ +/* VD$ NOVECTOR */ +/* VDIR NOVECTOR */ +/* VOCL LOOP,SCALAR */ +/* IBM PREFER SCALAR */ +/* $PL$ CMCHAR='*' */ + + i__3 = nw; + for (jw = 1; jw <= i__3; ++jw) { + +/* $PL$ CMCHAR=' ' */ +/* DIR$ NEXTSCALAR */ +/* $DIR SCALAR */ +/* DIR$ NEXT SCALAR */ +/* VD$L NOVECTOR */ +/* DEC$ NOVECTOR */ +/* VD$ NOVECTOR */ +/* VDIR NOVECTOR */ +/* VOCL LOOP,SCALAR */ +/* IBM PREFER SCALAR */ +/* $PL$ CMCHAR='*' */ + + i__4 = na; + for (ja = 1; ja <= i__4; ++ja) { + sums[ja + (jw << 1) - 3] = 0.; + sump[ja + (jw << 1) - 3] = 0.; + + i__5 = j - 1; + for (jr = je; jr <= i__5; ++jr) { + sums[ja + (jw << 1) - 3] += s[jr + (j + ja - 1) * + s_dim1] * work[(jw + 1) * *n + jr]; + sump[ja + (jw << 1) - 3] += p[jr + (j + ja - 1) * + p_dim1] * work[(jw + 1) * *n + jr]; +/* L100: */ + } +/* L110: */ + } +/* L120: */ + } + +/* $PL$ CMCHAR=' ' */ +/* DIR$ NEXTSCALAR */ +/* $DIR SCALAR */ +/* DIR$ NEXT SCALAR */ +/* VD$L NOVECTOR */ +/* DEC$ NOVECTOR */ +/* VD$ NOVECTOR */ +/* VDIR NOVECTOR */ +/* VOCL LOOP,SCALAR */ +/* IBM PREFER SCALAR */ +/* $PL$ CMCHAR='*' */ + + i__3 = na; + for (ja = 1; ja <= i__3; ++ja) { + if (ilcplx) { + sum[ja - 1] = -acoef * sums[ja - 1] + bcoefr * sump[ + ja - 1] - bcoefi * sump[ja + 1]; + sum[ja + 1] = -acoef * sums[ja + 1] + bcoefr * sump[ + ja + 1] + bcoefi * sump[ja - 1]; + } else { + sum[ja - 1] = -acoef * sums[ja - 1] + bcoefr * sump[ + ja - 1]; + } +/* L130: */ + } + +/* T */ +/* Solve ( a A - b B ) y = SUM(,) */ +/* with scaling and perturbation of the denominator */ + + dlaln2_(&c_true, &na, &nw, &dmin__, &acoef, &s[j + j * s_dim1] +, lds, bdiag, &bdiag[1], sum, &c__2, &bcoefr, &bcoefi, + &work[(*n << 1) + j], n, &scale, &temp, &iinfo); + if (scale < 1.) { + i__3 = nw - 1; + for (jw = 0; jw <= i__3; ++jw) { + i__4 = j - 1; + for (jr = je; jr <= i__4; ++jr) { + work[(jw + 2) * *n + jr] = scale * work[(jw + 2) * + *n + jr]; +/* L140: */ + } +/* L150: */ + } + xmax = scale * xmax; + } + xmax = max(xmax,temp); +L160: + ; + } + +/* Copy eigenvector to VL, back transforming if */ +/* HOWMNY='B'. */ + + ++ieig; + if (ilback) { + i__2 = nw - 1; + for (jw = 0; jw <= i__2; ++jw) { + i__3 = *n + 1 - je; + dgemv_("N", n, &i__3, &c_b34, &vl[je * vl_dim1 + 1], ldvl, + &work[(jw + 2) * *n + je], &c__1, &c_b36, &work[( + jw + 4) * *n + 1], &c__1); +/* L170: */ + } + dlacpy_(" ", n, &nw, &work[(*n << 2) + 1], n, &vl[je * + vl_dim1 + 1], ldvl); + ibeg = 1; + } else { + dlacpy_(" ", n, &nw, &work[(*n << 1) + 1], n, &vl[ieig * + vl_dim1 + 1], ldvl); + ibeg = je; + } + +/* Scale eigenvector */ + + xmax = 0.; + if (ilcplx) { + i__2 = *n; + for (j = ibeg; j <= i__2; ++j) { +/* Computing MAX */ + d__3 = xmax, d__4 = (d__1 = vl[j + ieig * vl_dim1], abs( + d__1)) + (d__2 = vl[j + (ieig + 1) * vl_dim1], + abs(d__2)); + xmax = max(d__3,d__4); +/* L180: */ + } + } else { + i__2 = *n; + for (j = ibeg; j <= i__2; ++j) { +/* Computing MAX */ + d__2 = xmax, d__3 = (d__1 = vl[j + ieig * vl_dim1], abs( + d__1)); + xmax = max(d__2,d__3); +/* L190: */ + } + } + + if (xmax > safmin) { + xscale = 1. / xmax; + + i__2 = nw - 1; + for (jw = 0; jw <= i__2; ++jw) { + i__3 = *n; + for (jr = ibeg; jr <= i__3; ++jr) { + vl[jr + (ieig + jw) * vl_dim1] = xscale * vl[jr + ( + ieig + jw) * vl_dim1]; +/* L200: */ + } +/* L210: */ + } + } + ieig = ieig + nw - 1; + +L220: + ; + } + } + +/* Right eigenvectors */ + + if (compr) { + ieig = im + 1; + +/* Main loop over eigenvalues */ + + ilcplx = FALSE_; + for (je = *n; je >= 1; --je) { + +/* Skip this iteration if (a) HOWMNY='S' and SELECT=.FALSE., or */ +/* (b) this would be the second of a complex pair. */ +/* Check for complex eigenvalue, so as to be sure of which */ +/* entry(-ies) of SELECT to look at -- if complex, SELECT(JE) */ +/* or SELECT(JE-1). */ +/* If this is a complex pair, the 2-by-2 diagonal block */ +/* corresponding to the eigenvalue is in rows/columns JE-1:JE */ + + if (ilcplx) { + ilcplx = FALSE_; + goto L500; + } + nw = 1; + if (je > 1) { + if (s[je + (je - 1) * s_dim1] != 0.) { + ilcplx = TRUE_; + nw = 2; + } + } + if (ilall) { + ilcomp = TRUE_; + } else if (ilcplx) { + ilcomp = select[je] || select[je - 1]; + } else { + ilcomp = select[je]; + } + if (! ilcomp) { + goto L500; + } + +/* Decide if (a) singular pencil, (b) real eigenvalue, or */ +/* (c) complex eigenvalue. */ + + if (! ilcplx) { + if ((d__1 = s[je + je * s_dim1], abs(d__1)) <= safmin && ( + d__2 = p[je + je * p_dim1], abs(d__2)) <= safmin) { + +/* Singular matrix pencil -- unit eigenvector */ + + --ieig; + i__1 = *n; + for (jr = 1; jr <= i__1; ++jr) { + vr[jr + ieig * vr_dim1] = 0.; +/* L230: */ + } + vr[ieig + ieig * vr_dim1] = 1.; + goto L500; + } + } + +/* Clear vector */ + + i__1 = nw - 1; + for (jw = 0; jw <= i__1; ++jw) { + i__2 = *n; + for (jr = 1; jr <= i__2; ++jr) { + work[(jw + 2) * *n + jr] = 0.; +/* L240: */ + } +/* L250: */ + } + +/* Compute coefficients in ( a A - b B ) x = 0 */ +/* a is ACOEF */ +/* b is BCOEFR + i*BCOEFI */ + + if (! ilcplx) { + +/* Real eigenvalue */ + +/* Computing MAX */ + d__3 = (d__1 = s[je + je * s_dim1], abs(d__1)) * ascale, d__4 + = (d__2 = p[je + je * p_dim1], abs(d__2)) * bscale, + d__3 = max(d__3,d__4); + temp = 1. / max(d__3,safmin); + salfar = temp * s[je + je * s_dim1] * ascale; + sbeta = temp * p[je + je * p_dim1] * bscale; + acoef = sbeta * ascale; + bcoefr = salfar * bscale; + bcoefi = 0.; + +/* Scale to avoid underflow */ + + scale = 1.; + lsa = abs(sbeta) >= safmin && abs(acoef) < small; + lsb = abs(salfar) >= safmin && abs(bcoefr) < small; + if (lsa) { + scale = small / abs(sbeta) * min(anorm,big); + } + if (lsb) { +/* Computing MAX */ + d__1 = scale, d__2 = small / abs(salfar) * min(bnorm,big); + scale = max(d__1,d__2); + } + if (lsa || lsb) { +/* Computing MIN */ +/* Computing MAX */ + d__3 = 1., d__4 = abs(acoef), d__3 = max(d__3,d__4), d__4 + = abs(bcoefr); + d__1 = scale, d__2 = 1. / (safmin * max(d__3,d__4)); + scale = min(d__1,d__2); + if (lsa) { + acoef = ascale * (scale * sbeta); + } else { + acoef = scale * acoef; + } + if (lsb) { + bcoefr = bscale * (scale * salfar); + } else { + bcoefr = scale * bcoefr; + } + } + acoefa = abs(acoef); + bcoefa = abs(bcoefr); + +/* First component is 1 */ + + work[(*n << 1) + je] = 1.; + xmax = 1.; + +/* Compute contribution from column JE of A and B to sum */ +/* (See "Further Details", above.) */ + + i__1 = je - 1; + for (jr = 1; jr <= i__1; ++jr) { + work[(*n << 1) + jr] = bcoefr * p[jr + je * p_dim1] - + acoef * s[jr + je * s_dim1]; +/* L260: */ + } + } else { + +/* Complex eigenvalue */ + + d__1 = safmin * 100.; + dlag2_(&s[je - 1 + (je - 1) * s_dim1], lds, &p[je - 1 + (je - + 1) * p_dim1], ldp, &d__1, &acoef, &temp, &bcoefr, & + temp2, &bcoefi); + if (bcoefi == 0.) { + *info = je - 1; + return 0; + } + +/* Scale to avoid over/underflow */ + + acoefa = abs(acoef); + bcoefa = abs(bcoefr) + abs(bcoefi); + scale = 1.; + if (acoefa * ulp < safmin && acoefa >= safmin) { + scale = safmin / ulp / acoefa; + } + if (bcoefa * ulp < safmin && bcoefa >= safmin) { +/* Computing MAX */ + d__1 = scale, d__2 = safmin / ulp / bcoefa; + scale = max(d__1,d__2); + } + if (safmin * acoefa > ascale) { + scale = ascale / (safmin * acoefa); + } + if (safmin * bcoefa > bscale) { +/* Computing MIN */ + d__1 = scale, d__2 = bscale / (safmin * bcoefa); + scale = min(d__1,d__2); + } + if (scale != 1.) { + acoef = scale * acoef; + acoefa = abs(acoef); + bcoefr = scale * bcoefr; + bcoefi = scale * bcoefi; + bcoefa = abs(bcoefr) + abs(bcoefi); + } + +/* Compute first two components of eigenvector */ +/* and contribution to sums */ + + temp = acoef * s[je + (je - 1) * s_dim1]; + temp2r = acoef * s[je + je * s_dim1] - bcoefr * p[je + je * + p_dim1]; + temp2i = -bcoefi * p[je + je * p_dim1]; + if (abs(temp) >= abs(temp2r) + abs(temp2i)) { + work[(*n << 1) + je] = 1.; + work[*n * 3 + je] = 0.; + work[(*n << 1) + je - 1] = -temp2r / temp; + work[*n * 3 + je - 1] = -temp2i / temp; + } else { + work[(*n << 1) + je - 1] = 1.; + work[*n * 3 + je - 1] = 0.; + temp = acoef * s[je - 1 + je * s_dim1]; + work[(*n << 1) + je] = (bcoefr * p[je - 1 + (je - 1) * + p_dim1] - acoef * s[je - 1 + (je - 1) * s_dim1]) / + temp; + work[*n * 3 + je] = bcoefi * p[je - 1 + (je - 1) * p_dim1] + / temp; + } + +/* Computing MAX */ + d__5 = (d__1 = work[(*n << 1) + je], abs(d__1)) + (d__2 = + work[*n * 3 + je], abs(d__2)), d__6 = (d__3 = work[(* + n << 1) + je - 1], abs(d__3)) + (d__4 = work[*n * 3 + + je - 1], abs(d__4)); + xmax = max(d__5,d__6); + +/* Compute contribution from columns JE and JE-1 */ +/* of A and B to the sums. */ + + creala = acoef * work[(*n << 1) + je - 1]; + cimaga = acoef * work[*n * 3 + je - 1]; + crealb = bcoefr * work[(*n << 1) + je - 1] - bcoefi * work[*n + * 3 + je - 1]; + cimagb = bcoefi * work[(*n << 1) + je - 1] + bcoefr * work[*n + * 3 + je - 1]; + cre2a = acoef * work[(*n << 1) + je]; + cim2a = acoef * work[*n * 3 + je]; + cre2b = bcoefr * work[(*n << 1) + je] - bcoefi * work[*n * 3 + + je]; + cim2b = bcoefi * work[(*n << 1) + je] + bcoefr * work[*n * 3 + + je]; + i__1 = je - 2; + for (jr = 1; jr <= i__1; ++jr) { + work[(*n << 1) + jr] = -creala * s[jr + (je - 1) * s_dim1] + + crealb * p[jr + (je - 1) * p_dim1] - cre2a * s[ + jr + je * s_dim1] + cre2b * p[jr + je * p_dim1]; + work[*n * 3 + jr] = -cimaga * s[jr + (je - 1) * s_dim1] + + cimagb * p[jr + (je - 1) * p_dim1] - cim2a * s[jr + + je * s_dim1] + cim2b * p[jr + je * p_dim1]; +/* L270: */ + } + } + +/* Computing MAX */ + d__1 = ulp * acoefa * anorm, d__2 = ulp * bcoefa * bnorm, d__1 = + max(d__1,d__2); + dmin__ = max(d__1,safmin); + +/* Columnwise triangular solve of (a A - b B) x = 0 */ + + il2by2 = FALSE_; + for (j = je - nw; j >= 1; --j) { + +/* If a 2-by-2 block, is in position j-1:j, wait until */ +/* next iteration to process it (when it will be j:j+1) */ + + if (! il2by2 && j > 1) { + if (s[j + (j - 1) * s_dim1] != 0.) { + il2by2 = TRUE_; + goto L370; + } + } + bdiag[0] = p[j + j * p_dim1]; + if (il2by2) { + na = 2; + bdiag[1] = p[j + 1 + (j + 1) * p_dim1]; + } else { + na = 1; + } + +/* Compute x(j) (and x(j+1), if 2-by-2 block) */ + + dlaln2_(&c_false, &na, &nw, &dmin__, &acoef, &s[j + j * + s_dim1], lds, bdiag, &bdiag[1], &work[(*n << 1) + j], + n, &bcoefr, &bcoefi, sum, &c__2, &scale, &temp, & + iinfo); + if (scale < 1.) { + + i__1 = nw - 1; + for (jw = 0; jw <= i__1; ++jw) { + i__2 = je; + for (jr = 1; jr <= i__2; ++jr) { + work[(jw + 2) * *n + jr] = scale * work[(jw + 2) * + *n + jr]; +/* L280: */ + } +/* L290: */ + } + } +/* Computing MAX */ + d__1 = scale * xmax; + xmax = max(d__1,temp); + + i__1 = nw; + for (jw = 1; jw <= i__1; ++jw) { + i__2 = na; + for (ja = 1; ja <= i__2; ++ja) { + work[(jw + 1) * *n + j + ja - 1] = sum[ja + (jw << 1) + - 3]; +/* L300: */ + } +/* L310: */ + } + +/* w = w + x(j)*(a S(*,j) - b P(*,j) ) with scaling */ + + if (j > 1) { + +/* Check whether scaling is necessary for sum. */ + + xscale = 1. / max(1.,xmax); + temp = acoefa * work[j] + bcoefa * work[*n + j]; + if (il2by2) { +/* Computing MAX */ + d__1 = temp, d__2 = acoefa * work[j + 1] + bcoefa * + work[*n + j + 1]; + temp = max(d__1,d__2); + } +/* Computing MAX */ + d__1 = max(temp,acoefa); + temp = max(d__1,bcoefa); + if (temp > bignum * xscale) { + + i__1 = nw - 1; + for (jw = 0; jw <= i__1; ++jw) { + i__2 = je; + for (jr = 1; jr <= i__2; ++jr) { + work[(jw + 2) * *n + jr] = xscale * work[(jw + + 2) * *n + jr]; +/* L320: */ + } +/* L330: */ + } + xmax *= xscale; + } + +/* Compute the contributions of the off-diagonals of */ +/* column j (and j+1, if 2-by-2 block) of A and B to the */ +/* sums. */ + + + i__1 = na; + for (ja = 1; ja <= i__1; ++ja) { + if (ilcplx) { + creala = acoef * work[(*n << 1) + j + ja - 1]; + cimaga = acoef * work[*n * 3 + j + ja - 1]; + crealb = bcoefr * work[(*n << 1) + j + ja - 1] - + bcoefi * work[*n * 3 + j + ja - 1]; + cimagb = bcoefi * work[(*n << 1) + j + ja - 1] + + bcoefr * work[*n * 3 + j + ja - 1]; + i__2 = j - 1; + for (jr = 1; jr <= i__2; ++jr) { + work[(*n << 1) + jr] = work[(*n << 1) + jr] - + creala * s[jr + (j + ja - 1) * s_dim1] + + crealb * p[jr + (j + ja - 1) * + p_dim1]; + work[*n * 3 + jr] = work[*n * 3 + jr] - + cimaga * s[jr + (j + ja - 1) * s_dim1] + + cimagb * p[jr + (j + ja - 1) * + p_dim1]; +/* L340: */ + } + } else { + creala = acoef * work[(*n << 1) + j + ja - 1]; + crealb = bcoefr * work[(*n << 1) + j + ja - 1]; + i__2 = j - 1; + for (jr = 1; jr <= i__2; ++jr) { + work[(*n << 1) + jr] = work[(*n << 1) + jr] - + creala * s[jr + (j + ja - 1) * s_dim1] + + crealb * p[jr + (j + ja - 1) * + p_dim1]; +/* L350: */ + } + } +/* L360: */ + } + } + + il2by2 = FALSE_; +L370: + ; + } + +/* Copy eigenvector to VR, back transforming if */ +/* HOWMNY='B'. */ + + ieig -= nw; + if (ilback) { + + i__1 = nw - 1; + for (jw = 0; jw <= i__1; ++jw) { + i__2 = *n; + for (jr = 1; jr <= i__2; ++jr) { + work[(jw + 4) * *n + jr] = work[(jw + 2) * *n + 1] * + vr[jr + vr_dim1]; +/* L380: */ + } + +/* A series of compiler directives to defeat */ +/* vectorization for the next loop */ + + + i__2 = je; + for (jc = 2; jc <= i__2; ++jc) { + i__3 = *n; + for (jr = 1; jr <= i__3; ++jr) { + work[(jw + 4) * *n + jr] += work[(jw + 2) * *n + + jc] * vr[jr + jc * vr_dim1]; +/* L390: */ + } +/* L400: */ + } +/* L410: */ + } + + i__1 = nw - 1; + for (jw = 0; jw <= i__1; ++jw) { + i__2 = *n; + for (jr = 1; jr <= i__2; ++jr) { + vr[jr + (ieig + jw) * vr_dim1] = work[(jw + 4) * *n + + jr]; +/* L420: */ + } +/* L430: */ + } + + iend = *n; + } else { + i__1 = nw - 1; + for (jw = 0; jw <= i__1; ++jw) { + i__2 = *n; + for (jr = 1; jr <= i__2; ++jr) { + vr[jr + (ieig + jw) * vr_dim1] = work[(jw + 2) * *n + + jr]; +/* L440: */ + } +/* L450: */ + } + + iend = je; + } + +/* Scale eigenvector */ + + xmax = 0.; + if (ilcplx) { + i__1 = iend; + for (j = 1; j <= i__1; ++j) { +/* Computing MAX */ + d__3 = xmax, d__4 = (d__1 = vr[j + ieig * vr_dim1], abs( + d__1)) + (d__2 = vr[j + (ieig + 1) * vr_dim1], + abs(d__2)); + xmax = max(d__3,d__4); +/* L460: */ + } + } else { + i__1 = iend; + for (j = 1; j <= i__1; ++j) { +/* Computing MAX */ + d__2 = xmax, d__3 = (d__1 = vr[j + ieig * vr_dim1], abs( + d__1)); + xmax = max(d__2,d__3); +/* L470: */ + } + } + + if (xmax > safmin) { + xscale = 1. / xmax; + i__1 = nw - 1; + for (jw = 0; jw <= i__1; ++jw) { + i__2 = iend; + for (jr = 1; jr <= i__2; ++jr) { + vr[jr + (ieig + jw) * vr_dim1] = xscale * vr[jr + ( + ieig + jw) * vr_dim1]; +/* L480: */ + } +/* L490: */ + } + } +L500: + ; + } + } + + return 0; + +/* End of DTGEVC */ + +} /* dtgevc_ */ |