/* Subroutine */ int zhpsvx_(char *fact, char *uplo, integer *n, integer *
nrhs, doublecomplex *ap, doublecomplex *afp, integer *ipiv,
doublecomplex *b, integer *ldb, doublecomplex *x, integer *ldx,
doublereal *rcond, doublereal *ferr, doublereal *berr, doublecomplex *
work, doublereal *rwork, integer *info)
{
/* -- LAPACK driver routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
June 30, 1999
Purpose
=======
ZHPSVX uses the diagonal pivoting factorization A = U*D*U**H or
A = L*D*L**H to compute the solution to a complex system of linear
equations A * X = B, where A is an N-by-N Hermitian 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 = 'N', the diagonal pivoting method is used to factor A as
A = U * D * U**H, if UPLO = 'U', or
A = L * D * L**H, if UPLO = 'L',
where U (or L) is a product of permutation and unit upper (lower)
triangular matrices and D is Hermitian and block diagonal with
1-by-1 and 2-by-2 diagonal blocks.
2. If some D(i,i)=0, so that D 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.
3. The system of equations is solved for X using the factored form
of A.
4. Iterative refinement is applied to improve the computed solution
matrix and calculate error bounds and backward error estimates
for it.
Arguments
=========
FACT (input) CHARACTER*1
Specifies whether or not the factored form of A has been
supplied on entry.
= 'F': On entry, AFP and IPIV contain the factored form of
A. AFP and IPIV will not be modified.
= 'N': The matrix A will be 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) COMPLEX*16 array, dimension (N*(N+1)/2)
The upper or lower triangle of the Hermitian matrix A, packed
columnwise in a linear array. The j-th column of A is stored
in the array AP as follows:
if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
See below for further details.
AFP (input or output) COMPLEX*16 array, dimension (N*(N+1)/2)
If FACT = 'F', then AFP is an input argument and on entry
contains the block diagonal matrix D and the multipliers used
to obtain the factor U or L from the factorization
A = U*D*U**H or A = L*D*L**H as computed by ZHPTRF, stored as
a packed triangular matrix in the same storage format as A.
If FACT = 'N', then AFP is an output argument and on exit
contains the block diagonal matrix D and the multipliers used
to obtain the factor U or L from the factorization
A = U*D*U**H or A = L*D*L**H as computed by ZHPTRF, stored as
a packed triangular matrix in the same storage format as A.
IPIV (input or output) INTEGER array, dimension (N)
If FACT = 'F', then IPIV is an input argument and on entry
contains details of the interchanges and the block structure
of D, as determined by ZHPTRF.
If IPIV(k) > 0, then rows and columns k and IPIV(k) were
interchanged and D(k,k) is a 1-by-1 diagonal block.
If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and
columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k)
is a 2-by-2 diagonal block. If UPLO = 'L' and IPIV(k) =
IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were
interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
If FACT = 'N', then IPIV is an output argument and on exit
contains details of the interchanges and the block structure
of D, as determined by ZHPTRF.
B (input) COMPLEX*16 array, dimension (LDB,NRHS)
The N-by-NRHS right hand side matrix B.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).
X (output) COMPLEX*16 array, dimension (LDX,NRHS)
If INFO = 0 or INFO = N+1, the N-by-NRHS solution matrix X.
LDX (input) INTEGER
The leading dimension of the array X. LDX >= max(1,N).
RCOND (output) DOUBLE PRECISION
The estimate of the reciprocal condition number of the matrix
A. 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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*16 array, dimension (2*N)
RWORK (workspace) DOUBLE PRECISION 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: D(i,i) is exactly zero. The factorization
has been completed but the factor D is exactly
singular, so the solution and error bounds could
not be computed. RCOND = 0 is returned.
= N+1: D 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 ]
=====================================================================
Test the input parameters.
Parameter adjustments */
/* Table of constant values */
static integer c__1 = 1;
/* System generated locals */
integer b_dim1, b_offset, x_dim1, x_offset, i__1;
/* Local variables */
extern logical lsame_(char *, char *);
static doublereal anorm;
extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *,
doublecomplex *, integer *);
extern doublereal dlamch_(char *);
static logical nofact;
extern /* Subroutine */ int xerbla_(char *, integer *);
extern doublereal zlanhp_(char *, char *, integer *, doublecomplex *,
doublereal *);
extern /* Subroutine */ int zhpcon_(char *, integer *, doublecomplex *,
integer *, doublereal *, doublereal *, doublecomplex *, integer *), zlacpy_(char *, integer *, integer *, doublecomplex *,
integer *, doublecomplex *, integer *), zhprfs_(char *,
integer *, integer *, doublecomplex *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublereal *, doublereal *, doublecomplex *, doublereal *,
integer *), zhptrf_(char *, integer *, doublecomplex *,
integer *, integer *), zhptrs_(char *, integer *, integer
*, doublecomplex *, integer *, doublecomplex *, integer *,
integer *);
--ap;
--afp;
--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;
nofact = lsame_(fact, "N");
if (! nofact && ! 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 (*ldb < max(1,*n)) {
*info = -9;
} else if (*ldx < max(1,*n)) {
*info = -11;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZHPSVX", &i__1);
return 0;
}
if (nofact) {
/* Compute the factorization A = U*D*U' or A = L*D*L'. */
i__1 = *n * (*n + 1) / 2;
zcopy_(&i__1, &ap[1], &c__1, &afp[1], &c__1);
zhptrf_(uplo, n, &afp[1], &ipiv[1], info);
/* Return if INFO is non-zero. */
if (*info != 0) {
if (*info > 0) {
*rcond = 0.;
}
return 0;
}
}
/* Compute the norm of the matrix A. */
anorm = zlanhp_("I", uplo, n, &ap[1], &rwork[1]);
/* Compute the reciprocal of the condition number of A. */
zhpcon_(uplo, n, &afp[1], &ipiv[1], &anorm, rcond, &work[1], info);
/* Set INFO = N+1 if the matrix is singular to working precision. */
if (*rcond < dlamch_("Epsilon")) {
*info = *n + 1;
}
/* Compute the solution vectors X. */
zlacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx);
zhptrs_(uplo, n, nrhs, &afp[1], &ipiv[1], &x[x_offset], ldx, info);
/* Use iterative refinement to improve the computed solutions and
compute error bounds and backward error estimates for them. */
zhprfs_(uplo, n, nrhs, &ap[1], &afp[1], &ipiv[1], &b[b_offset], ldb, &x[
x_offset], ldx, &ferr[1], &berr[1], &work[1], &rwork[1], info);
return 0;
/* End of ZHPSVX */
} /* zhpsvx_ */
/* Subroutine */ int zchkhp_(logical *dotype, integer *nn, integer *nval,
integer *nns, integer *nsval, doublereal *thresh, logical *tsterr,
integer *nmax, doublecomplex *a, doublecomplex *afac, doublecomplex *
ainv, doublecomplex *b, doublecomplex *x, doublecomplex *xact,
doublecomplex *work, doublereal *rwork, integer *iwork, integer *nout)
{
/* Initialized data */
static integer iseedy[4] = { 1988,1989,1990,1991 };
static char uplos[1*2] = "U" "L";
/* Format strings */
static char fmt_9999[] = "(\002 UPLO = '\002,a1,\002', N =\002,i5,\002, "
"type \002,i2,\002, test \002,i2,\002, ratio =\002,g12.5)";
static char fmt_9998[] = "(\002 UPLO = '\002,a1,\002', N =\002,i5,\002, "
"NRHS=\002,i3,\002, type \002,i2,\002, test(\002,i2,\002) =\002,g"
"12.5)";
/* System generated locals */
integer i__1, i__2, i__3, i__4, i__5;
/* Builtin functions */
/* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void);
/* Local variables */
integer i__, j, k, n, i1, i2, in, kl, ku, nt, lda, npp, ioff, mode, imat,
info;
char path[3], dist[1];
integer irhs, nrhs;
char uplo[1], type__[1];
integer nrun;
extern /* Subroutine */ int alahd_(integer *, char *);
integer nfail, iseed[4];
extern doublereal dget06_(doublereal *, doublereal *);
extern logical lsame_(char *, char *);
doublereal rcond;
integer nimat;
doublereal anorm;
extern /* Subroutine */ int zget04_(integer *, integer *, doublecomplex *,
integer *, doublecomplex *, integer *, doublereal *, doublereal *
), zhpt01_(char *, integer *, doublecomplex *, doublecomplex *,
integer *, doublecomplex *, integer *, doublereal *, doublereal *);
integer iuplo, izero, nerrs;
extern /* Subroutine */ int zppt02_(char *, integer *, integer *,
doublecomplex *, doublecomplex *, integer *, doublecomplex *,
integer *, doublereal *, doublereal *), zppt03_(char *,
integer *, doublecomplex *, doublecomplex *, doublecomplex *,
integer *, doublereal *, doublereal *, doublereal *);
logical zerot;
extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *,
doublecomplex *, integer *), zppt05_(char *, integer *, integer *,
doublecomplex *, doublecomplex *, integer *, doublecomplex *,
integer *, doublecomplex *, integer *, doublereal *, doublereal *,
doublereal *);
char xtype[1];
extern /* Subroutine */ int zlatb4_(char *, integer *, integer *, integer
*, char *, integer *, integer *, doublereal *, integer *,
doublereal *, char *), alaerh_(char *,
char *, integer *, integer *, char *, integer *, integer *,
integer *, integer *, integer *, integer *, integer *, integer *,
integer *);
doublereal rcondc;
char packit[1];
extern /* Subroutine */ int alasum_(char *, integer *, integer *, integer
*, integer *);
doublereal cndnum;
extern /* Subroutine */ int zlaipd_(integer *, doublecomplex *, integer *,
integer *);
logical trfcon;
extern doublereal zlanhp_(char *, char *, integer *, doublecomplex *,
doublereal *);
extern /* Subroutine */ int zhpcon_(char *, integer *, doublecomplex *,
integer *, doublereal *, doublereal *, doublecomplex *, integer *), zlacpy_(char *, integer *, integer *, doublecomplex *,
integer *, doublecomplex *, integer *), zlarhs_(char *,
char *, char *, char *, integer *, integer *, integer *, integer *
, integer *, doublecomplex *, integer *, doublecomplex *, integer
*, doublecomplex *, integer *, integer *, integer *), zlatms_(integer *, integer *, char *,
integer *, char *, doublereal *, integer *, doublereal *,
doublereal *, integer *, integer *, char *, doublecomplex *,
integer *, doublecomplex *, integer *),
zhprfs_(char *, integer *, integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublereal *, doublereal *,
doublecomplex *, doublereal *, integer *), zhptrf_(char *,
integer *, doublecomplex *, integer *, integer *);
doublereal result[8];
extern /* Subroutine */ int zhptri_(char *, integer *, doublecomplex *,
integer *, doublecomplex *, integer *), zhptrs_(char *,
integer *, integer *, doublecomplex *, integer *, doublecomplex *,
integer *, integer *), zerrsy_(char *, integer *)
;
/* Fortran I/O blocks */
static cilist io___38 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___41 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___43 = { 0, 0, 0, fmt_9999, 0 };
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZCHKHP tests ZHPTRF, -TRI, -TRS, -RFS, and -CON */
/* 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. */
/* NNS (input) INTEGER */
/* The number of values of NRHS contained in the vector NSVAL. */
/* NSVAL (input) INTEGER array, dimension (NNS) */
/* The values of the number of right hand sides NRHS. */
/* THRESH (input) DOUBLE PRECISION */
/* 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*16 array, dimension */
/* (NMAX*(NMAX+1)/2) */
/* AFAC (workspace) COMPLEX*16 array, dimension */
/* (NMAX*(NMAX+1)/2) */
/* AINV (workspace) COMPLEX*16 array, dimension */
/* (NMAX*(NMAX+1)/2) */
/* B (workspace) COMPLEX*16 array, dimension (NMAX*NSMAX) */
/* where NSMAX is the largest entry in NSVAL. */
/* X (workspace) COMPLEX*16 array, dimension (NMAX*NSMAX) */
/* XACT (workspace) COMPLEX*16 array, dimension (NMAX*NSMAX) */
/* WORK (workspace) COMPLEX*16 array, dimension */
/* (NMAX*max(2,NSMAX)) */
/* RWORK (workspace) DOUBLE PRECISION array, */
/* dimension (NMAX+2*NSMAX) */
/* IWORK (workspace) INTEGER array, dimension (NMAX) */
/* NOUT (input) INTEGER */
/* The unit number for output. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Scalars in Common .. */
/* .. */
/* .. Common blocks .. */
/* .. */
/* .. Data statements .. */
/* Parameter adjustments */
--iwork;
--rwork;
--work;
--xact;
--x;
--b;
--ainv;
--afac;
--a;
--nsval;
--nval;
--dotype;
/* Function Body */
/* .. */
/* .. Executable Statements .. */
/* Initialize constants and the random number seed. */
s_copy(path, "Zomplex precision", (ftnlen)1, (ftnlen)17);
s_copy(path + 1, "HP", (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) {
zerrsy_(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);
*(unsigned char *)xtype = 'N';
nimat = 10;
if (n <= 0) {
nimat = 1;
}
izero = 0;
i__2 = nimat;
for (imat = 1; imat <= i__2; ++imat) {
/* Do the tests only if DOTYPE( IMAT ) is true. */
if (! dotype[imat]) {
goto L160;
}
/* Skip types 3, 4, 5, or 6 if the matrix size is too small. */
zerot = imat >= 3 && imat <= 6;
if (zerot && n < imat - 2) {
goto L160;
}
/* Do first for UPLO = 'U', then for UPLO = 'L' */
for (iuplo = 1; iuplo <= 2; ++iuplo) {
*(unsigned char *)uplo = *(unsigned char *)&uplos[iuplo - 1];
if (lsame_(uplo, "U")) {
*(unsigned char *)packit = 'C';
} else {
*(unsigned char *)packit = 'R';
}
/* Set up parameters with ZLATB4 and generate a test matrix */
/* with ZLATMS. */
zlatb4_(path, &imat, &n, &n, type__, &kl, &ku, &anorm, &mode,
&cndnum, dist);
s_copy(srnamc_1.srnamt, "ZLATMS", (ftnlen)6, (ftnlen)6);
zlatms_(&n, &n, dist, iseed, type__, &rwork[1], &mode, &
cndnum, &anorm, &kl, &ku, packit, &a[1], &lda, &work[
1], &info);
/* Check error code from ZLATMS. */
if (info != 0) {
alaerh_(path, "ZLATMS", &info, &c__0, uplo, &n, &n, &c_n1,
&c_n1, &c_n1, &imat, &nfail, &nerrs, nout);
goto L150;
}
/* For types 3-6, zero one or more rows and columns 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;
}
if (imat < 6) {
/* Set row and column IZERO to zero. */
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., a[i__4].i = 0.;
/* L20: */
}
ioff += izero;
i__3 = n;
for (i__ = izero; i__ <= i__3; ++i__) {
i__4 = ioff;
a[i__4].r = 0., a[i__4].i = 0.;
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., a[i__4].i = 0.;
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., a[i__4].i = 0.;
/* L50: */
}
}
} else {
ioff = 0;
if (iuplo == 1) {
/* Set the first IZERO rows and columns to zero. */
i__3 = n;
for (j = 1; j <= i__3; ++j) {
i2 = min(j,izero);
i__4 = i2;
for (i__ = 1; i__ <= i__4; ++i__) {
i__5 = ioff + i__;
a[i__5].r = 0., a[i__5].i = 0.;
/* L60: */
}
ioff += j;
/* L70: */
}
} else {
/* Set the last IZERO rows and columns to zero. */
i__3 = n;
for (j = 1; j <= i__3; ++j) {
i1 = max(j,izero);
i__4 = n;
for (i__ = i1; i__ <= i__4; ++i__) {
i__5 = ioff + i__;
a[i__5].r = 0., a[i__5].i = 0.;
/* L80: */
}
ioff = ioff + n - j;
/* L90: */
}
}
}
} else {
izero = 0;
}
/* Set the imaginary part of the diagonals. */
if (iuplo == 1) {
zlaipd_(&n, &a[1], &c__2, &c__1);
} else {
zlaipd_(&n, &a[1], &n, &c_n1);
}
/* Compute the L*D*L' or U*D*U' factorization of the matrix. */
npp = n * (n + 1) / 2;
zcopy_(&npp, &a[1], &c__1, &afac[1], &c__1);
s_copy(srnamc_1.srnamt, "ZHPTRF", (ftnlen)6, (ftnlen)6);
zhptrf_(uplo, &n, &afac[1], &iwork[1], &info);
/* Adjust the expected value of INFO to account for */
/* pivoting. */
k = izero;
if (k > 0) {
L100:
if (iwork[k] < 0) {
if (iwork[k] != -k) {
k = -iwork[k];
goto L100;
}
} else if (iwork[k] != k) {
k = iwork[k];
goto L100;
}
}
/* Check error code from ZHPTRF. */
if (info != k) {
alaerh_(path, "ZHPTRF", &info, &k, uplo, &n, &n, &c_n1, &
c_n1, &c_n1, &imat, &nfail, &nerrs, nout);
}
if (info != 0) {
trfcon = TRUE_;
} else {
trfcon = FALSE_;
}
/* + TEST 1 */
/* Reconstruct matrix from factors and compute residual. */
zhpt01_(uplo, &n, &a[1], &afac[1], &iwork[1], &ainv[1], &lda,
&rwork[1], result);
nt = 1;
/* + TEST 2 */
/* Form the inverse and compute the residual. */
if (! trfcon) {
zcopy_(&npp, &afac[1], &c__1, &ainv[1], &c__1);
s_copy(srnamc_1.srnamt, "ZHPTRI", (ftnlen)6, (ftnlen)6);
zhptri_(uplo, &n, &ainv[1], &iwork[1], &work[1], &info);
/* Check error code from ZHPTRI. */
if (info != 0) {
alaerh_(path, "ZHPTRI", &info, &c__0, uplo, &n, &n, &
c_n1, &c_n1, &c_n1, &imat, &nfail, &nerrs,
nout);
}
zppt03_(uplo, &n, &a[1], &ainv[1], &work[1], &lda, &rwork[
1], &rcondc, &result[1]);
nt = 2;
}
/* Print information about the tests that did not pass */
/* the threshold. */
i__3 = nt;
for (k = 1; k <= i__3; ++k) {
if (result[k - 1] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
alahd_(nout, path);
}
io___38.ciunit = *nout;
s_wsfe(&io___38);
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(
doublereal));
e_wsfe();
++nfail;
}
/* L110: */
}
nrun += nt;
/* Do only the condition estimate if INFO is not 0. */
if (trfcon) {
rcondc = 0.;
goto L140;
}
i__3 = *nns;
for (irhs = 1; irhs <= i__3; ++irhs) {
nrhs = nsval[irhs];
/* + TEST 3 */
/* Solve and compute residual for A * X = B. */
s_copy(srnamc_1.srnamt, "ZLARHS", (ftnlen)6, (ftnlen)6);
zlarhs_(path, xtype, uplo, " ", &n, &n, &kl, &ku, &nrhs, &
a[1], &lda, &xact[1], &lda, &b[1], &lda, iseed, &
info);
*(unsigned char *)xtype = 'C';
zlacpy_("Full", &n, &nrhs, &b[1], &lda, &x[1], &lda);
s_copy(srnamc_1.srnamt, "ZHPTRS", (ftnlen)6, (ftnlen)6);
zhptrs_(uplo, &n, &nrhs, &afac[1], &iwork[1], &x[1], &lda,
&info);
/* Check error code from ZHPTRS. */
if (info != 0) {
alaerh_(path, "ZHPTRS", &info, &c__0, uplo, &n, &n, &
c_n1, &c_n1, &nrhs, &imat, &nfail, &nerrs,
nout);
}
zlacpy_("Full", &n, &nrhs, &b[1], &lda, &work[1], &lda);
zppt02_(uplo, &n, &nrhs, &a[1], &x[1], &lda, &work[1], &
lda, &rwork[1], &result[2]);
/* + TEST 4 */
/* Check solution from generated exact solution. */
zget04_(&n, &nrhs, &x[1], &lda, &xact[1], &lda, &rcondc, &
result[3]);
/* + TESTS 5, 6, and 7 */
/* Use iterative refinement to improve the solution. */
s_copy(srnamc_1.srnamt, "ZHPRFS", (ftnlen)6, (ftnlen)6);
zhprfs_(uplo, &n, &nrhs, &a[1], &afac[1], &iwork[1], &b[1]
, &lda, &x[1], &lda, &rwork[1], &rwork[nrhs + 1],
&work[1], &rwork[(nrhs << 1) + 1], &info);
/* Check error code from ZHPRFS. */
if (info != 0) {
alaerh_(path, "ZHPRFS", &info, &c__0, uplo, &n, &n, &
c_n1, &c_n1, &nrhs, &imat, &nfail, &nerrs,
nout);
}
zget04_(&n, &nrhs, &x[1], &lda, &xact[1], &lda, &rcondc, &
result[4]);
zppt05_(uplo, &n, &nrhs, &a[1], &b[1], &lda, &x[1], &lda,
&xact[1], &lda, &rwork[1], &rwork[nrhs + 1], &
result[5]);
/* Print information about the tests that did not pass */
/* the threshold. */
for (k = 3; k <= 7; ++k) {
if (result[k - 1] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
alahd_(nout, path);
}
io___41.ciunit = *nout;
s_wsfe(&io___41);
do_fio(&c__1, uplo, (ftnlen)1);
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer))
;
do_fio(&c__1, (char *)&nrhs, (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(doublereal));
e_wsfe();
++nfail;
}
/* L120: */
}
nrun += 5;
/* L130: */
}
/* + TEST 8 */
/* Get an estimate of RCOND = 1/CNDNUM. */
L140:
anorm = zlanhp_("1", uplo, &n, &a[1], &rwork[1]);
s_copy(srnamc_1.srnamt, "ZHPCON", (ftnlen)6, (ftnlen)6);
zhpcon_(uplo, &n, &afac[1], &iwork[1], &anorm, &rcond, &work[
1], &info);
/* Check error code from ZHPCON. */
if (info != 0) {
alaerh_(path, "ZHPCON", &info, &c__0, uplo, &n, &n, &c_n1,
&c_n1, &c_n1, &imat, &nfail, &nerrs, nout);
}
result[7] = dget06_(&rcond, &rcondc);
/* Print the test ratio if it is .GE. THRESH. */
if (result[7] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
alahd_(nout, path);
}
io___43.ciunit = *nout;
s_wsfe(&io___43);
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 *)&c__8, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&result[7], (ftnlen)sizeof(
doublereal));
e_wsfe();
++nfail;
}
++nrun;
L150:
;
}
L160:
;
}
/* L170: */
}
/* Print a summary of the results. */
alasum_(path, nout, &nfail, &nrun, &nerrs);
return 0;
/* End of ZCHKHP */
} /* zchkhp_ */
int main(void)
{
/* Local scalars */
char uplo, uplo_i;
lapack_int n, n_i;
lapack_int nrhs, nrhs_i;
lapack_int ldb, ldb_i;
lapack_int ldb_r;
lapack_int ldx, ldx_i;
lapack_int ldx_r;
lapack_int info, info_i;
lapack_int i;
int failed;
/* Local arrays */
lapack_complex_double *ap = NULL, *ap_i = NULL;
lapack_complex_double *afp = NULL, *afp_i = NULL;
lapack_int *ipiv = NULL, *ipiv_i = NULL;
lapack_complex_double *b = NULL, *b_i = NULL;
lapack_complex_double *x = NULL, *x_i = NULL;
double *ferr = NULL, *ferr_i = NULL;
double *berr = NULL, *berr_i = NULL;
lapack_complex_double *work = NULL, *work_i = NULL;
double *rwork = NULL, *rwork_i = NULL;
lapack_complex_double *x_save = NULL;
double *ferr_save = NULL;
double *berr_save = NULL;
lapack_complex_double *ap_r = NULL;
lapack_complex_double *afp_r = NULL;
lapack_complex_double *b_r = NULL;
lapack_complex_double *x_r = NULL;
/* Iniitialize the scalar parameters */
init_scalars_zhprfs( &uplo, &n, &nrhs, &ldb, &ldx );
ldb_r = nrhs+2;
ldx_r = nrhs+2;
uplo_i = uplo;
n_i = n;
nrhs_i = nrhs;
ldb_i = ldb;
ldx_i = ldx;
/* Allocate memory for the LAPACK routine arrays */
ap = (lapack_complex_double *)
LAPACKE_malloc( ((n*(n+1)/2)) * sizeof(lapack_complex_double) );
afp = (lapack_complex_double *)
LAPACKE_malloc( ((n*(n+1)/2)) * sizeof(lapack_complex_double) );
ipiv = (lapack_int *)LAPACKE_malloc( n * sizeof(lapack_int) );
b = (lapack_complex_double *)
LAPACKE_malloc( ldb*nrhs * sizeof(lapack_complex_double) );
x = (lapack_complex_double *)
LAPACKE_malloc( ldx*nrhs * sizeof(lapack_complex_double) );
ferr = (double *)LAPACKE_malloc( nrhs * sizeof(double) );
berr = (double *)LAPACKE_malloc( nrhs * sizeof(double) );
work = (lapack_complex_double *)
LAPACKE_malloc( 2*n * sizeof(lapack_complex_double) );
rwork = (double *)LAPACKE_malloc( n * sizeof(double) );
/* Allocate memory for the C interface function arrays */
ap_i = (lapack_complex_double *)
LAPACKE_malloc( ((n*(n+1)/2)) * sizeof(lapack_complex_double) );
afp_i = (lapack_complex_double *)
LAPACKE_malloc( ((n*(n+1)/2)) * sizeof(lapack_complex_double) );
ipiv_i = (lapack_int *)LAPACKE_malloc( n * sizeof(lapack_int) );
b_i = (lapack_complex_double *)
LAPACKE_malloc( ldb*nrhs * sizeof(lapack_complex_double) );
x_i = (lapack_complex_double *)
LAPACKE_malloc( ldx*nrhs * sizeof(lapack_complex_double) );
ferr_i = (double *)LAPACKE_malloc( nrhs * sizeof(double) );
berr_i = (double *)LAPACKE_malloc( nrhs * sizeof(double) );
work_i = (lapack_complex_double *)
LAPACKE_malloc( 2*n * sizeof(lapack_complex_double) );
rwork_i = (double *)LAPACKE_malloc( n * sizeof(double) );
/* Allocate memory for the backup arrays */
x_save = (lapack_complex_double *)
LAPACKE_malloc( ldx*nrhs * sizeof(lapack_complex_double) );
ferr_save = (double *)LAPACKE_malloc( nrhs * sizeof(double) );
berr_save = (double *)LAPACKE_malloc( nrhs * sizeof(double) );
/* Allocate memory for the row-major arrays */
ap_r = (lapack_complex_double *)
LAPACKE_malloc( n*(n+1)/2 * sizeof(lapack_complex_double) );
afp_r = (lapack_complex_double *)
LAPACKE_malloc( n*(n+1)/2 * sizeof(lapack_complex_double) );
b_r = (lapack_complex_double *)
LAPACKE_malloc( n*(nrhs+2) * sizeof(lapack_complex_double) );
x_r = (lapack_complex_double *)
LAPACKE_malloc( n*(nrhs+2) * sizeof(lapack_complex_double) );
/* Initialize input arrays */
init_ap( (n*(n+1)/2), ap );
init_afp( (n*(n+1)/2), afp );
init_ipiv( n, ipiv );
init_b( ldb*nrhs, b );
init_x( ldx*nrhs, x );
init_ferr( nrhs, ferr );
init_berr( nrhs, berr );
init_work( 2*n, work );
init_rwork( n, rwork );
/* Backup the ouptut arrays */
for( i = 0; i < ldx*nrhs; i++ ) {
x_save[i] = x[i];
}
for( i = 0; i < nrhs; i++ ) {
ferr_save[i] = ferr[i];
}
for( i = 0; i < nrhs; i++ ) {
berr_save[i] = berr[i];
}
/* Call the LAPACK routine */
zhprfs_( &uplo, &n, &nrhs, ap, afp, ipiv, b, &ldb, x, &ldx, ferr, berr,
work, rwork, &info );
/* Initialize input data, call the column-major middle-level
* interface to LAPACK routine and check the results */
for( i = 0; i < (n*(n+1)/2); i++ ) {
ap_i[i] = ap[i];
}
for( i = 0; i < (n*(n+1)/2); i++ ) {
afp_i[i] = afp[i];
}
for( i = 0; i < n; i++ ) {
ipiv_i[i] = ipiv[i];
}
for( i = 0; i < ldb*nrhs; i++ ) {
b_i[i] = b[i];
}
for( i = 0; i < ldx*nrhs; i++ ) {
x_i[i] = x_save[i];
}
for( i = 0; i < nrhs; i++ ) {
ferr_i[i] = ferr_save[i];
}
for( i = 0; i < nrhs; i++ ) {
berr_i[i] = berr_save[i];
}
for( i = 0; i < 2*n; i++ ) {
work_i[i] = work[i];
}
for( i = 0; i < n; i++ ) {
rwork_i[i] = rwork[i];
}
info_i = LAPACKE_zhprfs_work( LAPACK_COL_MAJOR, uplo_i, n_i, nrhs_i, ap_i,
afp_i, ipiv_i, b_i, ldb_i, x_i, ldx_i, ferr_i,
berr_i, work_i, rwork_i );
failed = compare_zhprfs( x, x_i, ferr, ferr_i, berr, berr_i, info, info_i,
ldx, nrhs );
if( failed == 0 ) {
printf( "PASSED: column-major middle-level interface to zhprfs\n" );
} else {
printf( "FAILED: column-major middle-level interface to zhprfs\n" );
}
/* Initialize input data, call the column-major high-level
* interface to LAPACK routine and check the results */
for( i = 0; i < (n*(n+1)/2); i++ ) {
ap_i[i] = ap[i];
}
for( i = 0; i < (n*(n+1)/2); i++ ) {
afp_i[i] = afp[i];
}
for( i = 0; i < n; i++ ) {
ipiv_i[i] = ipiv[i];
}
for( i = 0; i < ldb*nrhs; i++ ) {
b_i[i] = b[i];
}
for( i = 0; i < ldx*nrhs; i++ ) {
x_i[i] = x_save[i];
}
for( i = 0; i < nrhs; i++ ) {
ferr_i[i] = ferr_save[i];
}
for( i = 0; i < nrhs; i++ ) {
berr_i[i] = berr_save[i];
}
for( i = 0; i < 2*n; i++ ) {
work_i[i] = work[i];
}
for( i = 0; i < n; i++ ) {
rwork_i[i] = rwork[i];
}
info_i = LAPACKE_zhprfs( LAPACK_COL_MAJOR, uplo_i, n_i, nrhs_i, ap_i, afp_i,
ipiv_i, b_i, ldb_i, x_i, ldx_i, ferr_i, berr_i );
failed = compare_zhprfs( x, x_i, ferr, ferr_i, berr, berr_i, info, info_i,
ldx, nrhs );
if( failed == 0 ) {
printf( "PASSED: column-major high-level interface to zhprfs\n" );
} else {
printf( "FAILED: column-major high-level interface to zhprfs\n" );
}
/* Initialize input data, call the row-major middle-level
* interface to LAPACK routine and check the results */
for( i = 0; i < (n*(n+1)/2); i++ ) {
ap_i[i] = ap[i];
}
for( i = 0; i < (n*(n+1)/2); i++ ) {
afp_i[i] = afp[i];
}
for( i = 0; i < n; i++ ) {
ipiv_i[i] = ipiv[i];
}
for( i = 0; i < ldb*nrhs; i++ ) {
b_i[i] = b[i];
}
for( i = 0; i < ldx*nrhs; i++ ) {
x_i[i] = x_save[i];
}
for( i = 0; i < nrhs; i++ ) {
ferr_i[i] = ferr_save[i];
}
for( i = 0; i < nrhs; i++ ) {
berr_i[i] = berr_save[i];
}
for( i = 0; i < 2*n; i++ ) {
work_i[i] = work[i];
}
for( i = 0; i < n; i++ ) {
rwork_i[i] = rwork[i];
}
LAPACKE_zpp_trans( LAPACK_COL_MAJOR, uplo, n, ap_i, ap_r );
LAPACKE_zpp_trans( LAPACK_COL_MAJOR, uplo, n, afp_i, afp_r );
LAPACKE_zge_trans( LAPACK_COL_MAJOR, n, nrhs, b_i, ldb, b_r, nrhs+2 );
LAPACKE_zge_trans( LAPACK_COL_MAJOR, n, nrhs, x_i, ldx, x_r, nrhs+2 );
info_i = LAPACKE_zhprfs_work( LAPACK_ROW_MAJOR, uplo_i, n_i, nrhs_i, ap_r,
afp_r, ipiv_i, b_r, ldb_r, x_r, ldx_r, ferr_i,
berr_i, work_i, rwork_i );
LAPACKE_zge_trans( LAPACK_ROW_MAJOR, n, nrhs, x_r, nrhs+2, x_i, ldx );
failed = compare_zhprfs( x, x_i, ferr, ferr_i, berr, berr_i, info, info_i,
ldx, nrhs );
if( failed == 0 ) {
printf( "PASSED: row-major middle-level interface to zhprfs\n" );
} else {
printf( "FAILED: row-major middle-level interface to zhprfs\n" );
}
/* Initialize input data, call the row-major high-level
* interface to LAPACK routine and check the results */
for( i = 0; i < (n*(n+1)/2); i++ ) {
ap_i[i] = ap[i];
}
for( i = 0; i < (n*(n+1)/2); i++ ) {
afp_i[i] = afp[i];
}
for( i = 0; i < n; i++ ) {
ipiv_i[i] = ipiv[i];
}
for( i = 0; i < ldb*nrhs; i++ ) {
b_i[i] = b[i];
}
for( i = 0; i < ldx*nrhs; i++ ) {
x_i[i] = x_save[i];
}
for( i = 0; i < nrhs; i++ ) {
ferr_i[i] = ferr_save[i];
}
for( i = 0; i < nrhs; i++ ) {
berr_i[i] = berr_save[i];
}
for( i = 0; i < 2*n; i++ ) {
work_i[i] = work[i];
}
for( i = 0; i < n; i++ ) {
rwork_i[i] = rwork[i];
}
/* Init row_major arrays */
LAPACKE_zpp_trans( LAPACK_COL_MAJOR, uplo, n, ap_i, ap_r );
LAPACKE_zpp_trans( LAPACK_COL_MAJOR, uplo, n, afp_i, afp_r );
LAPACKE_zge_trans( LAPACK_COL_MAJOR, n, nrhs, b_i, ldb, b_r, nrhs+2 );
LAPACKE_zge_trans( LAPACK_COL_MAJOR, n, nrhs, x_i, ldx, x_r, nrhs+2 );
info_i = LAPACKE_zhprfs( LAPACK_ROW_MAJOR, uplo_i, n_i, nrhs_i, ap_r, afp_r,
ipiv_i, b_r, ldb_r, x_r, ldx_r, ferr_i, berr_i );
LAPACKE_zge_trans( LAPACK_ROW_MAJOR, n, nrhs, x_r, nrhs+2, x_i, ldx );
failed = compare_zhprfs( x, x_i, ferr, ferr_i, berr, berr_i, info, info_i,
ldx, nrhs );
if( failed == 0 ) {
printf( "PASSED: row-major high-level interface to zhprfs\n" );
} else {
printf( "FAILED: row-major high-level interface to zhprfs\n" );
}
/* Release memory */
if( ap != NULL ) {
LAPACKE_free( ap );
}
if( ap_i != NULL ) {
LAPACKE_free( ap_i );
}
if( ap_r != NULL ) {
LAPACKE_free( ap_r );
}
if( afp != NULL ) {
LAPACKE_free( afp );
}
if( afp_i != NULL ) {
LAPACKE_free( afp_i );
}
if( afp_r != NULL ) {
LAPACKE_free( afp_r );
}
if( ipiv != NULL ) {
LAPACKE_free( ipiv );
}
if( ipiv_i != NULL ) {
LAPACKE_free( ipiv_i );
}
if( b != NULL ) {
LAPACKE_free( b );
}
if( b_i != NULL ) {
LAPACKE_free( b_i );
}
if( b_r != NULL ) {
LAPACKE_free( b_r );
}
if( x != NULL ) {
LAPACKE_free( x );
}
if( x_i != NULL ) {
LAPACKE_free( x_i );
}
if( x_r != NULL ) {
LAPACKE_free( x_r );
}
if( x_save != NULL ) {
LAPACKE_free( x_save );
}
if( ferr != NULL ) {
LAPACKE_free( ferr );
}
if( ferr_i != NULL ) {
LAPACKE_free( ferr_i );
}
if( ferr_save != NULL ) {
LAPACKE_free( ferr_save );
}
if( berr != NULL ) {
LAPACKE_free( berr );
}
if( berr_i != NULL ) {
LAPACKE_free( berr_i );
}
if( berr_save != NULL ) {
LAPACKE_free( berr_save );
}
if( work != NULL ) {
LAPACKE_free( work );
}
if( work_i != NULL ) {
LAPACKE_free( work_i );
}
if( rwork != NULL ) {
LAPACKE_free( rwork );
}
if( rwork_i != NULL ) {
LAPACKE_free( rwork_i );
}
return 0;
}