本文整理汇总了C++中caxpy_函数的典型用法代码示例。如果您正苦于以下问题：C++ caxpy_函数的具体用法？C++ caxpy_怎么用？C++ caxpy_使用的例子？那么恭喜您, 这里精选的函数代码示例或许可以为您提供帮助。
在下文中一共展示了caxpy_函数的15个代码示例，这些例子默认根据受欢迎程度排序。您可以为喜欢或者感觉有用的代码点赞，您的评价将有助于系统推荐出更棒的C++代码示例。
示例1: cblas_caxpy
void cblas_caxpy( const integer N, const void *alpha, const void *X,
const integer incX, void *Y, const integer incY)
{
#define F77_N N
#define F77_incX incX
#define F77_incY incY
caxpy_( &F77_N, alpha, X, &F77_incX, Y, &F77_incY);
}示例2: f2c_caxpy
int
f2c_caxpy(integer* N,
complex* alpha,
complex* X, integer* incX,
complex* Y, integer* incY)
{
caxpy_(N, alpha, X, incX, Y, incY);
return 0;
}示例3: r_imag
/* Subroutine */ int csyrfs_(char *uplo, integer *n, integer *nrhs, complex *
a, integer *lda, complex *af, integer *ldaf, integer *ipiv, complex *
b, integer *ldb, complex *x, integer *ldx, real *ferr, real *berr,
complex *work, real *rwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, af_dim1, af_offset, b_dim1, b_offset, x_dim1,
x_offset, i__1, i__2, i__3, i__4, i__5;
real r__1, r__2, r__3, r__4;
complex q__1;
/* Builtin functions */
double r_imag(complex *);
/* Local variables */
integer i__, j, k;
real s, xk;
integer nz;
real eps;
integer kase;
real safe1, safe2;
extern logical lsame_(char *, char *);
integer isave[3];
extern /* Subroutine */ int ccopy_(integer *, complex *, integer *,
complex *, integer *), caxpy_(integer *, complex *, complex *,
integer *, complex *, integer *);
integer count;
logical upper;
extern /* Subroutine */ int csymv_(char *, integer *, complex *, complex *
, integer *, complex *, integer *, complex *, complex *, integer *
), clacn2_(integer *, complex *, complex *, real *,
integer *, integer *);
extern doublereal slamch_(char *);
real safmin;
extern /* Subroutine */ int xerbla_(char *, integer *);
real lstres;
extern /* Subroutine */ int csytrs_(char *, integer *, integer *, complex
*, integer *, integer *, complex *, integer *, integer *);
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* Modified to call CLACN2 in place of CLACON, 10 Feb 03, SJH. */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CSYRFS improves the computed solution to a system of linear */
/* equations when the coefficient matrix is symmetric indefinite, and */
/* provides error bounds and backward error estimates for the solution. */
/* 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. */
/* NRHS (input) INTEGER */
/* The number of right hand sides, i.e., the number of columns */
/* of the matrices B and X. NRHS >= 0. */
/* A (input) COMPLEX array, dimension (LDA,N) */
/* 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, and the strictly lower triangular part of A */
/* is not referenced. If UPLO = 'L', the leading N-by-N lower */
/* triangular part of A contains the lower triangular part of */
/* the matrix A, and the strictly upper triangular part of A is */
/* not referenced. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,N). */
/* AF (input) COMPLEX array, dimension (LDAF,N) */
/* The factored form of the matrix A. AF contains the block */
/* diagonal matrix D and the multipliers used to obtain the */
/* factor U or L from the factorization A = U*D*U**T or */
/* A = L*D*L**T as computed by CSYTRF. */
/* LDAF (input) INTEGER */
/* The leading dimension of the array AF. LDAF >= max(1,N). */
/* IPIV (input) INTEGER array, dimension (N) */
/* Details of the interchanges and the block structure of D */
/* as determined by CSYTRF. */
/* B (input) COMPLEX array, dimension (LDB,NRHS) */
/* The right hand side matrix B. */
//.........这里部分代码省略.........
示例4: UPLO
//.........这里部分代码省略.........
< 0: if INFO = -i, the i-th argument had an illegal value
Internal Parameters
===================
ITMAX is the maximum number of steps of iterative refinement.
=====================================================================
Test the input parameters.
Parameter adjustments */
/* Table of constant values */
static complex c_b1 = {1.f,0.f};
static integer c__1 = 1;
/* System generated locals */
integer a_dim1, a_offset, af_dim1, af_offset, b_dim1, b_offset, x_dim1,
x_offset, i__1, i__2, i__3, i__4, i__5;
real r__1, r__2, r__3, r__4;
complex q__1;
/* Builtin functions */
double r_imag(complex *);
/* Local variables */
static integer kase;
static real safe1, safe2;
static integer i__, j, k;
static real s;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int chemv_(char *, integer *, complex *, complex *
, integer *, complex *, integer *, complex *, complex *, integer *
), ccopy_(integer *, complex *, integer *, complex *,
integer *), caxpy_(integer *, complex *, complex *, integer *,
complex *, integer *);
static integer count;
static logical upper;
extern /* Subroutine */ int clacon_(integer *, complex *, complex *, real
*, integer *);
static real xk;
extern doublereal slamch_(char *);
static integer nz;
static real safmin;
extern /* Subroutine */ int xerbla_(char *, integer *), chetrs_(
char *, integer *, integer *, complex *, integer *, integer *,
complex *, integer *, integer *);
static real lstres, eps;
#define a_subscr(a_1,a_2) (a_2)*a_dim1 + a_1
#define a_ref(a_1,a_2) a[a_subscr(a_1,a_2)]
#define b_subscr(a_1,a_2) (a_2)*b_dim1 + a_1
#define b_ref(a_1,a_2) b[b_subscr(a_1,a_2)]
#define x_subscr(a_1,a_2) (a_2)*x_dim1 + a_1
#define x_ref(a_1,a_2) x[x_subscr(a_1,a_2)]
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
af_dim1 = *ldaf;
af_offset = 1 + af_dim1 * 1;
af -= af_offset;
--ipiv;
b_dim1 = *ldb;
b_offset = 1 + b_dim1 * 1;
b -= b_offset;
x_dim1 = *ldx;示例5: r_imag
/* Subroutine */ int cgbrfs_(char *trans, integer *n, integer *kl, integer *
ku, integer *nrhs, complex *ab, integer *ldab, complex *afb, integer *
ldafb, integer *ipiv, complex *b, integer *ldb, complex *x, integer *
ldx, real *ferr, real *berr, complex *work, real *rwork, integer *
info)
{
/* System generated locals */
integer ab_dim1, ab_offset, afb_dim1, afb_offset, b_dim1, b_offset,
x_dim1, x_offset, i__1, i__2, i__3, i__4, i__5, i__6, i__7;
real r__1, r__2, r__3, r__4;
complex q__1;
/* Builtin functions */
double r_imag(complex *);
/* Local variables */
integer i__, j, k;
real s;
integer kk;
real xk;
integer nz;
real eps;
integer kase;
real safe1, safe2;
extern /* Subroutine */ int cgbmv_(char *, integer *, integer *, integer *
, integer *, complex *, complex *, integer *, complex *, integer *
, complex *, complex *, integer *);
extern logical lsame_(char *, char *);
integer isave[3];
extern /* Subroutine */ int ccopy_(integer *, complex *, integer *,
complex *, integer *), caxpy_(integer *, complex *, complex *,
integer *, complex *, integer *);
integer count;
extern /* Subroutine */ int clacn2_(integer *, complex *, complex *, real
*, integer *, integer *);
extern doublereal slamch_(char *);
real safmin;
extern /* Subroutine */ int xerbla_(char *, integer *), cgbtrs_(
char *, integer *, integer *, integer *, integer *, complex *,
integer *, integer *, complex *, integer *, integer *);
logical notran;
char transn[1], transt[1];
real lstres;
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* Modified to call CLACN2 in place of CLACON, 10 Feb 03, SJH. */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CGBRFS improves the computed solution to a system of linear */
/* equations when the coefficient matrix is banded, and provides */
/* error bounds and backward error estimates for the solution. */
/* Arguments */
/* ========= */
/* TRANS (input) CHARACTER*1 */
/* Specifies the form of the system of equations: */
/* = 'N': A * X = B (No transpose) */
/* = 'T': A**T * X = B (Transpose) */
/* = 'C': A**H * X = B (Conjugate transpose) */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* KL (input) INTEGER */
/* The number of subdiagonals within the band of A. KL >= 0. */
/* KU (input) INTEGER */
/* The number of superdiagonals within the band of A. KU >= 0. */
/* NRHS (input) INTEGER */
/* The number of right hand sides, i.e., the number of columns */
/* of the matrices B and X. NRHS >= 0. */
/* AB (input) COMPLEX array, dimension (LDAB,N) */
/* The original band matrix A, stored in rows 1 to KL+KU+1. */
/* The j-th column of A is stored in the j-th column of the */
/* array AB as follows: */
/* AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl). */
/* LDAB (input) INTEGER */
/* The leading dimension of the array AB. LDAB >= KL+KU+1. */
/* AFB (input) COMPLEX array, dimension (LDAFB,N) */
/* Details of the LU factorization of the band matrix A, as */
/* computed by CGBTRF. U is stored as an upper triangular band */
/* matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and */
/* the multipliers used during the factorization are stored in */
/* rows KL+KU+2 to 2*KL+KU+1. */
//.........这里部分代码省略.........
示例6: cgsrfs
//.........这里部分代码省略.........
*
*/
#define ITMAX 5
/* Table of constant values */
int ione = 1;
complex ndone = {-1., 0.};
complex done = {1., 0.};
/* Local variables */
NCformat *Astore;
complex *Aval;
SuperMatrix Bjcol;
DNformat *Bstore, *Xstore, *Bjcol_store;
complex *Bmat, *Xmat, *Bptr, *Xptr;
int kase;
float safe1, safe2;
int i, j, k, irow, nz, count, notran, rowequ, colequ;
int ldb, ldx, nrhs;
float s, xk, lstres, eps, safmin;
char transc[1];
trans_t transt;
complex *work;
float *rwork;
int *iwork;
extern double slamch_(char *);
extern int clacon_(int *, complex *, complex *, float *, int *);
#ifdef _CRAY
extern int CCOPY(int *, complex *, int *, complex *, int *);
extern int CSAXPY(int *, complex *, complex *, int *, complex *, int *);
#else
extern int ccopy_(int *, complex *, int *, complex *, int *);
extern int caxpy_(int *, complex *, complex *, int *, complex *, int *);
#endif
Astore = A->Store;
Aval = Astore->nzval;
Bstore = B->Store;
Xstore = X->Store;
Bmat = Bstore->nzval;
Xmat = Xstore->nzval;
ldb = Bstore->lda;
ldx = Xstore->lda;
nrhs = B->ncol;
/* Test the input parameters */
*info = 0;
notran = (trans == NOTRANS);
if ( !notran && trans != TRANS && trans != CONJ ) *info = -1;
else if ( A->nrow != A->ncol || A->nrow < 0 ||
A->Stype != SLU_NC || A->Dtype != SLU_C || A->Mtype != SLU_GE )
*info = -2;
else if ( L->nrow != L->ncol || L->nrow < 0 ||
L->Stype != SLU_SCP || L->Dtype != SLU_C || L->Mtype != SLU_TRLU )
*info = -3;
else if ( U->nrow != U->ncol || U->nrow < 0 ||
U->Stype != SLU_NCP || U->Dtype != SLU_C || U->Mtype != SLU_TRU )
*info = -4;
else if ( ldb < SUPERLU_MAX(0, A->nrow) ||
B->Stype != SLU_DN || B->Dtype != SLU_C || B->Mtype != SLU_GE )
*info = -10;
else if ( ldx < SUPERLU_MAX(0, A->nrow) ||
X->Stype != SLU_DN || X->Dtype != SLU_C || X->Mtype != SLU_GE )
*info = -11;
if (*info != 0) {示例7: ccopy_
/* DECK CSIDI */
/* Subroutine */ int csidi_(complex *a, integer *lda, integer *n, integer *
kpvt, complex *det, complex *work, integer *job)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3;
real r__1, r__2;
complex q__1, q__2, q__3;
/* Local variables */
static complex d__;
static integer j, k;
static complex t, ak;
static integer jb, ks, km1;
static real ten;
static complex akp1, temp, akkp1;
static logical nodet;
extern /* Subroutine */ int ccopy_(integer *, complex *, integer *,
complex *, integer *);
extern /* Complex */ void cdotu_(complex *, integer *, complex *, integer
*, complex *, integer *);
extern /* Subroutine */ int cswap_(integer *, complex *, integer *,
complex *, integer *), caxpy_(integer *, complex *, complex *,
integer *, complex *, integer *);
static integer kstep;
static logical noinv;
/* ***BEGIN PROLOGUE CSIDI */
/* ***PURPOSE Compute the determinant and inverse of a complex symmetric */
/* matrix using the factors from CSIFA. */
/* ***LIBRARY SLATEC (LINPACK) */
/* ***CATEGORY D2C1, D3C1 */
/* ***TYPE COMPLEX (SSIDI-S, DSIDI-D, CHIDI-C, CSIDI-C) */
/* ***KEYWORDS DETERMINANT, INVERSE, LINEAR ALGEBRA, LINPACK, MATRIX, */
/* SYMMETRIC */
/* ***AUTHOR Bunch, J., (UCSD) */
/* ***DESCRIPTION */
/* CSIDI computes the determinant and inverse */
/* of a complex symmetric matrix using the factors from CSIFA. */
/* On Entry */
/* A COMPLEX(LDA,N) */
/* the output from CSIFA. */
/* LDA INTEGER */
/* the leading dimension of the array A . */
/* N INTEGER */
/* the order of the matrix A . */
/* KVPT INTEGER(N) */
/* the pivot vector from CSIFA. */
/* WORK COMPLEX(N) */
/* work vector. Contents destroyed. */
/* JOB INTEGER */
/* JOB has the decimal expansion AB where */
/* If B .NE. 0, the inverse is computed, */
/* If A .NE. 0, the determinant is computed, */
/* For example, JOB = 11 gives both. */
/* On Return */
/* Variables not requested by JOB are not used. */
/* A contains the upper triangle of the inverse of */
/* the original matrix. The strict lower triangle */
/* is never referenced. */
/* DET COMPLEX(2) */
/* determinant of original matrix. */
/* Determinant = DET(1) * 10.0**DET(2) */
/* with 1.0 .LE. ABS(DET(1)) .LT. 10.0 */
/* or DET(1) = 0.0. */
/* Error Condition */
/* A division by zero may occur if the inverse is requested */
/* and CSICO has set RCOND .EQ. 0.0 */
/* or CSIFA has set INFO .NE. 0 . */
/* ***REFERENCES J. J. Dongarra, J. R. Bunch, C. B. Moler, and G. W. */
/* Stewart, LINPACK Users' Guide, SIAM, 1979. */
/* ***ROUTINES CALLED CAXPY, CCOPY, CDOTU, CSWAP */
/* ***REVISION HISTORY (YYMMDD) */
/* 780814 DATE WRITTEN */
/* 890531 Changed all specific intrinsics to generic. (WRB) */
/* 890831 Modified array declarations. (WRB) */
/* 891107 Corrected category and modified routine equivalence */
/* list. (WRB) */
/* 891107 REVISION DATE from Version 3.2 */
/* 891214 Prologue converted to Version 4.0 format. (BAB) */
/* 900326 Removed duplicate information from DESCRIPTION section. */
/* (WRB) */
/* 920501 Reformatted the REFERENCES section. (WRB) */
/* ***END PROLOGUE CSIDI */
//.........这里部分代码省略.........
示例8: lsame_
/* Subroutine */ int ctpt02_(char *uplo, char *trans, char *diag, integer *n,
integer *nrhs, complex *ap, complex *x, integer *ldx, complex *b,
integer *ldb, complex *work, real *rwork, real *resid)
{
/* System generated locals */
integer b_dim1, b_offset, x_dim1, x_offset, i__1;
real r__1, r__2;
/* Local variables */
static integer j;
extern logical lsame_(char *, char *);
static real anorm, bnorm;
extern /* Subroutine */ int ccopy_(integer *, complex *, integer *,
complex *, integer *), caxpy_(integer *, complex *, complex *,
integer *, complex *, integer *), ctpmv_(char *, char *, char *,
integer *, complex *, complex *, integer *);
static real xnorm;
extern doublereal slamch_(char *), clantp_(char *, char *, char *,
integer *, complex *, real *), scasum_(
integer *, complex *, integer *);
static real eps;
#define b_subscr(a_1,a_2) (a_2)*b_dim1 + a_1
#define b_ref(a_1,a_2) b[b_subscr(a_1,a_2)]
#define x_subscr(a_1,a_2) (a_2)*x_dim1 + a_1
#define x_ref(a_1,a_2) x[x_subscr(a_1,a_2)]
/* -- LAPACK test routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
February 29, 1992
Purpose
=======
CTPT02 computes the residual for the computed solution to a
triangular system of linear equations A*x = b, A**T *x = b, or
A**H *x = b, when the triangular matrix A is stored in packed format.
Here A**T denotes the transpose of A, A**H denotes the conjugate
transpose of A, and x and b are N by NRHS matrices. The test ratio
is the maximum over the number of right hand sides of
the maximum over the number of right hand sides of
norm(b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
where op(A) denotes A, A**T, or A**H, and EPS is the machine epsilon.
Arguments
=========
UPLO (input) CHARACTER*1
Specifies whether the matrix A is upper or lower triangular.
= 'U': Upper triangular
= 'L': Lower triangular
TRANS (input) CHARACTER*1
Specifies the operation applied to A.
= 'N': A *x = b (No transpose)
= 'T': A**T *x = b (Transpose)
= 'C': A**H *x = b (Conjugate transpose)
DIAG (input) CHARACTER*1
Specifies whether or not the matrix A is unit triangular.
= 'N': Non-unit triangular
= 'U': Unit triangular
N (input) INTEGER
The order of the matrix A. N >= 0.
NRHS (input) INTEGER
The number of right hand sides, i.e., the number of columns
of the matrices X and B. NRHS >= 0.
AP (input) COMPLEX array, dimension (N*(N+1)/2)
The upper or lower triangular 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((j-1)*j/2 + i) = A(i,j) for 1<=i<=j;
if UPLO = 'L',
AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n.
X (input) COMPLEX array, dimension (LDX,NRHS)
The computed solution vectors for the system of linear
equations.
LDX (input) INTEGER
The leading dimension of the array X. LDX >= max(1,N).
B (input) COMPLEX array, dimension (LDB,NRHS)
The right hand side vectors for the system of linear
equations.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).
WORK (workspace) COMPLEX array, dimension (N)
RWORK (workspace) REAL array, dimension (N)
//.........这里部分代码省略.........
示例9: cgehrd_
int cgehrd_(int *n, int *ilo, int *ihi, complex *
a, int *lda, complex *tau, complex *work, int *lwork, int
*info)
{
/* System generated locals */
int a_dim1, a_offset, i__1, i__2, i__3, i__4;
complex q__1;
/* Local variables */
int i__, j;
complex t[4160] /* was [65][64] */;
int ib;
complex ei;
int nb, nh, nx, iws;
extern int cgemm_(char *, char *, int *, int *,
int *, complex *, complex *, int *, complex *, int *,
complex *, complex *, int *);
int nbmin, iinfo;
extern int ctrmm_(char *, char *, char *, char *,
int *, int *, complex *, complex *, int *, complex *,
int *), caxpy_(int *,
complex *, complex *, int *, complex *, int *), cgehd2_(
int *, int *, int *, complex *, int *, complex *,
complex *, int *), clahr2_(int *, int *, int *,
complex *, int *, complex *, complex *, int *, complex *,
int *), clarfb_(char *, char *, char *, char *, int *,
int *, int *, complex *, int *, complex *, int *,
complex *, int *, complex *, int *), xerbla_(char *, int *);
extern int ilaenv_(int *, char *, char *, int *, int *,
int *, int *);
int ldwork, lwkopt;
int lquery;
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CGEHRD reduces a complex general matrix A to upper Hessenberg form H by */
/* an unitary similarity transformation: Q' * A * Q = H . */
/* Arguments */
/* ========= */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* ILO (input) INTEGER */
/* IHI (input) INTEGER */
/* It is assumed that A is already upper triangular in rows */
/* and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally */
/* set by a previous call to CGEBAL; otherwise they should be */
/* set to 1 and N respectively. See Further Details. */
/* 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0. */
/* A (input/output) COMPLEX array, dimension (LDA,N) */
/* On entry, the N-by-N general matrix to be reduced. */
/* On exit, the upper triangle and the first subdiagonal of A */
/* are overwritten with the upper Hessenberg matrix H, and the */
/* elements below the first subdiagonal, with the array TAU, */
/* represent the unitary matrix Q as a product of elementary */
/* reflectors. See Further Details. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= MAX(1,N). */
/* TAU (output) COMPLEX array, dimension (N-1) */
/* The scalar factors of the elementary reflectors (see Further */
/* Details). Elements 1:ILO-1 and IHI:N-1 of TAU are set to */
/* zero. */
/* WORK (workspace/output) COMPLEX 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,N). */
/* For optimum performance LWORK >= N*NB, where NB is the */
/* optimal blocksize. */
/* 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. */
/* Further Details */
/* =============== */
/* The matrix Q is represented as a product of (ihi-ilo) elementary */
//.........这里部分代码省略.........
示例10: cdotu_
/* DECK CSPSL */
/* Subroutine */ int cspsl_(complex *ap, integer *n, integer *kpvt, complex *
b)
{
/* System generated locals */
integer i__1, i__2, i__3;
complex q__1, q__2, q__3;
/* Local variables */
static integer k;
static complex ak, bk;
static integer ik, kk, kp;
static complex akm1, bkm1;
static integer ikm1, km1k, ikp1;
static complex temp;
static integer km1km1;
static complex denom;
extern /* Complex */ void cdotu_(complex *, integer *, complex *, integer
*, complex *, integer *);
extern /* Subroutine */ int caxpy_(integer *, complex *, complex *,
integer *, complex *, integer *);
/* ***BEGIN PROLOGUE CSPSL */
/* ***PURPOSE Solve a complex symmetric system using the factors obtained */
/* from CSPFA. */
/* ***LIBRARY SLATEC (LINPACK) */
/* ***CATEGORY D2C1 */
/* ***TYPE COMPLEX (SSPSL-S, DSPSL-D, CHPSL-C, CSPSL-C) */
/* ***KEYWORDS LINEAR ALGEBRA, LINPACK, MATRIX, PACKED, SOLVE, SYMMETRIC */
/* ***AUTHOR Bunch, J., (UCSD) */
/* ***DESCRIPTION */
/* CSISL solves the complex symmetric system */
/* A * X = B */
/* using the factors computed by CSPFA. */
/* On Entry */
/* AP COMPLEX(N*(N+1)/2) */
/* the output from CSPFA. */
/* N INTEGER */
/* the order of the matrix A . */
/* KVPT INTEGER(N) */
/* the pivot vector from CSPFA. */
/* B COMPLEX(N) */
/* the right hand side vector. */
/* On Return */
/* B the solution vector X . */
/* Error Condition */
/* A division by zero may occur if CSPCO has set RCOND .EQ. 0.0 */
/* or CSPFA has set INFO .NE. 0 . */
/* To compute INVERSE(A) * C where C is a matrix */
/* with P columns */
/* CALL CSPFA(AP,N,KVPT,INFO) */
/* IF (INFO .NE. 0) GO TO ... */
/* DO 10 J = 1, P */
/* CALL CSPSL(AP,N,KVPT,C(1,J)) */
/* 10 CONTINUE */
/* ***REFERENCES J. J. Dongarra, J. R. Bunch, C. B. Moler, and G. W. */
/* Stewart, LINPACK Users' Guide, SIAM, 1979. */
/* ***ROUTINES CALLED CAXPY, CDOTU */
/* ***REVISION HISTORY (YYMMDD) */
/* 780814 DATE WRITTEN */
/* 890531 Changed all specific intrinsics to generic. (WRB) */
/* 890831 Modified array declarations. (WRB) */
/* 891107 Corrected category and modified routine equivalence */
/* list. (WRB) */
/* 891107 REVISION DATE from Version 3.2 */
/* 891214 Prologue converted to Version 4.0 format. (BAB) */
/* 900326 Removed duplicate information from DESCRIPTION section. */
/* (WRB) */
/* 920501 Reformatted the REFERENCES section. (WRB) */
/* ***END PROLOGUE CSPSL */
/* LOOP BACKWARD APPLYING THE TRANSFORMATIONS AND */
/* D INVERSE TO B. */
/* ***FIRST EXECUTABLE STATEMENT CSPSL */
/* Parameter adjustments */
--b;
--kpvt;
--ap;
/* Function Body */
k = *n;
ik = *n * (*n - 1) / 2;
L10:
if (k == 0) {
goto L80;
}
//.........这里部分代码省略.........
示例11: chpr2_
/* Subroutine */ int chpgst_(integer *itype, char *uplo, integer *n, complex *
ap, complex *bp, integer *info, ftnlen uplo_len)
{
/* System generated locals */
integer i__1, i__2, i__3, i__4;
real r__1, r__2;
complex q__1, q__2, q__3;
/* Local variables */
static integer j, k, j1, k1, jj, kk;
static complex ct;
static real ajj;
static integer j1j1;
static real akk;
static integer k1k1;
static real bjj, bkk;
extern /* Subroutine */ int chpr2_(char *, integer *, complex *, complex *
, integer *, complex *, integer *, complex *, ftnlen);
extern /* Complex */ VOID cdotc_(complex *, integer *, complex *, integer
*, complex *, integer *);
extern logical lsame_(char *, char *, ftnlen, ftnlen);
extern /* Subroutine */ int chpmv_(char *, integer *, complex *, complex *
, complex *, integer *, complex *, complex *, integer *, ftnlen),
caxpy_(integer *, complex *, complex *, integer *, complex *,
integer *), ctpmv_(char *, char *, char *, integer *, complex *,
complex *, integer *, ftnlen, ftnlen, ftnlen);
static logical upper;
extern /* Subroutine */ int ctpsv_(char *, char *, char *, integer *,
complex *, complex *, integer *, ftnlen, ftnlen, ftnlen), csscal_(
integer *, real *, complex *, integer *), xerbla_(char *, integer
*, ftnlen);
/* -- LAPACK routine (version 3.0) -- */
/* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
/* Courant Institute, Argonne National Lab, and Rice University */
/* September 30, 1994 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CHPGST reduces a complex Hermitian-definite generalized */
/* eigenproblem to standard form, using packed storage. */
/* If ITYPE = 1, the problem is A*x = lambda*B*x, */
/* and A is overwritten by inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H) */
/* If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or */
/* B*A*x = lambda*x, and A is overwritten by U*A*U**H or L**H*A*L. */
/* B must have been previously factorized as U**H*U or L*L**H by CPPTRF. */
/* Arguments */
/* ========= */
/* ITYPE (input) INTEGER */
/* = 1: compute inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H); */
/* = 2 or 3: compute U*A*U**H or L**H*A*L. */
/* UPLO (input) CHARACTER */
/* = 'U': Upper triangle of A is stored and B is factored as */
/* U**H*U; */
/* = 'L': Lower triangle of A is stored and B is factored as */
/* L*L**H. */
/* N (input) INTEGER */
/* The order of the matrices A and B. N >= 0. */
/* AP (input/output) COMPLEX array, dimension (N*(N+1)/2) */
/* On entry, the upper or lower triangle of the Hermitian 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, if INFO = 0, the transformed matrix, stored in the */
/* same format as A. */
/* BP (input) COMPLEX array, dimension (N*(N+1)/2) */
/* The triangular factor from the Cholesky factorization of B, */
/* stored in the same format as A, as returned by CPPTRF. */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
//.........这里部分代码省略.........
示例12: r_imag
/* Subroutine */ int cla_gerfsx_extended__(integer *prec_type__, integer *
trans_type__, integer *n, integer *nrhs, complex *a, integer *lda,
complex *af, integer *ldaf, integer *ipiv, logical *colequ, real *c__,
complex *b, integer *ldb, complex *y, integer *ldy, real *berr_out__,
integer *n_norms__, real *errs_n__, real *errs_c__, complex *res,
real *ayb, complex *dy, complex *y_tail__, real *rcond, integer *
ithresh, real *rthresh, real *dz_ub__, logical *ignore_cwise__,
integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, af_dim1, af_offset, b_dim1, b_offset, y_dim1,
y_offset, errs_n_dim1, errs_n_offset, errs_c_dim1, errs_c_offset,
i__1, i__2, i__3, i__4;
real r__1, r__2;
char ch__1[1];
/* Builtin functions */
double r_imag(complex *);
/* Local variables */
real dxratmax, dzratmax;
integer i__, j;
extern /* Subroutine */ int cla_geamv__(integer *, integer *, integer *,
real *, complex *, integer *, complex *, integer *, real *, real *
, integer *);
logical incr_prec__;
real prev_dz_z__, yk, final_dx_x__;
extern /* Subroutine */ int cla_wwaddw__(integer *, complex *, complex *,
complex *);
real final_dz_z__, prevnormdx;
integer cnt;
real dyk, eps, incr_thresh__, dx_x__, dz_z__;
extern /* Subroutine */ int cla_lin_berr__(integer *, integer *, integer *
, complex *, real *, real *);
real ymin;
extern /* Subroutine */ int blas_cgemv_x__(integer *, integer *, integer *
, complex *, complex *, integer *, complex *, integer *, complex *
, complex *, integer *, integer *);
integer y_prec_state__;
extern /* Subroutine */ int blas_cgemv2_x__(integer *, integer *, integer
*, complex *, complex *, integer *, complex *, complex *, integer
*, complex *, complex *, integer *, integer *), cgemv_(char *,
integer *, integer *, complex *, complex *, integer *, complex *,
integer *, complex *, complex *, integer *), ccopy_(
integer *, complex *, integer *, complex *, integer *);
real dxrat, dzrat;
extern /* Subroutine */ int caxpy_(integer *, complex *, complex *,
integer *, complex *, integer *);
char trans[1];
real normx, normy;
extern doublereal slamch_(char *);
extern /* Subroutine */ int cgetrs_(char *, integer *, integer *, complex
*, integer *, integer *, complex *, integer *, integer *);
real normdx;
extern /* Character */ VOID chla_transtype__(char *, ftnlen, integer *);
real hugeval;
integer x_state__, z_state__;
/* -- LAPACK routine (version 3.2.1) -- */
/* -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and -- */
/* -- Jason Riedy of Univ. of California Berkeley. -- */
/* -- April 2009 -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley and NAG Ltd. -- */
/* .. */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments */
/* .. */
/* Purpose */
/* ======= */
/* CLA_GERFSX_EXTENDED improves the computed solution to a system of */
/* linear equations by performing extra-precise iterative refinement */
/* and provides error bounds and backward error estimates for the solution. */
/* This subroutine is called by CGERFSX to perform iterative refinement. */
/* In addition to normwise error bound, the code provides maximum */
/* componentwise error bound if possible. See comments for ERR_BNDS_NORM */
/* and ERR_BNDS_COMP for details of the error bounds. Note that this */
/* subroutine is only resonsible for setting the second fields of */
/* ERR_BNDS_NORM and ERR_BNDS_COMP. */
/* Arguments */
/* ========= */
/* PREC_TYPE (input) INTEGER */
/* Specifies the intermediate precision to be used in refinement. */
/* The value is defined by ILAPREC(P) where P is a CHARACTER and */
/* P = 'S': Single */
/* = 'D': Double */
/* = 'I': Indigenous */
/* = 'X', 'E': Extra */
/* TRANS_TYPE (input) INTEGER */
/* Specifies the transposition operation on A. */
/* The value is defined by ILATRANS(T) where T is a CHARACTER and */
//.........这里部分代码省略.........
示例13: c_abs
/* Subroutine */ int ctbt03_(char *uplo, char *trans, char *diag, integer *n,
integer *kd, integer *nrhs, complex *ab, integer *ldab, real *scale,
real *cnorm, real *tscal, complex *x, integer *ldx, complex *b,
integer *ldb, complex *work, real *resid)
{
/* System generated locals */
integer ab_dim1, ab_offset, b_dim1, b_offset, x_dim1, x_offset, i__1;
real r__1, r__2;
complex q__1;
/* Builtin functions */
double c_abs(complex *);
/* Local variables */
static integer j;
extern logical lsame_(char *, char *);
static real xscal;
extern /* Subroutine */ int ctbmv_(char *, char *, char *, integer *,
integer *, complex *, integer *, complex *, integer *), ccopy_(integer *, complex *, integer *, complex *
, integer *), caxpy_(integer *, complex *, complex *, integer *,
complex *, integer *);
static real tnorm, xnorm;
static integer ix;
extern integer icamax_(integer *, complex *, integer *);
extern doublereal slamch_(char *);
extern /* Subroutine */ int csscal_(integer *, real *, complex *, integer
*);
static real smlnum, eps, err;
#define b_subscr(a_1,a_2) (a_2)*b_dim1 + a_1
#define b_ref(a_1,a_2) b[b_subscr(a_1,a_2)]
#define x_subscr(a_1,a_2) (a_2)*x_dim1 + a_1
#define x_ref(a_1,a_2) x[x_subscr(a_1,a_2)]
#define ab_subscr(a_1,a_2) (a_2)*ab_dim1 + a_1
#define ab_ref(a_1,a_2) ab[ab_subscr(a_1,a_2)]
/* -- LAPACK test routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
February 29, 1992
Purpose
=======
CTBT03 computes the residual for the solution to a scaled triangular
system of equations A*x = s*b, A**T *x = s*b, or A**H *x = s*b
when A is a triangular band matrix. Here A**T denotes the transpose
of A, A**H denotes the conjugate transpose of A, s is a scalar, and
x and b are N by NRHS matrices. The test ratio is the maximum over
the number of right hand sides of
norm(s*b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
where op(A) denotes A, A**T, or A**H, and EPS is the machine epsilon.
Arguments
=========
UPLO (input) CHARACTER*1
Specifies whether the matrix A is upper or lower triangular.
= 'U': Upper triangular
= 'L': Lower triangular
TRANS (input) CHARACTER*1
Specifies the operation applied to A.
= 'N': A *x = s*b (No transpose)
= 'T': A**T *x = s*b (Transpose)
= 'C': A**H *x = s*b (Conjugate transpose)
DIAG (input) CHARACTER*1
Specifies whether or not the matrix A is unit triangular.
= 'N': Non-unit triangular
= 'U': Unit triangular
N (input) INTEGER
The order of the matrix A. N >= 0.
KD (input) INTEGER
The number of superdiagonals or subdiagonals of the
triangular band matrix A. KD >= 0.
NRHS (input) INTEGER
The number of right hand sides, i.e., the number of columns
of the matrices X and B. NRHS >= 0.
AB (input) COMPLEX array, dimension (LDAB,N)
The upper or lower triangular 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).
LDAB (input) INTEGER
The leading dimension of the array AB. LDAB >= KD+1.
SCALE (input) REAL
The scaling factor s used in solving the triangular system.
CNORM (input) REAL array, dimension (N)
//.........这里部分代码省略.........
示例14: if
//.........这里部分代码省略.........
i__1 = *n - i__;
c_div(&q__1, &c_b2, &wb);
cscal_(&i__1, &q__1, &work[2], &c__1);
work[1].r = 1.f, work[1].i = 0.f;
c_div(&q__1, &wb, &wa);
r__1 = q__1.r;
tau.r = r__1, tau.i = 0.f;
}
/* apply random reflection to A(i:n,i:n) from the left */
/* and the right */
/* compute y := tau * A * conjg(u) */
i__1 = *n - i__ + 1;
clacgv_(&i__1, &work[1], &c__1);
i__1 = *n - i__ + 1;
csymv_("Lower", &i__1, &tau, &a[i__ + i__ * a_dim1], lda, &work[1], &
c__1, &c_b1, &work[*n + 1], &c__1);
i__1 = *n - i__ + 1;
clacgv_(&i__1, &work[1], &c__1);
/* compute v := y - 1/2 * tau * ( u, y ) * u */
q__3.r = -.5f, q__3.i = -0.f;
q__2.r = q__3.r * tau.r - q__3.i * tau.i, q__2.i = q__3.r * tau.i +
q__3.i * tau.r;
i__1 = *n - i__ + 1;
cdotc_(&q__4, &i__1, &work[1], &c__1, &work[*n + 1], &c__1);
q__1.r = q__2.r * q__4.r - q__2.i * q__4.i, q__1.i = q__2.r * q__4.i
+ q__2.i * q__4.r;
alpha.r = q__1.r, alpha.i = q__1.i;
i__1 = *n - i__ + 1;
caxpy_(&i__1, &alpha, &work[1], &c__1, &work[*n + 1], &c__1);
/* apply the transformation as a rank-2 update to A(i:n,i:n) */
/* CALL CSYR2( 'Lower', N-I+1, -ONE, WORK, 1, WORK( N+1 ), 1, */
/* $ A( I, I ), LDA ) */
i__1 = *n;
for (jj = i__; jj <= i__1; ++jj) {
i__2 = *n;
for (ii = jj; ii <= i__2; ++ii) {
i__3 = ii + jj * a_dim1;
i__4 = ii + jj * a_dim1;
i__5 = ii - i__ + 1;
i__6 = *n + jj - i__ + 1;
q__3.r = work[i__5].r * work[i__6].r - work[i__5].i * work[
i__6].i, q__3.i = work[i__5].r * work[i__6].i + work[
i__5].i * work[i__6].r;
q__2.r = a[i__4].r - q__3.r, q__2.i = a[i__4].i - q__3.i;
i__7 = *n + ii - i__ + 1;
i__8 = jj - i__ + 1;
q__4.r = work[i__7].r * work[i__8].r - work[i__7].i * work[
i__8].i, q__4.i = work[i__7].r * work[i__8].i + work[
i__7].i * work[i__8].r;
q__1.r = q__2.r - q__4.r, q__1.i = q__2.i - q__4.i;
a[i__3].r = q__1.r, a[i__3].i = q__1.i;
/* L40: */
}
/* L50: */
}
/* L60: */
}
示例15: slamch_
//.........这里部分代码省略.........
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Quick exit if N = 0 */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--cnorm;
x_dim1 = *ldx;
x_offset = 1 + x_dim1;
x -= x_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
--work;
/* Function Body */
if (*n <= 0 || *nrhs <= 0) {
*resid = 0.f;
return 0;
}
eps = slamch_("Epsilon");
smlnum = slamch_("Safe minimum");
/* Compute the norm of the triangular matrix A using the column */
/* norms already computed by CLATRS. */
tnorm = 0.f;
if (lsame_(diag, "N")) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
r__1 = tnorm, r__2 = *tscal * c_abs(&a[j + j * a_dim1]) + cnorm[j]
;
tnorm = dmax(r__1,r__2);
/* L10: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
r__1 = tnorm, r__2 = *tscal + cnorm[j];
tnorm = dmax(r__1,r__2);
/* L20: */
}
}
/* Compute the maximum over the number of right hand sides of */
/* norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ). */
*resid = 0.f;
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
ccopy_(n, &x[j * x_dim1 + 1], &c__1, &work[1], &c__1);
ix = icamax_(n, &work[1], &c__1);
/* Computing MAX */
r__1 = 1.f, r__2 = c_abs(&x[ix + j * x_dim1]);
xnorm = dmax(r__1,r__2);
xscal = 1.f / xnorm / (real) (*n);
csscal_(n, &xscal, &work[1], &c__1);
ctrmv_(uplo, trans, diag, n, &a[a_offset], lda, &work[1], &c__1);
r__1 = -(*scale) * xscal;
q__1.r = r__1, q__1.i = 0.f;
caxpy_(n, &q__1, &b[j * b_dim1 + 1], &c__1, &work[1], &c__1);
ix = icamax_(n, &work[1], &c__1);
err = *tscal * c_abs(&work[ix]);
ix = icamax_(n, &x[j * x_dim1 + 1], &c__1);
xnorm = c_abs(&x[ix + j * x_dim1]);
if (err * smlnum <= xnorm) {
if (xnorm > 0.f) {
err /= xnorm;
}
} else {
if (err > 0.f) {
err = 1.f / eps;
}
}
if (err * smlnum <= tnorm) {
if (tnorm > 0.f) {
err /= tnorm;
}
} else {
if (err > 0.f) {
err = 1.f / eps;
}
}
*resid = dmax(*resid,err);
/* L30: */
}
return 0;
/* End of CTRT03 */
} /* ctrt03_ */