/* Subroutine */ int zpptri_(char *uplo, integer *n, doublecomplex *ap,
integer *info, ftnlen uplo_len)
{
/* System generated locals */
integer i__1, i__2, i__3;
doublereal d__1;
doublecomplex z__1;
/* Local variables */
static integer j, jc, jj;
static doublereal ajj;
static integer jjn;
extern /* Subroutine */ int zhpr_(char *, integer *, doublereal *,
doublecomplex *, integer *, doublecomplex *, ftnlen);
extern logical lsame_(char *, char *, ftnlen, ftnlen);
extern /* Double Complex */ VOID zdotc_(doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *);
static logical upper;
extern /* Subroutine */ int ztpmv_(char *, char *, char *, integer *,
doublecomplex *, doublecomplex *, integer *, ftnlen, ftnlen,
ftnlen), xerbla_(char *, integer *, ftnlen), zdscal_(integer *,
doublereal *, doublecomplex *, integer *), ztptri_(char *, char *,
integer *, doublecomplex *, integer *, ftnlen, ftnlen);
/* -- LAPACK routine (version 3.0) -- */
/* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
/* Courant Institute, Argonne National Lab, and Rice University */
/* March 31, 1993 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZPPTRI computes the inverse of a complex Hermitian positive definite */
/* matrix A using the Cholesky factorization A = U**H*U or A = L*L**H */
/* computed by ZPPTRF. */
/* Arguments */
/* ========= */
/* UPLO (input) CHARACTER*1 */
/* = 'U': Upper triangular factor is stored in AP; */
/* = 'L': Lower triangular factor is stored in AP. */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* AP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2) */
/* On entry, the triangular factor U or L from the Cholesky */
/* factorization A = U**H*U or A = L*L**H, packed columnwise as */
/* a linear array. The j-th column of U or L is stored in the */
/* array AP as follows: */
/* if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j; */
/* if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n. */
/* On exit, the upper or lower triangle of the (Hermitian) */
/* inverse of A, overwriting the input factor U or L. */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* > 0: if INFO = i, the (i,i) element of the factor U or L is */
/* zero, and the inverse could not be computed. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
--ap;
/* Function Body */
*info = 0;
upper = lsame_(uplo, "U", (ftnlen)1, (ftnlen)1);
if (! upper && ! lsame_(uplo, "L", (ftnlen)1, (ftnlen)1)) {
*info = -1;
} else if (*n < 0) {
*info = -2;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZPPTRI", &i__1, (ftnlen)6);
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/* Invert the triangular Cholesky factor U or L. */
ztptri_(uplo, "Non-unit", n, &ap[1], info, (ftnlen)1, (ftnlen)8);
if (*info > 0) {
return 0;
}
if (upper) {
/* Compute the product inv(U) * inv(U)'. */
jj = 0;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
jc = jj + 1;
jj += j;
if (j > 1) {
i__2 = j - 1;
zhpr_("Upper", &i__2, &c_b8, &ap[jc], &c__1, &ap[1], (ftnlen)
5);
}
i__2 = jj;
ajj = ap[i__2].r;
zdscal_(&j, &ajj, &ap[jc], &c__1);
/* L10: */
}
} else {
/* Compute the product inv(L)' * inv(L). */
jj = 1;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
jjn = jj + *n - j + 1;
i__2 = jj;
i__3 = *n - j + 1;
zdotc_(&z__1, &i__3, &ap[jj], &c__1, &ap[jj], &c__1);
d__1 = z__1.r;
ap[i__2].r = d__1, ap[i__2].i = 0.;
if (j < *n) {
i__2 = *n - j;
ztpmv_("Lower", "Conjugate transpose", "Non-unit", &i__2, &ap[
jjn], &ap[jj + 1], &c__1, (ftnlen)5, (ftnlen)19, (
ftnlen)8);
}
jj = jjn;
/* L20: */
}
}
return 0;
/* End of ZPPTRI */
} /* zpptri_ */
/* Subroutine */ int ztimtp_(char *line, integer *nn, integer *nval, integer *
nns, integer *nsval, integer *la, doublereal *timmin, doublecomplex *
a, doublecomplex *b, doublereal *reslts, integer *ldr1, integer *ldr2,
integer *ldr3, integer *nout, ftnlen line_len)
{
/* Initialized data */
static char subnam[6*2] = "ZTPTRI" "ZTPTRS";
static char uplos[1*2] = "U" "L";
/* Format strings */
static char fmt_9999[] = "(1x,a6,\002 timing run not attempted\002,/)";
static char fmt_9998[] = "(/\002 *** Speed of \002,a6,\002 in megaflops "
"***\002,/)";
static char fmt_9997[] = "(5x,a6,\002 with UPLO = '\002,a1,\002'\002,/)";
/* System generated locals */
integer reslts_dim1, reslts_dim2, reslts_dim3, reslts_offset, i__1, i__2;
/* Builtin functions
Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void);
/* Local variables */
static integer info;
static char path[3];
static doublereal time;
static integer isub, nrhs;
static char uplo[1];
static integer i__, n;
static char cname[6];
static integer laval[1];
extern doublereal dopla_(char *, integer *, integer *, integer *, integer
*, integer *);
extern logical lsame_(char *, char *);
static integer iuplo;
static doublereal s1, s2;
static integer ic, in;
extern doublereal dsecnd_(void);
extern /* Subroutine */ int atimck_(integer *, char *, integer *, integer
*, integer *, integer *, integer *, integer *, ftnlen);
extern doublereal dmflop_(doublereal *, doublereal *, integer *);
extern /* Subroutine */ int atimin_(char *, char *, integer *, char *,
logical *, integer *, integer *, ftnlen, ftnlen, ftnlen), dprtbl_(
char *, char *, integer *, integer *, integer *, integer *,
integer *, doublereal *, integer *, integer *, integer *, ftnlen,
ftnlen);
static doublereal untime;
static logical timsub[2];
static integer idummy[1];
extern /* Subroutine */ int ztimmg_(integer *, integer *, integer *,
doublecomplex *, integer *, integer *, integer *), ztptri_(char *,
char *, integer *, doublecomplex *, integer *),
ztptrs_(char *, char *, char *, integer *, integer *,
doublecomplex *, doublecomplex *, integer *, integer *);
static integer lda, ldb, icl, mat;
static doublereal ops;
/* Fortran I/O blocks */
static cilist io___8 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___26 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___27 = { 0, 0, 0, fmt_9997, 0 };
#define subnam_ref(a_0,a_1) &subnam[(a_1)*6 + a_0 - 6]
#define reslts_ref(a_1,a_2,a_3,a_4) reslts[(((a_4)*reslts_dim3 + (a_3))*\
reslts_dim2 + (a_2))*reslts_dim1 + a_1]
/* -- LAPACK timing 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
=======
ZTIMTP times ZTPTRI and -TRS.
Arguments
=========
LINE (input) CHARACTER*80
The input line that requested this routine. The first six
characters contain either the name of a subroutine or a
generic path name. The remaining characters may be used to
specify the individual routines to be timed. See ATIMIN for
a full description of the format of the input line.
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 size 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.
LA (input) INTEGER
The size of the arrays A and B.
TIMMIN (input) DOUBLE PRECISION
The minimum time a subroutine will be timed.
A (workspace) COMPLEX*16 array, dimension (LA)
B (workspace) COMPLEX*16 array, dimension (NMAX*NMAX)
where NMAX is the maximum value of N in NVAL.
RESLTS (output) DOUBLE PRECISION array, dimension
(LDR1,LDR2,LDR3,NSUBS)
The timing results for each subroutine over the relevant
values of N.
LDR1 (input) INTEGER
The first dimension of RESLTS. LDR1 >= 1.
LDR2 (input) INTEGER
The second dimension of RESLTS. LDR2 >= max(1,NN).
LDR3 (input) INTEGER
The third dimension of RESLTS. LDR3 >= 2.
NOUT (input) INTEGER
The unit number for output.
=====================================================================
Parameter adjustments */
--nval;
--nsval;
--a;
--b;
reslts_dim1 = *ldr1;
reslts_dim2 = *ldr2;
reslts_dim3 = *ldr3;
reslts_offset = 1 + reslts_dim1 * (1 + reslts_dim2 * (1 + reslts_dim3 * 1)
);
reslts -= reslts_offset;
/* Function Body
Extract the timing request from the input line. */
s_copy(path, "Zomplex precision", (ftnlen)1, (ftnlen)17);
s_copy(path + 1, "TP", (ftnlen)2, (ftnlen)2);
atimin_(path, line, &c__2, subnam, timsub, nout, &info, (ftnlen)3, (
ftnlen)80, (ftnlen)6);
if (info != 0) {
goto L100;
}
/* Check that N*(N+1)/2 <= LA for the input values. */
s_copy(cname, line, (ftnlen)6, (ftnlen)6);
laval[0] = *la;
atimck_(&c__4, cname, nn, &nval[1], &c__1, laval, nout, &info, (ftnlen)6);
if (info > 0) {
io___8.ciunit = *nout;
s_wsfe(&io___8);
do_fio(&c__1, cname, (ftnlen)6);
e_wsfe();
goto L100;
}
/* 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")) {
mat = 12;
} else {
mat = -12;
}
/* Do for each value of N: */
i__1 = *nn;
for (in = 1; in <= i__1; ++in) {
n = nval[in];
lda = n * (n + 1) / 2;
ldb = n;
if (n % 2 == 0) {
++ldb;
}
/* Time ZTPTRI */
if (timsub[0]) {
ztimmg_(&mat, &n, &n, &a[1], &lda, &c__0, &c__0);
ic = 0;
s1 = dsecnd_();
L10:
ztptri_(uplo, "Non-unit", &n, &a[1], &info);
s2 = dsecnd_();
time = s2 - s1;
++ic;
if (time < *timmin) {
ztimmg_(&mat, &n, &n, &a[1], &lda, &c__0, &c__0);
goto L10;
}
/* Subtract the time used in ZTIMMG. */
icl = 1;
s1 = dsecnd_();
L20:
s2 = dsecnd_();
untime = s2 - s1;
++icl;
if (icl <= ic) {
ztimmg_(&mat, &n, &n, &a[1], &lda, &c__0, &c__0);
goto L20;
}
time = (time - untime) / (doublereal) ic;
ops = dopla_("ZTPTRI", &n, &n, &c__0, &c__0, &c__0)
;
reslts_ref(1, in, iuplo, 1) = dmflop_(&ops, &time, &info);
} else {
/* Generate a triangular matrix A. */
ztimmg_(&mat, &n, &n, &a[1], &lda, &c__0, &c__0);
}
/* Time ZTPTRS */
if (timsub[1]) {
i__2 = *nns;
for (i__ = 1; i__ <= i__2; ++i__) {
nrhs = nsval[i__];
ztimmg_(&c__0, &n, &nrhs, &b[1], &ldb, &c__0, &c__0);
ic = 0;
s1 = dsecnd_();
L30:
ztptrs_(uplo, "No transpose", "Non-unit", &n, &nrhs, &a[1]
, &b[1], &ldb, &info);
s2 = dsecnd_();
time = s2 - s1;
++ic;
if (time < *timmin) {
ztimmg_(&c__0, &n, &nrhs, &b[1], &ldb, &c__0, &c__0);
goto L30;
}
/* Subtract the time used in ZTIMMG. */
icl = 1;
s1 = dsecnd_();
L40:
s2 = dsecnd_();
untime = s2 - s1;
++icl;
if (icl <= ic) {
ztimmg_(&c__0, &n, &nrhs, &b[1], &ldb, &c__0, &c__0);
goto L40;
}
time = (time - untime) / (doublereal) ic;
ops = dopla_("ZTPTRS", &n, &nrhs, &c__0, &c__0, &c__0);
reslts_ref(i__, in, iuplo, 2) = dmflop_(&ops, &time, &
info);
/* L50: */
}
}
/* L60: */
}
/* L70: */
}
/* Print a table of results. */
for (isub = 1; isub <= 2; ++isub) {
if (! timsub[isub - 1]) {
goto L90;
}
io___26.ciunit = *nout;
s_wsfe(&io___26);
do_fio(&c__1, subnam_ref(0, isub), (ftnlen)6);
e_wsfe();
for (iuplo = 1; iuplo <= 2; ++iuplo) {
io___27.ciunit = *nout;
s_wsfe(&io___27);
do_fio(&c__1, subnam_ref(0, isub), (ftnlen)6);
do_fio(&c__1, uplos + (iuplo - 1), (ftnlen)1);
e_wsfe();
if (isub == 1) {
dprtbl_(" ", "N", &c__1, idummy, nn, &nval[1], &c__1, &
reslts_ref(1, 1, iuplo, 1), ldr1, ldr2, nout, (ftnlen)
1, (ftnlen)1);
} else if (isub == 2) {
dprtbl_("NRHS", "N", nns, &nsval[1], nn, &nval[1], &c__1, &
reslts_ref(1, 1, iuplo, 2), ldr1, ldr2, nout, (ftnlen)
4, (ftnlen)1);
}
/* L80: */
}
L90:
;
}
L100:
return 0;
/* End of ZTIMTP */
} /* ztimtp_ */
