int main(void)
{
/* Local scalars */
char uplo, uplo_i;
lapack_int n, n_i;
lapack_int lda, lda_i;
lapack_int lda_r;
lapack_int lwork, lwork_i;
lapack_int info, info_i;
lapack_int i;
int failed;
/* Local arrays */
float *a = NULL, *a_i = NULL;
lapack_int *ipiv = NULL, *ipiv_i = NULL;
float *work = NULL, *work_i = NULL;
float *a_save = NULL;
lapack_int *ipiv_save = NULL;
float *a_r = NULL;
/* Iniitialize the scalar parameters */
init_scalars_ssytrf( &uplo, &n, &lda, &lwork );
lda_r = n+2;
uplo_i = uplo;
n_i = n;
lda_i = lda;
lwork_i = lwork;
/* Allocate memory for the LAPACK routine arrays */
a = (float *)LAPACKE_malloc( lda*n * sizeof(float) );
ipiv = (lapack_int *)LAPACKE_malloc( n * sizeof(lapack_int) );
work = (float *)LAPACKE_malloc( lwork * sizeof(float) );
/* Allocate memory for the C interface function arrays */
a_i = (float *)LAPACKE_malloc( lda*n * sizeof(float) );
ipiv_i = (lapack_int *)LAPACKE_malloc( n * sizeof(lapack_int) );
work_i = (float *)LAPACKE_malloc( lwork * sizeof(float) );
/* Allocate memory for the backup arrays */
a_save = (float *)LAPACKE_malloc( lda*n * sizeof(float) );
ipiv_save = (lapack_int *)LAPACKE_malloc( n * sizeof(lapack_int) );
/* Allocate memory for the row-major arrays */
a_r = (float *)LAPACKE_malloc( n*(n+2) * sizeof(float) );
/* Initialize input arrays */
init_a( lda*n, a );
init_ipiv( n, ipiv );
init_work( lwork, work );
/* Backup the ouptut arrays */
for( i = 0; i < lda*n; i++ ) {
a_save[i] = a[i];
}
for( i = 0; i < n; i++ ) {
ipiv_save[i] = ipiv[i];
}
/* Call the LAPACK routine */
ssytrf_( &uplo, &n, a, &lda, ipiv, work, &lwork, &info );
/* Initialize input data, call the column-major middle-level
* interface to LAPACK routine and check the results */
for( i = 0; i < lda*n; i++ ) {
a_i[i] = a_save[i];
}
for( i = 0; i < n; i++ ) {
ipiv_i[i] = ipiv_save[i];
}
for( i = 0; i < lwork; i++ ) {
work_i[i] = work[i];
}
info_i = LAPACKE_ssytrf_work( LAPACK_COL_MAJOR, uplo_i, n_i, a_i, lda_i,
ipiv_i, work_i, lwork_i );
failed = compare_ssytrf( a, a_i, ipiv, ipiv_i, info, info_i, lda, n );
if( failed == 0 ) {
printf( "PASSED: column-major middle-level interface to ssytrf\n" );
} else {
printf( "FAILED: column-major middle-level interface to ssytrf\n" );
}
/* Initialize input data, call the column-major high-level
* interface to LAPACK routine and check the results */
for( i = 0; i < lda*n; i++ ) {
a_i[i] = a_save[i];
}
for( i = 0; i < n; i++ ) {
ipiv_i[i] = ipiv_save[i];
}
for( i = 0; i < lwork; i++ ) {
work_i[i] = work[i];
}
info_i = LAPACKE_ssytrf( LAPACK_COL_MAJOR, uplo_i, n_i, a_i, lda_i,
ipiv_i );
failed = compare_ssytrf( a, a_i, ipiv, ipiv_i, info, info_i, lda, n );
if( failed == 0 ) {
printf( "PASSED: column-major high-level interface to ssytrf\n" );
} else {
printf( "FAILED: column-major high-level interface to ssytrf\n" );
}
/* Initialize input data, call the row-major middle-level
* interface to LAPACK routine and check the results */
for( i = 0; i < lda*n; i++ ) {
a_i[i] = a_save[i];
}
for( i = 0; i < n; i++ ) {
ipiv_i[i] = ipiv_save[i];
}
for( i = 0; i < lwork; i++ ) {
work_i[i] = work[i];
}
LAPACKE_sge_trans( LAPACK_COL_MAJOR, n, n, a_i, lda, a_r, n+2 );
info_i = LAPACKE_ssytrf_work( LAPACK_ROW_MAJOR, uplo_i, n_i, a_r, lda_r,
ipiv_i, work_i, lwork_i );
LAPACKE_sge_trans( LAPACK_ROW_MAJOR, n, n, a_r, n+2, a_i, lda );
failed = compare_ssytrf( a, a_i, ipiv, ipiv_i, info, info_i, lda, n );
if( failed == 0 ) {
printf( "PASSED: row-major middle-level interface to ssytrf\n" );
} else {
printf( "FAILED: row-major middle-level interface to ssytrf\n" );
}
/* Initialize input data, call the row-major high-level
* interface to LAPACK routine and check the results */
for( i = 0; i < lda*n; i++ ) {
a_i[i] = a_save[i];
}
for( i = 0; i < n; i++ ) {
ipiv_i[i] = ipiv_save[i];
}
for( i = 0; i < lwork; i++ ) {
work_i[i] = work[i];
}
/* Init row_major arrays */
LAPACKE_sge_trans( LAPACK_COL_MAJOR, n, n, a_i, lda, a_r, n+2 );
info_i = LAPACKE_ssytrf( LAPACK_ROW_MAJOR, uplo_i, n_i, a_r, lda_r,
ipiv_i );
LAPACKE_sge_trans( LAPACK_ROW_MAJOR, n, n, a_r, n+2, a_i, lda );
failed = compare_ssytrf( a, a_i, ipiv, ipiv_i, info, info_i, lda, n );
if( failed == 0 ) {
printf( "PASSED: row-major high-level interface to ssytrf\n" );
} else {
printf( "FAILED: row-major high-level interface to ssytrf\n" );
}
/* Release memory */
if( a != NULL ) {
LAPACKE_free( a );
}
if( a_i != NULL ) {
LAPACKE_free( a_i );
}
if( a_r != NULL ) {
LAPACKE_free( a_r );
}
if( a_save != NULL ) {
LAPACKE_free( a_save );
}
if( ipiv != NULL ) {
LAPACKE_free( ipiv );
}
if( ipiv_i != NULL ) {
LAPACKE_free( ipiv_i );
}
if( ipiv_save != NULL ) {
LAPACKE_free( ipiv_save );
}
if( work != NULL ) {
LAPACKE_free( work );
}
if( work_i != NULL ) {
LAPACKE_free( work_i );
}
return 0;
}
/* Subroutine */ int ssysvx_(char *fact, char *uplo, integer *n, integer *
nrhs, real *a, integer *lda, real *af, integer *ldaf, integer *ipiv,
real *b, integer *ldb, real *x, integer *ldx, real *rcond, real *ferr,
real *berr, real *work, integer *lwork, integer *iwork, integer *
info)
{
/* System generated locals */
integer a_dim1, a_offset, af_dim1, af_offset, b_dim1, b_offset, x_dim1,
x_offset, i__1, i__2;
/* Local variables */
integer nb;
real anorm;
logical nofact;
integer lwkopt;
logical lquery;
/* -- LAPACK driver routine (version 3.2) -- */
/* November 2006 */
/* Purpose */
/* ======= */
/* SSYSVX uses the diagonal pivoting factorization to compute the */
/* solution to a real system of linear equations A * X = B, */
/* where A is an N-by-N symmetric matrix and X and B are N-by-NRHS */
/* matrices. */
/* Error bounds on the solution and a condition estimate are also */
/* provided. */
/* Description */
/* =========== */
/* The following steps are performed: */
/* 1. If FACT = 'N', the diagonal pivoting method is used to factor A. */
/* The form of the factorization is */
/* A = U * D * U**T, if UPLO = 'U', or */
/* A = L * D * L**T, if UPLO = 'L', */
/* where U (or L) is a product of permutation and unit upper (lower) */
/* triangular matrices, and D is symmetric and block diagonal with */
/* 1-by-1 and 2-by-2 diagonal blocks. */
/* 2. If some D(i,i)=0, so that D is exactly singular, then the routine */
/* returns with INFO = i. Otherwise, the factored form of A is used */
/* to estimate the condition number of the matrix A. If the */
/* reciprocal of the condition number is less than machine precision, */
/* INFO = N+1 is returned as a warning, but the routine still goes on */
/* to solve for X and compute error bounds as described below. */
/* 3. The system of equations is solved for X using the factored form */
/* of A. */
/* 4. Iterative refinement is applied to improve the computed solution */
/* matrix and calculate error bounds and backward error estimates */
/* for it. */
/* Arguments */
/* ========= */
/* FACT (input) CHARACTER*1 */
/* Specifies whether or not the factored form of A has been */
/* supplied on entry. */
/* = 'F': On entry, AF and IPIV contain the factored form of */
/* A. AF and IPIV will not be modified. */
/* = 'N': The matrix A will be copied to AF and factored. */
/* UPLO (input) CHARACTER*1 */
/* = 'U': Upper triangle of A is stored; */
/* = 'L': Lower triangle of A is stored. */
/* N (input) INTEGER */
/* The number of linear equations, i.e., the order of the */
/* matrix A. N >= 0. */
/* NRHS (input) INTEGER */
/* The number of right hand sides, i.e., the number of columns */
/* of the matrices B and X. NRHS >= 0. */
/* A (input) REAL array, dimension (LDA,N) */
/* The symmetric matrix A. If UPLO = 'U', the leading N-by-N */
/* upper triangular part of A contains the upper triangular part */
/* of the matrix A, and the strictly lower triangular part of A */
/* is not referenced. If UPLO = 'L', the leading N-by-N lower */
/* triangular part of A contains the lower triangular part of */
/* the matrix A, and the strictly upper triangular part of A is */
/* not referenced. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,N). */
/* AF (input or output) REAL array, dimension (LDAF,N) */
/* If FACT = 'F', then AF is an input argument and on entry */
/* contains the block diagonal matrix D and the multipliers used */
/* to obtain the factor U or L from the factorization */
/* A = U*D*U**T or A = L*D*L**T as computed by SSYTRF. */
/* If FACT = 'N', then AF is an output argument and on exit */
/* returns the block diagonal matrix D and the multipliers used */
/* to obtain the factor U or L from the factorization */
/* A = U*D*U**T or A = L*D*L**T. */
/* LDAF (input) INTEGER */
/* The leading dimension of the array AF. LDAF >= max(1,N). */
/* IPIV (input or output) INTEGER array, dimension (N) */
/* If FACT = 'F', then IPIV is an input argument and on entry */
/* contains details of the interchanges and the block structure */
/* of D, as determined by SSYTRF. */
/* If IPIV(k) > 0, then rows and columns k and IPIV(k) were */
/* interchanged and D(k,k) is a 1-by-1 diagonal block. */
/* If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and */
/* columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) */
/* is a 2-by-2 diagonal block. If UPLO = 'L' and IPIV(k) = */
/* IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were */
/* interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block. */
/* If FACT = 'N', then IPIV is an output argument and on exit */
/* contains details of the interchanges and the block structure */
/* of D, as determined by SSYTRF. */
/* B (input) REAL 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) REAL 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) REAL */
/* 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) REAL 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) REAL 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/output) REAL array, dimension (MAX(1,LWORK)) */
/* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
/* LWORK (input) INTEGER */
/* The length of WORK. LWORK >= max(1,3*N), and for best */
/* performance, when FACT = 'N', LWORK >= max(1,3*N,N*NB), where */
/* NB is the optimal blocksize for SSYTRF. */
/* 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. */
/* IWORK (workspace) INTEGER array, dimension (N) */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* > 0: if INFO = i, and i is */
/* <= N: D(i,i) is exactly zero. The factorization */
/* has been completed but the factor D is exactly */
/* singular, so the solution and error bounds could */
/* not be computed. RCOND = 0 is returned. */
/* = N+1: D is nonsingular, but RCOND is less than machine */
/* precision, meaning that the matrix is singular */
/* to working precision. Nevertheless, the */
/* solution and error bounds are computed because */
/* there are a number of situations where the */
/* computed solution can be more accurate than the */
/* value of RCOND would suggest. */
/* ===================================================================== */
/* Test the input parameters. */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
af_dim1 = *ldaf;
af_offset = 1 + af_dim1;
af -= af_offset;
--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;
--iwork;
/* Function Body */
*info = 0;
nofact = lsame_(fact, "N");
lquery = *lwork == -1;
if (! nofact && ! lsame_(fact, "F")) {
*info = -1;
} else if (! lsame_(uplo, "U") && ! lsame_(uplo,
"L")) {
*info = -2;
} else if (*n < 0) {
*info = -3;
} else if (*nrhs < 0) {
*info = -4;
} else if (*lda < max(1,*n)) {
*info = -6;
} else if (*ldaf < max(1,*n)) {
*info = -8;
} else if (*ldb < max(1,*n)) {
*info = -11;
} else if (*ldx < max(1,*n)) {
*info = -13;
} else /* if(complicated condition) */ {
/* Computing MAX */
i__1 = 1, i__2 = *n * 3;
if (*lwork < max(i__1,i__2) && ! lquery) {
*info = -18;
}
}
if (*info == 0) {
/* Computing MAX */
i__1 = 1, i__2 = *n * 3;
lwkopt = max(i__1,i__2);
if (nofact) {
nb = ilaenv_(&c__1, "SSYTRF", uplo, n, &c_n1, &c_n1, &c_n1);
/* Computing MAX */
i__1 = lwkopt, i__2 = *n * nb;
lwkopt = max(i__1,i__2);
}
work[1] = (real) lwkopt;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SSYSVX", &i__1);
return 0;
} else if (lquery) {
return 0;
}
if (nofact) {
/* Compute the factorization A = U*D*U' or A = L*D*L'. */
slacpy_(uplo, n, n, &a[a_offset], lda, &af[af_offset], ldaf);
ssytrf_(uplo, n, &af[af_offset], ldaf, &ipiv[1], &work[1], lwork,
info);
/* Return if INFO is non-zero. */
if (*info > 0) {
*rcond = 0.f;
return 0;
}
}
/* Compute the norm of the matrix A. */
anorm = slansy_("I", uplo, n, &a[a_offset], lda, &work[1]);
/* Compute the reciprocal of the condition number of A. */
ssycon_(uplo, n, &af[af_offset], ldaf, &ipiv[1], &anorm, rcond, &work[1],
&iwork[1], info);
/* Compute the solution vectors X. */
slacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx);
ssytrs_(uplo, n, nrhs, &af[af_offset], ldaf, &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. */
ssyrfs_(uplo, n, nrhs, &a[a_offset], lda, &af[af_offset], ldaf, &ipiv[1],
&b[b_offset], ldb, &x[x_offset], ldx, &ferr[1], &berr[1], &work[1]
, &iwork[1], info);
/* Set INFO = N+1 if the matrix is singular to working precision. */
if (*rcond < slamch_("Epsilon")) {
*info = *n + 1;
}
work[1] = (real) lwkopt;
return 0;
/* End of SSYSVX */
} /* ssysvx_ */
/* Subroutine */ int sdrvsy_(logical *dotype, integer *nn, integer *nval,
integer *nrhs, real *thresh, logical *tsterr, integer *nmax, real *a,
real *afac, real *ainv, real *b, real *x, real *xact, real *work,
real *rwork, integer *iwork, integer *nout)
{
/* Initialized data */
static integer iseedy[4] = { 1988,1989,1990,1991 };
static char uplos[1*2] = "U" "L";
static char facts[1*2] = "F" "N";
/* Format strings */
static char fmt_9999[] = "(1x,a,\002, UPLO='\002,a1,\002', N =\002,i5"
",\002, type \002,i2,\002, test \002,i2,\002, ratio =\002,g12.5)";
static char fmt_9998[] = "(1x,a,\002, FACT='\002,a1,\002', UPLO='\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[2];
char ch__1[2];
/* Local variables */
integer i__, j, k, n, i1, i2, k1, nb, in, kl, ku, nt, lda;
char fact[1];
integer ioff, mode, imat, info;
char path[3], dist[1], uplo[1], type__[1];
integer nrun, ifact, nfail, iseed[4], nbmin;
real rcond;
integer nimat;
real anorm;
integer iuplo, izero, nerrs;
integer lwork;
logical zerot;
char xtype[1];
real rcondc;
real cndnum, ainvnm;
real result[6];
/* Fortran I/O blocks */
static cilist io___42 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___45 = { 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 */
/* ======= */
/* SDRVSY tests the driver routines SSYSV 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. */
/* NRHS (input) INTEGER */
/* The number of right hand side vectors to be generated for */
/* each linear system. */
/* THRESH (input) REAL */
/* The threshold value for the test ratios. A result is */
/* included in the output file if RESULT >= THRESH. To have */
/* every test ratio printed, use THRESH = 0. */
/* TSTERR (input) LOGICAL */
/* Flag that indicates whether error exits are to be tested. */
/* NMAX (input) INTEGER */
/* The maximum value permitted for N, used in dimensioning the */
/* work arrays. */
/* A (workspace) REAL array, dimension (NMAX*NMAX) */
/* AFAC (workspace) REAL array, dimension (NMAX*NMAX) */
/* AINV (workspace) REAL array, dimension (NMAX*NMAX) */
/* B (workspace) REAL array, dimension (NMAX*NRHS) */
/* X (workspace) REAL array, dimension (NMAX*NRHS) */
/* XACT (workspace) REAL array, dimension (NMAX*NRHS) */
/* WORK (workspace) REAL array, dimension */
/* (NMAX*max(2,NRHS)) */
/* RWORK (workspace) REAL array, dimension (NMAX+2*NRHS) */
/* IWORK (workspace) INTEGER array, dimension (2*NMAX) */
/* 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 */
--iwork;
--rwork;
--work;
--xact;
--x;
--b;
--ainv;
--afac;
--a;
--nval;
--dotype;
/* Function Body */
/* .. */
/* .. Executable Statements .. */
/* Initialize constants and the random number seed. */
s_copy(path, "Single precision", (ftnlen)1, (ftnlen)16);
s_copy(path + 1, "SY", (ftnlen)2, (ftnlen)2);
nrun = 0;
nfail = 0;
nerrs = 0;
for (i__ = 1; i__ <= 4; ++i__) {
iseed[i__ - 1] = iseedy[i__ - 1];
/* L10: */
}
/* Computing MAX */
i__1 = *nmax << 1, i__2 = *nmax * *nrhs;
lwork = max(i__1,i__2);
/* Test the error exits */
if (*tsterr) {
serrvx_(path, nout);
}
infoc_1.infot = 0;
/* Set the block size and minimum block size for testing. */
nb = 1;
nbmin = 2;
xlaenv_(&c__1, &nb);
xlaenv_(&c__2, &nbmin);
/* Do for each value of N in NVAL */
i__1 = *nn;
for (in = 1; in <= i__1; ++in) {
n = nval[in];
lda = max(n,1);
*(unsigned char *)xtype = 'N';
nimat = 10;
if (n <= 0) {
nimat = 1;
}
i__2 = nimat;
for (imat = 1; imat <= i__2; ++imat) {
/* Do the tests only if DOTYPE( IMAT ) is true. */
if (! dotype[imat]) {
goto L170;
}
/* Skip types 3, 4, 5, or 6 if the matrix size is too small. */
zerot = imat >= 3 && imat <= 6;
if (zerot && n < imat - 2) {
goto L170;
}
/* Do first for UPLO = 'U', then for UPLO = 'L' */
for (iuplo = 1; iuplo <= 2; ++iuplo) {
*(unsigned char *)uplo = *(unsigned char *)&uplos[iuplo - 1];
/* Set up parameters with SLATB4 and generate a test matrix */
/* with SLATMS. */
slatb4_(path, &imat, &n, &n, type__, &kl, &ku, &anorm, &mode,
&cndnum, dist);
s_copy(srnamc_1.srnamt, "SLATMS", (ftnlen)32, (ftnlen)6);
slatms_(&n, &n, dist, iseed, type__, &rwork[1], &mode, &
cndnum, &anorm, &kl, &ku, uplo, &a[1], &lda, &work[1],
&info);
/* Check error code from SLATMS. */
if (info != 0) {
alaerh_(path, "SLATMS", &info, &c__0, uplo, &n, &n, &c_n1,
&c_n1, &c_n1, &imat, &nfail, &nerrs, nout);
goto L160;
}
/* For types 3-6, zero one or more rows and columns of the */
/* matrix to test that INFO is returned correctly. */
if (zerot) {
if (imat == 3) {
izero = 1;
} else if (imat == 4) {
izero = n;
} else {
izero = n / 2 + 1;
}
if (imat < 6) {
/* Set row and column IZERO to zero. */
if (iuplo == 1) {
ioff = (izero - 1) * lda;
i__3 = izero - 1;
for (i__ = 1; i__ <= i__3; ++i__) {
a[ioff + i__] = 0.f;
/* L20: */
}
ioff += izero;
i__3 = n;
for (i__ = izero; i__ <= i__3; ++i__) {
a[ioff] = 0.f;
ioff += lda;
/* L30: */
}
} else {
ioff = izero;
i__3 = izero - 1;
for (i__ = 1; i__ <= i__3; ++i__) {
a[ioff] = 0.f;
ioff += lda;
/* L40: */
}
ioff -= izero;
i__3 = n;
for (i__ = izero; i__ <= i__3; ++i__) {
a[ioff + i__] = 0.f;
/* L50: */
}
}
} else {
ioff = 0;
if (iuplo == 1) {
/* Set the first IZERO rows and columns to zero. */
i__3 = n;
for (j = 1; j <= i__3; ++j) {
i2 = min(j,izero);
i__4 = i2;
for (i__ = 1; i__ <= i__4; ++i__) {
a[ioff + i__] = 0.f;
/* L60: */
}
ioff += lda;
/* L70: */
}
} else {
/* Set the last IZERO rows and columns to zero. */
i__3 = n;
for (j = 1; j <= i__3; ++j) {
i1 = max(j,izero);
i__4 = n;
for (i__ = i1; i__ <= i__4; ++i__) {
a[ioff + i__] = 0.f;
/* L80: */
}
ioff += lda;
/* L90: */
}
}
}
} else {
izero = 0;
}
for (ifact = 1; ifact <= 2; ++ifact) {
/* Do first for FACT = 'F', then for other values. */
*(unsigned char *)fact = *(unsigned char *)&facts[ifact -
1];
/* Compute the condition number for comparison with */
/* the value returned by SSYSVX. */
if (zerot) {
if (ifact == 1) {
goto L150;
}
rcondc = 0.f;
} else if (ifact == 1) {
/* Compute the 1-norm of A. */
anorm = slansy_("1", uplo, &n, &a[1], &lda, &rwork[1]);
/* Factor the matrix A. */
slacpy_(uplo, &n, &n, &a[1], &lda, &afac[1], &lda);
ssytrf_(uplo, &n, &afac[1], &lda, &iwork[1], &work[1],
&lwork, &info);
/* Compute inv(A) and take its norm. */
slacpy_(uplo, &n, &n, &afac[1], &lda, &ainv[1], &lda);
ssytri_(uplo, &n, &ainv[1], &lda, &iwork[1], &work[1],
&info);
ainvnm = slansy_("1", uplo, &n, &ainv[1], &lda, &
rwork[1]);
/* Compute the 1-norm condition number of A. */
if (anorm <= 0.f || ainvnm <= 0.f) {
rcondc = 1.f;
} else {
rcondc = 1.f / anorm / ainvnm;
}
}
/* Form an exact solution and set the right hand side. */
s_copy(srnamc_1.srnamt, "SLARHS", (ftnlen)32, (ftnlen)6);
slarhs_(path, xtype, uplo, " ", &n, &n, &kl, &ku, nrhs, &
a[1], &lda, &xact[1], &lda, &b[1], &lda, iseed, &
info);
*(unsigned char *)xtype = 'C';
/* --- Test SSYSV --- */
if (ifact == 2) {
slacpy_(uplo, &n, &n, &a[1], &lda, &afac[1], &lda);
slacpy_("Full", &n, nrhs, &b[1], &lda, &x[1], &lda);
/* Factor the matrix and solve the system using SSYSV. */
s_copy(srnamc_1.srnamt, "SSYSV ", (ftnlen)32, (ftnlen)
6);
ssysv_(uplo, &n, nrhs, &afac[1], &lda, &iwork[1], &x[
1], &lda, &work[1], &lwork, &info);
/* Adjust the expected value of INFO to account for */
/* pivoting. */
k = izero;
if (k > 0) {
L100:
if (iwork[k] < 0) {
if (iwork[k] != -k) {
k = -iwork[k];
goto L100;
}
} else if (iwork[k] != k) {
k = iwork[k];
goto L100;
}
}
/* Check error code from SSYSV . */
if (info != k) {
alaerh_(path, "SSYSV ", &info, &k, uplo, &n, &n, &
c_n1, &c_n1, nrhs, &imat, &nfail, &nerrs,
nout);
goto L120;
} else if (info != 0) {
goto L120;
}
/* Reconstruct matrix from factors and compute */
/* residual. */
ssyt01_(uplo, &n, &a[1], &lda, &afac[1], &lda, &iwork[
1], &ainv[1], &lda, &rwork[1], result);
/* Compute residual of the computed solution. */
slacpy_("Full", &n, nrhs, &b[1], &lda, &work[1], &lda);
spot02_(uplo, &n, nrhs, &a[1], &lda, &x[1], &lda, &
work[1], &lda, &rwork[1], &result[1]);
/* Check solution from generated exact solution. */
sget04_(&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 = 1; 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, "SSYSV ", (ftnlen)6);
do_fio(&c__1, uplo, (ftnlen)1);
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&imat, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&k, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&result[k - 1], (ftnlen)
sizeof(real));
e_wsfe();
++nfail;
}
/* L110: */
}
nrun += nt;
L120:
;
}
/* --- Test SSYSVX --- */
if (ifact == 2) {
slaset_(uplo, &n, &n, &c_b49, &c_b49, &afac[1], &lda);
}
slaset_("Full", &n, nrhs, &c_b49, &c_b49, &x[1], &lda);
/* Solve the system and compute the condition number and */
/* error bounds using SSYSVX. */
s_copy(srnamc_1.srnamt, "SSYSVX", (ftnlen)32, (ftnlen)6);
ssysvx_(fact, uplo, &n, nrhs, &a[1], &lda, &afac[1], &lda,
&iwork[1], &b[1], &lda, &x[1], &lda, &rcond, &
rwork[1], &rwork[*nrhs + 1], &work[1], &lwork, &
iwork[n + 1], &info);
/* Adjust the expected value of INFO to account for */
/* pivoting. */
k = izero;
if (k > 0) {
L130:
if (iwork[k] < 0) {
if (iwork[k] != -k) {
k = -iwork[k];
goto L130;
}
} else if (iwork[k] != k) {
k = iwork[k];
goto L130;
}
}
/* Check the error code from SSYSVX. */
if (info != k) {
/* Writing concatenation */
i__5[0] = 1, a__1[0] = fact;
i__5[1] = 1, a__1[1] = uplo;
s_cat(ch__1, a__1, i__5, &c__2, (ftnlen)2);
alaerh_(path, "SSYSVX", &info, &k, ch__1, &n, &n, &
c_n1, &c_n1, nrhs, &imat, &nfail, &nerrs,
nout);
goto L150;
}
if (info == 0) {
if (ifact >= 2) {
/* Reconstruct matrix from factors and compute */
/* residual. */
ssyt01_(uplo, &n, &a[1], &lda, &afac[1], &lda, &
iwork[1], &ainv[1], &lda, &rwork[(*nrhs <<
1) + 1], result);
k1 = 1;
} else {
k1 = 2;
}
/* Compute residual of the computed solution. */
slacpy_("Full", &n, nrhs, &b[1], &lda, &work[1], &lda);
spot02_(uplo, &n, nrhs, &a[1], &lda, &x[1], &lda, &
work[1], &lda, &rwork[(*nrhs << 1) + 1], &
result[1]);
/* Check solution from generated exact solution. */
sget04_(&n, nrhs, &x[1], &lda, &xact[1], &lda, &
rcondc, &result[2]);
/* Check the error bounds from iterative refinement. */
spot05_(uplo, &n, nrhs, &a[1], &lda, &b[1], &lda, &x[
1], &lda, &xact[1], &lda, &rwork[1], &rwork[*
nrhs + 1], &result[3]);
} else {
k1 = 6;
}
/* Compare RCOND from SSYSVX with the computed value */
/* in RCONDC. */
result[5] = sget06_(&rcond, &rcondc);
/* Print information about the tests that did not pass */
/* the threshold. */
for (k = k1; k <= 6; ++k) {
if (result[k - 1] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
aladhd_(nout, path);
}
io___45.ciunit = *nout;
s_wsfe(&io___45);
do_fio(&c__1, "SSYSVX", (ftnlen)6);
do_fio(&c__1, fact, (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 *)&k, (ftnlen)sizeof(integer))
;
do_fio(&c__1, (char *)&result[k - 1], (ftnlen)
sizeof(real));
e_wsfe();
++nfail;
}
/* L140: */
}
nrun = nrun + 7 - k1;
L150:
;
}
L160:
;
}
L170:
;
}
/* L180: */
}
/* Print a summary of the results. */
alasvm_(path, nout, &nfail, &nrun, &nerrs);
return 0;
/* End of SDRVSY */
} /* sdrvsy_ */
/* Subroutine */
int ssysvx_(char *fact, char *uplo, integer *n, integer * nrhs, real *a, integer *lda, real *af, integer *ldaf, integer *ipiv, real *b, integer *ldb, real *x, integer *ldx, real *rcond, real *ferr, real *berr, real *work, integer *lwork, integer *iwork, integer * info)
{
/* System generated locals */
integer a_dim1, a_offset, af_dim1, af_offset, b_dim1, b_offset, x_dim1, x_offset, i__1, i__2;
/* Local variables */
integer nb;
extern logical lsame_(char *, char *);
real anorm;
extern real slamch_(char *);
logical nofact;
extern /* Subroutine */
int xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *);
extern /* Subroutine */
int slacpy_(char *, integer *, integer *, real *, integer *, real *, integer *);
extern real slansy_(char *, char *, integer *, real *, integer *, real *);
extern /* Subroutine */
int ssycon_(char *, integer *, real *, integer *, integer *, real *, real *, real *, integer *, integer *);
integer lwkopt;
logical lquery;
extern /* Subroutine */
int ssyrfs_(char *, integer *, integer *, real *, integer *, real *, integer *, integer *, real *, integer *, real * , integer *, real *, real *, real *, integer *, integer *) , ssytrf_(char *, integer *, real *, integer *, integer *, real *, integer *, integer *), ssytrs_(char *, integer *, integer *, real *, integer *, integer *, real *, integer *, integer *);
/* -- LAPACK driver routine (version 3.4.1) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* April 2012 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* ===================================================================== */
/* .. 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;
af_dim1 = *ldaf;
af_offset = 1 + af_dim1;
af -= af_offset;
--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;
--iwork;
/* Function Body */
*info = 0;
nofact = lsame_(fact, "N");
lquery = *lwork == -1;
if (! nofact && ! lsame_(fact, "F"))
{
*info = -1;
}
else if (! lsame_(uplo, "U") && ! lsame_(uplo, "L"))
{
*info = -2;
}
else if (*n < 0)
{
*info = -3;
}
else if (*nrhs < 0)
{
*info = -4;
}
else if (*lda < max(1,*n))
{
*info = -6;
}
else if (*ldaf < max(1,*n))
{
*info = -8;
}
else if (*ldb < max(1,*n))
{
*info = -11;
}
else if (*ldx < max(1,*n))
{
*info = -13;
}
else /* if(complicated condition) */
{
/* Computing MAX */
i__1 = 1;
i__2 = *n * 3; // , expr subst
if (*lwork < max(i__1,i__2) && ! lquery)
{
*info = -18;
}
}
if (*info == 0)
{
/* Computing MAX */
i__1 = 1;
i__2 = *n * 3; // , expr subst
lwkopt = max(i__1,i__2);
if (nofact)
{
nb = ilaenv_(&c__1, "SSYTRF", uplo, n, &c_n1, &c_n1, &c_n1);
/* Computing MAX */
i__1 = lwkopt;
i__2 = *n * nb; // , expr subst
lwkopt = max(i__1,i__2);
}
work[1] = (real) lwkopt;
}
if (*info != 0)
{
i__1 = -(*info);
xerbla_("SSYSVX", &i__1);
return 0;
}
else if (lquery)
{
return 0;
}
if (nofact)
{
/* Compute the factorization A = U*D*U**T or A = L*D*L**T. */
slacpy_(uplo, n, n, &a[a_offset], lda, &af[af_offset], ldaf);
ssytrf_(uplo, n, &af[af_offset], ldaf, &ipiv[1], &work[1], lwork, info);
/* Return if INFO is non-zero. */
if (*info > 0)
{
*rcond = 0.f;
return 0;
}
}
/* Compute the norm of the matrix A. */
anorm = slansy_("I", uplo, n, &a[a_offset], lda, &work[1]);
/* Compute the reciprocal of the condition number of A. */
ssycon_(uplo, n, &af[af_offset], ldaf, &ipiv[1], &anorm, rcond, &work[1], &iwork[1], info);
/* Compute the solution vectors X. */
slacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx);
ssytrs_(uplo, n, nrhs, &af[af_offset], ldaf, &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. */
ssyrfs_(uplo, n, nrhs, &a[a_offset], lda, &af[af_offset], ldaf, &ipiv[1], &b[b_offset], ldb, &x[x_offset], ldx, &ferr[1], &berr[1], &work[1] , &iwork[1], info);
/* Set INFO = N+1 if the matrix is singular to working precision. */
if (*rcond < slamch_("Epsilon"))
{
*info = *n + 1;
}
work[1] = (real) lwkopt;
return 0;
/* End of SSYSVX */
}
/* Subroutine */ int ssysv_(char *uplo, integer *n, integer *nrhs, real *a,
integer *lda, integer *ipiv, real *b, integer *ldb, real *work,
integer *lwork, integer *info)
{
/* -- LAPACK driver routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
June 30, 1999
Purpose
=======
SSYSV computes the solution to a real system of linear equations
A * X = B,
where A is an N-by-N symmetric matrix and X and B are N-by-NRHS
matrices.
The diagonal pivoting method is used to factor A as
A = U * D * U**T, if UPLO = 'U', or
A = L * D * L**T, if UPLO = 'L',
where U (or L) is a product of permutation and unit upper (lower)
triangular matrices, and D is symmetric and block diagonal with
1-by-1 and 2-by-2 diagonal blocks. The factored form of A is then
used to solve the system of equations A * X = B.
Arguments
=========
UPLO (input) CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) INTEGER
The number of linear equations, i.e., the order of the
matrix A. N >= 0.
NRHS (input) INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 0.
A (input/output) REAL array, dimension (LDA,N)
On entry, the symmetric matrix A. If UPLO = 'U', the leading
N-by-N upper triangular part of A contains the upper
triangular part of the matrix A, and the strictly lower
triangular part of A is not referenced. If UPLO = 'L', the
leading N-by-N lower triangular part of A contains the lower
triangular part of the matrix A, and the strictly upper
triangular part of A is not referenced.
On exit, if INFO = 0, the block diagonal matrix D and the
multipliers used to obtain the factor U or L from the
factorization A = U*D*U**T or A = L*D*L**T as computed by
SSYTRF.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
IPIV (output) INTEGER array, dimension (N)
Details of the interchanges and the block structure of D, as
determined by SSYTRF. If IPIV(k) > 0, then rows and columns
k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1
diagonal block. If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0,
then rows and columns k-1 and -IPIV(k) were interchanged and
D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = 'L' and
IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and
-IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2
diagonal block.
B (input/output) REAL array, dimension (LDB,NRHS)
On entry, the N-by-NRHS right hand side matrix B.
On exit, if INFO = 0, the N-by-NRHS solution matrix X.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).
WORK (workspace/output) REAL array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The length of WORK. LWORK >= 1, and for best performance
LWORK >= N*NB, where NB is the optimal blocksize for
SSYTRF.
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, D(i,i) is exactly zero. The factorization
has been completed, but the block diagonal matrix D is
exactly singular, so the solution could not be computed.
=====================================================================
Test the input parameters.
Parameter adjustments */
/* Table of constant values */
static integer c__1 = 1;
static integer c_n1 = -1;
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, i__1;
/* Local variables */
extern logical lsame_(char *, char *);
static integer nb;
extern /* Subroutine */ int xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
static integer lwkopt;
static logical lquery;
extern /* Subroutine */ int ssytrf_(char *, integer *, real *, integer *,
integer *, real *, integer *, integer *), ssytrs_(char *,
integer *, integer *, real *, integer *, integer *, real *,
integer *, integer *);
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--ipiv;
b_dim1 = *ldb;
b_offset = 1 + b_dim1 * 1;
b -= b_offset;
--work;
/* Function Body */
*info = 0;
lquery = *lwork == -1;
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 = -8;
} else if (*lwork < 1 && ! lquery) {
*info = -10;
}
if (*info == 0) {
nb = ilaenv_(&c__1, "SSYTRF", uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6,
(ftnlen)1);
lwkopt = *n * nb;
work[1] = (real) lwkopt;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SSYSV ", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Compute the factorization A = U*D*U' or A = L*D*L'. */
ssytrf_(uplo, n, &a[a_offset], lda, &ipiv[1], &work[1], lwork, info);
if (*info == 0) {
/* Solve the system A*X = B, overwriting B with X. */
ssytrs_(uplo, n, nrhs, &a[a_offset], lda, &ipiv[1], &b[b_offset], ldb,
info);
}
work[1] = (real) lwkopt;
return 0;
/* End of SSYSV */
} /* ssysv_ */
void StrandBlockSolver::lspMap()
{
int mm,nn,jj,ii,j1,j2,jm,jmax,nmax,info,ldu,ldvt,rows,cols,lwork;
double dsm,dx,dy,ds,w,r1,r2,rs,cond,rcond,xn,yn,ax,ay,xu,xl,bu,bl,xcn,ycn;
double b[4];
double* sv;
double* work1;
double* uu;
double* vt;
double* dr;
double** lspT;
char u='U',jobu='n',jobvt='a';
cond = 0.;
ldu = 1;
ldvt = 2;
cols = 2;
for (int n=0; n<nNodes-nGnodes; n++){
mm = ncsp(n);
rows = mm;
ii = cols;
if (rows < ii) ii = rows;
jj = cols;
if (rows > jj) jj = rows;
lwork = 1;
if (3*ii+jj > lwork) lwork = 3*ii+jj;
if (5*ii > lwork) lwork = 5*ii;
uu = new double[ldu*ldu];
sv = new double[cols];
vt = new double[ldvt*cols];
work1 = new double[lwork];
dr = new double[rows*2];
lspT = new double*[nPstr+1];
for (int j=0; j<nPstr+1; j++) lspT[j] = new double[rows];
rcond = 0.;
info = 0;
for (int m=0; m<ldu*ldu; m++) uu [m] = 0.;
for (int m=0; m<cols; m++) sv [m] = 0.;
for (int m=0; m<ldvt*cols; m++) vt [m] = 0.;
for (int m=0; m<lwork; m++) work1[m] = 0.;
double work [2] = {0.,0.};
double work2[4] = {0.,0.,0.,0.};
int iwork[2] = {0,0};
int ipiv [2] = {0,0};
for (int j=1; j<nPstr+1; j++){ //mid strand nodes
// coordinates of the mid-strand location in question
jm = j-1;
xn = .5*(x(0,j,n)+x(0,jm,n));
yn = .5*(x(1,j,n)+x(1,jm,n));
// find data centroid
xcn = 0.;
ycn = 0.;
for (int m=0; m<mm; m++){
nn = csp[n][m];
xcn = xcn+xc(0,j,nn);
ycn = ycn+xc(1,j,nn);
}
xcn = xcn/double(mm);
ycn = ycn/double(mm);
// find plane which most closely fits surrounding cell centers
for (int m=0; m<mm; m++){
nn = csp[n][m];
dr[m ] = xc(0,j,nn)-xcn;
dr[m+mm] = xc(1,j,nn)-ycn;
}
sgesvd_(jobu,jobvt,rows,cols,dr,rows,sv,uu,ldu,vt,ldvt,work1,lwork,info);
if (info != 0){
cout << "\n*** svd procedure failure in lspMap ***" << endl;
exit(0);
}
ax = vt[0];
ay = vt[2];
ds = 1./sqrt(ax*ax+ay*ay);
ax = ax*ds;
ay = ay*ds;
// compute 2d least squares problem with projected distances
// largest distance in stencil
dsm = 0.;
for (int m=0; m<mm; m++){
nn = csp[n][m];
dx = xc(0,j,nn)-xn;
dy = xc(1,j,nn)-yn;
ds = dx*ax+dy*ay;
ds = ds*ds;
if (ds > dsm) dsm = ds;
}
dsm = 1./sqrt(dsm);
// form least squares matrix
jj = jm;
for (int m=0; m<4; m++) b[m] = 0.;
for (int m=0; m<mm; m++){
nn = csp[n][m];
dx = xc(0,j,nn)-xn;
dy = xc(1,j,nn)-yn;
ds =(dx*ax+dy*ay)*dsm;
w = 1./(ds*ds);
b[0] = b[0]+w;
b[2] = b[2]+w*ds;
b[3] = b[3]+w*ds*ds;
}
// find max abs row sum for condition number computation
r1 = fabs(b[0])+fabs(b[2]);
r2 = fabs(b[1])+fabs(b[3]);
rs = r1;
if (r2 > rs) rs = r2;
// invert matrix and determine condition number
ii = 2;
ssytrf_(u,ii,b,ii,ipiv,work,ii,info);
ssycon_(u,ii,b,ii,ipiv,rs,rcond,work2,iwork,info);
ssytri_(u,ii,b,ii,ipiv,work,info);
rcond = 1./rcond;
if (rcond > cond){
nmax = n;
jmax = j;
cond = rcond;
}
// form and store least squares coefficient
for (int m=0; m<mm; m++){
nn = csp[n][m];
dx = xc(0,j,nn)-xn;
dy = xc(1,j,nn)-yn;
ds =(dx*ax+dy*ay)*dsm;
w = 1./(ds*ds);
lspT[j][m] =(b[0]*w +
b[2]*w*ds);
}
}
// interpolate projected coefficients to the nodal positions along each strand
for (int j=0; j<nPstr+1; j++){
if (j == 0 ){
j1 = 1;
j2 = 2;
}
else if (j == nPstr){
j1 = nPstr-1;
j2 = nPstr;
}
else{
j1 = j;
j2 = j+1;
}
xn = xStr(j);
jm = j1-1;
xl = .5*(xStr(jm)+xStr(j1));
jm = j2-1;
xu = .5*(xStr(jm)+xStr(j2));
bl =(xu-xn)/(xu-xl);
bu =(xn-xl)/(xu-xl);
indlsp(0,j,n,ii);
for (int m=0; m<mm; m++){
lsp[ii ][m] = bl*lspT[j1][m];
lsp[ii+1][m] = bu*lspT[j2][m];
}
}
delete [] sv;
delete [] uu;
delete [] vt;
delete [] work1;
delete [] dr;
for (int j=0; j<nPstr+1; j++) delete [] lspT[j];
delete [] lspT;
}
// output condition information
xn = x(0,jmax,nmax);
yn = x(1,jmax,nmax);
cout << "\nMaximum condition number for LS procedure: "
<< cond << endl
<< "Index of maximum condition number: "
<< nmax << "\t" << jmax << endl
<< "Coordinates of maximum condition number: "
<< xn << "\t" << yn << "\n" << endl;
/*
// try using volume averaging on outer boundary nodes
for (int n=0; n<nNodes-nGnodes; n++){
mm = ncsp(n);
for (int j=nPstr; j<nPstr+1; j++){
if (j == 0 ) jj = 1;
else if (j == nPstr) jj = nPstr-1;
else jj = j;
w = 0.;
for (int k=0; k<2; k++){
indlsp(k,j,n,ii);
for (int m=0; m<mm; m++){
nn = csp[n][m];
lsp[ii][m] = v(jj,nn);
w += v(jj,nn);
}
jj++;
}
w = 1./w;
for (int k=0; k<2; k++){
indlsp(k,j,n,ii);
for (int m=0; m<mm; m++){
lsp[ii][m] = lsp[ii][m]*w;
}}}}
*/
}
/* Subroutine */ int schksy_(logical *dotype, integer *nn, integer *nval,
integer *nnb, integer *nbval, integer *nns, integer *nsval, real *
thresh, logical *tsterr, integer *nmax, real *a, real *afac, real *
ainv, real *b, real *x, real *xact, real *work, real *rwork, integer *
iwork, integer *nout)
{
/* Initialized data */
static integer iseedy[4] = { 1988,1989,1990,1991 };
static char uplos[1*2] = "U" "L";
/* Format strings */
static char fmt_9999[] = "(\002 UPLO = '\002,a1,\002', N =\002,i5,\002, "
"NB =\002,i4,\002, type \002,i2,\002, test \002,i2,\002, ratio "
"=\002,g12.5)";
static char fmt_9998[] = "(\002 UPLO = '\002,a1,\002', N =\002,i5,\002, "
"NRHS=\002,i3,\002, type \002,i2,\002, test(\002,i2,\002) =\002,g"
"12.5)";
static char fmt_9997[] = "(\002 UPLO = '\002,a1,\002', N =\002,i5,\002"
",\002,10x,\002 type \002,i2,\002, test(\002,i2,\002) =\002,g12.5)"
;
/* System generated locals */
integer i__1, i__2, i__3, i__4;
/* Builtin functions */
/* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void);
/* Local variables */
integer i__, j, k, n, i1, i2, nb, in, kl, ku, nt, lda, inb, ioff, mode,
imat, info;
char path[3], dist[1];
integer irhs, nrhs;
char uplo[1], type__[1];
integer nrun;
extern /* Subroutine */ int alahd_(integer *, char *);
integer nfail, iseed[4];
real rcond;
extern /* Subroutine */ int sget04_(integer *, integer *, real *, integer
*, real *, integer *, real *, real *);
integer nimat;
extern doublereal sget06_(real *, real *);
real anorm;
extern /* Subroutine */ int spot02_(char *, integer *, integer *, real *,
integer *, real *, integer *, real *, integer *, real *, real *);
integer iuplo, izero, nerrs;
extern /* Subroutine */ int spot03_(char *, integer *, real *, integer *,
real *, integer *, real *, integer *, real *, real *, real *), spot05_(char *, integer *, integer *, real *, integer *,
real *, integer *, real *, integer *, real *, integer *, real *,
real *, real *);
integer lwork;
logical zerot;
extern /* Subroutine */ int ssyt01_(char *, integer *, real *, integer *,
real *, integer *, integer *, real *, integer *, real *, real *);
char xtype[1];
extern /* Subroutine */ int slatb4_(char *, integer *, integer *, integer
*, char *, integer *, integer *, real *, integer *, real *, char *
), alaerh_(char *, char *, integer *,
integer *, char *, integer *, integer *, integer *, integer *,
integer *, integer *, integer *, integer *, integer *);
real rcondc;
extern /* Subroutine */ int alasum_(char *, integer *, integer *, integer
*, integer *);
real cndnum;
logical trfcon;
extern /* Subroutine */ int slacpy_(char *, integer *, integer *, real *,
integer *, real *, integer *), slarhs_(char *, char *,
char *, char *, integer *, integer *, integer *, integer *,
integer *, real *, integer *, real *, integer *, real *, integer *
, integer *, integer *), xlaenv_(
integer *, integer *), slatms_(integer *, integer *, char *,
integer *, char *, real *, integer *, real *, real *, integer *,
integer *, char *, real *, integer *, real *, integer *);
extern doublereal slansy_(char *, char *, integer *, real *, integer *,
real *);
real result[8];
extern /* Subroutine */ int ssycon_(char *, integer *, real *, integer *,
integer *, real *, real *, real *, integer *, integer *),
serrsy_(char *, integer *), ssyrfs_(char *, integer *,
integer *, real *, integer *, real *, integer *, integer *, real *
, integer *, real *, integer *, real *, real *, real *, integer *,
integer *), ssytrf_(char *, integer *, real *, integer *,
integer *, real *, integer *, integer *), ssytri_(char *,
integer *, real *, integer *, integer *, real *, integer *), ssytrs_(char *, integer *, integer *, real *, integer *,
integer *, real *, integer *, integer *);
/* Fortran I/O blocks */
static cilist io___39 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___42 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___44 = { 0, 0, 0, fmt_9997, 0 };
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* SCHKSY tests SSYTRF, -TRI, -TRS, -RFS, and -CON. */
/* Arguments */
/* ========= */
/* DOTYPE (input) LOGICAL array, dimension (NTYPES) */
/* The matrix types to be used for testing. Matrices of type j */
/* (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) = */
/* .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used. */
/* NN (input) INTEGER */
/* The number of values of N contained in the vector NVAL. */
/* NVAL (input) INTEGER array, dimension (NN) */
/* The values of the matrix dimension N. */
/* NNB (input) INTEGER */
/* The number of values of NB contained in the vector NBVAL. */
/* NBVAL (input) INTEGER array, dimension (NBVAL) */
/* 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) REAL */
/* The threshold value for the test ratios. A result is */
/* included in the output file if RESULT >= THRESH. To have */
/* every test ratio printed, use THRESH = 0. */
/* TSTERR (input) LOGICAL */
/* Flag that indicates whether error exits are to be tested. */
/* NMAX (input) INTEGER */
/* The maximum value permitted for N, used in dimensioning the */
/* work arrays. */
/* A (workspace) REAL array, dimension (NMAX*NMAX) */
/* AFAC (workspace) REAL array, dimension (NMAX*NMAX) */
/* AINV (workspace) REAL array, dimension (NMAX*NMAX) */
/* B (workspace) REAL array, dimension (NMAX*NSMAX) */
/* where NSMAX is the largest entry in NSVAL. */
/* X (workspace) REAL array, dimension (NMAX*NSMAX) */
/* XACT (workspace) REAL array, dimension (NMAX*NSMAX) */
/* WORK (workspace) REAL array, dimension */
/* (NMAX*max(3,NSMAX)) */
/* RWORK (workspace) REAL array, dimension */
/* (max(NMAX,2*NSMAX)) */
/* IWORK (workspace) INTEGER array, dimension (2*NMAX) */
/* NOUT (input) INTEGER */
/* The unit number for output. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Scalars in Common .. */
/* .. */
/* .. Common blocks .. */
/* .. */
/* .. Data statements .. */
/* Parameter adjustments */
--iwork;
--rwork;
--work;
--xact;
--x;
--b;
--ainv;
--afac;
--a;
--nsval;
--nbval;
--nval;
--dotype;
/* Function Body */
/* .. */
/* .. Executable Statements .. */
/* Initialize constants and the random number seed. */
s_copy(path, "Single precision", (ftnlen)1, (ftnlen)16);
s_copy(path + 1, "SY", (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) {
serrsy_(path, nout);
}
infoc_1.infot = 0;
xlaenv_(&c__2, &c__2);
/* Do for each value of N in NVAL */
i__1 = *nn;
for (in = 1; in <= i__1; ++in) {
n = nval[in];
lda = max(n,1);
*(unsigned char *)xtype = 'N';
nimat = 10;
if (n <= 0) {
nimat = 1;
}
izero = 0;
i__2 = nimat;
for (imat = 1; imat <= i__2; ++imat) {
/* Do the tests only if DOTYPE( IMAT ) is true. */
if (! dotype[imat]) {
goto L170;
}
/* Skip types 3, 4, 5, or 6 if the matrix size is too small. */
zerot = imat >= 3 && imat <= 6;
if (zerot && n < imat - 2) {
goto L170;
}
/* Do first for UPLO = 'U', then for UPLO = 'L' */
for (iuplo = 1; iuplo <= 2; ++iuplo) {
*(unsigned char *)uplo = *(unsigned char *)&uplos[iuplo - 1];
/* Set up parameters with SLATB4 and generate a test matrix */
/* with SLATMS. */
slatb4_(path, &imat, &n, &n, type__, &kl, &ku, &anorm, &mode,
&cndnum, dist);
s_copy(srnamc_1.srnamt, "SLATMS", (ftnlen)32, (ftnlen)6);
slatms_(&n, &n, dist, iseed, type__, &rwork[1], &mode, &
cndnum, &anorm, &kl, &ku, uplo, &a[1], &lda, &work[1],
&info);
/* Check error code from SLATMS. */
if (info != 0) {
alaerh_(path, "SLATMS", &info, &c__0, uplo, &n, &n, &c_n1,
&c_n1, &c_n1, &imat, &nfail, &nerrs, nout);
goto L160;
}
/* For types 3-6, zero one or more rows and columns of */
/* the matrix to test that INFO is returned correctly. */
if (zerot) {
if (imat == 3) {
izero = 1;
} else if (imat == 4) {
izero = n;
} else {
izero = n / 2 + 1;
}
if (imat < 6) {
/* Set row and column IZERO to zero. */
if (iuplo == 1) {
ioff = (izero - 1) * lda;
i__3 = izero - 1;
for (i__ = 1; i__ <= i__3; ++i__) {
a[ioff + i__] = 0.f;
/* L20: */
}
ioff += izero;
i__3 = n;
for (i__ = izero; i__ <= i__3; ++i__) {
a[ioff] = 0.f;
ioff += lda;
/* L30: */
}
} else {
ioff = izero;
i__3 = izero - 1;
for (i__ = 1; i__ <= i__3; ++i__) {
a[ioff] = 0.f;
ioff += lda;
/* L40: */
}
ioff -= izero;
i__3 = n;
for (i__ = izero; i__ <= i__3; ++i__) {
a[ioff + i__] = 0.f;
/* L50: */
}
}
} else {
ioff = 0;
if (iuplo == 1) {
/* Set the first IZERO rows and columns to zero. */
i__3 = n;
for (j = 1; j <= i__3; ++j) {
i2 = min(j,izero);
i__4 = i2;
for (i__ = 1; i__ <= i__4; ++i__) {
a[ioff + i__] = 0.f;
/* L60: */
}
ioff += lda;
/* L70: */
}
} else {
/* Set the last IZERO rows and columns to zero. */
i__3 = n;
for (j = 1; j <= i__3; ++j) {
i1 = max(j,izero);
i__4 = n;
for (i__ = i1; i__ <= i__4; ++i__) {
a[ioff + i__] = 0.f;
/* L80: */
}
ioff += lda;
/* L90: */
}
}
}
} else {
izero = 0;
}
/* Do for each value of NB in NBVAL */
i__3 = *nnb;
for (inb = 1; inb <= i__3; ++inb) {
nb = nbval[inb];
xlaenv_(&c__1, &nb);
/* Compute the L*D*L' or U*D*U' factorization of the */
/* matrix. */
slacpy_(uplo, &n, &n, &a[1], &lda, &afac[1], &lda);
lwork = max(2,nb) * lda;
s_copy(srnamc_1.srnamt, "SSYTRF", (ftnlen)32, (ftnlen)6);
ssytrf_(uplo, &n, &afac[1], &lda, &iwork[1], &ainv[1], &
lwork, &info);
/* Adjust the expected value of INFO to account for */
/* pivoting. */
k = izero;
if (k > 0) {
L100:
if (iwork[k] < 0) {
if (iwork[k] != -k) {
k = -iwork[k];
goto L100;
}
} else if (iwork[k] != k) {
k = iwork[k];
goto L100;
}
}
/* Check error code from SSYTRF. */
if (info != k) {
alaerh_(path, "SSYTRF", &info, &k, uplo, &n, &n, &
c_n1, &c_n1, &nb, &imat, &nfail, &nerrs, nout);
}
if (info != 0) {
trfcon = TRUE_;
} else {
trfcon = FALSE_;
}
/* + TEST 1 */
/* Reconstruct matrix from factors and compute residual. */
ssyt01_(uplo, &n, &a[1], &lda, &afac[1], &lda, &iwork[1],
&ainv[1], &lda, &rwork[1], result);
nt = 1;
/* + TEST 2 */
/* Form the inverse and compute the residual. */
if (inb == 1 && ! trfcon) {
slacpy_(uplo, &n, &n, &afac[1], &lda, &ainv[1], &lda);
s_copy(srnamc_1.srnamt, "SSYTRI", (ftnlen)32, (ftnlen)
6);
ssytri_(uplo, &n, &ainv[1], &lda, &iwork[1], &work[1],
&info);
/* Check error code from SSYTRI. */
if (info != 0) {
alaerh_(path, "SSYTRI", &info, &c_n1, uplo, &n, &
n, &c_n1, &c_n1, &c_n1, &imat, &nfail, &
nerrs, nout);
}
spot03_(uplo, &n, &a[1], &lda, &ainv[1], &lda, &work[
1], &lda, &rwork[1], &rcondc, &result[1]);
nt = 2;
}
/* Print information about the tests that did not pass */
/* the threshold. */
i__4 = nt;
for (k = 1; k <= i__4; ++k) {
if (result[k - 1] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
alahd_(nout, path);
}
io___39.ciunit = *nout;
s_wsfe(&io___39);
do_fio(&c__1, uplo, (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 *)&k, (ftnlen)sizeof(integer))
;
do_fio(&c__1, (char *)&result[k - 1], (ftnlen)
sizeof(real));
e_wsfe();
++nfail;
}
/* L110: */
}
nrun += nt;
/* Skip the other tests if this is not the first block */
/* size. */
if (inb > 1) {
goto L150;
}
/* Do only the condition estimate if INFO is not 0. */
if (trfcon) {
rcondc = 0.f;
goto L140;
}
i__4 = *nns;
for (irhs = 1; irhs <= i__4; ++irhs) {
nrhs = nsval[irhs];
/* + TEST 3 */
/* Solve and compute residual for A * X = B. */
s_copy(srnamc_1.srnamt, "SLARHS", (ftnlen)32, (ftnlen)
6);
slarhs_(path, xtype, uplo, " ", &n, &n, &kl, &ku, &
nrhs, &a[1], &lda, &xact[1], &lda, &b[1], &
lda, iseed, &info);
slacpy_("Full", &n, &nrhs, &b[1], &lda, &x[1], &lda);
s_copy(srnamc_1.srnamt, "SSYTRS", (ftnlen)32, (ftnlen)
6);
ssytrs_(uplo, &n, &nrhs, &afac[1], &lda, &iwork[1], &
x[1], &lda, &info);
/* Check error code from SSYTRS. */
if (info != 0) {
alaerh_(path, "SSYTRS", &info, &c__0, uplo, &n, &
n, &c_n1, &c_n1, &nrhs, &imat, &nfail, &
nerrs, nout);
}
slacpy_("Full", &n, &nrhs, &b[1], &lda, &work[1], &
lda);
spot02_(uplo, &n, &nrhs, &a[1], &lda, &x[1], &lda, &
work[1], &lda, &rwork[1], &result[2]);
/* + TEST 4 */
/* Check solution from generated exact solution. */
sget04_(&n, &nrhs, &x[1], &lda, &xact[1], &lda, &
rcondc, &result[3]);
/* + TESTS 5, 6, and 7 */
/* Use iterative refinement to improve the solution. */
s_copy(srnamc_1.srnamt, "SSYRFS", (ftnlen)32, (ftnlen)
6);
ssyrfs_(uplo, &n, &nrhs, &a[1], &lda, &afac[1], &lda,
&iwork[1], &b[1], &lda, &x[1], &lda, &rwork[1]
, &rwork[nrhs + 1], &work[1], &iwork[n + 1], &
info);
/* Check error code from SSYRFS. */
if (info != 0) {
alaerh_(path, "SSYRFS", &info, &c__0, uplo, &n, &
n, &c_n1, &c_n1, &nrhs, &imat, &nfail, &
nerrs, nout);
}
sget04_(&n, &nrhs, &x[1], &lda, &xact[1], &lda, &
rcondc, &result[4]);
spot05_(uplo, &n, &nrhs, &a[1], &lda, &b[1], &lda, &x[
1], &lda, &xact[1], &lda, &rwork[1], &rwork[
nrhs + 1], &result[5]);
/* Print information about the tests that did not pass */
/* the threshold. */
for (k = 3; k <= 7; ++k) {
if (result[k - 1] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
alahd_(nout, path);
}
io___42.ciunit = *nout;
s_wsfe(&io___42);
do_fio(&c__1, uplo, (ftnlen)1);
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&nrhs, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&imat, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&k, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&result[k - 1], (ftnlen)
sizeof(real));
e_wsfe();
++nfail;
}
/* L120: */
}
nrun += 5;
/* L130: */
}
/* + TEST 8 */
/* Get an estimate of RCOND = 1/CNDNUM. */
L140:
anorm = slansy_("1", uplo, &n, &a[1], &lda, &rwork[1]);
s_copy(srnamc_1.srnamt, "SSYCON", (ftnlen)32, (ftnlen)6);
ssycon_(uplo, &n, &afac[1], &lda, &iwork[1], &anorm, &
rcond, &work[1], &iwork[n + 1], &info);
/* Check error code from SSYCON. */
if (info != 0) {
alaerh_(path, "SSYCON", &info, &c__0, uplo, &n, &n, &
c_n1, &c_n1, &c_n1, &imat, &nfail, &nerrs,
nout);
}
result[7] = sget06_(&rcond, &rcondc);
/* Print information about the tests that did not pass */
/* the threshold. */
if (result[7] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
alahd_(nout, path);
}
io___44.ciunit = *nout;
s_wsfe(&io___44);
do_fio(&c__1, uplo, (ftnlen)1);
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&imat, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&c__8, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&result[7], (ftnlen)sizeof(real)
);
e_wsfe();
++nfail;
}
++nrun;
L150:
;
}
L160:
;
}
L170:
;
}
/* L180: */
}
/* Print a summary of the results. */
alasum_(path, nout, &nfail, &nrun, &nerrs);
return 0;
/* End of SCHKSY */
} /* schksy_ */
int ssysv_(char *uplo, int *n, int *nrhs, float *a,
int *lda, int *ipiv, float *b, int *ldb, float *work,
int *lwork, int *info)
{
/* System generated locals */
int a_dim1, a_offset, b_dim1, b_offset, i__1;
/* Local variables */
int nb;
extern int lsame_(char *, char *);
extern int xerbla_(char *, int *);
extern int ilaenv_(int *, char *, char *, int *, int *,
int *, int *);
int lwkopt;
int lquery;
extern int ssytrf_(char *, int *, float *, int *,
int *, float *, int *, int *), ssytrs_(char *,
int *, int *, float *, int *, int *, float *,
int *, int *);
/* -- LAPACK driver routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* SSYSV computes the solution to a float system of linear equations */
/* A * X = B, */
/* where A is an N-by-N symmetric matrix and X and B are N-by-NRHS */
/* matrices. */
/* The diagonal pivoting method is used to factor A as */
/* A = U * D * U**T, if UPLO = 'U', or */
/* A = L * D * L**T, if UPLO = 'L', */
/* where U (or L) is a product of permutation and unit upper (lower) */
/* triangular matrices, and D is symmetric and block diagonal with */
/* 1-by-1 and 2-by-2 diagonal blocks. The factored form of A is then */
/* used to solve the system of equations A * X = B. */
/* Arguments */
/* ========= */
/* UPLO (input) CHARACTER*1 */
/* = 'U': Upper triangle of A is stored; */
/* = 'L': Lower triangle of A is stored. */
/* N (input) INTEGER */
/* The number of linear equations, i.e., the order of the */
/* matrix A. N >= 0. */
/* NRHS (input) INTEGER */
/* The number of right hand sides, i.e., the number of columns */
/* of the matrix B. NRHS >= 0. */
/* A (input/output) REAL array, dimension (LDA,N) */
/* On entry, the symmetric matrix A. If UPLO = 'U', the leading */
/* N-by-N upper triangular part of A contains the upper */
/* triangular part of the matrix A, and the strictly lower */
/* triangular part of A is not referenced. If UPLO = 'L', the */
/* leading N-by-N lower triangular part of A contains the lower */
/* triangular part of the matrix A, and the strictly upper */
/* triangular part of A is not referenced. */
/* On exit, if INFO = 0, the block diagonal matrix D and the */
/* multipliers used to obtain the factor U or L from the */
/* factorization A = U*D*U**T or A = L*D*L**T as computed by */
/* SSYTRF. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= MAX(1,N). */
/* IPIV (output) INTEGER array, dimension (N) */
/* Details of the interchanges and the block structure of D, as */
/* determined by SSYTRF. If IPIV(k) > 0, then rows and columns */
/* k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1 */
/* diagonal block. If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, */
/* then rows and columns k-1 and -IPIV(k) were interchanged and */
/* D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = 'L' and */
/* IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and */
/* -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2 */
/* diagonal block. */
/* B (input/output) REAL array, dimension (LDB,NRHS) */
/* On entry, the N-by-NRHS right hand side matrix B. */
/* On exit, if INFO = 0, the N-by-NRHS solution matrix X. */
/* LDB (input) INTEGER */
/* The leading dimension of the array B. LDB >= MAX(1,N). */
/* WORK (workspace/output) REAL array, dimension (MAX(1,LWORK)) */
/* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
/* LWORK (input) INTEGER */
/* The length of WORK. LWORK >= 1, and for best performance */
/* LWORK >= MAX(1,N*NB), where NB is the optimal blocksize for */
/* SSYTRF. */
/* 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, D(i,i) is exactly zero. The factorization */
/* has been completed, but the block diagonal matrix D is */
/* exactly singular, so the solution could not be computed. */
/* ===================================================================== */
/* .. 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;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
--work;
/* Function Body */
*info = 0;
lquery = *lwork == -1;
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 = -8;
} else if (*lwork < 1 && ! lquery) {
*info = -10;
}
if (*info == 0) {
if (*n == 0) {
lwkopt = 1;
} else {
nb = ilaenv_(&c__1, "SSYTRF", uplo, n, &c_n1, &c_n1, &c_n1);
lwkopt = *n * nb;
}
work[1] = (float) lwkopt;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SSYSV ", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Compute the factorization A = U*D*U' or A = L*D*L'. */
ssytrf_(uplo, n, &a[a_offset], lda, &ipiv[1], &work[1], lwork, info);
if (*info == 0) {
/* Solve the system A*X = B, overwriting B with X. */
ssytrs_(uplo, n, nrhs, &a[a_offset], lda, &ipiv[1], &b[b_offset], ldb,
info);
}
work[1] = (float) lwkopt;
return 0;
/* End of SSYSV */
} /* ssysv_ */
