/* Find determinant through LU decomposition. */
float64
determinant(float32 ** a, int32 n)
{
float32 **tmp_a;
float64 det;
char uplo;
int32 info, i;
/* a is assumed to be symmetric, so we don't need to switch the
* ordering of the data. But we do need to copy it since it is
* overwritten by LAPACK. */
tmp_a = (float32 **)ckd_calloc_2d(n, n, sizeof(float32));
memcpy(tmp_a[0], a[0], n*n*sizeof(float32));
uplo = 'L';
spotrf_(&uplo, &n, tmp_a[0], &n, &info);
det = tmp_a[0][0];
/* det = prod(diag(l))^2 */
for (i = 1; i < n; ++i)
det *= tmp_a[i][i];
ckd_free_2d((void **)tmp_a);
if (info > 0)
return -1.0; /* Generic "not positive-definite" answer */
else
return det * det;
}
int main(int argc, char* argv[])
{
if (argc != 2) return usage(argv[0]);
int n = atoi(argv[1]), n2 = n * n;
if (n <= 0) return usage(argv[0]);
// Generate random matrix.
size_t size = sizeof(float) * n2;
float* A1 = (float*)malloc(size);
int one = 1, seed[4] = { 0, 0, 0, 1 };
slarnv_(&one, seed, &n2, A1);
// Symmetrize and increase the diagonal.
for (int i = 0; i < n; i++)
{
A1[i * n + i] += n;
for (int j = 0; j < i; j++)
A1[i * n + j] = A1[j * n + i];
}
// Clone generated matrix for GPU version
// (we can't use one copy of A, because
// spotrf rewrites the input matrix).
float* A2 = (float*)malloc(size);
memcpy(A2, A1, size);
// Use upper part of input matrix and
// rewrite it with Cholessky factor.
char uplo = 'U';
// The status info (routine must return 0 into info).
int info = 0;
// Perform decomposition on CPU.
printf("Computing on CPU ... "); fflush(stdout);
spotrf_(&uplo, &n, A1, &n, &info);
chkerr(info);
// Perform decomposition on GPU.
printf("Computing on GPU ... "); fflush(stdout);
magma_spotrf(uplo, n, A2, n, &info);
chkerr(info);
// Compare results.
float maxdiff = fabs(A1[0] - A2[0]);
for (int i = 0; i < n; i++)
for (int j = 0; j < i; j++)
{
maxdiff = fmax(maxdiff,
fabs(A1[i * n + j] - A2[i * n + j]));
maxdiff = fmax(maxdiff,
fabs(A1[j * n + i] - A2[j * n + i]));
}
printf("Done! max diff = %f\n", maxdiff);
free(A1); free(A2);
}
bool my_inverse(const float in[N][N], float out[N][N], float &det)
{
int errorHandler;
int n = N;
char chU[] = "U";
for (int j = 0; j < N; j++)
for (int i = 0; i < N; i++)
out[j][i] = in[j][i];
spotrf_(chU, &n, &out[0][0], &n, &errorHandler);
assert(errorHandler >= 0);
if (errorHandler > 0)
return true;
det = 1.0;
for (int i = 0; i < N; i++)
det *= out[i][i];
det *= det;
assert(det > 0.0);
spotri_(chU, &n, &out[0][0], &n, &errorHandler);
assert(0 == errorHandler);
for (int i = 0; i < N; i++)
for (int j = i; j < N; j++)
out[i][j] = out[j][i];
return false;
}
/**
* Cholesky factorization of a square, symmetric matrix. The function computes
* an upper triangular matrix <b>Z</b> such that <b>Z</b>'·<b>Z</b> =
* <b>A</b>.
*
* @param Z
* Pointer to output matrix, buffer must be able to hold
* <code>nXD</code><sup>2</sup> double values
* @param A
* Pointer to square, symmetric input matrix, must not be equal
* <code>Z</code>.
* @param nXD
* Number of rows and columns of <code>A</code> and <code>Z</code>
* @return <code>O_K</code> if successful, a (negative) error code otherwise
*/
INT16 dlm_cholf(FLOAT64* Z, const FLOAT64* A, INT32 nXD) {
integer info = 0;
integer n = (integer) nXD;
char uplo[1] = { 'U' };
#ifdef __MAX_TYPE_32BIT
extern int slacpy_(char*,integer*,integer*,real*,integer*,real*,integer *ldb);
extern int spotrf_(char*,integer*,real*,integer*,integer*);
#else
extern int dlacpy_(char*,integer*,integer*,doublereal*,integer*,doublereal*,integer *ldb);
extern int dpotrf_(char*,integer*,doublereal*,integer*,integer*);
#endif
/* Declare variables */
DLPASSERT(Z != A); /* Assert input is not output */
DLPASSERT(dlp_size(Z) >= nXD * nXD * sizeof(FLOAT64)); /* Check size of output buffer */
DLPASSERT(dlp_size(A) >= nXD * nXD * sizeof(FLOAT64)); /* Check size of input buffer */
/* ... computation ... *//* --------------------------------- */
#ifdef __MAX_TYPE_32BIT
spotrf_(uplo, &n, (real*)A, &n, &info);
slacpy_(uplo, &n, &n, (real*)A, &n, (real*)Z, &n);
#else
dpotrf_(uplo, &n, (doublereal*)A, &n, &info);
dlacpy_(uplo, &n, &n, (doublereal*)A, &n, (doublereal*)Z, &n);
#endif
return (info == 0) ? O_K : NOT_EXEC; /* All done successfully */
}
/* Cholesky factorization */
void THLapack_(potrf)(char uplo, int n, real *a, int lda, int *info)
{
#ifdef USE_LAPACK
#if defined(TH_REAL_IS_DOUBLE)
dpotrf_(&uplo, &n, a, &lda, info);
#else
spotrf_(&uplo, &n, a, &lda, info);
#endif
#else
THError("potrf : Lapack library not found in compile time\n");
#endif
}
DLLEXPORT int s_cholesky_factor(int n, float a[]){
char uplo = 'L';
int info = 0;
spotrf_(&uplo, &n, a, &n, &info);
for (int i = 0; i < n; ++i)
{
int index = i * n;
for (int j = 0; j < n && i > j; ++j)
{
a[index + j] = 0;
}
}
return info;
}
/* Cholesky decomposition */
void THLapack_(gpotrf)(char uplo, int n, real *a, int lda, int *info)
{
#ifdef USE_LAPACK
#if defined(TH_REAL_IS_DOUBLE)
extern void dpotrf_(char *uplo, int *n, double *a, int *lda, int *info);
dpotrf_(&uplo, &n, a, &lda, info);
#else
extern void spotrf_(char *uplo, int *n, float *a, int *lda, int *info);
spotrf_(&uplo, &n, a, &lda, info);
#endif
#else
THError("gpotrf : Lapack library not found in compile time\n");
#endif
}
DLLEXPORT MKL_INT s_cholesky_factor(MKL_INT n, float a[]){
char uplo = 'L';
MKL_INT info = 0;
spotrf_(&uplo, &n, a, &n, &info);
for (MKL_INT i = 0; i < n; ++i)
{
MKL_INT index = i * n;
for (MKL_INT j = 0; j < n && i > j; ++j)
{
a[index + j] = 0;
}
}
return info;
}
void cholesky_(char &UPLO, int* N, float*& A, int* LDA, int* INFO){
spotrf_(&UPLO, N, A, LDA, INFO);
// fill the lower part with zeroes
if ('U' == UPLO){
for (int i = 1; i < *N; i++){
for (int j = 0; j < i; j++)
A[j * (*N) + i] = 0.0;
}
} else { // or the upper part if it's 'L'
for (int i = 0; i < (*N - 1); i++){
for (int j = i + 1; j < *N; j++)
A[j * (*N) + i] = 0.0;
}
}
}
DLLEXPORT int s_cholesky_solve(int n, int nrhs, float a[], float b[])
{
float* clone = new float[n*n];
memcpy(clone, a, n*n*sizeof(float));
char uplo = 'L';
int info = 0;
spotrf_(&uplo, &n, clone, &n, &info);
if (info != 0){
delete[] clone;
return info;
}
spotrs_(&uplo, &n, &nrhs, clone, &n, b, &n, &info);
return info;
}
DLLEXPORT MKL_INT s_cholesky_solve(MKL_INT n, MKL_INT nrhs, float a[], float b[])
{
float* clone = new float[n*n];
std::memcpy(clone, a, n*n*sizeof(float));
char uplo = 'L';
MKL_INT info = 0;
spotrf_(&uplo, &n, clone, &n, &info);
if (info != 0){
delete[] clone;
return info;
}
spotrs_(&uplo, &n, &nrhs, clone, &n, b, &n, &info);
delete[] clone;
return info;
}
template <typename fptype> static inline int
lapack_Cholesky(fptype* a, size_t a_step, int m, fptype* b, size_t b_step, int n, bool* info)
{
int lapackStatus;
int lda = a_step / sizeof(fptype);
char L[] = {'L', '\0'};
if(b)
{
if(n == 1 && b_step == sizeof(fptype))
{
if(typeid(fptype) == typeid(float))
sposv_(L, &m, &n, (float*)a, &lda, (float*)b, &m, &lapackStatus);
else if(typeid(fptype) == typeid(double))
dposv_(L, &m, &n, (double*)a, &lda, (double*)b, &m, &lapackStatus);
}
else
{
int ldb = b_step / sizeof(fptype);
fptype* tmpB = new fptype[m*n];
transpose(b, ldb, tmpB, m, m, n);
if(typeid(fptype) == typeid(float))
sposv_(L, &m, &n, (float*)a, &lda, (float*)tmpB, &m, &lapackStatus);
else if(typeid(fptype) == typeid(double))
dposv_(L, &m, &n, (double*)a, &lda, (double*)tmpB, &m, &lapackStatus);
transpose(tmpB, m, b, ldb, n, m);
delete[] tmpB;
}
}
else
{
if(typeid(fptype) == typeid(float))
spotrf_(L, &m, (float*)a, &lda, &lapackStatus);
else if(typeid(fptype) == typeid(double))
dpotrf_(L, &m, (double*)a, &lda, &lapackStatus);
}
if(lapackStatus == 0) *info = true;
else *info = false; //in opencv Cholesky function false means error
return CV_HAL_ERROR_OK;
}
GURLS_EXPORT void cholesky(const gMat2D<float>& A, gMat2D<float>& L, bool upper){
typedef float T;
L = A;
int LDA = A.rows();
int n = A.cols();
char UPLO = upper? 'U' : 'L';
int info;
spotrf_(&UPLO,&n, L.getData(),&LDA,&info);
// This is required because we adopted a column major order to store the
// data into matrices
gMat2D<T> tmp(L.rows(), L.cols());
if (!upper){
L.uppertriangular(tmp);
} else {
L.lowertriangular(tmp);
}
tmp.transpose(L);
}
/* Subroutine */ int ssygv_(integer *itype, char *jobz, char *uplo, integer *
n, real *a, integer *lda, real *b, integer *ldb, real *w, real *work,
integer *lwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2;
/* Local variables */
integer nb, neig;
char trans[1];
logical upper;
logical wantz;
integer lwkmin;
integer lwkopt;
logical lquery;
/* -- LAPACK driver routine (version 3.2) -- */
/* November 2006 */
/* Purpose */
/* ======= */
/* SSYGV computes all the eigenvalues, and optionally, the eigenvectors */
/* of a real generalized symmetric-definite eigenproblem, of the form */
/* A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. */
/* Here A and B are assumed to be symmetric and B is also */
/* positive definite. */
/* Arguments */
/* ========= */
/* ITYPE (input) INTEGER */
/* Specifies the problem type to be solved: */
/* = 1: A*x = (lambda)*B*x */
/* = 2: A*B*x = (lambda)*x */
/* = 3: B*A*x = (lambda)*x */
/* JOBZ (input) CHARACTER*1 */
/* = 'N': Compute eigenvalues only; */
/* = 'V': Compute eigenvalues and eigenvectors. */
/* UPLO (input) CHARACTER*1 */
/* = 'U': Upper triangles of A and B are stored; */
/* = 'L': Lower triangles of A and B are stored. */
/* N (input) INTEGER */
/* The order of the matrices A and B. N >= 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. If UPLO = 'L', */
/* the leading N-by-N lower triangular part of A contains */
/* the lower triangular part of the matrix A. */
/* On exit, if JOBZ = 'V', then if INFO = 0, A contains the */
/* matrix Z of eigenvectors. The eigenvectors are normalized */
/* as follows: */
/* if ITYPE = 1 or 2, Z**T*B*Z = I; */
/* if ITYPE = 3, Z**T*inv(B)*Z = I. */
/* If JOBZ = 'N', then on exit the upper triangle (if UPLO='U') */
/* or the lower triangle (if UPLO='L') of A, including the */
/* diagonal, is destroyed. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,N). */
/* B (input/output) REAL array, dimension (LDB, N) */
/* On entry, the symmetric positive definite matrix B. */
/* If UPLO = 'U', the leading N-by-N upper triangular part of B */
/* contains the upper triangular part of the matrix B. */
/* If UPLO = 'L', the leading N-by-N lower triangular part of B */
/* contains the lower triangular part of the matrix B. */
/* On exit, if INFO <= N, the part of B containing the matrix is */
/* overwritten by the triangular factor U or L from the Cholesky */
/* factorization B = U**T*U or B = L*L**T. */
/* LDB (input) INTEGER */
/* The leading dimension of the array B. LDB >= max(1,N). */
/* W (output) REAL array, dimension (N) */
/* If INFO = 0, the eigenvalues in ascending order. */
/* 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 the array WORK. LWORK >= max(1,3*N-1). */
/* For optimal efficiency, LWORK >= (NB+2)*N, */
/* where NB is the blocksize for SSYTRD returned by ILAENV. */
/* If LWORK = -1, then a workspace query is assumed; the routine */
/* only calculates the optimal size of the WORK array, returns */
/* this value as the first entry of the WORK array, and no error */
/* message related to LWORK is issued by XERBLA. */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* > 0: SPOTRF or SSYEV returned an error code: */
/* <= N: if INFO = i, SSYEV failed to converge; */
/* i off-diagonal elements of an intermediate */
/* tridiagonal form did not converge to zero; */
/* > N: if INFO = N + i, for 1 <= i <= N, then the leading */
/* minor of order i of B is not positive definite. */
/* The factorization of B could not be completed and */
/* no eigenvalues or eigenvectors were computed. */
/* ===================================================================== */
/* Test the input parameters. */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
--w;
--work;
/* Function Body */
wantz = lsame_(jobz, "V");
upper = lsame_(uplo, "U");
lquery = *lwork == -1;
*info = 0;
if (*itype < 1 || *itype > 3) {
*info = -1;
} else if (! (wantz || lsame_(jobz, "N"))) {
*info = -2;
} else if (! (upper || lsame_(uplo, "L"))) {
*info = -3;
} else if (*n < 0) {
*info = -4;
} else if (*lda < max(1,*n)) {
*info = -6;
} else if (*ldb < max(1,*n)) {
*info = -8;
}
if (*info == 0) {
/* Computing MAX */
i__1 = 1, i__2 = *n * 3 - 1;
lwkmin = max(i__1,i__2);
nb = ilaenv_(&c__1, "SSYTRD", uplo, n, &c_n1, &c_n1, &c_n1);
/* Computing MAX */
i__1 = lwkmin, i__2 = (nb + 2) * *n;
lwkopt = max(i__1,i__2);
work[1] = (real) lwkopt;
if (*lwork < lwkmin && ! lquery) {
*info = -11;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SSYGV ", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/* Form a Cholesky factorization of B. */
spotrf_(uplo, n, &b[b_offset], ldb, info);
if (*info != 0) {
*info = *n + *info;
return 0;
}
/* Transform problem to standard eigenvalue problem and solve. */
ssygst_(itype, uplo, n, &a[a_offset], lda, &b[b_offset], ldb, info);
ssyev_(jobz, uplo, n, &a[a_offset], lda, &w[1], &work[1], lwork, info);
if (wantz) {
/* Backtransform eigenvectors to the original problem. */
neig = *n;
if (*info > 0) {
neig = *info - 1;
}
if (*itype == 1 || *itype == 2) {
/* For A*x=(lambda)*B*x and A*B*x=(lambda)*x; */
/* backtransform eigenvectors: x = inv(L)'*y or inv(U)*y */
if (upper) {
*(unsigned char *)trans = 'N';
} else {
*(unsigned char *)trans = 'T';
}
strsm_("Left", uplo, trans, "Non-unit", n, &neig, &c_b16, &b[
b_offset], ldb, &a[a_offset], lda);
} else if (*itype == 3) {
/* For B*A*x=(lambda)*x; */
/* backtransform eigenvectors: x = L*y or U'*y */
if (upper) {
*(unsigned char *)trans = 'T';
} else {
*(unsigned char *)trans = 'N';
}
strmm_("Left", uplo, trans, "Non-unit", n, &neig, &c_b16, &b[
b_offset], ldb, &a[a_offset], lda);
}
}
work[1] = (real) lwkopt;
return 0;
/* End of SSYGV */
} /* ssygv_ */
/* Subroutine */ int ssygvd_(integer *itype, char *jobz, char *uplo, integer *
n, real *a, integer *lda, real *b, integer *ldb, real *w, real *work,
integer *lwork, integer *iwork, integer *liwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, i__1;
real r__1, r__2;
/* Local variables */
integer lopt;
extern logical lsame_(char *, char *);
integer lwmin;
char trans[1];
integer liopt;
logical upper;
extern /* Subroutine */ int strmm_(char *, char *, char *, char *,
integer *, integer *, real *, real *, integer *, real *, integer *
);
logical wantz;
extern /* Subroutine */ int strsm_(char *, char *, char *, char *,
integer *, integer *, real *, real *, integer *, real *, integer *
), xerbla_(char *, integer *);
integer liwmin;
extern /* Subroutine */ int spotrf_(char *, integer *, real *, integer *,
integer *), ssyevd_(char *, char *, integer *, real *,
integer *, real *, real *, integer *, integer *, integer *,
integer *);
logical lquery;
extern /* Subroutine */ int ssygst_(integer *, char *, integer *, real *,
integer *, real *, integer *, integer *);
/* -- LAPACK driver routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* SSYGVD computes all the eigenvalues, and optionally, the eigenvectors */
/* of a real generalized symmetric-definite eigenproblem, of the form */
/* A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and */
/* B are assumed to be symmetric and B is also positive definite. */
/* If eigenvectors are desired, it uses a divide and conquer algorithm. */
/* The divide and conquer algorithm makes very mild assumptions about */
/* floating point arithmetic. It will work on machines with a guard */
/* digit in add/subtract, or on those binary machines without guard */
/* digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or */
/* Cray-2. It could conceivably fail on hexadecimal or decimal machines */
/* without guard digits, but we know of none. */
/* Arguments */
/* ========= */
/* ITYPE (input) INTEGER */
/* Specifies the problem type to be solved: */
/* = 1: A*x = (lambda)*B*x */
/* = 2: A*B*x = (lambda)*x */
/* = 3: B*A*x = (lambda)*x */
/* JOBZ (input) CHARACTER*1 */
/* = 'N': Compute eigenvalues only; */
/* = 'V': Compute eigenvalues and eigenvectors. */
/* UPLO (input) CHARACTER*1 */
/* = 'U': Upper triangles of A and B are stored; */
/* = 'L': Lower triangles of A and B are stored. */
/* N (input) INTEGER */
/* The order of the matrices A and B. N >= 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. If UPLO = 'L', */
/* the leading N-by-N lower triangular part of A contains */
/* the lower triangular part of the matrix A. */
/* On exit, if JOBZ = 'V', then if INFO = 0, A contains the */
/* matrix Z of eigenvectors. The eigenvectors are normalized */
/* as follows: */
/* if ITYPE = 1 or 2, Z**T*B*Z = I; */
/* if ITYPE = 3, Z**T*inv(B)*Z = I. */
/* If JOBZ = 'N', then on exit the upper triangle (if UPLO='U') */
/* or the lower triangle (if UPLO='L') of A, including the */
/* diagonal, is destroyed. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,N). */
/* B (input/output) REAL array, dimension (LDB, N) */
/* On entry, the symmetric matrix B. If UPLO = 'U', the */
/* leading N-by-N upper triangular part of B contains the */
/* upper triangular part of the matrix B. If UPLO = 'L', */
/* the leading N-by-N lower triangular part of B contains */
/* the lower triangular part of the matrix B. */
/* On exit, if INFO <= N, the part of B containing the matrix is */
/* overwritten by the triangular factor U or L from the Cholesky */
/* factorization B = U**T*U or B = L*L**T. */
/* LDB (input) INTEGER */
/* The leading dimension of the array B. LDB >= max(1,N). */
/* W (output) REAL array, dimension (N) */
/* If INFO = 0, the eigenvalues in ascending order. */
/* WORK (workspace/output) REAL array, dimension (MAX(1,LWORK)) */
/* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
/* LWORK (input) INTEGER */
/* The dimension of the array WORK. */
/* If N <= 1, LWORK >= 1. */
/* If JOBZ = 'N' and N > 1, LWORK >= 2*N+1. */
/* If JOBZ = 'V' and N > 1, LWORK >= 1 + 6*N + 2*N**2. */
/* If LWORK = -1, then a workspace query is assumed; the routine */
/* only calculates the optimal sizes of the WORK and IWORK */
/* arrays, returns these values as the first entries of the WORK */
/* and IWORK arrays, and no error message related to LWORK or */
/* LIWORK is issued by XERBLA. */
/* IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK)) */
/* On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. */
/* LIWORK (input) INTEGER */
/* The dimension of the array IWORK. */
/* If N <= 1, LIWORK >= 1. */
/* If JOBZ = 'N' and N > 1, LIWORK >= 1. */
/* If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N. */
/* If LIWORK = -1, then a workspace query is assumed; the */
/* routine only calculates the optimal sizes of the WORK and */
/* IWORK arrays, returns these values as the first entries of */
/* the WORK and IWORK arrays, and no error message related to */
/* LWORK or LIWORK is issued by XERBLA. */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* > 0: SPOTRF or SSYEVD returned an error code: */
/* <= N: if INFO = i and JOBZ = 'N', then the algorithm */
/* failed to converge; i off-diagonal elements of an */
/* intermediate tridiagonal form did not converge to */
/* zero; */
/* if INFO = i and JOBZ = 'V', then the algorithm */
/* failed to compute an eigenvalue while working on */
/* the submatrix lying in rows and columns INFO/(N+1) */
/* through mod(INFO,N+1); */
/* > N: if INFO = N + i, for 1 <= i <= N, then the leading */
/* minor of order i of B is not positive definite. */
/* The factorization of B could not be completed and */
/* no eigenvalues or eigenvectors were computed. */
/* Further Details */
/* =============== */
/* Based on contributions by */
/* Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA */
/* Modified so that no backsubstitution is performed if SSYEVD fails to */
/* converge (NEIG in old code could be greater than N causing out of */
/* bounds reference to A - reported by Ralf Meyer). Also corrected the */
/* description of INFO and the test on ITYPE. Sven, 16 Feb 05. */
/* ===================================================================== */
/* .. 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;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
--w;
--work;
--iwork;
/* Function Body */
wantz = lsame_(jobz, "V");
upper = lsame_(uplo, "U");
lquery = *lwork == -1 || *liwork == -1;
*info = 0;
if (*n <= 1) {
liwmin = 1;
lwmin = 1;
} else if (wantz) {
liwmin = *n * 5 + 3;
/* Computing 2nd power */
i__1 = *n;
lwmin = *n * 6 + 1 + (i__1 * i__1 << 1);
} else {
liwmin = 1;
lwmin = (*n << 1) + 1;
}
lopt = lwmin;
liopt = liwmin;
if (*itype < 1 || *itype > 3) {
*info = -1;
} else if (! (wantz || lsame_(jobz, "N"))) {
*info = -2;
} else if (! (upper || lsame_(uplo, "L"))) {
*info = -3;
} else if (*n < 0) {
*info = -4;
} else if (*lda < max(1,*n)) {
*info = -6;
} else if (*ldb < max(1,*n)) {
*info = -8;
}
if (*info == 0) {
work[1] = (real) lopt;
iwork[1] = liopt;
if (*lwork < lwmin && ! lquery) {
*info = -11;
} else if (*liwork < liwmin && ! lquery) {
*info = -13;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SSYGVD", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/* Form a Cholesky factorization of B. */
spotrf_(uplo, n, &b[b_offset], ldb, info);
if (*info != 0) {
*info = *n + *info;
return 0;
}
/* Transform problem to standard eigenvalue problem and solve. */
ssygst_(itype, uplo, n, &a[a_offset], lda, &b[b_offset], ldb, info);
ssyevd_(jobz, uplo, n, &a[a_offset], lda, &w[1], &work[1], lwork, &iwork[
1], liwork, info);
/* Computing MAX */
r__1 = (real) lopt;
lopt = dmax(r__1,work[1]);
/* Computing MAX */
r__1 = (real) liopt, r__2 = (real) iwork[1];
liopt = dmax(r__1,r__2);
if (wantz && *info == 0) {
/* Backtransform eigenvectors to the original problem. */
if (*itype == 1 || *itype == 2) {
/* For A*x=(lambda)*B*x and A*B*x=(lambda)*x; */
/* backtransform eigenvectors: x = inv(L)'*y or inv(U)*y */
if (upper) {
*(unsigned char *)trans = 'N';
} else {
*(unsigned char *)trans = 'T';
}
strsm_("Left", uplo, trans, "Non-unit", n, n, &c_b11, &b[b_offset]
, ldb, &a[a_offset], lda);
} else if (*itype == 3) {
/* For B*A*x=(lambda)*x; */
/* backtransform eigenvectors: x = L*y or U'*y */
if (upper) {
*(unsigned char *)trans = 'T';
} else {
*(unsigned char *)trans = 'N';
}
strmm_("Left", uplo, trans, "Non-unit", n, n, &c_b11, &b[b_offset]
, ldb, &a[a_offset], lda);
}
}
work[1] = (real) lopt;
iwork[1] = liopt;
return 0;
/* End of SSYGVD */
} /* ssygvd_ */
/* Subroutine */ int sposvxx_(char *fact, char *uplo, integer *n, integer *
nrhs, real *a, integer *lda, real *af, integer *ldaf, char *equed,
real *s, real *b, integer *ldb, real *x, integer *ldx, real *rcond,
real *rpvgrw, real *berr, integer *n_err_bnds__, real *
err_bnds_norm__, real *err_bnds_comp__, integer *nparams, real *
params, real *work, integer *iwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, af_dim1, af_offset, b_dim1, b_offset, x_dim1,
x_offset, err_bnds_norm_dim1, err_bnds_norm_offset,
err_bnds_comp_dim1, err_bnds_comp_offset, i__1;
real r__1, r__2;
/* Local variables */
integer j;
real amax, smin, smax;
extern doublereal sla_porpvgrw__(char *, integer *, real *, integer *,
real *, integer *, real *, ftnlen);
extern logical lsame_(char *, char *);
real scond;
logical equil, rcequ;
extern doublereal slamch_(char *);
logical nofact;
extern /* Subroutine */ int xerbla_(char *, integer *);
real bignum;
integer infequ;
extern /* Subroutine */ int slacpy_(char *, integer *, integer *, real *,
integer *, real *, integer *);
real smlnum;
extern /* Subroutine */ int slaqsy_(char *, integer *, real *, integer *,
real *, real *, real *, char *), spotrf_(char *,
integer *, real *, integer *, integer *), spotrs_(char *,
integer *, integer *, real *, integer *, real *, integer *,
integer *), slascl2_(integer *, integer *, real *, real *,
integer *), spoequb_(integer *, real *, integer *, real *, real *
, real *, integer *), sporfsx_(char *, char *, integer *, integer
*, real *, integer *, real *, integer *, real *, real *, integer *
, real *, integer *, real *, real *, integer *, real *, real *,
integer *, real *, real *, integer *, integer *);
/* -- LAPACK driver routine (version 3.2) -- */
/* -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and -- */
/* -- Jason Riedy of Univ. of California Berkeley. -- */
/* -- November 2008 -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley and NAG Ltd. -- */
/* .. */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* SPOSVXX uses the Cholesky factorization A = U**T*U or A = L*L**T */
/* to compute the solution to a real system of linear equations */
/* A * X = B, where A is an N-by-N symmetric positive definite matrix */
/* and X and B are N-by-NRHS matrices. */
/* If requested, both normwise and maximum componentwise error bounds */
/* are returned. SPOSVXX will return a solution with a tiny */
/* guaranteed error (O(eps) where eps is the working machine */
/* precision) unless the matrix is very ill-conditioned, in which */
/* case a warning is returned. Relevant condition numbers also are */
/* calculated and returned. */
/* SPOSVXX accepts user-provided factorizations and equilibration */
/* factors; see the definitions of the FACT and EQUED options. */
/* Solving with refinement and using a factorization from a previous */
/* SPOSVXX call will also produce a solution with either O(eps) */
/* errors or warnings, but we cannot make that claim for general */
/* user-provided factorizations and equilibration factors if they */
/* differ from what SPOSVXX would itself produce. */
/* Description */
/* =========== */
/* The following steps are performed: */
/* 1. If FACT = 'E', real scaling factors are computed to equilibrate */
/* the system: */
/* diag(S)*A*diag(S) *inv(diag(S))*X = diag(S)*B */
/* Whether or not the system will be equilibrated depends on the */
/* scaling of the matrix A, but if equilibration is used, A is */
/* overwritten by diag(S)*A*diag(S) and B by diag(S)*B. */
/* 2. If FACT = 'N' or 'E', the Cholesky decomposition is used to */
/* factor the matrix A (after equilibration if FACT = 'E') as */
/* A = U**T* U, if UPLO = 'U', or */
/* A = L * L**T, if UPLO = 'L', */
/* where U is an upper triangular matrix and L is a lower triangular */
/* matrix. */
/* 3. If the leading i-by-i principal minor is not positive definite, */
/* then the routine returns with INFO = i. Otherwise, the factored */
/* form of A is used to estimate the condition number of the matrix */
/* A (see argument RCOND). If the reciprocal of the condition number */
/* is less than machine precision, the routine still goes on to solve */
/* for X and compute error bounds as described below. */
/* 4. The system of equations is solved for X using the factored form */
/* of A. */
/* 5. By default (unless PARAMS(LA_LINRX_ITREF_I) is set to zero), */
/* the routine will use iterative refinement to try to get a small */
/* error and error bounds. Refinement calculates the residual to at */
/* least twice the working precision. */
/* 6. If equilibration was used, the matrix X is premultiplied by */
/* diag(S) so that it solves the original system before */
/* equilibration. */
/* Arguments */
/* ========= */
/* Some optional parameters are bundled in the PARAMS array. These */
/* settings determine how refinement is performed, but often the */
/* defaults are acceptable. If the defaults are acceptable, users */
/* can pass NPARAMS = 0 which prevents the source code from accessing */
/* the PARAMS argument. */
/* FACT (input) CHARACTER*1 */
/* Specifies whether or not the factored form of the matrix A is */
/* supplied on entry, and if not, whether the matrix A should be */
/* equilibrated before it is factored. */
/* = 'F': On entry, AF contains the factored form of A. */
/* If EQUED is not 'N', the matrix A has been */
/* equilibrated with scaling factors given by S. */
/* A and AF are not modified. */
/* = 'N': The matrix A will be copied to AF and factored. */
/* = 'E': The matrix A will be equilibrated if necessary, then */
/* 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/output) REAL array, dimension (LDA,N) */
/* On entry, the symmetric matrix A, except if FACT = 'F' and EQUED = */
/* 'Y', then A must contain the equilibrated matrix */
/* diag(S)*A*diag(S). 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. A is */
/* not modified if FACT = 'F' or 'N', or if FACT = 'E' and EQUED = */
/* 'N' on exit. */
/* On exit, if FACT = 'E' and EQUED = 'Y', A is overwritten by */
/* diag(S)*A*diag(S). */
/* 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 triangular factor U or L from the Cholesky */
/* factorization A = U**T*U or A = L*L**T, in the same storage */
/* format as A. If EQUED .ne. 'N', then AF is the factored */
/* form of the equilibrated matrix diag(S)*A*diag(S). */
/* If FACT = 'N', then AF is an output argument and on exit */
/* returns the triangular factor U or L from the Cholesky */
/* factorization A = U**T*U or A = L*L**T of the original */
/* matrix A. */
/* If FACT = 'E', then AF is an output argument and on exit */
/* returns the triangular factor U or L from the Cholesky */
/* factorization A = U**T*U or A = L*L**T of the equilibrated */
/* matrix A (see the description of A for the form of the */
/* equilibrated matrix). */
/* LDAF (input) INTEGER */
/* The leading dimension of the array AF. LDAF >= max(1,N). */
/* EQUED (input or output) CHARACTER*1 */
/* Specifies the form of equilibration that was done. */
/* = 'N': No equilibration (always true if FACT = 'N'). */
/* = 'Y': Both row and column equilibration, i.e., A has been */
/* replaced by diag(S) * A * diag(S). */
/* EQUED is an input argument if FACT = 'F'; otherwise, it is an */
/* output argument. */
/* S (input or output) REAL array, dimension (N) */
/* The row scale factors for A. If EQUED = 'Y', A is multiplied on */
/* the left and right by diag(S). S is an input argument if FACT = */
/* 'F'; otherwise, S is an output argument. If FACT = 'F' and EQUED */
/* = 'Y', each element of S must be positive. If S is output, each */
/* element of S is a power of the radix. If S is input, each element */
/* of S should be a power of the radix to ensure a reliable solution */
/* and error estimates. Scaling by powers of the radix does not cause */
/* rounding errors unless the result underflows or overflows. */
/* Rounding errors during scaling lead to refining with a matrix that */
/* is not equivalent to the input matrix, producing error estimates */
/* that may not be reliable. */
/* B (input/output) REAL array, dimension (LDB,NRHS) */
/* On entry, the N-by-NRHS right hand side matrix B. */
/* On exit, */
/* if EQUED = 'N', B is not modified; */
/* if EQUED = 'Y', B is overwritten by diag(S)*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, the N-by-NRHS solution matrix X to the original */
/* system of equations. Note that A and B are modified on exit if */
/* EQUED .ne. 'N', and the solution to the equilibrated system is */
/* inv(diag(S))*X. */
/* LDX (input) INTEGER */
/* The leading dimension of the array X. LDX >= max(1,N). */
/* RCOND (output) REAL */
/* Reciprocal scaled condition number. This is an estimate of the */
/* reciprocal Skeel condition number of the matrix A after */
/* equilibration (if done). If this is less than the machine */
/* precision (in particular, if it is zero), the matrix is singular */
/* to working precision. Note that the error may still be small even */
/* if this number is very small and the matrix appears ill- */
/* conditioned. */
/* RPVGRW (output) REAL */
/* Reciprocal pivot growth. On exit, this contains the reciprocal */
/* pivot growth factor norm(A)/norm(U). The "max absolute element" */
/* norm is used. If this is much less than 1, then the stability of */
/* the LU factorization of the (equilibrated) matrix A could be poor. */
/* This also means that the solution X, estimated condition numbers, */
/* and error bounds could be unreliable. If factorization fails with */
/* 0<INFO<=N, then this contains the reciprocal pivot growth factor */
/* for the leading INFO columns of A. */
/* BERR (output) REAL array, dimension (NRHS) */
/* Componentwise relative backward error. This is 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). */
/* N_ERR_BNDS (input) INTEGER */
/* Number of error bounds to return for each right hand side */
/* and each type (normwise or componentwise). See ERR_BNDS_NORM and */
/* ERR_BNDS_COMP below. */
/* ERR_BNDS_NORM (output) REAL array, dimension (NRHS, N_ERR_BNDS) */
/* For each right-hand side, this array contains information about */
/* various error bounds and condition numbers corresponding to the */
/* normwise relative error, which is defined as follows: */
/* Normwise relative error in the ith solution vector: */
/* max_j (abs(XTRUE(j,i) - X(j,i))) */
/* ------------------------------ */
/* max_j abs(X(j,i)) */
/* The array is indexed by the type of error information as described */
/* below. There currently are up to three pieces of information */
/* returned. */
/* The first index in ERR_BNDS_NORM(i,:) corresponds to the ith */
/* right-hand side. */
/* The second index in ERR_BNDS_NORM(:,err) contains the following */
/* three fields: */
/* err = 1 "Trust/don't trust" boolean. Trust the answer if the */
/* reciprocal condition number is less than the threshold */
/* sqrt(n) * slamch('Epsilon'). */
/* err = 2 "Guaranteed" error bound: The estimated forward error, */
/* almost certainly within a factor of 10 of the true error */
/* so long as the next entry is greater than the threshold */
/* sqrt(n) * slamch('Epsilon'). This error bound should only */
/* be trusted if the previous boolean is true. */
/* err = 3 Reciprocal condition number: Estimated normwise */
/* reciprocal condition number. Compared with the threshold */
/* sqrt(n) * slamch('Epsilon') to determine if the error */
/* estimate is "guaranteed". These reciprocal condition */
/* numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */
/* appropriately scaled matrix Z. */
/* Let Z = S*A, where S scales each row by a power of the */
/* radix so all absolute row sums of Z are approximately 1. */
/* See Lapack Working Note 165 for further details and extra */
/* cautions. */
/* ERR_BNDS_COMP (output) REAL array, dimension (NRHS, N_ERR_BNDS) */
/* For each right-hand side, this array contains information about */
/* various error bounds and condition numbers corresponding to the */
/* componentwise relative error, which is defined as follows: */
/* Componentwise relative error in the ith solution vector: */
/* abs(XTRUE(j,i) - X(j,i)) */
/* max_j ---------------------- */
/* abs(X(j,i)) */
/* The array is indexed by the right-hand side i (on which the */
/* componentwise relative error depends), and the type of error */
/* information as described below. There currently are up to three */
/* pieces of information returned for each right-hand side. If */
/* componentwise accuracy is not requested (PARAMS(3) = 0.0), then */
/* ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most */
/* the first (:,N_ERR_BNDS) entries are returned. */
/* The first index in ERR_BNDS_COMP(i,:) corresponds to the ith */
/* right-hand side. */
/* The second index in ERR_BNDS_COMP(:,err) contains the following */
/* three fields: */
/* err = 1 "Trust/don't trust" boolean. Trust the answer if the */
/* reciprocal condition number is less than the threshold */
/* sqrt(n) * slamch('Epsilon'). */
/* err = 2 "Guaranteed" error bound: The estimated forward error, */
/* almost certainly within a factor of 10 of the true error */
/* so long as the next entry is greater than the threshold */
/* sqrt(n) * slamch('Epsilon'). This error bound should only */
/* be trusted if the previous boolean is true. */
/* err = 3 Reciprocal condition number: Estimated componentwise */
/* reciprocal condition number. Compared with the threshold */
/* sqrt(n) * slamch('Epsilon') to determine if the error */
/* estimate is "guaranteed". These reciprocal condition */
/* numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */
/* appropriately scaled matrix Z. */
/* Let Z = S*(A*diag(x)), where x is the solution for the */
/* current right-hand side and S scales each row of */
/* A*diag(x) by a power of the radix so all absolute row */
/* sums of Z are approximately 1. */
/* See Lapack Working Note 165 for further details and extra */
/* cautions. */
/* NPARAMS (input) INTEGER */
/* Specifies the number of parameters set in PARAMS. If .LE. 0, the */
/* PARAMS array is never referenced and default values are used. */
/* PARAMS (input / output) REAL array, dimension NPARAMS */
/* Specifies algorithm parameters. If an entry is .LT. 0.0, then */
/* that entry will be filled with default value used for that */
/* parameter. Only positions up to NPARAMS are accessed; defaults */
/* are used for higher-numbered parameters. */
/* PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative */
/* refinement or not. */
/* Default: 1.0 */
/* = 0.0 : No refinement is performed, and no error bounds are */
/* computed. */
/* = 1.0 : Use the double-precision refinement algorithm, */
/* possibly with doubled-single computations if the */
/* compilation environment does not support DOUBLE */
/* PRECISION. */
/* (other values are reserved for future use) */
/* PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual */
/* computations allowed for refinement. */
/* Default: 10 */
/* Aggressive: Set to 100 to permit convergence using approximate */
/* factorizations or factorizations other than LU. If */
/* the factorization uses a technique other than */
/* Gaussian elimination, the guarantees in */
/* err_bnds_norm and err_bnds_comp may no longer be */
/* trustworthy. */
/* PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code */
/* will attempt to find a solution with small componentwise */
/* relative error in the double-precision algorithm. Positive */
/* is true, 0.0 is false. */
/* Default: 1.0 (attempt componentwise convergence) */
/* WORK (workspace) REAL array, dimension (4*N) */
/* IWORK (workspace) INTEGER array, dimension (N) */
/* INFO (output) INTEGER */
/* = 0: Successful exit. The solution to every right-hand side is */
/* guaranteed. */
/* < 0: If INFO = -i, the i-th argument had an illegal value */
/* > 0 and <= N: U(INFO,INFO) is exactly zero. The factorization */
/* has been completed, but the factor U is exactly singular, so */
/* the solution and error bounds could not be computed. RCOND = 0 */
/* is returned. */
/* = N+J: The solution corresponding to the Jth right-hand side is */
/* not guaranteed. The solutions corresponding to other right- */
/* hand sides K with K > J may not be guaranteed as well, but */
/* only the first such right-hand side is reported. If a small */
/* componentwise error is not requested (PARAMS(3) = 0.0) then */
/* the Jth right-hand side is the first with a normwise error */
/* bound that is not guaranteed (the smallest J such */
/* that ERR_BNDS_NORM(J,1) = 0.0). By default (PARAMS(3) = 1.0) */
/* the Jth right-hand side is the first with either a normwise or */
/* componentwise error bound that is not guaranteed (the smallest */
/* J such that either ERR_BNDS_NORM(J,1) = 0.0 or */
/* ERR_BNDS_COMP(J,1) = 0.0). See the definition of */
/* ERR_BNDS_NORM(:,1) and ERR_BNDS_COMP(:,1). To get information */
/* about all of the right-hand sides check ERR_BNDS_NORM or */
/* ERR_BNDS_COMP. */
/* ================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
err_bnds_comp_dim1 = *nrhs;
err_bnds_comp_offset = 1 + err_bnds_comp_dim1;
err_bnds_comp__ -= err_bnds_comp_offset;
err_bnds_norm_dim1 = *nrhs;
err_bnds_norm_offset = 1 + err_bnds_norm_dim1;
err_bnds_norm__ -= err_bnds_norm_offset;
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
af_dim1 = *ldaf;
af_offset = 1 + af_dim1;
af -= af_offset;
--s;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
x_dim1 = *ldx;
x_offset = 1 + x_dim1;
x -= x_offset;
--berr;
--params;
--work;
--iwork;
/* Function Body */
*info = 0;
nofact = lsame_(fact, "N");
equil = lsame_(fact, "E");
smlnum = slamch_("Safe minimum");
bignum = 1.f / smlnum;
if (nofact || equil) {
*(unsigned char *)equed = 'N';
rcequ = FALSE_;
} else {
rcequ = lsame_(equed, "Y");
}
/* Default is failure. If an input parameter is wrong or */
/* factorization fails, make everything look horrible. Only the */
/* pivot growth is set here, the rest is initialized in SPORFSX. */
*rpvgrw = 0.f;
/* Test the input parameters. PARAMS is not tested until SPORFSX. */
if (! nofact && ! equil && ! 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 (lsame_(fact, "F") && ! (rcequ || lsame_(
equed, "N"))) {
*info = -9;
} else {
if (rcequ) {
smin = bignum;
smax = 0.f;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
r__1 = smin, r__2 = s[j];
smin = dmin(r__1,r__2);
/* Computing MAX */
r__1 = smax, r__2 = s[j];
smax = dmax(r__1,r__2);
/* L10: */
}
if (smin <= 0.f) {
*info = -10;
} else if (*n > 0) {
scond = dmax(smin,smlnum) / dmin(smax,bignum);
} else {
scond = 1.f;
}
}
if (*info == 0) {
if (*ldb < max(1,*n)) {
*info = -12;
} else if (*ldx < max(1,*n)) {
*info = -14;
}
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SPOSVXX", &i__1);
return 0;
}
if (equil) {
/* Compute row and column scalings to equilibrate the matrix A. */
spoequb_(n, &a[a_offset], lda, &s[1], &scond, &amax, &infequ);
if (infequ == 0) {
/* Equilibrate the matrix. */
slaqsy_(uplo, n, &a[a_offset], lda, &s[1], &scond, &amax, equed);
rcequ = lsame_(equed, "Y");
}
}
/* Scale the right-hand side. */
if (rcequ) {
slascl2_(n, nrhs, &s[1], &b[b_offset], ldb);
}
if (nofact || equil) {
/* Compute the LU factorization of A. */
slacpy_(uplo, n, n, &a[a_offset], lda, &af[af_offset], ldaf);
spotrf_(uplo, n, &af[af_offset], ldaf, info);
/* Return if INFO is non-zero. */
if (*info != 0) {
/* Pivot in column INFO is exactly 0 */
/* Compute the reciprocal pivot growth factor of the */
/* leading rank-deficient INFO columns of A. */
*rpvgrw = sla_porpvgrw__(uplo, info, &a[a_offset], lda, &af[
af_offset], ldaf, &work[1], (ftnlen)1);
return 0;
}
}
/* Compute the reciprocal growth factor RPVGRW. */
*rpvgrw = sla_porpvgrw__(uplo, n, &a[a_offset], lda, &af[af_offset], ldaf,
&work[1], (ftnlen)1);
/* Compute the solution matrix X. */
slacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx);
spotrs_(uplo, n, nrhs, &af[af_offset], ldaf, &x[x_offset], ldx, info);
/* Use iterative refinement to improve the computed solution and */
/* compute error bounds and backward error estimates for it. */
sporfsx_(uplo, equed, n, nrhs, &a[a_offset], lda, &af[af_offset], ldaf, &
s[1], &b[b_offset], ldb, &x[x_offset], ldx, rcond, &berr[1],
n_err_bnds__, &err_bnds_norm__[err_bnds_norm_offset], &
err_bnds_comp__[err_bnds_comp_offset], nparams, ¶ms[1], &work[
1], &iwork[1], info);
/* Scale solutions. */
if (rcequ) {
slascl2_(n, nrhs, &s[1], &x[x_offset], ldx);
}
return 0;
/* End of SPOSVXX */
} /* sposvxx_ */
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 info, info_i;
lapack_int i;
int failed;
/* Local arrays */
float *a = NULL, *a_i = NULL;
float *a_save = NULL;
float *a_r = NULL;
/* Iniitialize the scalar parameters */
init_scalars_spotrf( &uplo, &n, &lda );
lda_r = n+2;
uplo_i = uplo;
n_i = n;
lda_i = lda;
/* Allocate memory for the LAPACK routine arrays */
a = (float *)LAPACKE_malloc( lda*n * sizeof(float) );
/* Allocate memory for the C interface function arrays */
a_i = (float *)LAPACKE_malloc( lda*n * sizeof(float) );
/* Allocate memory for the backup arrays */
a_save = (float *)LAPACKE_malloc( lda*n * sizeof(float) );
/* 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 );
/* Backup the ouptut arrays */
for( i = 0; i < lda*n; i++ ) {
a_save[i] = a[i];
}
/* Call the LAPACK routine */
spotrf_( &uplo, &n, a, &lda, &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];
}
info_i = LAPACKE_spotrf_work( LAPACK_COL_MAJOR, uplo_i, n_i, a_i, lda_i );
failed = compare_spotrf( a, a_i, info, info_i, lda, n );
if( failed == 0 ) {
printf( "PASSED: column-major middle-level interface to spotrf\n" );
} else {
printf( "FAILED: column-major middle-level interface to spotrf\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];
}
info_i = LAPACKE_spotrf( LAPACK_COL_MAJOR, uplo_i, n_i, a_i, lda_i );
failed = compare_spotrf( a, a_i, info, info_i, lda, n );
if( failed == 0 ) {
printf( "PASSED: column-major high-level interface to spotrf\n" );
} else {
printf( "FAILED: column-major high-level interface to spotrf\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];
}
LAPACKE_sge_trans( LAPACK_COL_MAJOR, n, n, a_i, lda, a_r, n+2 );
info_i = LAPACKE_spotrf_work( LAPACK_ROW_MAJOR, uplo_i, n_i, a_r, lda_r );
LAPACKE_sge_trans( LAPACK_ROW_MAJOR, n, n, a_r, n+2, a_i, lda );
failed = compare_spotrf( a, a_i, info, info_i, lda, n );
if( failed == 0 ) {
printf( "PASSED: row-major middle-level interface to spotrf\n" );
} else {
printf( "FAILED: row-major middle-level interface to spotrf\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];
}
/* Init row_major arrays */
LAPACKE_sge_trans( LAPACK_COL_MAJOR, n, n, a_i, lda, a_r, n+2 );
info_i = LAPACKE_spotrf( LAPACK_ROW_MAJOR, uplo_i, n_i, a_r, lda_r );
LAPACKE_sge_trans( LAPACK_ROW_MAJOR, n, n, a_r, n+2, a_i, lda );
failed = compare_spotrf( a, a_i, info, info_i, lda, n );
if( failed == 0 ) {
printf( "PASSED: row-major high-level interface to spotrf\n" );
} else {
printf( "FAILED: row-major high-level interface to spotrf\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 );
}
return 0;
}
/* Subroutine */
int sposvxx_(char *fact, char *uplo, integer *n, integer * nrhs, real *a, integer *lda, real *af, integer *ldaf, char *equed, real *s, real *b, integer *ldb, real *x, integer *ldx, real *rcond, real *rpvgrw, real *berr, integer *n_err_bnds__, real * err_bnds_norm__, real *err_bnds_comp__, integer *nparams, real * params, real *work, integer *iwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, af_dim1, af_offset, b_dim1, b_offset, x_dim1, x_offset, err_bnds_norm_dim1, err_bnds_norm_offset, err_bnds_comp_dim1, err_bnds_comp_offset, i__1;
real r__1, r__2;
/* Local variables */
integer j;
real amax, smin, smax;
extern real sla_porpvgrw_(char *, integer *, real *, integer *, real *, integer *, real *);
extern logical lsame_(char *, char *);
real scond;
logical equil, rcequ;
extern real slamch_(char *);
logical nofact;
extern /* Subroutine */
int xerbla_(char *, integer *);
real bignum;
integer infequ;
extern /* Subroutine */
int slacpy_(char *, integer *, integer *, real *, integer *, real *, integer *);
real smlnum;
extern /* Subroutine */
int slaqsy_(char *, integer *, real *, integer *, real *, real *, real *, char *), spotrf_(char *, integer *, real *, integer *, integer *), spotrs_(char *, integer *, integer *, real *, integer *, real *, integer *, integer *), slascl2_(integer *, integer *, real *, real *, integer *), spoequb_(integer *, real *, integer *, real *, real * , real *, integer *), sporfsx_(char *, char *, integer *, integer *, real *, integer *, real *, integer *, real *, real *, integer * , real *, integer *, real *, real *, integer *, real *, real *, integer *, real *, 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 .. */
/* Parameter adjustments */
err_bnds_comp_dim1 = *nrhs;
err_bnds_comp_offset = 1 + err_bnds_comp_dim1;
err_bnds_comp__ -= err_bnds_comp_offset;
err_bnds_norm_dim1 = *nrhs;
err_bnds_norm_offset = 1 + err_bnds_norm_dim1;
err_bnds_norm__ -= err_bnds_norm_offset;
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
af_dim1 = *ldaf;
af_offset = 1 + af_dim1;
af -= af_offset;
--s;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
x_dim1 = *ldx;
x_offset = 1 + x_dim1;
x -= x_offset;
--berr;
--params;
--work;
--iwork;
/* Function Body */
*info = 0;
nofact = lsame_(fact, "N");
equil = lsame_(fact, "E");
smlnum = slamch_("Safe minimum");
bignum = 1.f / smlnum;
if (nofact || equil)
{
*(unsigned char *)equed = 'N';
rcequ = FALSE_;
}
else
{
rcequ = lsame_(equed, "Y");
}
/* Default is failure. If an input parameter is wrong or */
/* factorization fails, make everything look horrible. Only the */
/* pivot growth is set here, the rest is initialized in SPORFSX. */
*rpvgrw = 0.f;
/* Test the input parameters. PARAMS is not tested until SPORFSX. */
if (! nofact && ! equil && ! 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 (lsame_(fact, "F") && ! (rcequ || lsame_( equed, "N")))
{
*info = -9;
}
else
{
if (rcequ)
{
smin = bignum;
smax = 0.f;
i__1 = *n;
for (j = 1;
j <= i__1;
++j)
{
/* Computing MIN */
r__1 = smin;
r__2 = s[j]; // , expr subst
smin = min(r__1,r__2);
/* Computing MAX */
r__1 = smax;
r__2 = s[j]; // , expr subst
smax = max(r__1,r__2);
/* L10: */
}
if (smin <= 0.f)
{
*info = -10;
}
else if (*n > 0)
{
scond = max(smin,smlnum) / min(smax,bignum);
}
else
{
scond = 1.f;
}
}
if (*info == 0)
{
if (*ldb < max(1,*n))
{
*info = -12;
}
else if (*ldx < max(1,*n))
{
*info = -14;
}
}
}
if (*info != 0)
{
i__1 = -(*info);
xerbla_("SPOSVXX", &i__1);
return 0;
}
if (equil)
{
/* Compute row and column scalings to equilibrate the matrix A. */
spoequb_(n, &a[a_offset], lda, &s[1], &scond, &amax, &infequ);
if (infequ == 0)
{
/* Equilibrate the matrix. */
slaqsy_(uplo, n, &a[a_offset], lda, &s[1], &scond, &amax, equed);
rcequ = lsame_(equed, "Y");
}
}
/* Scale the right-hand side. */
if (rcequ)
{
slascl2_(n, nrhs, &s[1], &b[b_offset], ldb);
}
if (nofact || equil)
{
/* Compute the Cholesky factorization of A. */
slacpy_(uplo, n, n, &a[a_offset], lda, &af[af_offset], ldaf);
spotrf_(uplo, n, &af[af_offset], ldaf, info);
/* Return if INFO is non-zero. */
if (*info != 0)
{
/* Pivot in column INFO is exactly 0 */
/* Compute the reciprocal pivot growth factor of the */
/* leading rank-deficient INFO columns of A. */
*rpvgrw = sla_porpvgrw_(uplo, info, &a[a_offset], lda, &af[ af_offset], ldaf, &work[1]);
return 0;
}
}
/* Compute the reciprocal growth factor RPVGRW. */
*rpvgrw = sla_porpvgrw_(uplo, n, &a[a_offset], lda, &af[af_offset], ldaf, &work[1]);
/* Compute the solution matrix X. */
slacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx);
spotrs_(uplo, n, nrhs, &af[af_offset], ldaf, &x[x_offset], ldx, info);
/* Use iterative refinement to improve the computed solution and */
/* compute error bounds and backward error estimates for it. */
sporfsx_(uplo, equed, n, nrhs, &a[a_offset], lda, &af[af_offset], ldaf, & s[1], &b[b_offset], ldb, &x[x_offset], ldx, rcond, &berr[1], n_err_bnds__, &err_bnds_norm__[err_bnds_norm_offset], & err_bnds_comp__[err_bnds_comp_offset], nparams, ¶ms[1], &work[ 1], &iwork[1], info);
/* Scale solutions. */
if (rcequ)
{
slascl2_(n, nrhs, &s[1], &x[x_offset], ldx);
}
return 0;
/* End of SPOSVXX */
}
/* Subroutine */ int spftrf_(char *transr, char *uplo, integer *n, real *a,
integer *info)
{
/* System generated locals */
integer i__1, i__2;
/* Local variables */
integer k, n1, n2;
logical normaltransr;
extern logical lsame_(char *, char *);
logical lower;
extern /* Subroutine */ int strsm_(char *, char *, char *, char *,
integer *, integer *, real *, real *, integer *, real *, integer *
), ssyrk_(char *, char *, integer
*, integer *, real *, real *, integer *, real *, real *, integer *
), xerbla_(char *, integer *);
logical nisodd;
extern /* Subroutine */ int spotrf_(char *, integer *, real *, integer *,
integer *);
/* -- LAPACK routine (version 3.2) -- */
/* -- Contributed by Fred Gustavson of the IBM Watson Research Center -- */
/* -- November 2008 -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* .. */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* Purpose */
/* ======= */
/* SPFTRF computes the Cholesky factorization of a real symmetric */
/* positive definite matrix A. */
/* The factorization has the form */
/* A = U**T * U, if UPLO = 'U', or */
/* A = L * L**T, if UPLO = 'L', */
/* where U is an upper triangular matrix and L is lower triangular. */
/* This is the block version of the algorithm, calling Level 3 BLAS. */
/* Arguments */
/* ========= */
/* TRANSR (input) CHARACTER */
/* = 'N': The Normal TRANSR of RFP A is stored; */
/* = 'T': The Transpose TRANSR of RFP A is stored. */
/* UPLO (input) CHARACTER */
/* = 'U': Upper triangle of RFP A is stored; */
/* = 'L': Lower triangle of RFP A is stored. */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* A (input/output) REAL array, dimension ( N*(N+1)/2 ); */
/* On entry, the symmetric matrix A in RFP format. RFP format is */
/* described by TRANSR, UPLO, and N as follows: If TRANSR = 'N' */
/* then RFP A is (0:N,0:k-1) when N is even; k=N/2. RFP A is */
/* (0:N-1,0:k) when N is odd; k=N/2. IF TRANSR = 'T' then RFP is */
/* the transpose of RFP A as defined when */
/* TRANSR = 'N'. The contents of RFP A are defined by UPLO as */
/* follows: If UPLO = 'U' the RFP A contains the NT elements of */
/* upper packed A. If UPLO = 'L' the RFP A contains the elements */
/* of lower packed A. The LDA of RFP A is (N+1)/2 when TRANSR = */
/* 'T'. When TRANSR is 'N' the LDA is N+1 when N is even and N */
/* is odd. See the Note below for more details. */
/* On exit, if INFO = 0, the factor U or L from the Cholesky */
/* factorization RFP A = U**T*U or RFP A = L*L**T. */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* > 0: if INFO = i, the leading minor of order i is not */
/* positive definite, and the factorization could not be */
/* completed. */
/* Notes */
/* ===== */
/* We first consider Rectangular Full Packed (RFP) Format when N is */
/* even. We give an example where N = 6. */
/* AP is Upper AP is Lower */
/* 00 01 02 03 04 05 00 */
/* 11 12 13 14 15 10 11 */
/* 22 23 24 25 20 21 22 */
/* 33 34 35 30 31 32 33 */
/* 44 45 40 41 42 43 44 */
/* 55 50 51 52 53 54 55 */
/* Let TRANSR = 'N'. RFP holds AP as follows: */
/* For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last */
/* three columns of AP upper. The lower triangle A(4:6,0:2) consists of */
/* the transpose of the first three columns of AP upper. */
/* For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first */
/* three columns of AP lower. The upper triangle A(0:2,0:2) consists of */
/* the transpose of the last three columns of AP lower. */
/* This covers the case N even and TRANSR = 'N'. */
/* RFP A RFP A */
/* 03 04 05 33 43 53 */
/* 13 14 15 00 44 54 */
/* 23 24 25 10 11 55 */
/* 33 34 35 20 21 22 */
/* 00 44 45 30 31 32 */
/* 01 11 55 40 41 42 */
/* 02 12 22 50 51 52 */
/* Now let TRANSR = 'T'. RFP A in both UPLO cases is just the */
/* transpose of RFP A above. One therefore gets: */
/* RFP A RFP A */
/* 03 13 23 33 00 01 02 33 00 10 20 30 40 50 */
/* 04 14 24 34 44 11 12 43 44 11 21 31 41 51 */
/* 05 15 25 35 45 55 22 53 54 55 22 32 42 52 */
/* We first consider Rectangular Full Packed (RFP) Format when N is */
/* odd. We give an example where N = 5. */
/* AP is Upper AP is Lower */
/* 00 01 02 03 04 00 */
/* 11 12 13 14 10 11 */
/* 22 23 24 20 21 22 */
/* 33 34 30 31 32 33 */
/* 44 40 41 42 43 44 */
/* Let TRANSR = 'N'. RFP holds AP as follows: */
/* For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last */
/* three columns of AP upper. The lower triangle A(3:4,0:1) consists of */
/* the transpose of the first two columns of AP upper. */
/* For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first */
/* three columns of AP lower. The upper triangle A(0:1,1:2) consists of */
/* the transpose of the last two columns of AP lower. */
/* This covers the case N odd and TRANSR = 'N'. */
/* RFP A RFP A */
/* 02 03 04 00 33 43 */
/* 12 13 14 10 11 44 */
/* 22 23 24 20 21 22 */
/* 00 33 34 30 31 32 */
/* 01 11 44 40 41 42 */
/* Now let TRANSR = 'T'. RFP A in both UPLO cases is just the */
/* transpose of RFP A above. One therefore gets: */
/* RFP A RFP A */
/* 02 12 22 00 01 00 10 20 30 40 50 */
/* 03 13 23 33 11 33 11 21 31 41 51 */
/* 04 14 24 34 44 43 44 22 32 42 52 */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
*info = 0;
normaltransr = lsame_(transr, "N");
lower = lsame_(uplo, "L");
if (! normaltransr && ! lsame_(transr, "T")) {
*info = -1;
} else if (! lower && ! lsame_(uplo, "U")) {
*info = -2;
} else if (*n < 0) {
*info = -3;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SPFTRF", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/* If N is odd, set NISODD = .TRUE. */
/* If N is even, set K = N/2 and NISODD = .FALSE. */
if (*n % 2 == 0) {
k = *n / 2;
nisodd = FALSE_;
} else {
nisodd = TRUE_;
}
/* Set N1 and N2 depending on LOWER */
if (lower) {
n2 = *n / 2;
n1 = *n - n2;
} else {
n1 = *n / 2;
n2 = *n - n1;
}
/* start execution: there are eight cases */
if (nisodd) {
/* N is odd */
if (normaltransr) {
/* N is odd and TRANSR = 'N' */
if (lower) {
/* SRPA for LOWER, NORMAL and N is odd ( a(0:n-1,0:n1-1) ) */
/* T1 -> a(0,0), T2 -> a(0,1), S -> a(n1,0) */
/* T1 -> a(0), T2 -> a(n), S -> a(n1) */
spotrf_("L", &n1, a, n, info);
if (*info > 0) {
return 0;
}
strsm_("R", "L", "T", "N", &n2, &n1, &c_b12, a, n, &a[n1], n);
ssyrk_("U", "N", &n2, &n1, &c_b15, &a[n1], n, &c_b12, &a[*n],
n);
spotrf_("U", &n2, &a[*n], n, info);
if (*info > 0) {
*info += n1;
}
} else {
/* SRPA for UPPER, NORMAL and N is odd ( a(0:n-1,0:n2-1) */
/* T1 -> a(n1+1,0), T2 -> a(n1,0), S -> a(0,0) */
/* T1 -> a(n2), T2 -> a(n1), S -> a(0) */
spotrf_("L", &n1, &a[n2], n, info);
if (*info > 0) {
return 0;
}
strsm_("L", "L", "N", "N", &n1, &n2, &c_b12, &a[n2], n, a, n);
ssyrk_("U", "T", &n2, &n1, &c_b15, a, n, &c_b12, &a[n1], n);
spotrf_("U", &n2, &a[n1], n, info);
if (*info > 0) {
*info += n1;
}
}
} else {
/* N is odd and TRANSR = 'T' */
if (lower) {
/* SRPA for LOWER, TRANSPOSE and N is odd */
/* T1 -> A(0,0) , T2 -> A(1,0) , S -> A(0,n1) */
/* T1 -> a(0+0) , T2 -> a(1+0) , S -> a(0+n1*n1); lda=n1 */
spotrf_("U", &n1, a, &n1, info);
if (*info > 0) {
return 0;
}
strsm_("L", "U", "T", "N", &n1, &n2, &c_b12, a, &n1, &a[n1 *
n1], &n1);
ssyrk_("L", "T", &n2, &n1, &c_b15, &a[n1 * n1], &n1, &c_b12, &
a[1], &n1);
spotrf_("L", &n2, &a[1], &n1, info);
if (*info > 0) {
*info += n1;
}
} else {
/* SRPA for UPPER, TRANSPOSE and N is odd */
/* T1 -> A(0,n1+1), T2 -> A(0,n1), S -> A(0,0) */
/* T1 -> a(n2*n2), T2 -> a(n1*n2), S -> a(0); lda = n2 */
spotrf_("U", &n1, &a[n2 * n2], &n2, info);
if (*info > 0) {
return 0;
}
strsm_("R", "U", "N", "N", &n2, &n1, &c_b12, &a[n2 * n2], &n2,
a, &n2);
ssyrk_("L", "N", &n2, &n1, &c_b15, a, &n2, &c_b12, &a[n1 * n2]
, &n2);
spotrf_("L", &n2, &a[n1 * n2], &n2, info);
if (*info > 0) {
*info += n1;
}
}
}
} else {
/* N is even */
if (normaltransr) {
/* N is even and TRANSR = 'N' */
if (lower) {
/* SRPA for LOWER, NORMAL, and N is even ( a(0:n,0:k-1) ) */
/* T1 -> a(1,0), T2 -> a(0,0), S -> a(k+1,0) */
/* T1 -> a(1), T2 -> a(0), S -> a(k+1) */
i__1 = *n + 1;
spotrf_("L", &k, &a[1], &i__1, info);
if (*info > 0) {
return 0;
}
i__1 = *n + 1;
i__2 = *n + 1;
strsm_("R", "L", "T", "N", &k, &k, &c_b12, &a[1], &i__1, &a[k
+ 1], &i__2);
i__1 = *n + 1;
i__2 = *n + 1;
ssyrk_("U", "N", &k, &k, &c_b15, &a[k + 1], &i__1, &c_b12, a,
&i__2);
i__1 = *n + 1;
spotrf_("U", &k, a, &i__1, info);
if (*info > 0) {
*info += k;
}
} else {
/* SRPA for UPPER, NORMAL, and N is even ( a(0:n,0:k-1) ) */
/* T1 -> a(k+1,0) , T2 -> a(k,0), S -> a(0,0) */
/* T1 -> a(k+1), T2 -> a(k), S -> a(0) */
i__1 = *n + 1;
spotrf_("L", &k, &a[k + 1], &i__1, info);
if (*info > 0) {
return 0;
}
i__1 = *n + 1;
i__2 = *n + 1;
strsm_("L", "L", "N", "N", &k, &k, &c_b12, &a[k + 1], &i__1,
a, &i__2);
i__1 = *n + 1;
i__2 = *n + 1;
ssyrk_("U", "T", &k, &k, &c_b15, a, &i__1, &c_b12, &a[k], &
i__2);
i__1 = *n + 1;
spotrf_("U", &k, &a[k], &i__1, info);
if (*info > 0) {
*info += k;
}
}
} else {
/* N is even and TRANSR = 'T' */
if (lower) {
/* SRPA for LOWER, TRANSPOSE and N is even (see paper) */
/* T1 -> B(0,1), T2 -> B(0,0), S -> B(0,k+1) */
/* T1 -> a(0+k), T2 -> a(0+0), S -> a(0+k*(k+1)); lda=k */
spotrf_("U", &k, &a[k], &k, info);
if (*info > 0) {
return 0;
}
strsm_("L", "U", "T", "N", &k, &k, &c_b12, &a[k], &n1, &a[k *
(k + 1)], &k);
ssyrk_("L", "T", &k, &k, &c_b15, &a[k * (k + 1)], &k, &c_b12,
a, &k);
spotrf_("L", &k, a, &k, info);
if (*info > 0) {
*info += k;
}
} else {
/* SRPA for UPPER, TRANSPOSE and N is even (see paper) */
/* T1 -> B(0,k+1), T2 -> B(0,k), S -> B(0,0) */
/* T1 -> a(0+k*(k+1)), T2 -> a(0+k*k), S -> a(0+0)); lda=k */
spotrf_("U", &k, &a[k * (k + 1)], &k, info);
if (*info > 0) {
return 0;
}
strsm_("R", "U", "N", "N", &k, &k, &c_b12, &a[k * (k + 1)], &
k, a, &k);
ssyrk_("L", "N", &k, &k, &c_b15, a, &k, &c_b12, &a[k * k], &k);
spotrf_("L", &k, &a[k * k], &k, info);
if (*info > 0) {
*info += k;
}
}
}
}
return 0;
/* End of SPFTRF */
} /* spftrf_ */
/* Subroutine */ int ssygv_(integer *itype, char *jobz, char *uplo, integer *
n, real *a, integer *lda, real *b, integer *ldb, real *w, real *work,
integer *lwork, integer *info)
{
/* -- LAPACK driver 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
=======
SSYGV computes all the eigenvalues, and optionally, the eigenvectors
of a real generalized symmetric-definite eigenproblem, of the form
A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x.
Here A and B are assumed to be symmetric and B is also
positive definite.
Arguments
=========
ITYPE (input) INTEGER
Specifies the problem type to be solved:
= 1: A*x = (lambda)*B*x
= 2: A*B*x = (lambda)*x
= 3: B*A*x = (lambda)*x
JOBZ (input) CHARACTER*1
= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors.
UPLO (input) CHARACTER*1
= 'U': Upper triangles of A and B are stored;
= 'L': Lower triangles of A and B are stored.
N (input) INTEGER
The order of the matrices A and B. N >= 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. If UPLO = 'L',
the leading N-by-N lower triangular part of A contains
the lower triangular part of the matrix A.
On exit, if JOBZ = 'V', then if INFO = 0, A contains the
matrix Z of eigenvectors. The eigenvectors are normalized
as follows:
if ITYPE = 1 or 2, Z**T*B*Z = I;
if ITYPE = 3, Z**T*inv(B)*Z = I.
If JOBZ = 'N', then on exit the upper triangle (if UPLO='U')
or the lower triangle (if UPLO='L') of A, including the
diagonal, is destroyed.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
B (input/output) REAL array, dimension (LDB, N)
On entry, the symmetric matrix B. If UPLO = 'U', the
leading N-by-N upper triangular part of B contains the
upper triangular part of the matrix B. If UPLO = 'L',
the leading N-by-N lower triangular part of B contains
the lower triangular part of the matrix B.
On exit, if INFO <= N, the part of B containing the matrix is
overwritten by the triangular factor U or L from the Cholesky
factorization B = U**T*U or B = L*L**T.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).
W (output) REAL array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.
WORK (workspace/output) REAL array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The length of the array WORK. LWORK >= max(1,3*N-1).
For optimal efficiency, LWORK >= (NB+2)*N,
where NB is the blocksize for SSYTRD returned by ILAENV.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: SPOTRF or SSYEV returned an error code:
<= N: if INFO = i, SSYEV failed to converge;
i off-diagonal elements of an intermediate
tridiagonal form did not converge to zero;
> N: if INFO = N + i, for 1 <= i <= N, then the leading
minor of order i of B is not positive definite.
The factorization of B could not be completed and
no eigenvalues or eigenvectors were computed.
=====================================================================
Test the input parameters.
Parameter adjustments
Function Body */
/* Table of constant values */
static real c_b11 = 1.f;
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2;
/* Local variables */
static integer neig;
extern logical lsame_(char *, char *);
static char trans[1];
static logical upper;
extern /* Subroutine */ int strmm_(char *, char *, char *, char *,
integer *, integer *, real *, real *, integer *, real *, integer *
);
static logical wantz;
extern /* Subroutine */ int strsm_(char *, char *, char *, char *,
integer *, integer *, real *, real *, integer *, real *, integer *
), ssyev_(char *, char *, integer
*, real *, integer *, real *, real *, integer *, integer *), xerbla_(char *, integer *), spotrf_(char
*, integer *, real *, integer *, integer *), ssygst_(
integer *, char *, integer *, real *, integer *, real *, integer *
, integer *);
#define W(I) w[(I)-1]
#define WORK(I) work[(I)-1]
#define A(I,J) a[(I)-1 + ((J)-1)* ( *lda)]
#define B(I,J) b[(I)-1 + ((J)-1)* ( *ldb)]
wantz = lsame_(jobz, "V");
upper = lsame_(uplo, "U");
*info = 0;
if (*itype < 0 || *itype > 3) {
*info = -1;
} else if (! (wantz || lsame_(jobz, "N"))) {
*info = -2;
} else if (! (upper || lsame_(uplo, "L"))) {
*info = -3;
} else if (*n < 0) {
*info = -4;
} else if (*lda < max(1,*n)) {
*info = -6;
} else if (*ldb < max(1,*n)) {
*info = -8;
} else /* if(complicated condition) */ {
/* Computing MAX */
i__1 = 1, i__2 = *n * 3 - 1;
if (*lwork < max(i__1,i__2)) {
*info = -11;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SSYGV ", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/* Form a Cholesky factorization of B. */
spotrf_(uplo, n, &B(1,1), ldb, info);
if (*info != 0) {
*info = *n + *info;
return 0;
}
/* Transform problem to standard eigenvalue problem and solve. */
ssygst_(itype, uplo, n, &A(1,1), lda, &B(1,1), ldb, info);
ssyev_(jobz, uplo, n, &A(1,1), lda, &W(1), &WORK(1), lwork, info);
if (wantz) {
/* Backtransform eigenvectors to the original problem. */
neig = *n;
if (*info > 0) {
neig = *info - 1;
}
if (*itype == 1 || *itype == 2) {
/* For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
backtransform eigenvectors: x = inv(L)'*y or inv(U)*y
*/
if (upper) {
*(unsigned char *)trans = 'N';
} else {
*(unsigned char *)trans = 'T';
}
strsm_("Left", uplo, trans, "Non-unit", n, &neig, &c_b11, &B(1,1), ldb, &A(1,1), lda);
} else if (*itype == 3) {
/* For B*A*x=(lambda)*x;
backtransform eigenvectors: x = L*y or U'*y */
if (upper) {
*(unsigned char *)trans = 'T';
} else {
*(unsigned char *)trans = 'N';
}
strmm_("Left", uplo, trans, "Non-unit", n, &neig, &c_b11, &B(1,1), ldb, &A(1,1), lda);
}
}
return 0;
/* End of SSYGV */
} /* ssygv_ */
GURLS_EXPORT int potrf_(char *UPLO, int *n, float *a, int *lda , int *info)
{
return spotrf_(UPLO, n, a, lda, info);
}
/* Subroutine */ int sposv_(char *uplo, integer *n, integer *nrhs, real *a,
integer *lda, real *b, integer *ldb, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, i__1;
/* Local variables */
extern logical lsame_(char *, char *);
extern /* Subroutine */ int xerbla_(char *, integer *), spotrf_(
char *, integer *, real *, integer *, integer *), spotrs_(
char *, integer *, integer *, real *, integer *, real *, integer *
, integer *);
/*
-- LAPACK driver routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
March 31, 1993
Purpose
=======
SPOSV computes the solution to a real system of linear equations
A * X = B,
where A is an N-by-N symmetric positive definite matrix and X and B
are N-by-NRHS matrices.
The Cholesky decomposition is used to factor A as
A = U**T* U, if UPLO = 'U', or
A = L * L**T, if UPLO = 'L',
where U is an upper triangular matrix and L is a lower triangular
matrix. 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 factor U or L from the Cholesky
factorization A = U**T*U or A = L*L**T.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
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).
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, the leading minor of order i of A is not
positive definite, so the factorization could not be
completed, and the solution has not been computed.
=====================================================================
Test the input parameters.
*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
/* Function Body */
*info = 0;
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;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SPOSV ", &i__1);
return 0;
}
/* Compute the Cholesky factorization A = U'*U or A = L*L'. */
spotrf_(uplo, n, &a[a_offset], lda, info);
if (*info == 0) {
/* Solve the system A*X = B, overwriting B with X. */
spotrs_(uplo, n, nrhs, &a[a_offset], lda, &b[b_offset], ldb, info);
}
return 0;
/* End of SPOSV */
} /* sposv_ */
void STARPU_SPOTRF(const char*uplo, const int n, float *a, const int lda)
{
int info = 0;
spotrf_(uplo, &n, a, &lda, &info);
}
/* Subroutine */ int serrpo_(char *path, integer *nunit)
{
/* Builtin functions */
integer s_wsle(cilist *), e_wsle(void);
/* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
/* Local variables */
real a[16] /* was [4][4] */, b[4];
integer i__, j;
real w[12], x[4];
char c2[2];
real r1[4], r2[4], af[16] /* was [4][4] */;
integer iw[4], info;
real anrm, rcond;
extern /* Subroutine */ int spbtf2_(char *, integer *, integer *, real *,
integer *, integer *), spotf2_(char *, integer *, real *,
integer *, integer *), alaesm_(char *, logical *, integer
*);
extern logical lsamen_(integer *, char *, char *);
extern /* Subroutine */ int chkxer_(char *, integer *, integer *, logical
*, logical *), spbcon_(char *, integer *, integer *, real
*, integer *, real *, real *, real *, integer *, integer *), spbequ_(char *, integer *, integer *, real *, integer *,
real *, real *, real *, integer *), spbrfs_(char *,
integer *, integer *, integer *, real *, integer *, real *,
integer *, real *, integer *, real *, integer *, real *, real *,
real *, integer *, integer *), spbtrf_(char *, integer *,
integer *, real *, integer *, integer *), spocon_(char *,
integer *, real *, integer *, real *, real *, real *, integer *,
integer *), sppcon_(char *, integer *, real *, real *,
real *, real *, integer *, integer *), spoequ_(integer *,
real *, integer *, real *, real *, real *, integer *), spbtrs_(
char *, integer *, integer *, integer *, real *, integer *, real *
, integer *, integer *), sporfs_(char *, integer *,
integer *, real *, integer *, real *, integer *, real *, integer *
, real *, integer *, real *, real *, real *, integer *, integer *), spotrf_(char *, integer *, real *, integer *, integer *), spotri_(char *, integer *, real *, integer *, integer *), sppequ_(char *, integer *, real *, real *, real *, real
*, integer *), spprfs_(char *, integer *, integer *, real
*, real *, real *, integer *, real *, integer *, real *, real *,
real *, integer *, integer *), spptrf_(char *, integer *,
real *, integer *), spptri_(char *, integer *, real *,
integer *), spotrs_(char *, integer *, integer *, real *,
integer *, real *, integer *, integer *), spptrs_(char *,
integer *, integer *, real *, real *, integer *, integer *);
/* Fortran I/O blocks */
static cilist io___1 = { 0, 0, 0, 0, 0 };
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* SERRPO tests the error exits for the REAL routines */
/* for symmetric positive definite matrices. */
/* Arguments */
/* ========= */
/* PATH (input) CHARACTER*3 */
/* The LAPACK path name for the routines to be tested. */
/* NUNIT (input) INTEGER */
/* The unit number for output. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Scalars in Common .. */
/* .. */
/* .. Common blocks .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
infoc_1.nout = *nunit;
io___1.ciunit = infoc_1.nout;
s_wsle(&io___1);
e_wsle();
s_copy(c2, path + 1, (ftnlen)2, (ftnlen)2);
/* Set the variables to innocuous values. */
for (j = 1; j <= 4; ++j) {
for (i__ = 1; i__ <= 4; ++i__) {
a[i__ + (j << 2) - 5] = 1.f / (real) (i__ + j);
af[i__ + (j << 2) - 5] = 1.f / (real) (i__ + j);
/* L10: */
}
b[j - 1] = 0.f;
r1[j - 1] = 0.f;
r2[j - 1] = 0.f;
w[j - 1] = 0.f;
x[j - 1] = 0.f;
iw[j - 1] = j;
/* L20: */
}
infoc_1.ok = TRUE_;
if (lsamen_(&c__2, c2, "PO")) {
/* Test error exits of the routines that use the Cholesky */
/* decomposition of a symmetric positive definite matrix. */
/* SPOTRF */
s_copy(srnamc_1.srnamt, "SPOTRF", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
spotrf_("/", &c__0, a, &c__1, &info);
chkxer_("SPOTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
spotrf_("U", &c_n1, a, &c__1, &info);
chkxer_("SPOTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
spotrf_("U", &c__2, a, &c__1, &info);
chkxer_("SPOTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SPOTF2 */
s_copy(srnamc_1.srnamt, "SPOTF2", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
spotf2_("/", &c__0, a, &c__1, &info);
chkxer_("SPOTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
spotf2_("U", &c_n1, a, &c__1, &info);
chkxer_("SPOTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
spotf2_("U", &c__2, a, &c__1, &info);
chkxer_("SPOTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SPOTRI */
s_copy(srnamc_1.srnamt, "SPOTRI", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
spotri_("/", &c__0, a, &c__1, &info);
chkxer_("SPOTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
spotri_("U", &c_n1, a, &c__1, &info);
chkxer_("SPOTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
spotri_("U", &c__2, a, &c__1, &info);
chkxer_("SPOTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SPOTRS */
s_copy(srnamc_1.srnamt, "SPOTRS", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
spotrs_("/", &c__0, &c__0, a, &c__1, b, &c__1, &info);
chkxer_("SPOTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
spotrs_("U", &c_n1, &c__0, a, &c__1, b, &c__1, &info);
chkxer_("SPOTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
spotrs_("U", &c__0, &c_n1, a, &c__1, b, &c__1, &info);
chkxer_("SPOTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
spotrs_("U", &c__2, &c__1, a, &c__1, b, &c__2, &info);
chkxer_("SPOTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
spotrs_("U", &c__2, &c__1, a, &c__2, b, &c__1, &info);
chkxer_("SPOTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SPORFS */
s_copy(srnamc_1.srnamt, "SPORFS", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
sporfs_("/", &c__0, &c__0, a, &c__1, af, &c__1, b, &c__1, x, &c__1,
r1, r2, w, iw, &info);
chkxer_("SPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sporfs_("U", &c_n1, &c__0, a, &c__1, af, &c__1, b, &c__1, x, &c__1,
r1, r2, w, iw, &info);
chkxer_("SPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
sporfs_("U", &c__0, &c_n1, a, &c__1, af, &c__1, b, &c__1, x, &c__1,
r1, r2, w, iw, &info);
chkxer_("SPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
sporfs_("U", &c__2, &c__1, a, &c__1, af, &c__2, b, &c__2, x, &c__2,
r1, r2, w, iw, &info);
chkxer_("SPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
sporfs_("U", &c__2, &c__1, a, &c__2, af, &c__1, b, &c__2, x, &c__2,
r1, r2, w, iw, &info);
chkxer_("SPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 9;
sporfs_("U", &c__2, &c__1, a, &c__2, af, &c__2, b, &c__1, x, &c__2,
r1, r2, w, iw, &info);
chkxer_("SPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 11;
sporfs_("U", &c__2, &c__1, a, &c__2, af, &c__2, b, &c__2, x, &c__1,
r1, r2, w, iw, &info);
chkxer_("SPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SPOCON */
s_copy(srnamc_1.srnamt, "SPOCON", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
spocon_("/", &c__0, a, &c__1, &anrm, &rcond, w, iw, &info);
chkxer_("SPOCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
spocon_("U", &c_n1, a, &c__1, &anrm, &rcond, w, iw, &info);
chkxer_("SPOCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
spocon_("U", &c__2, a, &c__1, &anrm, &rcond, w, iw, &info);
chkxer_("SPOCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SPOEQU */
s_copy(srnamc_1.srnamt, "SPOEQU", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
spoequ_(&c_n1, a, &c__1, r1, &rcond, &anrm, &info);
chkxer_("SPOEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
spoequ_(&c__2, a, &c__1, r1, &rcond, &anrm, &info);
chkxer_("SPOEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
} else if (lsamen_(&c__2, c2, "PP")) {
/* Test error exits of the routines that use the Cholesky */
/* decomposition of a symmetric positive definite packed matrix. */
/* SPPTRF */
s_copy(srnamc_1.srnamt, "SPPTRF", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
spptrf_("/", &c__0, a, &info);
chkxer_("SPPTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
spptrf_("U", &c_n1, a, &info);
chkxer_("SPPTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SPPTRI */
s_copy(srnamc_1.srnamt, "SPPTRI", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
spptri_("/", &c__0, a, &info);
chkxer_("SPPTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
spptri_("U", &c_n1, a, &info);
chkxer_("SPPTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SPPTRS */
s_copy(srnamc_1.srnamt, "SPPTRS", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
spptrs_("/", &c__0, &c__0, a, b, &c__1, &info);
chkxer_("SPPTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
spptrs_("U", &c_n1, &c__0, a, b, &c__1, &info);
chkxer_("SPPTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
spptrs_("U", &c__0, &c_n1, a, b, &c__1, &info);
chkxer_("SPPTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
spptrs_("U", &c__2, &c__1, a, b, &c__1, &info);
chkxer_("SPPTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SPPRFS */
s_copy(srnamc_1.srnamt, "SPPRFS", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
spprfs_("/", &c__0, &c__0, a, af, b, &c__1, x, &c__1, r1, r2, w, iw, &
info);
chkxer_("SPPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
spprfs_("U", &c_n1, &c__0, a, af, b, &c__1, x, &c__1, r1, r2, w, iw, &
info);
chkxer_("SPPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
spprfs_("U", &c__0, &c_n1, a, af, b, &c__1, x, &c__1, r1, r2, w, iw, &
info);
chkxer_("SPPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
spprfs_("U", &c__2, &c__1, a, af, b, &c__1, x, &c__2, r1, r2, w, iw, &
info);
chkxer_("SPPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 9;
spprfs_("U", &c__2, &c__1, a, af, b, &c__2, x, &c__1, r1, r2, w, iw, &
info);
chkxer_("SPPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SPPCON */
s_copy(srnamc_1.srnamt, "SPPCON", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
sppcon_("/", &c__0, a, &anrm, &rcond, w, iw, &info);
chkxer_("SPPCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sppcon_("U", &c_n1, a, &anrm, &rcond, w, iw, &info);
chkxer_("SPPCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SPPEQU */
s_copy(srnamc_1.srnamt, "SPPEQU", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
sppequ_("/", &c__0, a, r1, &rcond, &anrm, &info);
chkxer_("SPPEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sppequ_("U", &c_n1, a, r1, &rcond, &anrm, &info);
chkxer_("SPPEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
} else if (lsamen_(&c__2, c2, "PB")) {
/* Test error exits of the routines that use the Cholesky */
/* decomposition of a symmetric positive definite band matrix. */
/* SPBTRF */
s_copy(srnamc_1.srnamt, "SPBTRF", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
spbtrf_("/", &c__0, &c__0, a, &c__1, &info);
chkxer_("SPBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
spbtrf_("U", &c_n1, &c__0, a, &c__1, &info);
chkxer_("SPBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
spbtrf_("U", &c__1, &c_n1, a, &c__1, &info);
chkxer_("SPBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
spbtrf_("U", &c__2, &c__1, a, &c__1, &info);
chkxer_("SPBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SPBTF2 */
s_copy(srnamc_1.srnamt, "SPBTF2", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
spbtf2_("/", &c__0, &c__0, a, &c__1, &info);
chkxer_("SPBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
spbtf2_("U", &c_n1, &c__0, a, &c__1, &info);
chkxer_("SPBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
spbtf2_("U", &c__1, &c_n1, a, &c__1, &info);
chkxer_("SPBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
spbtf2_("U", &c__2, &c__1, a, &c__1, &info);
chkxer_("SPBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SPBTRS */
s_copy(srnamc_1.srnamt, "SPBTRS", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
spbtrs_("/", &c__0, &c__0, &c__0, a, &c__1, b, &c__1, &info);
chkxer_("SPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
spbtrs_("U", &c_n1, &c__0, &c__0, a, &c__1, b, &c__1, &info);
chkxer_("SPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
spbtrs_("U", &c__1, &c_n1, &c__0, a, &c__1, b, &c__1, &info);
chkxer_("SPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
spbtrs_("U", &c__0, &c__0, &c_n1, a, &c__1, b, &c__1, &info);
chkxer_("SPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
spbtrs_("U", &c__2, &c__1, &c__1, a, &c__1, b, &c__1, &info);
chkxer_("SPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
spbtrs_("U", &c__2, &c__0, &c__1, a, &c__1, b, &c__1, &info);
chkxer_("SPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SPBRFS */
s_copy(srnamc_1.srnamt, "SPBRFS", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
spbrfs_("/", &c__0, &c__0, &c__0, a, &c__1, af, &c__1, b, &c__1, x, &
c__1, r1, r2, w, iw, &info);
chkxer_("SPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
spbrfs_("U", &c_n1, &c__0, &c__0, a, &c__1, af, &c__1, b, &c__1, x, &
c__1, r1, r2, w, iw, &info);
chkxer_("SPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
spbrfs_("U", &c__1, &c_n1, &c__0, a, &c__1, af, &c__1, b, &c__1, x, &
c__1, r1, r2, w, iw, &info);
chkxer_("SPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
spbrfs_("U", &c__0, &c__0, &c_n1, a, &c__1, af, &c__1, b, &c__1, x, &
c__1, r1, r2, w, iw, &info);
chkxer_("SPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
spbrfs_("U", &c__2, &c__1, &c__1, a, &c__1, af, &c__2, b, &c__2, x, &
c__2, r1, r2, w, iw, &info);
chkxer_("SPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
spbrfs_("U", &c__2, &c__1, &c__1, a, &c__2, af, &c__1, b, &c__2, x, &
c__2, r1, r2, w, iw, &info);
chkxer_("SPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
spbrfs_("U", &c__2, &c__0, &c__1, a, &c__1, af, &c__1, b, &c__1, x, &
c__2, r1, r2, w, iw, &info);
chkxer_("SPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 12;
spbrfs_("U", &c__2, &c__0, &c__1, a, &c__1, af, &c__1, b, &c__2, x, &
c__1, r1, r2, w, iw, &info);
chkxer_("SPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SPBCON */
s_copy(srnamc_1.srnamt, "SPBCON", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
spbcon_("/", &c__0, &c__0, a, &c__1, &anrm, &rcond, w, iw, &info);
chkxer_("SPBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
spbcon_("U", &c_n1, &c__0, a, &c__1, &anrm, &rcond, w, iw, &info);
chkxer_("SPBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
spbcon_("U", &c__1, &c_n1, a, &c__1, &anrm, &rcond, w, iw, &info);
chkxer_("SPBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
spbcon_("U", &c__2, &c__1, a, &c__1, &anrm, &rcond, w, iw, &info);
chkxer_("SPBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SPBEQU */
s_copy(srnamc_1.srnamt, "SPBEQU", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
spbequ_("/", &c__0, &c__0, a, &c__1, r1, &rcond, &anrm, &info);
chkxer_("SPBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
spbequ_("U", &c_n1, &c__0, a, &c__1, r1, &rcond, &anrm, &info);
chkxer_("SPBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
spbequ_("U", &c__1, &c_n1, a, &c__1, r1, &rcond, &anrm, &info);
chkxer_("SPBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
spbequ_("U", &c__2, &c__1, a, &c__1, r1, &rcond, &anrm, &info);
chkxer_("SPBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
}
/* Print a summary line. */
alaesm_(path, &infoc_1.ok, &infoc_1.nout);
return 0;
/* End of SERRPO */
} /* serrpo_ */
/* Subroutine */ int serrpo_(char *path, integer *nunit)
{
/* Builtin functions */
integer s_wsle(cilist *), e_wsle(void);
/* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
/* Local variables */
static integer info;
static real anrm, a[16] /* was [4][4] */, b[4];
static integer i__, j;
static real w[12], x[4], rcond;
static char c2[2];
static real r1[4], r2[4];
extern /* Subroutine */ int spbtf2_(char *, integer *, integer *, real *,
integer *, integer *);
static real af[16] /* was [4][4] */;
extern /* Subroutine */ int spotf2_(char *, integer *, real *, integer *,
integer *);
static integer iw[4];
extern /* Subroutine */ int alaesm_(char *, logical *, integer *);
extern logical lsamen_(integer *, char *, char *);
extern /* Subroutine */ int chkxer_(char *, integer *, integer *, logical
*, logical *), spbcon_(char *, integer *, integer *, real
*, integer *, real *, real *, real *, integer *, integer *), spbequ_(char *, integer *, integer *, real *, integer *,
real *, real *, real *, integer *), spbrfs_(char *,
integer *, integer *, integer *, real *, integer *, real *,
integer *, real *, integer *, real *, integer *, real *, real *,
real *, integer *, integer *), spbtrf_(char *, integer *,
integer *, real *, integer *, integer *), spocon_(char *,
integer *, real *, integer *, real *, real *, real *, integer *,
integer *), sppcon_(char *, integer *, real *, real *,
real *, real *, integer *, integer *), spoequ_(integer *,
real *, integer *, real *, real *, real *, integer *), spbtrs_(
char *, integer *, integer *, integer *, real *, integer *, real *
, integer *, integer *), sporfs_(char *, integer *,
integer *, real *, integer *, real *, integer *, real *, integer *
, real *, integer *, real *, real *, real *, integer *, integer *), spotrf_(char *, integer *, real *, integer *, integer *), spotri_(char *, integer *, real *, integer *, integer *), sppequ_(char *, integer *, real *, real *, real *, real
*, integer *), spprfs_(char *, integer *, integer *, real
*, real *, real *, integer *, real *, integer *, real *, real *,
real *, integer *, integer *), spptrf_(char *, integer *,
real *, integer *), spptri_(char *, integer *, real *,
integer *), spotrs_(char *, integer *, integer *, real *,
integer *, real *, integer *, integer *), spptrs_(char *,
integer *, integer *, real *, real *, integer *, integer *);
/* Fortran I/O blocks */
static cilist io___1 = { 0, 0, 0, 0, 0 };
#define a_ref(a_1,a_2) a[(a_2)*4 + a_1 - 5]
#define af_ref(a_1,a_2) af[(a_2)*4 + a_1 - 5]
/* -- LAPACK test routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
February 29, 1992
Purpose
=======
SERRPO tests the error exits for the REAL routines
for symmetric positive definite matrices.
Arguments
=========
PATH (input) CHARACTER*3
The LAPACK path name for the routines to be tested.
NUNIT (input) INTEGER
The unit number for output.
===================================================================== */
infoc_1.nout = *nunit;
io___1.ciunit = infoc_1.nout;
s_wsle(&io___1);
e_wsle();
s_copy(c2, path + 1, (ftnlen)2, (ftnlen)2);
/* Set the variables to innocuous values. */
for (j = 1; j <= 4; ++j) {
for (i__ = 1; i__ <= 4; ++i__) {
a_ref(i__, j) = 1.f / (real) (i__ + j);
af_ref(i__, j) = 1.f / (real) (i__ + j);
/* L10: */
}
b[j - 1] = 0.f;
r1[j - 1] = 0.f;
r2[j - 1] = 0.f;
w[j - 1] = 0.f;
x[j - 1] = 0.f;
iw[j - 1] = j;
/* L20: */
}
infoc_1.ok = TRUE_;
if (lsamen_(&c__2, c2, "PO")) {
/* Test error exits of the routines that use the Cholesky
decomposition of a symmetric positive definite matrix.
SPOTRF */
s_copy(srnamc_1.srnamt, "SPOTRF", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
spotrf_("/", &c__0, a, &c__1, &info);
chkxer_("SPOTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
spotrf_("U", &c_n1, a, &c__1, &info);
chkxer_("SPOTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
spotrf_("U", &c__2, a, &c__1, &info);
chkxer_("SPOTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SPOTF2 */
s_copy(srnamc_1.srnamt, "SPOTF2", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
spotf2_("/", &c__0, a, &c__1, &info);
chkxer_("SPOTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
spotf2_("U", &c_n1, a, &c__1, &info);
chkxer_("SPOTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
spotf2_("U", &c__2, a, &c__1, &info);
chkxer_("SPOTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SPOTRI */
s_copy(srnamc_1.srnamt, "SPOTRI", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
spotri_("/", &c__0, a, &c__1, &info);
chkxer_("SPOTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
spotri_("U", &c_n1, a, &c__1, &info);
chkxer_("SPOTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
spotri_("U", &c__2, a, &c__1, &info);
chkxer_("SPOTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SPOTRS */
s_copy(srnamc_1.srnamt, "SPOTRS", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
spotrs_("/", &c__0, &c__0, a, &c__1, b, &c__1, &info);
chkxer_("SPOTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
spotrs_("U", &c_n1, &c__0, a, &c__1, b, &c__1, &info);
chkxer_("SPOTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
spotrs_("U", &c__0, &c_n1, a, &c__1, b, &c__1, &info);
chkxer_("SPOTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
spotrs_("U", &c__2, &c__1, a, &c__1, b, &c__2, &info);
chkxer_("SPOTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
spotrs_("U", &c__2, &c__1, a, &c__2, b, &c__1, &info);
chkxer_("SPOTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SPORFS */
s_copy(srnamc_1.srnamt, "SPORFS", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
sporfs_("/", &c__0, &c__0, a, &c__1, af, &c__1, b, &c__1, x, &c__1,
r1, r2, w, iw, &info);
chkxer_("SPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sporfs_("U", &c_n1, &c__0, a, &c__1, af, &c__1, b, &c__1, x, &c__1,
r1, r2, w, iw, &info);
chkxer_("SPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
sporfs_("U", &c__0, &c_n1, a, &c__1, af, &c__1, b, &c__1, x, &c__1,
r1, r2, w, iw, &info);
chkxer_("SPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
sporfs_("U", &c__2, &c__1, a, &c__1, af, &c__2, b, &c__2, x, &c__2,
r1, r2, w, iw, &info);
chkxer_("SPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
sporfs_("U", &c__2, &c__1, a, &c__2, af, &c__1, b, &c__2, x, &c__2,
r1, r2, w, iw, &info);
chkxer_("SPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 9;
sporfs_("U", &c__2, &c__1, a, &c__2, af, &c__2, b, &c__1, x, &c__2,
r1, r2, w, iw, &info);
chkxer_("SPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 11;
sporfs_("U", &c__2, &c__1, a, &c__2, af, &c__2, b, &c__2, x, &c__1,
r1, r2, w, iw, &info);
chkxer_("SPORFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SPOCON */
s_copy(srnamc_1.srnamt, "SPOCON", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
spocon_("/", &c__0, a, &c__1, &anrm, &rcond, w, iw, &info);
chkxer_("SPOCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
spocon_("U", &c_n1, a, &c__1, &anrm, &rcond, w, iw, &info);
chkxer_("SPOCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
spocon_("U", &c__2, a, &c__1, &anrm, &rcond, w, iw, &info);
chkxer_("SPOCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SPOEQU */
s_copy(srnamc_1.srnamt, "SPOEQU", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
spoequ_(&c_n1, a, &c__1, r1, &rcond, &anrm, &info);
chkxer_("SPOEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
spoequ_(&c__2, a, &c__1, r1, &rcond, &anrm, &info);
chkxer_("SPOEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
} else if (lsamen_(&c__2, c2, "PP")) {
/* Test error exits of the routines that use the Cholesky
decomposition of a symmetric positive definite packed matrix.
SPPTRF */
s_copy(srnamc_1.srnamt, "SPPTRF", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
spptrf_("/", &c__0, a, &info);
chkxer_("SPPTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
spptrf_("U", &c_n1, a, &info);
chkxer_("SPPTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SPPTRI */
s_copy(srnamc_1.srnamt, "SPPTRI", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
spptri_("/", &c__0, a, &info);
chkxer_("SPPTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
spptri_("U", &c_n1, a, &info);
chkxer_("SPPTRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SPPTRS */
s_copy(srnamc_1.srnamt, "SPPTRS", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
spptrs_("/", &c__0, &c__0, a, b, &c__1, &info);
chkxer_("SPPTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
spptrs_("U", &c_n1, &c__0, a, b, &c__1, &info);
chkxer_("SPPTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
spptrs_("U", &c__0, &c_n1, a, b, &c__1, &info);
chkxer_("SPPTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
spptrs_("U", &c__2, &c__1, a, b, &c__1, &info);
chkxer_("SPPTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SPPRFS */
s_copy(srnamc_1.srnamt, "SPPRFS", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
spprfs_("/", &c__0, &c__0, a, af, b, &c__1, x, &c__1, r1, r2, w, iw, &
info);
chkxer_("SPPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
spprfs_("U", &c_n1, &c__0, a, af, b, &c__1, x, &c__1, r1, r2, w, iw, &
info);
chkxer_("SPPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
spprfs_("U", &c__0, &c_n1, a, af, b, &c__1, x, &c__1, r1, r2, w, iw, &
info);
chkxer_("SPPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
spprfs_("U", &c__2, &c__1, a, af, b, &c__1, x, &c__2, r1, r2, w, iw, &
info);
chkxer_("SPPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 9;
spprfs_("U", &c__2, &c__1, a, af, b, &c__2, x, &c__1, r1, r2, w, iw, &
info);
chkxer_("SPPRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SPPCON */
s_copy(srnamc_1.srnamt, "SPPCON", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
sppcon_("/", &c__0, a, &anrm, &rcond, w, iw, &info);
chkxer_("SPPCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sppcon_("U", &c_n1, a, &anrm, &rcond, w, iw, &info);
chkxer_("SPPCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SPPEQU */
s_copy(srnamc_1.srnamt, "SPPEQU", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
sppequ_("/", &c__0, a, r1, &rcond, &anrm, &info);
chkxer_("SPPEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
sppequ_("U", &c_n1, a, r1, &rcond, &anrm, &info);
chkxer_("SPPEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
} else if (lsamen_(&c__2, c2, "PB")) {
/* Test error exits of the routines that use the Cholesky
decomposition of a symmetric positive definite band matrix.
SPBTRF */
s_copy(srnamc_1.srnamt, "SPBTRF", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
spbtrf_("/", &c__0, &c__0, a, &c__1, &info);
chkxer_("SPBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
spbtrf_("U", &c_n1, &c__0, a, &c__1, &info);
chkxer_("SPBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
spbtrf_("U", &c__1, &c_n1, a, &c__1, &info);
chkxer_("SPBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
spbtrf_("U", &c__2, &c__1, a, &c__1, &info);
chkxer_("SPBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SPBTF2 */
s_copy(srnamc_1.srnamt, "SPBTF2", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
spbtf2_("/", &c__0, &c__0, a, &c__1, &info);
chkxer_("SPBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
spbtf2_("U", &c_n1, &c__0, a, &c__1, &info);
chkxer_("SPBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
spbtf2_("U", &c__1, &c_n1, a, &c__1, &info);
chkxer_("SPBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
spbtf2_("U", &c__2, &c__1, a, &c__1, &info);
chkxer_("SPBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SPBTRS */
s_copy(srnamc_1.srnamt, "SPBTRS", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
spbtrs_("/", &c__0, &c__0, &c__0, a, &c__1, b, &c__1, &info);
chkxer_("SPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
spbtrs_("U", &c_n1, &c__0, &c__0, a, &c__1, b, &c__1, &info);
chkxer_("SPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
spbtrs_("U", &c__1, &c_n1, &c__0, a, &c__1, b, &c__1, &info);
chkxer_("SPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
spbtrs_("U", &c__0, &c__0, &c_n1, a, &c__1, b, &c__1, &info);
chkxer_("SPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
spbtrs_("U", &c__2, &c__1, &c__1, a, &c__1, b, &c__1, &info);
chkxer_("SPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
spbtrs_("U", &c__2, &c__0, &c__1, a, &c__1, b, &c__1, &info);
chkxer_("SPBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SPBRFS */
s_copy(srnamc_1.srnamt, "SPBRFS", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
spbrfs_("/", &c__0, &c__0, &c__0, a, &c__1, af, &c__1, b, &c__1, x, &
c__1, r1, r2, w, iw, &info);
chkxer_("SPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
spbrfs_("U", &c_n1, &c__0, &c__0, a, &c__1, af, &c__1, b, &c__1, x, &
c__1, r1, r2, w, iw, &info);
chkxer_("SPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
spbrfs_("U", &c__1, &c_n1, &c__0, a, &c__1, af, &c__1, b, &c__1, x, &
c__1, r1, r2, w, iw, &info);
chkxer_("SPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
spbrfs_("U", &c__0, &c__0, &c_n1, a, &c__1, af, &c__1, b, &c__1, x, &
c__1, r1, r2, w, iw, &info);
chkxer_("SPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
spbrfs_("U", &c__2, &c__1, &c__1, a, &c__1, af, &c__2, b, &c__2, x, &
c__2, r1, r2, w, iw, &info);
chkxer_("SPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
spbrfs_("U", &c__2, &c__1, &c__1, a, &c__2, af, &c__1, b, &c__2, x, &
c__2, r1, r2, w, iw, &info);
chkxer_("SPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
spbrfs_("U", &c__2, &c__0, &c__1, a, &c__1, af, &c__1, b, &c__1, x, &
c__2, r1, r2, w, iw, &info);
chkxer_("SPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 12;
spbrfs_("U", &c__2, &c__0, &c__1, a, &c__1, af, &c__1, b, &c__2, x, &
c__1, r1, r2, w, iw, &info);
chkxer_("SPBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SPBCON */
s_copy(srnamc_1.srnamt, "SPBCON", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
spbcon_("/", &c__0, &c__0, a, &c__1, &anrm, &rcond, w, iw, &info);
chkxer_("SPBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
spbcon_("U", &c_n1, &c__0, a, &c__1, &anrm, &rcond, w, iw, &info);
chkxer_("SPBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
spbcon_("U", &c__1, &c_n1, a, &c__1, &anrm, &rcond, w, iw, &info);
chkxer_("SPBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
spbcon_("U", &c__2, &c__1, a, &c__1, &anrm, &rcond, w, iw, &info);
chkxer_("SPBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* SPBEQU */
s_copy(srnamc_1.srnamt, "SPBEQU", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
spbequ_("/", &c__0, &c__0, a, &c__1, r1, &rcond, &anrm, &info);
chkxer_("SPBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
spbequ_("U", &c_n1, &c__0, a, &c__1, r1, &rcond, &anrm, &info);
chkxer_("SPBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
spbequ_("U", &c__1, &c_n1, a, &c__1, r1, &rcond, &anrm, &info);
chkxer_("SPBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
spbequ_("U", &c__2, &c__1, a, &c__1, r1, &rcond, &anrm, &info);
chkxer_("SPBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
}
/* Print a summary line. */
alaesm_(path, &infoc_1.ok, &infoc_1.nout);
return 0;
/* End of SERRPO */
} /* serrpo_ */
/* Subroutine */ int sposvx_(char *fact, char *uplo, integer *n, integer *
nrhs, real *a, integer *lda, real *af, integer *ldaf, char *equed,
real *s, real *b, integer *ldb, real *x, integer *ldx, real *rcond,
real *ferr, real *berr, real *work, integer *iwork, integer *info,
ftnlen fact_len, ftnlen uplo_len, ftnlen equed_len)
{
/* System generated locals */
integer a_dim1, a_offset, af_dim1, af_offset, b_dim1, b_offset, x_dim1,
x_offset, i__1, i__2;
real r__1, r__2;
/* Local variables */
static integer i__, j;
static real amax, smin, smax;
extern logical lsame_(char *, char *, ftnlen, ftnlen);
static real scond, anorm;
static logical equil, rcequ;
extern doublereal slamch_(char *, ftnlen);
static logical nofact;
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
static real bignum;
static integer infequ;
extern /* Subroutine */ int slacpy_(char *, integer *, integer *, real *,
integer *, real *, integer *, ftnlen), spocon_(char *, integer *,
real *, integer *, real *, real *, real *, integer *, integer *,
ftnlen);
extern doublereal slansy_(char *, char *, integer *, real *, integer *,
real *, ftnlen, ftnlen);
static real smlnum;
extern /* Subroutine */ int slaqsy_(char *, integer *, real *, integer *,
real *, real *, real *, char *, ftnlen, ftnlen), spoequ_(integer *
, real *, integer *, real *, real *, real *, integer *), sporfs_(
char *, integer *, integer *, real *, integer *, real *, integer *
, real *, integer *, real *, integer *, real *, real *, real *,
integer *, integer *, ftnlen), spotrf_(char *, integer *, real *,
integer *, integer *, ftnlen), spotrs_(char *, integer *, integer
*, real *, integer *, real *, integer *, integer *, ftnlen);
/* -- 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 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* SPOSVX uses the Cholesky factorization A = U**T*U or A = L*L**T to */
/* compute the solution to a real system of linear equations */
/* A * X = B, */
/* where A is an N-by-N symmetric positive definite 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 = 'E', real scaling factors are computed to equilibrate */
/* the system: */
/* diag(S) * A * diag(S) * inv(diag(S)) * X = diag(S) * B */
/* Whether or not the system will be equilibrated depends on the */
/* scaling of the matrix A, but if equilibration is used, A is */
/* overwritten by diag(S)*A*diag(S) and B by diag(S)*B. */
/* 2. If FACT = 'N' or 'E', the Cholesky decomposition is used to */
/* factor the matrix A (after equilibration if FACT = 'E') as */
/* A = U**T* U, if UPLO = 'U', or */
/* A = L * L**T, if UPLO = 'L', */
/* where U is an upper triangular matrix and L is a lower triangular */
/* matrix. */
/* 3. If the leading i-by-i principal minor is not positive definite, */
/* 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. */
/* 4. The system of equations is solved for X using the factored form */
/* of A. */
/* 5. Iterative refinement is applied to improve the computed solution */
/* matrix and calculate error bounds and backward error estimates */
/* for it. */
/* 6. If equilibration was used, the matrix X is premultiplied by */
/* diag(S) so that it solves the original system before */
/* equilibration. */
/* Arguments */
/* ========= */
/* FACT (input) CHARACTER*1 */
/* Specifies whether or not the factored form of the matrix A is */
/* supplied on entry, and if not, whether the matrix A should be */
/* equilibrated before it is factored. */
/* = 'F': On entry, AF contains the factored form of A. */
/* If EQUED = 'Y', the matrix A has been equilibrated */
/* with scaling factors given by S. A and AF will not */
/* be modified. */
/* = 'N': The matrix A will be copied to AF and factored. */
/* = 'E': The matrix A will be equilibrated if necessary, then */
/* 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/output) REAL array, dimension (LDA,N) */
/* On entry, the symmetric matrix A, except if FACT = 'F' and */
/* EQUED = 'Y', then A must contain the equilibrated matrix */
/* diag(S)*A*diag(S). 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. A is not modified if */
/* FACT = 'F' or 'N', or if FACT = 'E' and EQUED = 'N' on exit. */
/* On exit, if FACT = 'E' and EQUED = 'Y', A is overwritten by */
/* diag(S)*A*diag(S). */
/* 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 triangular factor U or L from the Cholesky */
/* factorization A = U**T*U or A = L*L**T, in the same storage */
/* format as A. If EQUED .ne. 'N', then AF is the factored form */
/* of the equilibrated matrix diag(S)*A*diag(S). */
/* If FACT = 'N', then AF is an output argument and on exit */
/* returns the triangular factor U or L from the Cholesky */
/* factorization A = U**T*U or A = L*L**T of the original */
/* matrix A. */
/* If FACT = 'E', then AF is an output argument and on exit */
/* returns the triangular factor U or L from the Cholesky */
/* factorization A = U**T*U or A = L*L**T of the equilibrated */
/* matrix A (see the description of A for the form of the */
/* equilibrated matrix). */
/* LDAF (input) INTEGER */
/* The leading dimension of the array AF. LDAF >= max(1,N). */
/* EQUED (input or output) CHARACTER*1 */
/* Specifies the form of equilibration that was done. */
/* = 'N': No equilibration (always true if FACT = 'N'). */
/* = 'Y': Equilibration was done, i.e., A has been replaced by */
/* diag(S) * A * diag(S). */
/* EQUED is an input argument if FACT = 'F'; otherwise, it is an */
/* output argument. */
/* S (input or output) REAL array, dimension (N) */
/* The scale factors for A; not accessed if EQUED = 'N'. S is */
/* an input argument if FACT = 'F'; otherwise, S is an output */
/* argument. If FACT = 'F' and EQUED = 'Y', each element of S */
/* must be positive. */
/* B (input/output) REAL array, dimension (LDB,NRHS) */
/* On entry, the N-by-NRHS right hand side matrix B. */
/* On exit, if EQUED = 'N', B is not modified; if EQUED = 'Y', */
/* B is overwritten by diag(S) * 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 to */
/* the original system of equations. Note that if EQUED = 'Y', */
/* A and B are modified on exit, and the solution to the */
/* equilibrated system is inv(diag(S))*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 after equilibration (if done). 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) REAL array, dimension (3*N) */
/* 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: the leading minor of order i of A is */
/* not positive definite, so the factorization */
/* could not be completed, and the solution has not */
/* been 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 */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
af_dim1 = *ldaf;
af_offset = 1 + af_dim1;
af -= af_offset;
--s;
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", (ftnlen)1, (ftnlen)1);
equil = lsame_(fact, "E", (ftnlen)1, (ftnlen)1);
if (nofact || equil) {
*(unsigned char *)equed = 'N';
rcequ = FALSE_;
} else {
rcequ = lsame_(equed, "Y", (ftnlen)1, (ftnlen)1);
smlnum = slamch_("Safe minimum", (ftnlen)12);
bignum = 1.f / smlnum;
}
/* Test the input parameters. */
if (! nofact && ! equil && ! lsame_(fact, "F", (ftnlen)1, (ftnlen)1)) {
*info = -1;
} else if (! lsame_(uplo, "U", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo,
"L", (ftnlen)1, (ftnlen)1)) {
*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 (lsame_(fact, "F", (ftnlen)1, (ftnlen)1) && ! (rcequ || lsame_(
equed, "N", (ftnlen)1, (ftnlen)1))) {
*info = -9;
} else {
if (rcequ) {
smin = bignum;
smax = 0.f;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
r__1 = smin, r__2 = s[j];
smin = dmin(r__1,r__2);
/* Computing MAX */
r__1 = smax, r__2 = s[j];
smax = dmax(r__1,r__2);
/* L10: */
}
if (smin <= 0.f) {
*info = -10;
} else if (*n > 0) {
scond = dmax(smin,smlnum) / dmin(smax,bignum);
} else {
scond = 1.f;
}
}
if (*info == 0) {
if (*ldb < max(1,*n)) {
*info = -12;
} else if (*ldx < max(1,*n)) {
*info = -14;
}
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SPOSVX", &i__1, (ftnlen)6);
return 0;
}
if (equil) {
/* Compute row and column scalings to equilibrate the matrix A. */
spoequ_(n, &a[a_offset], lda, &s[1], &scond, &amax, &infequ);
if (infequ == 0) {
/* Equilibrate the matrix. */
slaqsy_(uplo, n, &a[a_offset], lda, &s[1], &scond, &amax, equed, (
ftnlen)1, (ftnlen)1);
rcequ = lsame_(equed, "Y", (ftnlen)1, (ftnlen)1);
}
}
/* Scale the right hand side. */
if (rcequ) {
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
b[i__ + j * b_dim1] = s[i__] * b[i__ + j * b_dim1];
/* L20: */
}
/* L30: */
}
}
if (nofact || equil) {
/* Compute the Cholesky factorization A = U'*U or A = L*L'. */
slacpy_(uplo, n, n, &a[a_offset], lda, &af[af_offset], ldaf, (ftnlen)
1);
spotrf_(uplo, n, &af[af_offset], ldaf, info, (ftnlen)1);
/* Return if INFO is non-zero. */
if (*info != 0) {
if (*info > 0) {
*rcond = 0.f;
}
return 0;
}
}
/* Compute the norm of the matrix A. */
anorm = slansy_("1", uplo, n, &a[a_offset], lda, &work[1], (ftnlen)1, (
ftnlen)1);
/* Compute the reciprocal of the condition number of A. */
spocon_(uplo, n, &af[af_offset], ldaf, &anorm, rcond, &work[1], &iwork[1],
info, (ftnlen)1);
/* Set INFO = N+1 if the matrix is singular to working precision. */
if (*rcond < slamch_("Epsilon", (ftnlen)7)) {
*info = *n + 1;
}
/* Compute the solution matrix X. */
slacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx, (ftnlen)4);
spotrs_(uplo, n, nrhs, &af[af_offset], ldaf, &x[x_offset], ldx, info, (
ftnlen)1);
/* Use iterative refinement to improve the computed solution and */
/* compute error bounds and backward error estimates for it. */
sporfs_(uplo, n, nrhs, &a[a_offset], lda, &af[af_offset], ldaf, &b[
b_offset], ldb, &x[x_offset], ldx, &ferr[1], &berr[1], &work[1], &
iwork[1], info, (ftnlen)1);
/* Transform the solution matrix X to a solution of the original */
/* system. */
if (rcequ) {
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
x[i__ + j * x_dim1] = s[i__] * x[i__ + j * x_dim1];
/* L40: */
}
/* L50: */
}
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
ferr[j] /= scond;
/* L60: */
}
}
return 0;
/* End of SPOSVX */
} /* sposvx_ */
/* Subroutine */ int ssygvx_(integer *itype, char *jobz, char *range, char *
uplo, integer *n, real *a, integer *lda, real *b, integer *ldb, real *
vl, real *vu, integer *il, integer *iu, real *abstol, integer *m,
real *w, real *z__, integer *ldz, real *work, integer *lwork, integer
*iwork, integer *ifail, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, z_dim1, z_offset, i__1, i__2;
/* Local variables */
integer nb;
char trans[1];
logical upper;
logical wantz;
logical alleig, indeig, valeig;
integer lwkmin;
integer lwkopt;
logical lquery;
/* -- LAPACK driver routine (version 3.2) -- */
/* November 2006 */
/* Purpose */
/* ======= */
/* SSYGVX computes selected eigenvalues, and optionally, eigenvectors */
/* of a real generalized symmetric-definite eigenproblem, of the form */
/* A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A */
/* and B are assumed to be symmetric and B is also positive definite. */
/* Eigenvalues and eigenvectors can be selected by specifying either a */
/* range of values or a range of indices for the desired eigenvalues. */
/* Arguments */
/* ========= */
/* ITYPE (input) INTEGER */
/* Specifies the problem type to be solved: */
/* = 1: A*x = (lambda)*B*x */
/* = 2: A*B*x = (lambda)*x */
/* = 3: B*A*x = (lambda)*x */
/* JOBZ (input) CHARACTER*1 */
/* = 'N': Compute eigenvalues only; */
/* = 'V': Compute eigenvalues and eigenvectors. */
/* RANGE (input) CHARACTER*1 */
/* = 'A': all eigenvalues will be found. */
/* = 'V': all eigenvalues in the half-open interval (VL,VU] */
/* will be found. */
/* = 'I': the IL-th through IU-th eigenvalues will be found. */
/* UPLO (input) CHARACTER*1 */
/* = 'U': Upper triangle of A and B are stored; */
/* = 'L': Lower triangle of A and B are stored. */
/* N (input) INTEGER */
/* The order of the matrix pencil (A,B). N >= 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. If UPLO = 'L', */
/* the leading N-by-N lower triangular part of A contains */
/* the lower triangular part of the matrix A. */
/* On exit, the lower triangle (if UPLO='L') or the upper */
/* triangle (if UPLO='U') of A, including the diagonal, is */
/* destroyed. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,N). */
/* B (input/output) REAL array, dimension (LDA, N) */
/* On entry, the symmetric matrix B. If UPLO = 'U', the */
/* leading N-by-N upper triangular part of B contains the */
/* upper triangular part of the matrix B. If UPLO = 'L', */
/* the leading N-by-N lower triangular part of B contains */
/* the lower triangular part of the matrix B. */
/* On exit, if INFO <= N, the part of B containing the matrix is */
/* overwritten by the triangular factor U or L from the Cholesky */
/* factorization B = U**T*U or B = L*L**T. */
/* LDB (input) INTEGER */
/* The leading dimension of the array B. LDB >= max(1,N). */
/* VL (input) REAL */
/* VU (input) REAL */
/* If RANGE='V', the lower and upper bounds of the interval to */
/* be searched for eigenvalues. VL < VU. */
/* Not referenced if RANGE = 'A' or 'I'. */
/* IL (input) INTEGER */
/* IU (input) INTEGER */
/* If RANGE='I', the indices (in ascending order) of the */
/* smallest and largest eigenvalues to be returned. */
/* 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. */
/* Not referenced if RANGE = 'A' or 'V'. */
/* ABSTOL (input) REAL */
/* The absolute error tolerance for the eigenvalues. */
/* An approximate eigenvalue is accepted as converged */
/* when it is determined to lie in an interval [a,b] */
/* of width less than or equal to */
/* ABSTOL + EPS * max( |a|,|b| ) , */
/* where EPS is the machine precision. If ABSTOL is less than */
/* or equal to zero, then EPS*|T| will be used in its place, */
/* where |T| is the 1-norm of the tridiagonal matrix obtained */
/* by reducing A to tridiagonal form. */
/* Eigenvalues will be computed most accurately when ABSTOL is */
/* set to twice the underflow threshold 2*DLAMCH('S'), not zero. */
/* If this routine returns with INFO>0, indicating that some */
/* eigenvectors did not converge, try setting ABSTOL to */
/* 2*SLAMCH('S'). */
/* M (output) INTEGER */
/* The total number of eigenvalues found. 0 <= M <= N. */
/* If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1. */
/* W (output) REAL array, dimension (N) */
/* On normal exit, the first M elements contain the selected */
/* eigenvalues in ascending order. */
/* Z (output) REAL array, dimension (LDZ, max(1,M)) */
/* If JOBZ = 'N', then Z is not referenced. */
/* If JOBZ = 'V', then if INFO = 0, the first M columns of Z */
/* contain the orthonormal eigenvectors of the matrix A */
/* corresponding to the selected eigenvalues, with the i-th */
/* column of Z holding the eigenvector associated with W(i). */
/* The eigenvectors are normalized as follows: */
/* if ITYPE = 1 or 2, Z**T*B*Z = I; */
/* if ITYPE = 3, Z**T*inv(B)*Z = I. */
/* If an eigenvector fails to converge, then that column of Z */
/* contains the latest approximation to the eigenvector, and the */
/* index of the eigenvector is returned in IFAIL. */
/* Note: the user must ensure that at least max(1,M) columns are */
/* supplied in the array Z; if RANGE = 'V', the exact value of M */
/* is not known in advance and an upper bound must be used. */
/* LDZ (input) INTEGER */
/* The leading dimension of the array Z. LDZ >= 1, and if */
/* JOBZ = 'V', LDZ >= 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 the array WORK. LWORK >= max(1,8*N). */
/* For optimal efficiency, LWORK >= (NB+3)*N, */
/* where NB is the blocksize for SSYTRD returned by ILAENV. */
/* If LWORK = -1, then a workspace query is assumed; the routine */
/* only calculates the optimal size of the WORK array, returns */
/* this value as the first entry of the WORK array, and no error */
/* message related to LWORK is issued by XERBLA. */
/* IWORK (workspace) INTEGER array, dimension (5*N) */
/* IFAIL (output) INTEGER array, dimension (N) */
/* If JOBZ = 'V', then if INFO = 0, the first M elements of */
/* IFAIL are zero. If INFO > 0, then IFAIL contains the */
/* indices of the eigenvectors that failed to converge. */
/* If JOBZ = 'N', then IFAIL is not referenced. */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* > 0: SPOTRF or SSYEVX returned an error code: */
/* <= N: if INFO = i, SSYEVX failed to converge; */
/* i eigenvectors failed to converge. Their indices */
/* are stored in array IFAIL. */
/* > N: if INFO = N + i, for 1 <= i <= N, then the leading */
/* minor of order i of B is not positive definite. */
/* The factorization of B could not be completed and */
/* no eigenvalues or eigenvectors were computed. */
/* Further Details */
/* =============== */
/* Based on contributions by */
/* Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA */
/* ===================================================================== */
/* Test the input parameters. */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
--w;
z_dim1 = *ldz;
z_offset = 1 + z_dim1;
z__ -= z_offset;
--work;
--iwork;
--ifail;
/* Function Body */
upper = lsame_(uplo, "U");
wantz = lsame_(jobz, "V");
alleig = lsame_(range, "A");
valeig = lsame_(range, "V");
indeig = lsame_(range, "I");
lquery = *lwork == -1;
*info = 0;
if (*itype < 1 || *itype > 3) {
*info = -1;
} else if (! (wantz || lsame_(jobz, "N"))) {
*info = -2;
} else if (! (alleig || valeig || indeig)) {
*info = -3;
} else if (! (upper || lsame_(uplo, "L"))) {
*info = -4;
} else if (*n < 0) {
*info = -5;
} else if (*lda < max(1,*n)) {
*info = -7;
} else if (*ldb < max(1,*n)) {
*info = -9;
} else {
if (valeig) {
if (*n > 0 && *vu <= *vl) {
*info = -11;
}
} else if (indeig) {
if (*il < 1 || *il > max(1,*n)) {
*info = -12;
} else if (*iu < min(*n,*il) || *iu > *n) {
*info = -13;
}
}
}
if (*info == 0) {
if (*ldz < 1 || wantz && *ldz < *n) {
*info = -18;
}
}
if (*info == 0) {
/* Computing MAX */
i__1 = 1, i__2 = *n << 3;
lwkmin = max(i__1,i__2);
nb = ilaenv_(&c__1, "SSYTRD", uplo, n, &c_n1, &c_n1, &c_n1);
/* Computing MAX */
i__1 = lwkmin, i__2 = (nb + 3) * *n;
lwkopt = max(i__1,i__2);
work[1] = (real) lwkopt;
if (*lwork < lwkmin && ! lquery) {
*info = -20;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SSYGVX", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
*m = 0;
if (*n == 0) {
return 0;
}
/* Form a Cholesky factorization of B. */
spotrf_(uplo, n, &b[b_offset], ldb, info);
if (*info != 0) {
*info = *n + *info;
return 0;
}
/* Transform problem to standard eigenvalue problem and solve. */
ssygst_(itype, uplo, n, &a[a_offset], lda, &b[b_offset], ldb, info);
ssyevx_(jobz, range, uplo, n, &a[a_offset], lda, vl, vu, il, iu, abstol,
m, &w[1], &z__[z_offset], ldz, &work[1], lwork, &iwork[1], &ifail[
1], info);
if (wantz) {
/* Backtransform eigenvectors to the original problem. */
if (*info > 0) {
*m = *info - 1;
}
if (*itype == 1 || *itype == 2) {
/* For A*x=(lambda)*B*x and A*B*x=(lambda)*x; */
/* backtransform eigenvectors: x = inv(L)'*y or inv(U)*y */
if (upper) {
*(unsigned char *)trans = 'N';
} else {
*(unsigned char *)trans = 'T';
}
strsm_("Left", uplo, trans, "Non-unit", n, m, &c_b19, &b[b_offset]
, ldb, &z__[z_offset], ldz);
} else if (*itype == 3) {
/* For B*A*x=(lambda)*x; */
/* backtransform eigenvectors: x = L*y or U'*y */
if (upper) {
*(unsigned char *)trans = 'T';
} else {
*(unsigned char *)trans = 'N';
}
strmm_("Left", uplo, trans, "Non-unit", n, m, &c_b19, &b[b_offset]
, ldb, &z__[z_offset], ldz);
}
}
/* Set WORK(1) to optimal workspace size. */
work[1] = (real) lwkopt;
return 0;
/* End of SSYGVX */
} /* ssygvx_ */
/* Subroutine */ int sposvx_(char *fact, char *uplo, integer *n, integer *
nrhs, real *a, integer *lda, real *af, integer *ldaf, char *equed,
real *s, real *b, integer *ldb, real *x, integer *ldx, real *rcond,
real *ferr, real *berr, real *work, integer *iwork, integer *info)
{
/* -- LAPACK driver 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
=======
SPOSVX uses the Cholesky factorization A = U**T*U or A = L*L**T to
compute the solution to a real system of linear equations
A * X = B,
where A is an N-by-N symmetric positive definite 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 = 'E', real scaling factors are computed to equilibrate
the system:
diag(S) * A * diag(S) * inv(diag(S)) * X = diag(S) * B
Whether or not the system will be equilibrated depends on the
scaling of the matrix A, but if equilibration is used, A is
overwritten by diag(S)*A*diag(S) and B by diag(S)*B.
2. If FACT = 'N' or 'E', the Cholesky decomposition is used to
factor the matrix A (after equilibration if FACT = 'E') as
A = U**T* U, if UPLO = 'U', or
A = L * L**T, if UPLO = 'L',
where U is an upper triangular matrix and L is a lower triangular
matrix.
3. 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 4-6 are skipped.
4. The system of equations is solved for X using the factored form
of A.
5. Iterative refinement is applied to improve the computed solution
matrix and calculate error bounds and backward error estimates
for it.
6. If equilibration was used, the matrix X is premultiplied by
diag(S) so that it solves the original system before
equilibration.
Arguments
=========
FACT (input) CHARACTER*1
Specifies whether or not the factored form of the matrix A is
supplied on entry, and if not, whether the matrix A should be
equilibrated before it is factored.
= 'F': On entry, AF contains the factored form of A.
If EQUED = 'Y', the matrix A has been equilibrated
with scaling factors given by S. A and AF will not
be modified.
= 'N': The matrix A will be copied to AF and factored.
= 'E': The matrix A will be equilibrated if necessary, then
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/output) REAL array, dimension (LDA,N)
On entry, the symmetric matrix A, except if FACT = 'F' and
EQUED = 'Y', then A must contain the equilibrated matrix
diag(S)*A*diag(S). 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. A is not modified if
FACT = 'F' or 'N', or if FACT = 'E' and EQUED = 'N' on exit.
On exit, if FACT = 'E' and EQUED = 'Y', A is overwritten by
diag(S)*A*diag(S).
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 triangular factor U or L from the Cholesky
factorization A = U**T*U or A = L*L**T, in the same storage
format as A. If EQUED .ne. 'N', then AF is the factored form
of the equilibrated matrix diag(S)*A*diag(S).
If FACT = 'N', then AF is an output argument and on exit
returns the triangular factor U or L from the Cholesky
factorization A = U**T*U or A = L*L**T of the original
matrix A.
If FACT = 'E', then AF is an output argument and on exit
returns the triangular factor U or L from the Cholesky
factorization A = U**T*U or A = L*L**T of the equilibrated
matrix A (see the description of A for the form of the
equilibrated matrix).
LDAF (input) INTEGER
The leading dimension of the array AF. LDAF >= max(1,N).
EQUED (input or output) CHARACTER*1
Specifies the form of equilibration that was done.
= 'N': No equilibration (always true if FACT = 'N').
= 'Y': Equilibration was done, i.e., A has been replaced by
diag(S) * A * diag(S).
EQUED is an input argument if FACT = 'F'; otherwise, it is an
output argument.
S (input or output) REAL array, dimension (N)
The scale factors for A; not accessed if EQUED = 'N'. S is
an input argument if FACT = 'F'; otherwise, S is an output
argument. If FACT = 'F' and EQUED = 'Y', each element of S
must be positive.
B (input/output) REAL array, dimension (LDB,NRHS)
On entry, the N-by-NRHS right hand side matrix B.
On exit, if EQUED = 'N', B is not modified; if EQUED = 'Y',
B is overwritten by diag(S) * 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, the N-by-NRHS solution matrix X to the original
system of equations. Note that if EQUED = 'Y', A and B are
modified on exit, and the solution to the equilibrated system
is inv(diag(S))*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 after equilibration (if done). 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) 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) REAL array, dimension (3*N)
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: the leading minor of order i of A
is not positive definite, so the factorization
could not be completed, and 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 */
/* System generated locals */
integer a_dim1, a_offset, af_dim1, af_offset, b_dim1, b_offset, x_dim1,
x_offset, i__1, i__2;
real r__1, r__2;
/* Local variables */
static real amax, smin, smax;
static integer i, j;
extern logical lsame_(char *, char *);
static real scond, anorm;
static logical equil, rcequ;
extern doublereal slamch_(char *);
static logical nofact;
extern /* Subroutine */ int xerbla_(char *, integer *);
static real bignum;
static integer infequ;
extern /* Subroutine */ int slacpy_(char *, integer *, integer *, real *,
integer *, real *, integer *), spocon_(char *, integer *,
real *, integer *, real *, real *, real *, integer *, integer *);
extern doublereal slansy_(char *, char *, integer *, real *, integer *,
real *);
static real smlnum;
extern /* Subroutine */ int slaqsy_(char *, integer *, real *, integer *,
real *, real *, real *, char *), spoequ_(integer *
, real *, integer *, real *, real *, real *, integer *), sporfs_(
char *, integer *, integer *, real *, integer *, real *, integer *
, real *, integer *, real *, integer *, real *, real *, real *,
integer *, integer *), spotrf_(char *, integer *, real *,
integer *, integer *), spotrs_(char *, integer *, integer
*, real *, integer *, real *, integer *, integer *);
#define S(I) s[(I)-1]
#define FERR(I) ferr[(I)-1]
#define BERR(I) berr[(I)-1]
#define WORK(I) work[(I)-1]
#define IWORK(I) iwork[(I)-1]
#define A(I,J) a[(I)-1 + ((J)-1)* ( *lda)]
#define AF(I,J) af[(I)-1 + ((J)-1)* ( *ldaf)]
#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");
equil = lsame_(fact, "E");
if (nofact || equil) {
*(unsigned char *)equed = 'N';
rcequ = FALSE_;
} else {
rcequ = lsame_(equed, "Y");
smlnum = slamch_("Safe minimum");
bignum = 1.f / smlnum;
}
/* Test the input parameters. */
if (! nofact && ! equil && ! 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 (lsame_(fact, "F") && ! (rcequ || lsame_(equed, "N"))) {
*info = -9;
} else {
if (rcequ) {
smin = bignum;
smax = 0.f;
i__1 = *n;
for (j = 1; j <= *n; ++j) {
/* Computing MIN */
r__1 = smin, r__2 = S(j);
smin = dmin(r__1,r__2);
/* Computing MAX */
r__1 = smax, r__2 = S(j);
smax = dmax(r__1,r__2);
/* L10: */
}
if (smin <= 0.f) {
*info = -10;
} else if (*n > 0) {
scond = dmax(smin,smlnum) / dmin(smax,bignum);
} else {
scond = 1.f;
}
}
if (*info == 0) {
if (*ldb < max(1,*n)) {
*info = -12;
} else if (*ldx < max(1,*n)) {
*info = -14;
}
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SPOSVX", &i__1);
return 0;
}
if (equil) {
/* Compute row and column scalings to equilibrate the matrix A.
*/
spoequ_(n, &A(1,1), lda, &S(1), &scond, &amax, &infequ);
if (infequ == 0) {
/* Equilibrate the matrix. */
slaqsy_(uplo, n, &A(1,1), lda, &S(1), &scond, &amax, equed);
rcequ = lsame_(equed, "Y");
}
}
/* Scale the right hand side. */
if (rcequ) {
i__1 = *nrhs;
for (j = 1; j <= *nrhs; ++j) {
i__2 = *n;
for (i = 1; i <= *n; ++i) {
B(i,j) = S(i) * B(i,j);
/* L20: */
}
/* L30: */
}
}
if (nofact || equil) {
/* Compute the Cholesky factorization A = U'*U or A = L*L'. */
slacpy_(uplo, n, n, &A(1,1), lda, &AF(1,1), ldaf);
spotrf_(uplo, n, &AF(1,1), ldaf, info);
/* Return if INFO is non-zero. */
if (*info != 0) {
if (*info > 0) {
*rcond = 0.f;
}
return 0;
}
}
/* Compute the norm of the matrix A. */
anorm = slansy_("1", uplo, n, &A(1,1), lda, &WORK(1));
/* Compute the reciprocal of the condition number of A. */
spocon_(uplo, n, &AF(1,1), ldaf, &anorm, rcond, &WORK(1), &IWORK(1),
info);
/* Return if the matrix is singular to working precision. */
if (*rcond < slamch_("Epsilon")) {
*info = *n + 1;
return 0;
}
/* Compute the solution matrix X. */
slacpy_("Full", n, nrhs, &B(1,1), ldb, &X(1,1), ldx);
spotrs_(uplo, n, nrhs, &AF(1,1), ldaf, &X(1,1), ldx, info);
/* Use iterative refinement to improve the computed solution and
compute error bounds and backward error estimates for it. */
sporfs_(uplo, n, nrhs, &A(1,1), lda, &AF(1,1), ldaf, &B(1,1), ldb, &X(1,1), ldx, &FERR(1), &BERR(1), &WORK(1), &
IWORK(1), info);
/* Transform the solution matrix X to a solution of the original
system. */
if (rcequ) {
i__1 = *nrhs;
for (j = 1; j <= *nrhs; ++j) {
i__2 = *n;
for (i = 1; i <= *n; ++i) {
X(i,j) = S(i) * X(i,j);
/* L40: */
}
/* L50: */
}
i__1 = *nrhs;
for (j = 1; j <= *nrhs; ++j) {
FERR(j) /= scond;
/* L60: */
}
}
return 0;
/* End of SPOSVX */
} /* sposvx_ */
/* 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. */
}
