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440 lines
12 KiB
440 lines
12 KiB
15 years ago
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#include "clapack.h"
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/* Subroutine */ int slasr_(char *side, char *pivot, char *direct, integer *m,
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integer *n, real *c__, real *s, real *a, integer *lda)
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{
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/* System generated locals */
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integer a_dim1, a_offset, i__1, i__2;
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/* Local variables */
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integer i__, j, info;
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real temp;
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extern logical lsame_(char *, char *);
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real ctemp, stemp;
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extern /* Subroutine */ int xerbla_(char *, integer *);
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/* -- LAPACK auxiliary routine (version 3.1) -- */
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/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
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/* November 2006 */
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/* .. Scalar Arguments .. */
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/* .. */
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/* .. Array Arguments .. */
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/* .. */
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/* Purpose */
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/* ======= */
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/* SLASR applies a sequence of plane rotations to a real matrix A, */
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/* from either the left or the right. */
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/* When SIDE = 'L', the transformation takes the form */
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/* A := P*A */
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/* and when SIDE = 'R', the transformation takes the form */
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/* A := A*P**T */
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/* where P is an orthogonal matrix consisting of a sequence of z plane */
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/* rotations, with z = M when SIDE = 'L' and z = N when SIDE = 'R', */
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/* and P**T is the transpose of P. */
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/* When DIRECT = 'F' (Forward sequence), then */
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/* P = P(z-1) * ... * P(2) * P(1) */
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/* and when DIRECT = 'B' (Backward sequence), then */
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/* P = P(1) * P(2) * ... * P(z-1) */
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/* where P(k) is a plane rotation matrix defined by the 2-by-2 rotation */
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/* R(k) = ( c(k) s(k) ) */
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/* = ( -s(k) c(k) ). */
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/* When PIVOT = 'V' (Variable pivot), the rotation is performed */
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/* for the plane (k,k+1), i.e., P(k) has the form */
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/* P(k) = ( 1 ) */
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/* ( ... ) */
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/* ( 1 ) */
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/* ( c(k) s(k) ) */
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/* ( -s(k) c(k) ) */
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/* ( 1 ) */
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/* ( ... ) */
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/* ( 1 ) */
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/* where R(k) appears as a rank-2 modification to the identity matrix in */
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/* rows and columns k and k+1. */
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/* When PIVOT = 'T' (Top pivot), the rotation is performed for the */
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/* plane (1,k+1), so P(k) has the form */
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/* P(k) = ( c(k) s(k) ) */
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/* ( 1 ) */
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/* ( ... ) */
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/* ( 1 ) */
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/* ( -s(k) c(k) ) */
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/* ( 1 ) */
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/* ( ... ) */
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/* ( 1 ) */
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/* where R(k) appears in rows and columns 1 and k+1. */
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/* Similarly, when PIVOT = 'B' (Bottom pivot), the rotation is */
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/* performed for the plane (k,z), giving P(k) the form */
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/* P(k) = ( 1 ) */
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/* ( ... ) */
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/* ( 1 ) */
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/* ( c(k) s(k) ) */
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/* ( 1 ) */
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/* ( ... ) */
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/* ( 1 ) */
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/* ( -s(k) c(k) ) */
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/* where R(k) appears in rows and columns k and z. The rotations are */
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/* performed without ever forming P(k) explicitly. */
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/* Arguments */
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/* ========= */
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/* SIDE (input) CHARACTER*1 */
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/* Specifies whether the plane rotation matrix P is applied to */
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/* A on the left or the right. */
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/* = 'L': Left, compute A := P*A */
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/* = 'R': Right, compute A:= A*P**T */
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/* PIVOT (input) CHARACTER*1 */
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/* Specifies the plane for which P(k) is a plane rotation */
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/* matrix. */
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/* = 'V': Variable pivot, the plane (k,k+1) */
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/* = 'T': Top pivot, the plane (1,k+1) */
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/* = 'B': Bottom pivot, the plane (k,z) */
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/* DIRECT (input) CHARACTER*1 */
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/* Specifies whether P is a forward or backward sequence of */
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/* plane rotations. */
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/* = 'F': Forward, P = P(z-1)*...*P(2)*P(1) */
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/* = 'B': Backward, P = P(1)*P(2)*...*P(z-1) */
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/* M (input) INTEGER */
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/* The number of rows of the matrix A. If m <= 1, an immediate */
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/* return is effected. */
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/* N (input) INTEGER */
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/* The number of columns of the matrix A. If n <= 1, an */
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/* immediate return is effected. */
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/* C (input) REAL array, dimension */
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/* (M-1) if SIDE = 'L' */
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/* (N-1) if SIDE = 'R' */
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/* The cosines c(k) of the plane rotations. */
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/* S (input) REAL array, dimension */
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/* (M-1) if SIDE = 'L' */
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/* (N-1) if SIDE = 'R' */
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/* The sines s(k) of the plane rotations. The 2-by-2 plane */
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/* rotation part of the matrix P(k), R(k), has the form */
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/* R(k) = ( c(k) s(k) ) */
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/* ( -s(k) c(k) ). */
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/* A (input/output) REAL array, dimension (LDA,N) */
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/* The M-by-N matrix A. On exit, A is overwritten by P*A if */
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/* SIDE = 'R' or by A*P**T if SIDE = 'L'. */
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/* LDA (input) INTEGER */
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/* The leading dimension of the array A. LDA >= max(1,M). */
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/* ===================================================================== */
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/* .. Parameters .. */
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/* .. */
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/* .. Local Scalars .. */
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/* .. */
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/* .. External Functions .. */
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/* .. */
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/* .. External Subroutines .. */
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/* .. */
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/* .. Intrinsic Functions .. */
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/* .. */
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/* .. Executable Statements .. */
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/* Test the input parameters */
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/* Parameter adjustments */
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--c__;
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--s;
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a_dim1 = *lda;
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a_offset = 1 + a_dim1;
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a -= a_offset;
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/* Function Body */
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info = 0;
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if (! (lsame_(side, "L") || lsame_(side, "R"))) {
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info = 1;
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} else if (! (lsame_(pivot, "V") || lsame_(pivot,
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"T") || lsame_(pivot, "B"))) {
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info = 2;
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} else if (! (lsame_(direct, "F") || lsame_(direct,
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"B"))) {
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info = 3;
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} else if (*m < 0) {
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info = 4;
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} else if (*n < 0) {
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info = 5;
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} else if (*lda < max(1,*m)) {
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info = 9;
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}
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if (info != 0) {
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xerbla_("SLASR ", &info);
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return 0;
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}
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/* Quick return if possible */
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if (*m == 0 || *n == 0) {
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return 0;
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}
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if (lsame_(side, "L")) {
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/* Form P * A */
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if (lsame_(pivot, "V")) {
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if (lsame_(direct, "F")) {
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i__1 = *m - 1;
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for (j = 1; j <= i__1; ++j) {
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ctemp = c__[j];
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stemp = s[j];
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if (ctemp != 1.f || stemp != 0.f) {
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i__2 = *n;
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for (i__ = 1; i__ <= i__2; ++i__) {
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temp = a[j + 1 + i__ * a_dim1];
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a[j + 1 + i__ * a_dim1] = ctemp * temp - stemp *
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a[j + i__ * a_dim1];
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a[j + i__ * a_dim1] = stemp * temp + ctemp * a[j
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+ i__ * a_dim1];
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/* L10: */
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}
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}
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/* L20: */
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}
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} else if (lsame_(direct, "B")) {
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for (j = *m - 1; j >= 1; --j) {
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ctemp = c__[j];
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stemp = s[j];
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if (ctemp != 1.f || stemp != 0.f) {
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i__1 = *n;
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for (i__ = 1; i__ <= i__1; ++i__) {
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temp = a[j + 1 + i__ * a_dim1];
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a[j + 1 + i__ * a_dim1] = ctemp * temp - stemp *
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a[j + i__ * a_dim1];
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a[j + i__ * a_dim1] = stemp * temp + ctemp * a[j
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+ i__ * a_dim1];
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/* L30: */
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}
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}
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/* L40: */
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}
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}
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} else if (lsame_(pivot, "T")) {
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if (lsame_(direct, "F")) {
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i__1 = *m;
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for (j = 2; j <= i__1; ++j) {
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ctemp = c__[j - 1];
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stemp = s[j - 1];
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if (ctemp != 1.f || stemp != 0.f) {
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i__2 = *n;
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for (i__ = 1; i__ <= i__2; ++i__) {
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temp = a[j + i__ * a_dim1];
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a[j + i__ * a_dim1] = ctemp * temp - stemp * a[
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i__ * a_dim1 + 1];
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a[i__ * a_dim1 + 1] = stemp * temp + ctemp * a[
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i__ * a_dim1 + 1];
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/* L50: */
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}
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}
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/* L60: */
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}
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} else if (lsame_(direct, "B")) {
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for (j = *m; j >= 2; --j) {
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ctemp = c__[j - 1];
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stemp = s[j - 1];
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if (ctemp != 1.f || stemp != 0.f) {
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i__1 = *n;
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for (i__ = 1; i__ <= i__1; ++i__) {
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temp = a[j + i__ * a_dim1];
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a[j + i__ * a_dim1] = ctemp * temp - stemp * a[
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i__ * a_dim1 + 1];
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a[i__ * a_dim1 + 1] = stemp * temp + ctemp * a[
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i__ * a_dim1 + 1];
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/* L70: */
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}
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}
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/* L80: */
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}
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}
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} else if (lsame_(pivot, "B")) {
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if (lsame_(direct, "F")) {
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i__1 = *m - 1;
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for (j = 1; j <= i__1; ++j) {
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ctemp = c__[j];
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stemp = s[j];
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if (ctemp != 1.f || stemp != 0.f) {
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i__2 = *n;
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for (i__ = 1; i__ <= i__2; ++i__) {
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temp = a[j + i__ * a_dim1];
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a[j + i__ * a_dim1] = stemp * a[*m + i__ * a_dim1]
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+ ctemp * temp;
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a[*m + i__ * a_dim1] = ctemp * a[*m + i__ *
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a_dim1] - stemp * temp;
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/* L90: */
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}
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}
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/* L100: */
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}
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} else if (lsame_(direct, "B")) {
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for (j = *m - 1; j >= 1; --j) {
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ctemp = c__[j];
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stemp = s[j];
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if (ctemp != 1.f || stemp != 0.f) {
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i__1 = *n;
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for (i__ = 1; i__ <= i__1; ++i__) {
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temp = a[j + i__ * a_dim1];
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a[j + i__ * a_dim1] = stemp * a[*m + i__ * a_dim1]
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+ ctemp * temp;
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a[*m + i__ * a_dim1] = ctemp * a[*m + i__ *
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a_dim1] - stemp * temp;
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/* L110: */
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}
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}
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/* L120: */
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}
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}
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}
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} else if (lsame_(side, "R")) {
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/* Form A * P' */
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if (lsame_(pivot, "V")) {
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if (lsame_(direct, "F")) {
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i__1 = *n - 1;
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for (j = 1; j <= i__1; ++j) {
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ctemp = c__[j];
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stemp = s[j];
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if (ctemp != 1.f || stemp != 0.f) {
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i__2 = *m;
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for (i__ = 1; i__ <= i__2; ++i__) {
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temp = a[i__ + (j + 1) * a_dim1];
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a[i__ + (j + 1) * a_dim1] = ctemp * temp - stemp *
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a[i__ + j * a_dim1];
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a[i__ + j * a_dim1] = stemp * temp + ctemp * a[
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i__ + j * a_dim1];
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/* L130: */
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}
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}
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/* L140: */
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}
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} else if (lsame_(direct, "B")) {
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for (j = *n - 1; j >= 1; --j) {
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ctemp = c__[j];
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stemp = s[j];
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if (ctemp != 1.f || stemp != 0.f) {
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i__1 = *m;
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for (i__ = 1; i__ <= i__1; ++i__) {
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temp = a[i__ + (j + 1) * a_dim1];
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a[i__ + (j + 1) * a_dim1] = ctemp * temp - stemp *
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a[i__ + j * a_dim1];
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a[i__ + j * a_dim1] = stemp * temp + ctemp * a[
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i__ + j * a_dim1];
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/* L150: */
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}
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}
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/* L160: */
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}
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}
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} else if (lsame_(pivot, "T")) {
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if (lsame_(direct, "F")) {
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i__1 = *n;
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for (j = 2; j <= i__1; ++j) {
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ctemp = c__[j - 1];
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stemp = s[j - 1];
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if (ctemp != 1.f || stemp != 0.f) {
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i__2 = *m;
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for (i__ = 1; i__ <= i__2; ++i__) {
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temp = a[i__ + j * a_dim1];
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a[i__ + j * a_dim1] = ctemp * temp - stemp * a[
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i__ + a_dim1];
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a[i__ + a_dim1] = stemp * temp + ctemp * a[i__ +
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a_dim1];
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/* L170: */
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}
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}
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/* L180: */
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}
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} else if (lsame_(direct, "B")) {
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for (j = *n; j >= 2; --j) {
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ctemp = c__[j - 1];
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stemp = s[j - 1];
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if (ctemp != 1.f || stemp != 0.f) {
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i__1 = *m;
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for (i__ = 1; i__ <= i__1; ++i__) {
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temp = a[i__ + j * a_dim1];
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a[i__ + j * a_dim1] = ctemp * temp - stemp * a[
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i__ + a_dim1];
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a[i__ + a_dim1] = stemp * temp + ctemp * a[i__ +
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a_dim1];
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/* L190: */
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}
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}
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/* L200: */
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}
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}
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} else if (lsame_(pivot, "B")) {
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if (lsame_(direct, "F")) {
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i__1 = *n - 1;
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for (j = 1; j <= i__1; ++j) {
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ctemp = c__[j];
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stemp = s[j];
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if (ctemp != 1.f || stemp != 0.f) {
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i__2 = *m;
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for (i__ = 1; i__ <= i__2; ++i__) {
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temp = a[i__ + j * a_dim1];
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|
a[i__ + j * a_dim1] = stemp * a[i__ + *n * a_dim1]
|
||
|
+ ctemp * temp;
|
||
|
a[i__ + *n * a_dim1] = ctemp * a[i__ + *n *
|
||
|
a_dim1] - stemp * temp;
|
||
|
/* L210: */
|
||
|
}
|
||
|
}
|
||
|
/* L220: */
|
||
|
}
|
||
|
} else if (lsame_(direct, "B")) {
|
||
|
for (j = *n - 1; j >= 1; --j) {
|
||
|
ctemp = c__[j];
|
||
|
stemp = s[j];
|
||
|
if (ctemp != 1.f || stemp != 0.f) {
|
||
|
i__1 = *m;
|
||
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
||
|
temp = a[i__ + j * a_dim1];
|
||
|
a[i__ + j * a_dim1] = stemp * a[i__ + *n * a_dim1]
|
||
|
+ ctemp * temp;
|
||
|
a[i__ + *n * a_dim1] = ctemp * a[i__ + *n *
|
||
|
a_dim1] - stemp * temp;
|
||
|
/* L230: */
|
||
|
}
|
||
|
}
|
||
|
/* L240: */
|
||
|
}
|
||
|
}
|
||
|
}
|
||
|
}
|
||
|
|
||
|
return 0;
|
||
|
|
||
|
/* End of SLASR */
|
||
|
|
||
|
} /* slasr_ */
|