/* dsptrs.f -- translated by f2c (version 20061008).
You must link the resulting object file with libf2c:
on Microsoft Windows system, link with libf2c.lib;
on Linux or Unix systems, link with .../path/to/libf2c.a -lm
or, if you install libf2c.a in a standard place, with -lf2c -lm
-- in that order, at the end of the command line, as in
cc *.o -lf2c -lm
Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
http://www.netlib.org/f2c/libf2c.zip
*/
#include "f2c.h"
#include "blaswrap.h"
/* Table of constant values */
static doublereal c_b7 = -1.;
static integer c__1 = 1;
static doublereal c_b19 = 1.;
/* Subroutine */ int dsptrs_(char *uplo, integer *n, integer *nrhs,
doublereal *ap, integer *ipiv, doublereal *b, integer *ldb, integer *
info)
{
/* System generated locals */
integer b_dim1, b_offset, i__1;
doublereal d__1;
/* Local variables */
integer j, k;
doublereal ak, bk;
integer kc, kp;
doublereal akm1, bkm1;
extern /* Subroutine */ int dger_(integer *, integer *, doublereal *,
doublereal *, integer *, doublereal *, integer *, doublereal *,
integer *);
doublereal akm1k;
extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *,
integer *);
extern logical lsame_(char *, char *);
doublereal denom;
extern /* Subroutine */ int dgemv_(char *, integer *, integer *,
doublereal *, doublereal *, integer *, doublereal *, integer *,
doublereal *, doublereal *, integer *), dswap_(integer *,
doublereal *, integer *, doublereal *, integer *);
logical upper;
extern /* Subroutine */ int xerbla_(char *, integer *);
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DSPTRS solves a system of linear equations A*X = B with a real */
/* symmetric matrix A stored in packed format using the factorization */
/* A = U*D*U**T or A = L*D*L**T computed by DSPTRF. */
/* Arguments */
/* ========= */
/* UPLO (input) CHARACTER*1 */
/* Specifies whether the details of the factorization are stored */
/* as an upper or lower triangular matrix. */
/* = 'U': Upper triangular, form is A = U*D*U**T; */
/* = 'L': Lower triangular, form is A = L*D*L**T. */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* NRHS (input) INTEGER */
/* The number of right hand sides, i.e., the number of columns */
/* of the matrix B. NRHS >= 0. */
/* AP (input) DOUBLE PRECISION array, dimension (N*(N+1)/2) */
/* The block diagonal matrix D and the multipliers used to */
/* obtain the factor U or L as computed by DSPTRF, stored as a */
/* packed triangular matrix. */
/* IPIV (input) INTEGER array, dimension (N) */
/* Details of the interchanges and the block structure of D */
/* as determined by DSPTRF. */
/* B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS) */
/* On entry, the right hand side matrix B. */
/* On exit, the 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 */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
--ap;
--ipiv;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
/* Function Body */
*info = 0;
upper = lsame_(uplo, "U");
if (! upper && ! lsame_(uplo, "L")) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*nrhs < 0) {
*info = -3;
} else if (*ldb < max(1,*n)) {
*info = -7;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("DSPTRS", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0 || *nrhs == 0) {
return 0;
}
if (upper) {
/* Solve A*X = B, where A = U*D*U'. */
/* First solve U*D*X = B, overwriting B with X. */
/* K is the main loop index, decreasing from N to 1 in steps of */
/* 1 or 2, depending on the size of the diagonal blocks. */
k = *n;
kc = *n * (*n + 1) / 2 + 1;
L10:
/* If K < 1, exit from loop. */
if (k < 1) {
goto L30;
}
kc -= k;
if (ipiv[k] > 0) {
/* 1 x 1 diagonal block */
/* Interchange rows K and IPIV(K). */
kp = ipiv[k];
if (kp != k) {
dswap_(nrhs, &b[k + b_dim1], ldb, &b[kp + b_dim1], ldb);
}
/* Multiply by inv(U(K)), where U(K) is the transformation */
/* stored in column K of A. */
i__1 = k - 1;
dger_(&i__1, nrhs, &c_b7, &ap[kc], &c__1, &b[k + b_dim1], ldb, &b[
b_dim1 + 1], ldb);
/* Multiply by the inverse of the diagonal block. */
d__1 = 1. / ap[kc + k - 1];
dscal_(nrhs, &d__1, &b[k + b_dim1], ldb);
--k;
} else {
/* 2 x 2 diagonal block */
/* Interchange rows K-1 and -IPIV(K). */
kp = -ipiv[k];
if (kp != k - 1) {
dswap_(nrhs, &b[k - 1 + b_dim1], ldb, &b[kp + b_dim1], ldb);
}
/* Multiply by inv(U(K)), where U(K) is the transformation */
/* stored in columns K-1 and K of A. */
i__1 = k - 2;
dger_(&i__1, nrhs, &c_b7, &ap[kc], &c__1, &b[k + b_dim1], ldb, &b[
b_dim1 + 1], ldb);
i__1 = k - 2;
dger_(&i__1, nrhs, &c_b7, &ap[kc - (k - 1)], &c__1, &b[k - 1 +
b_dim1], ldb, &b[b_dim1 + 1], ldb);
/* Multiply by the inverse of the diagonal block. */
akm1k = ap[kc + k - 2];
akm1 = ap[kc - 1] / akm1k;
ak = ap[kc + k - 1] / akm1k;
denom = akm1 * ak - 1.;
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
bkm1 = b[k - 1 + j * b_dim1] / akm1k;
bk = b[k + j * b_dim1] / akm1k;
b[k - 1 + j * b_dim1] = (ak * bkm1 - bk) / denom;
b[k + j * b_dim1] = (akm1 * bk - bkm1) / denom;
/* L20: */
}
kc = kc - k + 1;
k += -2;
}
goto L10;
L30:
/* Next solve U'*X = B, overwriting B with X. */
/* K is the main loop index, increasing from 1 to N in steps of */
/* 1 or 2, depending on the size of the diagonal blocks. */
k = 1;
kc = 1;
L40:
/* If K > N, exit from loop. */
if (k > *n) {
goto L50;
}
if (ipiv[k] > 0) {
/* 1 x 1 diagonal block */
/* Multiply by inv(U'(K)), where U(K) is the transformation */
/* stored in column K of A. */
i__1 = k - 1;
dgemv_("Transpose", &i__1, nrhs, &c_b7, &b[b_offset], ldb, &ap[kc]
, &c__1, &c_b19, &b[k + b_dim1], ldb);
/* Interchange rows K and IPIV(K). */
kp = ipiv[k];
if (kp != k) {
dswap_(nrhs, &b[k + b_dim1], ldb, &b[kp + b_dim1], ldb);
}
kc += k;
++k;
} else {
/* 2 x 2 diagonal block */
/* Multiply by inv(U'(K+1)), where U(K+1) is the transformation */
/* stored in columns K and K+1 of A. */
i__1 = k - 1;
dgemv_("Transpose", &i__1, nrhs, &c_b7, &b[b_offset], ldb, &ap[kc]
, &c__1, &c_b19, &b[k + b_dim1], ldb);
i__1 = k - 1;
dgemv_("Transpose", &i__1, nrhs, &c_b7, &b[b_offset], ldb, &ap[kc
+ k], &c__1, &c_b19, &b[k + 1 + b_dim1], ldb);
/* Interchange rows K and -IPIV(K). */
kp = -ipiv[k];
if (kp != k) {
dswap_(nrhs, &b[k + b_dim1], ldb, &b[kp + b_dim1], ldb);
}
kc = kc + (k << 1) + 1;
k += 2;
}
goto L40;
L50:
;
} else {
/* Solve A*X = B, where A = L*D*L'. */
/* First solve L*D*X = B, overwriting B with X. */
/* K is the main loop index, increasing from 1 to N in steps of */
/* 1 or 2, depending on the size of the diagonal blocks. */
k = 1;
kc = 1;
L60:
/* If K > N, exit from loop. */
if (k > *n) {
goto L80;
}
if (ipiv[k] > 0) {
/* 1 x 1 diagonal block */
/* Interchange rows K and IPIV(K). */
kp = ipiv[k];
if (kp != k) {
dswap_(nrhs, &b[k + b_dim1], ldb, &b[kp + b_dim1], ldb);
}
/* Multiply by inv(L(K)), where L(K) is the transformation */
/* stored in column K of A. */
if (k < *n) {
i__1 = *n - k;
dger_(&i__1, nrhs, &c_b7, &ap[kc + 1], &c__1, &b[k + b_dim1],
ldb, &b[k + 1 + b_dim1], ldb);
}
/* Multiply by the inverse of the diagonal block. */
d__1 = 1. / ap[kc];
dscal_(nrhs, &d__1, &b[k + b_dim1], ldb);
kc = kc + *n - k + 1;
++k;
} else {
/* 2 x 2 diagonal block */
/* Interchange rows K+1 and -IPIV(K). */
kp = -ipiv[k];
if (kp != k + 1) {
dswap_(nrhs, &b[k + 1 + b_dim1], ldb, &b[kp + b_dim1], ldb);
}
/* Multiply by inv(L(K)), where L(K) is the transformation */
/* stored in columns K and K+1 of A. */
if (k < *n - 1) {
i__1 = *n - k - 1;
dger_(&i__1, nrhs, &c_b7, &ap[kc + 2], &c__1, &b[k + b_dim1],
ldb, &b[k + 2 + b_dim1], ldb);
i__1 = *n - k - 1;
dger_(&i__1, nrhs, &c_b7, &ap[kc + *n - k + 2], &c__1, &b[k +
1 + b_dim1], ldb, &b[k + 2 + b_dim1], ldb);
}
/* Multiply by the inverse of the diagonal block. */
akm1k = ap[kc + 1];
akm1 = ap[kc] / akm1k;
ak = ap[kc + *n - k + 1] / akm1k;
denom = akm1 * ak - 1.;
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
bkm1 = b[k + j * b_dim1] / akm1k;
bk = b[k + 1 + j * b_dim1] / akm1k;
b[k + j * b_dim1] = (ak * bkm1 - bk) / denom;
b[k + 1 + j * b_dim1] = (akm1 * bk - bkm1) / denom;
/* L70: */
}
kc = kc + (*n - k << 1) + 1;
k += 2;
}
goto L60;
L80:
/* Next solve L'*X = B, overwriting B with X. */
/* K is the main loop index, decreasing from N to 1 in steps of */
/* 1 or 2, depending on the size of the diagonal blocks. */
k = *n;
kc = *n * (*n + 1) / 2 + 1;
L90:
/* If K < 1, exit from loop. */
if (k < 1) {
goto L100;
}
kc -= *n - k + 1;
if (ipiv[k] > 0) {
/* 1 x 1 diagonal block */
/* Multiply by inv(L'(K)), where L(K) is the transformation */
/* stored in column K of A. */
if (k < *n) {
i__1 = *n - k;
dgemv_("Transpose", &i__1, nrhs, &c_b7, &b[k + 1 + b_dim1],
ldb, &ap[kc + 1], &c__1, &c_b19, &b[k + b_dim1], ldb);
}
/* Interchange rows K and IPIV(K). */
kp = ipiv[k];
if (kp != k) {
dswap_(nrhs, &b[k + b_dim1], ldb, &b[kp + b_dim1], ldb);
}
--k;
} else {
/* 2 x 2 diagonal block */
/* Multiply by inv(L'(K-1)), where L(K-1) is the transformation */
/* stored in columns K-1 and K of A. */
if (k < *n) {
i__1 = *n - k;
dgemv_("Transpose", &i__1, nrhs, &c_b7, &b[k + 1 + b_dim1],
ldb, &ap[kc + 1], &c__1, &c_b19, &b[k + b_dim1], ldb);
i__1 = *n - k;
dgemv_("Transpose", &i__1, nrhs, &c_b7, &b[k + 1 + b_dim1],
ldb, &ap[kc - (*n - k)], &c__1, &c_b19, &b[k - 1 +
b_dim1], ldb);
}
/* Interchange rows K and -IPIV(K). */
kp = -ipiv[k];
if (kp != k) {
dswap_(nrhs, &b[k + b_dim1], ldb, &b[kp + b_dim1], ldb);
}
kc -= *n - k + 2;
k += -2;
}
goto L90;
L100:
;
}
return 0;
/* End of DSPTRS */
} /* dsptrs_ */