#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int cgbbrd_(char *vect, integer *m, integer *n, integer *ncc, integer *kl, integer *ku, complex *ab, integer *ldab, real *d__, real *e, complex *q, integer *ldq, complex *pt, integer *ldpt, complex *c__, integer *ldc, complex *work, real *rwork, integer *info) { /* -- LAPACK routine (version 3.0) -- Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., Courant Institute, Argonne National Lab, and Rice University September 30, 1994 Purpose ======= CGBBRD reduces a complex general m-by-n band matrix A to real upper bidiagonal form B by a unitary transformation: Q' * A * P = B. The routine computes B, and optionally forms Q or P', or computes Q'*C for a given matrix C. Arguments ========= VECT (input) CHARACTER*1 Specifies whether or not the matrices Q and P' are to be formed. = 'N': do not form Q or P'; = 'Q': form Q only; = 'P': form P' only; = 'B': form both. M (input) INTEGER The number of rows of the matrix A. M >= 0. N (input) INTEGER The number of columns of the matrix A. N >= 0. NCC (input) INTEGER The number of columns of the matrix C. NCC >= 0. KL (input) INTEGER The number of subdiagonals of the matrix A. KL >= 0. KU (input) INTEGER The number of superdiagonals of the matrix A. KU >= 0. AB (input/output) COMPLEX array, dimension (LDAB,N) On entry, the m-by-n band matrix A, stored in rows 1 to KL+KU+1. The j-th column of A is stored in the j-th column of the array AB as follows: AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl). On exit, A is overwritten by values generated during the reduction. LDAB (input) INTEGER The leading dimension of the array A. LDAB >= KL+KU+1. D (output) REAL array, dimension (min(M,N)) The diagonal elements of the bidiagonal matrix B. E (output) REAL array, dimension (min(M,N)-1) The superdiagonal elements of the bidiagonal matrix B. Q (output) COMPLEX array, dimension (LDQ,M) If VECT = 'Q' or 'B', the m-by-m unitary matrix Q. If VECT = 'N' or 'P', the array Q is not referenced. LDQ (input) INTEGER The leading dimension of the array Q. LDQ >= max(1,M) if VECT = 'Q' or 'B'; LDQ >= 1 otherwise. PT (output) COMPLEX array, dimension (LDPT,N) If VECT = 'P' or 'B', the n-by-n unitary matrix P'. If VECT = 'N' or 'Q', the array PT is not referenced. LDPT (input) INTEGER The leading dimension of the array PT. LDPT >= max(1,N) if VECT = 'P' or 'B'; LDPT >= 1 otherwise. C (input/output) COMPLEX array, dimension (LDC,NCC) On entry, an m-by-ncc matrix C. On exit, C is overwritten by Q'*C. C is not referenced if NCC = 0. LDC (input) INTEGER The leading dimension of the array C. LDC >= max(1,M) if NCC > 0; LDC >= 1 if NCC = 0. WORK (workspace) COMPLEX array, dimension (max(M,N)) RWORK (workspace) REAL array, dimension (max(M,N)) INFO (output) INTEGER = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. ===================================================================== Test the input parameters Parameter adjustments */ /* Table of constant values */ static complex c_b1 = {0.f,0.f}; static complex c_b2 = {1.f,0.f}; static integer c__1 = 1; /* System generated locals */ integer ab_dim1, ab_offset, c_dim1, c_offset, pt_dim1, pt_offset, q_dim1, q_offset, i__1, i__2, i__3, i__4, i__5, i__6, i__7; complex q__1, q__2, q__3; /* Builtin functions */ void r_cnjg(complex *, complex *); double c_abs(complex *); /* Local variables */ static integer inca; static real abst; extern /* Subroutine */ int crot_(integer *, complex *, integer *, complex *, integer *, real *, complex *); static integer i__, j, l; static complex t; extern /* Subroutine */ int cscal_(integer *, complex *, complex *, integer *); extern logical lsame_(char *, char *); static logical wantb, wantc; static integer minmn; static logical wantq; static integer j1, j2, kb; static complex ra; static real rc; static integer kk; static complex rb; static integer ml, nr, mu; static complex rs; extern /* Subroutine */ int claset_(char *, integer *, integer *, complex *, complex *, complex *, integer *), clartg_(complex *, complex *, real *, complex *, complex *), xerbla_(char *, integer *), clargv_(integer *, complex *, integer *, complex *, integer *, real *, integer *), clartv_(integer *, complex *, integer *, complex *, integer *, real *, complex *, integer *); static integer kb1, ml0; static logical wantpt; static integer mu0, klm, kun, nrt, klu1; #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)] #define q_subscr(a_1,a_2) (a_2)*q_dim1 + a_1 #define q_ref(a_1,a_2) q[q_subscr(a_1,a_2)] #define ab_subscr(a_1,a_2) (a_2)*ab_dim1 + a_1 #define ab_ref(a_1,a_2) ab[ab_subscr(a_1,a_2)] #define pt_subscr(a_1,a_2) (a_2)*pt_dim1 + a_1 #define pt_ref(a_1,a_2) pt[pt_subscr(a_1,a_2)] ab_dim1 = *ldab; ab_offset = 1 + ab_dim1 * 1; ab -= ab_offset; --d__; --e; q_dim1 = *ldq; q_offset = 1 + q_dim1 * 1; q -= q_offset; pt_dim1 = *ldpt; pt_offset = 1 + pt_dim1 * 1; pt -= pt_offset; c_dim1 = *ldc; c_offset = 1 + c_dim1 * 1; c__ -= c_offset; --work; --rwork; /* Function Body */ wantb = lsame_(vect, "B"); wantq = lsame_(vect, "Q") || wantb; wantpt = lsame_(vect, "P") || wantb; wantc = *ncc > 0; klu1 = *kl + *ku + 1; *info = 0; if (! wantq && ! wantpt && ! lsame_(vect, "N")) { *info = -1; } else if (*m < 0) { *info = -2; } else if (*n < 0) { *info = -3; } else if (*ncc < 0) { *info = -4; } else if (*kl < 0) { *info = -5; } else if (*ku < 0) { *info = -6; } else if (*ldab < klu1) { *info = -8; } else if (*ldq < 1 || wantq && *ldq < max(1,*m)) { *info = -12; } else if (*ldpt < 1 || wantpt && *ldpt < max(1,*n)) { *info = -14; } else if (*ldc < 1 || wantc && *ldc < max(1,*m)) { *info = -16; } if (*info != 0) { i__1 = -(*info); xerbla_("CGBBRD", &i__1); return 0; } /* Initialize Q and P' to the unit matrix, if needed */ if (wantq) { claset_("Full", m, m, &c_b1, &c_b2, &q[q_offset], ldq); } if (wantpt) { claset_("Full", n, n, &c_b1, &c_b2, &pt[pt_offset], ldpt); } /* Quick return if possible. */ if (*m == 0 || *n == 0) { return 0; } minmn = min(*m,*n); if (*kl + *ku > 1) { /* Reduce to upper bidiagonal form if KU > 0; if KU = 0, reduce first to lower bidiagonal form and then transform to upper bidiagonal */ if (*ku > 0) { ml0 = 1; mu0 = 2; } else { ml0 = 2; mu0 = 1; } /* Wherever possible, plane rotations are generated and applied in vector operations of length NR over the index set J1:J2:KLU1. The complex sines of the plane rotations are stored in WORK, and the real cosines in RWORK. Computing MIN */ i__1 = *m - 1; klm = min(i__1,*kl); /* Computing MIN */ i__1 = *n - 1; kun = min(i__1,*ku); kb = klm + kun; kb1 = kb + 1; inca = kb1 * *ldab; nr = 0; j1 = klm + 2; j2 = 1 - kun; i__1 = minmn; for (i__ = 1; i__ <= i__1; ++i__) { /* Reduce i-th column and i-th row of matrix to bidiagonal form */ ml = klm + 1; mu = kun + 1; i__2 = kb; for (kk = 1; kk <= i__2; ++kk) { j1 += kb; j2 += kb; /* generate plane rotations to annihilate nonzero elements which have been created below the band */ if (nr > 0) { clargv_(&nr, &ab_ref(klu1, j1 - klm - 1), &inca, &work[j1] , &kb1, &rwork[j1], &kb1); } /* apply plane rotations from the left */ i__3 = kb; for (l = 1; l <= i__3; ++l) { if (j2 - klm + l - 1 > *n) { nrt = nr - 1; } else { nrt = nr; } if (nrt > 0) { clartv_(&nrt, &ab_ref(klu1 - l, j1 - klm + l - 1), & inca, &ab_ref(klu1 - l + 1, j1 - klm + l - 1), &inca, &rwork[j1], &work[j1], &kb1); } /* L10: */ } if (ml > ml0) { if (ml <= *m - i__ + 1) { /* generate plane rotation to annihilate a(i+ml-1,i) within the band, and apply rotation from the left */ clartg_(&ab_ref(*ku + ml - 1, i__), &ab_ref(*ku + ml, i__), &rwork[i__ + ml - 1], &work[i__ + ml - 1], &ra); i__3 = ab_subscr(*ku + ml - 1, i__); ab[i__3].r = ra.r, ab[i__3].i = ra.i; if (i__ < *n) { /* Computing MIN */ i__4 = *ku + ml - 2, i__5 = *n - i__; i__3 = min(i__4,i__5); i__6 = *ldab - 1; i__7 = *ldab - 1; crot_(&i__3, &ab_ref(*ku + ml - 2, i__ + 1), & i__6, &ab_ref(*ku + ml - 1, i__ + 1), & i__7, &rwork[i__ + ml - 1], &work[i__ + ml - 1]); } } ++nr; j1 -= kb1; } if (wantq) { /* accumulate product of plane rotations in Q */ i__3 = j2; i__4 = kb1; for (j = j1; i__4 < 0 ? j >= i__3 : j <= i__3; j += i__4) { r_cnjg(&q__1, &work[j]); crot_(m, &q_ref(1, j - 1), &c__1, &q_ref(1, j), &c__1, &rwork[j], &q__1); /* L20: */ } } if (wantc) { /* apply plane rotations to C */ i__4 = j2; i__3 = kb1; for (j = j1; i__3 < 0 ? j >= i__4 : j <= i__4; j += i__3) { crot_(ncc, &c___ref(j - 1, 1), ldc, &c___ref(j, 1), ldc, &rwork[j], &work[j]); /* L30: */ } } if (j2 + kun > *n) { /* adjust J2 to keep within the bounds of the matrix */ --nr; j2 -= kb1; } i__3 = j2; i__4 = kb1; for (j = j1; i__4 < 0 ? j >= i__3 : j <= i__3; j += i__4) { /* create nonzero element a(j-1,j+ku) above the band and store it in WORK(n+1:2*n) */ i__5 = j + kun; i__6 = j; i__7 = ab_subscr(1, j + kun); q__1.r = work[i__6].r * ab[i__7].r - work[i__6].i * ab[ i__7].i, q__1.i = work[i__6].r * ab[i__7].i + work[i__6].i * ab[i__7].r; work[i__5].r = q__1.r, work[i__5].i = q__1.i; i__5 = ab_subscr(1, j + kun); i__6 = j; i__7 = ab_subscr(1, j + kun); q__1.r = rwork[i__6] * ab[i__7].r, q__1.i = rwork[i__6] * ab[i__7].i; ab[i__5].r = q__1.r, ab[i__5].i = q__1.i; /* L40: */ } /* generate plane rotations to annihilate nonzero elements which have been generated above the band */ if (nr > 0) { clargv_(&nr, &ab_ref(1, j1 + kun - 1), &inca, &work[j1 + kun], &kb1, &rwork[j1 + kun], &kb1); } /* apply plane rotations from the right */ i__4 = kb; for (l = 1; l <= i__4; ++l) { if (j2 + l - 1 > *m) { nrt = nr - 1; } else { nrt = nr; } if (nrt > 0) { clartv_(&nrt, &ab_ref(l + 1, j1 + kun - 1), &inca, & ab_ref(l, j1 + kun), &inca, &rwork[j1 + kun], &work[j1 + kun], &kb1); } /* L50: */ } if (ml == ml0 && mu > mu0) { if (mu <= *n - i__ + 1) { /* generate plane rotation to annihilate a(i,i+mu-1) within the band, and apply rotation from the right */ clartg_(&ab_ref(*ku - mu + 3, i__ + mu - 2), &ab_ref(* ku - mu + 2, i__ + mu - 1), &rwork[i__ + mu - 1], &work[i__ + mu - 1], &ra); i__4 = ab_subscr(*ku - mu + 3, i__ + mu - 2); ab[i__4].r = ra.r, ab[i__4].i = ra.i; /* Computing MIN */ i__3 = *kl + mu - 2, i__5 = *m - i__; i__4 = min(i__3,i__5); crot_(&i__4, &ab_ref(*ku - mu + 4, i__ + mu - 2), & c__1, &ab_ref(*ku - mu + 3, i__ + mu - 1), & c__1, &rwork[i__ + mu - 1], &work[i__ + mu - 1]); } ++nr; j1 -= kb1; } if (wantpt) { /* accumulate product of plane rotations in P' */ i__4 = j2; i__3 = kb1; for (j = j1; i__3 < 0 ? j >= i__4 : j <= i__4; j += i__3) { r_cnjg(&q__1, &work[j + kun]); crot_(n, &pt_ref(j + kun - 1, 1), ldpt, &pt_ref(j + kun, 1), ldpt, &rwork[j + kun], &q__1); /* L60: */ } } if (j2 + kb > *m) { /* adjust J2 to keep within the bounds of the matrix */ --nr; j2 -= kb1; } i__3 = j2; i__4 = kb1; for (j = j1; i__4 < 0 ? j >= i__3 : j <= i__3; j += i__4) { /* create nonzero element a(j+kl+ku,j+ku-1) below the band and store it in WORK(1:n) */ i__5 = j + kb; i__6 = j + kun; i__7 = ab_subscr(klu1, j + kun); q__1.r = work[i__6].r * ab[i__7].r - work[i__6].i * ab[ i__7].i, q__1.i = work[i__6].r * ab[i__7].i + work[i__6].i * ab[i__7].r; work[i__5].r = q__1.r, work[i__5].i = q__1.i; i__5 = ab_subscr(klu1, j + kun); i__6 = j + kun; i__7 = ab_subscr(klu1, j + kun); q__1.r = rwork[i__6] * ab[i__7].r, q__1.i = rwork[i__6] * ab[i__7].i; ab[i__5].r = q__1.r, ab[i__5].i = q__1.i; /* L70: */ } if (ml > ml0) { --ml; } else { --mu; } /* L80: */ } /* L90: */ } } if (*ku == 0 && *kl > 0) { /* A has been reduced to complex lower bidiagonal form Transform lower bidiagonal form to upper bidiagonal by applying plane rotations from the left, overwriting superdiagonal elements on subdiagonal elements Computing MIN */ i__2 = *m - 1; i__1 = min(i__2,*n); for (i__ = 1; i__ <= i__1; ++i__) { clartg_(&ab_ref(1, i__), &ab_ref(2, i__), &rc, &rs, &ra); i__2 = ab_subscr(1, i__); ab[i__2].r = ra.r, ab[i__2].i = ra.i; if (i__ < *n) { i__2 = ab_subscr(2, i__); i__4 = ab_subscr(1, i__ + 1); q__1.r = rs.r * ab[i__4].r - rs.i * ab[i__4].i, q__1.i = rs.r * ab[i__4].i + rs.i * ab[i__4].r; ab[i__2].r = q__1.r, ab[i__2].i = q__1.i; i__2 = ab_subscr(1, i__ + 1); i__4 = ab_subscr(1, i__ + 1); q__1.r = rc * ab[i__4].r, q__1.i = rc * ab[i__4].i; ab[i__2].r = q__1.r, ab[i__2].i = q__1.i; } if (wantq) { r_cnjg(&q__1, &rs); crot_(m, &q_ref(1, i__), &c__1, &q_ref(1, i__ + 1), &c__1, & rc, &q__1); } if (wantc) { crot_(ncc, &c___ref(i__, 1), ldc, &c___ref(i__ + 1, 1), ldc, & rc, &rs); } /* L100: */ } } else { /* A has been reduced to complex upper bidiagonal form or is diagonal */ if (*ku > 0 && *m < *n) { /* Annihilate a(m,m+1) by applying plane rotations from the right */ i__1 = ab_subscr(*ku, *m + 1); rb.r = ab[i__1].r, rb.i = ab[i__1].i; for (i__ = *m; i__ >= 1; --i__) { clartg_(&ab_ref(*ku + 1, i__), &rb, &rc, &rs, &ra); i__1 = ab_subscr(*ku + 1, i__); ab[i__1].r = ra.r, ab[i__1].i = ra.i; if (i__ > 1) { r_cnjg(&q__3, &rs); q__2.r = -q__3.r, q__2.i = -q__3.i; i__1 = ab_subscr(*ku, i__); q__1.r = q__2.r * ab[i__1].r - q__2.i * ab[i__1].i, q__1.i = q__2.r * ab[i__1].i + q__2.i * ab[i__1] .r; rb.r = q__1.r, rb.i = q__1.i; i__1 = ab_subscr(*ku, i__); i__2 = ab_subscr(*ku, i__); q__1.r = rc * ab[i__2].r, q__1.i = rc * ab[i__2].i; ab[i__1].r = q__1.r, ab[i__1].i = q__1.i; } if (wantpt) { r_cnjg(&q__1, &rs); crot_(n, &pt_ref(i__, 1), ldpt, &pt_ref(*m + 1, 1), ldpt, &rc, &q__1); } /* L110: */ } } } /* Make diagonal and superdiagonal elements real, storing them in D and E */ i__1 = ab_subscr(*ku + 1, 1); t.r = ab[i__1].r, t.i = ab[i__1].i; i__1 = minmn; for (i__ = 1; i__ <= i__1; ++i__) { abst = c_abs(&t); d__[i__] = abst; if (abst != 0.f) { q__1.r = t.r / abst, q__1.i = t.i / abst; t.r = q__1.r, t.i = q__1.i; } else { t.r = 1.f, t.i = 0.f; } if (wantq) { cscal_(m, &t, &q_ref(1, i__), &c__1); } if (wantc) { r_cnjg(&q__1, &t); cscal_(ncc, &q__1, &c___ref(i__, 1), ldc); } if (i__ < minmn) { if (*ku == 0 && *kl == 0) { e[i__] = 0.f; i__2 = ab_subscr(1, i__ + 1); t.r = ab[i__2].r, t.i = ab[i__2].i; } else { if (*ku == 0) { i__2 = ab_subscr(2, i__); r_cnjg(&q__2, &t); q__1.r = ab[i__2].r * q__2.r - ab[i__2].i * q__2.i, q__1.i = ab[i__2].r * q__2.i + ab[i__2].i * q__2.r; t.r = q__1.r, t.i = q__1.i; } else { i__2 = ab_subscr(*ku, i__ + 1); r_cnjg(&q__2, &t); q__1.r = ab[i__2].r * q__2.r - ab[i__2].i * q__2.i, q__1.i = ab[i__2].r * q__2.i + ab[i__2].i * q__2.r; t.r = q__1.r, t.i = q__1.i; } abst = c_abs(&t); e[i__] = abst; if (abst != 0.f) { q__1.r = t.r / abst, q__1.i = t.i / abst; t.r = q__1.r, t.i = q__1.i; } else { t.r = 1.f, t.i = 0.f; } if (wantpt) { cscal_(n, &t, &pt_ref(i__ + 1, 1), ldpt); } i__2 = ab_subscr(*ku + 1, i__ + 1); r_cnjg(&q__2, &t); q__1.r = ab[i__2].r * q__2.r - ab[i__2].i * q__2.i, q__1.i = ab[i__2].r * q__2.i + ab[i__2].i * q__2.r; t.r = q__1.r, t.i = q__1.i; } } /* L120: */ } return 0; /* End of CGBBRD */ } /* cgbbrd_ */ #undef pt_ref #undef pt_subscr #undef ab_ref #undef ab_subscr #undef q_ref #undef q_subscr #undef c___ref #undef c___subscr