#include "f2c.h" #include "blaswrap.h" /* Table of constant values */ static doublecomplex c_b1 = {1.,0.}; static integer c__1 = 1; /* Subroutine */ int zlarfb_(char *side, char *trans, char *direct, char * storev, integer *m, integer *n, integer *k, doublecomplex *v, integer *ldv, doublecomplex *t, integer *ldt, doublecomplex *c__, integer * ldc, doublecomplex *work, integer *ldwork) { /* 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; doublecomplex z__1, z__2; /* Builtin functions */ void d_cnjg(doublecomplex *, doublecomplex *); /* Local variables */ integer i__, j; extern logical lsame_(char *, char *); extern /* Subroutine */ int zgemm_(char *, char *, integer *, integer *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *), zcopy_(integer *, doublecomplex *, integer *, doublecomplex *, integer *), ztrmm_(char *, char *, char *, char *, integer *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *), zlacgv_(integer *, doublecomplex *, integer *); char transt[1]; /* -- LAPACK auxiliary routine (version 3.1) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* ZLARFB 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*16 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*16 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*16 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*16 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). */ /* ===================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Executable Statements .. */ /* Quick return if possible */ /* Parameter adjustments */ 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) { zcopy_(n, &c__[j + c_dim1], ldc, &work[j * work_dim1 + 1], &c__1); zlacgv_(n, &work[j * work_dim1 + 1], &c__1); /* L10: */ } /* W := W * V1 */ ztrmm_("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; zgemm_("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 */ ztrmm_("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; z__1.r = -1., z__1.i = -0.; zgemm_("No transpose", "Conjugate transpose", &i__1, n, k, &z__1, &v[*k + 1 + v_dim1], ldv, &work[ work_offset], ldwork, &c_b1, &c__[*k + 1 + c_dim1] , ldc); } /* W := W * V1' */ ztrmm_("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; d_cnjg(&z__2, &work[i__ + j * work_dim1]); z__1.r = c__[i__4].r - z__2.r, z__1.i = c__[i__4].i - z__2.i; c__[i__3].r = z__1.r, c__[i__3].i = z__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) { zcopy_(m, &c__[j * c_dim1 + 1], &c__1, &work[j * work_dim1 + 1], &c__1); /* L40: */ } /* W := W * V1 */ ztrmm_("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; zgemm_("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' */ ztrmm_("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; z__1.r = -1., z__1.i = -0.; zgemm_("No transpose", "Conjugate transpose", m, &i__1, k, &z__1, &work[work_offset], ldwork, &v[*k + 1 + v_dim1], ldv, &c_b1, &c__[(*k + 1) * c_dim1 + 1], ldc); } /* W := W * V1' */ ztrmm_("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; z__1.r = c__[i__4].r - work[i__5].r, z__1.i = c__[ i__4].i - work[i__5].i; c__[i__3].r = z__1.r, c__[i__3].i = z__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) { zcopy_(n, &c__[*m - *k + j + c_dim1], ldc, &work[j * work_dim1 + 1], &c__1); zlacgv_(n, &work[j * work_dim1 + 1], &c__1); /* L70: */ } /* W := W * V2 */ ztrmm_("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; zgemm_("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 */ ztrmm_("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; z__1.r = -1., z__1.i = -0.; zgemm_("No transpose", "Conjugate transpose", &i__1, n, k, &z__1, &v[v_offset], ldv, &work[work_offset], ldwork, &c_b1, &c__[c_offset], ldc); } /* W := W * V2' */ ztrmm_("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; d_cnjg(&z__2, &work[i__ + j * work_dim1]); z__1.r = c__[i__4].r - z__2.r, z__1.i = c__[i__4].i - z__2.i; c__[i__3].r = z__1.r, c__[i__3].i = z__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) { zcopy_(m, &c__[(*n - *k + j) * c_dim1 + 1], &c__1, &work[ j * work_dim1 + 1], &c__1); /* L100: */ } /* W := W * V2 */ ztrmm_("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; zgemm_("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' */ ztrmm_("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; z__1.r = -1., z__1.i = -0.; zgemm_("No transpose", "Conjugate transpose", m, &i__1, k, &z__1, &work[work_offset], ldwork, &v[v_offset], ldv, &c_b1, &c__[c_offset], ldc); } /* W := W * V2' */ ztrmm_("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; z__1.r = c__[i__4].r - work[i__5].r, z__1.i = c__[ i__4].i - work[i__5].i; c__[i__3].r = z__1.r, c__[i__3].i = z__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) { zcopy_(n, &c__[j + c_dim1], ldc, &work[j * work_dim1 + 1], &c__1); zlacgv_(n, &work[j * work_dim1 + 1], &c__1); /* L130: */ } /* W := W * V1' */ ztrmm_("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; zgemm_("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 */ ztrmm_("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; z__1.r = -1., z__1.i = -0.; zgemm_("Conjugate transpose", "Conjugate transpose", & i__1, n, k, &z__1, &v[(*k + 1) * v_dim1 + 1], ldv, &work[work_offset], ldwork, &c_b1, &c__[*k + 1 + c_dim1], ldc); } /* W := W * V1 */ ztrmm_("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; d_cnjg(&z__2, &work[i__ + j * work_dim1]); z__1.r = c__[i__4].r - z__2.r, z__1.i = c__[i__4].i - z__2.i; c__[i__3].r = z__1.r, c__[i__3].i = z__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) { zcopy_(m, &c__[j * c_dim1 + 1], &c__1, &work[j * work_dim1 + 1], &c__1); /* L160: */ } /* W := W * V1' */ ztrmm_("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; zgemm_("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' */ ztrmm_("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; z__1.r = -1., z__1.i = -0.; zgemm_("No transpose", "No transpose", m, &i__1, k, &z__1, &work[work_offset], ldwork, &v[(*k + 1) * v_dim1 + 1], ldv, &c_b1, &c__[(*k + 1) * c_dim1 + 1], ldc); } /* W := W * V1 */ ztrmm_("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; z__1.r = c__[i__4].r - work[i__5].r, z__1.i = c__[ i__4].i - work[i__5].i; c__[i__3].r = z__1.r, c__[i__3].i = z__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) { zcopy_(n, &c__[*m - *k + j + c_dim1], ldc, &work[j * work_dim1 + 1], &c__1); zlacgv_(n, &work[j * work_dim1 + 1], &c__1); /* L190: */ } /* W := W * V2' */ ztrmm_("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; zgemm_("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 */ ztrmm_("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; z__1.r = -1., z__1.i = -0.; zgemm_("Conjugate transpose", "Conjugate transpose", & i__1, n, k, &z__1, &v[v_offset], ldv, &work[ work_offset], ldwork, &c_b1, &c__[c_offset], ldc); } /* W := W * V2 */ ztrmm_("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; d_cnjg(&z__2, &work[i__ + j * work_dim1]); z__1.r = c__[i__4].r - z__2.r, z__1.i = c__[i__4].i - z__2.i; c__[i__3].r = z__1.r, c__[i__3].i = z__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) { zcopy_(m, &c__[(*n - *k + j) * c_dim1 + 1], &c__1, &work[ j * work_dim1 + 1], &c__1); /* L220: */ } /* W := W * V2' */ ztrmm_("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; zgemm_("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' */ ztrmm_("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; z__1.r = -1., z__1.i = -0.; zgemm_("No transpose", "No transpose", m, &i__1, k, &z__1, &work[work_offset], ldwork, &v[v_offset], ldv, & c_b1, &c__[c_offset], ldc) ; } /* W := W * V2 */ ztrmm_("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; z__1.r = c__[i__4].r - work[i__5].r, z__1.i = c__[ i__4].i - work[i__5].i; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; /* L230: */ } /* L240: */ } } } } return 0; /* End of ZLARFB */ } /* zlarfb_ */