/* Subroutine */ int zpotri_(char *uplo, integer *n, doublecomplex *a,
integer *lda, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1;
/* Local variables */
/* -- LAPACK routine (version 3.2) -- */
/* November 2006 */
/* Purpose */
/* ======= */
/* ZPOTRI 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 ZPOTRF. */
/* Arguments */
/* ========= */
/* UPLO (input) CHARACTER*1 */
/* = 'U': Upper triangle of A is stored; */
/* = 'L': Lower triangle of A is stored. */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* A (input/output) COMPLEX*16 array, dimension (LDA,N) */
/* On entry, the triangular factor U or L from the Cholesky */
/* factorization A = U**H*U or A = L*L**H, as computed by */
/* ZPOTRF. */
/* On exit, the upper or lower triangle of the (Hermitian) */
/* inverse of A, overwriting the input factor U or L. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= 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, the (i,i) element of the factor U or L is */
/* zero, and the inverse could not be computed. */
/* ===================================================================== */
/* Test the input parameters. */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
/* Function Body */
*info = 0;
if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*lda < max(1,*n)) {
*info = -4;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZPOTRI", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/* Invert the triangular Cholesky factor U or L. */
ztrtri_(uplo, "Non-unit", n, &a[a_offset], lda, info);
if (*info > 0) {
return 0;
}
/* Form inv(U)*inv(U)' or inv(L)'*inv(L). */
zlauum_(uplo, n, &a[a_offset], lda, info);
return 0;
/* End of ZPOTRI */
} /* zpotri_ */
/* Subroutine */ int zpotri_(char *uplo, integer *n, doublecomplex *a,
integer *lda, integer *info)
{
/* -- 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
Purpose
=======
ZPOTRI 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 ZPOTRF.
Arguments
=========
UPLO (input) CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) INTEGER
The order of the matrix A. N >= 0.
A (input/output) COMPLEX*16 array, dimension (LDA,N)
On entry, the triangular factor U or L from the Cholesky
factorization A = U**H*U or A = L*L**H, as computed by
ZPOTRF.
On exit, the upper or lower triangle of the (Hermitian)
inverse of A, overwriting the input factor U or L.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= 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, the (i,i) element of the factor U or L is
zero, and the inverse could not be computed.
=====================================================================
Test the input parameters.
Parameter adjustments */
/* System generated locals */
integer a_dim1, a_offset, i__1;
/* Local variables */
extern logical lsame_(char *, char *);
extern /* Subroutine */ int xerbla_(char *, integer *), zlauum_(
char *, integer *, doublecomplex *, integer *, integer *),
ztrtri_(char *, char *, integer *, doublecomplex *, integer *,
integer *);
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
/* Function Body */
*info = 0;
if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*lda < max(1,*n)) {
*info = -4;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZPOTRI", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/* Invert the triangular Cholesky factor U or L. */
ztrtri_(uplo, "Non-unit", n, &a[a_offset], lda, info);
if (*info > 0) {
return 0;
}
/* Form inv(U)*inv(U)' or inv(L)'*inv(L). */
zlauum_(uplo, n, &a[a_offset], lda, info);
return 0;
/* End of ZPOTRI */
} /* zpotri_ */
/* Subroutine */ int zchktr_(logical *dotype, integer *nn, integer *nval,
integer *nnb, integer *nbval, integer *nns, integer *nsval,
doublereal *thresh, logical *tsterr, integer *nmax, doublecomplex *a,
doublecomplex *ainv, doublecomplex *b, doublecomplex *x,
doublecomplex *xact, doublecomplex *work, doublereal *rwork, integer *
nout)
{
/* Initialized data */
static integer iseedy[4] = { 1988,1989,1990,1991 };
static char uplos[1*2] = "U" "L";
static char transs[1*3] = "N" "T" "C";
/* Format strings */
static char fmt_9999[] = "(\002 UPLO='\002,a1,\002', DIAG='\002,a1,\002'"
", N=\002,i5,\002, NB=\002,i4,\002, type \002,i2,\002, test(\002,"
"i2,\002)= \002,g12.5)";
static char fmt_9998[] = "(\002 UPLO='\002,a1,\002', TRANS='\002,a1,\002"
"', DIAG='\002,a1,\002', N=\002,i5,\002, NB=\002,i4,\002, type"
" \002,i2,\002, test(\002,i2,\002)= \002,g12"
".5)";
static char fmt_9997[] = "(\002 NORM='\002,a1,\002', UPLO ='\002,a1,\002"
"', N=\002,i5,\002,\002,11x,\002 type \002,i2,\002, test(\002,i2"
",\002)=\002,g12.5)";
static char fmt_9996[] = "(1x,a,\002( '\002,a1,\002', '\002,a1,\002', "
"'\002,a1,\002', '\002,a1,\002',\002,i5,\002, ... ), type \002,i2,"
"\002, test(\002,i2,\002)=\002,g12.5)";
/* System generated locals */
address a__1[2], a__2[3], a__3[4];
integer i__1, i__2, i__3[2], i__4, i__5[3], i__6[4];
char ch__1[2], ch__2[3], ch__3[4];
/* Builtin functions */
/* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen), s_cat(char *,
char **, integer *, integer *, ftnlen);
integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void);
/* Local variables */
integer i__, k, n, nb, in, lda, inb;
char diag[1];
integer imat, info;
char path[3];
integer irhs, nrhs;
char norm[1], uplo[1];
integer nrun;
extern /* Subroutine */ int alahd_(integer *, char *);
integer idiag;
doublereal scale;
integer nfail, iseed[4];
extern logical lsame_(char *, char *);
doublereal rcond, anorm;
integer itran;
extern /* Subroutine */ int zget04_(integer *, integer *, doublecomplex *,
integer *, doublecomplex *, integer *, doublereal *, doublereal *
);
char trans[1];
integer iuplo, nerrs;
doublereal dummy;
extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *,
doublecomplex *, integer *), ztrt01_(char *, char *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublereal *, doublereal *, doublereal *),
ztrt02_(char *, char *, char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, doublereal *,
doublereal *), ztrt03_(char *, char *,
char *, integer *, integer *, doublecomplex *, integer *,
doublereal *, doublereal *, doublereal *, doublecomplex *,
integer *, doublecomplex *, integer *, doublecomplex *,
doublereal *);
char xtype[1];
extern /* Subroutine */ int ztrt05_(char *, char *, char *, integer *,
integer *, doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublereal *, doublereal *, doublereal *),
ztrt06_(doublereal *, doublereal *, char *, char *, integer *,
doublecomplex *, integer *, doublereal *, doublereal *), alaerh_(char *, char *, integer *, integer *, char *,
integer *, integer *, integer *, integer *, integer *, integer *,
integer *, integer *, integer *);
doublereal rcondc, rcondi;
extern /* Subroutine */ int alasum_(char *, integer *, integer *, integer
*, integer *);
doublereal rcondo, ainvnm;
extern /* Subroutine */ int xlaenv_(integer *, 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 *);
extern doublereal zlantr_(char *, char *, char *, integer *, integer *,
doublecomplex *, integer *, doublereal *);
doublereal result[9];
extern /* Subroutine */ int zlatrs_(char *, char *, char *, char *,
integer *, doublecomplex *, integer *, doublecomplex *,
doublereal *, doublereal *, integer *), zlattr_(integer *, char *, char *, char *, integer *,
integer *, doublecomplex *, integer *, doublecomplex *,
doublecomplex *, doublereal *, integer *),
ztrcon_(char *, char *, char *, integer *, doublecomplex *,
integer *, doublereal *, doublecomplex *, doublereal *, integer *), zerrtr_(char *, integer *),
ztrrfs_(char *, char *, char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublereal *, doublereal *,
doublecomplex *, doublereal *, integer *),
ztrtri_(char *, char *, integer *, doublecomplex *, integer *,
integer *), ztrtrs_(char *, char *, char *,
integer *, integer *, doublecomplex *, integer *, doublecomplex *,
integer *, integer *);
/* Fortran I/O blocks */
static cilist io___27 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___36 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___38 = { 0, 0, 0, fmt_9997, 0 };
static cilist io___40 = { 0, 0, 0, fmt_9996, 0 };
static cilist io___41 = { 0, 0, 0, fmt_9996, 0 };
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZCHKTR tests ZTRTRI, -TRS, -RFS, and -CON, and ZLATRS */
/* 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 column dimension N. */
/* NNB (input) INTEGER */
/* The number of values of NB contained in the vector NBVAL. */
/* NBVAL (input) INTEGER array, dimension (NNB) */
/* The values of the blocksize NB. */
/* 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 leading dimension of the work arrays. */
/* NMAX >= the maximum value of N in NVAL. */
/* A (workspace) COMPLEX*16 array, dimension (NMAX*NMAX) */
/* AINV (workspace) COMPLEX*16 array, dimension (NMAX*NMAX) */
/* 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(3,NSMAX)) */
/* RWORK (workspace) DOUBLE PRECISION array, dimension */
/* (max(NMAX,2*NSMAX)) */
/* NOUT (input) INTEGER */
/* The unit number for output. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Scalars in Common .. */
/* .. */
/* .. Common blocks .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Data statements .. */
/* Parameter adjustments */
--rwork;
--work;
--xact;
--x;
--b;
--ainv;
--a;
--nsval;
--nbval;
--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, "TR", (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) {
zerrtr_(path, nout);
}
infoc_1.infot = 0;
i__1 = *nn;
for (in = 1; in <= i__1; ++in) {
/* Do for each value of N in NVAL */
n = nval[in];
lda = max(1,n);
*(unsigned char *)xtype = 'N';
for (imat = 1; imat <= 10; ++imat) {
/* Do the tests only if DOTYPE( IMAT ) is true. */
if (! dotype[imat]) {
goto L80;
}
for (iuplo = 1; iuplo <= 2; ++iuplo) {
/* Do first for UPLO = 'U', then for UPLO = 'L' */
*(unsigned char *)uplo = *(unsigned char *)&uplos[iuplo - 1];
/* Call ZLATTR to generate a triangular test matrix. */
s_copy(srnamc_1.srnamt, "ZLATTR", (ftnlen)32, (ftnlen)6);
zlattr_(&imat, uplo, "No transpose", diag, iseed, &n, &a[1], &
lda, &x[1], &work[1], &rwork[1], &info);
/* Set IDIAG = 1 for non-unit matrices, 2 for unit. */
if (lsame_(diag, "N")) {
idiag = 1;
} else {
idiag = 2;
}
i__2 = *nnb;
for (inb = 1; inb <= i__2; ++inb) {
/* Do for each blocksize in NBVAL */
nb = nbval[inb];
xlaenv_(&c__1, &nb);
/* + TEST 1 */
/* Form the inverse of A. */
zlacpy_(uplo, &n, &n, &a[1], &lda, &ainv[1], &lda);
s_copy(srnamc_1.srnamt, "ZTRTRI", (ftnlen)32, (ftnlen)6);
ztrtri_(uplo, diag, &n, &ainv[1], &lda, &info);
/* Check error code from ZTRTRI. */
if (info != 0) {
/* Writing concatenation */
i__3[0] = 1, a__1[0] = uplo;
i__3[1] = 1, a__1[1] = diag;
s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2);
alaerh_(path, "ZTRTRI", &info, &c__0, ch__1, &n, &n, &
c_n1, &c_n1, &nb, &imat, &nfail, &nerrs, nout);
}
/* Compute the infinity-norm condition number of A. */
anorm = zlantr_("I", uplo, diag, &n, &n, &a[1], &lda, &
rwork[1]);
ainvnm = zlantr_("I", uplo, diag, &n, &n, &ainv[1], &lda,
&rwork[1]);
if (anorm <= 0. || ainvnm <= 0.) {
rcondi = 1.;
} else {
rcondi = 1. / anorm / ainvnm;
}
/* Compute the residual for the triangular matrix times */
/* its inverse. Also compute the 1-norm condition number */
/* of A. */
ztrt01_(uplo, diag, &n, &a[1], &lda, &ainv[1], &lda, &
rcondo, &rwork[1], result);
/* Print the test ratio if it is .GE. THRESH. */
if (result[0] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
alahd_(nout, path);
}
io___27.ciunit = *nout;
s_wsfe(&io___27);
do_fio(&c__1, uplo, (ftnlen)1);
do_fio(&c__1, diag, (ftnlen)1);
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&nb, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&imat, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&c__1, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&result[0], (ftnlen)sizeof(
doublereal));
e_wsfe();
++nfail;
}
++nrun;
/* Skip remaining tests if not the first block size. */
if (inb != 1) {
goto L60;
}
i__4 = *nns;
for (irhs = 1; irhs <= i__4; ++irhs) {
nrhs = nsval[irhs];
*(unsigned char *)xtype = 'N';
for (itran = 1; itran <= 3; ++itran) {
/* Do for op(A) = A, A**T, or A**H. */
*(unsigned char *)trans = *(unsigned char *)&
transs[itran - 1];
if (itran == 1) {
*(unsigned char *)norm = 'O';
rcondc = rcondo;
} else {
*(unsigned char *)norm = 'I';
rcondc = rcondi;
}
/* + TEST 2 */
/* Solve and compute residual for op(A)*x = b. */
s_copy(srnamc_1.srnamt, "ZLARHS", (ftnlen)32, (
ftnlen)6);
zlarhs_(path, xtype, uplo, trans, &n, &n, &c__0, &
idiag, &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, "ZTRTRS", (ftnlen)32, (
ftnlen)6);
ztrtrs_(uplo, trans, diag, &n, &nrhs, &a[1], &lda,
&x[1], &lda, &info);
/* Check error code from ZTRTRS. */
if (info != 0) {
/* Writing concatenation */
i__5[0] = 1, a__2[0] = uplo;
i__5[1] = 1, a__2[1] = trans;
i__5[2] = 1, a__2[2] = diag;
s_cat(ch__2, a__2, i__5, &c__3, (ftnlen)3);
alaerh_(path, "ZTRTRS", &info, &c__0, ch__2, &
n, &n, &c_n1, &c_n1, &nrhs, &imat, &
nfail, &nerrs, nout);
}
/* This line is needed on a Sun SPARCstation. */
if (n > 0) {
dummy = a[1].r;
}
ztrt02_(uplo, trans, diag, &n, &nrhs, &a[1], &lda,
&x[1], &lda, &b[1], &lda, &work[1], &
rwork[1], &result[1]);
/* + TEST 3 */
/* Check solution from generated exact solution. */
zget04_(&n, &nrhs, &x[1], &lda, &xact[1], &lda, &
rcondc, &result[2]);
/* + TESTS 4, 5, and 6 */
/* Use iterative refinement to improve the solution */
/* and compute error bounds. */
s_copy(srnamc_1.srnamt, "ZTRRFS", (ftnlen)32, (
ftnlen)6);
ztrrfs_(uplo, trans, diag, &n, &nrhs, &a[1], &lda,
&b[1], &lda, &x[1], &lda, &rwork[1], &
rwork[nrhs + 1], &work[1], &rwork[(nrhs <<
1) + 1], &info);
/* Check error code from ZTRRFS. */
if (info != 0) {
/* Writing concatenation */
i__5[0] = 1, a__2[0] = uplo;
i__5[1] = 1, a__2[1] = trans;
i__5[2] = 1, a__2[2] = diag;
s_cat(ch__2, a__2, i__5, &c__3, (ftnlen)3);
alaerh_(path, "ZTRRFS", &info, &c__0, ch__2, &
n, &n, &c_n1, &c_n1, &nrhs, &imat, &
nfail, &nerrs, nout);
}
zget04_(&n, &nrhs, &x[1], &lda, &xact[1], &lda, &
rcondc, &result[3]);
ztrt05_(uplo, trans, diag, &n, &nrhs, &a[1], &lda,
&b[1], &lda, &x[1], &lda, &xact[1], &lda,
&rwork[1], &rwork[nrhs + 1], &result[4]);
/* Print information about the tests that did not */
/* pass the threshold. */
for (k = 2; k <= 6; ++k) {
if (result[k - 1] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
alahd_(nout, path);
}
io___36.ciunit = *nout;
s_wsfe(&io___36);
do_fio(&c__1, uplo, (ftnlen)1);
do_fio(&c__1, trans, (ftnlen)1);
do_fio(&c__1, diag, (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;
}
/* L20: */
}
nrun += 5;
/* L30: */
}
/* L40: */
}
/* + TEST 7 */
/* Get an estimate of RCOND = 1/CNDNUM. */
for (itran = 1; itran <= 2; ++itran) {
if (itran == 1) {
*(unsigned char *)norm = 'O';
rcondc = rcondo;
} else {
*(unsigned char *)norm = 'I';
rcondc = rcondi;
}
s_copy(srnamc_1.srnamt, "ZTRCON", (ftnlen)32, (ftnlen)
6);
ztrcon_(norm, uplo, diag, &n, &a[1], &lda, &rcond, &
work[1], &rwork[1], &info);
/* Check error code from ZTRCON. */
if (info != 0) {
/* Writing concatenation */
i__5[0] = 1, a__2[0] = norm;
i__5[1] = 1, a__2[1] = uplo;
i__5[2] = 1, a__2[2] = diag;
s_cat(ch__2, a__2, i__5, &c__3, (ftnlen)3);
alaerh_(path, "ZTRCON", &info, &c__0, ch__2, &n, &
n, &c_n1, &c_n1, &c_n1, &imat, &nfail, &
nerrs, nout);
}
ztrt06_(&rcond, &rcondc, uplo, diag, &n, &a[1], &lda,
&rwork[1], &result[6]);
/* Print the test ratio if it is .GE. THRESH. */
if (result[6] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
alahd_(nout, path);
}
io___38.ciunit = *nout;
s_wsfe(&io___38);
do_fio(&c__1, norm, (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 *)&c__7, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&result[6], (ftnlen)sizeof(
doublereal));
e_wsfe();
++nfail;
}
++nrun;
/* L50: */
}
L60:
;
}
/* L70: */
}
L80:
;
}
/* Use pathological test matrices to test ZLATRS. */
for (imat = 11; imat <= 18; ++imat) {
/* Do the tests only if DOTYPE( IMAT ) is true. */
if (! dotype[imat]) {
goto L110;
}
for (iuplo = 1; iuplo <= 2; ++iuplo) {
/* Do first for UPLO = 'U', then for UPLO = 'L' */
*(unsigned char *)uplo = *(unsigned char *)&uplos[iuplo - 1];
for (itran = 1; itran <= 3; ++itran) {
/* Do for op(A) = A, A**T, and A**H. */
*(unsigned char *)trans = *(unsigned char *)&transs[itran
- 1];
/* Call ZLATTR to generate a triangular test matrix. */
s_copy(srnamc_1.srnamt, "ZLATTR", (ftnlen)32, (ftnlen)6);
zlattr_(&imat, uplo, trans, diag, iseed, &n, &a[1], &lda,
&x[1], &work[1], &rwork[1], &info);
/* + TEST 8 */
/* Solve the system op(A)*x = b. */
s_copy(srnamc_1.srnamt, "ZLATRS", (ftnlen)32, (ftnlen)6);
zcopy_(&n, &x[1], &c__1, &b[1], &c__1);
zlatrs_(uplo, trans, diag, "N", &n, &a[1], &lda, &b[1], &
scale, &rwork[1], &info);
/* Check error code from ZLATRS. */
if (info != 0) {
/* Writing concatenation */
i__6[0] = 1, a__3[0] = uplo;
i__6[1] = 1, a__3[1] = trans;
i__6[2] = 1, a__3[2] = diag;
i__6[3] = 1, a__3[3] = "N";
s_cat(ch__3, a__3, i__6, &c__4, (ftnlen)4);
alaerh_(path, "ZLATRS", &info, &c__0, ch__3, &n, &n, &
c_n1, &c_n1, &c_n1, &imat, &nfail, &nerrs,
nout);
}
ztrt03_(uplo, trans, diag, &n, &c__1, &a[1], &lda, &scale,
&rwork[1], &c_b99, &b[1], &lda, &x[1], &lda, &
work[1], &result[7]);
/* + TEST 9 */
/* Solve op(A)*X = b again with NORMIN = 'Y'. */
zcopy_(&n, &x[1], &c__1, &b[n + 1], &c__1);
zlatrs_(uplo, trans, diag, "Y", &n, &a[1], &lda, &b[n + 1]
, &scale, &rwork[1], &info);
/* Check error code from ZLATRS. */
if (info != 0) {
/* Writing concatenation */
i__6[0] = 1, a__3[0] = uplo;
i__6[1] = 1, a__3[1] = trans;
i__6[2] = 1, a__3[2] = diag;
i__6[3] = 1, a__3[3] = "Y";
s_cat(ch__3, a__3, i__6, &c__4, (ftnlen)4);
alaerh_(path, "ZLATRS", &info, &c__0, ch__3, &n, &n, &
c_n1, &c_n1, &c_n1, &imat, &nfail, &nerrs,
nout);
}
ztrt03_(uplo, trans, diag, &n, &c__1, &a[1], &lda, &scale,
&rwork[1], &c_b99, &b[n + 1], &lda, &x[1], &lda,
&work[1], &result[8]);
/* Print information about the tests that did not pass */
/* the threshold. */
if (result[7] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
alahd_(nout, path);
}
io___40.ciunit = *nout;
s_wsfe(&io___40);
do_fio(&c__1, "ZLATRS", (ftnlen)6);
do_fio(&c__1, uplo, (ftnlen)1);
do_fio(&c__1, trans, (ftnlen)1);
do_fio(&c__1, diag, (ftnlen)1);
do_fio(&c__1, "N", (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;
}
if (result[8] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
alahd_(nout, path);
}
io___41.ciunit = *nout;
s_wsfe(&io___41);
do_fio(&c__1, "ZLATRS", (ftnlen)6);
do_fio(&c__1, uplo, (ftnlen)1);
do_fio(&c__1, trans, (ftnlen)1);
do_fio(&c__1, diag, (ftnlen)1);
do_fio(&c__1, "Y", (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__9, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&result[8], (ftnlen)sizeof(
doublereal));
e_wsfe();
++nfail;
}
nrun += 2;
/* L90: */
}
/* L100: */
}
L110:
;
}
/* L120: */
}
/* Print a summary of the results. */
alasum_(path, nout, &nfail, &nrun, &nerrs);
return 0;
/* End of ZCHKTR */
} /* zchktr_ */
/* Subroutine */ int zgetri_(integer *n, doublecomplex *a, integer *lda,
integer *ipiv, doublecomplex *work, integer *lwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5;
doublecomplex z__1;
/* Local variables */
static integer i__, j, jb, nb, jj, jp, nn, iws, nbmin;
extern /* Subroutine */ int zgemm_(char *, char *, integer *, integer *,
integer *, doublecomplex *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *, ftnlen, ftnlen), zgemv_(char *, integer *, integer *,
doublecomplex *, doublecomplex *, integer *, doublecomplex *,
integer *, doublecomplex *, doublecomplex *, integer *, ftnlen),
zswap_(integer *, doublecomplex *, integer *, doublecomplex *,
integer *), ztrsm_(char *, char *, char *, char *, integer *,
integer *, doublecomplex *, doublecomplex *, integer *,
doublecomplex *, integer *, ftnlen, ftnlen, ftnlen, ftnlen),
xerbla_(char *, integer *, ftnlen);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
static integer ldwork, lwkopt;
static logical lquery;
extern /* Subroutine */ int ztrtri_(char *, char *, integer *,
doublecomplex *, integer *, 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 */
/* June 30, 1999 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZGETRI computes the inverse of a matrix using the LU factorization */
/* computed by ZGETRF. */
/* This method inverts U and then computes inv(A) by solving the system */
/* inv(A)*L = inv(U) for inv(A). */
/* Arguments */
/* ========= */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* A (input/output) COMPLEX*16 array, dimension (LDA,N) */
/* On entry, the factors L and U from the factorization */
/* A = P*L*U as computed by ZGETRF. */
/* On exit, if INFO = 0, the inverse of the original matrix A. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,N). */
/* IPIV (input) INTEGER array, dimension (N) */
/* The pivot indices from ZGETRF; for 1<=i<=N, row i of the */
/* matrix was interchanged with row IPIV(i). */
/* WORK (workspace/output) COMPLEX*16 array, dimension (LWORK) */
/* On exit, if INFO=0, then WORK(1) returns the optimal LWORK. */
/* LWORK (input) INTEGER */
/* The dimension of the array WORK. LWORK >= max(1,N). */
/* For optimal performance LWORK >= N*NB, where NB is */
/* the optimal blocksize returned by ILAENV. */
/* If LWORK = -1, then a workspace query is assumed; the routine */
/* only calculates the optimal size of the WORK array, returns */
/* this value as the first entry of the WORK array, and no error */
/* message related to LWORK is issued by XERBLA. */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* > 0: if INFO = i, U(i,i) is exactly zero; the matrix is */
/* singular and its inverse could not be computed. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--ipiv;
--work;
/* Function Body */
*info = 0;
nb = ilaenv_(&c__1, "ZGETRI", " ", n, &c_n1, &c_n1, &c_n1, (ftnlen)6, (
ftnlen)1);
lwkopt = *n * nb;
work[1].r = (doublereal) lwkopt, work[1].i = 0.;
lquery = *lwork == -1;
if (*n < 0) {
*info = -1;
} else if (*lda < max(1,*n)) {
*info = -3;
} else if (*lwork < max(1,*n) && ! lquery) {
*info = -6;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZGETRI", &i__1, (ftnlen)6);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/* Form inv(U). If INFO > 0 from ZTRTRI, then U is singular, */
/* and the inverse is not computed. */
ztrtri_("Upper", "Non-unit", n, &a[a_offset], lda, info, (ftnlen)5, (
ftnlen)8);
if (*info > 0) {
return 0;
}
nbmin = 2;
ldwork = *n;
if (nb > 1 && nb < *n) {
/* Computing MAX */
i__1 = ldwork * nb;
iws = max(i__1,1);
if (*lwork < iws) {
nb = *lwork / ldwork;
/* Computing MAX */
i__1 = 2, i__2 = ilaenv_(&c__2, "ZGETRI", " ", n, &c_n1, &c_n1, &
c_n1, (ftnlen)6, (ftnlen)1);
nbmin = max(i__1,i__2);
}
} else {
iws = *n;
}
/* Solve the equation inv(A)*L = inv(U) for inv(A). */
if (nb < nbmin || nb >= *n) {
/* Use unblocked code. */
for (j = *n; j >= 1; --j) {
/* Copy current column of L to WORK and replace with zeros. */
i__1 = *n;
for (i__ = j + 1; i__ <= i__1; ++i__) {
i__2 = i__;
i__3 = i__ + j * a_dim1;
work[i__2].r = a[i__3].r, work[i__2].i = a[i__3].i;
i__2 = i__ + j * a_dim1;
a[i__2].r = 0., a[i__2].i = 0.;
/* L10: */
}
/* Compute current column of inv(A). */
if (j < *n) {
i__1 = *n - j;
z__1.r = -1., z__1.i = -0.;
zgemv_("No transpose", n, &i__1, &z__1, &a[(j + 1) * a_dim1 +
1], lda, &work[j + 1], &c__1, &c_b2, &a[j * a_dim1 +
1], &c__1, (ftnlen)12);
}
/* L20: */
}
} else {
/* Use blocked code. */
nn = (*n - 1) / nb * nb + 1;
i__1 = -nb;
for (j = nn; i__1 < 0 ? j >= 1 : j <= 1; j += i__1) {
/* Computing MIN */
i__2 = nb, i__3 = *n - j + 1;
jb = min(i__2,i__3);
/* Copy current block column of L to WORK and replace with */
/* zeros. */
i__2 = j + jb - 1;
for (jj = j; jj <= i__2; ++jj) {
i__3 = *n;
for (i__ = jj + 1; i__ <= i__3; ++i__) {
i__4 = i__ + (jj - j) * ldwork;
i__5 = i__ + jj * a_dim1;
work[i__4].r = a[i__5].r, work[i__4].i = a[i__5].i;
i__4 = i__ + jj * a_dim1;
a[i__4].r = 0., a[i__4].i = 0.;
/* L30: */
}
/* L40: */
}
/* Compute current block column of inv(A). */
if (j + jb <= *n) {
i__2 = *n - j - jb + 1;
z__1.r = -1., z__1.i = -0.;
zgemm_("No transpose", "No transpose", n, &jb, &i__2, &z__1, &
a[(j + jb) * a_dim1 + 1], lda, &work[j + jb], &ldwork,
&c_b2, &a[j * a_dim1 + 1], lda, (ftnlen)12, (ftnlen)
12);
}
ztrsm_("Right", "Lower", "No transpose", "Unit", n, &jb, &c_b2, &
work[j], &ldwork, &a[j * a_dim1 + 1], lda, (ftnlen)5, (
ftnlen)5, (ftnlen)12, (ftnlen)4);
/* L50: */
}
}
/* Apply column interchanges. */
for (j = *n - 1; j >= 1; --j) {
jp = ipiv[j];
if (jp != j) {
zswap_(n, &a[j * a_dim1 + 1], &c__1, &a[jp * a_dim1 + 1], &c__1);
}
/* L60: */
}
work[1].r = (doublereal) iws, work[1].i = 0.;
return 0;
/* End of ZGETRI */
} /* zgetri_ */
