#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int dlasr_(char *side, char *pivot, char *direct, integer *m, integer *n, doublereal *c__, doublereal *s, doublereal *a, integer * lda) { /* -- LAPACK auxiliary routine (version 3.1) -- Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. November 2006 Purpose ======= DLASR applies a sequence of plane rotations to a real matrix A, from either the left or the right. When SIDE = 'L', the transformation takes the form A := P*A and when SIDE = 'R', the transformation takes the form A := A*P**T where P is an orthogonal matrix consisting of a sequence of z plane rotations, with z = M when SIDE = 'L' and z = N when SIDE = 'R', and P**T is the transpose of P. When DIRECT = 'F' (Forward sequence), then P = P(z-1) * ... * P(2) * P(1) and when DIRECT = 'B' (Backward sequence), then P = P(1) * P(2) * ... * P(z-1) where P(k) is a plane rotation matrix defined by the 2-by-2 rotation R(k) = ( c(k) s(k) ) = ( -s(k) c(k) ). When PIVOT = 'V' (Variable pivot), the rotation is performed for the plane (k,k+1), i.e., P(k) has the form P(k) = ( 1 ) ( ... ) ( 1 ) ( c(k) s(k) ) ( -s(k) c(k) ) ( 1 ) ( ... ) ( 1 ) where R(k) appears as a rank-2 modification to the identity matrix in rows and columns k and k+1. When PIVOT = 'T' (Top pivot), the rotation is performed for the plane (1,k+1), so P(k) has the form P(k) = ( c(k) s(k) ) ( 1 ) ( ... ) ( 1 ) ( -s(k) c(k) ) ( 1 ) ( ... ) ( 1 ) where R(k) appears in rows and columns 1 and k+1. Similarly, when PIVOT = 'B' (Bottom pivot), the rotation is performed for the plane (k,z), giving P(k) the form P(k) = ( 1 ) ( ... ) ( 1 ) ( c(k) s(k) ) ( 1 ) ( ... ) ( 1 ) ( -s(k) c(k) ) where R(k) appears in rows and columns k and z. The rotations are performed without ever forming P(k) explicitly. Arguments ========= SIDE (input) CHARACTER*1 Specifies whether the plane rotation matrix P is applied to A on the left or the right. = 'L': Left, compute A := P*A = 'R': Right, compute A:= A*P**T PIVOT (input) CHARACTER*1 Specifies the plane for which P(k) is a plane rotation matrix. = 'V': Variable pivot, the plane (k,k+1) = 'T': Top pivot, the plane (1,k+1) = 'B': Bottom pivot, the plane (k,z) DIRECT (input) CHARACTER*1 Specifies whether P is a forward or backward sequence of plane rotations. = 'F': Forward, P = P(z-1)*...*P(2)*P(1) = 'B': Backward, P = P(1)*P(2)*...*P(z-1) M (input) INTEGER The number of rows of the matrix A. If m <= 1, an immediate return is effected. N (input) INTEGER The number of columns of the matrix A. If n <= 1, an immediate return is effected. C (input) DOUBLE PRECISION array, dimension (M-1) if SIDE = 'L' (N-1) if SIDE = 'R' The cosines c(k) of the plane rotations. S (input) DOUBLE PRECISION array, dimension (M-1) if SIDE = 'L' (N-1) if SIDE = 'R' The sines s(k) of the plane rotations. The 2-by-2 plane rotation part of the matrix P(k), R(k), has the form R(k) = ( c(k) s(k) ) ( -s(k) c(k) ). A (input/output) DOUBLE PRECISION array, dimension (LDA,N) The M-by-N matrix A. On exit, A is overwritten by P*A if SIDE = 'R' or by A*P**T if SIDE = 'L'. LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,M). ===================================================================== Test the input parameters Parameter adjustments */ /* System generated locals */ integer a_dim1, a_offset, i__1, i__2; /* Local variables */ static integer i__, j, info; static doublereal temp; extern logical lsame_(char *, char *); static doublereal ctemp, stemp; extern /* Subroutine */ int xerbla_(char *, integer *); --c__; --s; a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; /* Function Body */ info = 0; if (! (lsame_(side, "L") || lsame_(side, "R"))) { info = 1; } else if (! (lsame_(pivot, "V") || lsame_(pivot, "T") || lsame_(pivot, "B"))) { info = 2; } else if (! (lsame_(direct, "F") || lsame_(direct, "B"))) { info = 3; } else if (*m < 0) { info = 4; } else if (*n < 0) { info = 5; } else if (*lda < max(1,*m)) { info = 9; } if (info != 0) { xerbla_("DLASR ", &info); return 0; } /* Quick return if possible */ if (*m == 0 || *n == 0) { return 0; } if (lsame_(side, "L")) { /* Form P * A */ if (lsame_(pivot, "V")) { if (lsame_(direct, "F")) { i__1 = *m - 1; for (j = 1; j <= i__1; ++j) { ctemp = c__[j]; stemp = s[j]; if (ctemp != 1. || stemp != 0.) { i__2 = *n; for (i__ = 1; i__ <= i__2; ++i__) { temp = a[j + 1 + i__ * a_dim1]; a[j + 1 + i__ * a_dim1] = ctemp * temp - stemp * a[j + i__ * a_dim1]; a[j + i__ * a_dim1] = stemp * temp + ctemp * a[j + i__ * a_dim1]; /* L10: */ } } /* L20: */ } } else if (lsame_(direct, "B")) { for (j = *m - 1; j >= 1; --j) { ctemp = c__[j]; stemp = s[j]; if (ctemp != 1. || stemp != 0.) { i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { temp = a[j + 1 + i__ * a_dim1]; a[j + 1 + i__ * a_dim1] = ctemp * temp - stemp * a[j + i__ * a_dim1]; a[j + i__ * a_dim1] = stemp * temp + ctemp * a[j + i__ * a_dim1]; /* L30: */ } } /* L40: */ } } } else if (lsame_(pivot, "T")) { if (lsame_(direct, "F")) { i__1 = *m; for (j = 2; j <= i__1; ++j) { ctemp = c__[j - 1]; stemp = s[j - 1]; if (ctemp != 1. || stemp != 0.) { i__2 = *n; for (i__ = 1; i__ <= i__2; ++i__) { temp = a[j + i__ * a_dim1]; a[j + i__ * a_dim1] = ctemp * temp - stemp * a[ i__ * a_dim1 + 1]; a[i__ * a_dim1 + 1] = stemp * temp + ctemp * a[ i__ * a_dim1 + 1]; /* L50: */ } } /* L60: */ } } else if (lsame_(direct, "B")) { for (j = *m; j >= 2; --j) { ctemp = c__[j - 1]; stemp = s[j - 1]; if (ctemp != 1. || stemp != 0.) { i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { temp = a[j + i__ * a_dim1]; a[j + i__ * a_dim1] = ctemp * temp - stemp * a[ i__ * a_dim1 + 1]; a[i__ * a_dim1 + 1] = stemp * temp + ctemp * a[ i__ * a_dim1 + 1]; /* L70: */ } } /* L80: */ } } } else if (lsame_(pivot, "B")) { if (lsame_(direct, "F")) { i__1 = *m - 1; for (j = 1; j <= i__1; ++j) { ctemp = c__[j]; stemp = s[j]; if (ctemp != 1. || stemp != 0.) { i__2 = *n; for (i__ = 1; i__ <= i__2; ++i__) { temp = a[j + i__ * a_dim1]; a[j + i__ * a_dim1] = stemp * a[*m + i__ * a_dim1] + ctemp * temp; a[*m + i__ * a_dim1] = ctemp * a[*m + i__ * a_dim1] - stemp * temp; /* L90: */ } } /* L100: */ } } else if (lsame_(direct, "B")) { for (j = *m - 1; j >= 1; --j) { ctemp = c__[j]; stemp = s[j]; if (ctemp != 1. || stemp != 0.) { i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { temp = a[j + i__ * a_dim1]; a[j + i__ * a_dim1] = stemp * a[*m + i__ * a_dim1] + ctemp * temp; a[*m + i__ * a_dim1] = ctemp * a[*m + i__ * a_dim1] - stemp * temp; /* L110: */ } } /* L120: */ } } } } else if (lsame_(side, "R")) { /* Form A * P' */ if (lsame_(pivot, "V")) { if (lsame_(direct, "F")) { i__1 = *n - 1; for (j = 1; j <= i__1; ++j) { ctemp = c__[j]; stemp = s[j]; if (ctemp != 1. || stemp != 0.) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { temp = a[i__ + (j + 1) * a_dim1]; a[i__ + (j + 1) * a_dim1] = ctemp * temp - stemp * a[i__ + j * a_dim1]; a[i__ + j * a_dim1] = stemp * temp + ctemp * a[ i__ + j * a_dim1]; /* L130: */ } } /* L140: */ } } else if (lsame_(direct, "B")) { for (j = *n - 1; j >= 1; --j) { ctemp = c__[j]; stemp = s[j]; if (ctemp != 1. || stemp != 0.) { i__1 = *m; for (i__ = 1; i__ <= i__1; ++i__) { temp = a[i__ + (j + 1) * a_dim1]; a[i__ + (j + 1) * a_dim1] = ctemp * temp - stemp * a[i__ + j * a_dim1]; a[i__ + j * a_dim1] = stemp * temp + ctemp * a[ i__ + j * a_dim1]; /* L150: */ } } /* L160: */ } } } else if (lsame_(pivot, "T")) { if (lsame_(direct, "F")) { i__1 = *n; for (j = 2; j <= i__1; ++j) { ctemp = c__[j - 1]; stemp = s[j - 1]; if (ctemp != 1. || stemp != 0.) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { temp = a[i__ + j * a_dim1]; a[i__ + j * a_dim1] = ctemp * temp - stemp * a[ i__ + a_dim1]; a[i__ + a_dim1] = stemp * temp + ctemp * a[i__ + a_dim1]; /* L170: */ } } /* L180: */ } } else if (lsame_(direct, "B")) { for (j = *n; j >= 2; --j) { ctemp = c__[j - 1]; stemp = s[j - 1]; if (ctemp != 1. || stemp != 0.) { i__1 = *m; for (i__ = 1; i__ <= i__1; ++i__) { temp = a[i__ + j * a_dim1]; a[i__ + j * a_dim1] = ctemp * temp - stemp * a[ i__ + a_dim1]; a[i__ + a_dim1] = stemp * temp + ctemp * a[i__ + a_dim1]; /* L190: */ } } /* L200: */ } } } else if (lsame_(pivot, "B")) { if (lsame_(direct, "F")) { i__1 = *n - 1; for (j = 1; j <= i__1; ++j) { ctemp = c__[j]; stemp = s[j]; if (ctemp != 1. || stemp != 0.) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++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; /* L210: */ } } /* L220: */ } } else if (lsame_(direct, "B")) { for (j = *n - 1; j >= 1; --j) { ctemp = c__[j]; stemp = s[j]; if (ctemp != 1. || stemp != 0.) { 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 DLASR */ } /* dlasr_ */