/* Subroutine */ int dpptri_(char *uplo, integer *n, doublereal *ap, integer *
info)
{
/* System generated locals */
integer i__1, i__2;
/* Local variables */
integer j, jc, jj;
doublereal ajj;
integer jjn;
logical upper;
/* -- LAPACK routine (version 3.2) -- */
/* November 2006 */
/* Purpose */
/* ======= */
/* DPPTRI computes the inverse of a real symmetric positive definite */
/* matrix A using the Cholesky factorization A = U**T*U or A = L*L**T */
/* computed by DPPTRF. */
/* Arguments */
/* ========= */
/* UPLO (input) CHARACTER*1 */
/* = 'U': Upper triangular factor is stored in AP; */
/* = 'L': Lower triangular factor is stored in AP. */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* AP (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2) */
/* On entry, the triangular factor U or L from the Cholesky */
/* factorization A = U**T*U or A = L*L**T, packed columnwise as */
/* a linear array. The j-th column of U or L is stored in the */
/* array AP as follows: */
/* if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j; */
/* if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n. */
/* On exit, the upper or lower triangle of the (symmetric) */
/* inverse of A, overwriting the input factor U or L. */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* > 0: if INFO = i, the (i,i) element of the factor U or L is */
/* zero, and the inverse could not be computed. */
/* ===================================================================== */
/* Test the input parameters. */
/* Parameter adjustments */
--ap;
/* Function Body */
*info = 0;
upper = lsame_(uplo, "U");
if (! upper && ! lsame_(uplo, "L")) {
*info = -1;
} else if (*n < 0) {
*info = -2;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("DPPTRI", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/* Invert the triangular Cholesky factor U or L. */
dtptri_(uplo, "Non-unit", n, &ap[1], info);
if (*info > 0) {
return 0;
}
if (upper) {
/* Compute the product inv(U) * inv(U)'. */
jj = 0;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
jc = jj + 1;
jj += j;
if (j > 1) {
i__2 = j - 1;
dspr_("Upper", &i__2, &c_b8, &ap[jc], &c__1, &ap[1]);
}
ajj = ap[jj];
dscal_(&j, &ajj, &ap[jc], &c__1);
}
//.........这里部分代码省略.........
/*< SUBROUTINE DSPTRF( UPLO, N, AP, IPIV, INFO ) >*/
/* Subroutine */ int dsptrf_(char *uplo, integer *n, doublereal *ap, integer *ipiv,
integer *info, ftnlen uplo_len)
{
/* System generated locals */
integer i__1;
doublereal d__1, d__2, d__3;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
doublereal c__;
integer j, k;
doublereal s, t, r1, r2;
integer kc, kk, kp, kx, knc, kpc=0, npp, imax=0, jmax;
extern /* Subroutine */ int drot_(integer *, doublereal *, integer *,
doublereal *, integer *, doublereal *, doublereal *), dspr_(char *
, integer *, doublereal *, doublereal *, integer *, doublereal *,
ftnlen);
doublereal alpha;
extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *,
integer *);
extern logical lsame_(const char *, const char *, ftnlen, ftnlen);
extern /* Subroutine */ int dswap_(integer *, doublereal *, integer *,
doublereal *, integer *);
integer kstep;
logical upper;
extern /* Subroutine */ int dlaev2_(doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *);
doublereal absakk;
extern integer idamax_(integer *, doublereal *, integer *);
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
doublereal colmax, rowmax;
(void)uplo_len;
/* -- LAPACK routine (version 2.0) -- */
/* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
/* Courant Institute, Argonne National Lab, and Rice University */
/* March 31, 1993 */
/* .. Scalar Arguments .. */
/*< CHARACTER UPLO >*/
/*< INTEGER INFO, N >*/
/* .. */
/* .. Array Arguments .. */
/*< INTEGER IPIV( * ) >*/
/*< DOUBLE PRECISION AP( * ) >*/
/* .. */
/* Purpose */
/* ======= */
/* DSPTRF computes the factorization of a real symmetric matrix A stored */
/* in packed format using the Bunch-Kaufman diagonal pivoting method: */
/* A = U*D*U**T or A = L*D*L**T */
/* where U (or L) is a product of permutation and unit upper (lower) */
/* triangular matrices, and D is symmetric and block diagonal with */
/* 1-by-1 and 2-by-2 diagonal blocks. */
/* Arguments */
/* ========= */
/* UPLO (input) CHARACTER*1 */
/* = 'U': Upper triangle of A is stored; */
/* = 'L': Lower triangle of A is stored. */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* AP (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2) */
/* On entry, the upper or lower triangle of the symmetric matrix */
/* A, packed columnwise in a linear array. The j-th column of A */
/* is stored in the array AP as follows: */
/* if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; */
/* if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. */
/* On exit, the block diagonal matrix D and the multipliers used */
/* to obtain the factor U or L, stored as a packed triangular */
/* matrix overwriting A (see below for further details). */
/* IPIV (output) INTEGER array, dimension (N) */
/* Details of the interchanges and the block structure of D. */
/* If IPIV(k) > 0, then rows and columns k and IPIV(k) were */
/* interchanged and D(k,k) is a 1-by-1 diagonal block. */
/* If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and */
/* columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) */
/* is a 2-by-2 diagonal block. If UPLO = 'L' and IPIV(k) = */
/* IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were */
/* interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block. */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* > 0: if INFO = i, D(i,i) is exactly zero. The factorization */
/* has been completed, but the block diagonal matrix D is */
/* exactly singular, and division by zero will occur if it */
//.........这里部分代码省略.........
int dsptrf_(char *uplo, int *n, double *ap, int *
ipiv, int *info)
{
/* System generated locals */
int i__1, i__2;
double d__1, d__2, d__3;
/* Builtin functions */
double sqrt(double);
/* Local variables */
int i__, j, k;
double t, r1, d11, d12, d21, d22;
int kc, kk, kp;
double wk;
int kx, knc, kpc, npp;
double wkm1, wkp1;
int imax, jmax;
extern int dspr_(char *, int *, double *,
double *, int *, double *);
double alpha;
extern int dscal_(int *, double *, double *,
int *);
extern int lsame_(char *, char *);
extern int dswap_(int *, double *, int *,
double *, int *);
int kstep;
int upper;
double absakk;
extern int idamax_(int *, double *, int *);
extern int xerbla_(char *, int *);
double colmax, rowmax;
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DSPTRF computes the factorization of a float symmetric matrix A stored */
/* in packed format using the Bunch-Kaufman diagonal pivoting method: */
/* A = U*D*U**T or A = L*D*L**T */
/* where U (or L) is a product of permutation and unit upper (lower) */
/* triangular matrices, and D is symmetric and block diagonal with */
/* 1-by-1 and 2-by-2 diagonal blocks. */
/* Arguments */
/* ========= */
/* UPLO (input) CHARACTER*1 */
/* = 'U': Upper triangle of A is stored; */
/* = 'L': Lower triangle of A is stored. */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* AP (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2) */
/* On entry, the upper or lower triangle of the symmetric matrix */
/* A, packed columnwise in a linear array. The j-th column of A */
/* is stored in the array AP as follows: */
/* if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; */
/* if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. */
/* On exit, the block diagonal matrix D and the multipliers used */
/* to obtain the factor U or L, stored as a packed triangular */
/* matrix overwriting A (see below for further details). */
/* IPIV (output) INTEGER array, dimension (N) */
/* Details of the interchanges and the block structure of D. */
/* If IPIV(k) > 0, then rows and columns k and IPIV(k) were */
/* interchanged and D(k,k) is a 1-by-1 diagonal block. */
/* If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and */
/* columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) */
/* is a 2-by-2 diagonal block. If UPLO = 'L' and IPIV(k) = */
/* IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were */
/* interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block. */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* > 0: if INFO = i, D(i,i) is exactly zero. The factorization */
/* has been completed, but the block diagonal matrix D is */
/* exactly singular, and division by zero will occur if it */
/* is used to solve a system of equations. */
/* Further Details */
/* =============== */
/* 5-96 - Based on modifications by J. Lewis, Boeing Computer Services */
/* Company */
//.........这里部分代码省略.........
/* Subroutine */ HYPRE_Int dsyev_(char *jobz, char *uplo, integer *n, doublereal *a,
integer *lda, doublereal *w, doublereal *work, integer *lwork,
integer *info)
{
/* -- LAPACK driver routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
June 30, 1999
Purpose
=======
DSYEV computes all eigenvalues and, optionally, eigenvectors of a
real symmetric matrix A.
Arguments
=========
JOBZ (input) CHARACTER*1
= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors.
UPLO (input) CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) INTEGER
The order of the matrix A. N >= 0.
A (input/output) DOUBLE PRECISION array, dimension (LDA, N)
On entry, the symmetric matrix A. If UPLO = 'U', the
leading N-by-N upper triangular part of A contains the
upper triangular part of the matrix A. If UPLO = 'L',
the leading N-by-N lower triangular part of A contains
the lower triangular part of the matrix A.
On exit, if JOBZ = 'V', then if INFO = 0, A contains the
orthonormal eigenvectors of the matrix A.
If JOBZ = 'N', then on exit the lower triangle (if UPLO='L')
or the upper triangle (if UPLO='U') of A, including the
diagonal, is destroyed.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
W (output) DOUBLE PRECISION array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.
WORK (workspace/output) DOUBLE PRECISION array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The length of the array WORK. LWORK >= max(1,3*N-1).
For optimal efficiency, LWORK >= (NB+2)*N,
where NB is the blocksize for DSYTRD returned by ILAENV.
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
> 0: if INFO = i, the algorithm failed to converge; i
off-diagonal elements of an intermediate tridiagonal
form did not converge to zero.
=====================================================================
Test the input parameters.
Parameter adjustments */
/* Table of constant values */
static integer c__1 = 1;
static integer c_n1 = -1;
static integer c__0 = 0;
static doublereal c_b17 = 1.;
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2;
doublereal d__1;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
static integer inde;
static doublereal anrm;
static integer imax;
static doublereal rmin, rmax;
/***static integer lopt;***/
extern /* Subroutine */ HYPRE_Int dscal_(integer *, doublereal *, doublereal *,
integer *);
static doublereal sigma;
extern logical lsame_(char *, char *);
static integer iinfo;
static logical lower, wantz;
static integer nb;
extern doublereal dlamch_(char *);
static integer iscale;
//.........这里部分代码省略.........
/*< SUBROUTINE LPDP(A, MDA, M, N1, N2, PRGOPT, X, WNORM, MODE, WS, IS) >*/
/* Subroutine */ int lpdp_(doublereal *a, integer *mda, integer *m, integer *
n1, integer *n2, doublereal *prgopt, doublereal *x, doublereal *wnorm,
integer *mode, doublereal *ws, integer *is)
{
/* Initialized data */
static doublereal zero = 0.;
static doublereal one = 1.;
static doublereal fac = .1;
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2;
/* Local variables */
integer i__, j, l, n;
doublereal sc;
integer iw, ix, np1;
extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *,
integer *), dnrm2_(integer *, doublereal *, integer *);
extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *,
integer *);
integer modew;
extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *,
doublereal *, integer *);
doublereal rnorm;
extern /* Subroutine */ int wnnls_(doublereal *, integer *, integer *,
integer *, integer *, integer *, doublereal *, doublereal *,
doublereal *, integer *, integer *, doublereal *);
doublereal ynorm;
/* THE EDITING REQUIRED TO CONVERT THIS SUBROUTINE FROM SINGLE TO */
/* DOUBLE PRECISION INVOLVES THE FOLLOWING CHARACTER STRING CHANGES. */
/* USE AN EDITING COMMAND (CHANGE) /STRING-1/(TO)STRING-2/. */
/* (START EDITING AT LINE WITH C++ IN COLS. 1-3.) */
/* /REAL (12 BLANKS)/DOUBLE PRECISION/,/DNRM2/DNRM2/,/DDOT/DDOT/, */
/* /DCOPY/DCOPY/,/DSCAL/DSCAL/,/DABS(/DABS(/, DABS/, DABS/,/D0/D0/ */
/* DIMENSION A(MDA,N+1),PRGOPT(*),X(N),WS((M+2)*(N+7)),IS(M+N+1), */
/* WHERE N=N1+N2. THIS IS A SLIGHT OVERESTIMATE FOR WS(*). */
/* WRITTEN BY R. J. HANSON AND K. H. HASKELL, SANDIA LABS */
/* REVISED OCT. 1, 1981. */
/* DETERMINE AN N1-VECTOR W, AND */
/* AN N2-VECTOR Z */
/* WHICH MINIMIZES THE EUCLIDEAN LENGTH OF W */
/* SUBJECT TO G*W+H*Z .GE. Y. */
/* THIS IS THE LEAST PROJECTED DISTANCE PROBLEM, LPDP. */
/* THE MATRICES G AND H ARE OF RESPECTIVE */
/* DIMENSIONS M BY N1 AND M BY N2. */
/* CALLED BY SUBPROGRAM LSI( ). */
/* THE MATRIX */
/* (G H Y) */
/* OCCUPIES ROWS 1,...,M AND COLS 1,...,N1+N2+1 OF A(*,*). */
/* THE SOLUTION (W) IS RETURNED IN X(*). */
/* (Z) */
/* THE VALUE OF MODE INDICATES THE STATUS OF */
/* THE COMPUTATION AFTER RETURNING TO THE USER. */
/* MODE=1 THE SOLUTION WAS SUCCESSFULLY OBTAINED. */
/* MODE=2 THE INEQUALITIES ARE INCONSISTENT. */
/* SUBROUTINES CALLED */
/* WNNLS SOLVES A NONNEGATIVELY CONSTRAINED LINEAR LEAST */
/* SQUARES PROBLEM WITH LINEAR EQUALITY CONSTRAINTS. */
/* PART OF THIS PACKAGE. */
/* ++ */
/* DDOT, SUBROUTINES FROM THE BLAS PACKAGE. */
/* DSCAL,DNRM2, SEE TRANS. MATH. SOFT., VOL. 5, NO. 3, P. 308. */
/* DCOPY */
/*< DOUBLE PRECISION A(MDA,1), PRGOPT(1), WS(1), WNORM, X(1) >*/
/*< INTEGER IS(1) >*/
/*< DOUBLE PRECISION FAC, ONE, RNORM, SC, YNORM, ZERO >*/
/*< DOUBLE PRECISION DDOT, DNRM2, DABS >*/
/*< DATA ZERO, ONE /0.D0,1.D0/, FAC /0.1E0/ >*/
#line 56 "../fortran/lpdp.f"
/* Parameter adjustments */
#line 56 "../fortran/lpdp.f"
a_dim1 = *mda;
#line 56 "../fortran/lpdp.f"
a_offset = 1 + a_dim1;
#line 56 "../fortran/lpdp.f"
a -= a_offset;
#line 56 "../fortran/lpdp.f"
--prgopt;
#line 56 "../fortran/lpdp.f"
--x;
#line 56 "../fortran/lpdp.f"
--ws;
//.........这里部分代码省略.........
/* Subroutine */ int dorgl2_(const integer *m, const integer *n, const integer *k, doublereal *
a, const integer *lda, const doublereal *tau, const doublereal *work, integer *info)
{
/* -- LAPACK routine (version 3.1) --
Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
November 2006
Purpose
=======
DORGL2 generates an m by n real matrix Q with orthonormal rows,
which is defined as the first m rows of a product of k elementary
reflectors of order n
Q = H(k) . . . H(2) H(1)
as returned by DGELQF.
Arguments
=========
M (input) INTEGER
The number of rows of the matrix Q. M >= 0.
N (input) INTEGER
The number of columns of the matrix Q. N >= M.
K (input) INTEGER
The number of elementary reflectors whose product defines the
matrix Q. M >= K >= 0.
A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
On entry, the i-th row must contain the vector which defines
the elementary reflector H(i), for i = 1,2,...,k, as returned
by DGELQF in the first k rows of its array argument A.
On exit, the m-by-n matrix Q.
LDA (input) INTEGER
The first dimension of the array A. LDA >= max(1,M).
TAU (input) DOUBLE PRECISION array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by DGELQF.
WORK (workspace) DOUBLE PRECISION array, dimension (M)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument has an illegal value
=====================================================================
Test the input arguments
Parameter adjustments */
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2;
doublereal d__1;
/* Local variables */
_THREAD_STATIC_ integer i__, j, l;
extern /* Subroutine */ int dscal_(const integer *, const doublereal *, const doublereal *,
const integer *), dlarf_(const char *, const integer *, const integer *, const doublereal *,
const integer *, const doublereal *, const doublereal *, const integer *, const doublereal *), xerbla_(const char *, const integer *);
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--tau;
--work;
/* Function Body */
*info = 0;
if (*m < 0) {
*info = -1;
} else if (*n < *m) {
*info = -2;
} else if (*k < 0 || *k > *m) {
*info = -3;
} else if (*lda < max(1,*m)) {
*info = -5;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("DORGL2", &i__1);
return 0;
}
/* Quick return if possible */
if (*m <= 0) {
return 0;
}
if (*k < *m) {
/* Initialise rows k+1:m to rows of the unit matrix */
i__1 = *n;
//.........这里部分代码省略.........
开发者ID:vopl，项目名称:sp，代码行数:101，代码来源:dorgl2.c
示例19: zhbev_
int zhbev_(char *jobz, char *uplo, int *n, int *kd,
doublecomplex *ab, int *ldab, double *w, doublecomplex *z__,
int *ldz, doublecomplex *work, double *rwork, int *info)
{
/* System generated locals */
int ab_dim1, ab_offset, z_dim1, z_offset, i__1;
double d__1;
/* Builtin functions */
double sqrt(double);
/* Local variables */
double eps;
int inde;
double anrm;
int imax;
double rmin, rmax;
extern int dscal_(int *, double *, double *,
int *);
double sigma;
extern int lsame_(char *, char *);
int iinfo;
int lower, wantz;
extern double dlamch_(char *);
int iscale;
double safmin;
extern double zlanhb_(char *, char *, int *, int *,
doublecomplex *, int *, double *);
extern int xerbla_(char *, int *);
double bignum;
extern int dsterf_(int *, double *, double *,
int *), zlascl_(char *, int *, int *, double *,
double *, int *, int *, doublecomplex *, int *,
int *), zhbtrd_(char *, char *, int *, int *,
doublecomplex *, int *, double *, double *,
doublecomplex *, int *, doublecomplex *, int *);
int indrwk;
double smlnum;
extern int zsteqr_(char *, int *, double *,
double *, doublecomplex *, int *, double *, int *);
/* -- LAPACK driver routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZHBEV computes all the eigenvalues and, optionally, eigenvectors of */
/* a complex Hermitian band matrix A. */
/* Arguments */
/* ========= */
/* JOBZ (input) CHARACTER*1 */
/* = 'N': Compute eigenvalues only; */
/* = 'V': Compute eigenvalues and eigenvectors. */
/* UPLO (input) CHARACTER*1 */
/* = 'U': Upper triangle of A is stored; */
/* = 'L': Lower triangle of A is stored. */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* KD (input) INTEGER */
/* The number of superdiagonals of the matrix A if UPLO = 'U', */
/* or the number of subdiagonals if UPLO = 'L'. KD >= 0. */
/* AB (input/output) COMPLEX*16 array, dimension (LDAB, N) */
/* On entry, the upper or lower triangle of the Hermitian band */
/* matrix A, stored in the first KD+1 rows of the array. The */
/* j-th column of A is stored in the j-th column of the array AB */
/* as follows: */
/* if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for MAX(1,j-kd)<=i<=j; */
/* if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=MIN(n,j+kd). */
/* On exit, AB is overwritten by values generated during the */
/* reduction to tridiagonal form. If UPLO = 'U', the first */
/* superdiagonal and the diagonal of the tridiagonal matrix T */
/* are returned in rows KD and KD+1 of AB, and if UPLO = 'L', */
/* the diagonal and first subdiagonal of T are returned in the */
/* first two rows of AB. */
/* LDAB (input) INTEGER */
/* The leading dimension of the array AB. LDAB >= KD + 1. */
/* W (output) DOUBLE PRECISION array, dimension (N) */
/* If INFO = 0, the eigenvalues in ascending order. */
/* Z (output) COMPLEX*16 array, dimension (LDZ, N) */
/* If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal */
/* eigenvectors of the matrix A, with the i-th column of Z */
/* holding the eigenvector associated with W(i). */
//.........这里部分代码省略.........
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