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439 lines
12 KiB
439 lines
12 KiB
#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] |
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+ ctemp * temp; |
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a[i__ + *n * a_dim1] = ctemp * a[i__ + *n * |
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a_dim1] - stemp * temp; |
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/* L210: */ |
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} |
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} |
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/* L220: */ |
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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 * a_dim1]; |
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a[i__ + j * a_dim1] = stemp * a[i__ + *n * a_dim1] |
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+ ctemp * temp; |
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a[i__ + *n * a_dim1] = ctemp * a[i__ + *n * |
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a_dim1] - stemp * temp; |
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/* L230: */ |
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} |
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} |
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/* L240: */ |
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} |
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} |
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} |
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} |
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return 0; |
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/* End of SLASR */ |
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} /* slasr_ */
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