#include "clapack.h" /* Table of constant values */ static integer c__1 = 1; static real c_b8 = 0.f; /* Subroutine */ int slarft_(char *direct, char *storev, integer *n, integer * k, real *v, integer *ldv, real *tau, real *t, integer *ldt) { /* System generated locals */ integer t_dim1, t_offset, v_dim1, v_offset, i__1, i__2, i__3; real r__1; /* Local variables */ integer i__, j; real vii; extern logical lsame_(char *, char *); extern /* Subroutine */ int sgemv_(char *, integer *, integer *, real *, real *, integer *, real *, integer *, real *, real *, integer *), strmv_(char *, char *, char *, integer *, real *, integer *, real *, integer *); /* -- LAPACK auxiliary routine (version 3.1) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* SLARFT forms the triangular factor T of a real block reflector H */ /* of order n, which is defined as a product of k elementary reflectors. */ /* If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular; */ /* If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular. */ /* If STOREV = 'C', the vector which defines the elementary reflector */ /* H(i) is stored in the i-th column of the array V, and */ /* H = I - V * T * V' */ /* If STOREV = 'R', the vector which defines the elementary reflector */ /* H(i) is stored in the i-th row of the array V, and */ /* H = I - V' * T * V */ /* Arguments */ /* ========= */ /* DIRECT (input) CHARACTER*1 */ /* Specifies the order in which the elementary reflectors are */ /* multiplied to form the block reflector: */ /* = 'F': H = H(1) H(2) . . . H(k) (Forward) */ /* = 'B': H = H(k) . . . H(2) H(1) (Backward) */ /* STOREV (input) CHARACTER*1 */ /* Specifies how the vectors which define the elementary */ /* reflectors are stored (see also Further Details): */ /* = 'C': columnwise */ /* = 'R': rowwise */ /* N (input) INTEGER */ /* The order of the block reflector H. N >= 0. */ /* K (input) INTEGER */ /* The order of the triangular factor T (= the number of */ /* elementary reflectors). K >= 1. */ /* V (input/output) REAL array, dimension */ /* (LDV,K) if STOREV = 'C' */ /* (LDV,N) if STOREV = 'R' */ /* The matrix V. See further details. */ /* LDV (input) INTEGER */ /* The leading dimension of the array V. */ /* If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K. */ /* TAU (input) REAL array, dimension (K) */ /* TAU(i) must contain the scalar factor of the elementary */ /* reflector H(i). */ /* T (output) REAL array, dimension (LDT,K) */ /* The k by k triangular factor T of the block reflector. */ /* If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is */ /* lower triangular. The rest of the array is not used. */ /* LDT (input) INTEGER */ /* The leading dimension of the array T. LDT >= K. */ /* Further Details */ /* =============== */ /* The shape of the matrix V and the storage of the vectors which define */ /* the H(i) is best illustrated by the following example with n = 5 and */ /* k = 3. The elements equal to 1 are not stored; the corresponding */ /* array elements are modified but restored on exit. The rest of the */ /* array is not used. */ /* DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R': */ /* V = ( 1 ) V = ( 1 v1 v1 v1 v1 ) */ /* ( v1 1 ) ( 1 v2 v2 v2 ) */ /* ( v1 v2 1 ) ( 1 v3 v3 ) */ /* ( v1 v2 v3 ) */ /* ( v1 v2 v3 ) */ /* DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R': */ /* V = ( v1 v2 v3 ) V = ( v1 v1 1 ) */ /* ( v1 v2 v3 ) ( v2 v2 v2 1 ) */ /* ( 1 v2 v3 ) ( v3 v3 v3 v3 1 ) */ /* ( 1 v3 ) */ /* ( 1 ) */ /* ===================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. Executable Statements .. */ /* Quick return if possible */ /* Parameter adjustments */ v_dim1 = *ldv; v_offset = 1 + v_dim1; v -= v_offset; --tau; t_dim1 = *ldt; t_offset = 1 + t_dim1; t -= t_offset; /* Function Body */ if (*n == 0) { return 0; } if (lsame_(direct, "F")) { i__1 = *k; for (i__ = 1; i__ <= i__1; ++i__) { if (tau[i__] == 0.f) { /* H(i) = I */ i__2 = i__; for (j = 1; j <= i__2; ++j) { t[j + i__ * t_dim1] = 0.f; /* L10: */ } } else { /* general case */ vii = v[i__ + i__ * v_dim1]; v[i__ + i__ * v_dim1] = 1.f; if (lsame_(storev, "C")) { /* T(1:i-1,i) := - tau(i) * V(i:n,1:i-1)' * V(i:n,i) */ i__2 = *n - i__ + 1; i__3 = i__ - 1; r__1 = -tau[i__]; sgemv_("Transpose", &i__2, &i__3, &r__1, &v[i__ + v_dim1], ldv, &v[i__ + i__ * v_dim1], &c__1, &c_b8, &t[ i__ * t_dim1 + 1], &c__1); } else { /* T(1:i-1,i) := - tau(i) * V(1:i-1,i:n) * V(i,i:n)' */ i__2 = i__ - 1; i__3 = *n - i__ + 1; r__1 = -tau[i__]; sgemv_("No transpose", &i__2, &i__3, &r__1, &v[i__ * v_dim1 + 1], ldv, &v[i__ + i__ * v_dim1], ldv, & c_b8, &t[i__ * t_dim1 + 1], &c__1); } v[i__ + i__ * v_dim1] = vii; /* T(1:i-1,i) := T(1:i-1,1:i-1) * T(1:i-1,i) */ i__2 = i__ - 1; strmv_("Upper", "No transpose", "Non-unit", &i__2, &t[ t_offset], ldt, &t[i__ * t_dim1 + 1], &c__1); t[i__ + i__ * t_dim1] = tau[i__]; } /* L20: */ } } else { for (i__ = *k; i__ >= 1; --i__) { if (tau[i__] == 0.f) { /* H(i) = I */ i__1 = *k; for (j = i__; j <= i__1; ++j) { t[j + i__ * t_dim1] = 0.f; /* L30: */ } } else { /* general case */ if (i__ < *k) { if (lsame_(storev, "C")) { vii = v[*n - *k + i__ + i__ * v_dim1]; v[*n - *k + i__ + i__ * v_dim1] = 1.f; /* T(i+1:k,i) := */ /* - tau(i) * V(1:n-k+i,i+1:k)' * V(1:n-k+i,i) */ i__1 = *n - *k + i__; i__2 = *k - i__; r__1 = -tau[i__]; sgemv_("Transpose", &i__1, &i__2, &r__1, &v[(i__ + 1) * v_dim1 + 1], ldv, &v[i__ * v_dim1 + 1], & c__1, &c_b8, &t[i__ + 1 + i__ * t_dim1], & c__1); v[*n - *k + i__ + i__ * v_dim1] = vii; } else { vii = v[i__ + (*n - *k + i__) * v_dim1]; v[i__ + (*n - *k + i__) * v_dim1] = 1.f; /* T(i+1:k,i) := */ /* - tau(i) * V(i+1:k,1:n-k+i) * V(i,1:n-k+i)' */ i__1 = *k - i__; i__2 = *n - *k + i__; r__1 = -tau[i__]; sgemv_("No transpose", &i__1, &i__2, &r__1, &v[i__ + 1 + v_dim1], ldv, &v[i__ + v_dim1], ldv, & c_b8, &t[i__ + 1 + i__ * t_dim1], &c__1); v[i__ + (*n - *k + i__) * v_dim1] = vii; } /* T(i+1:k,i) := T(i+1:k,i+1:k) * T(i+1:k,i) */ i__1 = *k - i__; strmv_("Lower", "No transpose", "Non-unit", &i__1, &t[i__ + 1 + (i__ + 1) * t_dim1], ldt, &t[i__ + 1 + i__ * t_dim1], &c__1) ; } t[i__ + i__ * t_dim1] = tau[i__]; } /* L40: */ } } return 0; /* End of SLARFT */ } /* slarft_ */