/* dgbbrd.f -- translated by f2c (version 20061008).
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"
#include "blaswrap.h"
/* Table of constant values */
static doublereal c_b8 = 0.;
static doublereal c_b9 = 1.;
static integer c__1 = 1;
/* Subroutine */ int dgbbrd_(char *vect, integer *m, integer *n, integer *ncc,
integer *kl, integer *ku, doublereal *ab, integer *ldab, doublereal *
d__, doublereal *e, doublereal *q, integer *ldq, doublereal *pt,
integer *ldpt, doublereal *c__, integer *ldc, doublereal *work,
integer *info)
{
/* 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;
/* Local variables */
integer i__, j, l, j1, j2, kb;
doublereal ra, rb, rc;
integer kk, ml, mn, nr, mu;
doublereal rs;
integer kb1, ml0, mu0, klm, kun, nrt, klu1, inca;
extern /* Subroutine */ int drot_(integer *, doublereal *, integer *,
doublereal *, integer *, doublereal *, doublereal *);
extern logical lsame_(char *, char *);
logical wantb, wantc;
integer minmn;
logical wantq;
extern /* Subroutine */ int dlaset_(char *, integer *, integer *,
doublereal *, doublereal *, doublereal *, integer *),
dlartg_(doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *), xerbla_(char *, integer *), dlargv_(
integer *, doublereal *, integer *, doublereal *, integer *,
doublereal *, integer *), dlartv_(integer *, doublereal *,
integer *, doublereal *, integer *, doublereal *, doublereal *,
integer *);
logical wantpt;
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DGBBRD reduces a real general m-by-n band matrix A to upper */
/* bidiagonal form B by an orthogonal 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) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (min(M,N)) */
/* The diagonal elements of the bidiagonal matrix B. */
/* E (output) DOUBLE PRECISION array, dimension (min(M,N)-1) */
/* The superdiagonal elements of the bidiagonal matrix B. */
/* Q (output) DOUBLE PRECISION array, dimension (LDQ,M) */
/* If VECT = 'Q' or 'B', the m-by-m orthogonal 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) DOUBLE PRECISION array, dimension (LDPT,N) */
/* If VECT = 'P' or 'B', the n-by-n orthogonal 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) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (2*max(M,N)) */
/* INFO (output) INTEGER */
/* = 0: successful exit. */
/* < 0: if INFO = -i, the i-th argument had an illegal value. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters */
/* Parameter adjustments */
ab_dim1 = *ldab;
ab_offset = 1 + ab_dim1;
ab -= ab_offset;
--d__;
--e;
q_dim1 = *ldq;
q_offset = 1 + q_dim1;
q -= q_offset;
pt_dim1 = *ldpt;
pt_offset = 1 + pt_dim1;
pt -= pt_offset;
c_dim1 = *ldc;
c_offset = 1 + c_dim1;
c__ -= c_offset;
--work;
/* 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_("DGBBRD", &i__1);
return 0;
}
/* Initialize Q and P' to the unit matrix, if needed */
if (wantq) {
dlaset_("Full", m, m, &c_b8, &c_b9, &q[q_offset], ldq);
}
if (wantpt) {
dlaset_("Full", n, n, &c_b8, &c_b9, &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 sines of the plane rotations are stored in WORK(1:max(m,n)) */
/* and the cosines in WORK(max(m,n)+1:2*max(m,n)). */
mn = max(*m,*n);
/* 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) {
dlargv_(&nr, &ab[klu1 + (j1 - klm - 1) * ab_dim1], &inca,
&work[j1], &kb1, &work[mn + 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) {
dlartv_(&nrt, &ab[klu1 - l + (j1 - klm + l - 1) *
ab_dim1], &inca, &ab[klu1 - l + 1 + (j1 - klm
+ l - 1) * ab_dim1], &inca, &work[mn + 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 */
dlartg_(&ab[*ku + ml - 1 + i__ * ab_dim1], &ab[*ku +
ml + i__ * ab_dim1], &work[mn + i__ + ml - 1],
&work[i__ + ml - 1], &ra);
ab[*ku + ml - 1 + i__ * ab_dim1] = ra;
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;
drot_(&i__3, &ab[*ku + ml - 2 + (i__ + 1) *
ab_dim1], &i__6, &ab[*ku + ml - 1 + (i__
+ 1) * ab_dim1], &i__7, &work[mn + 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)
{
drot_(m, &q[(j - 1) * q_dim1 + 1], &c__1, &q[j *
q_dim1 + 1], &c__1, &work[mn + j], &work[j]);
/* 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)
{
drot_(ncc, &c__[j - 1 + c_dim1], ldc, &c__[j + c_dim1]
, ldc, &work[mn + 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) */
work[j + kun] = work[j] * ab[(j + kun) * ab_dim1 + 1];
ab[(j + kun) * ab_dim1 + 1] = work[mn + j] * ab[(j + kun)
* ab_dim1 + 1];
/* L40: */
}
/* generate plane rotations to annihilate nonzero elements */
/* which have been generated above the band */
if (nr > 0) {
dlargv_(&nr, &ab[(j1 + kun - 1) * ab_dim1 + 1], &inca, &
work[j1 + kun], &kb1, &work[mn + 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) {
dlartv_(&nrt, &ab[l + 1 + (j1 + kun - 1) * ab_dim1], &
inca, &ab[l + (j1 + kun) * ab_dim1], &inca, &
work[mn + 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 */
dlartg_(&ab[*ku - mu + 3 + (i__ + mu - 2) * ab_dim1],
&ab[*ku - mu + 2 + (i__ + mu - 1) * ab_dim1],
&work[mn + i__ + mu - 1], &work[i__ + mu - 1],
&ra);
ab[*ku - mu + 3 + (i__ + mu - 2) * ab_dim1] = ra;
/* Computing MIN */
i__3 = *kl + mu - 2, i__5 = *m - i__;
i__4 = min(i__3,i__5);
drot_(&i__4, &ab[*ku - mu + 4 + (i__ + mu - 2) *
ab_dim1], &c__1, &ab[*ku - mu + 3 + (i__ + mu
- 1) * ab_dim1], &c__1, &work[mn + 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)
{
drot_(n, &pt[j + kun - 1 + pt_dim1], ldpt, &pt[j +
kun + pt_dim1], ldpt, &work[mn + j + kun], &
work[j + kun]);
/* 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) */
work[j + kb] = work[j + kun] * ab[klu1 + (j + kun) *
ab_dim1];
ab[klu1 + (j + kun) * ab_dim1] = work[mn + j + kun] * ab[
klu1 + (j + kun) * ab_dim1];
/* L70: */
}
if (ml > ml0) {
--ml;
} else {
--mu;
}
/* L80: */
}
/* L90: */
}
}
if (*ku == 0 && *kl > 0) {
/* A has been reduced to lower bidiagonal form */
/* Transform lower bidiagonal form to upper bidiagonal by applying */
/* plane rotations from the left, storing diagonal elements in D */
/* and off-diagonal elements in E */
/* Computing MIN */
i__2 = *m - 1;
i__1 = min(i__2,*n);
for (i__ = 1; i__ <= i__1; ++i__) {
dlartg_(&ab[i__ * ab_dim1 + 1], &ab[i__ * ab_dim1 + 2], &rc, &rs,
&ra);
d__[i__] = ra;
if (i__ < *n) {
e[i__] = rs * ab[(i__ + 1) * ab_dim1 + 1];
ab[(i__ + 1) * ab_dim1 + 1] = rc * ab[(i__ + 1) * ab_dim1 + 1]
;
}
if (wantq) {
drot_(m, &q[i__ * q_dim1 + 1], &c__1, &q[(i__ + 1) * q_dim1 +
1], &c__1, &rc, &rs);
}
if (wantc) {
drot_(ncc, &c__[i__ + c_dim1], ldc, &c__[i__ + 1 + c_dim1],
ldc, &rc, &rs);
}
/* L100: */
}
if (*m <= *n) {
d__[*m] = ab[*m * ab_dim1 + 1];
}
} else if (*ku > 0) {
/* A has been reduced to upper bidiagonal form */
if (*m < *n) {
/* Annihilate a(m,m+1) by applying plane rotations from the */
/* right, storing diagonal elements in D and off-diagonal */
/* elements in E */
rb = ab[*ku + (*m + 1) * ab_dim1];
for (i__ = *m; i__ >= 1; --i__) {
dlartg_(&ab[*ku + 1 + i__ * ab_dim1], &rb, &rc, &rs, &ra);
d__[i__] = ra;
if (i__ > 1) {
rb = -rs * ab[*ku + i__ * ab_dim1];
e[i__ - 1] = rc * ab[*ku + i__ * ab_dim1];
}
if (wantpt) {
drot_(n, &pt[i__ + pt_dim1], ldpt, &pt[*m + 1 + pt_dim1],
ldpt, &rc, &rs);
}
/* L110: */
}
} else {
/* Copy off-diagonal elements to E and diagonal elements to D */
i__1 = minmn - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
e[i__] = ab[*ku + (i__ + 1) * ab_dim1];
/* L120: */
}
i__1 = minmn;
for (i__ = 1; i__ <= i__1; ++i__) {
d__[i__] = ab[*ku + 1 + i__ * ab_dim1];
/* L130: */
}
}
} else {
/* A is diagonal. Set elements of E to zero and copy diagonal */
/* elements to D. */
i__1 = minmn - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
e[i__] = 0.;
/* L140: */
}
i__1 = minmn;
for (i__ = 1; i__ <= i__1; ++i__) {
d__[i__] = ab[i__ * ab_dim1 + 1];
/* L150: */
}
}
return 0;
/* End of DGBBRD */
} /* dgbbrd_ */