/* Subroutine */ int dormrz_(char *side, char *trans, integer *m, integer *n,
integer *k, integer *l, doublereal *a, integer *lda, doublereal *tau,
doublereal *c__, integer *ldc, doublereal *work, integer *lwork,
integer *info)
{
/* System generated locals */
address a__1[2];
integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__3[2], i__4,
i__5;
char ch__1[2];
/* Builtin functions */
/* Subroutine */ int s_cat(char *, char **, integer *, integer *, ftnlen);
/* Local variables */
integer i__;
#ifdef LAPACK_DISABLE_MEMORY_HOGS
doublereal t[1] /* was [65][64] */;
/** This function uses too much memory, so we stopped allocating the memory
* above and assert false here. */
assert(0 && "dormrz_ was called. This function allocates too much"
" memory and has been disabled.");
#else
doublereal t[4160] /* was [65][64] */;
#endif
integer i1, i2, i3, ib, ic, ja, jc, nb, mi, ni, nq, nw, iws;
logical left;
extern logical lsame_(char *, char *);
integer nbmin, iinfo;
extern /* Subroutine */ int dormr3_(char *, char *, integer *, integer *,
integer *, integer *, doublereal *, integer *, doublereal *,
doublereal *, integer *, doublereal *, integer *),
xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *);
extern /* Subroutine */ int dlarzb_(char *, char *, char *, char *,
integer *, integer *, integer *, integer *, doublereal *, integer
*, doublereal *, integer *, doublereal *, integer *, doublereal *,
integer *), dlarzt_(char *, char
*, integer *, integer *, doublereal *, integer *, doublereal *,
doublereal *, integer *);
logical notran;
integer ldwork;
char transt[1];
integer lwkopt;
logical lquery;
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* January 2007 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DORMRZ overwrites the general real M-by-N matrix C with */
/* SIDE = 'L' SIDE = 'R' */
/* TRANS = 'N': Q * C C * Q */
/* TRANS = 'T': Q**T * C C * Q**T */
/* where Q is a real orthogonal matrix defined as the product of k */
/* elementary reflectors */
/* Q = H(1) H(2) . . . H(k) */
/* as returned by DTZRZF. Q is of order M if SIDE = 'L' and of order N */
/* if SIDE = 'R'. */
/* Arguments */
/* ========= */
/* SIDE (input) CHARACTER*1 */
/* = 'L': apply Q or Q**T from the Left; */
/* = 'R': apply Q or Q**T from the Right. */
/* TRANS (input) CHARACTER*1 */
/* = 'N': No transpose, apply Q; */
/* = 'T': Transpose, apply Q**T. */
/* 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 */
/* The number of elementary reflectors whose product defines */
/* the matrix Q. */
/* If SIDE = 'L', M >= K >= 0; */
/* if SIDE = 'R', N >= K >= 0. */
/* L (input) INTEGER */
/* The number of columns of the matrix A containing */
/* the meaningful part of the Householder reflectors. */
/* If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0. */
/* A (input) DOUBLE PRECISION array, dimension */
/* (LDA,M) if SIDE = 'L', */
/* (LDA,N) if SIDE = 'R' */
/* The i-th row must contain the vector which defines the */
/* elementary reflector H(i), for i = 1,2,...,k, as returned by */
/* DTZRZF in the last k rows of its array argument A. */
/* A is modified by the routine but restored on exit. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,K). */
/* TAU (input) DOUBLE PRECISION array, dimension (K) */
/* TAU(i) must contain the scalar factor of the elementary */
/* reflector H(i), as returned by DTZRZF. */
/* C (input/output) DOUBLE PRECISION 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. */
/* LDC (input) INTEGER */
/* The leading dimension of the array C. LDC >= max(1,M). */
/* WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,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 */
/* Further Details */
/* =============== */
/* Based on contributions by */
/* A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input arguments */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--tau;
c_dim1 = *ldc;
c_offset = 1 + c_dim1;
c__ -= c_offset;
--work;
/* Function Body */
*info = 0;
left = lsame_(side, "L");
notran = lsame_(trans, "N");
lquery = *lwork == -1;
/* NQ is the order of Q and NW is the minimum dimension of WORK */
if (left) {
nq = *m;
nw = max(1,*n);
} else {
nq = *n;
nw = max(1,*m);
}
if (! left && ! lsame_(side, "R")) {
*info = -1;
} else if (! notran && ! lsame_(trans, "T")) {
*info = -2;
} else if (*m < 0) {
*info = -3;
} else if (*n < 0) {
*info = -4;
} else if (*k < 0 || *k > nq) {
*info = -5;
} else if (*l < 0 || left && *l > *m || ! left && *l > *n) {
*info = -6;
} else if (*lda < max(1,*k)) {
*info = -8;
} else if (*ldc < max(1,*m)) {
*info = -11;
}
if (*info == 0) {
if (*m == 0 || *n == 0) {
lwkopt = 1;
} else {
/* Determine the block size. NB may be at most NBMAX, where */
/* NBMAX is used to define the local array T. */
/* Computing MIN */
/* 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 = 64, i__2 = ilaenv_(&c__1, "DORMRQ", ch__1, m, n, k, &c_n1);
nb = min(i__1,i__2);
lwkopt = nw * nb;
}
work[1] = (doublereal) lwkopt;
if (*lwork < max(1,nw) && ! lquery) {
*info = -13;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("DORMRZ", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*m == 0 || *n == 0) {
work[1] = 1.;
return 0;
}
nbmin = 2;
ldwork = nw;
if (nb > 1 && nb < *k) {
iws = nw * nb;
if (*lwork < iws) {
nb = *lwork / ldwork;
/* Computing MAX */
/* 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 = 2, i__2 = ilaenv_(&c__2, "DORMRQ", ch__1, m, n, k, &c_n1);
nbmin = max(i__1,i__2);
}
} else {
iws = nw;
}
if (nb < nbmin || nb >= *k) {
/* Use unblocked code */
dormr3_(side, trans, m, n, k, l, &a[a_offset], lda, &tau[1], &c__[
c_offset], ldc, &work[1], &iinfo);
} else {
/* Use blocked code */
if (left && ! notran || ! left && notran) {
i1 = 1;
i2 = *k;
i3 = nb;
} else {
i1 = (*k - 1) / nb * nb + 1;
i2 = 1;
i3 = -nb;
}
if (left) {
ni = *n;
jc = 1;
ja = *m - *l + 1;
} else {
mi = *m;
ic = 1;
ja = *n - *l + 1;
}
if (notran) {
*(unsigned char *)transt = 'T';
} else {
*(unsigned char *)transt = 'N';
}
i__1 = i2;
i__2 = i3;
for (i__ = i1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
/* Computing MIN */
i__4 = nb, i__5 = *k - i__ + 1;
ib = min(i__4,i__5);
/* Form the triangular factor of the block reflector */
/* H = H(i+ib-1) . . . H(i+1) H(i) */
dlarzt_("Backward", "Rowwise", l, &ib, &a[i__ + ja * a_dim1], lda,
&tau[i__], t, &c__65);
if (left) {
/* H or H' is applied to C(i:m,1:n) */
mi = *m - i__ + 1;
ic = i__;
} else {
/* H or H' is applied to C(1:m,i:n) */
ni = *n - i__ + 1;
jc = i__;
}
/* Apply H or H' */
dlarzb_(side, transt, "Backward", "Rowwise", &mi, &ni, &ib, l, &a[
i__ + ja * a_dim1], lda, t, &c__65, &c__[ic + jc * c_dim1]
, ldc, &work[1], &ldwork);
/* L10: */
}
}
work[1] = (doublereal) lwkopt;
return 0;
/* End of DORMRZ */
} /* dormrz_ */
int dtzrzf_(int *m, int *n, double *a, int *
lda, double *tau, double *work, int *lwork, int *info)
{
/* System generated locals */
int a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5;
/* Local variables */
int i__, m1, ib, nb, ki, kk, mu, nx, iws, nbmin;
extern int xerbla_(char *, int *), dlarzb_(
char *, char *, char *, char *, int *, int *, int *,
int *, double *, int *, double *, int *,
double *, int *, double *, int *);
extern int ilaenv_(int *, char *, char *, int *, int *,
int *, int *);
extern int dlarzt_(char *, char *, int *, int *,
double *, int *, double *, double *, int *), dlatrz_(int *, int *, int *,
double *, int *, double *, double *);
int ldwork, lwkopt;
int lquery;
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DTZRZF reduces the M-by-N ( M<=N ) float upper trapezoidal matrix A */
/* to upper triangular form by means of orthogonal transformations. */
/* The upper trapezoidal matrix A is factored as */
/* A = ( R 0 ) * Z, */
/* where Z is an N-by-N orthogonal matrix and R is an M-by-M upper */
/* triangular matrix. */
/* Arguments */
/* ========= */
/* 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 >= M. */
/* A (input/output) DOUBLE PRECISION array, dimension (LDA,N) */
/* On entry, the leading M-by-N upper trapezoidal part of the */
/* array A must contain the matrix to be factorized. */
/* On exit, the leading M-by-M upper triangular part of A */
/* contains the upper triangular matrix R, and elements M+1 to */
/* N of the first M rows of A, with the array TAU, represent the */
/* orthogonal matrix Z as a product of M elementary reflectors. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= MAX(1,M). */
/* TAU (output) DOUBLE PRECISION array, dimension (M) */
/* The scalar factors of the elementary reflectors. */
/* WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */
/* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
/* LWORK (input) INTEGER */
/* The dimension of the array WORK. LWORK >= MAX(1,M). */
/* For optimum performance LWORK >= M*NB, 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 */
/* Further Details */
/* =============== */
/* Based on contributions by */
/* A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA */
/* The factorization is obtained by Householder's method. The kth */
/* transformation matrix, Z( k ), which is used to introduce zeros into */
/* the ( m - k + 1 )th row of A, is given in the form */
/* Z( k ) = ( I 0 ), */
/* ( 0 T( k ) ) */
/* where */
/* T( k ) = I - tau*u( k )*u( k )', u( k ) = ( 1 ), */
/* ( 0 ) */
/* ( z( k ) ) */
/* tau is a scalar and z( k ) is an ( n - m ) element vector. */
/* tau and z( k ) are chosen to annihilate the elements of the kth row */
/* of X. */
/* The scalar tau is returned in the kth element of TAU and the vector */
/* u( k ) in the kth row of A, such that the elements of z( k ) are */
/* in a( k, m + 1 ), ..., a( k, n ). The elements of R are returned in */
/* the upper triangular part of A. */
/* Z is given by */
/* Z = Z( 1 ) * Z( 2 ) * ... * Z( m ). */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input arguments */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--tau;
--work;
/* Function Body */
*info = 0;
lquery = *lwork == -1;
if (*m < 0) {
*info = -1;
} else if (*n < *m) {
*info = -2;
} else if (*lda < MAX(1,*m)) {
*info = -4;
}
if (*info == 0) {
if (*m == 0 || *m == *n) {
lwkopt = 1;
} else {
/* Determine the block size. */
nb = ilaenv_(&c__1, "DGERQF", " ", m, n, &c_n1, &c_n1);
lwkopt = *m * nb;
}
work[1] = (double) lwkopt;
if (*lwork < MAX(1,*m) && ! lquery) {
*info = -7;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("DTZRZF", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*m == 0) {
return 0;
} else if (*m == *n) {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
tau[i__] = 0.;
/* L10: */
}
return 0;
}
nbmin = 2;
nx = 1;
iws = *m;
if (nb > 1 && nb < *m) {
/* Determine when to cross over from blocked to unblocked code. */
/* Computing MAX */
i__1 = 0, i__2 = ilaenv_(&c__3, "DGERQF", " ", m, n, &c_n1, &c_n1);
nx = MAX(i__1,i__2);
if (nx < *m) {
/* Determine if workspace is large enough for blocked code. */
ldwork = *m;
iws = ldwork * nb;
if (*lwork < iws) {
/* Not enough workspace to use optimal NB: reduce NB and */
/* determine the minimum value of NB. */
nb = *lwork / ldwork;
/* Computing MAX */
i__1 = 2, i__2 = ilaenv_(&c__2, "DGERQF", " ", m, n, &c_n1, &
c_n1);
nbmin = MAX(i__1,i__2);
}
}
}
if (nb >= nbmin && nb < *m && nx < *m) {
/* Use blocked code initially. */
/* The last kk rows are handled by the block method. */
/* Computing MIN */
i__1 = *m + 1;
m1 = MIN(i__1,*n);
ki = (*m - nx - 1) / nb * nb;
/* Computing MIN */
i__1 = *m, i__2 = ki + nb;
kk = MIN(i__1,i__2);
i__1 = *m - kk + 1;
i__2 = -nb;
for (i__ = *m - kk + ki + 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1;
i__ += i__2) {
/* Computing MIN */
i__3 = *m - i__ + 1;
ib = MIN(i__3,nb);
/* Compute the TZ factorization of the current block */
/* A(i:i+ib-1,i:n) */
i__3 = *n - i__ + 1;
i__4 = *n - *m;
dlatrz_(&ib, &i__3, &i__4, &a[i__ + i__ * a_dim1], lda, &tau[i__],
&work[1]);
if (i__ > 1) {
/* Form the triangular factor of the block reflector */
/* H = H(i+ib-1) . . . H(i+1) H(i) */
i__3 = *n - *m;
dlarzt_("Backward", "Rowwise", &i__3, &ib, &a[i__ + m1 *
a_dim1], lda, &tau[i__], &work[1], &ldwork);
/* Apply H to A(1:i-1,i:n) from the right */
i__3 = i__ - 1;
i__4 = *n - i__ + 1;
i__5 = *n - *m;
dlarzb_("Right", "No transpose", "Backward", "Rowwise", &i__3,
&i__4, &ib, &i__5, &a[i__ + m1 * a_dim1], lda, &work[
1], &ldwork, &a[i__ * a_dim1 + 1], lda, &work[ib + 1],
&ldwork)
;
}
/* L20: */
}
mu = i__ + nb - 1;
} else {
mu = *m;
}
/* Use unblocked code to factor the last or only block */
if (mu > 0) {
i__2 = *n - *m;
dlatrz_(&mu, n, &i__2, &a[a_offset], lda, &tau[1], &work[1]);
}
work[1] = (double) lwkopt;
return 0;
/* End of DTZRZF */
} /* dtzrzf_ */
