/* Subroutine */ int zgtt01_(integer *n, doublecomplex *dl, doublecomplex *
d__, doublecomplex *du, doublecomplex *dlf, doublecomplex *df,
doublecomplex *duf, doublecomplex *du2, integer *ipiv, doublecomplex *
work, integer *ldwork, doublereal *rwork, doublereal *resid)
{
/* System generated locals */
integer work_dim1, work_offset, i__1, i__2, i__3, i__4;
doublecomplex z__1;
/* Local variables */
integer i__, j;
doublecomplex li;
integer ip;
doublereal eps, anorm;
integer lastj;
extern /* Subroutine */ int zswap_(integer *, doublecomplex *, integer *,
doublecomplex *, integer *), zaxpy_(integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *);
extern doublereal dlamch_(char *), zlangt_(char *, integer *,
doublecomplex *, doublecomplex *, doublecomplex *),
zlanhs_(char *, integer *, doublecomplex *, integer *, doublereal
*);
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZGTT01 reconstructs a tridiagonal matrix A from its LU factorization */
/* and computes the residual */
/* norm(L*U - A) / ( norm(A) * EPS ), */
/* where EPS is the machine epsilon. */
/* Arguments */
/* ========= */
/* N (input) INTEGTER */
/* The order of the matrix A. N >= 0. */
/* DL (input) COMPLEX*16 array, dimension (N-1) */
/* The (n-1) sub-diagonal elements of A. */
/* D (input) COMPLEX*16 array, dimension (N) */
/* The diagonal elements of A. */
/* DU (input) COMPLEX*16 array, dimension (N-1) */
/* The (n-1) super-diagonal elements of A. */
/* DLF (input) COMPLEX*16 array, dimension (N-1) */
/* The (n-1) multipliers that define the matrix L from the */
/* LU factorization of A. */
/* DF (input) COMPLEX*16 array, dimension (N) */
/* The n diagonal elements of the upper triangular matrix U from */
/* the LU factorization of A. */
/* DUF (input) COMPLEX*16 array, dimension (N-1) */
/* The (n-1) elements of the first super-diagonal of U. */
/* DU2 (input) COMPLEX*16 array, dimension (N-2) */
/* The (n-2) elements of the second super-diagonal of U. */
/* IPIV (input) INTEGER array, dimension (N) */
/* The pivot indices; for 1 <= i <= n, row i of the matrix was */
/* interchanged with row IPIV(i). IPIV(i) will always be either */
/* i or i+1; IPIV(i) = i indicates a row interchange was not */
/* required. */
/* WORK (workspace) COMPLEX*16 array, dimension (LDWORK,N) */
/* LDWORK (input) INTEGER */
/* The leading dimension of the array WORK. LDWORK >= max(1,N). */
/* RWORK (workspace) DOUBLE PRECISION array, dimension (N) */
/* RESID (output) DOUBLE PRECISION */
/* The scaled residual: norm(L*U - A) / (norm(A) * EPS) */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Executable Statements .. */
/* Quick return if possible */
/* Parameter adjustments */
--dl;
--d__;
--du;
--dlf;
--df;
--duf;
--du2;
--ipiv;
work_dim1 = *ldwork;
work_offset = 1 + work_dim1;
work -= work_offset;
--rwork;
/* Function Body */
if (*n <= 0) {
*resid = 0.;
return 0;
}
eps = dlamch_("Epsilon");
/* Copy the matrix U to WORK. */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * work_dim1;
work[i__3].r = 0., work[i__3].i = 0.;
/* L10: */
}
/* L20: */
}
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
if (i__ == 1) {
i__2 = i__ + i__ * work_dim1;
i__3 = i__;
work[i__2].r = df[i__3].r, work[i__2].i = df[i__3].i;
if (*n >= 2) {
i__2 = i__ + (i__ + 1) * work_dim1;
i__3 = i__;
work[i__2].r = duf[i__3].r, work[i__2].i = duf[i__3].i;
}
if (*n >= 3) {
i__2 = i__ + (i__ + 2) * work_dim1;
i__3 = i__;
work[i__2].r = du2[i__3].r, work[i__2].i = du2[i__3].i;
}
} else if (i__ == *n) {
i__2 = i__ + i__ * work_dim1;
i__3 = i__;
work[i__2].r = df[i__3].r, work[i__2].i = df[i__3].i;
} else {
i__2 = i__ + i__ * work_dim1;
i__3 = i__;
work[i__2].r = df[i__3].r, work[i__2].i = df[i__3].i;
i__2 = i__ + (i__ + 1) * work_dim1;
i__3 = i__;
work[i__2].r = duf[i__3].r, work[i__2].i = duf[i__3].i;
if (i__ < *n - 1) {
i__2 = i__ + (i__ + 2) * work_dim1;
i__3 = i__;
work[i__2].r = du2[i__3].r, work[i__2].i = du2[i__3].i;
}
}
/* L30: */
}
/* Multiply on the left by L. */
lastj = *n;
for (i__ = *n - 1; i__ >= 1; --i__) {
i__1 = i__;
li.r = dlf[i__1].r, li.i = dlf[i__1].i;
i__1 = lastj - i__ + 1;
zaxpy_(&i__1, &li, &work[i__ + i__ * work_dim1], ldwork, &work[i__ +
1 + i__ * work_dim1], ldwork);
ip = ipiv[i__];
if (ip == i__) {
/* Computing MIN */
i__1 = i__ + 2;
lastj = min(i__1,*n);
} else {
i__1 = lastj - i__ + 1;
zswap_(&i__1, &work[i__ + i__ * work_dim1], ldwork, &work[i__ + 1
+ i__ * work_dim1], ldwork);
}
/* L40: */
}
/* Subtract the matrix A. */
i__1 = work_dim1 + 1;
i__2 = work_dim1 + 1;
z__1.r = work[i__2].r - d__[1].r, z__1.i = work[i__2].i - d__[1].i;
work[i__1].r = z__1.r, work[i__1].i = z__1.i;
if (*n > 1) {
i__1 = (work_dim1 << 1) + 1;
i__2 = (work_dim1 << 1) + 1;
z__1.r = work[i__2].r - du[1].r, z__1.i = work[i__2].i - du[1].i;
work[i__1].r = z__1.r, work[i__1].i = z__1.i;
i__1 = *n + (*n - 1) * work_dim1;
i__2 = *n + (*n - 1) * work_dim1;
i__3 = *n - 1;
z__1.r = work[i__2].r - dl[i__3].r, z__1.i = work[i__2].i - dl[i__3]
.i;
work[i__1].r = z__1.r, work[i__1].i = z__1.i;
i__1 = *n + *n * work_dim1;
i__2 = *n + *n * work_dim1;
i__3 = *n;
z__1.r = work[i__2].r - d__[i__3].r, z__1.i = work[i__2].i - d__[i__3]
.i;
work[i__1].r = z__1.r, work[i__1].i = z__1.i;
i__1 = *n - 1;
for (i__ = 2; i__ <= i__1; ++i__) {
i__2 = i__ + (i__ - 1) * work_dim1;
i__3 = i__ + (i__ - 1) * work_dim1;
i__4 = i__ - 1;
z__1.r = work[i__3].r - dl[i__4].r, z__1.i = work[i__3].i - dl[
i__4].i;
work[i__2].r = z__1.r, work[i__2].i = z__1.i;
i__2 = i__ + i__ * work_dim1;
i__3 = i__ + i__ * work_dim1;
i__4 = i__;
z__1.r = work[i__3].r - d__[i__4].r, z__1.i = work[i__3].i - d__[
i__4].i;
work[i__2].r = z__1.r, work[i__2].i = z__1.i;
i__2 = i__ + (i__ + 1) * work_dim1;
i__3 = i__ + (i__ + 1) * work_dim1;
i__4 = i__;
z__1.r = work[i__3].r - du[i__4].r, z__1.i = work[i__3].i - du[
i__4].i;
work[i__2].r = z__1.r, work[i__2].i = z__1.i;
/* L50: */
}
}
/* Compute the 1-norm of the tridiagonal matrix A. */
anorm = zlangt_("1", n, &dl[1], &d__[1], &du[1]);
/* Compute the 1-norm of WORK, which is only guaranteed to be */
/* upper Hessenberg. */
*resid = zlanhs_("1", n, &work[work_offset], ldwork, &rwork[1])
;
/* Compute norm(L*U - A) / (norm(A) * EPS) */
if (anorm <= 0.) {
if (*resid != 0.) {
*resid = 1. / eps;
}
} else {
*resid = *resid / anorm / eps;
}
return 0;
/* End of ZGTT01 */
} /* zgtt01_ */
/* Subroutine */ int zgtsvx_(char *fact, char *trans, integer *n, integer *
nrhs, doublecomplex *dl, doublecomplex *d__, doublecomplex *du,
doublecomplex *dlf, doublecomplex *df, doublecomplex *duf,
doublecomplex *du2, integer *ipiv, doublecomplex *b, integer *ldb,
doublecomplex *x, integer *ldx, doublereal *rcond, doublereal *ferr,
doublereal *berr, doublecomplex *work, doublereal *rwork, integer *
info)
{
/* System generated locals */
integer b_dim1, b_offset, x_dim1, x_offset, i__1;
/* Local variables */
char norm[1];
extern logical lsame_(char *, char *);
doublereal anorm;
extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *,
doublecomplex *, integer *);
extern doublereal dlamch_(char *);
logical nofact;
extern /* Subroutine */ int xerbla_(char *, integer *);
extern doublereal zlangt_(char *, integer *, doublecomplex *,
doublecomplex *, doublecomplex *);
logical notran;
extern /* Subroutine */ int zlacpy_(char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *),
zgtcon_(char *, integer *, doublecomplex *, doublecomplex *,
doublecomplex *, doublecomplex *, integer *, doublereal *,
doublereal *, doublecomplex *, integer *), zgtrfs_(char *,
integer *, integer *, doublecomplex *, doublecomplex *,
doublecomplex *, doublecomplex *, doublecomplex *, doublecomplex *
, doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublereal *, doublereal *,
doublecomplex *, doublereal *, integer *), zgttrf_(
integer *, doublecomplex *, doublecomplex *, doublecomplex *,
doublecomplex *, integer *, integer *), zgttrs_(char *, integer *,
integer *, doublecomplex *, doublecomplex *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *, integer *);
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZGTSVX uses the LU factorization to compute the solution to a complex */
/* system of linear equations A * X = B, A**T * X = B, or A**H * X = B, */
/* where A is a tridiagonal matrix of order N 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 LU decomposition is used to factor the matrix A */
/* as A = L * U, where L is a product of permutation and unit lower */
/* bidiagonal matrices and U is upper triangular with nonzeros in */
/* only the main diagonal and first two superdiagonals. */
/* 2. If some U(i,i)=0, so that U is exactly singular, then the routine */
/* returns with INFO = i. Otherwise, the factored form of A is used */
/* to estimate the condition number of the matrix A. If the */
/* reciprocal of the condition number is less than machine precision, */
/* INFO = N+1 is returned as a warning, but the routine still goes on */
/* to solve for X and compute error bounds as described below. */
/* 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': DLF, DF, DUF, DU2, and IPIV contain the factored form */
/* of A; DL, D, DU, DLF, DF, DUF, DU2 and IPIV will not */
/* be modified. */
/* = 'N': The matrix will be copied to DLF, DF, and DUF */
/* and factored. */
/* TRANS (input) CHARACTER*1 */
/* Specifies the form of the system of equations: */
/* = 'N': A * X = B (No transpose) */
/* = 'T': A**T * X = B (Transpose) */
/* = 'C': A**H * X = B (Conjugate transpose) */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* NRHS (input) INTEGER */
/* The number of right hand sides, i.e., the number of columns */
/* of the matrix B. NRHS >= 0. */
/* DL (input) COMPLEX*16 array, dimension (N-1) */
/* The (n-1) subdiagonal elements of A. */
/* D (input) COMPLEX*16 array, dimension (N) */
/* The n diagonal elements of A. */
/* DU (input) COMPLEX*16 array, dimension (N-1) */
/* The (n-1) superdiagonal elements of A. */
/* DLF (input or output) COMPLEX*16 array, dimension (N-1) */
/* If FACT = 'F', then DLF is an input argument and on entry */
/* contains the (n-1) multipliers that define the matrix L from */
/* the LU factorization of A as computed by ZGTTRF. */
/* If FACT = 'N', then DLF is an output argument and on exit */
/* contains the (n-1) multipliers that define the matrix L from */
/* the LU factorization of A. */
/* DF (input or output) COMPLEX*16 array, dimension (N) */
/* If FACT = 'F', then DF is an input argument and on entry */
/* contains the n diagonal elements of the upper triangular */
/* matrix U from the LU factorization of A. */
/* If FACT = 'N', then DF is an output argument and on exit */
/* contains the n diagonal elements of the upper triangular */
/* matrix U from the LU factorization of A. */
/* DUF (input or output) COMPLEX*16 array, dimension (N-1) */
/* If FACT = 'F', then DUF is an input argument and on entry */
/* contains the (n-1) elements of the first superdiagonal of U. */
/* If FACT = 'N', then DUF is an output argument and on exit */
/* contains the (n-1) elements of the first superdiagonal of U. */
/* DU2 (input or output) COMPLEX*16 array, dimension (N-2) */
/* If FACT = 'F', then DU2 is an input argument and on entry */
/* contains the (n-2) elements of the second superdiagonal of */
/* U. */
/* If FACT = 'N', then DU2 is an output argument and on exit */
/* contains the (n-2) elements of the second superdiagonal of */
/* U. */
/* IPIV (input or output) INTEGER array, dimension (N) */
/* If FACT = 'F', then IPIV is an input argument and on entry */
/* contains the pivot indices from the LU factorization of A as */
/* computed by ZGTTRF. */
/* If FACT = 'N', then IPIV is an output argument and on exit */
/* contains the pivot indices from the LU factorization of A; */
/* row i of the matrix was interchanged with row IPIV(i). */
/* IPIV(i) will always be either i or i+1; IPIV(i) = i indicates */
/* a row interchange was not required. */
/* 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: U(i,i) is exactly zero. The factorization */
/* has not been completed unless i = N, but the */
/* factor U is exactly singular, so the solution */
/* and error bounds could not be computed. */
/* RCOND = 0 is returned. */
/* = N+1: U is nonsingular, but RCOND is less than machine */
/* precision, meaning that the matrix is singular */
/* to working precision. Nevertheless, the */
/* solution and error bounds are computed because */
/* there are a number of situations where the */
/* computed solution can be more accurate than the */
/* value of RCOND would suggest. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
--dl;
--d__;
--du;
--dlf;
--df;
--duf;
--du2;
--ipiv;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
x_dim1 = *ldx;
x_offset = 1 + x_dim1;
x -= x_offset;
--ferr;
--berr;
--work;
--rwork;
/* Function Body */
*info = 0;
nofact = lsame_(fact, "N");
notran = lsame_(trans, "N");
if (! nofact && ! lsame_(fact, "F")) {
*info = -1;
} else if (! notran && ! lsame_(trans, "T") && !
lsame_(trans, "C")) {
*info = -2;
} else if (*n < 0) {
*info = -3;
} else if (*nrhs < 0) {
*info = -4;
} else if (*ldb < max(1,*n)) {
*info = -14;
} else if (*ldx < max(1,*n)) {
*info = -16;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZGTSVX", &i__1);
return 0;
}
if (nofact) {
/* Compute the LU factorization of A. */
zcopy_(n, &d__[1], &c__1, &df[1], &c__1);
if (*n > 1) {
i__1 = *n - 1;
zcopy_(&i__1, &dl[1], &c__1, &dlf[1], &c__1);
i__1 = *n - 1;
zcopy_(&i__1, &du[1], &c__1, &duf[1], &c__1);
}
zgttrf_(n, &dlf[1], &df[1], &duf[1], &du2[1], &ipiv[1], info);
/* Return if INFO is non-zero. */
if (*info > 0) {
*rcond = 0.;
return 0;
}
}
/* Compute the norm of the matrix A. */
if (notran) {
*(unsigned char *)norm = '1';
} else {
*(unsigned char *)norm = 'I';
}
anorm = zlangt_(norm, n, &dl[1], &d__[1], &du[1]);
/* Compute the reciprocal of the condition number of A. */
zgtcon_(norm, n, &dlf[1], &df[1], &duf[1], &du2[1], &ipiv[1], &anorm,
rcond, &work[1], info);
/* Compute the solution vectors X. */
zlacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx);
zgttrs_(trans, n, nrhs, &dlf[1], &df[1], &duf[1], &du2[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. */
zgtrfs_(trans, n, nrhs, &dl[1], &d__[1], &du[1], &dlf[1], &df[1], &duf[1],
&du2[1], &ipiv[1], &b[b_offset], ldb, &x[x_offset], ldx, &ferr[1]
, &berr[1], &work[1], &rwork[1], info);
/* Set INFO = N+1 if the matrix is singular to working precision. */
if (*rcond < dlamch_("Epsilon")) {
*info = *n + 1;
}
return 0;
/* End of ZGTSVX */
} /* zgtsvx_ */
/* Subroutine */ int zgtsvx_(char *fact, char *trans, integer *n, integer *
nrhs, doublecomplex *dl, doublecomplex *d, doublecomplex *du,
doublecomplex *dlf, doublecomplex *df, doublecomplex *duf,
doublecomplex *du2, integer *ipiv, doublecomplex *b, integer *ldb,
doublecomplex *x, integer *ldx, doublereal *rcond, doublereal *ferr,
doublereal *berr, doublecomplex *work, doublereal *rwork, integer *
info)
{
/* -- LAPACK routine (version 2.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
September 30, 1994
Purpose
=======
ZGTSVX uses the LU factorization to compute the solution to a complex
system of linear equations A * X = B, A**T * X = B, or A**H * X = B,
where A is a tridiagonal matrix of order N 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 LU decomposition is used to factor the matrix A
as A = L * U, where L is a product of permutation and unit lower
bidiagonal matrices and U is upper triangular with nonzeros in
only the main diagonal and first two superdiagonals.
2. 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, steps 3 and 4 are skipped.
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': DLF, DF, DUF, DU2, and IPIV contain the factored form
of A; DL, D, DU, DLF, DF, DUF, DU2 and IPIV will not
be modified.
= 'N': The matrix will be copied to DLF, DF, and DUF
and factored.
TRANS (input) CHARACTER*1
Specifies the form of the system of equations:
= 'N': A * X = B (No transpose)
= 'T': A**T * X = B (Transpose)
= 'C': A**H * X = B (Conjugate transpose)
N (input) INTEGER
The order of the matrix A. N >= 0.
NRHS (input) INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 0.
DL (input) COMPLEX*16 array, dimension (N-1)
The (n-1) subdiagonal elements of A.
D (input) COMPLEX*16 array, dimension (N)
The n diagonal elements of A.
DU (input) COMPLEX*16 array, dimension (N-1)
The (n-1) superdiagonal elements of A.
DLF (input or output) COMPLEX*16 array, dimension (N-1)
If FACT = 'F', then DLF is an input argument and on entry
contains the (n-1) multipliers that define the matrix L from
the LU factorization of A as computed by ZGTTRF.
If FACT = 'N', then DLF is an output argument and on exit
contains the (n-1) multipliers that define the matrix L from
the LU factorization of A.
DF (input or output) COMPLEX*16 array, dimension (N)
If FACT = 'F', then DF is an input argument and on entry
contains the n diagonal elements of the upper triangular
matrix U from the LU factorization of A.
If FACT = 'N', then DF is an output argument and on exit
contains the n diagonal elements of the upper triangular
matrix U from the LU factorization of A.
DUF (input or output) COMPLEX*16 array, dimension (N-1)
If FACT = 'F', then DUF is an input argument and on entry
contains the (n-1) elements of the first superdiagonal of U.
If FACT = 'N', then DUF is an output argument and on exit
contains the (n-1) elements of the first superdiagonal of U.
DU2 (input or output) COMPLEX*16 array, dimension (N-2)
If FACT = 'F', then DU2 is an input argument and on entry
contains the (n-2) elements of the second superdiagonal of
U.
If FACT = 'N', then DU2 is an output argument and on exit
contains the (n-2) elements of the second superdiagonal of
U.
IPIV (input or output) INTEGER array, dimension (N)
If FACT = 'F', then IPIV is an input argument and on entry
contains the pivot indices from the LU factorization of A as
computed by ZGTTRF.
If FACT = 'N', then IPIV is an output argument and on exit
contains the pivot indices from the LU factorization of A;
row i of the matrix was interchanged with row IPIV(i).
IPIV(i) will always be either i or i+1; IPIV(i) = i indicates
a row interchange was not required.
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, 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, and the solution and error bounds are not computed.
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: U(i,i) is exactly zero. The factorization
has not been completed unless i = N, but the
factor U is exactly singular, so the solution
and error bounds could not be computed.
= N+1: RCOND is less than machine precision. The
factorization has been completed, but the
matrix is singular to working precision, and
the solution and error bounds have not been
computed.
=====================================================================
Parameter adjustments
Function Body */
/* 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 */
static char norm[1];
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 zlangt_(char *, integer *, doublecomplex *,
doublecomplex *, doublecomplex *);
static logical notran;
extern /* Subroutine */ int zlacpy_(char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *),
zgtcon_(char *, integer *, doublecomplex *, doublecomplex *,
doublecomplex *, doublecomplex *, integer *, doublereal *,
doublereal *, doublecomplex *, integer *), zgtrfs_(char *,
integer *, integer *, doublecomplex *, doublecomplex *,
doublecomplex *, doublecomplex *, doublecomplex *, doublecomplex *
, doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublereal *, doublereal *,
doublecomplex *, doublereal *, integer *), zgttrf_(
integer *, doublecomplex *, doublecomplex *, doublecomplex *,
doublecomplex *, integer *, integer *), zgttrs_(char *, integer *,
integer *, doublecomplex *, doublecomplex *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *, integer *);
#define DL(I) dl[(I)-1]
#define D(I) d[(I)-1]
#define DU(I) du[(I)-1]
#define DLF(I) dlf[(I)-1]
#define DF(I) df[(I)-1]
#define DUF(I) duf[(I)-1]
#define DU2(I) du2[(I)-1]
#define IPIV(I) ipiv[(I)-1]
#define FERR(I) ferr[(I)-1]
#define BERR(I) berr[(I)-1]
#define WORK(I) work[(I)-1]
#define RWORK(I) rwork[(I)-1]
#define B(I,J) b[(I)-1 + ((J)-1)* ( *ldb)]
#define X(I,J) x[(I)-1 + ((J)-1)* ( *ldx)]
*info = 0;
nofact = lsame_(fact, "N");
notran = lsame_(trans, "N");
if (! nofact && ! lsame_(fact, "F")) {
*info = -1;
} else if (! notran && ! lsame_(trans, "T") && ! lsame_(trans,
"C")) {
*info = -2;
} else if (*n < 0) {
*info = -3;
} else if (*nrhs < 0) {
*info = -4;
} else if (*ldb < max(1,*n)) {
*info = -14;
} else if (*ldx < max(1,*n)) {
*info = -16;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZGTSVX", &i__1);
return 0;
}
if (nofact) {
/* Compute the LU factorization of A. */
zcopy_(n, &D(1), &c__1, &DF(1), &c__1);
if (*n > 1) {
i__1 = *n - 1;
zcopy_(&i__1, &DL(1), &c__1, &DLF(1), &c__1);
i__1 = *n - 1;
zcopy_(&i__1, &DU(1), &c__1, &DUF(1), &c__1);
}
zgttrf_(n, &DLF(1), &DF(1), &DUF(1), &DU2(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. */
if (notran) {
*(unsigned char *)norm = '1';
} else {
*(unsigned char *)norm = 'I';
}
anorm = zlangt_(norm, n, &DL(1), &D(1), &DU(1));
/* Compute the reciprocal of the condition number of A. */
zgtcon_(norm, n, &DLF(1), &DF(1), &DUF(1), &DU2(1), &IPIV(1), &anorm,
rcond, &WORK(1), info);
/* Return if the matrix is singular to working precision. */
if (*rcond < dlamch_("Epsilon")) {
*info = *n + 1;
return 0;
}
/* Compute the solution vectors X. */
zlacpy_("Full", n, nrhs, &B(1,1), ldb, &X(1,1), ldx);
zgttrs_(trans, n, nrhs, &DLF(1), &DF(1), &DUF(1), &DU2(1), &IPIV(1), &X(1,1), ldx, info);
/* Use iterative refinement to improve the computed solutions and
compute error bounds and backward error estimates for them. */
zgtrfs_(trans, n, nrhs, &DL(1), &D(1), &DU(1), &DLF(1), &DF(1), &DUF(1), &
DU2(1), &IPIV(1), &B(1,1), ldb, &X(1,1), ldx, &FERR(1),
&BERR(1), &WORK(1), &RWORK(1), info);
return 0;
/* End of ZGTSVX */
} /* zgtsvx_ */
/* Subroutine */ int zchkgt_(logical *dotype, integer *nn, integer *nval,
integer *nns, integer *nsval, doublereal *thresh, logical *tsterr,
doublecomplex *a, doublecomplex *af, doublecomplex *b, doublecomplex *
x, doublecomplex *xact, doublecomplex *work, doublereal *rwork,
integer *iwork, integer *nout)
{
/* Initialized data */
static integer iseedy[4] = { 0,0,0,1 };
static char transs[1*3] = "N" "T" "C";
/* Format strings */
static char fmt_9999[] = "(12x,\002N =\002,i5,\002,\002,10x,\002 type"
" \002,i2,\002, test(\002,i2,\002) = \002,g12.5)";
static char fmt_9997[] = "(\002 NORM ='\002,a1,\002', N =\002,i5,\002"
",\002,10x,\002 type \002,i2,\002, test(\002,i2,\002) = \002,g12."
"5)";
static char fmt_9998[] = "(\002 TRANS='\002,a1,\002', N =\002,i5,\002, N"
"RHS=\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;
doublereal d__1, d__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 */
integer i__, j, k, m, n;
doublecomplex z__[3];
integer in, kl, ku, ix, lda;
doublereal cond;
integer mode, koff, imat, info;
char path[3], dist[1];
integer irhs, nrhs;
char norm[1], type__[1];
integer nrun;
extern /* Subroutine */ int alahd_(integer *, char *);
integer nfail, iseed[4];
extern doublereal dget06_(doublereal *, doublereal *);
doublereal rcond;
integer nimat;
doublereal anorm;
integer itran;
extern /* Subroutine */ int zget04_(integer *, integer *, doublecomplex *,
integer *, doublecomplex *, integer *, doublereal *, doublereal *
);
char trans[1];
integer izero, nerrs;
extern /* Subroutine */ int zgtt01_(integer *, doublecomplex *,
doublecomplex *, doublecomplex *, doublecomplex *, doublecomplex *
, doublecomplex *, doublecomplex *, integer *, doublecomplex *,
integer *, doublereal *, doublereal *), zgtt02_(char *, integer *,
integer *, doublecomplex *, doublecomplex *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublereal *, doublereal *), zgtt05_(char *, integer *,
integer *, doublecomplex *, doublecomplex *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublereal *, doublereal *,
doublereal *);
logical zerot;
extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *,
doublecomplex *, integer *), 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, rcondi;
extern /* Subroutine */ int zdscal_(integer *, doublereal *,
doublecomplex *, integer *), alasum_(char *, integer *, integer *,
integer *, integer *);
doublereal rcondo, ainvnm;
logical trfcon;
extern /* Subroutine */ int zerrge_(char *, integer *);
extern doublereal zlangt_(char *, integer *, doublecomplex *,
doublecomplex *, doublecomplex *);
extern /* Subroutine */ int zlagtm_(char *, integer *, integer *,
doublereal *, doublecomplex *, doublecomplex *, doublecomplex *,
doublecomplex *, integer *, doublereal *, doublecomplex *,
integer *), zlacpy_(char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *);
extern doublereal dzasum_(integer *, doublecomplex *, integer *);
extern /* Subroutine */ int zgtcon_(char *, integer *, doublecomplex *,
doublecomplex *, doublecomplex *, doublecomplex *, integer *,
doublereal *, doublereal *, doublecomplex *, integer *),
zlatms_(integer *, integer *, char *, integer *, char *,
doublereal *, integer *, doublereal *, doublereal *, integer *,
integer *, char *, doublecomplex *, integer *, doublecomplex *,
integer *), zlarnv_(integer *, integer *,
integer *, doublecomplex *);
doublereal result[7];
extern /* Subroutine */ int zgtrfs_(char *, integer *, integer *,
doublecomplex *, doublecomplex *, doublecomplex *, doublecomplex *
, doublecomplex *, doublecomplex *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublereal *, doublereal *, doublecomplex *, doublereal *,
integer *), zgttrf_(integer *, doublecomplex *,
doublecomplex *, doublecomplex *, doublecomplex *, integer *,
integer *), zgttrs_(char *, integer *, integer *, doublecomplex *,
doublecomplex *, doublecomplex *, doublecomplex *, integer *,
doublecomplex *, integer *, integer *);
/* Fortran I/O blocks */
static cilist io___29 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___39 = { 0, 0, 0, fmt_9997, 0 };
static cilist io___44 = { 0, 0, 0, fmt_9998, 0 };
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZCHKGT tests ZGTTRF, -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. */
/* A (workspace) COMPLEX*16 array, dimension (NMAX*4) */
/* AF (workspace) COMPLEX*16 array, dimension (NMAX*4) */
/* 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) */
/* 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;
--af;
--a;
--nsval;
--nval;
--dotype;
/* Function Body */
/* .. */
/* .. Executable Statements .. */
s_copy(path, "Zomplex precision", (ftnlen)1, (ftnlen)17);
s_copy(path + 1, "GT", (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) {
zerrge_(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];
/* Computing MAX */
i__2 = n - 1;
m = max(i__2,0);
lda = max(1,n);
nimat = 12;
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 L100;
}
/* Set up parameters with ZLATB4. */
zlatb4_(path, &imat, &n, &n, type__, &kl, &ku, &anorm, &mode, &
cond, dist);
zerot = imat >= 8 && imat <= 10;
if (imat <= 6) {
/* Types 1-6: generate matrices of known condition number. */
/* Computing MAX */
i__3 = 2 - ku, i__4 = 3 - max(1,n);
koff = max(i__3,i__4);
s_copy(srnamc_1.srnamt, "ZLATMS", (ftnlen)32, (ftnlen)6);
zlatms_(&n, &n, dist, iseed, type__, &rwork[1], &mode, &cond,
&anorm, &kl, &ku, "Z", &af[koff], &c__3, &work[1], &
info);
/* Check the error code from ZLATMS. */
if (info != 0) {
alaerh_(path, "ZLATMS", &info, &c__0, " ", &n, &n, &kl, &
ku, &c_n1, &imat, &nfail, &nerrs, nout);
goto L100;
}
izero = 0;
if (n > 1) {
i__3 = n - 1;
zcopy_(&i__3, &af[4], &c__3, &a[1], &c__1);
i__3 = n - 1;
zcopy_(&i__3, &af[3], &c__3, &a[n + m + 1], &c__1);
}
zcopy_(&n, &af[2], &c__3, &a[m + 1], &c__1);
} else {
/* Types 7-12: generate tridiagonal matrices with */
/* unknown condition numbers. */
if (! zerot || ! dotype[7]) {
/* Generate a matrix with elements whose real and */
/* imaginary parts are from [-1,1]. */
i__3 = n + (m << 1);
zlarnv_(&c__2, iseed, &i__3, &a[1]);
if (anorm != 1.) {
i__3 = n + (m << 1);
zdscal_(&i__3, &anorm, &a[1], &c__1);
}
} else if (izero > 0) {
/* Reuse the last matrix by copying back the zeroed out */
/* elements. */
if (izero == 1) {
i__3 = n;
a[i__3].r = z__[1].r, a[i__3].i = z__[1].i;
if (n > 1) {
a[1].r = z__[2].r, a[1].i = z__[2].i;
}
} else if (izero == n) {
i__3 = n * 3 - 2;
a[i__3].r = z__[0].r, a[i__3].i = z__[0].i;
i__3 = (n << 1) - 1;
a[i__3].r = z__[1].r, a[i__3].i = z__[1].i;
} else {
i__3 = (n << 1) - 2 + izero;
a[i__3].r = z__[0].r, a[i__3].i = z__[0].i;
i__3 = n - 1 + izero;
a[i__3].r = z__[1].r, a[i__3].i = z__[1].i;
i__3 = izero;
a[i__3].r = z__[2].r, a[i__3].i = z__[2].i;
}
}
/* If IMAT > 7, set one column of the matrix to 0. */
if (! zerot) {
izero = 0;
} else if (imat == 8) {
izero = 1;
i__3 = n;
z__[1].r = a[i__3].r, z__[1].i = a[i__3].i;
i__3 = n;
a[i__3].r = 0., a[i__3].i = 0.;
if (n > 1) {
z__[2].r = a[1].r, z__[2].i = a[1].i;
a[1].r = 0., a[1].i = 0.;
}
} else if (imat == 9) {
izero = n;
i__3 = n * 3 - 2;
z__[0].r = a[i__3].r, z__[0].i = a[i__3].i;
i__3 = (n << 1) - 1;
z__[1].r = a[i__3].r, z__[1].i = a[i__3].i;
i__3 = n * 3 - 2;
a[i__3].r = 0., a[i__3].i = 0.;
i__3 = (n << 1) - 1;
a[i__3].r = 0., a[i__3].i = 0.;
} else {
izero = (n + 1) / 2;
i__3 = n - 1;
for (i__ = izero; i__ <= i__3; ++i__) {
i__4 = (n << 1) - 2 + i__;
a[i__4].r = 0., a[i__4].i = 0.;
i__4 = n - 1 + i__;
a[i__4].r = 0., a[i__4].i = 0.;
i__4 = i__;
a[i__4].r = 0., a[i__4].i = 0.;
/* L20: */
}
i__3 = n * 3 - 2;
a[i__3].r = 0., a[i__3].i = 0.;
i__3 = (n << 1) - 1;
a[i__3].r = 0., a[i__3].i = 0.;
}
}
/* + TEST 1 */
/* Factor A as L*U and compute the ratio */
/* norm(L*U - A) / (n * norm(A) * EPS ) */
i__3 = n + (m << 1);
zcopy_(&i__3, &a[1], &c__1, &af[1], &c__1);
s_copy(srnamc_1.srnamt, "ZGTTRF", (ftnlen)32, (ftnlen)6);
zgttrf_(&n, &af[1], &af[m + 1], &af[n + m + 1], &af[n + (m << 1)
+ 1], &iwork[1], &info);
/* Check error code from ZGTTRF. */
if (info != izero) {
alaerh_(path, "ZGTTRF", &info, &izero, " ", &n, &n, &c__1, &
c__1, &c_n1, &imat, &nfail, &nerrs, nout);
}
trfcon = info != 0;
zgtt01_(&n, &a[1], &a[m + 1], &a[n + m + 1], &af[1], &af[m + 1], &
af[n + m + 1], &af[n + (m << 1) + 1], &iwork[1], &work[1],
&lda, &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___29.ciunit = *nout;
s_wsfe(&io___29);
do_fio(&c__1, (char *)&n, (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;
for (itran = 1; itran <= 2; ++itran) {
*(unsigned char *)trans = *(unsigned char *)&transs[itran - 1]
;
if (itran == 1) {
*(unsigned char *)norm = 'O';
} else {
*(unsigned char *)norm = 'I';
}
anorm = zlangt_(norm, &n, &a[1], &a[m + 1], &a[n + m + 1]);
if (! trfcon) {
/* Use ZGTTRS to solve for one column at a time of */
/* inv(A), computing the maximum column sum as we go. */
ainvnm = 0.;
i__3 = n;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = n;
for (j = 1; j <= i__4; ++j) {
i__5 = j;
x[i__5].r = 0., x[i__5].i = 0.;
/* L30: */
}
i__4 = i__;
x[i__4].r = 1., x[i__4].i = 0.;
zgttrs_(trans, &n, &c__1, &af[1], &af[m + 1], &af[n +
m + 1], &af[n + (m << 1) + 1], &iwork[1], &x[
1], &lda, &info);
/* Computing MAX */
d__1 = ainvnm, d__2 = dzasum_(&n, &x[1], &c__1);
ainvnm = max(d__1,d__2);
/* L40: */
}
/* Compute RCONDC = 1 / (norm(A) * norm(inv(A)) */
if (anorm <= 0. || ainvnm <= 0.) {
rcondc = 1.;
} else {
rcondc = 1. / anorm / ainvnm;
}
if (itran == 1) {
rcondo = rcondc;
} else {
rcondi = rcondc;
}
} else {
rcondc = 0.;
}
/* + TEST 7 */
/* Estimate the reciprocal of the condition number of the */
/* matrix. */
s_copy(srnamc_1.srnamt, "ZGTCON", (ftnlen)32, (ftnlen)6);
zgtcon_(norm, &n, &af[1], &af[m + 1], &af[n + m + 1], &af[n +
(m << 1) + 1], &iwork[1], &anorm, &rcond, &work[1], &
info);
/* Check error code from ZGTCON. */
if (info != 0) {
alaerh_(path, "ZGTCON", &info, &c__0, norm, &n, &n, &c_n1,
&c_n1, &c_n1, &imat, &nfail, &nerrs, nout);
}
result[6] = dget06_(&rcond, &rcondc);
/* Print the test ratio if it is .GE. THRESH. */
if (result[6] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
alahd_(nout, path);
}
io___39.ciunit = *nout;
s_wsfe(&io___39);
do_fio(&c__1, norm, (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: */
}
/* Skip the remaining tests if the matrix is singular. */
if (trfcon) {
goto L100;
}
i__3 = *nns;
for (irhs = 1; irhs <= i__3; ++irhs) {
nrhs = nsval[irhs];
/* Generate NRHS random solution vectors. */
ix = 1;
i__4 = nrhs;
for (j = 1; j <= i__4; ++j) {
zlarnv_(&c__2, iseed, &n, &xact[ix]);
ix += lda;
/* L60: */
}
for (itran = 1; itran <= 3; ++itran) {
*(unsigned char *)trans = *(unsigned char *)&transs[itran
- 1];
if (itran == 1) {
rcondc = rcondo;
} else {
rcondc = rcondi;
}
/* Set the right hand side. */
zlagtm_(trans, &n, &nrhs, &c_b63, &a[1], &a[m + 1], &a[n
+ m + 1], &xact[1], &lda, &c_b64, &b[1], &lda);
/* + TEST 2 */
/* Solve op(A) * X = B and compute the residual. */
zlacpy_("Full", &n, &nrhs, &b[1], &lda, &x[1], &lda);
s_copy(srnamc_1.srnamt, "ZGTTRS", (ftnlen)32, (ftnlen)6);
zgttrs_(trans, &n, &nrhs, &af[1], &af[m + 1], &af[n + m +
1], &af[n + (m << 1) + 1], &iwork[1], &x[1], &lda,
&info);
/* Check error code from ZGTTRS. */
if (info != 0) {
alaerh_(path, "ZGTTRS", &info, &c__0, trans, &n, &n, &
c_n1, &c_n1, &nrhs, &imat, &nfail, &nerrs,
nout);
}
zlacpy_("Full", &n, &nrhs, &b[1], &lda, &work[1], &lda);
zgtt02_(trans, &n, &nrhs, &a[1], &a[m + 1], &a[n + m + 1],
&x[1], &lda, &work[1], &lda, &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. */
s_copy(srnamc_1.srnamt, "ZGTRFS", (ftnlen)32, (ftnlen)6);
zgtrfs_(trans, &n, &nrhs, &a[1], &a[m + 1], &a[n + m + 1],
&af[1], &af[m + 1], &af[n + m + 1], &af[n + (m <<
1) + 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 ZGTRFS. */
if (info != 0) {
alaerh_(path, "ZGTRFS", &info, &c__0, trans, &n, &n, &
c_n1, &c_n1, &nrhs, &imat, &nfail, &nerrs,
nout);
}
zget04_(&n, &nrhs, &x[1], &lda, &xact[1], &lda, &rcondc, &
result[3]);
zgtt05_(trans, &n, &nrhs, &a[1], &a[m + 1], &a[n + m + 1],
&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___44.ciunit = *nout;
s_wsfe(&io___44);
do_fio(&c__1, trans, (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;
}
/* L70: */
}
nrun += 5;
/* L80: */
}
/* L90: */
}
L100:
;
}
/* L110: */
}
/* Print a summary of the results. */
alasum_(path, nout, &nfail, &nrun, &nerrs);
return 0;
/* End of ZCHKGT */
} /* zchkgt_ */
/* Subroutine */ int zdrvgt_(logical *dotype, integer *nn, integer *nval,
integer *nrhs, doublereal *thresh, logical *tsterr, doublecomplex *a,
doublecomplex *af, doublecomplex *b, doublecomplex *x, doublecomplex *
xact, doublecomplex *work, doublereal *rwork, integer *iwork, integer
*nout)
{
/* Initialized data */
static integer iseedy[4] = { 0,0,0,1 };
static char transs[1*3] = "N" "T" "C";
/* Format strings */
static char fmt_9999[] = "(1x,a6,\002, N =\002,i5,\002, type \002,i2,"
"\002, test \002,i2,\002, ratio = \002,g12.5)";
static char fmt_9998[] = "(1x,a6,\002, FACT='\002,a1,\002', TRANS='\002,"
"a1,\002', N =\002,i5,\002, type \002,i2,\002, test \002,i2,\002,"
" ratio = \002,g12.5)";
/* System generated locals */
address a__1[2];
integer i__1, i__2, i__3, i__4, i__5, i__6[2];
doublereal d__1, d__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 doublereal cond;
static integer mode, koff, imat, info;
static char path[3], dist[1], type__[1];
static integer nrun, i__, j, k, m, n, ifact, nfail, iseed[4];
static doublereal z__[3];
extern doublereal dget06_(doublereal *, doublereal *);
static doublereal rcond;
static integer nimat;
static doublereal anorm;
static integer itran;
extern /* Subroutine */ int zget04_(integer *, integer *, doublecomplex *,
integer *, doublecomplex *, integer *, doublereal *, doublereal *
);
static char trans[1];
static integer izero, nerrs;
extern /* Subroutine */ int zgtt01_(integer *, doublecomplex *,
doublecomplex *, doublecomplex *, doublecomplex *, doublecomplex *
, doublecomplex *, doublecomplex *, integer *, doublecomplex *,
integer *, doublereal *, doublereal *);
static integer k1;
extern /* Subroutine */ int zgtt02_(char *, integer *, integer *,
doublecomplex *, doublecomplex *, doublecomplex *, doublecomplex *
, integer *, doublecomplex *, integer *, doublereal *, doublereal
*), zgtt05_(char *, integer *, integer *, doublecomplex *,
doublecomplex *, doublecomplex *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublereal *, doublereal *, doublereal *);
static logical zerot;
extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *,
doublecomplex *, integer *), zgtsv_(integer *, integer *,
doublecomplex *, doublecomplex *, doublecomplex *, doublecomplex *
, integer *, integer *), zlatb4_(char *, integer *, integer *,
integer *, char *, integer *, integer *, doublereal *, integer *,
doublereal *, 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 *);
static integer ku, ix, nt;
static doublereal rcondc, rcondi;
extern /* Subroutine */ int zdscal_(integer *, doublereal *,
doublecomplex *, integer *), alasvm_(char *, integer *, integer *,
integer *, integer *);
static doublereal rcondo, anormi, ainvnm;
static logical trfcon;
static doublereal anormo;
extern /* Subroutine */ int zlagtm_(char *, integer *, integer *,
doublereal *, doublecomplex *, doublecomplex *, doublecomplex *,
doublecomplex *, integer *, doublereal *, doublecomplex *,
integer *);
extern doublereal zlangt_(char *, integer *, doublecomplex *,
doublecomplex *, doublecomplex *);
extern /* Subroutine */ int zlacpy_(char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *);
extern doublereal dzasum_(integer *, doublecomplex *, integer *);
extern /* Subroutine */ int zlaset_(char *, integer *, integer *,
doublecomplex *, doublecomplex *, doublecomplex *, integer *), zlatms_(integer *, integer *, char *, integer *, char *,
doublereal *, integer *, doublereal *, doublereal *, integer *,
integer *, char *, doublecomplex *, integer *, doublecomplex *,
integer *), zlarnv_(integer *, integer *,
integer *, doublecomplex *);
static doublereal result[6];
extern /* Subroutine */ int zgttrf_(integer *, doublecomplex *,
doublecomplex *, doublecomplex *, doublecomplex *, integer *,
integer *), zgttrs_(char *, integer *, integer *, doublecomplex *,
doublecomplex *, doublecomplex *, doublecomplex *, integer *,
doublecomplex *, integer *, integer *), zerrvx_(char *,
integer *), zgtsvx_(char *, char *, integer *, integer *,
doublecomplex *, doublecomplex *, doublecomplex *, doublecomplex *
, doublecomplex *, doublecomplex *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublereal *, doublereal *, doublereal *, doublecomplex *,
doublereal *, integer *);
static integer lda;
/* Fortran I/O blocks */
static cilist io___42 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___46 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___47 = { 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
September 30, 1994
Purpose
=======
ZDRVGT tests ZGTSV 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.
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.
A (workspace) COMPLEX*16 array, dimension (NMAX*4)
AF (workspace) COMPLEX*16 array, dimension (NMAX*4)
B (workspace) COMPLEX*16 array, dimension (NMAX*NRHS)
X (workspace) COMPLEX*16 array, dimension (NMAX*NRHS)
XACT (workspace) COMPLEX*16 array, dimension (NMAX*NRHS)
WORK (workspace) COMPLEX*16 array, dimension
(NMAX*max(3,NRHS))
RWORK (workspace) DOUBLE PRECISION array, dimension (NMAX+2*NRHS)
IWORK (workspace) INTEGER array, dimension (2*NMAX)
NOUT (input) INTEGER
The unit number for output.
=====================================================================
Parameter adjustments */
--iwork;
--rwork;
--work;
--xact;
--x;
--b;
--af;
--a;
--nval;
--dotype;
/* Function Body */
s_copy(path, "Zomplex precision", (ftnlen)1, (ftnlen)17);
s_copy(path + 1, "GT", (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) {
zerrvx_(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];
/* Computing MAX */
i__2 = n - 1;
m = max(i__2,0);
lda = max(1,n);
nimat = 12;
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;
}
/* Set up parameters with ZLATB4. */
zlatb4_(path, &imat, &n, &n, type__, &kl, &ku, &anorm, &mode, &
cond, dist);
zerot = imat >= 8 && imat <= 10;
if (imat <= 6) {
/* Types 1-6: generate matrices of known condition number.
Computing MAX */
i__3 = 2 - ku, i__4 = 3 - max(1,n);
koff = max(i__3,i__4);
s_copy(srnamc_1.srnamt, "ZLATMS", (ftnlen)6, (ftnlen)6);
zlatms_(&n, &n, dist, iseed, type__, &rwork[1], &mode, &cond,
&anorm, &kl, &ku, "Z", &af[koff], &c__3, &work[1], &
info);
/* Check the error code from ZLATMS. */
if (info != 0) {
alaerh_(path, "ZLATMS", &info, &c__0, " ", &n, &n, &kl, &
ku, &c_n1, &imat, &nfail, &nerrs, nout);
goto L130;
}
izero = 0;
if (n > 1) {
i__3 = n - 1;
zcopy_(&i__3, &af[4], &c__3, &a[1], &c__1);
i__3 = n - 1;
zcopy_(&i__3, &af[3], &c__3, &a[n + m + 1], &c__1);
}
zcopy_(&n, &af[2], &c__3, &a[m + 1], &c__1);
} else {
/* Types 7-12: generate tridiagonal matrices with
unknown condition numbers. */
if (! zerot || ! dotype[7]) {
/* Generate a matrix with elements from [-1,1]. */
i__3 = n + (m << 1);
zlarnv_(&c__2, iseed, &i__3, &a[1]);
if (anorm != 1.) {
i__3 = n + (m << 1);
zdscal_(&i__3, &anorm, &a[1], &c__1);
}
} else if (izero > 0) {
/* Reuse the last matrix by copying back the zeroed out
elements. */
if (izero == 1) {
i__3 = n;
a[i__3].r = z__[1], a[i__3].i = 0.;
if (n > 1) {
a[1].r = z__[2], a[1].i = 0.;
}
} else if (izero == n) {
i__3 = n * 3 - 2;
a[i__3].r = z__[0], a[i__3].i = 0.;
i__3 = (n << 1) - 1;
a[i__3].r = z__[1], a[i__3].i = 0.;
} else {
i__3 = (n << 1) - 2 + izero;
a[i__3].r = z__[0], a[i__3].i = 0.;
i__3 = n - 1 + izero;
a[i__3].r = z__[1], a[i__3].i = 0.;
i__3 = izero;
a[i__3].r = z__[2], a[i__3].i = 0.;
}
}
/* If IMAT > 7, set one column of the matrix to 0. */
if (! zerot) {
izero = 0;
} else if (imat == 8) {
izero = 1;
i__3 = n;
z__[1] = a[i__3].r;
i__3 = n;
a[i__3].r = 0., a[i__3].i = 0.;
if (n > 1) {
z__[2] = a[1].r;
a[1].r = 0., a[1].i = 0.;
}
} else if (imat == 9) {
izero = n;
i__3 = n * 3 - 2;
z__[0] = a[i__3].r;
i__3 = (n << 1) - 1;
z__[1] = a[i__3].r;
i__3 = n * 3 - 2;
a[i__3].r = 0., a[i__3].i = 0.;
i__3 = (n << 1) - 1;
a[i__3].r = 0., a[i__3].i = 0.;
} else {
izero = (n + 1) / 2;
i__3 = n - 1;
for (i__ = izero; i__ <= i__3; ++i__) {
i__4 = (n << 1) - 2 + i__;
a[i__4].r = 0., a[i__4].i = 0.;
i__4 = n - 1 + i__;
a[i__4].r = 0., a[i__4].i = 0.;
i__4 = i__;
a[i__4].r = 0., a[i__4].i = 0.;
/* L20: */
}
i__3 = n * 3 - 2;
a[i__3].r = 0., a[i__3].i = 0.;
i__3 = (n << 1) - 1;
a[i__3].r = 0., a[i__3].i = 0.;
}
}
for (ifact = 1; ifact <= 2; ++ifact) {
if (ifact == 1) {
*(unsigned char *)fact = 'F';
} else {
*(unsigned char *)fact = 'N';
}
/* Compute the condition number for comparison with
the value returned by ZGTSVX. */
if (zerot) {
if (ifact == 1) {
goto L120;
}
rcondo = 0.;
rcondi = 0.;
} else if (ifact == 1) {
i__3 = n + (m << 1);
zcopy_(&i__3, &a[1], &c__1, &af[1], &c__1);
/* Compute the 1-norm and infinity-norm of A. */
anormo = zlangt_("1", &n, &a[1], &a[m + 1], &a[n + m + 1]);
anormi = zlangt_("I", &n, &a[1], &a[m + 1], &a[n + m + 1]);
/* Factor the matrix A. */
zgttrf_(&n, &af[1], &af[m + 1], &af[n + m + 1], &af[n + (
m << 1) + 1], &iwork[1], &info);
/* Use ZGTTRS to solve for one column at a time of
inv(A), computing the maximum column sum as we go. */
ainvnm = 0.;
i__3 = n;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = n;
for (j = 1; j <= i__4; ++j) {
i__5 = j;
x[i__5].r = 0., x[i__5].i = 0.;
/* L30: */
}
i__4 = i__;
x[i__4].r = 1., x[i__4].i = 0.;
zgttrs_("No transpose", &n, &c__1, &af[1], &af[m + 1],
&af[n + m + 1], &af[n + (m << 1) + 1], &
iwork[1], &x[1], &lda, &info);
/* Computing MAX */
d__1 = ainvnm, d__2 = dzasum_(&n, &x[1], &c__1);
ainvnm = max(d__1,d__2);
/* L40: */
}
/* Compute the 1-norm condition number of A. */
if (anormo <= 0. || ainvnm <= 0.) {
rcondo = 1.;
} else {
rcondo = 1. / anormo / ainvnm;
}
/* Use ZGTTRS to solve for one column at a time of
inv(A'), computing the maximum column sum as we go. */
ainvnm = 0.;
i__3 = n;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = n;
for (j = 1; j <= i__4; ++j) {
i__5 = j;
x[i__5].r = 0., x[i__5].i = 0.;
/* L50: */
}
i__4 = i__;
x[i__4].r = 1., x[i__4].i = 0.;
zgttrs_("Conjugate transpose", &n, &c__1, &af[1], &af[
m + 1], &af[n + m + 1], &af[n + (m << 1) + 1],
&iwork[1], &x[1], &lda, &info);
/* Computing MAX */
d__1 = ainvnm, d__2 = dzasum_(&n, &x[1], &c__1);
ainvnm = max(d__1,d__2);
/* L60: */
}
/* Compute the infinity-norm condition number of A. */
if (anormi <= 0. || ainvnm <= 0.) {
rcondi = 1.;
} else {
rcondi = 1. / anormi / ainvnm;
}
}
for (itran = 1; itran <= 3; ++itran) {
*(unsigned char *)trans = *(unsigned char *)&transs[itran
- 1];
if (itran == 1) {
rcondc = rcondo;
} else {
rcondc = rcondi;
}
/* Generate NRHS random solution vectors. */
ix = 1;
i__3 = *nrhs;
for (j = 1; j <= i__3; ++j) {
zlarnv_(&c__2, iseed, &n, &xact[ix]);
ix += lda;
/* L70: */
}
/* Set the right hand side. */
zlagtm_(trans, &n, nrhs, &c_b43, &a[1], &a[m + 1], &a[n +
m + 1], &xact[1], &lda, &c_b44, &b[1], &lda);
if (ifact == 2 && itran == 1) {
/* --- Test ZGTSV ---
Solve the system using Gaussian elimination with
partial pivoting. */
i__3 = n + (m << 1);
zcopy_(&i__3, &a[1], &c__1, &af[1], &c__1);
zlacpy_("Full", &n, nrhs, &b[1], &lda, &x[1], &lda);
s_copy(srnamc_1.srnamt, "ZGTSV ", (ftnlen)6, (ftnlen)
6);
zgtsv_(&n, nrhs, &af[1], &af[m + 1], &af[n + m + 1], &
x[1], &lda, &info);
/* Check error code from ZGTSV . */
if (info != izero) {
alaerh_(path, "ZGTSV ", &info, &izero, " ", &n, &
n, &c__1, &c__1, nrhs, &imat, &nfail, &
nerrs, nout);
}
nt = 1;
if (izero == 0) {
/* Check residual of computed solution. */
zlacpy_("Full", &n, nrhs, &b[1], &lda, &work[1], &
lda);
zgtt02_(trans, &n, nrhs, &a[1], &a[m + 1], &a[n +
m + 1], &x[1], &lda, &work[1], &lda, &
rwork[1], &result[1]);
/* Check solution from generated exact solution. */
zget04_(&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__3 = nt;
for (k = 2; k <= i__3; ++k) {
if (result[k - 1] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
aladhd_(nout, path);
}
io___42.ciunit = *nout;
s_wsfe(&io___42);
do_fio(&c__1, "ZGTSV ", (ftnlen)6);
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;
}
/* L80: */
}
nrun = nrun + nt - 1;
}
/* --- Test ZGTSVX --- */
if (ifact > 1) {
/* Initialize AF to zero. */
i__3 = n * 3 - 2;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = i__;
af[i__4].r = 0., af[i__4].i = 0.;
/* L90: */
}
}
zlaset_("Full", &n, nrhs, &c_b65, &c_b65, &x[1], &lda);
/* Solve the system and compute the condition number and
error bounds using ZGTSVX. */
s_copy(srnamc_1.srnamt, "ZGTSVX", (ftnlen)6, (ftnlen)6);
zgtsvx_(fact, trans, &n, nrhs, &a[1], &a[m + 1], &a[n + m
+ 1], &af[1], &af[m + 1], &af[n + m + 1], &af[n +
(m << 1) + 1], &iwork[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 ZGTSVX. */
if (info != izero) {
/* Writing concatenation */
i__6[0] = 1, a__1[0] = fact;
i__6[1] = 1, a__1[1] = trans;
s_cat(ch__1, a__1, i__6, &c__2, (ftnlen)2);
alaerh_(path, "ZGTSVX", &info, &izero, ch__1, &n, &n,
&c__1, &c__1, nrhs, &imat, &nfail, &nerrs,
nout);
}
if (ifact >= 2) {
/* Reconstruct matrix from factors and compute
residual. */
zgtt01_(&n, &a[1], &a[m + 1], &a[n + m + 1], &af[1], &
af[m + 1], &af[n + m + 1], &af[n + (m << 1) +
1], &iwork[1], &work[1], &lda, &rwork[1],
result);
k1 = 1;
} else {
k1 = 2;
}
if (info == 0) {
trfcon = FALSE_;
/* Check residual of computed solution. */
zlacpy_("Full", &n, nrhs, &b[1], &lda, &work[1], &lda);
zgtt02_(trans, &n, nrhs, &a[1], &a[m + 1], &a[n + m +
1], &x[1], &lda, &work[1], &lda, &rwork[1], &
result[1]);
/* Check solution from generated exact solution. */
zget04_(&n, nrhs, &x[1], &lda, &xact[1], &lda, &
rcondc, &result[2]);
/* Check the error bounds from iterative refinement. */
zgtt05_(trans, &n, nrhs, &a[1], &a[m + 1], &a[n + m +
1], &b[1], &lda, &x[1], &lda, &xact[1], &lda,
&rwork[1], &rwork[*nrhs + 1], &result[3]);
nt = 5;
}
/* Print information about the tests that did not pass
the threshold. */
i__3 = nt;
for (k = k1; k <= i__3; ++k) {
if (result[k - 1] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
aladhd_(nout, path);
}
io___46.ciunit = *nout;
s_wsfe(&io___46);
do_fio(&c__1, "ZGTSVX", (ftnlen)6);
do_fio(&c__1, fact, (ftnlen)1);
do_fio(&c__1, trans, (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;
}
/* L100: */
}
/* Check the reciprocal of the condition number. */
result[5] = dget06_(&rcond, &rcondc);
if (result[5] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
aladhd_(nout, path);
}
io___47.ciunit = *nout;
s_wsfe(&io___47);
do_fio(&c__1, "ZGTSVX", (ftnlen)6);
do_fio(&c__1, fact, (ftnlen)1);
do_fio(&c__1, trans, (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;
}
nrun = nrun + nt - k1 + 2;
/* L110: */
}
L120:
;
}
L130:
;
}
/* L140: */
}
/* Print a summary of the results. */
alasvm_(path, nout, &nfail, &nrun, &nerrs);
return 0;
/* End of ZDRVGT */
} /* zdrvgt_ */