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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/zgeevx.c | |
parent | 01f64c1ecd0d4ffa9e3a74478335f1745f26cc75 (diff) | |
download | ydb-90d450f74722da7859d6f510a869f6c6908fd12f.tar.gz |
[] add metering mode to CLI
Diffstat (limited to 'contrib/libs/clapack/zgeevx.c')
-rw-r--r-- | contrib/libs/clapack/zgeevx.c | 686 |
1 files changed, 686 insertions, 0 deletions
diff --git a/contrib/libs/clapack/zgeevx.c b/contrib/libs/clapack/zgeevx.c new file mode 100644 index 0000000000..3b3fbdf505 --- /dev/null +++ b/contrib/libs/clapack/zgeevx.c @@ -0,0 +1,686 @@ +/* zgeevx.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__0 = 0; +static integer c_n1 = -1; + +/* Subroutine */ int zgeevx_(char *balanc, char *jobvl, char *jobvr, char * + sense, integer *n, doublecomplex *a, integer *lda, doublecomplex *w, + doublecomplex *vl, integer *ldvl, doublecomplex *vr, integer *ldvr, + integer *ilo, integer *ihi, doublereal *scale, doublereal *abnrm, + doublereal *rconde, doublereal *rcondv, doublecomplex *work, integer * + lwork, doublereal *rwork, integer *info) +{ + /* System generated locals */ + integer a_dim1, a_offset, vl_dim1, vl_offset, vr_dim1, vr_offset, i__1, + i__2, i__3; + doublereal d__1, d__2; + doublecomplex z__1, z__2; + + /* Builtin functions */ + double sqrt(doublereal), d_imag(doublecomplex *); + void d_cnjg(doublecomplex *, doublecomplex *); + + /* Local variables */ + integer i__, k; + char job[1]; + doublereal scl, dum[1], eps; + doublecomplex tmp; + char side[1]; + doublereal anrm; + integer ierr, itau, iwrk, nout, icond; + extern logical lsame_(char *, char *); + extern /* Subroutine */ int zscal_(integer *, doublecomplex *, + doublecomplex *, integer *), dlabad_(doublereal *, doublereal *); + extern doublereal dznrm2_(integer *, doublecomplex *, integer *); + logical scalea; + extern doublereal dlamch_(char *); + doublereal cscale; + extern /* Subroutine */ int dlascl_(char *, integer *, integer *, + doublereal *, doublereal *, integer *, integer *, doublereal *, + integer *, integer *), zgebak_(char *, char *, integer *, + integer *, integer *, doublereal *, integer *, doublecomplex *, + integer *, integer *), zgebal_(char *, integer *, + doublecomplex *, integer *, integer *, integer *, doublereal *, + integer *); + extern integer idamax_(integer *, doublereal *, integer *); + extern /* Subroutine */ int xerbla_(char *, integer *); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *); + logical select[1]; + extern /* Subroutine */ int zdscal_(integer *, doublereal *, + doublecomplex *, integer *); + doublereal bignum; + extern doublereal zlange_(char *, integer *, integer *, doublecomplex *, + integer *, doublereal *); + extern /* Subroutine */ int zgehrd_(integer *, integer *, integer *, + doublecomplex *, integer *, doublecomplex *, doublecomplex *, + integer *, integer *), zlascl_(char *, integer *, integer *, + doublereal *, doublereal *, integer *, integer *, doublecomplex *, + integer *, integer *), zlacpy_(char *, integer *, + integer *, doublecomplex *, integer *, doublecomplex *, integer *); + integer minwrk, maxwrk; + logical wantvl, wntsnb; + integer hswork; + logical wntsne; + doublereal smlnum; + extern /* Subroutine */ int zhseqr_(char *, char *, integer *, integer *, + integer *, doublecomplex *, integer *, doublecomplex *, + doublecomplex *, integer *, doublecomplex *, integer *, integer *); + logical lquery, wantvr; + extern /* Subroutine */ int ztrevc_(char *, char *, logical *, integer *, + doublecomplex *, integer *, doublecomplex *, integer *, + doublecomplex *, integer *, integer *, integer *, doublecomplex *, + doublereal *, integer *), ztrsna_(char *, char *, + logical *, integer *, doublecomplex *, integer *, doublecomplex * +, integer *, doublecomplex *, integer *, doublereal *, doublereal + *, integer *, integer *, doublecomplex *, integer *, doublereal *, + integer *), zunghr_(integer *, integer *, + integer *, doublecomplex *, integer *, doublecomplex *, + doublecomplex *, integer *, integer *); + logical wntsnn, wntsnv; + + +/* -- LAPACK driver routine (version 3.2) -- */ +/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ +/* November 2006 */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* Purpose */ +/* ======= */ + +/* ZGEEVX computes for an N-by-N complex nonsymmetric matrix A, the */ +/* eigenvalues and, optionally, the left and/or right eigenvectors. */ + +/* Optionally also, it computes a balancing transformation to improve */ +/* the conditioning of the eigenvalues and eigenvectors (ILO, IHI, */ +/* SCALE, and ABNRM), reciprocal condition numbers for the eigenvalues */ +/* (RCONDE), and reciprocal condition numbers for the right */ +/* eigenvectors (RCONDV). */ + +/* The right eigenvector v(j) of A satisfies */ +/* A * v(j) = lambda(j) * v(j) */ +/* where lambda(j) is its eigenvalue. */ +/* The left eigenvector u(j) of A satisfies */ +/* u(j)**H * A = lambda(j) * u(j)**H */ +/* where u(j)**H denotes the conjugate transpose of u(j). */ + +/* The computed eigenvectors are normalized to have Euclidean norm */ +/* equal to 1 and largest component real. */ + +/* Balancing a matrix means permuting the rows and columns to make it */ +/* more nearly upper triangular, and applying a diagonal similarity */ +/* transformation D * A * D**(-1), where D is a diagonal matrix, to */ +/* make its rows and columns closer in norm and the condition numbers */ +/* of its eigenvalues and eigenvectors smaller. The computed */ +/* reciprocal condition numbers correspond to the balanced matrix. */ +/* Permuting rows and columns will not change the condition numbers */ +/* (in exact arithmetic) but diagonal scaling will. For further */ +/* explanation of balancing, see section 4.10.2 of the LAPACK */ +/* Users' Guide. */ + +/* Arguments */ +/* ========= */ + +/* BALANC (input) CHARACTER*1 */ +/* Indicates how the input matrix should be diagonally scaled */ +/* and/or permuted to improve the conditioning of its */ +/* eigenvalues. */ +/* = 'N': Do not diagonally scale or permute; */ +/* = 'P': Perform permutations to make the matrix more nearly */ +/* upper triangular. Do not diagonally scale; */ +/* = 'S': Diagonally scale the matrix, ie. replace A by */ +/* D*A*D**(-1), where D is a diagonal matrix chosen */ +/* to make the rows and columns of A more equal in */ +/* norm. Do not permute; */ +/* = 'B': Both diagonally scale and permute A. */ + +/* Computed reciprocal condition numbers will be for the matrix */ +/* after balancing and/or permuting. Permuting does not change */ +/* condition numbers (in exact arithmetic), but balancing does. */ + +/* JOBVL (input) CHARACTER*1 */ +/* = 'N': left eigenvectors of A are not computed; */ +/* = 'V': left eigenvectors of A are computed. */ +/* If SENSE = 'E' or 'B', JOBVL must = 'V'. */ + +/* JOBVR (input) CHARACTER*1 */ +/* = 'N': right eigenvectors of A are not computed; */ +/* = 'V': right eigenvectors of A are computed. */ +/* If SENSE = 'E' or 'B', JOBVR must = 'V'. */ + +/* SENSE (input) CHARACTER*1 */ +/* Determines which reciprocal condition numbers are computed. */ +/* = 'N': None are computed; */ +/* = 'E': Computed for eigenvalues only; */ +/* = 'V': Computed for right eigenvectors only; */ +/* = 'B': Computed for eigenvalues and right eigenvectors. */ + +/* If SENSE = 'E' or 'B', both left and right eigenvectors */ +/* must also be computed (JOBVL = 'V' and JOBVR = 'V'). */ + +/* N (input) INTEGER */ +/* The order of the matrix A. N >= 0. */ + +/* A (input/output) COMPLEX*16 array, dimension (LDA,N) */ +/* On entry, the N-by-N matrix A. */ +/* On exit, A has been overwritten. If JOBVL = 'V' or */ +/* JOBVR = 'V', A contains the Schur form of the balanced */ +/* version of the matrix A. */ + +/* LDA (input) INTEGER */ +/* The leading dimension of the array A. LDA >= max(1,N). */ + +/* W (output) COMPLEX*16 array, dimension (N) */ +/* W contains the computed eigenvalues. */ + +/* VL (output) COMPLEX*16 array, dimension (LDVL,N) */ +/* If JOBVL = 'V', the left eigenvectors u(j) are stored one */ +/* after another in the columns of VL, in the same order */ +/* as their eigenvalues. */ +/* If JOBVL = 'N', VL is not referenced. */ +/* u(j) = VL(:,j), the j-th column of VL. */ + +/* LDVL (input) INTEGER */ +/* The leading dimension of the array VL. LDVL >= 1; if */ +/* JOBVL = 'V', LDVL >= N. */ + +/* VR (output) COMPLEX*16 array, dimension (LDVR,N) */ +/* If JOBVR = 'V', the right eigenvectors v(j) are stored one */ +/* after another in the columns of VR, in the same order */ +/* as their eigenvalues. */ +/* If JOBVR = 'N', VR is not referenced. */ +/* v(j) = VR(:,j), the j-th column of VR. */ + +/* LDVR (input) INTEGER */ +/* The leading dimension of the array VR. LDVR >= 1; if */ +/* JOBVR = 'V', LDVR >= N. */ + +/* ILO (output) INTEGER */ +/* IHI (output) INTEGER */ +/* ILO and IHI are integer values determined when A was */ +/* balanced. The balanced A(i,j) = 0 if I > J and */ +/* J = 1,...,ILO-1 or I = IHI+1,...,N. */ + +/* SCALE (output) DOUBLE PRECISION array, dimension (N) */ +/* Details of the permutations and scaling factors applied */ +/* when balancing A. If P(j) is the index of the row and column */ +/* interchanged with row and column j, and D(j) is the scaling */ +/* factor applied to row and column j, then */ +/* SCALE(J) = P(J), for J = 1,...,ILO-1 */ +/* = D(J), for J = ILO,...,IHI */ +/* = P(J) for J = IHI+1,...,N. */ +/* The order in which the interchanges are made is N to IHI+1, */ +/* then 1 to ILO-1. */ + +/* ABNRM (output) DOUBLE PRECISION */ +/* The one-norm of the balanced matrix (the maximum */ +/* of the sum of absolute values of elements of any column). */ + +/* RCONDE (output) DOUBLE PRECISION array, dimension (N) */ +/* RCONDE(j) is the reciprocal condition number of the j-th */ +/* eigenvalue. */ + +/* RCONDV (output) DOUBLE PRECISION array, dimension (N) */ +/* RCONDV(j) is the reciprocal condition number of the j-th */ +/* right eigenvector. */ + +/* WORK (workspace/output) COMPLEX*16 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. If SENSE = 'N' or 'E', */ +/* LWORK >= max(1,2*N), and if SENSE = 'V' or 'B', */ +/* LWORK >= N*N+2*N. */ +/* For good performance, LWORK must generally be larger. */ + +/* 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. */ + +/* RWORK (workspace) DOUBLE PRECISION array, dimension (2*N) */ + +/* INFO (output) INTEGER */ +/* = 0: successful exit */ +/* < 0: if INFO = -i, the i-th argument had an illegal value. */ +/* > 0: if INFO = i, the QR algorithm failed to compute all the */ +/* eigenvalues, and no eigenvectors or condition numbers */ +/* have been computed; elements 1:ILO-1 and i+1:N of W */ +/* contain eigenvalues which have converged. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. Local Arrays .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input arguments */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --w; + vl_dim1 = *ldvl; + vl_offset = 1 + vl_dim1; + vl -= vl_offset; + vr_dim1 = *ldvr; + vr_offset = 1 + vr_dim1; + vr -= vr_offset; + --scale; + --rconde; + --rcondv; + --work; + --rwork; + + /* Function Body */ + *info = 0; + lquery = *lwork == -1; + wantvl = lsame_(jobvl, "V"); + wantvr = lsame_(jobvr, "V"); + wntsnn = lsame_(sense, "N"); + wntsne = lsame_(sense, "E"); + wntsnv = lsame_(sense, "V"); + wntsnb = lsame_(sense, "B"); + if (! (lsame_(balanc, "N") || lsame_(balanc, "S") || lsame_(balanc, "P") + || lsame_(balanc, "B"))) { + *info = -1; + } else if (! wantvl && ! lsame_(jobvl, "N")) { + *info = -2; + } else if (! wantvr && ! lsame_(jobvr, "N")) { + *info = -3; + } else if (! (wntsnn || wntsne || wntsnb || wntsnv) || (wntsne || wntsnb) + && ! (wantvl && wantvr)) { + *info = -4; + } else if (*n < 0) { + *info = -5; + } else if (*lda < max(1,*n)) { + *info = -7; + } else if (*ldvl < 1 || wantvl && *ldvl < *n) { + *info = -10; + } else if (*ldvr < 1 || wantvr && *ldvr < *n) { + *info = -12; + } + +/* Compute workspace */ +/* (Note: Comments in the code beginning "Workspace:" describe the */ +/* minimal amount of workspace needed at that point in the code, */ +/* as well as the preferred amount for good performance. */ +/* CWorkspace refers to complex workspace, and RWorkspace to real */ +/* workspace. NB refers to the optimal block size for the */ +/* immediately following subroutine, as returned by ILAENV. */ +/* HSWORK refers to the workspace preferred by ZHSEQR, as */ +/* calculated below. HSWORK is computed assuming ILO=1 and IHI=N, */ +/* the worst case.) */ + + if (*info == 0) { + if (*n == 0) { + minwrk = 1; + maxwrk = 1; + } else { + maxwrk = *n + *n * ilaenv_(&c__1, "ZGEHRD", " ", n, &c__1, n, & + c__0); + + if (wantvl) { + zhseqr_("S", "V", n, &c__1, n, &a[a_offset], lda, &w[1], &vl[ + vl_offset], ldvl, &work[1], &c_n1, info); + } else if (wantvr) { + zhseqr_("S", "V", n, &c__1, n, &a[a_offset], lda, &w[1], &vr[ + vr_offset], ldvr, &work[1], &c_n1, info); + } else { + if (wntsnn) { + zhseqr_("E", "N", n, &c__1, n, &a[a_offset], lda, &w[1], & + vr[vr_offset], ldvr, &work[1], &c_n1, info); + } else { + zhseqr_("S", "N", n, &c__1, n, &a[a_offset], lda, &w[1], & + vr[vr_offset], ldvr, &work[1], &c_n1, info); + } + } + hswork = (integer) work[1].r; + + if (! wantvl && ! wantvr) { + minwrk = *n << 1; + if (! (wntsnn || wntsne)) { +/* Computing MAX */ + i__1 = minwrk, i__2 = *n * *n + (*n << 1); + minwrk = max(i__1,i__2); + } + maxwrk = max(maxwrk,hswork); + if (! (wntsnn || wntsne)) { +/* Computing MAX */ + i__1 = maxwrk, i__2 = *n * *n + (*n << 1); + maxwrk = max(i__1,i__2); + } + } else { + minwrk = *n << 1; + if (! (wntsnn || wntsne)) { +/* Computing MAX */ + i__1 = minwrk, i__2 = *n * *n + (*n << 1); + minwrk = max(i__1,i__2); + } + maxwrk = max(maxwrk,hswork); +/* Computing MAX */ + i__1 = maxwrk, i__2 = *n + (*n - 1) * ilaenv_(&c__1, "ZUNGHR", + " ", n, &c__1, n, &c_n1); + maxwrk = max(i__1,i__2); + if (! (wntsnn || wntsne)) { +/* Computing MAX */ + i__1 = maxwrk, i__2 = *n * *n + (*n << 1); + maxwrk = max(i__1,i__2); + } +/* Computing MAX */ + i__1 = maxwrk, i__2 = *n << 1; + maxwrk = max(i__1,i__2); + } + maxwrk = max(maxwrk,minwrk); + } + work[1].r = (doublereal) maxwrk, work[1].i = 0.; + + if (*lwork < minwrk && ! lquery) { + *info = -20; + } + } + + if (*info != 0) { + i__1 = -(*info); + xerbla_("ZGEEVX", &i__1); + return 0; + } else if (lquery) { + return 0; + } + +/* Quick return if possible */ + + if (*n == 0) { + return 0; + } + +/* Get machine constants */ + + eps = dlamch_("P"); + smlnum = dlamch_("S"); + bignum = 1. / smlnum; + dlabad_(&smlnum, &bignum); + smlnum = sqrt(smlnum) / eps; + bignum = 1. / smlnum; + +/* Scale A if max element outside range [SMLNUM,BIGNUM] */ + + icond = 0; + anrm = zlange_("M", n, n, &a[a_offset], lda, dum); + scalea = FALSE_; + if (anrm > 0. && anrm < smlnum) { + scalea = TRUE_; + cscale = smlnum; + } else if (anrm > bignum) { + scalea = TRUE_; + cscale = bignum; + } + if (scalea) { + zlascl_("G", &c__0, &c__0, &anrm, &cscale, n, n, &a[a_offset], lda, & + ierr); + } + +/* Balance the matrix and compute ABNRM */ + + zgebal_(balanc, n, &a[a_offset], lda, ilo, ihi, &scale[1], &ierr); + *abnrm = zlange_("1", n, n, &a[a_offset], lda, dum); + if (scalea) { + dum[0] = *abnrm; + dlascl_("G", &c__0, &c__0, &cscale, &anrm, &c__1, &c__1, dum, &c__1, & + ierr); + *abnrm = dum[0]; + } + +/* Reduce to upper Hessenberg form */ +/* (CWorkspace: need 2*N, prefer N+N*NB) */ +/* (RWorkspace: none) */ + + itau = 1; + iwrk = itau + *n; + i__1 = *lwork - iwrk + 1; + zgehrd_(n, ilo, ihi, &a[a_offset], lda, &work[itau], &work[iwrk], &i__1, & + ierr); + + if (wantvl) { + +/* Want left eigenvectors */ +/* Copy Householder vectors to VL */ + + *(unsigned char *)side = 'L'; + zlacpy_("L", n, n, &a[a_offset], lda, &vl[vl_offset], ldvl) + ; + +/* Generate unitary matrix in VL */ +/* (CWorkspace: need 2*N-1, prefer N+(N-1)*NB) */ +/* (RWorkspace: none) */ + + i__1 = *lwork - iwrk + 1; + zunghr_(n, ilo, ihi, &vl[vl_offset], ldvl, &work[itau], &work[iwrk], & + i__1, &ierr); + +/* Perform QR iteration, accumulating Schur vectors in VL */ +/* (CWorkspace: need 1, prefer HSWORK (see comments) ) */ +/* (RWorkspace: none) */ + + iwrk = itau; + i__1 = *lwork - iwrk + 1; + zhseqr_("S", "V", n, ilo, ihi, &a[a_offset], lda, &w[1], &vl[ + vl_offset], ldvl, &work[iwrk], &i__1, info); + + if (wantvr) { + +/* Want left and right eigenvectors */ +/* Copy Schur vectors to VR */ + + *(unsigned char *)side = 'B'; + zlacpy_("F", n, n, &vl[vl_offset], ldvl, &vr[vr_offset], ldvr); + } + + } else if (wantvr) { + +/* Want right eigenvectors */ +/* Copy Householder vectors to VR */ + + *(unsigned char *)side = 'R'; + zlacpy_("L", n, n, &a[a_offset], lda, &vr[vr_offset], ldvr) + ; + +/* Generate unitary matrix in VR */ +/* (CWorkspace: need 2*N-1, prefer N+(N-1)*NB) */ +/* (RWorkspace: none) */ + + i__1 = *lwork - iwrk + 1; + zunghr_(n, ilo, ihi, &vr[vr_offset], ldvr, &work[itau], &work[iwrk], & + i__1, &ierr); + +/* Perform QR iteration, accumulating Schur vectors in VR */ +/* (CWorkspace: need 1, prefer HSWORK (see comments) ) */ +/* (RWorkspace: none) */ + + iwrk = itau; + i__1 = *lwork - iwrk + 1; + zhseqr_("S", "V", n, ilo, ihi, &a[a_offset], lda, &w[1], &vr[ + vr_offset], ldvr, &work[iwrk], &i__1, info); + + } else { + +/* Compute eigenvalues only */ +/* If condition numbers desired, compute Schur form */ + + if (wntsnn) { + *(unsigned char *)job = 'E'; + } else { + *(unsigned char *)job = 'S'; + } + +/* (CWorkspace: need 1, prefer HSWORK (see comments) ) */ +/* (RWorkspace: none) */ + + iwrk = itau; + i__1 = *lwork - iwrk + 1; + zhseqr_(job, "N", n, ilo, ihi, &a[a_offset], lda, &w[1], &vr[ + vr_offset], ldvr, &work[iwrk], &i__1, info); + } + +/* If INFO > 0 from ZHSEQR, then quit */ + + if (*info > 0) { + goto L50; + } + + if (wantvl || wantvr) { + +/* Compute left and/or right eigenvectors */ +/* (CWorkspace: need 2*N) */ +/* (RWorkspace: need N) */ + + ztrevc_(side, "B", select, n, &a[a_offset], lda, &vl[vl_offset], ldvl, + &vr[vr_offset], ldvr, n, &nout, &work[iwrk], &rwork[1], & + ierr); + } + +/* Compute condition numbers if desired */ +/* (CWorkspace: need N*N+2*N unless SENSE = 'E') */ +/* (RWorkspace: need 2*N unless SENSE = 'E') */ + + if (! wntsnn) { + ztrsna_(sense, "A", select, n, &a[a_offset], lda, &vl[vl_offset], + ldvl, &vr[vr_offset], ldvr, &rconde[1], &rcondv[1], n, &nout, + &work[iwrk], n, &rwork[1], &icond); + } + + if (wantvl) { + +/* Undo balancing of left eigenvectors */ + + zgebak_(balanc, "L", n, ilo, ihi, &scale[1], n, &vl[vl_offset], ldvl, + &ierr); + +/* Normalize left eigenvectors and make largest component real */ + + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + scl = 1. / dznrm2_(n, &vl[i__ * vl_dim1 + 1], &c__1); + zdscal_(n, &scl, &vl[i__ * vl_dim1 + 1], &c__1); + i__2 = *n; + for (k = 1; k <= i__2; ++k) { + i__3 = k + i__ * vl_dim1; +/* Computing 2nd power */ + d__1 = vl[i__3].r; +/* Computing 2nd power */ + d__2 = d_imag(&vl[k + i__ * vl_dim1]); + rwork[k] = d__1 * d__1 + d__2 * d__2; +/* L10: */ + } + k = idamax_(n, &rwork[1], &c__1); + d_cnjg(&z__2, &vl[k + i__ * vl_dim1]); + d__1 = sqrt(rwork[k]); + z__1.r = z__2.r / d__1, z__1.i = z__2.i / d__1; + tmp.r = z__1.r, tmp.i = z__1.i; + zscal_(n, &tmp, &vl[i__ * vl_dim1 + 1], &c__1); + i__2 = k + i__ * vl_dim1; + i__3 = k + i__ * vl_dim1; + d__1 = vl[i__3].r; + z__1.r = d__1, z__1.i = 0.; + vl[i__2].r = z__1.r, vl[i__2].i = z__1.i; +/* L20: */ + } + } + + if (wantvr) { + +/* Undo balancing of right eigenvectors */ + + zgebak_(balanc, "R", n, ilo, ihi, &scale[1], n, &vr[vr_offset], ldvr, + &ierr); + +/* Normalize right eigenvectors and make largest component real */ + + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + scl = 1. / dznrm2_(n, &vr[i__ * vr_dim1 + 1], &c__1); + zdscal_(n, &scl, &vr[i__ * vr_dim1 + 1], &c__1); + i__2 = *n; + for (k = 1; k <= i__2; ++k) { + i__3 = k + i__ * vr_dim1; +/* Computing 2nd power */ + d__1 = vr[i__3].r; +/* Computing 2nd power */ + d__2 = d_imag(&vr[k + i__ * vr_dim1]); + rwork[k] = d__1 * d__1 + d__2 * d__2; +/* L30: */ + } + k = idamax_(n, &rwork[1], &c__1); + d_cnjg(&z__2, &vr[k + i__ * vr_dim1]); + d__1 = sqrt(rwork[k]); + z__1.r = z__2.r / d__1, z__1.i = z__2.i / d__1; + tmp.r = z__1.r, tmp.i = z__1.i; + zscal_(n, &tmp, &vr[i__ * vr_dim1 + 1], &c__1); + i__2 = k + i__ * vr_dim1; + i__3 = k + i__ * vr_dim1; + d__1 = vr[i__3].r; + z__1.r = d__1, z__1.i = 0.; + vr[i__2].r = z__1.r, vr[i__2].i = z__1.i; +/* L40: */ + } + } + +/* Undo scaling if necessary */ + +L50: + if (scalea) { + i__1 = *n - *info; +/* Computing MAX */ + i__3 = *n - *info; + i__2 = max(i__3,1); + zlascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &w[*info + 1] +, &i__2, &ierr); + if (*info == 0) { + if ((wntsnv || wntsnb) && icond == 0) { + dlascl_("G", &c__0, &c__0, &cscale, &anrm, n, &c__1, &rcondv[ + 1], n, &ierr); + } + } else { + i__1 = *ilo - 1; + zlascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &w[1], n, + &ierr); + } + } + + work[1].r = (doublereal) maxwrk, work[1].i = 0.; + return 0; + +/* End of ZGEEVX */ + +} /* zgeevx_ */ |