#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int clarfb_(char *side, char *trans, char *direct, char * storev, integer *m, integer *n, integer *k, complex *v, integer *ldv, complex *t, integer *ldt, complex *c__, integer *ldc, complex *work, integer *ldwork) { /* -- LAPACK auxiliary routine (version 3.1) -- Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. November 2006 Purpose ======= CLARFB applies a complex block reflector H or its transpose H' to a complex M-by-N matrix C, from either the left or the right. Arguments ========= SIDE (input) CHARACTER*1 = 'L': apply H or H' from the Left = 'R': apply H or H' from the Right TRANS (input) CHARACTER*1 = 'N': apply H (No transpose) = 'C': apply H' (Conjugate transpose) DIRECT (input) CHARACTER*1 Indicates how H is formed from a product of elementary reflectors = 'F': H = H(1) H(2) . . . H(k) (Forward) = 'B': H = H(k) . . . H(2) H(1) (Backward) STOREV (input) CHARACTER*1 Indicates how the vectors which define the elementary reflectors are stored: = 'C': Columnwise = 'R': Rowwise M (input) INTEGER The number of rows of the matrix C. N (input) INTEGER The number of columns of the matrix C. K (input) INTEGER The order of the matrix T (= the number of elementary reflectors whose product defines the block reflector). V (input) COMPLEX array, dimension (LDV,K) if STOREV = 'C' (LDV,M) if STOREV = 'R' and SIDE = 'L' (LDV,N) if STOREV = 'R' and SIDE = 'R' The matrix V. See further details. LDV (input) INTEGER The leading dimension of the array V. If STOREV = 'C' and SIDE = 'L', LDV >= max(1,M); if STOREV = 'C' and SIDE = 'R', LDV >= max(1,N); if STOREV = 'R', LDV >= K. T (input) COMPLEX array, dimension (LDT,K) The triangular K-by-K matrix T in the representation of the block reflector. LDT (input) INTEGER The leading dimension of the array T. LDT >= K. C (input/output) COMPLEX array, dimension (LDC,N) On entry, the M-by-N matrix C. On exit, C is overwritten by H*C or H'*C or C*H or C*H'. LDC (input) INTEGER The leading dimension of the array C. LDC >= max(1,M). WORK (workspace) COMPLEX array, dimension (LDWORK,K) LDWORK (input) INTEGER The leading dimension of the array WORK. If SIDE = 'L', LDWORK >= max(1,N); if SIDE = 'R', LDWORK >= max(1,M). ===================================================================== Quick return if possible Parameter adjustments */ /* Table of constant values */ static complex c_b1 = {1.f,0.f}; static integer c__1 = 1; /* System generated locals */ integer c_dim1, c_offset, t_dim1, t_offset, v_dim1, v_offset, work_dim1, work_offset, i__1, i__2, i__3, i__4, i__5; complex q__1, q__2; /* Builtin functions */ void r_cnjg(complex *, complex *); /* Local variables */ static integer i__, j; extern /* Subroutine */ int cgemm_(char *, char *, integer *, integer *, integer *, complex *, complex *, integer *, complex *, integer *, complex *, complex *, integer *); extern logical lsame_(char *, char *); extern /* Subroutine */ int ccopy_(integer *, complex *, integer *, complex *, integer *), ctrmm_(char *, char *, char *, char *, integer *, integer *, complex *, complex *, integer *, complex *, integer *), clacgv_(integer *, complex *, integer *); static char transt[1]; v_dim1 = *ldv; v_offset = 1 + v_dim1; v -= v_offset; t_dim1 = *ldt; t_offset = 1 + t_dim1; t -= t_offset; c_dim1 = *ldc; c_offset = 1 + c_dim1; c__ -= c_offset; work_dim1 = *ldwork; work_offset = 1 + work_dim1; work -= work_offset; /* Function Body */ if (*m <= 0 || *n <= 0) { return 0; } if (lsame_(trans, "N")) { *(unsigned char *)transt = 'C'; } else { *(unsigned char *)transt = 'N'; } if (lsame_(storev, "C")) { if (lsame_(direct, "F")) { /* Let V = ( V1 ) (first K rows) ( V2 ) where V1 is unit lower triangular. */ if (lsame_(side, "L")) { /* Form H * C or H' * C where C = ( C1 ) ( C2 ) W := C' * V = (C1'*V1 + C2'*V2) (stored in WORK) W := C1' */ i__1 = *k; for (j = 1; j <= i__1; ++j) { ccopy_(n, &c__[j + c_dim1], ldc, &work[j * work_dim1 + 1], &c__1); clacgv_(n, &work[j * work_dim1 + 1], &c__1); /* L10: */ } /* W := W * V1 */ ctrmm_("Right", "Lower", "No transpose", "Unit", n, k, &c_b1, &v[v_offset], ldv, &work[work_offset], ldwork); if (*m > *k) { /* W := W + C2'*V2 */ i__1 = *m - *k; cgemm_("Conjugate transpose", "No transpose", n, k, &i__1, &c_b1, &c__[*k + 1 + c_dim1], ldc, &v[*k + 1 + v_dim1], ldv, &c_b1, &work[work_offset], ldwork); } /* W := W * T' or W * T */ ctrmm_("Right", "Upper", transt, "Non-unit", n, k, &c_b1, &t[ t_offset], ldt, &work[work_offset], ldwork); /* C := C - V * W' */ if (*m > *k) { /* C2 := C2 - V2 * W' */ i__1 = *m - *k; q__1.r = -1.f, q__1.i = -0.f; cgemm_("No transpose", "Conjugate transpose", &i__1, n, k, &q__1, &v[*k + 1 + v_dim1], ldv, &work[ work_offset], ldwork, &c_b1, &c__[*k + 1 + c_dim1] , ldc); } /* W := W * V1' */ ctrmm_("Right", "Lower", "Conjugate transpose", "Unit", n, k, &c_b1, &v[v_offset], ldv, &work[work_offset], ldwork); /* C1 := C1 - W' */ i__1 = *k; for (j = 1; j <= i__1; ++j) { i__2 = *n; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = j + i__ * c_dim1; i__4 = j + i__ * c_dim1; r_cnjg(&q__2, &work[i__ + j * work_dim1]); q__1.r = c__[i__4].r - q__2.r, q__1.i = c__[i__4].i - q__2.i; c__[i__3].r = q__1.r, c__[i__3].i = q__1.i; /* L20: */ } /* L30: */ } } else if (lsame_(side, "R")) { /* Form C * H or C * H' where C = ( C1 C2 ) W := C * V = (C1*V1 + C2*V2) (stored in WORK) W := C1 */ i__1 = *k; for (j = 1; j <= i__1; ++j) { ccopy_(m, &c__[j * c_dim1 + 1], &c__1, &work[j * work_dim1 + 1], &c__1); /* L40: */ } /* W := W * V1 */ ctrmm_("Right", "Lower", "No transpose", "Unit", m, k, &c_b1, &v[v_offset], ldv, &work[work_offset], ldwork); if (*n > *k) { /* W := W + C2 * V2 */ i__1 = *n - *k; cgemm_("No transpose", "No transpose", m, k, &i__1, &c_b1, &c__[(*k + 1) * c_dim1 + 1], ldc, &v[*k + 1 + v_dim1], ldv, &c_b1, &work[work_offset], ldwork); } /* W := W * T or W * T' */ ctrmm_("Right", "Upper", trans, "Non-unit", m, k, &c_b1, &t[ t_offset], ldt, &work[work_offset], ldwork); /* C := C - W * V' */ if (*n > *k) { /* C2 := C2 - W * V2' */ i__1 = *n - *k; q__1.r = -1.f, q__1.i = -0.f; cgemm_("No transpose", "Conjugate transpose", m, &i__1, k, &q__1, &work[work_offset], ldwork, &v[*k + 1 + v_dim1], ldv, &c_b1, &c__[(*k + 1) * c_dim1 + 1], ldc); } /* W := W * V1' */ ctrmm_("Right", "Lower", "Conjugate transpose", "Unit", m, k, &c_b1, &v[v_offset], ldv, &work[work_offset], ldwork); /* C1 := C1 - W */ i__1 = *k; for (j = 1; j <= i__1; ++j) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + j * c_dim1; i__4 = i__ + j * c_dim1; i__5 = i__ + j * work_dim1; q__1.r = c__[i__4].r - work[i__5].r, q__1.i = c__[ i__4].i - work[i__5].i; c__[i__3].r = q__1.r, c__[i__3].i = q__1.i; /* L50: */ } /* L60: */ } } } else { /* Let V = ( V1 ) ( V2 ) (last K rows) where V2 is unit upper triangular. */ if (lsame_(side, "L")) { /* Form H * C or H' * C where C = ( C1 ) ( C2 ) W := C' * V = (C1'*V1 + C2'*V2) (stored in WORK) W := C2' */ i__1 = *k; for (j = 1; j <= i__1; ++j) { ccopy_(n, &c__[*m - *k + j + c_dim1], ldc, &work[j * work_dim1 + 1], &c__1); clacgv_(n, &work[j * work_dim1 + 1], &c__1); /* L70: */ } /* W := W * V2 */ ctrmm_("Right", "Upper", "No transpose", "Unit", n, k, &c_b1, &v[*m - *k + 1 + v_dim1], ldv, &work[work_offset], ldwork); if (*m > *k) { /* W := W + C1'*V1 */ i__1 = *m - *k; cgemm_("Conjugate transpose", "No transpose", n, k, &i__1, &c_b1, &c__[c_offset], ldc, &v[v_offset], ldv, & c_b1, &work[work_offset], ldwork); } /* W := W * T' or W * T */ ctrmm_("Right", "Lower", transt, "Non-unit", n, k, &c_b1, &t[ t_offset], ldt, &work[work_offset], ldwork); /* C := C - V * W' */ if (*m > *k) { /* C1 := C1 - V1 * W' */ i__1 = *m - *k; q__1.r = -1.f, q__1.i = -0.f; cgemm_("No transpose", "Conjugate transpose", &i__1, n, k, &q__1, &v[v_offset], ldv, &work[work_offset], ldwork, &c_b1, &c__[c_offset], ldc); } /* W := W * V2' */ ctrmm_("Right", "Upper", "Conjugate transpose", "Unit", n, k, &c_b1, &v[*m - *k + 1 + v_dim1], ldv, &work[ work_offset], ldwork); /* C2 := C2 - W' */ i__1 = *k; for (j = 1; j <= i__1; ++j) { i__2 = *n; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = *m - *k + j + i__ * c_dim1; i__4 = *m - *k + j + i__ * c_dim1; r_cnjg(&q__2, &work[i__ + j * work_dim1]); q__1.r = c__[i__4].r - q__2.r, q__1.i = c__[i__4].i - q__2.i; c__[i__3].r = q__1.r, c__[i__3].i = q__1.i; /* L80: */ } /* L90: */ } } else if (lsame_(side, "R")) { /* Form C * H or C * H' where C = ( C1 C2 ) W := C * V = (C1*V1 + C2*V2) (stored in WORK) W := C2 */ i__1 = *k; for (j = 1; j <= i__1; ++j) { ccopy_(m, &c__[(*n - *k + j) * c_dim1 + 1], &c__1, &work[ j * work_dim1 + 1], &c__1); /* L100: */ } /* W := W * V2 */ ctrmm_("Right", "Upper", "No transpose", "Unit", m, k, &c_b1, &v[*n - *k + 1 + v_dim1], ldv, &work[work_offset], ldwork); if (*n > *k) { /* W := W + C1 * V1 */ i__1 = *n - *k; cgemm_("No transpose", "No transpose", m, k, &i__1, &c_b1, &c__[c_offset], ldc, &v[v_offset], ldv, &c_b1, & work[work_offset], ldwork) ; } /* W := W * T or W * T' */ ctrmm_("Right", "Lower", trans, "Non-unit", m, k, &c_b1, &t[ t_offset], ldt, &work[work_offset], ldwork); /* C := C - W * V' */ if (*n > *k) { /* C1 := C1 - W * V1' */ i__1 = *n - *k; q__1.r = -1.f, q__1.i = -0.f; cgemm_("No transpose", "Conjugate transpose", m, &i__1, k, &q__1, &work[work_offset], ldwork, &v[v_offset], ldv, &c_b1, &c__[c_offset], ldc); } /* W := W * V2' */ ctrmm_("Right", "Upper", "Conjugate transpose", "Unit", m, k, &c_b1, &v[*n - *k + 1 + v_dim1], ldv, &work[ work_offset], ldwork); /* C2 := C2 - W */ i__1 = *k; for (j = 1; j <= i__1; ++j) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + (*n - *k + j) * c_dim1; i__4 = i__ + (*n - *k + j) * c_dim1; i__5 = i__ + j * work_dim1; q__1.r = c__[i__4].r - work[i__5].r, q__1.i = c__[ i__4].i - work[i__5].i; c__[i__3].r = q__1.r, c__[i__3].i = q__1.i; /* L110: */ } /* L120: */ } } } } else if (lsame_(storev, "R")) { if (lsame_(direct, "F")) { /* Let V = ( V1 V2 ) (V1: first K columns) where V1 is unit upper triangular. */ if (lsame_(side, "L")) { /* Form H * C or H' * C where C = ( C1 ) ( C2 ) W := C' * V' = (C1'*V1' + C2'*V2') (stored in WORK) W := C1' */ i__1 = *k; for (j = 1; j <= i__1; ++j) { ccopy_(n, &c__[j + c_dim1], ldc, &work[j * work_dim1 + 1], &c__1); clacgv_(n, &work[j * work_dim1 + 1], &c__1); /* L130: */ } /* W := W * V1' */ ctrmm_("Right", "Upper", "Conjugate transpose", "Unit", n, k, &c_b1, &v[v_offset], ldv, &work[work_offset], ldwork); if (*m > *k) { /* W := W + C2'*V2' */ i__1 = *m - *k; cgemm_("Conjugate transpose", "Conjugate transpose", n, k, &i__1, &c_b1, &c__[*k + 1 + c_dim1], ldc, &v[(*k + 1) * v_dim1 + 1], ldv, &c_b1, &work[work_offset] , ldwork); } /* W := W * T' or W * T */ ctrmm_("Right", "Upper", transt, "Non-unit", n, k, &c_b1, &t[ t_offset], ldt, &work[work_offset], ldwork); /* C := C - V' * W' */ if (*m > *k) { /* C2 := C2 - V2' * W' */ i__1 = *m - *k; q__1.r = -1.f, q__1.i = -0.f; cgemm_("Conjugate transpose", "Conjugate transpose", & i__1, n, k, &q__1, &v[(*k + 1) * v_dim1 + 1], ldv, &work[work_offset], ldwork, &c_b1, &c__[*k + 1 + c_dim1], ldc); } /* W := W * V1 */ ctrmm_("Right", "Upper", "No transpose", "Unit", n, k, &c_b1, &v[v_offset], ldv, &work[work_offset], ldwork); /* C1 := C1 - W' */ i__1 = *k; for (j = 1; j <= i__1; ++j) { i__2 = *n; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = j + i__ * c_dim1; i__4 = j + i__ * c_dim1; r_cnjg(&q__2, &work[i__ + j * work_dim1]); q__1.r = c__[i__4].r - q__2.r, q__1.i = c__[i__4].i - q__2.i; c__[i__3].r = q__1.r, c__[i__3].i = q__1.i; /* L140: */ } /* L150: */ } } else if (lsame_(side, "R")) { /* Form C * H or C * H' where C = ( C1 C2 ) W := C * V' = (C1*V1' + C2*V2') (stored in WORK) W := C1 */ i__1 = *k; for (j = 1; j <= i__1; ++j) { ccopy_(m, &c__[j * c_dim1 + 1], &c__1, &work[j * work_dim1 + 1], &c__1); /* L160: */ } /* W := W * V1' */ ctrmm_("Right", "Upper", "Conjugate transpose", "Unit", m, k, &c_b1, &v[v_offset], ldv, &work[work_offset], ldwork); if (*n > *k) { /* W := W + C2 * V2' */ i__1 = *n - *k; cgemm_("No transpose", "Conjugate transpose", m, k, &i__1, &c_b1, &c__[(*k + 1) * c_dim1 + 1], ldc, &v[(*k + 1) * v_dim1 + 1], ldv, &c_b1, &work[work_offset] , ldwork); } /* W := W * T or W * T' */ ctrmm_("Right", "Upper", trans, "Non-unit", m, k, &c_b1, &t[ t_offset], ldt, &work[work_offset], ldwork); /* C := C - W * V */ if (*n > *k) { /* C2 := C2 - W * V2 */ i__1 = *n - *k; q__1.r = -1.f, q__1.i = -0.f; cgemm_("No transpose", "No transpose", m, &i__1, k, &q__1, &work[work_offset], ldwork, &v[(*k + 1) * v_dim1 + 1], ldv, &c_b1, &c__[(*k + 1) * c_dim1 + 1], ldc); } /* W := W * V1 */ ctrmm_("Right", "Upper", "No transpose", "Unit", m, k, &c_b1, &v[v_offset], ldv, &work[work_offset], ldwork); /* C1 := C1 - W */ i__1 = *k; for (j = 1; j <= i__1; ++j) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + j * c_dim1; i__4 = i__ + j * c_dim1; i__5 = i__ + j * work_dim1; q__1.r = c__[i__4].r - work[i__5].r, q__1.i = c__[ i__4].i - work[i__5].i; c__[i__3].r = q__1.r, c__[i__3].i = q__1.i; /* L170: */ } /* L180: */ } } } else { /* Let V = ( V1 V2 ) (V2: last K columns) where V2 is unit lower triangular. */ if (lsame_(side, "L")) { /* Form H * C or H' * C where C = ( C1 ) ( C2 ) W := C' * V' = (C1'*V1' + C2'*V2') (stored in WORK) W := C2' */ i__1 = *k; for (j = 1; j <= i__1; ++j) { ccopy_(n, &c__[*m - *k + j + c_dim1], ldc, &work[j * work_dim1 + 1], &c__1); clacgv_(n, &work[j * work_dim1 + 1], &c__1); /* L190: */ } /* W := W * V2' */ ctrmm_("Right", "Lower", "Conjugate transpose", "Unit", n, k, &c_b1, &v[(*m - *k + 1) * v_dim1 + 1], ldv, &work[ work_offset], ldwork); if (*m > *k) { /* W := W + C1'*V1' */ i__1 = *m - *k; cgemm_("Conjugate transpose", "Conjugate transpose", n, k, &i__1, &c_b1, &c__[c_offset], ldc, &v[v_offset], ldv, &c_b1, &work[work_offset], ldwork); } /* W := W * T' or W * T */ ctrmm_("Right", "Lower", transt, "Non-unit", n, k, &c_b1, &t[ t_offset], ldt, &work[work_offset], ldwork); /* C := C - V' * W' */ if (*m > *k) { /* C1 := C1 - V1' * W' */ i__1 = *m - *k; q__1.r = -1.f, q__1.i = -0.f; cgemm_("Conjugate transpose", "Conjugate transpose", & i__1, n, k, &q__1, &v[v_offset], ldv, &work[ work_offset], ldwork, &c_b1, &c__[c_offset], ldc); } /* W := W * V2 */ ctrmm_("Right", "Lower", "No transpose", "Unit", n, k, &c_b1, &v[(*m - *k + 1) * v_dim1 + 1], ldv, &work[ work_offset], ldwork); /* C2 := C2 - W' */ i__1 = *k; for (j = 1; j <= i__1; ++j) { i__2 = *n; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = *m - *k + j + i__ * c_dim1; i__4 = *m - *k + j + i__ * c_dim1; r_cnjg(&q__2, &work[i__ + j * work_dim1]); q__1.r = c__[i__4].r - q__2.r, q__1.i = c__[i__4].i - q__2.i; c__[i__3].r = q__1.r, c__[i__3].i = q__1.i; /* L200: */ } /* L210: */ } } else if (lsame_(side, "R")) { /* Form C * H or C * H' where C = ( C1 C2 ) W := C * V' = (C1*V1' + C2*V2') (stored in WORK) W := C2 */ i__1 = *k; for (j = 1; j <= i__1; ++j) { ccopy_(m, &c__[(*n - *k + j) * c_dim1 + 1], &c__1, &work[ j * work_dim1 + 1], &c__1); /* L220: */ } /* W := W * V2' */ ctrmm_("Right", "Lower", "Conjugate transpose", "Unit", m, k, &c_b1, &v[(*n - *k + 1) * v_dim1 + 1], ldv, &work[ work_offset], ldwork); if (*n > *k) { /* W := W + C1 * V1' */ i__1 = *n - *k; cgemm_("No transpose", "Conjugate transpose", m, k, &i__1, &c_b1, &c__[c_offset], ldc, &v[v_offset], ldv, & c_b1, &work[work_offset], ldwork); } /* W := W * T or W * T' */ ctrmm_("Right", "Lower", trans, "Non-unit", m, k, &c_b1, &t[ t_offset], ldt, &work[work_offset], ldwork); /* C := C - W * V */ if (*n > *k) { /* C1 := C1 - W * V1 */ i__1 = *n - *k; q__1.r = -1.f, q__1.i = -0.f; cgemm_("No transpose", "No transpose", m, &i__1, k, &q__1, &work[work_offset], ldwork, &v[v_offset], ldv, & c_b1, &c__[c_offset], ldc) ; } /* W := W * V2 */ ctrmm_("Right", "Lower", "No transpose", "Unit", m, k, &c_b1, &v[(*n - *k + 1) * v_dim1 + 1], ldv, &work[ work_offset], ldwork); /* C1 := C1 - W */ i__1 = *k; for (j = 1; j <= i__1; ++j) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + (*n - *k + j) * c_dim1; i__4 = i__ + (*n - *k + j) * c_dim1; i__5 = i__ + j * work_dim1; q__1.r = c__[i__4].r - work[i__5].r, q__1.i = c__[ i__4].i - work[i__5].i; c__[i__3].r = q__1.r, c__[i__3].i = q__1.i; /* L230: */ } /* L240: */ } } } } return 0; /* End of CLARFB */ } /* clarfb_ */