/* Subroutine */ int cunmr3_(char *side, char *trans, integer *m, integer *n,
integer *k, integer *l, complex *a, integer *lda, complex *tau,
complex *c__, integer *ldc, complex *work, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__3;
complex q__1;
/* Builtin functions */
void r_cnjg(complex *, complex *);
/* Local variables */
integer i__, i1, i2, i3, ja, ic, jc, mi, ni, nq;
logical left;
complex taui;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int clarz_(char *, integer *, integer *, integer *
, complex *, integer *, complex *, complex *, integer *, complex *
), xerbla_(char *, integer *);
logical notran;
/* -- LAPACK routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CUNMR3 overwrites the general complex m by n matrix C with */
/* Q * C if SIDE = 'L' and TRANS = 'N', or */
/* Q'* C if SIDE = 'L' and TRANS = 'C', or */
/* C * Q if SIDE = 'R' and TRANS = 'N', or */
/* C * Q' if SIDE = 'R' and TRANS = 'C', */
/* where Q is a complex unitary matrix defined as the product of k */
/* elementary reflectors */
/* Q = H(1) H(2) . . . H(k) */
/* as returned by CTZRZF. 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' from the Left */
/* = 'R': apply Q or Q' from the Right */
/* TRANS (input) CHARACTER*1 */
/* = 'N': apply Q (No transpose) */
/* = 'C': apply Q' (Conjugate transpose) */
/* 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) COMPLEX 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 */
/* CTZRZF 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) COMPLEX array, dimension (K) */
/* TAU(i) must contain the scalar factor of the elementary */
/* reflector H(i), as returned by CTZRZF. */
/* C (input/output) COMPLEX array, dimension (LDC,N) */
/* On entry, the m-by-n matrix C. */
/* On exit, C is overwritten by Q*C or Q'*C or C*Q' or C*Q. */
/* LDC (input) INTEGER */
/* The leading dimension of the array C. LDC >= max(1,M). */
/* WORK (workspace) COMPLEX array, dimension */
/* (N) if SIDE = 'L', */
/* (M) if SIDE = 'R' */
/* 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 */
/* ===================================================================== */
/* .. Local Scalars .. */
/* .. */
/* .. 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");
/* NQ is the order of Q */
if (left) {
nq = *m;
} else {
nq = *n;
}
if (! left && ! lsame_(side, "R")) {
*info = -1;
} else if (! notran && ! lsame_(trans, "C")) {
*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) {
i__1 = -(*info);
xerbla_("CUNMR3", &i__1);
return 0;
}
/* Quick return if possible */
if (*m == 0 || *n == 0 || *k == 0) {
return 0;
}
if (left && ! notran || ! left && notran) {
i1 = 1;
i2 = *k;
i3 = 1;
} else {
i1 = *k;
i2 = 1;
i3 = -1;
}
if (left) {
ni = *n;
ja = *m - *l + 1;
jc = 1;
} else {
mi = *m;
ja = *n - *l + 1;
ic = 1;
}
i__1 = i2;
i__2 = i3;
for (i__ = i1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
if (left) {
/* H(i) or H(i)' is applied to C(i:m,1:n) */
mi = *m - i__ + 1;
ic = i__;
} else {
/* H(i) or H(i)' is applied to C(1:m,i:n) */
ni = *n - i__ + 1;
jc = i__;
}
/* Apply H(i) or H(i)' */
if (notran) {
i__3 = i__;
taui.r = tau[i__3].r, taui.i = tau[i__3].i;
} else {
r_cnjg(&q__1, &tau[i__]);
taui.r = q__1.r, taui.i = q__1.i;
}
clarz_(side, &mi, &ni, l, &a[i__ + ja * a_dim1], lda, &taui, &c__[ic
+ jc * c_dim1], ldc, &work[1]);
/* L10: */
}
return 0;
/* End of CUNMR3 */
} /* cunmr3_ */
int clatrz_(int *m, int *n, int *l, complex *a,
int *lda, complex *tau, complex *work)
{
/* System generated locals */
int a_dim1, a_offset, i__1, i__2;
complex q__1;
/* Builtin functions */
void r_cnjg(complex *, complex *);
/* Local variables */
int i__;
complex alpha;
extern int clarz_(char *, int *, int *, int *
, complex *, int *, complex *, complex *, int *, complex *
), clacgv_(int *, complex *, int *), clarfp_(
int *, complex *, complex *, int *, complex *);
/* -- LAPACK routine (version 3.2) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CLATRZ factors the M-by-(M+L) complex upper trapezoidal matrix */
/* [ A1 A2 ] = [ A(1:M,1:M) A(1:M,N-L+1:N) ] as ( R 0 ) * Z by means */
/* of unitary transformations, where Z is an (M+L)-by-(M+L) unitary */
/* matrix and, R and A1 are M-by-M upper triangular matrices. */
/* 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 >= 0. */
/* L (input) INTEGER */
/* The number of columns of the matrix A containing the */
/* meaningful part of the Householder vectors. N-M >= L >= 0. */
/* A (input/output) COMPLEX 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 N-L+1 to */
/* N of the first M rows of A, with the array TAU, represent the */
/* unitary 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) COMPLEX array, dimension (M) */
/* The scalar factors of the elementary reflectors. */
/* WORK (workspace) COMPLEX array, dimension (M) */
/* 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 l element vector. tau and z( k ) */
/* are chosen to annihilate the elements of the kth row of A2. */
/* The scalar tau is returned in the kth element of TAU and the vector */
/* u( k ) in the kth row of A2, such that the elements of z( k ) are */
/* in a( k, l + 1 ), ..., a( k, n ). The elements of R are returned in */
/* the upper triangular part of A1. */
/* Z is given by */
/* Z = Z( 1 ) * Z( 2 ) * ... * Z( m ). */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Quick return if possible */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--tau;
--work;
/* Function Body */
if (*m == 0) {
return 0;
} else if (*m == *n) {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
tau[i__2].r = 0.f, tau[i__2].i = 0.f;
/* L10: */
}
return 0;
}
for (i__ = *m; i__ >= 1; --i__) {
/* Generate elementary reflector H(i) to annihilate */
/* [ A(i,i) A(i,n-l+1:n) ] */
clacgv_(l, &a[i__ + (*n - *l + 1) * a_dim1], lda);
r_cnjg(&q__1, &a[i__ + i__ * a_dim1]);
alpha.r = q__1.r, alpha.i = q__1.i;
i__1 = *l + 1;
clarfp_(&i__1, &alpha, &a[i__ + (*n - *l + 1) * a_dim1], lda, &tau[
i__]);
i__1 = i__;
r_cnjg(&q__1, &tau[i__]);
tau[i__1].r = q__1.r, tau[i__1].i = q__1.i;
/* Apply H(i) to A(1:i-1,i:n) from the right */
i__1 = i__ - 1;
i__2 = *n - i__ + 1;
r_cnjg(&q__1, &tau[i__]);
clarz_("Right", &i__1, &i__2, l, &a[i__ + (*n - *l + 1) * a_dim1],
lda, &q__1, &a[i__ * a_dim1 + 1], lda, &work[1]);
i__1 = i__ + i__ * a_dim1;
r_cnjg(&q__1, &alpha);
a[i__1].r = q__1.r, a[i__1].i = q__1.i;
/* L20: */
}
return 0;
/* End of CLATRZ */
} /* clatrz_ */
/* Subroutine */ int clatrz_(integer *m, integer *n, integer *l, complex *a,
integer *lda, complex *tau, complex *work)
{
/* -- 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
=======
CLATRZ factors the M-by-(M+L) complex upper trapezoidal matrix
[ A1 A2 ] = [ A(1:M,1:M) A(1:M,N-L+1:N) ] as ( R 0 ) * Z by means
of unitary transformations, where Z is an (M+L)-by-(M+L) unitary
matrix and, R and A1 are M-by-M upper triangular matrices.
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 >= 0.
L (input) INTEGER
The number of columns of the matrix A containing the
meaningful part of the Householder vectors. N-M >= L >= 0.
A (input/output) COMPLEX 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 N-L+1 to
N of the first M rows of A, with the array TAU, represent the
unitary 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) COMPLEX array, dimension (M)
The scalar factors of the elementary reflectors.
WORK (workspace) COMPLEX array, dimension (M)
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 l element vector. tau and z( k )
are chosen to annihilate the elements of the kth row of A2.
The scalar tau is returned in the kth element of TAU and the vector
u( k ) in the kth row of A2, such that the elements of z( k ) are
in a( k, l + 1 ), ..., a( k, n ). The elements of R are returned in
the upper triangular part of A1.
Z is given by
Z = Z( 1 ) * Z( 2 ) * ... * Z( m ).
=====================================================================
Quick return if possible
Parameter adjustments */
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2;
complex q__1;
/* Builtin functions */
void r_cnjg(complex *, complex *);
/* Local variables */
static integer i__;
static complex alpha;
extern /* Subroutine */ int clarz_(char *, integer *, integer *, integer *
, complex *, integer *, complex *, complex *, integer *, complex *
), clarfg_(integer *, complex *, complex *, integer *,
complex *), clacgv_(integer *, complex *, 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)]
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--tau;
--work;
/* Function Body */
if (*m == 0) {
return 0;
} else if (*m == *n) {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
tau[i__2].r = 0.f, tau[i__2].i = 0.f;
/* L10: */
}
return 0;
}
for (i__ = *m; i__ >= 1; --i__) {
/* Generate elementary reflector H(i) to annihilate
[ A(i,i) A(i,n-l+1:n) ] */
clacgv_(l, &a_ref(i__, *n - *l + 1), lda);
r_cnjg(&q__1, &a_ref(i__, i__));
alpha.r = q__1.r, alpha.i = q__1.i;
i__1 = *l + 1;
clarfg_(&i__1, &alpha, &a_ref(i__, *n - *l + 1), lda, &tau[i__]);
i__1 = i__;
r_cnjg(&q__1, &tau[i__]);
tau[i__1].r = q__1.r, tau[i__1].i = q__1.i;
/* Apply H(i) to A(1:i-1,i:n) from the right */
i__1 = i__ - 1;
i__2 = *n - i__ + 1;
r_cnjg(&q__1, &tau[i__]);
clarz_("Right", &i__1, &i__2, l, &a_ref(i__, *n - *l + 1), lda, &q__1,
&a_ref(1, i__), lda, &work[1]);
i__1 = a_subscr(i__, i__);
r_cnjg(&q__1, &alpha);
a[i__1].r = q__1.r, a[i__1].i = q__1.i;
/* L20: */
}
return 0;
/* End of CLATRZ */
} /* clatrz_ */
/* Subroutine */
int clatrz_(integer *m, integer *n, integer *l, complex *a, integer *lda, complex *tau, complex *work)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2;
complex q__1;
/* Builtin functions */
void r_cnjg(complex *, complex *);
/* Local variables */
integer i__;
complex alpha;
extern /* Subroutine */
int clarz_(char *, integer *, integer *, integer * , complex *, integer *, complex *, complex *, integer *, complex * ), clarfg_(integer *, complex *, complex *, integer *, complex *), clacgv_(integer *, complex *, integer *);
/* -- LAPACK computational routine (version 3.4.2) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* September 2012 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Quick return if possible */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--tau;
--work;
/* Function Body */
if (*m == 0)
{
return 0;
}
else if (*m == *n)
{
i__1 = *n;
for (i__ = 1;
i__ <= i__1;
++i__)
{
i__2 = i__;
tau[i__2].r = 0.f;
tau[i__2].i = 0.f; // , expr subst
/* L10: */
}
return 0;
}
for (i__ = *m;
i__ >= 1;
--i__)
{
/* Generate elementary reflector H(i) to annihilate */
/* [ A(i,i) A(i,n-l+1:n) ] */
clacgv_(l, &a[i__ + (*n - *l + 1) * a_dim1], lda);
r_cnjg(&q__1, &a[i__ + i__ * a_dim1]);
alpha.r = q__1.r;
alpha.i = q__1.i; // , expr subst
i__1 = *l + 1;
clarfg_(&i__1, &alpha, &a[i__ + (*n - *l + 1) * a_dim1], lda, &tau[ i__]);
i__1 = i__;
r_cnjg(&q__1, &tau[i__]);
tau[i__1].r = q__1.r;
tau[i__1].i = q__1.i; // , expr subst
/* Apply H(i) to A(1:i-1,i:n) from the right */
i__1 = i__ - 1;
i__2 = *n - i__ + 1;
r_cnjg(&q__1, &tau[i__]);
clarz_("Right", &i__1, &i__2, l, &a[i__ + (*n - *l + 1) * a_dim1], lda, &q__1, &a[i__ * a_dim1 + 1], lda, &work[1]);
i__1 = i__ + i__ * a_dim1;
r_cnjg(&q__1, &alpha);
a[i__1].r = q__1.r;
a[i__1].i = q__1.i; // , expr subst
/* L20: */
}
return 0;
/* End of CLATRZ */
}
