DLLEXPORT int c_lu_solve_factored(int n, int nrhs, complex a[], int ipiv[], complex b[])
{
int info = 0;
int i;
for(i = 0; i < n; ++i ){
ipiv[i] += 1;
}
char trans ='N';
cgetrs_(&trans, &n, &nrhs, a, &n, ipiv, b, &n, &info);
for(i = 0; i < n; ++i ){
ipiv[i] -= 1;
}
return info;
}
DLLEXPORT MKL_INT c_lu_solve_factored(MKL_INT n, MKL_INT nrhs, MKL_Complex8 a[], MKL_INT ipiv[], MKL_Complex8 b[])
{
MKL_INT info = 0;
MKL_INT i;
for(i = 0; i < n; ++i ){
ipiv[i] += 1;
}
char trans ='N';
cgetrs_(&trans, &n, &nrhs, a, &n, ipiv, b, &n, &info);
for(i = 0; i < n; ++i ){
ipiv[i] -= 1;
}
return info;
}
DLLEXPORT MKL_INT c_lu_solve(MKL_INT n, MKL_INT nrhs, MKL_Complex8 a[], MKL_Complex8 b[])
{
MKL_Complex8* clone = new MKL_Complex8[n*n];
std::memcpy(clone, a, n*n*sizeof(MKL_Complex8));
MKL_INT* ipiv = new MKL_INT[n];
MKL_INT info = 0;
cgetrf_(&n, &n, clone, &n, ipiv, &info);
if (info != 0){
delete[] ipiv;
delete[] clone;
return info;
}
char trans ='N';
cgetrs_(&trans, &n, &nrhs, clone, &n, ipiv, b, &n, &info);
delete[] ipiv;
delete[] clone;
return info;
}
DLLEXPORT int c_lu_solve(int n, int nrhs, complex a[], complex b[])
{
complex* clone = new complex[n*n];
memcpy(clone, a, n*n*sizeof(complex));
int* ipiv = new int[n];
int info = 0;
cgetrf_(&n, &n, clone, &n, ipiv, &info);
if (info != 0){
delete[] ipiv;
delete[] clone;
return info;
}
char trans ='N';
cgetrs_(&trans, &n, &nrhs, clone, &n, ipiv, b, &n, &info);
delete[] ipiv;
delete[] clone;
return info;
}
/* Subroutine */ int cgesv_(integer *n, integer *nrhs, complex *a, integer *
lda, integer *ipiv, complex *b, integer *ldb, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, i__1;
/* Local variables */
/* -- LAPACK driver routine (version 3.2) -- */
/* November 2006 */
/* Purpose */
/* ======= */
/* CGESV computes the solution to a complex system of linear equations */
/* A * X = B, */
/* where A is an N-by-N matrix and X and B are N-by-NRHS matrices. */
/* The LU decomposition with partial pivoting and row interchanges is */
/* used to factor A as */
/* A = P * L * U, */
/* where P is a permutation matrix, L is unit lower triangular, and U is */
/* upper triangular. The factored form of A is then used to solve the */
/* system of equations A * X = B. */
/* Arguments */
/* ========= */
/* N (input) INTEGER */
/* The number of linear equations, i.e., 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 matrix B. NRHS >= 0. */
/* A (input/output) COMPLEX array, dimension (LDA,N) */
/* On entry, the N-by-N coefficient matrix A. */
/* On exit, the factors L and U from the factorization */
/* A = P*L*U; the unit diagonal elements of L are not stored. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,N). */
/* IPIV (output) INTEGER array, dimension (N) */
/* The pivot indices that define the permutation matrix P; */
/* row i of the matrix was interchanged with row IPIV(i). */
/* B (input/output) COMPLEX array, dimension (LDB,NRHS) */
/* On entry, the N-by-NRHS matrix of right hand side matrix B. */
/* On exit, if INFO = 0, the N-by-NRHS solution matrix X. */
/* LDB (input) INTEGER */
/* The leading dimension of the array B. LDB >= max(1,N). */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* > 0: if INFO = i, U(i,i) is exactly zero. The factorization */
/* has been completed, but the factor U is exactly */
/* singular, so the solution could not be computed. */
/* ===================================================================== */
/* Test the input parameters. */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--ipiv;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
/* Function Body */
*info = 0;
if (*n < 0) {
*info = -1;
} else if (*nrhs < 0) {
*info = -2;
} else if (*lda < max(1,*n)) {
*info = -4;
} else if (*ldb < max(1,*n)) {
*info = -7;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CGESV ", &i__1);
return 0;
}
/* Compute the LU factorization of A. */
cgetrf_(n, n, &a[a_offset], lda, &ipiv[1], info);
if (*info == 0) {
/* Solve the system A*X = B, overwriting B with X. */
cgetrs_("No transpose", n, nrhs, &a[a_offset], lda, &ipiv[1], &b[
b_offset], ldb, info);
}
return 0;
/* End of CGESV */
} /* cgesv_ */
/* Subroutine */ int cgesvx_(char *fact, char *trans, integer *n, integer *
nrhs, complex *a, integer *lda, complex *af, integer *ldaf, integer *
ipiv, char *equed, real *r__, real *c__, complex *b, integer *ldb,
complex *x, integer *ldx, real *rcond, 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;
complex q__1;
/* Local variables */
integer i__, j;
real amax;
char norm[1];
extern logical lsame_(char *, char *);
real rcmin, rcmax, anorm;
logical equil;
extern doublereal clange_(char *, integer *, integer *, complex *,
integer *, real *);
extern /* Subroutine */ int claqge_(integer *, integer *, complex *,
integer *, real *, real *, real *, real *, real *, char *)
, cgecon_(char *, integer *, complex *, integer *, real *, real *,
complex *, real *, integer *);
real colcnd;
extern doublereal slamch_(char *);
extern /* Subroutine */ int cgeequ_(integer *, integer *, complex *,
integer *, real *, real *, real *, real *, real *, integer *);
logical nofact;
extern /* Subroutine */ int cgerfs_(char *, integer *, integer *, complex
*, integer *, complex *, integer *, integer *, complex *, integer
*, complex *, integer *, real *, real *, complex *, real *,
integer *), cgetrf_(integer *, integer *, complex *,
integer *, integer *, integer *), clacpy_(char *, integer *,
integer *, complex *, integer *, complex *, integer *),
xerbla_(char *, integer *);
real bignum;
extern doublereal clantr_(char *, char *, char *, integer *, integer *,
complex *, integer *, real *);
integer infequ;
logical colequ;
extern /* Subroutine */ int cgetrs_(char *, integer *, integer *, complex
*, integer *, integer *, complex *, integer *, integer *);
real rowcnd;
logical notran;
real smlnum;
logical rowequ;
real rpvgrw;
/* -- LAPACK driver routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CGESVX uses the LU factorization to compute the solution to a complex */
/* system of linear equations */
/* A * X = B, */
/* where A is an N-by-N matrix and X and B are N-by-NRHS matrices. */
/* Error bounds on the solution and a condition estimate are also */
/* provided. */
/* Description */
/* =========== */
/* The following steps are performed: */
/* 1. If FACT = 'E', real scaling factors are computed to equilibrate */
/* the system: */
/* TRANS = 'N': diag(R)*A*diag(C) *inv(diag(C))*X = diag(R)*B */
/* TRANS = 'T': (diag(R)*A*diag(C))**T *inv(diag(R))*X = diag(C)*B */
/* TRANS = 'C': (diag(R)*A*diag(C))**H *inv(diag(R))*X = diag(C)*B */
/* Whether or not the system will be equilibrated depends on the */
/* scaling of the matrix A, but if equilibration is used, A is */
/* overwritten by diag(R)*A*diag(C) and B by diag(R)*B (if TRANS='N') */
/* or diag(C)*B (if TRANS = 'T' or 'C'). */
/* 2. If FACT = 'N' or 'E', the LU decomposition is used to factor the */
/* matrix A (after equilibration if FACT = 'E') as */
/* A = P * L * U, */
/* where P is a permutation matrix, L is a unit lower triangular */
/* matrix, and U is upper triangular. */
/* 3. If some U(i,i)=0, so that U is exactly singular, then the routine */
/* returns with INFO = i. Otherwise, the factored form of A is used */
/* to estimate the condition number of the matrix A. If the */
/* reciprocal of the condition number is less than machine precision, */
/* INFO = N+1 is returned as a warning, but the routine still goes on */
/* to solve for X and compute error bounds as described below. */
/* 4. The system of equations is solved for X using the factored form */
/* of A. */
/* 5. Iterative refinement is applied to improve the computed solution */
/* matrix and calculate error bounds and backward error estimates */
/* for it. */
/* 6. If equilibration was used, the matrix X is premultiplied by */
/* diag(C) (if TRANS = 'N') or diag(R) (if TRANS = 'T' or 'C') so */
/* that it solves the original system before equilibration. */
/* Arguments */
/* ========= */
/* FACT (input) CHARACTER*1 */
/* Specifies whether or not the factored form of the matrix A is */
/* supplied on entry, and if not, whether the matrix A should be */
/* equilibrated before it is factored. */
/* = 'F': On entry, AF and IPIV contain the factored form of A. */
/* If EQUED is not 'N', the matrix A has been */
/* equilibrated with scaling factors given by R and C. */
/* A, AF, and IPIV are not modified. */
/* = 'N': The matrix A will be copied to AF and factored. */
/* = 'E': The matrix A will be equilibrated if necessary, then */
/* copied to AF and factored. */
/* 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 number of linear equations, i.e., 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/output) COMPLEX array, dimension (LDA,N) */
/* On entry, the N-by-N matrix A. If FACT = 'F' and EQUED is */
/* not 'N', then A must have been equilibrated by the scaling */
/* factors in R and/or C. A is not modified if FACT = 'F' or */
/* 'N', or if FACT = 'E' and EQUED = 'N' on exit. */
/* On exit, if EQUED .ne. 'N', A is scaled as follows: */
/* EQUED = 'R': A := diag(R) * A */
/* EQUED = 'C': A := A * diag(C) */
/* EQUED = 'B': A := diag(R) * A * diag(C). */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,N). */
/* AF (input or output) COMPLEX array, dimension (LDAF,N) */
/* If FACT = 'F', then AF is an input argument and on entry */
/* contains the factors L and U from the factorization */
/* A = P*L*U as computed by CGETRF. If EQUED .ne. 'N', then */
/* AF is the factored form of the equilibrated matrix A. */
/* If FACT = 'N', then AF is an output argument and on exit */
/* returns the factors L and U from the factorization A = P*L*U */
/* of the original matrix A. */
/* If FACT = 'E', then AF is an output argument and on exit */
/* returns the factors L and U from the factorization A = P*L*U */
/* of the equilibrated matrix A (see the description of A for */
/* the form of the equilibrated matrix). */
/* LDAF (input) INTEGER */
/* The leading dimension of the array AF. LDAF >= max(1,N). */
/* IPIV (input or output) INTEGER array, dimension (N) */
/* If FACT = 'F', then IPIV is an input argument and on entry */
/* contains the pivot indices from the factorization A = P*L*U */
/* as computed by CGETRF; row i of the matrix was interchanged */
/* with row IPIV(i). */
/* If FACT = 'N', then IPIV is an output argument and on exit */
/* contains the pivot indices from the factorization A = P*L*U */
/* of the original matrix A. */
/* If FACT = 'E', then IPIV is an output argument and on exit */
/* contains the pivot indices from the factorization A = P*L*U */
/* of the equilibrated matrix A. */
/* EQUED (input or output) CHARACTER*1 */
/* Specifies the form of equilibration that was done. */
/* = 'N': No equilibration (always true if FACT = 'N'). */
/* = 'R': Row equilibration, i.e., A has been premultiplied by */
/* diag(R). */
/* = 'C': Column equilibration, i.e., A has been postmultiplied */
/* by diag(C). */
/* = 'B': Both row and column equilibration, i.e., A has been */
/* replaced by diag(R) * A * diag(C). */
/* EQUED is an input argument if FACT = 'F'; otherwise, it is an */
/* output argument. */
/* R (input or output) REAL array, dimension (N) */
/* The row scale factors for A. If EQUED = 'R' or 'B', A is */
/* multiplied on the left by diag(R); if EQUED = 'N' or 'C', R */
/* is not accessed. R is an input argument if FACT = 'F'; */
/* otherwise, R is an output argument. If FACT = 'F' and */
/* EQUED = 'R' or 'B', each element of R must be positive. */
/* C (input or output) REAL array, dimension (N) */
/* The column scale factors for A. If EQUED = 'C' or 'B', A is */
/* multiplied on the right by diag(C); if EQUED = 'N' or 'R', C */
/* is not accessed. C is an input argument if FACT = 'F'; */
/* otherwise, C is an output argument. If FACT = 'F' and */
/* EQUED = 'C' or 'B', each element of C must be positive. */
/* B (input/output) COMPLEX array, dimension (LDB,NRHS) */
/* On entry, the N-by-NRHS right hand side matrix B. */
/* On exit, */
/* if EQUED = 'N', B is not modified; */
/* if TRANS = 'N' and EQUED = 'R' or 'B', B is overwritten by */
/* diag(R)*B; */
/* if TRANS = 'T' or 'C' and EQUED = 'C' or 'B', B is */
/* overwritten by diag(C)*B. */
/* LDB (input) INTEGER */
/* The leading dimension of the array B. LDB >= max(1,N). */
/* X (output) COMPLEX array, dimension (LDX,NRHS) */
/* If INFO = 0 or INFO = N+1, the N-by-NRHS solution matrix X */
/* to the original system of equations. Note that A and B are */
/* modified on exit if EQUED .ne. 'N', and the solution to the */
/* equilibrated system is inv(diag(C))*X if TRANS = 'N' and */
/* EQUED = 'C' or 'B', or inv(diag(R))*X if TRANS = 'T' or 'C' */
/* and EQUED = 'R' or 'B'. */
/* LDX (input) INTEGER */
/* The leading dimension of the array X. LDX >= max(1,N). */
/* RCOND (output) REAL */
/* The estimate of the reciprocal condition number of the matrix */
/* A after equilibration (if done). If RCOND is less than the */
/* machine precision (in particular, if RCOND = 0), the matrix */
/* is singular to working precision. This condition is */
/* indicated by a return code of INFO > 0. */
/* FERR (output) REAL array, dimension (NRHS) */
/* The estimated forward error bound for each solution vector */
/* X(j) (the j-th column of the solution matrix X). */
/* If XTRUE is the true solution corresponding to X(j), FERR(j) */
/* is an estimated upper bound for the magnitude of the largest */
/* element in (X(j) - XTRUE) divided by the magnitude of the */
/* largest element in X(j). The estimate is as reliable as */
/* the estimate for RCOND, and is almost always a slight */
/* overestimate of the true error. */
/* BERR (output) REAL array, dimension (NRHS) */
/* The componentwise relative backward error of each solution */
/* vector X(j) (i.e., the smallest relative change in */
/* any element of A or B that makes X(j) an exact solution). */
/* WORK (workspace) COMPLEX array, dimension (2*N) */
/* RWORK (workspace/output) REAL array, dimension (2*N) */
/* On exit, RWORK(1) contains the reciprocal pivot growth */
/* factor norm(A)/norm(U). The "max absolute element" norm is */
/* used. If RWORK(1) is much less than 1, then the stability */
/* of the LU factorization of the (equilibrated) matrix A */
/* could be poor. This also means that the solution X, condition */
/* estimator RCOND, and forward error bound FERR could be */
/* unreliable. If factorization fails with 0<INFO<=N, then */
/* RWORK(1) contains the reciprocal pivot growth factor for the */
/* leading INFO columns of A. */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* > 0: if INFO = i, and i is */
/* <= N: U(i,i) is exactly zero. The factorization has */
/* been completed, but the factor U is exactly */
/* singular, so the solution and error bounds */
/* could not be computed. RCOND = 0 is returned. */
/* = N+1: U is nonsingular, but RCOND is less than machine */
/* precision, meaning that the matrix is singular */
/* to working precision. Nevertheless, the */
/* solution and error bounds are computed because */
/* there are a number of situations where the */
/* computed solution can be more accurate than the */
/* value of RCOND would suggest. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
af_dim1 = *ldaf;
af_offset = 1 + af_dim1;
af -= af_offset;
--ipiv;
--r__;
--c__;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
x_dim1 = *ldx;
x_offset = 1 + x_dim1;
x -= x_offset;
--ferr;
--berr;
--work;
--rwork;
/* Function Body */
*info = 0;
nofact = lsame_(fact, "N");
equil = lsame_(fact, "E");
notran = lsame_(trans, "N");
if (nofact || equil) {
*(unsigned char *)equed = 'N';
rowequ = FALSE_;
colequ = FALSE_;
} else {
rowequ = lsame_(equed, "R") || lsame_(equed,
"B");
colequ = lsame_(equed, "C") || lsame_(equed,
"B");
smlnum = slamch_("Safe minimum");
bignum = 1.f / smlnum;
}
/* Test the input parameters. */
if (! nofact && ! equil && ! lsame_(fact, "F")) {
*info = -1;
} else if (! notran && ! lsame_(trans, "T") && !
lsame_(trans, "C")) {
*info = -2;
} else if (*n < 0) {
*info = -3;
} else if (*nrhs < 0) {
*info = -4;
} else if (*lda < max(1,*n)) {
*info = -6;
} else if (*ldaf < max(1,*n)) {
*info = -8;
} else if (lsame_(fact, "F") && ! (rowequ || colequ
|| lsame_(equed, "N"))) {
*info = -10;
} else {
if (rowequ) {
rcmin = bignum;
rcmax = 0.f;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
r__1 = rcmin, r__2 = r__[j];
rcmin = dmin(r__1,r__2);
/* Computing MAX */
r__1 = rcmax, r__2 = r__[j];
rcmax = dmax(r__1,r__2);
/* L10: */
}
if (rcmin <= 0.f) {
*info = -11;
} else if (*n > 0) {
rowcnd = dmax(rcmin,smlnum) / dmin(rcmax,bignum);
} else {
rowcnd = 1.f;
}
}
if (colequ && *info == 0) {
rcmin = bignum;
rcmax = 0.f;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
r__1 = rcmin, r__2 = c__[j];
rcmin = dmin(r__1,r__2);
/* Computing MAX */
r__1 = rcmax, r__2 = c__[j];
rcmax = dmax(r__1,r__2);
/* L20: */
}
if (rcmin <= 0.f) {
*info = -12;
} else if (*n > 0) {
colcnd = dmax(rcmin,smlnum) / dmin(rcmax,bignum);
} else {
colcnd = 1.f;
}
}
if (*info == 0) {
if (*ldb < max(1,*n)) {
*info = -14;
} else if (*ldx < max(1,*n)) {
*info = -16;
}
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CGESVX", &i__1);
return 0;
}
if (equil) {
/* Compute row and column scalings to equilibrate the matrix A. */
cgeequ_(n, n, &a[a_offset], lda, &r__[1], &c__[1], &rowcnd, &colcnd, &
amax, &infequ);
if (infequ == 0) {
/* Equilibrate the matrix. */
claqge_(n, n, &a[a_offset], lda, &r__[1], &c__[1], &rowcnd, &
colcnd, &amax, equed);
rowequ = lsame_(equed, "R") || lsame_(equed,
"B");
colequ = lsame_(equed, "C") || lsame_(equed,
"B");
}
}
/* Scale the right hand side. */
if (notran) {
if (rowequ) {
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
i__4 = i__;
i__5 = i__ + j * b_dim1;
q__1.r = r__[i__4] * b[i__5].r, q__1.i = r__[i__4] * b[
i__5].i;
b[i__3].r = q__1.r, b[i__3].i = q__1.i;
/* L30: */
}
/* L40: */
}
}
} else if (colequ) {
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
i__4 = i__;
i__5 = i__ + j * b_dim1;
q__1.r = c__[i__4] * b[i__5].r, q__1.i = c__[i__4] * b[i__5]
.i;
b[i__3].r = q__1.r, b[i__3].i = q__1.i;
/* L50: */
}
/* L60: */
}
}
if (nofact || equil) {
/* Compute the LU factorization of A. */
clacpy_("Full", n, n, &a[a_offset], lda, &af[af_offset], ldaf);
cgetrf_(n, n, &af[af_offset], ldaf, &ipiv[1], info);
/* Return if INFO is non-zero. */
if (*info > 0) {
/* Compute the reciprocal pivot growth factor of the */
/* leading rank-deficient INFO columns of A. */
rpvgrw = clantr_("M", "U", "N", info, info, &af[af_offset], ldaf,
&rwork[1]);
if (rpvgrw == 0.f) {
rpvgrw = 1.f;
} else {
rpvgrw = clange_("M", n, info, &a[a_offset], lda, &rwork[1]) / rpvgrw;
}
rwork[1] = rpvgrw;
*rcond = 0.f;
return 0;
}
}
/* Compute the norm of the matrix A and the */
/* reciprocal pivot growth factor RPVGRW. */
if (notran) {
*(unsigned char *)norm = '1';
} else {
*(unsigned char *)norm = 'I';
}
anorm = clange_(norm, n, n, &a[a_offset], lda, &rwork[1]);
rpvgrw = clantr_("M", "U", "N", n, n, &af[af_offset], ldaf, &rwork[1]);
if (rpvgrw == 0.f) {
rpvgrw = 1.f;
} else {
rpvgrw = clange_("M", n, n, &a[a_offset], lda, &rwork[1]) /
rpvgrw;
}
/* Compute the reciprocal of the condition number of A. */
cgecon_(norm, n, &af[af_offset], ldaf, &anorm, rcond, &work[1], &rwork[1],
info);
/* Compute the solution matrix X. */
clacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx);
cgetrs_(trans, n, nrhs, &af[af_offset], ldaf, &ipiv[1], &x[x_offset], ldx,
info);
/* Use iterative refinement to improve the computed solution and */
/* compute error bounds and backward error estimates for it. */
cgerfs_(trans, n, nrhs, &a[a_offset], lda, &af[af_offset], ldaf, &ipiv[1],
&b[b_offset], ldb, &x[x_offset], ldx, &ferr[1], &berr[1], &work[
1], &rwork[1], info);
/* Transform the solution matrix X to a solution of the original */
/* system. */
if (notran) {
if (colequ) {
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * x_dim1;
i__4 = i__;
i__5 = i__ + j * x_dim1;
q__1.r = c__[i__4] * x[i__5].r, q__1.i = c__[i__4] * x[
i__5].i;
x[i__3].r = q__1.r, x[i__3].i = q__1.i;
/* L70: */
}
/* L80: */
}
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
ferr[j] /= colcnd;
/* L90: */
}
}
} else if (rowequ) {
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * x_dim1;
i__4 = i__;
i__5 = i__ + j * x_dim1;
q__1.r = r__[i__4] * x[i__5].r, q__1.i = r__[i__4] * x[i__5]
.i;
x[i__3].r = q__1.r, x[i__3].i = q__1.i;
/* L100: */
}
/* L110: */
}
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
ferr[j] /= rowcnd;
/* L120: */
}
}
/* Set INFO = N+1 if the matrix is singular to working precision. */
if (*rcond < slamch_("Epsilon")) {
*info = *n + 1;
}
rwork[1] = rpvgrw;
return 0;
/* End of CGESVX */
} /* cgesvx_ */
/* 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 */
/* T = 'N': No transpose */
/* = 'T': Transpose */
/* = 'C': Conjugate transpose */
/* N (input) INTEGER */
/* The number of linear equations, i.e., 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 */
/* matrix B. */
/* A (input) COMPLEX array, dimension (LDA,N) */
/* On entry, the N-by-N matrix A. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,N). */
/* AF (input) COMPLEX array, dimension (LDAF,N) */
/* The factors L and U from the factorization */
/* A = P*L*U as computed by CGETRF. */
/* LDAF (input) INTEGER */
/* The leading dimension of the array AF. LDAF >= max(1,N). */
/* IPIV (input) INTEGER array, dimension (N) */
/* The pivot indices from the factorization A = P*L*U */
/* as computed by CGETRF; row i of the matrix was interchanged */
/* with row IPIV(i). */
/* COLEQU (input) LOGICAL */
/* If .TRUE. then column equilibration was done to A before calling */
/* this routine. This is needed to compute the solution and error */
/* bounds correctly. */
/* C (input) REAL array, dimension (N) */
/* The column scale factors for A. If COLEQU = .FALSE., C */
/* is not accessed. If C is input, each element of C should be a power */
/* of the radix to ensure a reliable solution and error estimates. */
/* Scaling by powers of the radix does not cause rounding errors unless */
/* the result underflows or overflows. Rounding errors during scaling */
/* lead to refining with a matrix that is not equivalent to the */
/* input matrix, producing error estimates that may not be */
/* reliable. */
/* B (input) COMPLEX array, dimension (LDB,NRHS) */
/* The right-hand-side matrix B. */
/* LDB (input) INTEGER */
/* The leading dimension of the array B. LDB >= max(1,N). */
/* Y (input/output) COMPLEX array, dimension (LDY,NRHS) */
/* On entry, the solution matrix X, as computed by CGETRS. */
/* On exit, the improved solution matrix Y. */
/* LDY (input) INTEGER */
/* The leading dimension of the array Y. LDY >= max(1,N). */
/* BERR_OUT (output) REAL array, dimension (NRHS) */
/* On exit, BERR_OUT(j) contains the componentwise relative backward */
/* error for right-hand-side j from the formula */
/* max(i) ( abs(RES(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) ) */
/* where abs(Z) is the componentwise absolute value of the matrix */
/* or vector Z. This is computed by CLA_LIN_BERR. */
/* N_NORMS (input) INTEGER */
/* Determines which error bounds to return (see ERR_BNDS_NORM */
/* and ERR_BNDS_COMP). */
/* If N_NORMS >= 1 return normwise error bounds. */
/* If N_NORMS >= 2 return componentwise error bounds. */
/* ERR_BNDS_NORM (input/output) REAL array, dimension (NRHS, N_ERR_BNDS) */
/* For each right-hand side, this array contains information about */
/* various error bounds and condition numbers corresponding to the */
/* normwise relative error, which is defined as follows: */
/* Normwise relative error in the ith solution vector: */
/* max_j (abs(XTRUE(j,i) - X(j,i))) */
/* ------------------------------ */
/* max_j abs(X(j,i)) */
/* The array is indexed by the type of error information as described */
/* below. There currently are up to three pieces of information */
/* returned. */
/* The first index in ERR_BNDS_NORM(i,:) corresponds to the ith */
/* right-hand side. */
/* The second index in ERR_BNDS_NORM(:,err) contains the following */
/* three fields: */
/* err = 1 "Trust/don't trust" boolean. Trust the answer if the */
/* reciprocal condition number is less than the threshold */
/* sqrt(n) * slamch('Epsilon'). */
/* err = 2 "Guaranteed" error bound: The estimated forward error, */
/* almost certainly within a factor of 10 of the true error */
/* so long as the next entry is greater than the threshold */
/* sqrt(n) * slamch('Epsilon'). This error bound should only */
/* be trusted if the previous boolean is true. */
/* err = 3 Reciprocal condition number: Estimated normwise */
/* reciprocal condition number. Compared with the threshold */
/* sqrt(n) * slamch('Epsilon') to determine if the error */
/* estimate is "guaranteed". These reciprocal condition */
/* numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */
/* appropriately scaled matrix Z. */
/* Let Z = S*A, where S scales each row by a power of the */
/* radix so all absolute row sums of Z are approximately 1. */
/* This subroutine is only responsible for setting the second field */
/* above. */
/* See Lapack Working Note 165 for further details and extra */
/* cautions. */
/* ERR_BNDS_COMP (input/output) REAL array, dimension (NRHS, N_ERR_BNDS) */
/* For each right-hand side, this array contains information about */
/* various error bounds and condition numbers corresponding to the */
/* componentwise relative error, which is defined as follows: */
/* Componentwise relative error in the ith solution vector: */
/* abs(XTRUE(j,i) - X(j,i)) */
/* max_j ---------------------- */
/* abs(X(j,i)) */
/* The array is indexed by the right-hand side i (on which the */
/* componentwise relative error depends), and the type of error */
/* information as described below. There currently are up to three */
/* pieces of information returned for each right-hand side. If */
/* componentwise accuracy is not requested (PARAMS(3) = 0.0), then */
/* ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most */
/* the first (:,N_ERR_BNDS) entries are returned. */
/* The first index in ERR_BNDS_COMP(i,:) corresponds to the ith */
/* right-hand side. */
/* The second index in ERR_BNDS_COMP(:,err) contains the following */
/* three fields: */
/* err = 1 "Trust/don't trust" boolean. Trust the answer if the */
/* reciprocal condition number is less than the threshold */
/* sqrt(n) * slamch('Epsilon'). */
/* err = 2 "Guaranteed" error bound: The estimated forward error, */
/* almost certainly within a factor of 10 of the true error */
/* so long as the next entry is greater than the threshold */
/* sqrt(n) * slamch('Epsilon'). This error bound should only */
/* be trusted if the previous boolean is true. */
/* err = 3 Reciprocal condition number: Estimated componentwise */
/* reciprocal condition number. Compared with the threshold */
/* sqrt(n) * slamch('Epsilon') to determine if the error */
/* estimate is "guaranteed". These reciprocal condition */
/* numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */
/* appropriately scaled matrix Z. */
/* Let Z = S*(A*diag(x)), where x is the solution for the */
/* current right-hand side and S scales each row of */
/* A*diag(x) by a power of the radix so all absolute row */
/* sums of Z are approximately 1. */
/* This subroutine is only responsible for setting the second field */
/* above. */
/* See Lapack Working Note 165 for further details and extra */
/* cautions. */
/* RES (input) COMPLEX array, dimension (N) */
/* Workspace to hold the intermediate residual. */
/* AYB (input) REAL array, dimension (N) */
/* Workspace. */
/* DY (input) COMPLEX array, dimension (N) */
/* Workspace to hold the intermediate solution. */
/* Y_TAIL (input) COMPLEX array, dimension (N) */
/* Workspace to hold the trailing bits of the intermediate solution. */
/* RCOND (input) REAL */
/* Reciprocal scaled condition number. This is an estimate of the */
/* reciprocal Skeel condition number of the matrix A after */
/* equilibration (if done). If this is less than the machine */
/* precision (in particular, if it is zero), the matrix is singular */
/* to working precision. Note that the error may still be small even */
/* if this number is very small and the matrix appears ill- */
/* conditioned. */
/* ITHRESH (input) INTEGER */
/* The maximum number of residual computations allowed for */
/* refinement. The default is 10. For 'aggressive' set to 100 to */
/* permit convergence using approximate factorizations or */
/* factorizations other than LU. If the factorization uses a */
/* technique other than Gaussian elimination, the guarantees in */
/* ERR_BNDS_NORM and ERR_BNDS_COMP may no longer be trustworthy. */
/* RTHRESH (input) REAL */
/* Determines when to stop refinement if the error estimate stops */
/* decreasing. Refinement will stop when the next solution no longer */
/* satisfies norm(dx_{i+1}) < RTHRESH * norm(dx_i) where norm(Z) is */
/* the infinity norm of Z. RTHRESH satisfies 0 < RTHRESH <= 1. The */
/* default value is 0.5. For 'aggressive' set to 0.9 to permit */
/* convergence on extremely ill-conditioned matrices. See LAWN 165 */
/* for more details. */
/* DZ_UB (input) REAL */
/* Determines when to start considering componentwise convergence. */
/* Componentwise convergence is only considered after each component */
/* of the solution Y is stable, which we definte as the relative */
/* change in each component being less than DZ_UB. The default value */
/* is 0.25, requiring the first bit to be stable. See LAWN 165 for */
/* more details. */
/* IGNORE_CWISE (input) LOGICAL */
/* If .TRUE. then ignore componentwise convergence. Default value */
/* is .FALSE.. */
/* INFO (output) INTEGER */
/* = 0: Successful exit. */
/* < 0: if INFO = -i, the ith argument to CGETRS had an illegal */
/* value */
/* ===================================================================== */
/* .. Local Scalars .. */
/* .. */
/* .. Parameters .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Statement Functions .. */
/* .. */
/* .. Statement Function Definitions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
errs_c_dim1 = *nrhs;
errs_c_offset = 1 + errs_c_dim1;
errs_c__ -= errs_c_offset;
errs_n_dim1 = *nrhs;
errs_n_offset = 1 + errs_n_dim1;
errs_n__ -= errs_n_offset;
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
af_dim1 = *ldaf;
af_offset = 1 + af_dim1;
af -= af_offset;
--ipiv;
--c__;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
y_dim1 = *ldy;
y_offset = 1 + y_dim1;
y -= y_offset;
--berr_out__;
--res;
--ayb;
--dy;
--y_tail__;
/* Function Body */
if (*info != 0) {
return 0;
}
chla_transtype__(ch__1, (ftnlen)1, trans_type__);
*(unsigned char *)trans = *(unsigned char *)&ch__1[0];
eps = slamch_("Epsilon");
hugeval = slamch_("Overflow");
/* Force HUGEVAL to Inf */
hugeval *= hugeval;
/* Using HUGEVAL may lead to spurious underflows. */
incr_thresh__ = (real) (*n) * eps;
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
y_prec_state__ = 1;
if (y_prec_state__ == 2) {
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__;
y_tail__[i__3].r = 0.f, y_tail__[i__3].i = 0.f;
}
}
dxrat = 0.f;
dxratmax = 0.f;
dzrat = 0.f;
dzratmax = 0.f;
final_dx_x__ = hugeval;
final_dz_z__ = hugeval;
prevnormdx = hugeval;
prev_dz_z__ = hugeval;
dz_z__ = hugeval;
dx_x__ = hugeval;
x_state__ = 1;
z_state__ = 0;
incr_prec__ = FALSE_;
i__2 = *ithresh;
for (cnt = 1; cnt <= i__2; ++cnt) {
/* Compute residual RES = B_s - op(A_s) * Y, */
/* op(A) = A, A**T, or A**H depending on TRANS (and type). */
ccopy_(n, &b[j * b_dim1 + 1], &c__1, &res[1], &c__1);
if (y_prec_state__ == 0) {
cgemv_(trans, n, n, &c_b6, &a[a_offset], lda, &y[j * y_dim1 +
1], &c__1, &c_b8, &res[1], &c__1);
} else if (y_prec_state__ == 1) {
blas_cgemv_x__(trans_type__, n, n, &c_b6, &a[a_offset], lda, &
y[j * y_dim1 + 1], &c__1, &c_b8, &res[1], &c__1,
prec_type__);
} else {
blas_cgemv2_x__(trans_type__, n, n, &c_b6, &a[a_offset], lda,
&y[j * y_dim1 + 1], &y_tail__[1], &c__1, &c_b8, &res[
1], &c__1, prec_type__);
}
/* XXX: RES is no longer needed. */
ccopy_(n, &res[1], &c__1, &dy[1], &c__1);
cgetrs_(trans, n, &c__1, &af[af_offset], ldaf, &ipiv[1], &dy[1],
n, info);
/* Calculate relative changes DX_X, DZ_Z and ratios DXRAT, DZRAT. */
normx = 0.f;
normy = 0.f;
normdx = 0.f;
dz_z__ = 0.f;
ymin = hugeval;
i__3 = *n;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = i__ + j * y_dim1;
yk = (r__1 = y[i__4].r, dabs(r__1)) + (r__2 = r_imag(&y[i__ +
j * y_dim1]), dabs(r__2));
i__4 = i__;
dyk = (r__1 = dy[i__4].r, dabs(r__1)) + (r__2 = r_imag(&dy[
i__]), dabs(r__2));
if (yk != 0.f) {
/* Computing MAX */
r__1 = dz_z__, r__2 = dyk / yk;
dz_z__ = dmax(r__1,r__2);
} else if (dyk != 0.f) {
dz_z__ = hugeval;
}
ymin = dmin(ymin,yk);
normy = dmax(normy,yk);
if (*colequ) {
/* Computing MAX */
r__1 = normx, r__2 = yk * c__[i__];
normx = dmax(r__1,r__2);
/* Computing MAX */
r__1 = normdx, r__2 = dyk * c__[i__];
normdx = dmax(r__1,r__2);
} else {
normx = normy;
normdx = dmax(normdx,dyk);
}
}
if (normx != 0.f) {
dx_x__ = normdx / normx;
} else if (normdx == 0.f) {
dx_x__ = 0.f;
} else {
dx_x__ = hugeval;
}
dxrat = normdx / prevnormdx;
dzrat = dz_z__ / prev_dz_z__;
/* Check termination criteria */
if (! (*ignore_cwise__) && ymin * *rcond < incr_thresh__ * normy
&& y_prec_state__ < 2) {
incr_prec__ = TRUE_;
}
if (x_state__ == 3 && dxrat <= *rthresh) {
x_state__ = 1;
}
if (x_state__ == 1) {
if (dx_x__ <= eps) {
x_state__ = 2;
} else if (dxrat > *rthresh) {
if (y_prec_state__ != 2) {
incr_prec__ = TRUE_;
} else {
x_state__ = 3;
}
} else {
if (dxrat > dxratmax) {
dxratmax = dxrat;
}
}
if (x_state__ > 1) {
final_dx_x__ = dx_x__;
}
}
if (z_state__ == 0 && dz_z__ <= *dz_ub__) {
z_state__ = 1;
}
if (z_state__ == 3 && dzrat <= *rthresh) {
z_state__ = 1;
}
if (z_state__ == 1) {
if (dz_z__ <= eps) {
z_state__ = 2;
} else if (dz_z__ > *dz_ub__) {
z_state__ = 0;
dzratmax = 0.f;
final_dz_z__ = hugeval;
} else if (dzrat > *rthresh) {
if (y_prec_state__ != 2) {
incr_prec__ = TRUE_;
} else {
z_state__ = 3;
}
} else {
if (dzrat > dzratmax) {
dzratmax = dzrat;
}
}
if (z_state__ > 1) {
final_dz_z__ = dz_z__;
}
}
/* Exit if both normwise and componentwise stopped working, */
/* but if componentwise is unstable, let it go at least two */
/* iterations. */
if (x_state__ != 1) {
if (*ignore_cwise__) {
goto L666;
}
if (z_state__ == 3 || z_state__ == 2) {
goto L666;
}
if (z_state__ == 0 && cnt > 1) {
goto L666;
}
}
if (incr_prec__) {
incr_prec__ = FALSE_;
++y_prec_state__;
i__3 = *n;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = i__;
y_tail__[i__4].r = 0.f, y_tail__[i__4].i = 0.f;
}
}
prevnormdx = normdx;
prev_dz_z__ = dz_z__;
/* Update soluton. */
if (y_prec_state__ < 2) {
caxpy_(n, &c_b8, &dy[1], &c__1, &y[j * y_dim1 + 1], &c__1);
} else {
cla_wwaddw__(n, &y[j * y_dim1 + 1], &y_tail__[1], &dy[1]);
}
}
/* Target of "IF (Z_STOP .AND. X_STOP)". Sun's f77 won't EXIT. */
L666:
/* Set final_* when cnt hits ithresh */
if (x_state__ == 1) {
final_dx_x__ = dx_x__;
}
if (z_state__ == 1) {
final_dz_z__ = dz_z__;
}
/* Compute error bounds */
if (*n_norms__ >= 1) {
errs_n__[j + (errs_n_dim1 << 1)] = final_dx_x__ / (1 - dxratmax);
}
if (*n_norms__ >= 2) {
errs_c__[j + (errs_c_dim1 << 1)] = final_dz_z__ / (1 - dzratmax);
}
/* Compute componentwise relative backward error from formula */
/* max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) ) */
/* where abs(Z) is the componentwise absolute value of the matrix */
/* or vector Z. */
/* Compute residual RES = B_s - op(A_s) * Y, */
/* op(A) = A, A**T, or A**H depending on TRANS (and type). */
ccopy_(n, &b[j * b_dim1 + 1], &c__1, &res[1], &c__1);
cgemv_(trans, n, n, &c_b6, &a[a_offset], lda, &y[j * y_dim1 + 1], &
c__1, &c_b8, &res[1], &c__1);
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
ayb[i__] = (r__1 = b[i__3].r, dabs(r__1)) + (r__2 = r_imag(&b[i__
+ j * b_dim1]), dabs(r__2));
}
/* Compute abs(op(A_s))*abs(Y) + abs(B_s). */
cla_geamv__(trans_type__, n, n, &c_b31, &a[a_offset], lda, &y[j *
y_dim1 + 1], &c__1, &c_b31, &ayb[1], &c__1);
cla_lin_berr__(n, n, &c__1, &res[1], &ayb[1], &berr_out__[j]);
/* End of loop for each RHS. */
}
return 0;
} /* cla_gerfsx_extended__ */
int cgerfs_(char *trans, int *n, int *nrhs, complex *
a, int *lda, complex *af, int *ldaf, int *ipiv, complex *
b, int *ldb, complex *x, int *ldx, float *ferr, float *berr,
complex *work, float *rwork, int *info)
{
/* System generated locals */
int 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;
float r__1, r__2, r__3, r__4;
complex q__1;
/* Builtin functions */
double r_imag(complex *);
/* Local variables */
int i__, j, k;
float s, xk;
int nz;
float eps;
int kase;
float safe1, safe2;
extern int lsame_(char *, char *);
extern int cgemv_(char *, int *, int *, complex *
, complex *, int *, complex *, int *, complex *, complex *
, int *);
int isave[3];
extern int ccopy_(int *, complex *, int *,
complex *, int *), caxpy_(int *, complex *, complex *,
int *, complex *, int *);
int count;
extern int clacn2_(int *, complex *, complex *, float
*, int *, int *);
extern double slamch_(char *);
float safmin;
extern int xerbla_(char *, int *), cgetrs_(
char *, int *, int *, complex *, int *, int *,
complex *, int *, int *);
int notran;
char transn[1], transt[1];
float 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 */
/* ======= */
/* CGERFS improves the computed solution to a system of linear */
/* equations 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. */
/* 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 original N-by-N matrix A. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= MAX(1,N). */
/* AF (input) COMPLEX array, dimension (LDAF,N) */
/* The factors L and U from the factorization A = P*L*U */
/* as computed by CGETRF. */
/* LDAF (input) INTEGER */
/* The leading dimension of the array AF. LDAF >= MAX(1,N). */
/* IPIV (input) INTEGER array, dimension (N) */
/* The pivot indices from CGETRF; for 1<=i<=N, row i of the */
/* matrix was interchanged with row IPIV(i). */
/* B (input) COMPLEX array, dimension (LDB,NRHS) */
/* The right hand side matrix B. */
/* LDB (input) INTEGER */
/* The leading dimension of the array B. LDB >= MAX(1,N). */
/* X (input/output) COMPLEX array, dimension (LDX,NRHS) */
/* On entry, the solution matrix X, as computed by CGETRS. */
/* On exit, the improved solution matrix X. */
/* LDX (input) INTEGER */
/* The leading dimension of the array X. LDX >= MAX(1,N). */
/* FERR (output) REAL array, dimension (NRHS) */
/* The estimated forward error bound for each solution vector */
/* X(j) (the j-th column of the solution matrix X). */
/* If XTRUE is the true solution corresponding to X(j), FERR(j) */
/* is an estimated upper bound for the magnitude of the largest */
/* element in (X(j) - XTRUE) divided by the magnitude of the */
/* largest element in X(j). The estimate is as reliable as */
/* the estimate for RCOND, and is almost always a slight */
/* overestimate of the true error. */
/* BERR (output) REAL array, dimension (NRHS) */
/* The componentwise relative backward error of each solution */
/* vector X(j) (i.e., the smallest relative change in */
/* any element of A or B that makes X(j) an exact solution). */
/* WORK (workspace) COMPLEX array, dimension (2*N) */
/* RWORK (workspace) REAL array, dimension (N) */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* Internal Parameters */
/* =================== */
/* ITMAX is the maximum number of steps of iterative refinement. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Statement Functions .. */
/* .. */
/* .. Statement Function definitions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
af_dim1 = *ldaf;
af_offset = 1 + af_dim1;
af -= af_offset;
--ipiv;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
x_dim1 = *ldx;
x_offset = 1 + x_dim1;
x -= x_offset;
--ferr;
--berr;
--work;
--rwork;
/* Function Body */
*info = 0;
notran = lsame_(trans, "N");
if (! notran && ! lsame_(trans, "T") && ! lsame_(
trans, "C")) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*nrhs < 0) {
*info = -3;
} else if (*lda < MAX(1,*n)) {
*info = -5;
} else if (*ldaf < MAX(1,*n)) {
*info = -7;
} else if (*ldb < MAX(1,*n)) {
*info = -10;
} else if (*ldx < MAX(1,*n)) {
*info = -12;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CGERFS", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0 || *nrhs == 0) {
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
ferr[j] = 0.f;
berr[j] = 0.f;
/* L10: */
}
return 0;
}
if (notran) {
*(unsigned char *)transn = 'N';
*(unsigned char *)transt = 'C';
} else {
*(unsigned char *)transn = 'C';
*(unsigned char *)transt = 'N';
}
/* NZ = maximum number of nonzero elements in each row of A, plus 1 */
nz = *n + 1;
eps = slamch_("Epsilon");
safmin = slamch_("Safe minimum");
safe1 = nz * safmin;
safe2 = safe1 / eps;
/* Do for each right hand side */
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
count = 1;
lstres = 3.f;
L20:
/* Loop until stopping criterion is satisfied. */
/* Compute residual R = B - op(A) * X, */
/* where op(A) = A, A**T, or A**H, depending on TRANS. */
ccopy_(n, &b[j * b_dim1 + 1], &c__1, &work[1], &c__1);
q__1.r = -1.f, q__1.i = -0.f;
cgemv_(trans, n, n, &q__1, &a[a_offset], lda, &x[j * x_dim1 + 1], &
c__1, &c_b1, &work[1], &c__1);
/* Compute componentwise relative backward error from formula */
/* MAX(i) ( ABS(R(i)) / ( ABS(op(A))*ABS(X) + ABS(B) )(i) ) */
/* where ABS(Z) is the componentwise absolute value of the matrix */
/* or vector Z. If the i-th component of the denominator is less */
/* than SAFE2, then SAFE1 is added to the i-th components of the */
/* numerator and denominator before dividing. */
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
rwork[i__] = (r__1 = b[i__3].r, ABS(r__1)) + (r__2 = r_imag(&b[
i__ + j * b_dim1]), ABS(r__2));
/* L30: */
}
/* Compute ABS(op(A))*ABS(X) + ABS(B). */
if (notran) {
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
i__3 = k + j * x_dim1;
xk = (r__1 = x[i__3].r, ABS(r__1)) + (r__2 = r_imag(&x[k + j
* x_dim1]), ABS(r__2));
i__3 = *n;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = i__ + k * a_dim1;
rwork[i__] += ((r__1 = a[i__4].r, ABS(r__1)) + (r__2 =
r_imag(&a[i__ + k * a_dim1]), ABS(r__2))) * xk;
/* L40: */
}
/* L50: */
}
} else {
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
s = 0.f;
i__3 = *n;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = i__ + k * a_dim1;
i__5 = i__ + j * x_dim1;
s += ((r__1 = a[i__4].r, ABS(r__1)) + (r__2 = r_imag(&a[
i__ + k * a_dim1]), ABS(r__2))) * ((r__3 = x[
i__5].r, ABS(r__3)) + (r__4 = r_imag(&x[i__ + j *
x_dim1]), ABS(r__4)));
/* L60: */
}
rwork[k] += s;
/* L70: */
}
}
s = 0.f;
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
if (rwork[i__] > safe2) {
/* Computing MAX */
i__3 = i__;
r__3 = s, r__4 = ((r__1 = work[i__3].r, ABS(r__1)) + (r__2 =
r_imag(&work[i__]), ABS(r__2))) / rwork[i__];
s = MAX(r__3,r__4);
} else {
/* Computing MAX */
i__3 = i__;
r__3 = s, r__4 = ((r__1 = work[i__3].r, ABS(r__1)) + (r__2 =
r_imag(&work[i__]), ABS(r__2)) + safe1) / (rwork[i__]
+ safe1);
s = MAX(r__3,r__4);
}
/* L80: */
}
berr[j] = s;
/* Test stopping criterion. Continue iterating if */
/* 1) The residual BERR(J) is larger than machine epsilon, and */
/* 2) BERR(J) decreased by at least a factor of 2 during the */
/* last iteration, and */
/* 3) At most ITMAX iterations tried. */
if (berr[j] > eps && berr[j] * 2.f <= lstres && count <= 5) {
/* Update solution and try again. */
cgetrs_(trans, n, &c__1, &af[af_offset], ldaf, &ipiv[1], &work[1],
n, info);
caxpy_(n, &c_b1, &work[1], &c__1, &x[j * x_dim1 + 1], &c__1);
lstres = berr[j];
++count;
goto L20;
}
/* Bound error from formula */
/* norm(X - XTRUE) / norm(X) .le. FERR = */
/* norm( ABS(inv(op(A)))* */
/* ( ABS(R) + NZ*EPS*( ABS(op(A))*ABS(X)+ABS(B) ))) / norm(X) */
/* where */
/* norm(Z) is the magnitude of the largest component of Z */
/* inv(op(A)) is the inverse of op(A) */
/* ABS(Z) is the componentwise absolute value of the matrix or */
/* vector Z */
/* NZ is the maximum number of nonzeros in any row of A, plus 1 */
/* EPS is machine epsilon */
/* The i-th component of ABS(R)+NZ*EPS*(ABS(op(A))*ABS(X)+ABS(B)) */
/* is incremented by SAFE1 if the i-th component of */
/* ABS(op(A))*ABS(X) + ABS(B) is less than SAFE2. */
/* Use CLACN2 to estimate the infinity-norm of the matrix */
/* inv(op(A)) * diag(W), */
/* where W = ABS(R) + NZ*EPS*( ABS(op(A))*ABS(X)+ABS(B) ))) */
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
if (rwork[i__] > safe2) {
i__3 = i__;
rwork[i__] = (r__1 = work[i__3].r, ABS(r__1)) + (r__2 =
r_imag(&work[i__]), ABS(r__2)) + nz * eps * rwork[
i__];
} else {
i__3 = i__;
rwork[i__] = (r__1 = work[i__3].r, ABS(r__1)) + (r__2 =
r_imag(&work[i__]), ABS(r__2)) + nz * eps * rwork[
i__] + safe1;
}
/* L90: */
}
kase = 0;
L100:
clacn2_(n, &work[*n + 1], &work[1], &ferr[j], &kase, isave);
if (kase != 0) {
if (kase == 1) {
/* Multiply by diag(W)*inv(op(A)**H). */
cgetrs_(transt, n, &c__1, &af[af_offset], ldaf, &ipiv[1], &
work[1], n, info);
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__;
i__4 = i__;
i__5 = i__;
q__1.r = rwork[i__4] * work[i__5].r, q__1.i = rwork[i__4]
* work[i__5].i;
work[i__3].r = q__1.r, work[i__3].i = q__1.i;
/* L110: */
}
} else {
/* Multiply by inv(op(A))*diag(W). */
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__;
i__4 = i__;
i__5 = i__;
q__1.r = rwork[i__4] * work[i__5].r, q__1.i = rwork[i__4]
* work[i__5].i;
work[i__3].r = q__1.r, work[i__3].i = q__1.i;
/* L120: */
}
cgetrs_(transn, n, &c__1, &af[af_offset], ldaf, &ipiv[1], &
work[1], n, info);
}
goto L100;
}
/* Normalize error. */
lstres = 0.f;
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
/* Computing MAX */
i__3 = i__ + j * x_dim1;
r__3 = lstres, r__4 = (r__1 = x[i__3].r, ABS(r__1)) + (r__2 =
r_imag(&x[i__ + j * x_dim1]), ABS(r__2));
lstres = MAX(r__3,r__4);
/* L130: */
}
if (lstres != 0.f) {
ferr[j] /= lstres;
}
/* L140: */
}
return 0;
/* End of CGERFS */
} /* cgerfs_ */
/* Subroutine */ int cgesv_(integer *n, integer *nrhs, complex *a, integer *
lda, integer *ipiv, complex *b, integer *ldb, 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
March 31, 1993
Purpose
=======
CGESV computes the solution to a complex system of linear equations
A * X = B,
where A is an N-by-N matrix and X and B are N-by-NRHS matrices.
The LU decomposition with partial pivoting and row interchanges is
used to factor A as
A = P * L * U,
where P is a permutation matrix, L is unit lower triangular, and U is
upper triangular. The factored form of A is then used to solve the
system of equations A * X = B.
Arguments
=========
N (input) INTEGER
The number of linear equations, i.e., 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 matrix B. NRHS >= 0.
A (input/output) COMPLEX array, dimension (LDA,N)
On entry, the N-by-N coefficient matrix A.
On exit, the factors L and U from the factorization
A = P*L*U; the unit diagonal elements of L are not stored.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
IPIV (output) INTEGER array, dimension (N)
The pivot indices that define the permutation matrix P;
row i of the matrix was interchanged with row IPIV(i).
B (input/output) COMPLEX array, dimension (LDB,NRHS)
On entry, the N-by-NRHS matrix of right hand side matrix B.
On exit, if INFO = 0, the N-by-NRHS solution matrix X.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, U(i,i) is exactly zero. The factorization
has been completed, but the factor U is exactly
singular, so the solution could not be computed.
=====================================================================
Test the input parameters.
Parameter adjustments */
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, i__1;
/* Local variables */
extern /* Subroutine */ int cgetrf_(integer *, integer *, complex *,
integer *, integer *, integer *), xerbla_(char *, integer *), cgetrs_(char *, integer *, integer *, complex *, integer
*, integer *, complex *, integer *, integer *);
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--ipiv;
b_dim1 = *ldb;
b_offset = 1 + b_dim1 * 1;
b -= b_offset;
/* Function Body */
*info = 0;
if (*n < 0) {
*info = -1;
} else if (*nrhs < 0) {
*info = -2;
} else if (*lda < max(1,*n)) {
*info = -4;
} else if (*ldb < max(1,*n)) {
*info = -7;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CGESV ", &i__1);
return 0;
}
/* Compute the LU factorization of A. */
cgetrf_(n, n, &a[a_offset], lda, &ipiv[1], info);
if (*info == 0) {
/* Solve the system A*X = B, overwriting B with X. */
cgetrs_("No transpose", n, nrhs, &a[a_offset], lda, &ipiv[1], &b[
b_offset], ldb, info);
}
return 0;
/* End of CGESV */
} /* cgesv_ */
doublereal cla_gercond_c__(char *trans, integer *n, complex *a, integer *lda,
complex *af, integer *ldaf, integer *ipiv, real *c__, logical *capply,
integer *info, complex *work, real *rwork, ftnlen trans_len)
{
/* System generated locals */
integer a_dim1, a_offset, af_dim1, af_offset, i__1, i__2, i__3, i__4;
real ret_val, r__1, r__2;
complex q__1;
/* Builtin functions */
double r_imag(complex *);
/* Local variables */
integer i__, j;
real tmp;
integer kase;
extern logical lsame_(char *, char *);
integer isave[3];
real anorm;
extern /* Subroutine */ int clacn2_(integer *, complex *, complex *, real
*, integer *, integer *), xerbla_(char *, integer *),
cgetrs_(char *, integer *, integer *, complex *, integer *,
integer *, complex *, integer *, integer *);
real ainvnm;
logical notrans;
/* -- 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 Aguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CLA_GERCOND_C computes the infinity norm condition number of */
/* op(A) * inv(diag(C)) where C is a REAL vector. */
/* 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 = Transpose) */
/* N (input) INTEGER */
/* The number of linear equations, i.e., the order of the */
/* matrix A. N >= 0. */
/* A (input) COMPLEX array, dimension (LDA,N) */
/* On entry, the N-by-N matrix A */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,N). */
/* AF (input) COMPLEX array, dimension (LDAF,N) */
/* The factors L and U from the factorization */
/* A = P*L*U as computed by CGETRF. */
/* LDAF (input) INTEGER */
/* The leading dimension of the array AF. LDAF >= max(1,N). */
/* IPIV (input) INTEGER array, dimension (N) */
/* The pivot indices from the factorization A = P*L*U */
/* as computed by CGETRF; row i of the matrix was interchanged */
/* with row IPIV(i). */
/* C (input) REAL array, dimension (N) */
/* The vector C in the formula op(A) * inv(diag(C)). */
/* CAPPLY (input) LOGICAL */
/* If .TRUE. then access the vector C in the formula above. */
/* INFO (output) INTEGER */
/* = 0: Successful exit. */
/* i > 0: The ith argument is invalid. */
/* WORK (input) COMPLEX array, dimension (2*N). */
/* Workspace. */
/* RWORK (input) REAL array, dimension (N). */
/* Workspace. */
/* ===================================================================== */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Statement Functions .. */
/* .. */
/* .. Statement Function Definitions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
af_dim1 = *ldaf;
af_offset = 1 + af_dim1;
af -= af_offset;
--ipiv;
--c__;
--work;
--rwork;
/* Function Body */
ret_val = 0.f;
*info = 0;
notrans = lsame_(trans, "N");
if (! notrans && ! lsame_(trans, "T") && ! lsame_(
trans, "C")) {
} else if (*n < 0) {
*info = -2;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CLA_GERCOND_C", &i__1);
return ret_val;
}
/* Compute norm of op(A)*op2(C). */
anorm = 0.f;
if (notrans) {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
tmp = 0.f;
if (*capply) {
i__2 = *n;
for (j = 1; j <= i__2; ++j) {
i__3 = i__ + j * a_dim1;
tmp += ((r__1 = a[i__3].r, dabs(r__1)) + (r__2 = r_imag(&
a[i__ + j * a_dim1]), dabs(r__2))) / c__[j];
}
} else {
i__2 = *n;
for (j = 1; j <= i__2; ++j) {
i__3 = i__ + j * a_dim1;
tmp += (r__1 = a[i__3].r, dabs(r__1)) + (r__2 = r_imag(&a[
i__ + j * a_dim1]), dabs(r__2));
}
}
rwork[i__] = tmp;
anorm = dmax(anorm,tmp);
}
} else {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
tmp = 0.f;
if (*capply) {
i__2 = *n;
for (j = 1; j <= i__2; ++j) {
i__3 = j + i__ * a_dim1;
tmp += ((r__1 = a[i__3].r, dabs(r__1)) + (r__2 = r_imag(&
a[j + i__ * a_dim1]), dabs(r__2))) / c__[j];
}
} else {
i__2 = *n;
for (j = 1; j <= i__2; ++j) {
i__3 = j + i__ * a_dim1;
tmp += (r__1 = a[i__3].r, dabs(r__1)) + (r__2 = r_imag(&a[
j + i__ * a_dim1]), dabs(r__2));
}
}
rwork[i__] = tmp;
anorm = dmax(anorm,tmp);
}
}
/* Quick return if possible. */
if (*n == 0) {
ret_val = 1.f;
return ret_val;
} else if (anorm == 0.f) {
return ret_val;
}
/* Estimate the norm of inv(op(A)). */
ainvnm = 0.f;
kase = 0;
L10:
clacn2_(n, &work[*n + 1], &work[1], &ainvnm, &kase, isave);
if (kase != 0) {
if (kase == 2) {
/* Multiply by R. */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
i__3 = i__;
i__4 = i__;
q__1.r = rwork[i__4] * work[i__3].r, q__1.i = rwork[i__4] *
work[i__3].i;
work[i__2].r = q__1.r, work[i__2].i = q__1.i;
}
if (notrans) {
cgetrs_("No transpose", n, &c__1, &af[af_offset], ldaf, &ipiv[
1], &work[1], n, info);
} else {
cgetrs_("Conjugate transpose", n, &c__1, &af[af_offset], ldaf,
&ipiv[1], &work[1], n, info);
}
/* Multiply by inv(C). */
if (*capply) {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
i__3 = i__;
i__4 = i__;
q__1.r = c__[i__4] * work[i__3].r, q__1.i = c__[i__4] *
work[i__3].i;
work[i__2].r = q__1.r, work[i__2].i = q__1.i;
}
}
} else {
/* Multiply by inv(C'). */
if (*capply) {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
i__3 = i__;
i__4 = i__;
q__1.r = c__[i__4] * work[i__3].r, q__1.i = c__[i__4] *
work[i__3].i;
work[i__2].r = q__1.r, work[i__2].i = q__1.i;
}
}
if (notrans) {
cgetrs_("Conjugate transpose", n, &c__1, &af[af_offset], ldaf,
&ipiv[1], &work[1], n, info);
} else {
cgetrs_("No transpose", n, &c__1, &af[af_offset], ldaf, &ipiv[
1], &work[1], n, info);
}
/* Multiply by R. */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
i__3 = i__;
i__4 = i__;
q__1.r = rwork[i__4] * work[i__3].r, q__1.i = rwork[i__4] *
work[i__3].i;
work[i__2].r = q__1.r, work[i__2].i = q__1.i;
}
}
goto L10;
}
/* Compute the estimate of the reciprocal condition number. */
if (ainvnm != 0.f) {
ret_val = 1.f / ainvnm;
}
return ret_val;
} /* cla_gercond_c__ */
/* Subroutine */ int cerrge_(char *path, integer *nunit)
{
/* System generated locals */
integer i__1;
real r__1, r__2;
complex q__1;
/* Local variables */
complex a[16] /* was [4][4] */, b[4];
integer i__, j;
real r__[4];
complex w[8], x[4];
char c2[2];
real r1[4], r2[4];
complex af[16] /* was [4][4] */;
integer ip[4], info;
real anrm, ccond, rcond;
/* Fortran I/O blocks */
static cilist io___1 = { 0, 0, 0, 0, 0 };
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CERRGE tests the error exits for the COMPLEX routines */
/* for general matrices. */
/* Arguments */
/* ========= */
/* PATH (input) CHARACTER*3 */
/* The LAPACK path name for the routines to be tested. */
/* NUNIT (input) INTEGER */
/* The unit number for output. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Scalars in Common .. */
/* .. */
/* .. Common blocks .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
infoc_1.nout = *nunit;
io___1.ciunit = infoc_1.nout;
s_wsle(&io___1);
e_wsle();
s_copy(c2, path + 1, (ftnlen)2, (ftnlen)2);
/* Set the variables to innocuous values. */
for (j = 1; j <= 4; ++j) {
for (i__ = 1; i__ <= 4; ++i__) {
i__1 = i__ + (j << 2) - 5;
r__1 = 1.f / (real) (i__ + j);
r__2 = -1.f / (real) (i__ + j);
q__1.r = r__1, q__1.i = r__2;
a[i__1].r = q__1.r, a[i__1].i = q__1.i;
i__1 = i__ + (j << 2) - 5;
r__1 = 1.f / (real) (i__ + j);
r__2 = -1.f / (real) (i__ + j);
q__1.r = r__1, q__1.i = r__2;
af[i__1].r = q__1.r, af[i__1].i = q__1.i;
/* L10: */
}
i__1 = j - 1;
b[i__1].r = 0.f, b[i__1].i = 0.f;
r1[j - 1] = 0.f;
r2[j - 1] = 0.f;
i__1 = j - 1;
w[i__1].r = 0.f, w[i__1].i = 0.f;
i__1 = j - 1;
x[i__1].r = 0.f, x[i__1].i = 0.f;
ip[j - 1] = j;
/* L20: */
}
infoc_1.ok = TRUE_;
/* Test error exits of the routines that use the LU decomposition */
/* of a general matrix. */
if (lsamen_(&c__2, c2, "GE")) {
/* CGETRF */
s_copy(srnamc_1.srnamt, "CGETRF", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cgetrf_(&c_n1, &c__0, a, &c__1, ip, &info);
chkxer_("CGETRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cgetrf_(&c__0, &c_n1, a, &c__1, ip, &info);
chkxer_("CGETRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
cgetrf_(&c__2, &c__1, a, &c__1, ip, &info);
chkxer_("CGETRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CGETF2 */
s_copy(srnamc_1.srnamt, "CGETF2", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cgetf2_(&c_n1, &c__0, a, &c__1, ip, &info);
chkxer_("CGETF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cgetf2_(&c__0, &c_n1, a, &c__1, ip, &info);
chkxer_("CGETF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
cgetf2_(&c__2, &c__1, a, &c__1, ip, &info);
chkxer_("CGETF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CGETRI */
s_copy(srnamc_1.srnamt, "CGETRI", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cgetri_(&c_n1, a, &c__1, ip, w, &c__1, &info);
chkxer_("CGETRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
cgetri_(&c__2, a, &c__1, ip, w, &c__2, &info);
chkxer_("CGETRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
cgetri_(&c__2, a, &c__2, ip, w, &c__1, &info);
chkxer_("CGETRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CGETRS */
s_copy(srnamc_1.srnamt, "CGETRS", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cgetrs_("/", &c__0, &c__0, a, &c__1, ip, b, &c__1, &info);
chkxer_("CGETRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cgetrs_("N", &c_n1, &c__0, a, &c__1, ip, b, &c__1, &info);
chkxer_("CGETRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
cgetrs_("N", &c__0, &c_n1, a, &c__1, ip, b, &c__1, &info);
chkxer_("CGETRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
cgetrs_("N", &c__2, &c__1, a, &c__1, ip, b, &c__2, &info);
chkxer_("CGETRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
cgetrs_("N", &c__2, &c__1, a, &c__2, ip, b, &c__1, &info);
chkxer_("CGETRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CGERFS */
s_copy(srnamc_1.srnamt, "CGERFS", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cgerfs_("/", &c__0, &c__0, a, &c__1, af, &c__1, ip, b, &c__1, x, &
c__1, r1, r2, w, r__, &info);
chkxer_("CGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cgerfs_("N", &c_n1, &c__0, a, &c__1, af, &c__1, ip, b, &c__1, x, &
c__1, r1, r2, w, r__, &info);
chkxer_("CGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
cgerfs_("N", &c__0, &c_n1, a, &c__1, af, &c__1, ip, b, &c__1, x, &
c__1, r1, r2, w, r__, &info);
chkxer_("CGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
cgerfs_("N", &c__2, &c__1, a, &c__1, af, &c__2, ip, b, &c__2, x, &
c__2, r1, r2, w, r__, &info);
chkxer_("CGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
cgerfs_("N", &c__2, &c__1, a, &c__2, af, &c__1, ip, b, &c__2, x, &
c__2, r1, r2, w, r__, &info);
chkxer_("CGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
cgerfs_("N", &c__2, &c__1, a, &c__2, af, &c__2, ip, b, &c__1, x, &
c__2, r1, r2, w, r__, &info);
chkxer_("CGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 12;
cgerfs_("N", &c__2, &c__1, a, &c__2, af, &c__2, ip, b, &c__2, x, &
c__1, r1, r2, w, r__, &info);
chkxer_("CGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CGECON */
s_copy(srnamc_1.srnamt, "CGECON", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cgecon_("/", &c__0, a, &c__1, &anrm, &rcond, w, r__, &info)
;
chkxer_("CGECON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cgecon_("1", &c_n1, a, &c__1, &anrm, &rcond, w, r__, &info)
;
chkxer_("CGECON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
cgecon_("1", &c__2, a, &c__1, &anrm, &rcond, w, r__, &info)
;
chkxer_("CGECON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CGEEQU */
s_copy(srnamc_1.srnamt, "CGEEQU", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cgeequ_(&c_n1, &c__0, a, &c__1, r1, r2, &rcond, &ccond, &anrm, &info);
chkxer_("CGEEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cgeequ_(&c__0, &c_n1, a, &c__1, r1, r2, &rcond, &ccond, &anrm, &info);
chkxer_("CGEEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
cgeequ_(&c__2, &c__2, a, &c__1, r1, r2, &rcond, &ccond, &anrm, &info);
chkxer_("CGEEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* Test error exits of the routines that use the LU decomposition */
/* of a general band matrix. */
} else if (lsamen_(&c__2, c2, "GB")) {
/* CGBTRF */
s_copy(srnamc_1.srnamt, "CGBTRF", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cgbtrf_(&c_n1, &c__0, &c__0, &c__0, a, &c__1, ip, &info);
chkxer_("CGBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cgbtrf_(&c__0, &c_n1, &c__0, &c__0, a, &c__1, ip, &info);
chkxer_("CGBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
cgbtrf_(&c__1, &c__1, &c_n1, &c__0, a, &c__1, ip, &info);
chkxer_("CGBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
cgbtrf_(&c__1, &c__1, &c__0, &c_n1, a, &c__1, ip, &info);
chkxer_("CGBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
cgbtrf_(&c__2, &c__2, &c__1, &c__1, a, &c__3, ip, &info);
chkxer_("CGBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CGBTF2 */
s_copy(srnamc_1.srnamt, "CGBTF2", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cgbtf2_(&c_n1, &c__0, &c__0, &c__0, a, &c__1, ip, &info);
chkxer_("CGBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cgbtf2_(&c__0, &c_n1, &c__0, &c__0, a, &c__1, ip, &info);
chkxer_("CGBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
cgbtf2_(&c__1, &c__1, &c_n1, &c__0, a, &c__1, ip, &info);
chkxer_("CGBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
cgbtf2_(&c__1, &c__1, &c__0, &c_n1, a, &c__1, ip, &info);
chkxer_("CGBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
cgbtf2_(&c__2, &c__2, &c__1, &c__1, a, &c__3, ip, &info);
chkxer_("CGBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CGBTRS */
s_copy(srnamc_1.srnamt, "CGBTRS", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cgbtrs_("/", &c__0, &c__0, &c__0, &c__1, a, &c__1, ip, b, &c__1, &
info);
chkxer_("CGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cgbtrs_("N", &c_n1, &c__0, &c__0, &c__1, a, &c__1, ip, b, &c__1, &
info);
chkxer_("CGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
cgbtrs_("N", &c__1, &c_n1, &c__0, &c__1, a, &c__1, ip, b, &c__1, &
info);
chkxer_("CGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
cgbtrs_("N", &c__1, &c__0, &c_n1, &c__1, a, &c__1, ip, b, &c__1, &
info);
chkxer_("CGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
cgbtrs_("N", &c__1, &c__0, &c__0, &c_n1, a, &c__1, ip, b, &c__1, &
info);
chkxer_("CGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
cgbtrs_("N", &c__2, &c__1, &c__1, &c__1, a, &c__3, ip, b, &c__2, &
info);
chkxer_("CGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
cgbtrs_("N", &c__2, &c__0, &c__0, &c__1, a, &c__1, ip, b, &c__1, &
info);
chkxer_("CGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CGBRFS */
s_copy(srnamc_1.srnamt, "CGBRFS", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cgbrfs_("/", &c__0, &c__0, &c__0, &c__0, a, &c__1, af, &c__1, ip, b, &
c__1, x, &c__1, r1, r2, w, r__, &info);
chkxer_("CGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cgbrfs_("N", &c_n1, &c__0, &c__0, &c__0, a, &c__1, af, &c__1, ip, b, &
c__1, x, &c__1, r1, r2, w, r__, &info);
chkxer_("CGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
cgbrfs_("N", &c__1, &c_n1, &c__0, &c__0, a, &c__1, af, &c__1, ip, b, &
c__1, x, &c__1, r1, r2, w, r__, &info);
chkxer_("CGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
cgbrfs_("N", &c__1, &c__0, &c_n1, &c__0, a, &c__1, af, &c__1, ip, b, &
c__1, x, &c__1, r1, r2, w, r__, &info);
chkxer_("CGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
cgbrfs_("N", &c__1, &c__0, &c__0, &c_n1, a, &c__1, af, &c__1, ip, b, &
c__1, x, &c__1, r1, r2, w, r__, &info);
chkxer_("CGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
cgbrfs_("N", &c__2, &c__1, &c__1, &c__1, a, &c__2, af, &c__4, ip, b, &
c__2, x, &c__2, r1, r2, w, r__, &info);
chkxer_("CGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 9;
cgbrfs_("N", &c__2, &c__1, &c__1, &c__1, a, &c__3, af, &c__3, ip, b, &
c__2, x, &c__2, r1, r2, w, r__, &info);
chkxer_("CGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 12;
cgbrfs_("N", &c__2, &c__0, &c__0, &c__1, a, &c__1, af, &c__1, ip, b, &
c__1, x, &c__2, r1, r2, w, r__, &info);
chkxer_("CGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 14;
cgbrfs_("N", &c__2, &c__0, &c__0, &c__1, a, &c__1, af, &c__1, ip, b, &
c__2, x, &c__1, r1, r2, w, r__, &info);
chkxer_("CGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CGBCON */
s_copy(srnamc_1.srnamt, "CGBCON", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cgbcon_("/", &c__0, &c__0, &c__0, a, &c__1, ip, &anrm, &rcond, w, r__,
&info);
chkxer_("CGBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cgbcon_("1", &c_n1, &c__0, &c__0, a, &c__1, ip, &anrm, &rcond, w, r__,
&info);
chkxer_("CGBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
cgbcon_("1", &c__1, &c_n1, &c__0, a, &c__1, ip, &anrm, &rcond, w, r__,
&info);
chkxer_("CGBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
cgbcon_("1", &c__1, &c__0, &c_n1, a, &c__1, ip, &anrm, &rcond, w, r__,
&info);
chkxer_("CGBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
cgbcon_("1", &c__2, &c__1, &c__1, a, &c__3, ip, &anrm, &rcond, w, r__,
&info);
chkxer_("CGBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CGBEQU */
s_copy(srnamc_1.srnamt, "CGBEQU", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cgbequ_(&c_n1, &c__0, &c__0, &c__0, a, &c__1, r1, r2, &rcond, &ccond,
&anrm, &info);
chkxer_("CGBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cgbequ_(&c__0, &c_n1, &c__0, &c__0, a, &c__1, r1, r2, &rcond, &ccond,
&anrm, &info);
chkxer_("CGBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
cgbequ_(&c__1, &c__1, &c_n1, &c__0, a, &c__1, r1, r2, &rcond, &ccond,
&anrm, &info);
chkxer_("CGBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
cgbequ_(&c__1, &c__1, &c__0, &c_n1, a, &c__1, r1, r2, &rcond, &ccond,
&anrm, &info);
chkxer_("CGBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
cgbequ_(&c__2, &c__2, &c__1, &c__1, a, &c__2, r1, r2, &rcond, &ccond,
&anrm, &info);
chkxer_("CGBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
}
/* Print a summary line. */
alaesm_(path, &infoc_1.ok, &infoc_1.nout);
return 0;
/* End of CERRGE */
} /* cerrge_ */
/* Subroutine */
int cgesvxx_(char *fact, char *trans, integer *n, integer * nrhs, complex *a, integer *lda, complex *af, integer *ldaf, integer * ipiv, char *equed, real *r__, real *c__, complex *b, integer *ldb, complex *x, integer *ldx, real *rcond, real *rpvgrw, real *berr, integer *n_err_bnds__, real *err_bnds_norm__, real *err_bnds_comp__, integer *nparams, real *params, 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, err_bnds_norm_dim1, err_bnds_norm_offset, err_bnds_comp_dim1, err_bnds_comp_offset, i__1;
real r__1, r__2;
/* Local variables */
integer j;
real amax;
extern real cla_gerpvgrw_(integer *, integer *, complex *, integer *, complex *, integer *);
extern logical lsame_(char *, char *);
real rcmin, rcmax;
logical equil;
extern /* Subroutine */
int claqge_(integer *, integer *, complex *, integer *, real *, real *, real *, real *, real *, char *) ;
real colcnd;
extern real slamch_(char *);
logical nofact;
extern /* Subroutine */
int cgetrf_(integer *, integer *, complex *, integer *, integer *, integer *), clacpy_(char *, integer *, integer *, complex *, integer *, complex *, integer *), xerbla_(char *, integer *);
real bignum;
integer infequ;
logical colequ;
extern /* Subroutine */
int cgetrs_(char *, integer *, integer *, complex *, integer *, integer *, complex *, integer *, integer *);
real rowcnd;
logical notran;
real smlnum;
logical rowequ;
extern /* Subroutine */
int clascl2_(integer *, integer *, real *, complex *, integer *), cgeequb_(integer *, integer *, complex *, integer *, real *, real *, real *, real *, real *, integer *), cgerfsx_(char *, char *, integer *, integer *, complex *, integer *, complex *, integer *, integer *, real *, real *, complex *, integer *, complex *, integer *, real *, real *, integer *, real * , real *, integer *, real *, complex *, real *, integer *);
/* -- LAPACK driver routine (version 3.4.1) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* April 2012 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* ================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
err_bnds_comp_dim1 = *nrhs;
err_bnds_comp_offset = 1 + err_bnds_comp_dim1;
err_bnds_comp__ -= err_bnds_comp_offset;
err_bnds_norm_dim1 = *nrhs;
err_bnds_norm_offset = 1 + err_bnds_norm_dim1;
err_bnds_norm__ -= err_bnds_norm_offset;
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
af_dim1 = *ldaf;
af_offset = 1 + af_dim1;
af -= af_offset;
--ipiv;
--r__;
--c__;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
x_dim1 = *ldx;
x_offset = 1 + x_dim1;
x -= x_offset;
--berr;
--params;
--work;
--rwork;
/* Function Body */
*info = 0;
nofact = lsame_(fact, "N");
equil = lsame_(fact, "E");
notran = lsame_(trans, "N");
smlnum = slamch_("Safe minimum");
bignum = 1.f / smlnum;
if (nofact || equil)
{
*(unsigned char *)equed = 'N';
rowequ = FALSE_;
colequ = FALSE_;
}
else
{
rowequ = lsame_(equed, "R") || lsame_(equed, "B");
colequ = lsame_(equed, "C") || lsame_(equed, "B");
}
/* Default is failure. If an input parameter is wrong or */
/* factorization fails, make everything look horrible. Only the */
/* pivot growth is set here, the rest is initialized in CGERFSX. */
*rpvgrw = 0.f;
/* Test the input parameters. PARAMS is not tested until CGERFSX. */
if (! nofact && ! equil && ! lsame_(fact, "F"))
{
*info = -1;
}
else if (! notran && ! lsame_(trans, "T") && ! lsame_(trans, "C"))
{
*info = -2;
}
else if (*n < 0)
{
*info = -3;
}
else if (*nrhs < 0)
{
*info = -4;
}
else if (*lda < max(1,*n))
{
*info = -6;
}
else if (*ldaf < max(1,*n))
{
*info = -8;
}
else if (lsame_(fact, "F") && ! (rowequ || colequ || lsame_(equed, "N")))
{
*info = -10;
}
else
{
if (rowequ)
{
rcmin = bignum;
rcmax = 0.f;
i__1 = *n;
for (j = 1;
j <= i__1;
++j)
{
/* Computing MIN */
r__1 = rcmin;
r__2 = r__[j]; // , expr subst
rcmin = min(r__1,r__2);
/* Computing MAX */
r__1 = rcmax;
r__2 = r__[j]; // , expr subst
rcmax = max(r__1,r__2);
/* L10: */
}
if (rcmin <= 0.f)
{
*info = -11;
}
else if (*n > 0)
{
rowcnd = max(rcmin,smlnum) / min(rcmax,bignum);
}
else
{
rowcnd = 1.f;
}
}
if (colequ && *info == 0)
{
rcmin = bignum;
rcmax = 0.f;
i__1 = *n;
for (j = 1;
j <= i__1;
++j)
{
/* Computing MIN */
r__1 = rcmin;
r__2 = c__[j]; // , expr subst
rcmin = min(r__1,r__2);
/* Computing MAX */
r__1 = rcmax;
r__2 = c__[j]; // , expr subst
rcmax = max(r__1,r__2);
/* L20: */
}
if (rcmin <= 0.f)
{
*info = -12;
}
else if (*n > 0)
{
colcnd = max(rcmin,smlnum) / min(rcmax,bignum);
}
else
{
colcnd = 1.f;
}
}
if (*info == 0)
{
if (*ldb < max(1,*n))
{
*info = -14;
}
else if (*ldx < max(1,*n))
{
*info = -16;
}
}
}
if (*info != 0)
{
i__1 = -(*info);
xerbla_("CGESVXX", &i__1);
return 0;
}
if (equil)
{
/* Compute row and column scalings to equilibrate the matrix A. */
cgeequb_(n, n, &a[a_offset], lda, &r__[1], &c__[1], &rowcnd, &colcnd, &amax, &infequ);
if (infequ == 0)
{
/* Equilibrate the matrix. */
claqge_(n, n, &a[a_offset], lda, &r__[1], &c__[1], &rowcnd, & colcnd, &amax, equed);
rowequ = lsame_(equed, "R") || lsame_(equed, "B");
colequ = lsame_(equed, "C") || lsame_(equed, "B");
}
/* If the scaling factors are not applied, set them to 1.0. */
if (! rowequ)
{
i__1 = *n;
for (j = 1;
j <= i__1;
++j)
{
r__[j] = 1.f;
}
}
if (! colequ)
{
i__1 = *n;
for (j = 1;
j <= i__1;
++j)
{
c__[j] = 1.f;
}
}
}
/* Scale the right-hand side. */
if (notran)
{
if (rowequ)
{
clascl2_(n, nrhs, &r__[1], &b[b_offset], ldb);
}
}
else
{
if (colequ)
{
clascl2_(n, nrhs, &c__[1], &b[b_offset], ldb);
}
}
if (nofact || equil)
{
/* Compute the LU factorization of A. */
clacpy_("Full", n, n, &a[a_offset], lda, &af[af_offset], ldaf);
cgetrf_(n, n, &af[af_offset], ldaf, &ipiv[1], info);
/* Return if INFO is non-zero. */
if (*info > 0)
{
/* Pivot in column INFO is exactly 0 */
/* Compute the reciprocal pivot growth factor of the */
/* leading rank-deficient INFO columns of A. */
*rpvgrw = cla_gerpvgrw_(n, info, &a[a_offset], lda, &af[ af_offset], ldaf);
return 0;
}
}
/* Compute the reciprocal pivot growth factor RPVGRW. */
*rpvgrw = cla_gerpvgrw_(n, n, &a[a_offset], lda, &af[af_offset], ldaf);
/* Compute the solution matrix X. */
clacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx);
cgetrs_(trans, n, nrhs, &af[af_offset], ldaf, &ipiv[1], &x[x_offset], ldx, info);
/* Use iterative refinement to improve the computed solution and */
/* compute error bounds and backward error estimates for it. */
cgerfsx_(trans, equed, n, nrhs, &a[a_offset], lda, &af[af_offset], ldaf, & ipiv[1], &r__[1], &c__[1], &b[b_offset], ldb, &x[x_offset], ldx, rcond, &berr[1], n_err_bnds__, &err_bnds_norm__[ err_bnds_norm_offset], &err_bnds_comp__[err_bnds_comp_offset], nparams, ¶ms[1], &work[1], &rwork[1], info);
/* Scale solutions. */
if (colequ && notran)
{
clascl2_(n, nrhs, &c__[1], &x[x_offset], ldx);
}
else if (rowequ && ! notran)
{
clascl2_(n, nrhs, &r__[1], &x[x_offset], ldx);
}
return 0;
/* End of CGESVXX */
}
/* Subroutine */ int cgerfs_(char *trans, 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)
{
/* -- 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
Purpose
=======
CGERFS improves the computed solution to a system of linear
equations 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.
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 original N-by-N matrix A.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
AF (input) COMPLEX array, dimension (LDAF,N)
The factors L and U from the factorization A = P*L*U
as computed by CGETRF.
LDAF (input) INTEGER
The leading dimension of the array AF. LDAF >= max(1,N).
IPIV (input) INTEGER array, dimension (N)
The pivot indices from CGETRF; for 1<=i<=N, row i of the
matrix was interchanged with row IPIV(i).
B (input) COMPLEX array, dimension (LDB,NRHS)
The right hand side matrix B.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).
X (input/output) COMPLEX array, dimension (LDX,NRHS)
On entry, the solution matrix X, as computed by CGETRS.
On exit, the improved solution matrix X.
LDX (input) INTEGER
The leading dimension of the array X. LDX >= max(1,N).
FERR (output) REAL array, dimension (NRHS)
The estimated forward error bound for each solution vector
X(j) (the j-th column of the solution matrix X).
If XTRUE is the true solution corresponding to X(j), FERR(j)
is an estimated upper bound for the magnitude of the largest
element in (X(j) - XTRUE) divided by the magnitude of the
largest element in X(j). The estimate is as reliable as
the estimate for RCOND, and is almost always a slight
overestimate of the true error.
BERR (output) REAL array, dimension (NRHS)
The componentwise relative backward error of each solution
vector X(j) (i.e., the smallest relative change in
any element of A or B that makes X(j) an exact solution).
WORK (workspace) COMPLEX array, dimension (2*N)
RWORK (workspace) REAL array, dimension (N)
INFO (output) INTEGER
= 0: successful exit
< 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 cgemv_(char *, integer *, 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;
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 *), cgetrs_(
char *, integer *, integer *, complex *, integer *, integer *,
complex *, integer *, integer *);
static logical notran;
static char transn[1], transt[1];
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;
x_offset = 1 + x_dim1 * 1;
x -= x_offset;
--ferr;
--berr;
--work;
--rwork;
/* Function Body */
*info = 0;
notran = lsame_(trans, "N");
if (! notran && ! lsame_(trans, "T") && ! lsame_(
trans, "C")) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*nrhs < 0) {
*info = -3;
} else if (*lda < max(1,*n)) {
*info = -5;
} else if (*ldaf < max(1,*n)) {
*info = -7;
} else if (*ldb < max(1,*n)) {
*info = -10;
} else if (*ldx < max(1,*n)) {
*info = -12;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CGERFS", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0 || *nrhs == 0) {
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
ferr[j] = 0.f;
berr[j] = 0.f;
/* L10: */
}
return 0;
}
if (notran) {
*(unsigned char *)transn = 'N';
*(unsigned char *)transt = 'C';
} else {
*(unsigned char *)transn = 'C';
*(unsigned char *)transt = 'N';
}
/* NZ = maximum number of nonzero elements in each row of A, plus 1 */
nz = *n + 1;
eps = slamch_("Epsilon");
safmin = slamch_("Safe minimum");
safe1 = nz * safmin;
safe2 = safe1 / eps;
/* Do for each right hand side */
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
count = 1;
lstres = 3.f;
L20:
/* Loop until stopping criterion is satisfied.
Compute residual R = B - op(A) * X,
where op(A) = A, A**T, or A**H, depending on TRANS. */
ccopy_(n, &b_ref(1, j), &c__1, &work[1], &c__1);
q__1.r = -1.f, q__1.i = 0.f;
cgemv_(trans, n, n, &q__1, &a[a_offset], lda, &x_ref(1, j), &c__1, &
c_b1, &work[1], &c__1);
/* Compute componentwise relative backward error from formula
max(i) ( abs(R(i)) / ( abs(op(A))*abs(X) + abs(B) )(i) )
where abs(Z) is the componentwise absolute value of the matrix
or vector Z. If the i-th component of the denominator is less
than SAFE2, then SAFE1 is added to the i-th components of the
numerator and denominator before dividing. */
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = b_subscr(i__, j);
rwork[i__] = (r__1 = b[i__3].r, dabs(r__1)) + (r__2 = r_imag(&
b_ref(i__, j)), dabs(r__2));
/* L30: */
}
/* Compute abs(op(A))*abs(X) + abs(B). */
if (notran) {
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
i__3 = x_subscr(k, j);
xk = (r__1 = x[i__3].r, dabs(r__1)) + (r__2 = r_imag(&x_ref(k,
j)), dabs(r__2));
i__3 = *n;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = a_subscr(i__, k);
rwork[i__] += ((r__1 = a[i__4].r, dabs(r__1)) + (r__2 =
r_imag(&a_ref(i__, k)), dabs(r__2))) * xk;
/* L40: */
}
/* L50: */
}
} else {
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
s = 0.f;
i__3 = *n;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = a_subscr(i__, k);
i__5 = x_subscr(i__, j);
s += ((r__1 = a[i__4].r, dabs(r__1)) + (r__2 = r_imag(&
a_ref(i__, k)), dabs(r__2))) * ((r__3 = x[i__5].r,
dabs(r__3)) + (r__4 = r_imag(&x_ref(i__, j)),
dabs(r__4)));
/* L60: */
}
rwork[k] += s;
/* L70: */
}
}
s = 0.f;
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
if (rwork[i__] > safe2) {
/* Computing MAX */
i__3 = i__;
r__3 = s, r__4 = ((r__1 = work[i__3].r, dabs(r__1)) + (r__2 =
r_imag(&work[i__]), dabs(r__2))) / rwork[i__];
s = dmax(r__3,r__4);
} else {
/* Computing MAX */
i__3 = i__;
r__3 = s, r__4 = ((r__1 = work[i__3].r, dabs(r__1)) + (r__2 =
r_imag(&work[i__]), dabs(r__2)) + safe1) / (rwork[i__]
+ safe1);
s = dmax(r__3,r__4);
}
/* L80: */
}
berr[j] = s;
/* Test stopping criterion. Continue iterating if
1) The residual BERR(J) is larger than machine epsilon, and
2) BERR(J) decreased by at least a factor of 2 during the
last iteration, and
3) At most ITMAX iterations tried. */
if (berr[j] > eps && berr[j] * 2.f <= lstres && count <= 5) {
/* Update solution and try again. */
cgetrs_(trans, n, &c__1, &af[af_offset], ldaf, &ipiv[1], &work[1],
n, info);
caxpy_(n, &c_b1, &work[1], &c__1, &x_ref(1, j), &c__1);
lstres = berr[j];
++count;
goto L20;
}
/* Bound error from formula
norm(X - XTRUE) / norm(X) .le. FERR =
norm( abs(inv(op(A)))*
( abs(R) + NZ*EPS*( abs(op(A))*abs(X)+abs(B) ))) / norm(X)
where
norm(Z) is the magnitude of the largest component of Z
inv(op(A)) is the inverse of op(A)
abs(Z) is the componentwise absolute value of the matrix or
vector Z
NZ is the maximum number of nonzeros in any row of A, plus 1
EPS is machine epsilon
The i-th component of abs(R)+NZ*EPS*(abs(op(A))*abs(X)+abs(B))
is incremented by SAFE1 if the i-th component of
abs(op(A))*abs(X) + abs(B) is less than SAFE2.
Use CLACON to estimate the infinity-norm of the matrix
inv(op(A)) * diag(W),
where W = abs(R) + NZ*EPS*( abs(op(A))*abs(X)+abs(B) ))) */
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
if (rwork[i__] > safe2) {
i__3 = i__;
rwork[i__] = (r__1 = work[i__3].r, dabs(r__1)) + (r__2 =
r_imag(&work[i__]), dabs(r__2)) + nz * eps * rwork[
i__];
} else {
i__3 = i__;
rwork[i__] = (r__1 = work[i__3].r, dabs(r__1)) + (r__2 =
r_imag(&work[i__]), dabs(r__2)) + nz * eps * rwork[
i__] + safe1;
}
/* L90: */
}
kase = 0;
L100:
clacon_(n, &work[*n + 1], &work[1], &ferr[j], &kase);
if (kase != 0) {
if (kase == 1) {
/* Multiply by diag(W)*inv(op(A)**H). */
cgetrs_(transt, n, &c__1, &af[af_offset], ldaf, &ipiv[1], &
work[1], n, info);
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__;
i__4 = i__;
i__5 = i__;
q__1.r = rwork[i__4] * work[i__5].r, q__1.i = rwork[i__4]
* work[i__5].i;
work[i__3].r = q__1.r, work[i__3].i = q__1.i;
/* L110: */
}
} else {
/* Multiply by inv(op(A))*diag(W). */
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__;
i__4 = i__;
i__5 = i__;
q__1.r = rwork[i__4] * work[i__5].r, q__1.i = rwork[i__4]
* work[i__5].i;
work[i__3].r = q__1.r, work[i__3].i = q__1.i;
/* L120: */
}
cgetrs_(transn, n, &c__1, &af[af_offset], ldaf, &ipiv[1], &
work[1], n, info);
}
goto L100;
}
/* Normalize error. */
lstres = 0.f;
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
/* Computing MAX */
i__3 = x_subscr(i__, j);
r__3 = lstres, r__4 = (r__1 = x[i__3].r, dabs(r__1)) + (r__2 =
r_imag(&x_ref(i__, j)), dabs(r__2));
lstres = dmax(r__3,r__4);
/* L130: */
}
if (lstres != 0.f) {
ferr[j] /= lstres;
}
/* L140: */
}
return 0;
/* End of CGERFS */
} /* cgerfs_ */
/* Subroutine */
int cgesvx_(char *fact, char *trans, integer *n, integer * nrhs, complex *a, integer *lda, complex *af, integer *ldaf, integer * ipiv, char *equed, real *r__, real *c__, complex *b, integer *ldb, complex *x, integer *ldx, real *rcond, 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;
complex q__1;
/* Local variables */
integer i__, j;
real amax;
char norm[1];
extern logical lsame_(char *, char *);
real rcmin, rcmax, anorm;
logical equil;
extern real clange_(char *, integer *, integer *, complex *, integer *, real *);
extern /* Subroutine */
int claqge_(integer *, integer *, complex *, integer *, real *, real *, real *, real *, real *, char *) , cgecon_(char *, integer *, complex *, integer *, real *, real *, complex *, real *, integer *);
real colcnd;
extern real slamch_(char *);
extern /* Subroutine */
int cgeequ_(integer *, integer *, complex *, integer *, real *, real *, real *, real *, real *, integer *);
logical nofact;
extern /* Subroutine */
int cgerfs_(char *, integer *, integer *, complex *, integer *, complex *, integer *, integer *, complex *, integer *, complex *, integer *, real *, real *, complex *, real *, integer *), cgetrf_(integer *, integer *, complex *, integer *, integer *, integer *), clacpy_(char *, integer *, integer *, complex *, integer *, complex *, integer *), xerbla_(char *, integer *);
real bignum;
extern real clantr_(char *, char *, char *, integer *, integer *, complex *, integer *, real *);
integer infequ;
logical colequ;
extern /* Subroutine */
int cgetrs_(char *, integer *, integer *, complex *, integer *, integer *, complex *, integer *, integer *);
real rowcnd;
logical notran;
real smlnum;
logical rowequ;
real rpvgrw;
/* -- LAPACK driver routine (version 3.4.1) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* April 2012 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
af_dim1 = *ldaf;
af_offset = 1 + af_dim1;
af -= af_offset;
--ipiv;
--r__;
--c__;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
x_dim1 = *ldx;
x_offset = 1 + x_dim1;
x -= x_offset;
--ferr;
--berr;
--work;
--rwork;
/* Function Body */
*info = 0;
nofact = lsame_(fact, "N");
equil = lsame_(fact, "E");
notran = lsame_(trans, "N");
if (nofact || equil)
{
*(unsigned char *)equed = 'N';
rowequ = FALSE_;
colequ = FALSE_;
}
else
{
rowequ = lsame_(equed, "R") || lsame_(equed, "B");
colequ = lsame_(equed, "C") || lsame_(equed, "B");
smlnum = slamch_("Safe minimum");
bignum = 1.f / smlnum;
}
/* Test the input parameters. */
if (! nofact && ! equil && ! lsame_(fact, "F"))
{
*info = -1;
}
else if (! notran && ! lsame_(trans, "T") && ! lsame_(trans, "C"))
{
*info = -2;
}
else if (*n < 0)
{
*info = -3;
}
else if (*nrhs < 0)
{
*info = -4;
}
else if (*lda < max(1,*n))
{
*info = -6;
}
else if (*ldaf < max(1,*n))
{
*info = -8;
}
else if (lsame_(fact, "F") && ! (rowequ || colequ || lsame_(equed, "N")))
{
*info = -10;
}
else
{
if (rowequ)
{
rcmin = bignum;
rcmax = 0.f;
i__1 = *n;
for (j = 1;
j <= i__1;
++j)
{
/* Computing MIN */
r__1 = rcmin;
r__2 = r__[j]; // , expr subst
rcmin = min(r__1,r__2);
/* Computing MAX */
r__1 = rcmax;
r__2 = r__[j]; // , expr subst
rcmax = max(r__1,r__2);
/* L10: */
}
if (rcmin <= 0.f)
{
*info = -11;
}
else if (*n > 0)
{
rowcnd = max(rcmin,smlnum) / min(rcmax,bignum);
}
else
{
rowcnd = 1.f;
}
}
if (colequ && *info == 0)
{
rcmin = bignum;
rcmax = 0.f;
i__1 = *n;
for (j = 1;
j <= i__1;
++j)
{
/* Computing MIN */
r__1 = rcmin;
r__2 = c__[j]; // , expr subst
rcmin = min(r__1,r__2);
/* Computing MAX */
r__1 = rcmax;
r__2 = c__[j]; // , expr subst
rcmax = max(r__1,r__2);
/* L20: */
}
if (rcmin <= 0.f)
{
*info = -12;
}
else if (*n > 0)
{
colcnd = max(rcmin,smlnum) / min(rcmax,bignum);
}
else
{
colcnd = 1.f;
}
}
if (*info == 0)
{
if (*ldb < max(1,*n))
{
*info = -14;
}
else if (*ldx < max(1,*n))
{
*info = -16;
}
}
}
if (*info != 0)
{
i__1 = -(*info);
xerbla_("CGESVX", &i__1);
return 0;
}
if (equil)
{
/* Compute row and column scalings to equilibrate the matrix A. */
cgeequ_(n, n, &a[a_offset], lda, &r__[1], &c__[1], &rowcnd, &colcnd, & amax, &infequ);
if (infequ == 0)
{
/* Equilibrate the matrix. */
claqge_(n, n, &a[a_offset], lda, &r__[1], &c__[1], &rowcnd, & colcnd, &amax, equed);
rowequ = lsame_(equed, "R") || lsame_(equed, "B");
colequ = lsame_(equed, "C") || lsame_(equed, "B");
}
}
/* Scale the right hand side. */
if (notran)
{
if (rowequ)
{
i__1 = *nrhs;
for (j = 1;
j <= i__1;
++j)
{
i__2 = *n;
for (i__ = 1;
i__ <= i__2;
++i__)
{
i__3 = i__ + j * b_dim1;
i__4 = i__;
i__5 = i__ + j * b_dim1;
q__1.r = r__[i__4] * b[i__5].r;
q__1.i = r__[i__4] * b[ i__5].i; // , expr subst
b[i__3].r = q__1.r;
b[i__3].i = q__1.i; // , expr subst
/* L30: */
}
/* L40: */
}
}
}
else if (colequ)
{
i__1 = *nrhs;
for (j = 1;
j <= i__1;
++j)
{
i__2 = *n;
for (i__ = 1;
i__ <= i__2;
++i__)
{
i__3 = i__ + j * b_dim1;
i__4 = i__;
i__5 = i__ + j * b_dim1;
q__1.r = c__[i__4] * b[i__5].r;
q__1.i = c__[i__4] * b[i__5] .i; // , expr subst
b[i__3].r = q__1.r;
b[i__3].i = q__1.i; // , expr subst
/* L50: */
}
/* L60: */
}
}
if (nofact || equil)
{
/* Compute the LU factorization of A. */
clacpy_("Full", n, n, &a[a_offset], lda, &af[af_offset], ldaf);
cgetrf_(n, n, &af[af_offset], ldaf, &ipiv[1], info);
/* Return if INFO is non-zero. */
if (*info > 0)
{
/* Compute the reciprocal pivot growth factor of the */
/* leading rank-deficient INFO columns of A. */
rpvgrw = clantr_("M", "U", "N", info, info, &af[af_offset], ldaf, &rwork[1]);
if (rpvgrw == 0.f)
{
rpvgrw = 1.f;
}
else
{
rpvgrw = clange_("M", n, info, &a[a_offset], lda, &rwork[1]) / rpvgrw;
}
rwork[1] = rpvgrw;
*rcond = 0.f;
return 0;
}
}
/* Compute the norm of the matrix A and the */
/* reciprocal pivot growth factor RPVGRW. */
if (notran)
{
*(unsigned char *)norm = '1';
}
else
{
*(unsigned char *)norm = 'I';
}
anorm = clange_(norm, n, n, &a[a_offset], lda, &rwork[1]);
rpvgrw = clantr_("M", "U", "N", n, n, &af[af_offset], ldaf, &rwork[1]);
if (rpvgrw == 0.f)
{
rpvgrw = 1.f;
}
else
{
rpvgrw = clange_("M", n, n, &a[a_offset], lda, &rwork[1]) / rpvgrw;
}
/* Compute the reciprocal of the condition number of A. */
cgecon_(norm, n, &af[af_offset], ldaf, &anorm, rcond, &work[1], &rwork[1], info);
/* Compute the solution matrix X. */
clacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx);
cgetrs_(trans, n, nrhs, &af[af_offset], ldaf, &ipiv[1], &x[x_offset], ldx, info);
/* Use iterative refinement to improve the computed solution and */
/* compute error bounds and backward error estimates for it. */
cgerfs_(trans, n, nrhs, &a[a_offset], lda, &af[af_offset], ldaf, &ipiv[1], &b[b_offset], ldb, &x[x_offset], ldx, &ferr[1], &berr[1], &work[ 1], &rwork[1], info);
/* Transform the solution matrix X to a solution of the original */
/* system. */
if (notran)
{
if (colequ)
{
i__1 = *nrhs;
for (j = 1;
j <= i__1;
++j)
{
i__2 = *n;
for (i__ = 1;
i__ <= i__2;
++i__)
{
i__3 = i__ + j * x_dim1;
i__4 = i__;
i__5 = i__ + j * x_dim1;
q__1.r = c__[i__4] * x[i__5].r;
q__1.i = c__[i__4] * x[ i__5].i; // , expr subst
x[i__3].r = q__1.r;
x[i__3].i = q__1.i; // , expr subst
/* L70: */
}
/* L80: */
}
i__1 = *nrhs;
for (j = 1;
j <= i__1;
++j)
{
ferr[j] /= colcnd;
/* L90: */
}
}
}
else if (rowequ)
{
i__1 = *nrhs;
for (j = 1;
j <= i__1;
++j)
{
i__2 = *n;
for (i__ = 1;
i__ <= i__2;
++i__)
{
i__3 = i__ + j * x_dim1;
i__4 = i__;
i__5 = i__ + j * x_dim1;
q__1.r = r__[i__4] * x[i__5].r;
q__1.i = r__[i__4] * x[i__5] .i; // , expr subst
x[i__3].r = q__1.r;
x[i__3].i = q__1.i; // , expr subst
/* L100: */
}
/* L110: */
}
i__1 = *nrhs;
for (j = 1;
j <= i__1;
++j)
{
ferr[j] /= rowcnd;
/* L120: */
}
}
/* Set INFO = N+1 if the matrix is singular to working precision. */
if (*rcond < slamch_("Epsilon"))
{
*info = *n + 1;
}
rwork[1] = rpvgrw;
return 0;
/* End of CGESVX */
}
