/* Subroutine */ int dsgesv_(integer *n, integer *nrhs, doublereal *a,
integer *lda, integer *ipiv, doublereal *b, integer *ldb, doublereal *
x, integer *ldx, doublereal *work, real *swork, integer *iter,
integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, work_dim1, work_offset,
x_dim1, x_offset, i__1;
doublereal d__1;
/* Local variables */
integer i__;
doublereal cte, eps, anrm;
integer ptsa;
doublereal rnrm, xnrm;
integer ptsx;
integer iiter;
/* -- LAPACK PROTOTYPE driver routine (version 3.2) -- */
/* February 2007 */
/* Purpose */
/* ======= */
/* DSGESV computes the solution to a real system of linear equations */
/* A * X = B, */
/* where A is an N-by-N matrix and X and B are N-by-NRHS matrices. */
/* DSGESV first attempts to factorize the matrix in SINGLE PRECISION */
/* and use this factorization within an iterative refinement procedure */
/* to produce a solution with DOUBLE PRECISION normwise backward error */
/* quality (see below). If the approach fails the method switches to a */
/* DOUBLE PRECISION factorization and solve. */
/* The iterative refinement is not going to be a winning strategy if */
/* the ratio SINGLE PRECISION performance over DOUBLE PRECISION */
/* performance is too small. A reasonable strategy should take the */
/* number of right-hand sides and the size of the matrix into account. */
/* This might be done with a call to ILAENV in the future. Up to now, we */
/* always try iterative refinement. */
/* The iterative refinement process is stopped if */
/* ITER > ITERMAX */
/* or for all the RHS we have: */
/* RNRM < SQRT(N)*XNRM*ANRM*EPS*BWDMAX */
/* where */
/* o ITER is the number of the current iteration in the iterative */
/* refinement process */
/* o RNRM is the infinity-norm of the residual */
/* o XNRM is the infinity-norm of the solution */
/* o ANRM is the infinity-operator-norm of the matrix A */
/* o EPS is the machine epsilon returned by DLAMCH('Epsilon') */
/* The value ITERMAX and BWDMAX are fixed to 30 and 1.0D+00 */
/* respectively. */
/* Arguments */
/* ========= */
/* N (input) INTEGER */
/* The number of linear equations, i.e., the order of the */
/* matrix A. N >= 0. */
/* NRHS (input) INTEGER */
/* The number of right hand sides, i.e., the number of columns */
/* of the matrix B. NRHS >= 0. */
/* A (input or input/ouptut) DOUBLE PRECISION array, */
/* dimension (LDA,N) */
/* On entry, the N-by-N coefficient matrix A. */
/* On exit, if iterative refinement has been successfully used */
/* (INFO.EQ.0 and ITER.GE.0, see description below), then A is */
/* unchanged, if double precision factorization has been used */
/* (INFO.EQ.0 and ITER.LT.0, see description below), then the */
/* array A contains the factors L and U from the factorization */
/* A = P*L*U; the unit diagonal elements of L are not stored. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,N). */
/* IPIV (output) INTEGER array, dimension (N) */
/* The pivot indices that define the permutation matrix P; */
/* row i of the matrix was interchanged with row IPIV(i). */
/* Corresponds either to the single precision factorization */
/* (if INFO.EQ.0 and ITER.GE.0) or the double precision */
/* factorization (if INFO.EQ.0 and ITER.LT.0). */
/* B (input) DOUBLE PRECISION 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) DOUBLE PRECISION 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). */
/* WORK (workspace) DOUBLE PRECISION array, dimension (N*NRHS) */
/* This array is used to hold the residual vectors. */
/* SWORK (workspace) REAL array, dimension (N*(N+NRHS)) */
/* This array is used to use the single precision matrix and the */
/* right-hand sides or solutions in single precision. */
/* ITER (output) INTEGER */
/* < 0: iterative refinement has failed, double precision */
/* factorization has been performed */
/* -1 : the routine fell back to full precision for */
/* implementation- or machine-specific reasons */
/* -2 : narrowing the precision induced an overflow, */
/* the routine fell back to full precision */
/* -3 : failure of SGETRF */
/* -31: stop the iterative refinement after the 30th */
/* iterations */
/* > 0: iterative refinement has been sucessfully used. */
/* Returns the number of iterations */
/* 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) computed in DOUBLE PRECISION is */
/* exactly zero. The factorization has been completed, */
/* but the factor U is exactly singular, so the solution */
/* could not be computed. */
/* ========= */
/* Parameter adjustments */
work_dim1 = *n;
work_offset = 1 + work_dim1;
work -= work_offset;
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--ipiv;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
x_dim1 = *ldx;
x_offset = 1 + x_dim1;
x -= x_offset;
--swork;
/* Function Body */
*info = 0;
*iter = 0;
/* Test the input parameters. */
if (*n < 0) {
*info = -1;
} else if (*nrhs < 0) {
*info = -2;
} else if (*lda < max(1,*n)) {
*info = -4;
} else if (*ldb < max(1,*n)) {
*info = -7;
} else if (*ldx < max(1,*n)) {
*info = -9;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("DSGESV", &i__1);
return 0;
}
/* Quick return if (N.EQ.0). */
if (*n == 0) {
return 0;
}
/* Skip single precision iterative refinement if a priori slower */
/* than double precision factorization. */
if (FALSE_) {
*iter = -1;
goto L40;
}
/* Compute some constants. */
anrm = dlange_("I", n, n, &a[a_offset], lda, &work[work_offset]);
eps = dlamch_("Epsilon");
cte = anrm * eps * sqrt((doublereal) (*n)) * 1.;
/* Set the indices PTSA, PTSX for referencing SA and SX in SWORK. */
ptsa = 1;
ptsx = ptsa + *n * *n;
/* Convert B from double precision to single precision and store the */
/* result in SX. */
dlag2s_(n, nrhs, &b[b_offset], ldb, &swork[ptsx], n, info);
if (*info != 0) {
*iter = -2;
goto L40;
}
/* Convert A from double precision to single precision and store the */
/* result in SA. */
dlag2s_(n, n, &a[a_offset], lda, &swork[ptsa], n, info);
if (*info != 0) {
*iter = -2;
goto L40;
}
/* Compute the LU factorization of SA. */
sgetrf_(n, n, &swork[ptsa], n, &ipiv[1], info);
if (*info != 0) {
*iter = -3;
goto L40;
}
/* Solve the system SA*SX = SB. */
sgetrs_("No transpose", n, nrhs, &swork[ptsa], n, &ipiv[1], &swork[ptsx],
n, info);
/* Convert SX back to double precision */
slag2d_(n, nrhs, &swork[ptsx], n, &x[x_offset], ldx, info);
/* Compute R = B - AX (R is WORK). */
dlacpy_("All", n, nrhs, &b[b_offset], ldb, &work[work_offset], n);
dgemm_("No Transpose", "No Transpose", n, nrhs, n, &c_b10, &a[a_offset],
lda, &x[x_offset], ldx, &c_b11, &work[work_offset], n);
/* Check whether the NRHS normwise backward errors satisfy the */
/* stopping criterion. If yes, set ITER=0 and return. */
i__1 = *nrhs;
for (i__ = 1; i__ <= i__1; ++i__) {
xnrm = (d__1 = x[idamax_(n, &x[i__ * x_dim1 + 1], &c__1) + i__ *
x_dim1], abs(d__1));
rnrm = (d__1 = work[idamax_(n, &work[i__ * work_dim1 + 1], &c__1) +
i__ * work_dim1], abs(d__1));
if (rnrm > xnrm * cte) {
goto L10;
}
}
/* If we are here, the NRHS normwise backward errors satisfy the */
/* stopping criterion. We are good to exit. */
*iter = 0;
return 0;
L10:
for (iiter = 1; iiter <= 30; ++iiter) {
/* Convert R (in WORK) from double precision to single precision */
/* and store the result in SX. */
dlag2s_(n, nrhs, &work[work_offset], n, &swork[ptsx], n, info);
if (*info != 0) {
*iter = -2;
goto L40;
}
/* Solve the system SA*SX = SR. */
sgetrs_("No transpose", n, nrhs, &swork[ptsa], n, &ipiv[1], &swork[
ptsx], n, info);
/* Convert SX back to double precision and update the current */
/* iterate. */
slag2d_(n, nrhs, &swork[ptsx], n, &work[work_offset], n, info);
i__1 = *nrhs;
for (i__ = 1; i__ <= i__1; ++i__) {
daxpy_(n, &c_b11, &work[i__ * work_dim1 + 1], &c__1, &x[i__ *
x_dim1 + 1], &c__1);
}
/* Compute R = B - AX (R is WORK). */
dlacpy_("All", n, nrhs, &b[b_offset], ldb, &work[work_offset], n);
dgemm_("No Transpose", "No Transpose", n, nrhs, n, &c_b10, &a[
a_offset], lda, &x[x_offset], ldx, &c_b11, &work[work_offset],
n);
/* Check whether the NRHS normwise backward errors satisfy the */
/* stopping criterion. If yes, set ITER=IITER>0 and return. */
i__1 = *nrhs;
for (i__ = 1; i__ <= i__1; ++i__) {
xnrm = (d__1 = x[idamax_(n, &x[i__ * x_dim1 + 1], &c__1) + i__ *
x_dim1], abs(d__1));
rnrm = (d__1 = work[idamax_(n, &work[i__ * work_dim1 + 1], &c__1)
+ i__ * work_dim1], abs(d__1));
if (rnrm > xnrm * cte) {
goto L20;
}
}
/* If we are here, the NRHS normwise backward errors satisfy the */
/* stopping criterion, we are good to exit. */
*iter = iiter;
return 0;
L20:
;
}
/* If we are at this place of the code, this is because we have */
/* performed ITER=ITERMAX iterations and never satisified the */
/* stopping criterion, set up the ITER flag accordingly and follow up */
/* on double precision routine. */
*iter = -31;
L40:
/* Single-precision iterative refinement failed to converge to a */
/* satisfactory solution, so we resort to double precision. */
dgetrf_(n, n, &a[a_offset], lda, &ipiv[1], info);
if (*info != 0) {
return 0;
}
dlacpy_("All", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx);
dgetrs_("No transpose", n, nrhs, &a[a_offset], lda, &ipiv[1], &x[x_offset]
, ldx, info);
return 0;
/* End of DSGESV. */
} /* dsgesv_ */
/* Subroutine */
int dsposv_(char *uplo, integer *n, integer *nrhs, doublereal *a, integer *lda, doublereal *b, integer *ldb, doublereal * x, integer *ldx, doublereal *work, real *swork, integer *iter, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, work_dim1, work_offset, x_dim1, x_offset, i__1;
doublereal d__1;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
integer i__;
doublereal cte, eps, anrm;
integer ptsa;
doublereal rnrm, xnrm;
integer ptsx;
extern logical lsame_(char *, char *);
integer iiter;
extern /* Subroutine */
int daxpy_(integer *, doublereal *, doublereal *, integer *, doublereal *, integer *), dsymm_(char *, char *, integer *, integer *, doublereal *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *), dlag2s_(integer *, integer *, doublereal *, integer *, real *, integer *, integer *), slag2d_(integer *, integer *, real *, integer *, doublereal *, integer *, integer *), dlat2s_(char *, integer *, doublereal *, integer *, real *, integer *, integer *);
extern doublereal dlamch_(char *);
extern integer idamax_(integer *, doublereal *, integer *);
extern /* Subroutine */
int dlacpy_(char *, integer *, integer *, doublereal *, integer *, doublereal *, integer *), xerbla_(char *, integer *);
extern doublereal dlansy_(char *, char *, integer *, doublereal *, integer *, doublereal *);
extern /* Subroutine */
int dpotrf_(char *, integer *, doublereal *, integer *, integer *), dpotrs_(char *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, integer *), spotrf_(char *, integer *, real *, integer *, integer *), spotrs_(char *, integer *, integer *, real *, integer *, real *, integer *, integer *);
/* -- LAPACK driver routine (version 3.4.0) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* November 2011 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. Local Scalars .. */
/* .. External Subroutines .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
work_dim1 = *n;
work_offset = 1 + work_dim1;
work -= work_offset;
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
x_dim1 = *ldx;
x_offset = 1 + x_dim1;
x -= x_offset;
--swork;
/* Function Body */
*info = 0;
*iter = 0;
/* Test the input parameters. */
if (! lsame_(uplo, "U") && ! lsame_(uplo, "L"))
{
*info = -1;
}
else if (*n < 0)
{
*info = -2;
}
else if (*nrhs < 0)
{
*info = -3;
}
else if (*lda < max(1,*n))
{
*info = -5;
}
else if (*ldb < max(1,*n))
{
*info = -7;
}
else if (*ldx < max(1,*n))
{
*info = -9;
}
if (*info != 0)
{
i__1 = -(*info);
xerbla_("DSPOSV", &i__1);
return 0;
}
/* Quick return if (N.EQ.0). */
if (*n == 0)
{
return 0;
}
/* Skip single precision iterative refinement if a priori slower */
/* than double precision factorization. */
if (FALSE_)
{
*iter = -1;
goto L40;
}
/* Compute some constants. */
anrm = dlansy_("I", uplo, n, &a[a_offset], lda, &work[work_offset]);
eps = dlamch_("Epsilon");
cte = anrm * eps * sqrt((doublereal) (*n)) * 1.;
/* Set the indices PTSA, PTSX for referencing SA and SX in SWORK. */
ptsa = 1;
ptsx = ptsa + *n * *n;
/* Convert B from double precision to single precision and store the */
/* result in SX. */
dlag2s_(n, nrhs, &b[b_offset], ldb, &swork[ptsx], n, info);
if (*info != 0)
{
*iter = -2;
goto L40;
}
/* Convert A from double precision to single precision and store the */
/* result in SA. */
dlat2s_(uplo, n, &a[a_offset], lda, &swork[ptsa], n, info);
if (*info != 0)
{
*iter = -2;
goto L40;
}
/* Compute the Cholesky factorization of SA. */
spotrf_(uplo, n, &swork[ptsa], n, info);
if (*info != 0)
{
*iter = -3;
goto L40;
}
/* Solve the system SA*SX = SB. */
spotrs_(uplo, n, nrhs, &swork[ptsa], n, &swork[ptsx], n, info);
/* Convert SX back to double precision */
slag2d_(n, nrhs, &swork[ptsx], n, &x[x_offset], ldx, info);
/* Compute R = B - AX (R is WORK). */
dlacpy_("All", n, nrhs, &b[b_offset], ldb, &work[work_offset], n);
dsymm_("Left", uplo, n, nrhs, &c_b10, &a[a_offset], lda, &x[x_offset], ldx, &c_b11, &work[work_offset], n);
/* Check whether the NRHS normwise backward errors satisfy the */
/* stopping criterion. If yes, set ITER=0 and return. */
i__1 = *nrhs;
for (i__ = 1;
i__ <= i__1;
++i__)
{
xnrm = (d__1 = x[idamax_(n, &x[i__ * x_dim1 + 1], &c__1) + i__ * x_dim1], f2c_abs(d__1));
rnrm = (d__1 = work[idamax_(n, &work[i__ * work_dim1 + 1], &c__1) + i__ * work_dim1], f2c_abs(d__1));
if (rnrm > xnrm * cte)
{
goto L10;
}
}
/* If we are here, the NRHS normwise backward errors satisfy the */
/* stopping criterion. We are good to exit. */
*iter = 0;
return 0;
L10:
for (iiter = 1;
iiter <= 30;
++iiter)
{
/* Convert R (in WORK) from double precision to single precision */
/* and store the result in SX. */
dlag2s_(n, nrhs, &work[work_offset], n, &swork[ptsx], n, info);
if (*info != 0)
{
*iter = -2;
goto L40;
}
/* Solve the system SA*SX = SR. */
spotrs_(uplo, n, nrhs, &swork[ptsa], n, &swork[ptsx], n, info);
/* Convert SX back to double precision and update the current */
/* iterate. */
slag2d_(n, nrhs, &swork[ptsx], n, &work[work_offset], n, info);
i__1 = *nrhs;
for (i__ = 1;
i__ <= i__1;
++i__)
{
daxpy_(n, &c_b11, &work[i__ * work_dim1 + 1], &c__1, &x[i__ * x_dim1 + 1], &c__1);
}
/* Compute R = B - AX (R is WORK). */
dlacpy_("All", n, nrhs, &b[b_offset], ldb, &work[work_offset], n);
dsymm_("L", uplo, n, nrhs, &c_b10, &a[a_offset], lda, &x[x_offset], ldx, &c_b11, &work[work_offset], n);
/* Check whether the NRHS normwise backward errors satisfy the */
/* stopping criterion. If yes, set ITER=IITER>0 and return. */
i__1 = *nrhs;
for (i__ = 1;
i__ <= i__1;
++i__)
{
xnrm = (d__1 = x[idamax_(n, &x[i__ * x_dim1 + 1], &c__1) + i__ * x_dim1], f2c_abs(d__1));
rnrm = (d__1 = work[idamax_(n, &work[i__ * work_dim1 + 1], &c__1) + i__ * work_dim1], f2c_abs(d__1));
if (rnrm > xnrm * cte)
{
goto L20;
}
}
/* If we are here, the NRHS normwise backward errors satisfy the */
/* stopping criterion, we are good to exit. */
*iter = iiter;
return 0;
L20: /* L30: */
;
}
/* If we are at this place of the code, this is because we have */
/* performed ITER=ITERMAX iterations and never satisified the */
/* stopping criterion, set up the ITER flag accordingly and follow */
/* up on double precision routine. */
*iter = -31;
L40: /* Single-precision iterative refinement failed to converge to a */
/* satisfactory solution, so we resort to double precision. */
dpotrf_(uplo, n, &a[a_offset], lda, info);
if (*info != 0)
{
return 0;
}
dlacpy_("All", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx);
dpotrs_(uplo, n, nrhs, &a[a_offset], lda, &x[x_offset], ldx, info);
return 0;
/* End of DSPOSV. */
}
