#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int zunmbr_(char *vect, char *side, char *trans, integer *m, integer *n, integer *k, doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex *c__, integer *ldc, doublecomplex *work, integer * lwork, integer *info) { /* -- LAPACK routine (version 3.0) -- Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., Courant Institute, Argonne National Lab, and Rice University June 30, 1999 Purpose ======= If VECT = 'Q', ZUNMBR overwrites the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'C': Q**H * C C * Q**H If VECT = 'P', ZUNMBR overwrites the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': P * C C * P TRANS = 'C': P**H * C C * P**H Here Q and P**H are the unitary matrices determined by ZGEBRD when reducing a complex matrix A to bidiagonal form: A = Q * B * P**H. Q and P**H are defined as products of elementary reflectors H(i) and G(i) respectively. Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the order of the unitary matrix Q or P**H that is applied. If VECT = 'Q', A is assumed to have been an NQ-by-K matrix: if nq >= k, Q = H(1) H(2) . . . H(k); if nq < k, Q = H(1) H(2) . . . H(nq-1). If VECT = 'P', A is assumed to have been a K-by-NQ matrix: if k < nq, P = G(1) G(2) . . . G(k); if k >= nq, P = G(1) G(2) . . . G(nq-1). Arguments ========= VECT (input) CHARACTER*1 = 'Q': apply Q or Q**H; = 'P': apply P or P**H. SIDE (input) CHARACTER*1 = 'L': apply Q, Q**H, P or P**H from the Left; = 'R': apply Q, Q**H, P or P**H from the Right. TRANS (input) CHARACTER*1 = 'N': No transpose, apply Q or P; = 'C': Conjugate transpose, apply Q**H or P**H. M (input) INTEGER The number of rows of the matrix C. M >= 0. N (input) INTEGER The number of columns of the matrix C. N >= 0. K (input) INTEGER If VECT = 'Q', the number of columns in the original matrix reduced by ZGEBRD. If VECT = 'P', the number of rows in the original matrix reduced by ZGEBRD. K >= 0. A (input) COMPLEX*16 array, dimension (LDA,min(nq,K)) if VECT = 'Q' (LDA,nq) if VECT = 'P' The vectors which define the elementary reflectors H(i) and G(i), whose products determine the matrices Q and P, as returned by ZGEBRD. LDA (input) INTEGER The leading dimension of the array A. If VECT = 'Q', LDA >= max(1,nq); if VECT = 'P', LDA >= max(1,min(nq,K)). TAU (input) COMPLEX*16 array, dimension (min(nq,K)) TAU(i) must contain the scalar factor of the elementary reflector H(i) or G(i) which determines Q or P, as returned by ZGEBRD in the array argument TAUQ or TAUP. C (input/output) COMPLEX*16 array, dimension (LDC,N) On entry, the M-by-N matrix C. On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q or P*C or P**H*C or C*P or C*P**H. LDC (input) INTEGER The leading dimension of the array C. LDC >= max(1,M). WORK (workspace/output) COMPLEX*16 array, dimension (LWORK) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. LWORK (input) INTEGER The dimension of the array WORK. If SIDE = 'L', LWORK >= max(1,N); if SIDE = 'R', LWORK >= max(1,M). For optimum performance LWORK >= N*NB if SIDE = 'L', and LWORK >= M*NB if SIDE = 'R', where NB is the optimal blocksize. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA. INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value ===================================================================== Test the input arguments Parameter adjustments */ /* Table of constant values */ static integer c__1 = 1; static integer c_n1 = -1; static integer c__2 = 2; /* System generated locals */ address a__1[2]; integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__3[2]; char ch__1[2]; /* Builtin functions Subroutine */ int s_cat(char *, char **, integer *, integer *, ftnlen); /* Local variables */ static logical left; extern logical lsame_(char *, char *); static integer iinfo, i1, i2, nb, mi, ni, nq, nw; extern /* Subroutine */ int xerbla_(char *, integer *); extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, ftnlen, ftnlen); static logical notran, applyq; static char transt[1]; static integer lwkopt; static logical lquery; extern /* Subroutine */ int zunmlq_(char *, char *, integer *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, integer *), zunmqr_(char *, char *, integer *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, integer *); #define a_subscr(a_1,a_2) (a_2)*a_dim1 + a_1 #define a_ref(a_1,a_2) a[a_subscr(a_1,a_2)] #define c___subscr(a_1,a_2) (a_2)*c_dim1 + a_1 #define c___ref(a_1,a_2) c__[c___subscr(a_1,a_2)] a_dim1 = *lda; a_offset = 1 + a_dim1 * 1; a -= a_offset; --tau; c_dim1 = *ldc; c_offset = 1 + c_dim1 * 1; c__ -= c_offset; --work; /* Function Body */ *info = 0; applyq = lsame_(vect, "Q"); left = lsame_(side, "L"); notran = lsame_(trans, "N"); lquery = *lwork == -1; /* NQ is the order of Q or P and NW is the minimum dimension of WORK */ if (left) { nq = *m; nw = *n; } else { nq = *n; nw = *m; } if (! applyq && ! lsame_(vect, "P")) { *info = -1; } else if (! left && ! lsame_(side, "R")) { *info = -2; } else if (! notran && ! lsame_(trans, "C")) { *info = -3; } else if (*m < 0) { *info = -4; } else if (*n < 0) { *info = -5; } else if (*k < 0) { *info = -6; } else /* if(complicated condition) */ { /* Computing MAX */ i__1 = 1, i__2 = min(nq,*k); if (applyq && *lda < max(1,nq) || ! applyq && *lda < max(i__1,i__2)) { *info = -8; } else if (*ldc < max(1,*m)) { *info = -11; } else if (*lwork < max(1,nw) && ! lquery) { *info = -13; } } if (*info == 0) { if (applyq) { if (left) { /* Writing concatenation */ i__3[0] = 1, a__1[0] = side; i__3[1] = 1, a__1[1] = trans; s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); i__1 = *m - 1; i__2 = *m - 1; nb = ilaenv_(&c__1, "ZUNMQR", ch__1, &i__1, n, &i__2, &c_n1, ( ftnlen)6, (ftnlen)2); } else { /* Writing concatenation */ i__3[0] = 1, a__1[0] = side; i__3[1] = 1, a__1[1] = trans; s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); i__1 = *n - 1; i__2 = *n - 1; nb = ilaenv_(&c__1, "ZUNMQR", ch__1, m, &i__1, &i__2, &c_n1, ( ftnlen)6, (ftnlen)2); } } else { if (left) { /* Writing concatenation */ i__3[0] = 1, a__1[0] = side; i__3[1] = 1, a__1[1] = trans; s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); i__1 = *m - 1; i__2 = *m - 1; nb = ilaenv_(&c__1, "ZUNMLQ", ch__1, &i__1, n, &i__2, &c_n1, ( ftnlen)6, (ftnlen)2); } else { /* Writing concatenation */ i__3[0] = 1, a__1[0] = side; i__3[1] = 1, a__1[1] = trans; s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); i__1 = *n - 1; i__2 = *n - 1; nb = ilaenv_(&c__1, "ZUNMLQ", ch__1, m, &i__1, &i__2, &c_n1, ( ftnlen)6, (ftnlen)2); } } lwkopt = max(1,nw) * nb; work[1].r = (doublereal) lwkopt, work[1].i = 0.; } if (*info != 0) { i__1 = -(*info); xerbla_("ZUNMBR", &i__1); return 0; } else if (lquery) { } /* Quick return if possible */ work[1].r = 1., work[1].i = 0.; if (*m == 0 || *n == 0) { return 0; } if (applyq) { /* Apply Q */ if (nq >= *k) { /* Q was determined by a call to ZGEBRD with nq >= k */ zunmqr_(side, trans, m, n, k, &a[a_offset], lda, &tau[1], &c__[ c_offset], ldc, &work[1], lwork, &iinfo); } else if (nq > 1) { /* Q was determined by a call to ZGEBRD with nq < k */ if (left) { mi = *m - 1; ni = *n; i1 = 2; i2 = 1; } else { mi = *m; ni = *n - 1; i1 = 1; i2 = 2; } i__1 = nq - 1; zunmqr_(side, trans, &mi, &ni, &i__1, &a_ref(2, 1), lda, &tau[1], &c___ref(i1, i2), ldc, &work[1], lwork, &iinfo); } } else { /* Apply P */ if (notran) { *(unsigned char *)transt = 'C'; } else { *(unsigned char *)transt = 'N'; } if (nq > *k) { /* P was determined by a call to ZGEBRD with nq > k */ zunmlq_(side, transt, m, n, k, &a[a_offset], lda, &tau[1], &c__[ c_offset], ldc, &work[1], lwork, &iinfo); } else if (nq > 1) { /* P was determined by a call to ZGEBRD with nq <= k */ if (left) { mi = *m - 1; ni = *n; i1 = 2; i2 = 1; } else { mi = *m; ni = *n - 1; i1 = 1; i2 = 2; } i__1 = nq - 1; zunmlq_(side, transt, &mi, &ni, &i__1, &a_ref(1, 2), lda, &tau[1], &c___ref(i1, i2), ldc, &work[1], lwork, &iinfo); } } work[1].r = (doublereal) lwkopt, work[1].i = 0.; return 0; /* End of ZUNMBR */ } /* zunmbr_ */ #undef c___ref #undef c___subscr #undef a_ref #undef a_subscr