/* Subroutine */ int cdrvpp_(logical *dotype, integer *nn, integer *nval,
integer *nrhs, real *thresh, logical *tsterr, integer *nmax, complex *
a, complex *afac, complex *asav, complex *b, complex *bsav, complex *
x, complex *xact, real *s, complex *work, real *rwork, integer *nout)
{
/* Initialized data */
static integer iseedy[4] = { 1988,1989,1990,1991 };
static char uplos[1*2] = "U" "L";
static char facts[1*3] = "F" "N" "E";
static char packs[1*2] = "C" "R";
static char equeds[1*2] = "N" "Y";
/* Format strings */
static char fmt_9999[] = "(1x,a6,\002, UPLO='\002,a1,\002', N =\002,i5"
",\002, type \002,i1,\002, test(\002,i1,\002)=\002,g12.5)";
static char fmt_9997[] = "(1x,a6,\002, FACT='\002,a1,\002', UPLO='\002,a"
"1,\002', N=\002,i5,\002, EQUED='\002,a1,\002', type \002,i1,\002"
", test(\002,i1,\002)=\002,g12.5)";
static char fmt_9998[] = "(1x,a6,\002, FACT='\002,a1,\002', UPLO='\002,a"
"1,\002', N=\002,i5,\002, type \002,i1,\002, test(\002,i1,\002)"
"=\002,g12.5)";
/* System generated locals */
address a__1[2];
integer i__1, i__2, i__3, i__4, i__5[2];
char ch__1[2];
/* Builtin functions
Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void);
/* Subroutine */ int s_cat(char *, char **, integer *, integer *, ftnlen);
/* Local variables */
static char fact[1];
static integer ioff, mode;
static real amax;
static char path[3];
static integer imat, info;
static char dist[1], uplo[1], type__[1];
static integer nrun, i__, k, n, ifact;
extern /* Subroutine */ int cget04_(integer *, integer *, complex *,
integer *, complex *, integer *, real *, real *);
static integer nfail, iseed[4], nfact;
extern logical lsame_(char *, char *);
static char equed[1];
static real roldc, rcond, scond;
extern /* Subroutine */ int cppt01_(char *, integer *, complex *, complex
*, real *, real *);
static integer nimat;
extern doublereal sget06_(real *, real *);
extern /* Subroutine */ int cppt02_(char *, integer *, integer *, complex
*, complex *, integer *, complex *, integer *, real *, real *), cppt05_(char *, integer *, integer *, complex *, complex
*, integer *, complex *, integer *, complex *, integer *, real *,
real *, real *);
static real anorm;
extern /* Subroutine */ int ccopy_(integer *, complex *, integer *,
complex *, integer *);
static logical equil;
static integer iuplo, izero, nerrs;
extern /* Subroutine */ int cppsv_(char *, integer *, integer *, complex *
, complex *, integer *, integer *);
static integer k1;
static logical zerot;
static char xtype[1];
extern /* Subroutine */ int clatb4_(char *, integer *, integer *, integer
*, char *, integer *, integer *, real *, integer *, real *, char *
), aladhd_(integer *, char *);
static integer in, kl;
extern /* Subroutine */ int alaerh_(char *, char *, integer *, integer *,
char *, integer *, integer *, integer *, integer *, integer *,
integer *, integer *, integer *, integer *), claipd_(integer *, complex *, integer *, integer *);
static logical prefac;
static integer ku, nt;
extern doublereal clanhp_(char *, char *, integer *, complex *, real *);
static real rcondc;
extern /* Subroutine */ int claqhp_(char *, integer *, complex *, real *,
real *, real *, char *);
static logical nofact;
static char packit[1];
static integer iequed;
extern /* Subroutine */ int clacpy_(char *, integer *, integer *, complex
*, integer *, complex *, integer *), clarhs_(char *, char
*, char *, char *, integer *, integer *, integer *, integer *,
integer *, complex *, integer *, complex *, integer *, complex *,
integer *, integer *, integer *),
claset_(char *, integer *, integer *, complex *, complex *,
complex *, integer *), alasvm_(char *, integer *, integer
*, integer *, integer *);
static real cndnum;
extern /* Subroutine */ int clatms_(integer *, integer *, char *, integer
*, char *, real *, integer *, real *, real *, integer *, integer *
, char *, complex *, integer *, complex *, integer *);
static real ainvnm;
extern /* Subroutine */ int cppequ_(char *, integer *, complex *, real *,
real *, real *, integer *), cpptrf_(char *, integer *,
complex *, integer *), cpptri_(char *, integer *, complex
*, integer *), cerrvx_(char *, integer *);
static real result[6];
extern /* Subroutine */ int cppsvx_(char *, char *, integer *, integer *,
complex *, complex *, char *, real *, complex *, integer *,
complex *, integer *, real *, real *, real *, complex *, real *,
integer *);
static integer lda, npp;
/* Fortran I/O blocks */
static cilist io___49 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___52 = { 0, 0, 0, fmt_9997, 0 };
static cilist io___53 = { 0, 0, 0, fmt_9998, 0 };
/* -- LAPACK test routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
June 30, 1999
Purpose
=======
CDRVPP tests the driver routines CPPSV and -SVX.
Arguments
=========
DOTYPE (input) LOGICAL array, dimension (NTYPES)
The matrix types to be used for testing. Matrices of type j
(for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
.TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
NN (input) INTEGER
The number of values of N contained in the vector NVAL.
NVAL (input) INTEGER array, dimension (NN)
The values of the matrix dimension N.
NRHS (input) INTEGER
The number of right hand side vectors to be generated for
each linear system.
THRESH (input) REAL
The threshold value for the test ratios. A result is
included in the output file if RESULT >= THRESH. To have
every test ratio printed, use THRESH = 0.
TSTERR (input) LOGICAL
Flag that indicates whether error exits are to be tested.
NMAX (input) INTEGER
The maximum value permitted for N, used in dimensioning the
work arrays.
A (workspace) COMPLEX array, dimension (NMAX*(NMAX+1)/2)
AFAC (workspace) COMPLEX array, dimension (NMAX*(NMAX+1)/2)
ASAV (workspace) COMPLEX array, dimension (NMAX*(NMAX+1)/2)
B (workspace) COMPLEX array, dimension (NMAX*NRHS)
BSAV (workspace) COMPLEX array, dimension (NMAX*NRHS)
X (workspace) COMPLEX array, dimension (NMAX*NRHS)
XACT (workspace) COMPLEX array, dimension (NMAX*NRHS)
S (workspace) REAL array, dimension (NMAX)
WORK (workspace) COMPLEX array, dimension
(NMAX*max(3,NRHS))
RWORK (workspace) REAL array, dimension (NMAX+2*NRHS)
NOUT (input) INTEGER
The unit number for output.
=====================================================================
Parameter adjustments */
--rwork;
--work;
--s;
--xact;
--x;
--bsav;
--b;
--asav;
--afac;
--a;
--nval;
--dotype;
/* Function Body
Initialize constants and the random number seed. */
s_copy(path, "Complex precision", (ftnlen)1, (ftnlen)17);
s_copy(path + 1, "PP", (ftnlen)2, (ftnlen)2);
nrun = 0;
nfail = 0;
nerrs = 0;
for (i__ = 1; i__ <= 4; ++i__) {
iseed[i__ - 1] = iseedy[i__ - 1];
/* L10: */
}
/* Test the error exits */
if (*tsterr) {
cerrvx_(path, nout);
}
infoc_1.infot = 0;
/* Do for each value of N in NVAL */
i__1 = *nn;
for (in = 1; in <= i__1; ++in) {
n = nval[in];
lda = max(n,1);
npp = n * (n + 1) / 2;
*(unsigned char *)xtype = 'N';
nimat = 9;
if (n <= 0) {
nimat = 1;
}
i__2 = nimat;
for (imat = 1; imat <= i__2; ++imat) {
/* Do the tests only if DOTYPE( IMAT ) is true. */
if (! dotype[imat]) {
goto L130;
}
/* Skip types 3, 4, or 5 if the matrix size is too small. */
zerot = imat >= 3 && imat <= 5;
if (zerot && n < imat - 2) {
goto L130;
}
/* Do first for UPLO = 'U', then for UPLO = 'L' */
for (iuplo = 1; iuplo <= 2; ++iuplo) {
*(unsigned char *)uplo = *(unsigned char *)&uplos[iuplo - 1];
*(unsigned char *)packit = *(unsigned char *)&packs[iuplo - 1]
;
/* Set up parameters with CLATB4 and generate a test matrix
with CLATMS. */
clatb4_(path, &imat, &n, &n, type__, &kl, &ku, &anorm, &mode,
&cndnum, dist);
rcondc = 1.f / cndnum;
s_copy(srnamc_1.srnamt, "CLATMS", (ftnlen)6, (ftnlen)6);
clatms_(&n, &n, dist, iseed, type__, &rwork[1], &mode, &
cndnum, &anorm, &kl, &ku, packit, &a[1], &lda, &work[
1], &info);
/* Check error code from CLATMS. */
if (info != 0) {
alaerh_(path, "CLATMS", &info, &c__0, uplo, &n, &n, &c_n1,
&c_n1, &c_n1, &imat, &nfail, &nerrs, nout);
goto L120;
}
/* For types 3-5, zero one row and column of the matrix to
test that INFO is returned correctly. */
if (zerot) {
if (imat == 3) {
izero = 1;
} else if (imat == 4) {
izero = n;
} else {
izero = n / 2 + 1;
}
/* Set row and column IZERO of A to 0. */
if (iuplo == 1) {
ioff = (izero - 1) * izero / 2;
i__3 = izero - 1;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = ioff + i__;
a[i__4].r = 0.f, a[i__4].i = 0.f;
/* L20: */
}
ioff += izero;
i__3 = n;
for (i__ = izero; i__ <= i__3; ++i__) {
i__4 = ioff;
a[i__4].r = 0.f, a[i__4].i = 0.f;
ioff += i__;
/* L30: */
}
} else {
ioff = izero;
i__3 = izero - 1;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = ioff;
a[i__4].r = 0.f, a[i__4].i = 0.f;
ioff = ioff + n - i__;
/* L40: */
}
ioff -= izero;
i__3 = n;
for (i__ = izero; i__ <= i__3; ++i__) {
i__4 = ioff + i__;
a[i__4].r = 0.f, a[i__4].i = 0.f;
/* L50: */
}
}
} else {
izero = 0;
}
/* Set the imaginary part of the diagonals. */
if (iuplo == 1) {
claipd_(&n, &a[1], &c__2, &c__1);
} else {
claipd_(&n, &a[1], &n, &c_n1);
}
/* Save a copy of the matrix A in ASAV. */
ccopy_(&npp, &a[1], &c__1, &asav[1], &c__1);
for (iequed = 1; iequed <= 2; ++iequed) {
*(unsigned char *)equed = *(unsigned char *)&equeds[
iequed - 1];
if (iequed == 1) {
nfact = 3;
} else {
nfact = 1;
}
i__3 = nfact;
for (ifact = 1; ifact <= i__3; ++ifact) {
*(unsigned char *)fact = *(unsigned char *)&facts[
ifact - 1];
prefac = lsame_(fact, "F");
nofact = lsame_(fact, "N");
equil = lsame_(fact, "E");
if (zerot) {
if (prefac) {
goto L100;
}
rcondc = 0.f;
} else if (! lsame_(fact, "N"))
{
/* Compute the condition number for comparison with
the value returned by CPPSVX (FACT = 'N' reuses
the condition number from the previous iteration
with FACT = 'F'). */
ccopy_(&npp, &asav[1], &c__1, &afac[1], &c__1);
if (equil || iequed > 1) {
/* Compute row and column scale factors to
equilibrate the matrix A. */
cppequ_(uplo, &n, &afac[1], &s[1], &scond, &
amax, &info);
if (info == 0 && n > 0) {
if (iequed > 1) {
scond = 0.f;
}
/* Equilibrate the matrix. */
claqhp_(uplo, &n, &afac[1], &s[1], &scond,
&amax, equed);
}
}
/* Save the condition number of the
non-equilibrated system for use in CGET04. */
if (equil) {
roldc = rcondc;
}
/* Compute the 1-norm of A. */
anorm = clanhp_("1", uplo, &n, &afac[1], &rwork[1]
);
/* Factor the matrix A. */
cpptrf_(uplo, &n, &afac[1], &info);
/* Form the inverse of A. */
ccopy_(&npp, &afac[1], &c__1, &a[1], &c__1);
cpptri_(uplo, &n, &a[1], &info);
/* Compute the 1-norm condition number of A. */
ainvnm = clanhp_("1", uplo, &n, &a[1], &rwork[1]);
if (anorm <= 0.f || ainvnm <= 0.f) {
rcondc = 1.f;
} else {
rcondc = 1.f / anorm / ainvnm;
}
}
/* Restore the matrix A. */
ccopy_(&npp, &asav[1], &c__1, &a[1], &c__1);
/* Form an exact solution and set the right hand side. */
s_copy(srnamc_1.srnamt, "CLARHS", (ftnlen)6, (ftnlen)
6);
clarhs_(path, xtype, uplo, " ", &n, &n, &kl, &ku,
nrhs, &a[1], &lda, &xact[1], &lda, &b[1], &
lda, iseed, &info);
*(unsigned char *)xtype = 'C';
clacpy_("Full", &n, nrhs, &b[1], &lda, &bsav[1], &lda);
if (nofact) {
/* --- Test CPPSV ---
Compute the L*L' or U'*U factorization of the
matrix and solve the system. */
ccopy_(&npp, &a[1], &c__1, &afac[1], &c__1);
clacpy_("Full", &n, nrhs, &b[1], &lda, &x[1], &
lda);
s_copy(srnamc_1.srnamt, "CPPSV ", (ftnlen)6, (
ftnlen)6);
cppsv_(uplo, &n, nrhs, &afac[1], &x[1], &lda, &
info);
/* Check error code from CPPSV . */
if (info != izero) {
alaerh_(path, "CPPSV ", &info, &izero, uplo, &
n, &n, &c_n1, &c_n1, nrhs, &imat, &
nfail, &nerrs, nout);
goto L70;
} else if (info != 0) {
goto L70;
}
/* Reconstruct matrix from factors and compute
residual. */
cppt01_(uplo, &n, &a[1], &afac[1], &rwork[1],
result);
/* Compute residual of the computed solution. */
clacpy_("Full", &n, nrhs, &b[1], &lda, &work[1], &
lda);
cppt02_(uplo, &n, nrhs, &a[1], &x[1], &lda, &work[
1], &lda, &rwork[1], &result[1]);
/* Check solution from generated exact solution. */
cget04_(&n, nrhs, &x[1], &lda, &xact[1], &lda, &
rcondc, &result[2]);
nt = 3;
/* Print information about the tests that did not
pass the threshold. */
i__4 = nt;
for (k = 1; k <= i__4; ++k) {
if (result[k - 1] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
aladhd_(nout, path);
}
io___49.ciunit = *nout;
s_wsfe(&io___49);
do_fio(&c__1, "CPPSV ", (ftnlen)6);
do_fio(&c__1, uplo, (ftnlen)1);
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&imat, (ftnlen)
sizeof(integer));
do_fio(&c__1, (char *)&k, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&result[k - 1], (
ftnlen)sizeof(real));
e_wsfe();
++nfail;
}
/* L60: */
}
nrun += nt;
L70:
;
}
/* --- Test CPPSVX --- */
if (! prefac && npp > 0) {
claset_("Full", &npp, &c__1, &c_b63, &c_b63, &
afac[1], &npp);
}
claset_("Full", &n, nrhs, &c_b63, &c_b63, &x[1], &lda);
if (iequed > 1 && n > 0) {
/* Equilibrate the matrix if FACT='F' and
EQUED='Y'. */
claqhp_(uplo, &n, &a[1], &s[1], &scond, &amax,
equed);
}
/* Solve the system and compute the condition number
and error bounds using CPPSVX. */
s_copy(srnamc_1.srnamt, "CPPSVX", (ftnlen)6, (ftnlen)
6);
cppsvx_(fact, uplo, &n, nrhs, &a[1], &afac[1], equed,
&s[1], &b[1], &lda, &x[1], &lda, &rcond, &
rwork[1], &rwork[*nrhs + 1], &work[1], &rwork[
(*nrhs << 1) + 1], &info);
/* Check the error code from CPPSVX. */
if (info != izero) {
/* Writing concatenation */
i__5[0] = 1, a__1[0] = fact;
i__5[1] = 1, a__1[1] = uplo;
s_cat(ch__1, a__1, i__5, &c__2, (ftnlen)2);
alaerh_(path, "CPPSVX", &info, &izero, ch__1, &n,
&n, &c_n1, &c_n1, nrhs, &imat, &nfail, &
nerrs, nout);
goto L90;
}
if (info == 0) {
if (! prefac) {
/* Reconstruct matrix from factors and compute
residual. */
cppt01_(uplo, &n, &a[1], &afac[1], &rwork[(*
nrhs << 1) + 1], result);
k1 = 1;
} else {
k1 = 2;
}
/* Compute residual of the computed solution. */
clacpy_("Full", &n, nrhs, &bsav[1], &lda, &work[1]
, &lda);
cppt02_(uplo, &n, nrhs, &asav[1], &x[1], &lda, &
work[1], &lda, &rwork[(*nrhs << 1) + 1], &
result[1]);
/* Check solution from generated exact solution. */
if (nofact || prefac && lsame_(equed, "N")) {
cget04_(&n, nrhs, &x[1], &lda, &xact[1], &lda,
&rcondc, &result[2]);
} else {
cget04_(&n, nrhs, &x[1], &lda, &xact[1], &lda,
&roldc, &result[2]);
}
/* Check the error bounds from iterative
refinement. */
cppt05_(uplo, &n, nrhs, &asav[1], &b[1], &lda, &x[
1], &lda, &xact[1], &lda, &rwork[1], &
rwork[*nrhs + 1], &result[3]);
} else {
k1 = 6;
}
/* Compare RCOND from CPPSVX with the computed value
in RCONDC. */
result[5] = sget06_(&rcond, &rcondc);
/* Print information about the tests that did not pass
the threshold. */
for (k = k1; k <= 6; ++k) {
if (result[k - 1] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
aladhd_(nout, path);
}
if (prefac) {
io___52.ciunit = *nout;
s_wsfe(&io___52);
do_fio(&c__1, "CPPSVX", (ftnlen)6);
do_fio(&c__1, fact, (ftnlen)1);
do_fio(&c__1, uplo, (ftnlen)1);
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(
integer));
do_fio(&c__1, equed, (ftnlen)1);
do_fio(&c__1, (char *)&imat, (ftnlen)
sizeof(integer));
do_fio(&c__1, (char *)&k, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&result[k - 1], (
ftnlen)sizeof(real));
e_wsfe();
} else {
io___53.ciunit = *nout;
s_wsfe(&io___53);
do_fio(&c__1, "CPPSVX", (ftnlen)6);
do_fio(&c__1, fact, (ftnlen)1);
do_fio(&c__1, uplo, (ftnlen)1);
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&imat, (ftnlen)
sizeof(integer));
do_fio(&c__1, (char *)&k, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&result[k - 1], (
ftnlen)sizeof(real));
e_wsfe();
}
++nfail;
}
/* L80: */
}
nrun = nrun + 7 - k1;
L90:
L100:
;
}
/* L110: */
}
L120:
;
}
L130:
;
}
/* L140: */
}
/* Print a summary of the results. */
alasvm_(path, nout, &nfail, &nrun, &nerrs);
return 0;
/* End of CDRVPP */
} /* cdrvpp_ */
/* Subroutine */ int cppsvx_(char *fact, char *uplo, integer *n, integer *
nrhs, complex *ap, complex *afp, char *equed, real *s, complex *b,
integer *ldb, complex *x, integer *ldx, real *rcond, real *ferr, real
*berr, complex *work, real *rwork, integer *info)
{
/* System generated locals */
integer 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, smin, smax;
real scond, anorm;
logical equil, rcequ;
logical nofact;
real bignum;
integer infequ;
real smlnum;
/* -- LAPACK driver routine (version 3.2) -- */
/* November 2006 */
/* Purpose */
/* ======= */
/* CPPSVX uses the Cholesky factorization A = U**H*U or A = L*L**H to */
/* compute the solution to a complex system of linear equations */
/* A * X = B, */
/* where A is an N-by-N Hermitian positive definite matrix stored in */
/* packed format 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: */
/* diag(S) * A * diag(S) * inv(diag(S)) * X = diag(S) * 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(S)*A*diag(S) and B by diag(S)*B. */
/* 2. If FACT = 'N' or 'E', the Cholesky decomposition is used to */
/* factor the matrix A (after equilibration if FACT = 'E') as */
/* A = U'* U , if UPLO = 'U', or */
/* A = L * L', if UPLO = 'L', */
/* where U is an upper triangular matrix, L is a lower triangular */
/* matrix, and ' indicates conjugate transpose. */
/* 3. If the leading i-by-i principal minor is not positive definite, */
/* 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(S) 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, AFP contains the factored form of A. */
/* If EQUED = 'Y', the matrix A has been equilibrated */
/* with scaling factors given by S. AP and AFP will not */
/* be modified. */
/* = 'N': The matrix A will be copied to AFP and factored. */
/* = 'E': The matrix A will be equilibrated if necessary, then */
/* copied to AFP and factored. */
/* UPLO (input) CHARACTER*1 */
/* = 'U': Upper triangle of A is stored; */
/* = 'L': Lower triangle of A is stored. */
/* 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. */
/* AP (input/output) COMPLEX array, dimension (N*(N+1)/2) */
/* On entry, the upper or lower triangle of the Hermitian matrix */
/* A, packed columnwise in a linear array, except if FACT = 'F' */
/* and EQUED = 'Y', then A must contain the equilibrated matrix */
/* diag(S)*A*diag(S). The j-th column of A is stored in the */
/* array AP as follows: */
/* if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; */
/* if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. */
/* See below for further details. A is not modified if */
/* FACT = 'F' or 'N', or if FACT = 'E' and EQUED = 'N' on exit. */
/* On exit, if FACT = 'E' and EQUED = 'Y', A is overwritten by */
/* diag(S)*A*diag(S). */
/* AFP (input or output) COMPLEX array, dimension (N*(N+1)/2) */
/* If FACT = 'F', then AFP is an input argument and on entry */
/* contains the triangular factor U or L from the Cholesky */
/* factorization A = U**H*U or A = L*L**H, in the same storage */
/* format as A. If EQUED .ne. 'N', then AFP is the factored */
/* form of the equilibrated matrix A. */
/* If FACT = 'N', then AFP is an output argument and on exit */
/* returns the triangular factor U or L from the Cholesky */
/* factorization A = U**H*U or A = L*L**H of the original */
/* matrix A. */
/* If FACT = 'E', then AFP is an output argument and on exit */
/* returns the triangular factor U or L from the Cholesky */
/* factorization A = U**H*U or A = L*L**H of the equilibrated */
/* matrix A (see the description of AP for the form of the */
/* equilibrated matrix). */
/* EQUED (input or output) CHARACTER*1 */
/* Specifies the form of equilibration that was done. */
/* = 'N': No equilibration (always true if FACT = 'N'). */
/* = 'Y': Equilibration was done, i.e., A has been replaced by */
/* diag(S) * A * diag(S). */
/* EQUED is an input argument if FACT = 'F'; otherwise, it is an */
/* output argument. */
/* S (input or output) REAL array, dimension (N) */
/* The scale factors for A; not accessed if EQUED = 'N'. S is */
/* an input argument if FACT = 'F'; otherwise, S is an output */
/* argument. If FACT = 'F' and EQUED = 'Y', each element of S */
/* 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 EQUED = 'Y', */
/* B is overwritten by diag(S) * 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 if EQUED = 'Y', */
/* A and B are modified on exit, and the solution to the */
/* equilibrated system is inv(diag(S))*X. */
/* 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) REAL array, dimension (N) */
/* 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: the leading minor of order i of A is */
/* not positive definite, so the factorization */
/* could not be completed, and the solution has not */
/* been 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. */
/* Further Details */
/* =============== */
/* The packed storage scheme is illustrated by the following example */
/* when N = 4, UPLO = 'U': */
/* Two-dimensional storage of the Hermitian matrix A: */
/* a11 a12 a13 a14 */
/* a22 a23 a24 */
/* a33 a34 (aij = conjg(aji)) */
/* a44 */
/* Packed storage of the upper triangle of A: */
/* AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ] */
/* ===================================================================== */
/* Parameter adjustments */
--ap;
--afp;
--s;
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");
if (nofact || equil) {
*(unsigned char *)equed = 'N';
rcequ = FALSE_;
} else {
rcequ = lsame_(equed, "Y");
smlnum = slamch_("Safe minimum");
bignum = 1.f / smlnum;
}
/* Test the input parameters. */
if (! nofact && ! equil && ! lsame_(fact, "F")) {
*info = -1;
} else if (! lsame_(uplo, "U") && ! lsame_(uplo,
"L")) {
*info = -2;
} else if (*n < 0) {
*info = -3;
} else if (*nrhs < 0) {
*info = -4;
} else if (lsame_(fact, "F") && ! (rcequ || lsame_(
equed, "N"))) {
*info = -7;
} else {
if (rcequ) {
smin = bignum;
smax = 0.f;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
r__1 = smin, r__2 = s[j];
smin = dmin(r__1,r__2);
/* Computing MAX */
r__1 = smax, r__2 = s[j];
smax = dmax(r__1,r__2);
}
if (smin <= 0.f) {
*info = -8;
} else if (*n > 0) {
scond = dmax(smin,smlnum) / dmin(smax,bignum);
} else {
scond = 1.f;
}
}
if (*info == 0) {
if (*ldb < max(1,*n)) {
*info = -10;
} else if (*ldx < max(1,*n)) {
*info = -12;
}
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CPPSVX", &i__1);
return 0;
}
if (equil) {
/* Compute row and column scalings to equilibrate the matrix A. */
cppequ_(uplo, n, &ap[1], &s[1], &scond, &amax, &infequ);
if (infequ == 0) {
/* Equilibrate the matrix. */
claqhp_(uplo, n, &ap[1], &s[1], &scond, &amax, equed);
rcequ = lsame_(equed, "Y");
}
}
/* Scale the right-hand side. */
if (rcequ) {
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 = s[i__4] * b[i__5].r, q__1.i = s[i__4] * b[i__5].i;
b[i__3].r = q__1.r, b[i__3].i = q__1.i;
}
}
}
if (nofact || equil) {
/* Compute the Cholesky factorization A = U'*U or A = L*L'. */
i__1 = *n * (*n + 1) / 2;
ccopy_(&i__1, &ap[1], &c__1, &afp[1], &c__1);
cpptrf_(uplo, n, &afp[1], info);
/* Return if INFO is non-zero. */
if (*info > 0) {
*rcond = 0.f;
return 0;
}
}
/* Compute the norm of the matrix A. */
anorm = clanhp_("I", uplo, n, &ap[1], &rwork[1]);
/* Compute the reciprocal of the condition number of A. */
cppcon_(uplo, n, &afp[1], &anorm, rcond, &work[1], &rwork[1], info);
/* Compute the solution matrix X. */
clacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx);
cpptrs_(uplo, n, nrhs, &afp[1], &x[x_offset], ldx, info);
/* Use iterative refinement to improve the computed solution and */
/* compute error bounds and backward error estimates for it. */
cpprfs_(uplo, n, nrhs, &ap[1], &afp[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 (rcequ) {
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 = s[i__4] * x[i__5].r, q__1.i = s[i__4] * x[i__5].i;
x[i__3].r = q__1.r, x[i__3].i = q__1.i;
}
}
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
ferr[j] /= scond;
}
}
/* Set INFO = N+1 if the matrix is singular to working precision. */
if (*rcond < slamch_("Epsilon")) {
*info = *n + 1;
}
return 0;
/* End of CPPSVX */
} /* cppsvx_ */
