/* -- translated by f2c (version 20191129). You must link the resulting object file with libf2c: on Microsoft Windows system, link with libf2c.lib; on Linux or Unix systems, link with .../path/to/libf2c.a -lm or, if you install libf2c.a in a standard place, with -lf2c -lm -- in that order, at the end of the command line, as in cc *.o -lf2c -lm Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., http://www.netlib.org/f2c/libf2c.zip */ #include "f2c.h" /* Table of constant values */ static integer c__1 = 1; static doublereal c_b14 = 1.; static doublereal c_b25 = -1.; /* > \brief \b DLARFB applies a block reflector or its transpose to a general rectangular matrix. =========== DOCUMENTATION =========== Online html documentation available at http://www.netlib.org/lapack/explore-html/ > \htmlonly > Download DLARFB + dependencies > > [TGZ] > > [ZIP] > > [TXT] > \endhtmlonly Definition: =========== SUBROUTINE DLARFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, T, LDT, C, LDC, WORK, LDWORK ) CHARACTER DIRECT, SIDE, STOREV, TRANS INTEGER K, LDC, LDT, LDV, LDWORK, M, N DOUBLE PRECISION C( LDC, * ), T( LDT, * ), V( LDV, * ), $ WORK( LDWORK, * ) > \par Purpose: ============= > > \verbatim > > DLARFB applies a real block reflector H or its transpose H**T to a > real m by n matrix C, from either the left or the right. > \endverbatim Arguments: ========== > \param[in] SIDE > \verbatim > SIDE is CHARACTER*1 > = 'L': apply H or H**T from the Left > = 'R': apply H or H**T from the Right > \endverbatim > > \param[in] TRANS > \verbatim > TRANS is CHARACTER*1 > = 'N': apply H (No transpose) > = 'T': apply H**T (Transpose) > \endverbatim > > \param[in] DIRECT > \verbatim > DIRECT is 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) > \endverbatim > > \param[in] STOREV > \verbatim > STOREV is CHARACTER*1 > Indicates how the vectors which define the elementary > reflectors are stored: > = 'C': Columnwise > = 'R': Rowwise > \endverbatim > > \param[in] M > \verbatim > M is INTEGER > The number of rows of the matrix C. > \endverbatim > > \param[in] N > \verbatim > N is INTEGER > The number of columns of the matrix C. > \endverbatim > > \param[in] K > \verbatim > K is INTEGER > The order of the matrix T (= the number of elementary > reflectors whose product defines the block reflector). > \endverbatim > > \param[in] V > \verbatim > V is DOUBLE PRECISION 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. > \endverbatim > > \param[in] LDV > \verbatim > LDV is 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. > \endverbatim > > \param[in] T > \verbatim > T is DOUBLE PRECISION array, dimension (LDT,K) > The triangular k by k matrix T in the representation of the > block reflector. > \endverbatim > > \param[in] LDT > \verbatim > LDT is INTEGER > The leading dimension of the array T. LDT >= K. > \endverbatim > > \param[in,out] C > \verbatim > C is DOUBLE PRECISION array, dimension (LDC,N) > On entry, the m by n matrix C. > On exit, C is overwritten by H*C or H**T*C or C*H or C*H**T. > \endverbatim > > \param[in] LDC > \verbatim > LDC is INTEGER > The leading dimension of the array C. LDC >= max(1,M). > \endverbatim > > \param[out] WORK > \verbatim > WORK is DOUBLE PRECISION array, dimension (LDWORK,K) > \endverbatim > > \param[in] LDWORK > \verbatim > LDWORK is INTEGER > The leading dimension of the array WORK. > If SIDE = 'L', LDWORK >= max(1,N); > if SIDE = 'R', LDWORK >= max(1,M). > \endverbatim Authors: ======== > \author Univ. of Tennessee > \author Univ. of California Berkeley > \author Univ. of Colorado Denver > \author NAG Ltd. > \date June 2013 > \ingroup doubleOTHERauxiliary > \par Further Details: ===================== > > \verbatim > > 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 ) > \endverbatim > ===================================================================== Subroutine */ int igraphdlarfb_(char *side, char *trans, char *direct, char * storev, integer *m, integer *n, integer *k, doublereal *v, integer * ldv, doublereal *t, integer *ldt, doublereal *c__, integer *ldc, doublereal *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; /* Local variables */ integer i__, j; extern /* Subroutine */ int igraphdgemm_(char *, char *, integer *, integer *, integer *, doublereal *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *); extern logical igraphlsame_(char *, char *); extern /* Subroutine */ int igraphdcopy_(integer *, doublereal *, integer *, doublereal *, integer *), igraphdtrmm_(char *, char *, char *, char *, integer *, integer *, doublereal *, doublereal *, integer *, doublereal *, integer *); char transt[1]; /* -- LAPACK auxiliary routine (version 3.5.0) -- -- LAPACK is a software package provided by Univ. of Tennessee, -- -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- June 2013 ===================================================================== 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 (igraphlsame_(trans, "N")) { *(unsigned char *)transt = 'T'; } else { *(unsigned char *)transt = 'N'; } if (igraphlsame_(storev, "C")) { if (igraphlsame_(direct, "F")) { /* Let V = ( V1 ) (first K rows) ( V2 ) where V1 is unit lower triangular. */ if (igraphlsame_(side, "L")) { /* Form H * C or H**T * C where C = ( C1 ) ( C2 ) W := C**T * V = (C1**T * V1 + C2**T * V2) (stored in WORK) W := C1**T */ i__1 = *k; for (j = 1; j <= i__1; ++j) { igraphdcopy_(n, &c__[j + c_dim1], ldc, &work[j * work_dim1 + 1], &c__1); /* L10: */ } /* W := W * V1 */ igraphdtrmm_("Right", "Lower", "No transpose", "Unit", n, k, &c_b14, &v[v_offset], ldv, &work[work_offset], ldwork); if (*m > *k) { /* W := W + C2**T * V2 */ i__1 = *m - *k; igraphdgemm_("Transpose", "No transpose", n, k, &i__1, &c_b14, & c__[*k + 1 + c_dim1], ldc, &v[*k + 1 + v_dim1], ldv, &c_b14, &work[work_offset], ldwork); } /* W := W * T**T or W * T */ igraphdtrmm_("Right", "Upper", transt, "Non-unit", n, k, &c_b14, &t[ t_offset], ldt, &work[work_offset], ldwork); /* C := C - V * W**T */ if (*m > *k) { /* C2 := C2 - V2 * W**T */ i__1 = *m - *k; igraphdgemm_("No transpose", "Transpose", &i__1, n, k, &c_b25, & v[*k + 1 + v_dim1], ldv, &work[work_offset], ldwork, &c_b14, &c__[*k + 1 + c_dim1], ldc); } /* W := W * V1**T */ igraphdtrmm_("Right", "Lower", "Transpose", "Unit", n, k, &c_b14, & v[v_offset], ldv, &work[work_offset], ldwork); /* C1 := C1 - W**T */ i__1 = *k; for (j = 1; j <= i__1; ++j) { i__2 = *n; for (i__ = 1; i__ <= i__2; ++i__) { c__[j + i__ * c_dim1] -= work[i__ + j * work_dim1]; /* L20: */ } /* L30: */ } } else if (igraphlsame_(side, "R")) { /* Form C * H or C * H**T 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) { igraphdcopy_(m, &c__[j * c_dim1 + 1], &c__1, &work[j * work_dim1 + 1], &c__1); /* L40: */ } /* W := W * V1 */ igraphdtrmm_("Right", "Lower", "No transpose", "Unit", m, k, &c_b14, &v[v_offset], ldv, &work[work_offset], ldwork); if (*n > *k) { /* W := W + C2 * V2 */ i__1 = *n - *k; igraphdgemm_("No transpose", "No transpose", m, k, &i__1, & c_b14, &c__[(*k + 1) * c_dim1 + 1], ldc, &v[*k + 1 + v_dim1], ldv, &c_b14, &work[work_offset], ldwork); } /* W := W * T or W * T**T */ igraphdtrmm_("Right", "Upper", trans, "Non-unit", m, k, &c_b14, &t[ t_offset], ldt, &work[work_offset], ldwork); /* C := C - W * V**T */ if (*n > *k) { /* C2 := C2 - W * V2**T */ i__1 = *n - *k; igraphdgemm_("No transpose", "Transpose", m, &i__1, k, &c_b25, & work[work_offset], ldwork, &v[*k + 1 + v_dim1], ldv, &c_b14, &c__[(*k + 1) * c_dim1 + 1], ldc); } /* W := W * V1**T */ igraphdtrmm_("Right", "Lower", "Transpose", "Unit", m, k, &c_b14, & 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__) { c__[i__ + j * c_dim1] -= work[i__ + j * work_dim1]; /* L50: */ } /* L60: */ } } } else { /* Let V = ( V1 ) ( V2 ) (last K rows) where V2 is unit upper triangular. */ if (igraphlsame_(side, "L")) { /* Form H * C or H**T * C where C = ( C1 ) ( C2 ) W := C**T * V = (C1**T * V1 + C2**T * V2) (stored in WORK) W := C2**T */ i__1 = *k; for (j = 1; j <= i__1; ++j) { igraphdcopy_(n, &c__[*m - *k + j + c_dim1], ldc, &work[j * work_dim1 + 1], &c__1); /* L70: */ } /* W := W * V2 */ igraphdtrmm_("Right", "Upper", "No transpose", "Unit", n, k, &c_b14, &v[*m - *k + 1 + v_dim1], ldv, &work[work_offset], ldwork); if (*m > *k) { /* W := W + C1**T * V1 */ i__1 = *m - *k; igraphdgemm_("Transpose", "No transpose", n, k, &i__1, &c_b14, & c__[c_offset], ldc, &v[v_offset], ldv, &c_b14, & work[work_offset], ldwork); } /* W := W * T**T or W * T */ igraphdtrmm_("Right", "Lower", transt, "Non-unit", n, k, &c_b14, &t[ t_offset], ldt, &work[work_offset], ldwork); /* C := C - V * W**T */ if (*m > *k) { /* C1 := C1 - V1 * W**T */ i__1 = *m - *k; igraphdgemm_("No transpose", "Transpose", &i__1, n, k, &c_b25, & v[v_offset], ldv, &work[work_offset], ldwork, & c_b14, &c__[c_offset], ldc) ; } /* W := W * V2**T */ igraphdtrmm_("Right", "Upper", "Transpose", "Unit", n, k, &c_b14, & v[*m - *k + 1 + v_dim1], ldv, &work[work_offset], ldwork); /* C2 := C2 - W**T */ i__1 = *k; for (j = 1; j <= i__1; ++j) { i__2 = *n; for (i__ = 1; i__ <= i__2; ++i__) { c__[*m - *k + j + i__ * c_dim1] -= work[i__ + j * work_dim1]; /* L80: */ } /* L90: */ } } else if (igraphlsame_(side, "R")) { /* Form C * H or C * H**T 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) { igraphdcopy_(m, &c__[(*n - *k + j) * c_dim1 + 1], &c__1, &work[ j * work_dim1 + 1], &c__1); /* L100: */ } /* W := W * V2 */ igraphdtrmm_("Right", "Upper", "No transpose", "Unit", m, k, &c_b14, &v[*n - *k + 1 + v_dim1], ldv, &work[work_offset], ldwork); if (*n > *k) { /* W := W + C1 * V1 */ i__1 = *n - *k; igraphdgemm_("No transpose", "No transpose", m, k, &i__1, & c_b14, &c__[c_offset], ldc, &v[v_offset], ldv, & c_b14, &work[work_offset], ldwork); } /* W := W * T or W * T**T */ igraphdtrmm_("Right", "Lower", trans, "Non-unit", m, k, &c_b14, &t[ t_offset], ldt, &work[work_offset], ldwork); /* C := C - W * V**T */ if (*n > *k) { /* C1 := C1 - W * V1**T */ i__1 = *n - *k; igraphdgemm_("No transpose", "Transpose", m, &i__1, k, &c_b25, & work[work_offset], ldwork, &v[v_offset], ldv, & c_b14, &c__[c_offset], ldc) ; } /* W := W * V2**T */ igraphdtrmm_("Right", "Upper", "Transpose", "Unit", m, k, &c_b14, & 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__) { c__[i__ + (*n - *k + j) * c_dim1] -= work[i__ + j * work_dim1]; /* L110: */ } /* L120: */ } } } } else if (igraphlsame_(storev, "R")) { if (igraphlsame_(direct, "F")) { /* Let V = ( V1 V2 ) (V1: first K columns) where V1 is unit upper triangular. */ if (igraphlsame_(side, "L")) { /* Form H * C or H**T * C where C = ( C1 ) ( C2 ) W := C**T * V**T = (C1**T * V1**T + C2**T * V2**T) (stored in WORK) W := C1**T */ i__1 = *k; for (j = 1; j <= i__1; ++j) { igraphdcopy_(n, &c__[j + c_dim1], ldc, &work[j * work_dim1 + 1], &c__1); /* L130: */ } /* W := W * V1**T */ igraphdtrmm_("Right", "Upper", "Transpose", "Unit", n, k, &c_b14, & v[v_offset], ldv, &work[work_offset], ldwork); if (*m > *k) { /* W := W + C2**T * V2**T */ i__1 = *m - *k; igraphdgemm_("Transpose", "Transpose", n, k, &i__1, &c_b14, & c__[*k + 1 + c_dim1], ldc, &v[(*k + 1) * v_dim1 + 1], ldv, &c_b14, &work[work_offset], ldwork); } /* W := W * T**T or W * T */ igraphdtrmm_("Right", "Upper", transt, "Non-unit", n, k, &c_b14, &t[ t_offset], ldt, &work[work_offset], ldwork); /* C := C - V**T * W**T */ if (*m > *k) { /* C2 := C2 - V2**T * W**T */ i__1 = *m - *k; igraphdgemm_("Transpose", "Transpose", &i__1, n, k, &c_b25, &v[( *k + 1) * v_dim1 + 1], ldv, &work[work_offset], ldwork, &c_b14, &c__[*k + 1 + c_dim1], ldc); } /* W := W * V1 */ igraphdtrmm_("Right", "Upper", "No transpose", "Unit", n, k, &c_b14, &v[v_offset], ldv, &work[work_offset], ldwork); /* C1 := C1 - W**T */ i__1 = *k; for (j = 1; j <= i__1; ++j) { i__2 = *n; for (i__ = 1; i__ <= i__2; ++i__) { c__[j + i__ * c_dim1] -= work[i__ + j * work_dim1]; /* L140: */ } /* L150: */ } } else if (igraphlsame_(side, "R")) { /* Form C * H or C * H**T where C = ( C1 C2 ) W := C * V**T = (C1*V1**T + C2*V2**T) (stored in WORK) W := C1 */ i__1 = *k; for (j = 1; j <= i__1; ++j) { igraphdcopy_(m, &c__[j * c_dim1 + 1], &c__1, &work[j * work_dim1 + 1], &c__1); /* L160: */ } /* W := W * V1**T */ igraphdtrmm_("Right", "Upper", "Transpose", "Unit", m, k, &c_b14, & v[v_offset], ldv, &work[work_offset], ldwork); if (*n > *k) { /* W := W + C2 * V2**T */ i__1 = *n - *k; igraphdgemm_("No transpose", "Transpose", m, k, &i__1, &c_b14, & c__[(*k + 1) * c_dim1 + 1], ldc, &v[(*k + 1) * v_dim1 + 1], ldv, &c_b14, &work[work_offset], ldwork); } /* W := W * T or W * T**T */ igraphdtrmm_("Right", "Upper", trans, "Non-unit", m, k, &c_b14, &t[ t_offset], ldt, &work[work_offset], ldwork); /* C := C - W * V */ if (*n > *k) { /* C2 := C2 - W * V2 */ i__1 = *n - *k; igraphdgemm_("No transpose", "No transpose", m, &i__1, k, & c_b25, &work[work_offset], ldwork, &v[(*k + 1) * v_dim1 + 1], ldv, &c_b14, &c__[(*k + 1) * c_dim1 + 1], ldc); } /* W := W * V1 */ igraphdtrmm_("Right", "Upper", "No transpose", "Unit", m, k, &c_b14, &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__) { c__[i__ + j * c_dim1] -= work[i__ + j * work_dim1]; /* L170: */ } /* L180: */ } } } else { /* Let V = ( V1 V2 ) (V2: last K columns) where V2 is unit lower triangular. */ if (igraphlsame_(side, "L")) { /* Form H * C or H**T * C where C = ( C1 ) ( C2 ) W := C**T * V**T = (C1**T * V1**T + C2**T * V2**T) (stored in WORK) W := C2**T */ i__1 = *k; for (j = 1; j <= i__1; ++j) { igraphdcopy_(n, &c__[*m - *k + j + c_dim1], ldc, &work[j * work_dim1 + 1], &c__1); /* L190: */ } /* W := W * V2**T */ igraphdtrmm_("Right", "Lower", "Transpose", "Unit", n, k, &c_b14, & v[(*m - *k + 1) * v_dim1 + 1], ldv, &work[work_offset] , ldwork); if (*m > *k) { /* W := W + C1**T * V1**T */ i__1 = *m - *k; igraphdgemm_("Transpose", "Transpose", n, k, &i__1, &c_b14, & c__[c_offset], ldc, &v[v_offset], ldv, &c_b14, & work[work_offset], ldwork); } /* W := W * T**T or W * T */ igraphdtrmm_("Right", "Lower", transt, "Non-unit", n, k, &c_b14, &t[ t_offset], ldt, &work[work_offset], ldwork); /* C := C - V**T * W**T */ if (*m > *k) { /* C1 := C1 - V1**T * W**T */ i__1 = *m - *k; igraphdgemm_("Transpose", "Transpose", &i__1, n, k, &c_b25, &v[ v_offset], ldv, &work[work_offset], ldwork, & c_b14, &c__[c_offset], ldc); } /* W := W * V2 */ igraphdtrmm_("Right", "Lower", "No transpose", "Unit", n, k, &c_b14, &v[(*m - *k + 1) * v_dim1 + 1], ldv, &work[ work_offset], ldwork); /* C2 := C2 - W**T */ i__1 = *k; for (j = 1; j <= i__1; ++j) { i__2 = *n; for (i__ = 1; i__ <= i__2; ++i__) { c__[*m - *k + j + i__ * c_dim1] -= work[i__ + j * work_dim1]; /* L200: */ } /* L210: */ } } else if (igraphlsame_(side, "R")) { /* Form C * H or C * H' where C = ( C1 C2 ) W := C * V**T = (C1*V1**T + C2*V2**T) (stored in WORK) W := C2 */ i__1 = *k; for (j = 1; j <= i__1; ++j) { igraphdcopy_(m, &c__[(*n - *k + j) * c_dim1 + 1], &c__1, &work[ j * work_dim1 + 1], &c__1); /* L220: */ } /* W := W * V2**T */ igraphdtrmm_("Right", "Lower", "Transpose", "Unit", m, k, &c_b14, & v[(*n - *k + 1) * v_dim1 + 1], ldv, &work[work_offset] , ldwork); if (*n > *k) { /* W := W + C1 * V1**T */ i__1 = *n - *k; igraphdgemm_("No transpose", "Transpose", m, k, &i__1, &c_b14, & c__[c_offset], ldc, &v[v_offset], ldv, &c_b14, & work[work_offset], ldwork); } /* W := W * T or W * T**T */ igraphdtrmm_("Right", "Lower", trans, "Non-unit", m, k, &c_b14, &t[ t_offset], ldt, &work[work_offset], ldwork); /* C := C - W * V */ if (*n > *k) { /* C1 := C1 - W * V1 */ i__1 = *n - *k; igraphdgemm_("No transpose", "No transpose", m, &i__1, k, & c_b25, &work[work_offset], ldwork, &v[v_offset], ldv, &c_b14, &c__[c_offset], ldc); } /* W := W * V2 */ igraphdtrmm_("Right", "Lower", "No transpose", "Unit", m, k, &c_b14, &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__) { c__[i__ + (*n - *k + j) * c_dim1] -= work[i__ + j * work_dim1]; /* L230: */ } /* L240: */ } } } } return 0; /* End of DLARFB */ } /* igraphdlarfb_ */