#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int dlarfx_(char *side, integer *m, integer *n, doublereal * v, doublereal *tau, doublereal *c__, integer *ldc, doublereal *work) { /* -- LAPACK auxiliary routine (version 3.1) -- Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. November 2006 Purpose ======= DLARFX applies a real elementary reflector H to a real m by n matrix C, from either the left or the right. H is represented in the form H = I - tau * v * v' where tau is a real scalar and v is a real vector. If tau = 0, then H is taken to be the unit matrix This version uses inline code if H has order < 11. Arguments ========= SIDE (input) CHARACTER*1 = 'L': form H * C = 'R': form C * H M (input) INTEGER The number of rows of the matrix C. N (input) INTEGER The number of columns of the matrix C. V (input) DOUBLE PRECISION array, dimension (M) if SIDE = 'L' or (N) if SIDE = 'R' The vector v in the representation of H. TAU (input) DOUBLE PRECISION The value tau in the representation of H. C (input/output) DOUBLE PRECISION array, dimension (LDC,N) On entry, the m by n matrix C. On exit, C is overwritten by the matrix H * C if SIDE = 'L', or C * H if SIDE = 'R'. LDC (input) INTEGER The leading dimension of the array C. LDA >= (1,M). WORK (workspace) DOUBLE PRECISION array, dimension (N) if SIDE = 'L' or (M) if SIDE = 'R' WORK is not referenced if H has order < 11. ===================================================================== Parameter adjustments */ /* Table of constant values */ static doublereal c_b14 = 1.; static integer c__1 = 1; static doublereal c_b16 = 0.; /* System generated locals */ integer c_dim1, c_offset, i__1; doublereal d__1; /* Local variables */ static integer j; static doublereal t1, t2, t3, t4, t5, t6, t7, t8, t9, v1, v2, v3, v4, v5, v6, v7, v8, v9, t10, v10, sum; extern /* Subroutine */ int dger_(integer *, integer *, doublereal *, doublereal *, integer *, doublereal *, integer *, doublereal *, integer *); extern logical lsame_(char *, char *); extern /* Subroutine */ int dgemv_(char *, integer *, integer *, doublereal *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *); --v; c_dim1 = *ldc; c_offset = 1 + c_dim1; c__ -= c_offset; --work; /* Function Body */ if (*tau == 0.) { return 0; } if (lsame_(side, "L")) { /* Form H * C, where H has order m. */ switch (*m) { case 1: goto L10; case 2: goto L30; case 3: goto L50; case 4: goto L70; case 5: goto L90; case 6: goto L110; case 7: goto L130; case 8: goto L150; case 9: goto L170; case 10: goto L190; } /* Code for general M w := C'*v */ dgemv_("Transpose", m, n, &c_b14, &c__[c_offset], ldc, &v[1], &c__1, & c_b16, &work[1], &c__1); /* C := C - tau * v * w' */ d__1 = -(*tau); dger_(m, n, &d__1, &v[1], &c__1, &work[1], &c__1, &c__[c_offset], ldc) ; goto L410; L10: /* Special code for 1 x 1 Householder */ t1 = 1. - *tau * v[1] * v[1]; i__1 = *n; for (j = 1; j <= i__1; ++j) { c__[j * c_dim1 + 1] = t1 * c__[j * c_dim1 + 1]; /* L20: */ } goto L410; L30: /* Special code for 2 x 2 Householder */ v1 = v[1]; t1 = *tau * v1; v2 = v[2]; t2 = *tau * v2; i__1 = *n; for (j = 1; j <= i__1; ++j) { sum = v1 * c__[j * c_dim1 + 1] + v2 * c__[j * c_dim1 + 2]; c__[j * c_dim1 + 1] -= sum * t1; c__[j * c_dim1 + 2] -= sum * t2; /* L40: */ } goto L410; L50: /* Special code for 3 x 3 Householder */ v1 = v[1]; t1 = *tau * v1; v2 = v[2]; t2 = *tau * v2; v3 = v[3]; t3 = *tau * v3; i__1 = *n; for (j = 1; j <= i__1; ++j) { sum = v1 * c__[j * c_dim1 + 1] + v2 * c__[j * c_dim1 + 2] + v3 * c__[j * c_dim1 + 3]; c__[j * c_dim1 + 1] -= sum * t1; c__[j * c_dim1 + 2] -= sum * t2; c__[j * c_dim1 + 3] -= sum * t3; /* L60: */ } goto L410; L70: /* Special code for 4 x 4 Householder */ v1 = v[1]; t1 = *tau * v1; v2 = v[2]; t2 = *tau * v2; v3 = v[3]; t3 = *tau * v3; v4 = v[4]; t4 = *tau * v4; i__1 = *n; for (j = 1; j <= i__1; ++j) { sum = v1 * c__[j * c_dim1 + 1] + v2 * c__[j * c_dim1 + 2] + v3 * c__[j * c_dim1 + 3] + v4 * c__[j * c_dim1 + 4]; c__[j * c_dim1 + 1] -= sum * t1; c__[j * c_dim1 + 2] -= sum * t2; c__[j * c_dim1 + 3] -= sum * t3; c__[j * c_dim1 + 4] -= sum * t4; /* L80: */ } goto L410; L90: /* Special code for 5 x 5 Householder */ v1 = v[1]; t1 = *tau * v1; v2 = v[2]; t2 = *tau * v2; v3 = v[3]; t3 = *tau * v3; v4 = v[4]; t4 = *tau * v4; v5 = v[5]; t5 = *tau * v5; i__1 = *n; for (j = 1; j <= i__1; ++j) { sum = v1 * c__[j * c_dim1 + 1] + v2 * c__[j * c_dim1 + 2] + v3 * c__[j * c_dim1 + 3] + v4 * c__[j * c_dim1 + 4] + v5 * c__[ j * c_dim1 + 5]; c__[j * c_dim1 + 1] -= sum * t1; c__[j * c_dim1 + 2] -= sum * t2; c__[j * c_dim1 + 3] -= sum * t3; c__[j * c_dim1 + 4] -= sum * t4; c__[j * c_dim1 + 5] -= sum * t5; /* L100: */ } goto L410; L110: /* Special code for 6 x 6 Householder */ v1 = v[1]; t1 = *tau * v1; v2 = v[2]; t2 = *tau * v2; v3 = v[3]; t3 = *tau * v3; v4 = v[4]; t4 = *tau * v4; v5 = v[5]; t5 = *tau * v5; v6 = v[6]; t6 = *tau * v6; i__1 = *n; for (j = 1; j <= i__1; ++j) { sum = v1 * c__[j * c_dim1 + 1] + v2 * c__[j * c_dim1 + 2] + v3 * c__[j * c_dim1 + 3] + v4 * c__[j * c_dim1 + 4] + v5 * c__[ j * c_dim1 + 5] + v6 * c__[j * c_dim1 + 6]; c__[j * c_dim1 + 1] -= sum * t1; c__[j * c_dim1 + 2] -= sum * t2; c__[j * c_dim1 + 3] -= sum * t3; c__[j * c_dim1 + 4] -= sum * t4; c__[j * c_dim1 + 5] -= sum * t5; c__[j * c_dim1 + 6] -= sum * t6; /* L120: */ } goto L410; L130: /* Special code for 7 x 7 Householder */ v1 = v[1]; t1 = *tau * v1; v2 = v[2]; t2 = *tau * v2; v3 = v[3]; t3 = *tau * v3; v4 = v[4]; t4 = *tau * v4; v5 = v[5]; t5 = *tau * v5; v6 = v[6]; t6 = *tau * v6; v7 = v[7]; t7 = *tau * v7; i__1 = *n; for (j = 1; j <= i__1; ++j) { sum = v1 * c__[j * c_dim1 + 1] + v2 * c__[j * c_dim1 + 2] + v3 * c__[j * c_dim1 + 3] + v4 * c__[j * c_dim1 + 4] + v5 * c__[ j * c_dim1 + 5] + v6 * c__[j * c_dim1 + 6] + v7 * c__[j * c_dim1 + 7]; c__[j * c_dim1 + 1] -= sum * t1; c__[j * c_dim1 + 2] -= sum * t2; c__[j * c_dim1 + 3] -= sum * t3; c__[j * c_dim1 + 4] -= sum * t4; c__[j * c_dim1 + 5] -= sum * t5; c__[j * c_dim1 + 6] -= sum * t6; c__[j * c_dim1 + 7] -= sum * t7; /* L140: */ } goto L410; L150: /* Special code for 8 x 8 Householder */ v1 = v[1]; t1 = *tau * v1; v2 = v[2]; t2 = *tau * v2; v3 = v[3]; t3 = *tau * v3; v4 = v[4]; t4 = *tau * v4; v5 = v[5]; t5 = *tau * v5; v6 = v[6]; t6 = *tau * v6; v7 = v[7]; t7 = *tau * v7; v8 = v[8]; t8 = *tau * v8; i__1 = *n; for (j = 1; j <= i__1; ++j) { sum = v1 * c__[j * c_dim1 + 1] + v2 * c__[j * c_dim1 + 2] + v3 * c__[j * c_dim1 + 3] + v4 * c__[j * c_dim1 + 4] + v5 * c__[ j * c_dim1 + 5] + v6 * c__[j * c_dim1 + 6] + v7 * c__[j * c_dim1 + 7] + v8 * c__[j * c_dim1 + 8]; c__[j * c_dim1 + 1] -= sum * t1; c__[j * c_dim1 + 2] -= sum * t2; c__[j * c_dim1 + 3] -= sum * t3; c__[j * c_dim1 + 4] -= sum * t4; c__[j * c_dim1 + 5] -= sum * t5; c__[j * c_dim1 + 6] -= sum * t6; c__[j * c_dim1 + 7] -= sum * t7; c__[j * c_dim1 + 8] -= sum * t8; /* L160: */ } goto L410; L170: /* Special code for 9 x 9 Householder */ v1 = v[1]; t1 = *tau * v1; v2 = v[2]; t2 = *tau * v2; v3 = v[3]; t3 = *tau * v3; v4 = v[4]; t4 = *tau * v4; v5 = v[5]; t5 = *tau * v5; v6 = v[6]; t6 = *tau * v6; v7 = v[7]; t7 = *tau * v7; v8 = v[8]; t8 = *tau * v8; v9 = v[9]; t9 = *tau * v9; i__1 = *n; for (j = 1; j <= i__1; ++j) { sum = v1 * c__[j * c_dim1 + 1] + v2 * c__[j * c_dim1 + 2] + v3 * c__[j * c_dim1 + 3] + v4 * c__[j * c_dim1 + 4] + v5 * c__[ j * c_dim1 + 5] + v6 * c__[j * c_dim1 + 6] + v7 * c__[j * c_dim1 + 7] + v8 * c__[j * c_dim1 + 8] + v9 * c__[j * c_dim1 + 9]; c__[j * c_dim1 + 1] -= sum * t1; c__[j * c_dim1 + 2] -= sum * t2; c__[j * c_dim1 + 3] -= sum * t3; c__[j * c_dim1 + 4] -= sum * t4; c__[j * c_dim1 + 5] -= sum * t5; c__[j * c_dim1 + 6] -= sum * t6; c__[j * c_dim1 + 7] -= sum * t7; c__[j * c_dim1 + 8] -= sum * t8; c__[j * c_dim1 + 9] -= sum * t9; /* L180: */ } goto L410; L190: /* Special code for 10 x 10 Householder */ v1 = v[1]; t1 = *tau * v1; v2 = v[2]; t2 = *tau * v2; v3 = v[3]; t3 = *tau * v3; v4 = v[4]; t4 = *tau * v4; v5 = v[5]; t5 = *tau * v5; v6 = v[6]; t6 = *tau * v6; v7 = v[7]; t7 = *tau * v7; v8 = v[8]; t8 = *tau * v8; v9 = v[9]; t9 = *tau * v9; v10 = v[10]; t10 = *tau * v10; i__1 = *n; for (j = 1; j <= i__1; ++j) { sum = v1 * c__[j * c_dim1 + 1] + v2 * c__[j * c_dim1 + 2] + v3 * c__[j * c_dim1 + 3] + v4 * c__[j * c_dim1 + 4] + v5 * c__[ j * c_dim1 + 5] + v6 * c__[j * c_dim1 + 6] + v7 * c__[j * c_dim1 + 7] + v8 * c__[j * c_dim1 + 8] + v9 * c__[j * c_dim1 + 9] + v10 * c__[j * c_dim1 + 10]; c__[j * c_dim1 + 1] -= sum * t1; c__[j * c_dim1 + 2] -= sum * t2; c__[j * c_dim1 + 3] -= sum * t3; c__[j * c_dim1 + 4] -= sum * t4; c__[j * c_dim1 + 5] -= sum * t5; c__[j * c_dim1 + 6] -= sum * t6; c__[j * c_dim1 + 7] -= sum * t7; c__[j * c_dim1 + 8] -= sum * t8; c__[j * c_dim1 + 9] -= sum * t9; c__[j * c_dim1 + 10] -= sum * t10; /* L200: */ } goto L410; } else { /* Form C * H, where H has order n. */ switch (*n) { case 1: goto L210; case 2: goto L230; case 3: goto L250; case 4: goto L270; case 5: goto L290; case 6: goto L310; case 7: goto L330; case 8: goto L350; case 9: goto L370; case 10: goto L390; } /* Code for general N w := C * v */ dgemv_("No transpose", m, n, &c_b14, &c__[c_offset], ldc, &v[1], & c__1, &c_b16, &work[1], &c__1); /* C := C - tau * w * v' */ d__1 = -(*tau); dger_(m, n, &d__1, &work[1], &c__1, &v[1], &c__1, &c__[c_offset], ldc) ; goto L410; L210: /* Special code for 1 x 1 Householder */ t1 = 1. - *tau * v[1] * v[1]; i__1 = *m; for (j = 1; j <= i__1; ++j) { c__[j + c_dim1] = t1 * c__[j + c_dim1]; /* L220: */ } goto L410; L230: /* Special code for 2 x 2 Householder */ v1 = v[1]; t1 = *tau * v1; v2 = v[2]; t2 = *tau * v2; i__1 = *m; for (j = 1; j <= i__1; ++j) { sum = v1 * c__[j + c_dim1] + v2 * c__[j + (c_dim1 << 1)]; c__[j + c_dim1] -= sum * t1; c__[j + (c_dim1 << 1)] -= sum * t2; /* L240: */ } goto L410; L250: /* Special code for 3 x 3 Householder */ v1 = v[1]; t1 = *tau * v1; v2 = v[2]; t2 = *tau * v2; v3 = v[3]; t3 = *tau * v3; i__1 = *m; for (j = 1; j <= i__1; ++j) { sum = v1 * c__[j + c_dim1] + v2 * c__[j + (c_dim1 << 1)] + v3 * c__[j + c_dim1 * 3]; c__[j + c_dim1] -= sum * t1; c__[j + (c_dim1 << 1)] -= sum * t2; c__[j + c_dim1 * 3] -= sum * t3; /* L260: */ } goto L410; L270: /* Special code for 4 x 4 Householder */ v1 = v[1]; t1 = *tau * v1; v2 = v[2]; t2 = *tau * v2; v3 = v[3]; t3 = *tau * v3; v4 = v[4]; t4 = *tau * v4; i__1 = *m; for (j = 1; j <= i__1; ++j) { sum = v1 * c__[j + c_dim1] + v2 * c__[j + (c_dim1 << 1)] + v3 * c__[j + c_dim1 * 3] + v4 * c__[j + (c_dim1 << 2)]; c__[j + c_dim1] -= sum * t1; c__[j + (c_dim1 << 1)] -= sum * t2; c__[j + c_dim1 * 3] -= sum * t3; c__[j + (c_dim1 << 2)] -= sum * t4; /* L280: */ } goto L410; L290: /* Special code for 5 x 5 Householder */ v1 = v[1]; t1 = *tau * v1; v2 = v[2]; t2 = *tau * v2; v3 = v[3]; t3 = *tau * v3; v4 = v[4]; t4 = *tau * v4; v5 = v[5]; t5 = *tau * v5; i__1 = *m; for (j = 1; j <= i__1; ++j) { sum = v1 * c__[j + c_dim1] + v2 * c__[j + (c_dim1 << 1)] + v3 * c__[j + c_dim1 * 3] + v4 * c__[j + (c_dim1 << 2)] + v5 * c__[j + c_dim1 * 5]; c__[j + c_dim1] -= sum * t1; c__[j + (c_dim1 << 1)] -= sum * t2; c__[j + c_dim1 * 3] -= sum * t3; c__[j + (c_dim1 << 2)] -= sum * t4; c__[j + c_dim1 * 5] -= sum * t5; /* L300: */ } goto L410; L310: /* Special code for 6 x 6 Householder */ v1 = v[1]; t1 = *tau * v1; v2 = v[2]; t2 = *tau * v2; v3 = v[3]; t3 = *tau * v3; v4 = v[4]; t4 = *tau * v4; v5 = v[5]; t5 = *tau * v5; v6 = v[6]; t6 = *tau * v6; i__1 = *m; for (j = 1; j <= i__1; ++j) { sum = v1 * c__[j + c_dim1] + v2 * c__[j + (c_dim1 << 1)] + v3 * c__[j + c_dim1 * 3] + v4 * c__[j + (c_dim1 << 2)] + v5 * c__[j + c_dim1 * 5] + v6 * c__[j + c_dim1 * 6]; c__[j + c_dim1] -= sum * t1; c__[j + (c_dim1 << 1)] -= sum * t2; c__[j + c_dim1 * 3] -= sum * t3; c__[j + (c_dim1 << 2)] -= sum * t4; c__[j + c_dim1 * 5] -= sum * t5; c__[j + c_dim1 * 6] -= sum * t6; /* L320: */ } goto L410; L330: /* Special code for 7 x 7 Householder */ v1 = v[1]; t1 = *tau * v1; v2 = v[2]; t2 = *tau * v2; v3 = v[3]; t3 = *tau * v3; v4 = v[4]; t4 = *tau * v4; v5 = v[5]; t5 = *tau * v5; v6 = v[6]; t6 = *tau * v6; v7 = v[7]; t7 = *tau * v7; i__1 = *m; for (j = 1; j <= i__1; ++j) { sum = v1 * c__[j + c_dim1] + v2 * c__[j + (c_dim1 << 1)] + v3 * c__[j + c_dim1 * 3] + v4 * c__[j + (c_dim1 << 2)] + v5 * c__[j + c_dim1 * 5] + v6 * c__[j + c_dim1 * 6] + v7 * c__[ j + c_dim1 * 7]; c__[j + c_dim1] -= sum * t1; c__[j + (c_dim1 << 1)] -= sum * t2; c__[j + c_dim1 * 3] -= sum * t3; c__[j + (c_dim1 << 2)] -= sum * t4; c__[j + c_dim1 * 5] -= sum * t5; c__[j + c_dim1 * 6] -= sum * t6; c__[j + c_dim1 * 7] -= sum * t7; /* L340: */ } goto L410; L350: /* Special code for 8 x 8 Householder */ v1 = v[1]; t1 = *tau * v1; v2 = v[2]; t2 = *tau * v2; v3 = v[3]; t3 = *tau * v3; v4 = v[4]; t4 = *tau * v4; v5 = v[5]; t5 = *tau * v5; v6 = v[6]; t6 = *tau * v6; v7 = v[7]; t7 = *tau * v7; v8 = v[8]; t8 = *tau * v8; i__1 = *m; for (j = 1; j <= i__1; ++j) { sum = v1 * c__[j + c_dim1] + v2 * c__[j + (c_dim1 << 1)] + v3 * c__[j + c_dim1 * 3] + v4 * c__[j + (c_dim1 << 2)] + v5 * c__[j + c_dim1 * 5] + v6 * c__[j + c_dim1 * 6] + v7 * c__[ j + c_dim1 * 7] + v8 * c__[j + (c_dim1 << 3)]; c__[j + c_dim1] -= sum * t1; c__[j + (c_dim1 << 1)] -= sum * t2; c__[j + c_dim1 * 3] -= sum * t3; c__[j + (c_dim1 << 2)] -= sum * t4; c__[j + c_dim1 * 5] -= sum * t5; c__[j + c_dim1 * 6] -= sum * t6; c__[j + c_dim1 * 7] -= sum * t7; c__[j + (c_dim1 << 3)] -= sum * t8; /* L360: */ } goto L410; L370: /* Special code for 9 x 9 Householder */ v1 = v[1]; t1 = *tau * v1; v2 = v[2]; t2 = *tau * v2; v3 = v[3]; t3 = *tau * v3; v4 = v[4]; t4 = *tau * v4; v5 = v[5]; t5 = *tau * v5; v6 = v[6]; t6 = *tau * v6; v7 = v[7]; t7 = *tau * v7; v8 = v[8]; t8 = *tau * v8; v9 = v[9]; t9 = *tau * v9; i__1 = *m; for (j = 1; j <= i__1; ++j) { sum = v1 * c__[j + c_dim1] + v2 * c__[j + (c_dim1 << 1)] + v3 * c__[j + c_dim1 * 3] + v4 * c__[j + (c_dim1 << 2)] + v5 * c__[j + c_dim1 * 5] + v6 * c__[j + c_dim1 * 6] + v7 * c__[ j + c_dim1 * 7] + v8 * c__[j + (c_dim1 << 3)] + v9 * c__[ j + c_dim1 * 9]; c__[j + c_dim1] -= sum * t1; c__[j + (c_dim1 << 1)] -= sum * t2; c__[j + c_dim1 * 3] -= sum * t3; c__[j + (c_dim1 << 2)] -= sum * t4; c__[j + c_dim1 * 5] -= sum * t5; c__[j + c_dim1 * 6] -= sum * t6; c__[j + c_dim1 * 7] -= sum * t7; c__[j + (c_dim1 << 3)] -= sum * t8; c__[j + c_dim1 * 9] -= sum * t9; /* L380: */ } goto L410; L390: /* Special code for 10 x 10 Householder */ v1 = v[1]; t1 = *tau * v1; v2 = v[2]; t2 = *tau * v2; v3 = v[3]; t3 = *tau * v3; v4 = v[4]; t4 = *tau * v4; v5 = v[5]; t5 = *tau * v5; v6 = v[6]; t6 = *tau * v6; v7 = v[7]; t7 = *tau * v7; v8 = v[8]; t8 = *tau * v8; v9 = v[9]; t9 = *tau * v9; v10 = v[10]; t10 = *tau * v10; i__1 = *m; for (j = 1; j <= i__1; ++j) { sum = v1 * c__[j + c_dim1] + v2 * c__[j + (c_dim1 << 1)] + v3 * c__[j + c_dim1 * 3] + v4 * c__[j + (c_dim1 << 2)] + v5 * c__[j + c_dim1 * 5] + v6 * c__[j + c_dim1 * 6] + v7 * c__[ j + c_dim1 * 7] + v8 * c__[j + (c_dim1 << 3)] + v9 * c__[ j + c_dim1 * 9] + v10 * c__[j + c_dim1 * 10]; c__[j + c_dim1] -= sum * t1; c__[j + (c_dim1 << 1)] -= sum * t2; c__[j + c_dim1 * 3] -= sum * t3; c__[j + (c_dim1 << 2)] -= sum * t4; c__[j + c_dim1 * 5] -= sum * t5; c__[j + c_dim1 * 6] -= sum * t6; c__[j + c_dim1 * 7] -= sum * t7; c__[j + (c_dim1 << 3)] -= sum * t8; c__[j + c_dim1 * 9] -= sum * t9; c__[j + c_dim1 * 10] -= sum * t10; /* L400: */ } goto L410; } L410: return 0; /* End of DLARFX */ } /* dlarfx_ */