/* Subroutine */ int zgeqlf_(integer *m, integer *n, doublecomplex *a,
integer *lda, doublecomplex *tau, doublecomplex *work, integer *lwork,
integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
/* Local variables */
integer i__, k, ib, nb, ki, kk, mu, nu, nx, iws, nbmin, iinfo;
extern /* Subroutine */ int zgeql2_(integer *, integer *, doublecomplex *,
integer *, doublecomplex *, doublecomplex *, integer *), xerbla_(
char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *);
extern /* Subroutine */ int zlarfb_(char *, char *, char *, char *,
integer *, integer *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *);
integer ldwork;
extern /* Subroutine */ int zlarft_(char *, char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *);
integer lwkopt;
logical lquery;
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZGEQLF computes a QL factorization of a complex M-by-N matrix A: */
/* A = Q * L. */
/* 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. */
/* A (input/output) COMPLEX*16 array, dimension (LDA,N) */
/* On entry, the M-by-N matrix A. */
/* On exit, */
/* if m >= n, the lower triangle of the subarray */
/* A(m-n+1:m,1:n) contains the N-by-N lower triangular matrix L; */
/* if m <= n, the elements on and below the (n-m)-th */
/* superdiagonal contain the M-by-N lower trapezoidal matrix L; */
/* the remaining elements, with the array TAU, represent the */
/* unitary matrix Q as a product of elementary reflectors */
/* (see Further Details). */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,M). */
/* TAU (output) COMPLEX*16 array, dimension (min(M,N)) */
/* The scalar factors of the elementary reflectors (see Further */
/* Details). */
/* WORK (workspace/output) COMPLEX*16 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,N). */
/* For optimum performance LWORK >= N*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 */
/* =============== */
/* The matrix Q is represented as a product of elementary reflectors */
/* Q = H(k) . . . H(2) H(1), where k = min(m,n). */
/* Each H(i) has the form */
/* H(i) = I - tau * v * v' */
/* where tau is a complex scalar, and v is a complex vector with */
/* v(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in */
/* A(1:m-k+i-1,n-k+i), and tau in TAU(i). */
/* ===================================================================== */
/* .. 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 < 0) {
*info = -2;
} else if (*lda < max(1,*m)) {
*info = -4;
}
if (*info == 0) {
k = min(*m,*n);
if (k == 0) {
lwkopt = 1;
} else {
nb = ilaenv_(&c__1, "ZGEQLF", " ", m, n, &c_n1, &c_n1);
lwkopt = *n * nb;
}
work[1].r = (doublereal) lwkopt, work[1].i = 0.;
if (*lwork < max(1,*n) && ! lquery) {
*info = -7;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZGEQLF", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (k == 0) {
return 0;
}
nbmin = 2;
nx = 1;
iws = *n;
if (nb > 1 && nb < k) {
/* Determine when to cross over from blocked to unblocked code. */
/* Computing MAX */
i__1 = 0, i__2 = ilaenv_(&c__3, "ZGEQLF", " ", m, n, &c_n1, &c_n1);
nx = max(i__1,i__2);
if (nx < k) {
/* Determine if workspace is large enough for blocked code. */
ldwork = *n;
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, "ZGEQLF", " ", m, n, &c_n1, &
c_n1);
nbmin = max(i__1,i__2);
}
}
}
if (nb >= nbmin && nb < k && nx < k) {
/* Use blocked code initially. */
/* The last kk columns are handled by the block method. */
ki = (k - nx - 1) / nb * nb;
/* Computing MIN */
i__1 = k, i__2 = ki + nb;
kk = min(i__1,i__2);
i__1 = k - kk + 1;
i__2 = -nb;
for (i__ = k - kk + ki + 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__
+= i__2) {
/* Computing MIN */
i__3 = k - i__ + 1;
ib = min(i__3,nb);
/* Compute the QL factorization of the current block */
/* A(1:m-k+i+ib-1,n-k+i:n-k+i+ib-1) */
i__3 = *m - k + i__ + ib - 1;
zgeql2_(&i__3, &ib, &a[(*n - k + i__) * a_dim1 + 1], lda, &tau[
i__], &work[1], &iinfo);
if (*n - k + i__ > 1) {
/* Form the triangular factor of the block reflector */
/* H = H(i+ib-1) . . . H(i+1) H(i) */
i__3 = *m - k + i__ + ib - 1;
zlarft_("Backward", "Columnwise", &i__3, &ib, &a[(*n - k +
i__) * a_dim1 + 1], lda, &tau[i__], &work[1], &ldwork);
/* Apply H' to A(1:m-k+i+ib-1,1:n-k+i-1) from the left */
i__3 = *m - k + i__ + ib - 1;
i__4 = *n - k + i__ - 1;
zlarfb_("Left", "Conjugate transpose", "Backward", "Columnwi"
"se", &i__3, &i__4, &ib, &a[(*n - k + i__) * a_dim1 +
1], lda, &work[1], &ldwork, &a[a_offset], lda, &work[
ib + 1], &ldwork);
}
/* L10: */
}
mu = *m - k + i__ + nb - 1;
nu = *n - k + i__ + nb - 1;
} else {
mu = *m;
nu = *n;
}
/* Use unblocked code to factor the last or only block */
if (mu > 0 && nu > 0) {
zgeql2_(&mu, &nu, &a[a_offset], lda, &tau[1], &work[1], &iinfo);
}
work[1].r = (doublereal) iws, work[1].i = 0.;
return 0;
/* End of ZGEQLF */
} /* zgeqlf_ */
/* Subroutine */ int zunmrq_(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)
{
/* 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__;
doublecomplex t[4160] /* was [65][64] */;
integer i1, i2, i3, ib, nb, mi, ni, nq, nw, iws;
logical left;
extern logical lsame_(char *, char *);
integer nbmin, iinfo;
extern /* Subroutine */ int zunmr2_(char *, char *, integer *, integer *,
integer *, doublecomplex *, integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *), xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *);
extern /* Subroutine */ int zlarfb_(char *, char *, char *, char *,
integer *, integer *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *);
logical notran;
integer ldwork;
extern /* Subroutine */ int zlarft_(char *, char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *);
char transt[1];
integer lwkopt;
logical lquery;
/* -- LAPACK routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZUNMRQ 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 */
/* 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 ZGERQF. 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**H from the Left; */
/* = 'R': apply Q or Q**H from the Right. */
/* TRANS (input) CHARACTER*1 */
/* = 'N': No transpose, apply Q; */
/* = 'C': Transpose, apply Q**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 */
/* The number of elementary reflectors whose product defines */
/* the matrix Q. */
/* If SIDE = 'L', M >= K >= 0; */
/* if SIDE = 'R', N >= K >= 0. */
/* A (input) COMPLEX*16 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 */
/* ZGERQF 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*16 array, dimension (K) */
/* TAU(i) must contain the scalar factor of the elementary */
/* reflector H(i), as returned by ZGERQF. */
/* 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. */
/* LDC (input) INTEGER */
/* The leading dimension of the array C. LDC >= max(1,M). */
/* WORK (workspace/output) COMPLEX*16 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 */
/* ===================================================================== */
/* .. 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, "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 (*lda < max(1,*k)) {
*info = -7;
} else if (*ldc < max(1,*m)) {
*info = -10;
}
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, "ZUNMRQ", ch__1, m, n, k, &c_n1);
nb = min(i__1,i__2);
lwkopt = nw * nb;
}
work[1].r = (doublereal) lwkopt, work[1].i = 0.;
if (*lwork < nw && ! lquery) {
*info = -12;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZUNMRQ", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*m == 0 || *n == 0) {
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, "ZUNMRQ", ch__1, m, n, k, &c_n1);
nbmin = max(i__1,i__2);
}
} else {
iws = nw;
}
if (nb < nbmin || nb >= *k) {
/* Use unblocked code */
zunmr2_(side, trans, m, n, k, &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;
} else {
mi = *m;
}
if (notran) {
*(unsigned char *)transt = 'C';
} 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) */
i__4 = nq - *k + i__ + ib - 1;
zlarft_("Backward", "Rowwise", &i__4, &ib, &a[i__ + a_dim1], lda,
&tau[i__], t, &c__65);
if (left) {
/* H or H' is applied to C(1:m-k+i+ib-1,1:n) */
mi = *m - *k + i__ + ib - 1;
} else {
/* H or H' is applied to C(1:m,1:n-k+i+ib-1) */
ni = *n - *k + i__ + ib - 1;
}
/* Apply H or H' */
zlarfb_(side, transt, "Backward", "Rowwise", &mi, &ni, &ib, &a[
i__ + a_dim1], lda, t, &c__65, &c__[c_offset], ldc, &work[
1], &ldwork);
/* L10: */
}
}
work[1].r = (doublereal) lwkopt, work[1].i = 0.;
return 0;
/* End of ZUNMRQ */
} /* zunmrq_ */
/*< SUBROUTINE ZGEQRF( M, N, A, LDA, TAU, WORK, LWORK, INFO ) >*/
/* Subroutine */ int zgeqrf_(integer *m, integer *n, doublecomplex *a,
integer *lda, doublecomplex *tau, doublecomplex *work, integer *lwork,
integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
/* Local variables */
integer i__, k, ib, nb, nx, iws, nbmin, iinfo;
extern /* Subroutine */ int zgeqr2_(integer *, integer *, doublecomplex *,
integer *, doublecomplex *, doublecomplex *, integer *), xerbla_(
char *, integer *, ftnlen);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
extern /* Subroutine */ int zlarfb_(char *, char *, char *, char *,
integer *, integer *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, ftnlen, ftnlen, ftnlen, ftnlen);
integer ldwork;
extern /* Subroutine */ int zlarft_(char *, char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *, ftnlen, ftnlen);
integer lwkopt;
logical lquery;
/* -- 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 .. */
/*< INTEGER INFO, LDA, LWORK, M, N >*/
/* .. */
/* .. Array Arguments .. */
/*< COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) >*/
/* .. */
/* Purpose */
/* ======= */
/* ZGEQRF computes a QR factorization of a complex M-by-N matrix A: */
/* A = Q * R. */
/* 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. */
/* A (input/output) COMPLEX*16 array, dimension (LDA,N) */
/* On entry, the M-by-N matrix A. */
/* On exit, the elements on and above the diagonal of the array */
/* contain the min(M,N)-by-N upper trapezoidal matrix R (R is */
/* upper triangular if m >= n); the elements below the diagonal, */
/* with the array TAU, represent the unitary matrix Q as a */
/* product of min(m,n) elementary reflectors (see Further */
/* Details). */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,M). */
/* TAU (output) COMPLEX*16 array, dimension (min(M,N)) */
/* The scalar factors of the elementary reflectors (see Further */
/* Details). */
/* WORK (workspace/output) COMPLEX*16 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,N). */
/* For optimum performance LWORK >= N*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 */
/* =============== */
/* The matrix Q is represented as a product of elementary reflectors */
/* Q = H(1) H(2) . . . H(k), where k = min(m,n). */
/* Each H(i) has the form */
/* H(i) = I - tau * v * v' */
/* where tau is a complex scalar, and v is a complex vector with */
/* v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i), */
/* and tau in TAU(i). */
/* ===================================================================== */
/* .. Local Scalars .. */
/*< LOGICAL LQUERY >*/
/*< >*/
/* .. */
/* .. External Subroutines .. */
/*< EXTERNAL XERBLA, ZGEQR2, ZLARFB, ZLARFT >*/
/* .. */
/* .. Intrinsic Functions .. */
/*< INTRINSIC MAX, MIN >*/
/* .. */
/* .. External Functions .. */
/*< INTEGER ILAENV >*/
/*< EXTERNAL ILAENV >*/
/* .. */
/* .. Executable Statements .. */
/* Test the input arguments */
/*< INFO = 0 >*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--tau;
--work;
/* Function Body */
*info = 0;
/*< NB = ILAENV( 1, 'ZGEQRF', ' ', M, N, -1, -1 ) >*/
nb = ilaenv_(&c__1, "ZGEQRF", " ", m, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)
1);
/*< LWKOPT = N*NB >*/
lwkopt = *n * nb;
/*< WORK( 1 ) = LWKOPT >*/
work[1].r = (doublereal) lwkopt, work[1].i = 0.;
/*< LQUERY = ( LWORK.EQ.-1 ) >*/
lquery = *lwork == -1;
/*< IF( M.LT.0 ) THEN >*/
if (*m < 0) {
/*< INFO = -1 >*/
*info = -1;
/*< ELSE IF( N.LT.0 ) THEN >*/
} else if (*n < 0) {
/*< INFO = -2 >*/
*info = -2;
/*< ELSE IF( LDA.LT.MAX( 1, M ) ) THEN >*/
} else if (*lda < max(1,*m)) {
/*< INFO = -4 >*/
*info = -4;
/*< ELSE IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN >*/
} else if (*lwork < max(1,*n) && ! lquery) {
/*< INFO = -7 >*/
*info = -7;
/*< END IF >*/
}
/*< IF( INFO.NE.0 ) THEN >*/
if (*info != 0) {
/*< CALL XERBLA( 'ZGEQRF', -INFO ) >*/
i__1 = -(*info);
xerbla_("ZGEQRF", &i__1, (ftnlen)6);
/*< RETURN >*/
return 0;
/*< ELSE IF( LQUERY ) THEN >*/
} else if (lquery) {
/*< RETURN >*/
return 0;
/*< END IF >*/
}
/* Quick return if possible */
/*< K = MIN( M, N ) >*/
k = min(*m,*n);
/*< IF( K.EQ.0 ) THEN >*/
if (k == 0) {
/*< WORK( 1 ) = 1 >*/
work[1].r = 1., work[1].i = 0.;
/*< RETURN >*/
return 0;
/*< END IF >*/
}
/*< NBMIN = 2 >*/
nbmin = 2;
/*< NX = 0 >*/
nx = 0;
/*< IWS = N >*/
iws = *n;
/*< IF( NB.GT.1 .AND. NB.LT.K ) THEN >*/
if (nb > 1 && nb < k) {
/* Determine when to cross over from blocked to unblocked code. */
/*< NX = MAX( 0, ILAENV( 3, 'ZGEQRF', ' ', M, N, -1, -1 ) ) >*/
/* Computing MAX */
i__1 = 0, i__2 = ilaenv_(&c__3, "ZGEQRF", " ", m, n, &c_n1, &c_n1, (
ftnlen)6, (ftnlen)1);
nx = max(i__1,i__2);
/*< IF( NX.LT.K ) THEN >*/
if (nx < k) {
/* Determine if workspace is large enough for blocked code. */
/*< LDWORK = N >*/
ldwork = *n;
/*< IWS = LDWORK*NB >*/
iws = ldwork * nb;
/*< IF( LWORK.LT.IWS ) THEN >*/
if (*lwork < iws) {
/* Not enough workspace to use optimal NB: reduce NB and */
/* determine the minimum value of NB. */
/*< NB = LWORK / LDWORK >*/
nb = *lwork / ldwork;
/*< >*/
/* Computing MAX */
i__1 = 2, i__2 = ilaenv_(&c__2, "ZGEQRF", " ", m, n, &c_n1, &
c_n1, (ftnlen)6, (ftnlen)1);
nbmin = max(i__1,i__2);
/*< END IF >*/
}
/*< END IF >*/
}
/*< END IF >*/
}
/*< IF( NB.GE.NBMIN .AND. NB.LT.K .AND. NX.LT.K ) THEN >*/
if (nb >= nbmin && nb < k && nx < k) {
/* Use blocked code initially */
/*< DO 10 I = 1, K - NX, NB >*/
i__1 = k - nx;
i__2 = nb;
for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
/*< IB = MIN( K-I+1, NB ) >*/
/* Computing MIN */
i__3 = k - i__ + 1;
ib = min(i__3,nb);
/* Compute the QR factorization of the current block */
/* A(i:m,i:i+ib-1) */
/*< >*/
i__3 = *m - i__ + 1;
zgeqr2_(&i__3, &ib, &a[i__ + i__ * a_dim1], lda, &tau[i__], &work[
1], &iinfo);
/*< IF( I+IB.LE.N ) THEN >*/
if (i__ + ib <= *n) {
/* Form the triangular factor of the block reflector */
/* H = H(i) H(i+1) . . . H(i+ib-1) */
/*< >*/
i__3 = *m - i__ + 1;
zlarft_("Forward", "Columnwise", &i__3, &ib, &a[i__ + i__ *
a_dim1], lda, &tau[i__], &work[1], &ldwork, (ftnlen)7,
(ftnlen)10);
/* Apply H' to A(i:m,i+ib:n) from the left */
/*< >*/
i__3 = *m - i__ + 1;
i__4 = *n - i__ - ib + 1;
zlarfb_("Left", "Conjugate transpose", "Forward", "Columnwise"
, &i__3, &i__4, &ib, &a[i__ + i__ * a_dim1], lda, &
work[1], &ldwork, &a[i__ + (i__ + ib) * a_dim1], lda,
&work[ib + 1], &ldwork, (ftnlen)4, (ftnlen)19, (
ftnlen)7, (ftnlen)10);
/*< END IF >*/
}
/*< 10 CONTINUE >*/
/* L10: */
}
/*< ELSE >*/
} else {
/*< I = 1 >*/
i__ = 1;
/*< END IF >*/
}
/* Use unblocked code to factor the last or only block. */
/*< >*/
if (i__ <= k) {
i__2 = *m - i__ + 1;
i__1 = *n - i__ + 1;
zgeqr2_(&i__2, &i__1, &a[i__ + i__ * a_dim1], lda, &tau[i__], &work[1]
, &iinfo);
}
/*< WORK( 1 ) = IWS >*/
work[1].r = (doublereal) iws, work[1].i = 0.;
/*< RETURN >*/
return 0;
/* End of ZGEQRF */
/*< END >*/
} /* zgeqrf_ */
/* Subroutine */ int zgeqrf_(integer *m, integer *n, doublecomplex *a,
integer *lda, doublecomplex *tau, doublecomplex *work, integer *lwork,
integer *info)
{
/* -- LAPACK routine (version 2.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
September 30, 1994
Purpose
=======
ZGEQRF computes a QR factorization of a complex M-by-N matrix A:
A = Q * R.
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.
A (input/output) COMPLEX*16 array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, the elements on and above the diagonal of the array
contain the min(M,N)-by-N upper trapezoidal matrix R (R is
upper triangular if m >= n); the elements below the diagonal,
with the array TAU, represent the unitary matrix Q as a
product of min(m,n) elementary reflectors (see Further
Details).
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
TAU (output) COMPLEX*16 array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).
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. LWORK >= max(1,N).
For optimum performance LWORK >= N*NB, where NB is
the optimal blocksize.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
Further Details
===============
The matrix Q is represented as a product of elementary reflectors
Q = H(1) H(2) . . . H(k), where k = min(m,n).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a complex scalar, and v is a complex vector with
v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
and tau in TAU(i).
=====================================================================
Test the input arguments
Parameter adjustments
Function Body */
/* Table of constant values */
static integer c__1 = 1;
static integer c_n1 = -1;
static integer c__3 = 3;
static integer c__2 = 2;
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
/* Local variables */
static integer i, k, nbmin, iinfo;
extern /* Subroutine */ int zgeqr2_(integer *, integer *, doublecomplex *,
integer *, doublecomplex *, doublecomplex *, integer *);
static integer ib, nb, nx;
extern /* Subroutine */ int xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
extern /* Subroutine */ int zlarfb_(char *, char *, char *, char *,
integer *, integer *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *);
static integer ldwork;
extern /* Subroutine */ int zlarft_(char *, char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *);
static integer iws;
#define TAU(I) tau[(I)-1]
#define WORK(I) work[(I)-1]
#define A(I,J) a[(I)-1 + ((J)-1)* ( *lda)]
*info = 0;
if (*m < 0) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*lda < max(1,*m)) {
*info = -4;
} else if (*lwork < max(1,*n)) {
*info = -7;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZGEQRF", &i__1);
return 0;
}
/* Quick return if possible */
k = min(*m,*n);
if (k == 0) {
WORK(1).r = 1., WORK(1).i = 0.;
return 0;
}
/* Determine the block size. */
nb = ilaenv_(&c__1, "ZGEQRF", " ", m, n, &c_n1, &c_n1, 6L, 1L);
nbmin = 2;
nx = 0;
iws = *n;
if (nb > 1 && nb < k) {
/* Determine when to cross over from blocked to unblocked code.
Computing MAX */
i__1 = 0, i__2 = ilaenv_(&c__3, "ZGEQRF", " ", m, n, &c_n1, &c_n1, 6L,
1L);
nx = max(i__1,i__2);
if (nx < k) {
/* Determine if workspace is large enough for blocked co
de. */
ldwork = *n;
iws = ldwork * nb;
if (*lwork < iws) {
/* Not enough workspace to use optimal NB: reduc
e NB and
determine the minimum value of NB. */
nb = *lwork / ldwork;
/* Computing MAX */
i__1 = 2, i__2 = ilaenv_(&c__2, "ZGEQRF", " ", m, n, &c_n1, &
c_n1, 6L, 1L);
nbmin = max(i__1,i__2);
}
}
}
if (nb >= nbmin && nb < k && nx < k) {
/* Use blocked code initially */
i__1 = k - nx;
i__2 = nb;
for (i = 1; nb < 0 ? i >= k-nx : i <= k-nx; i += nb) {
/* Computing MIN */
i__3 = k - i + 1;
ib = min(i__3,nb);
/* Compute the QR factorization of the current block
A(i:m,i:i+ib-1) */
i__3 = *m - i + 1;
zgeqr2_(&i__3, &ib, &A(i,i), lda, &TAU(i), &WORK(1), &
iinfo);
if (i + ib <= *n) {
/* Form the triangular factor of the block reflec
tor
H = H(i) H(i+1) . . . H(i+ib-1) */
i__3 = *m - i + 1;
zlarft_("Forward", "Columnwise", &i__3, &ib, &A(i,i), lda, &TAU(i), &WORK(1), &ldwork);
/* Apply H' to A(i:m,i+ib:n) from the left */
i__3 = *m - i + 1;
i__4 = *n - i - ib + 1;
zlarfb_("Left", "Conjugate transpose", "Forward", "Columnwise"
, &i__3, &i__4, &ib, &A(i,i), lda, &WORK(1)
, &ldwork, &A(i,i+ib), lda, &WORK(ib +
1), &ldwork);
}
/* L10: */
}
} else {
i = 1;
}
/* Use unblocked code to factor the last or only block. */
if (i <= k) {
i__2 = *m - i + 1;
i__1 = *n - i + 1;
zgeqr2_(&i__2, &i__1, &A(i,i), lda, &TAU(i), &WORK(1), &
iinfo);
}
WORK(1).r = (doublereal) iws, WORK(1).i = 0.;
return 0;
/* End of ZGEQRF */
} /* zgeqrf_ */
/* Subroutine */ int zungqr_(integer *m, integer *n, integer *k,
doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex *
work, integer *lwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
/* Local variables */
integer i__, j, l, ib, nb, ki, kk, nx, iws, nbmin, iinfo;
extern /* Subroutine */ int zung2r_(integer *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *), xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *);
extern /* Subroutine */ int zlarfb_(char *, char *, char *, char *,
integer *, integer *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *);
integer ldwork;
extern /* Subroutine */ int zlarft_(char *, char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *);
integer lwkopt;
logical lquery;
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZUNGQR generates an M-by-N complex matrix Q with orthonormal columns, */
/* which is defined as the first N columns of a product of K elementary */
/* reflectors of order M */
/* Q = H(1) H(2) . . . H(k) */
/* as returned by ZGEQRF. */
/* Arguments */
/* ========= */
/* M (input) INTEGER */
/* The number of rows of the matrix Q. M >= 0. */
/* N (input) INTEGER */
/* The number of columns of the matrix Q. M >= N >= 0. */
/* K (input) INTEGER */
/* The number of elementary reflectors whose product defines the */
/* matrix Q. N >= K >= 0. */
/* A (input/output) COMPLEX*16 array, dimension (LDA,N) */
/* On entry, the i-th column must contain the vector which */
/* defines the elementary reflector H(i), for i = 1,2,...,k, as */
/* returned by ZGEQRF in the first k columns of its array */
/* argument A. */
/* On exit, the M-by-N matrix Q. */
/* LDA (input) INTEGER */
/* The first dimension of the array A. LDA >= lmax(1,M). */
/* TAU (input) COMPLEX*16 array, dimension (K) */
/* TAU(i) must contain the scalar factor of the elementary */
/* reflector H(i), as returned by ZGEQRF. */
/* WORK (workspace/output) COMPLEX*16 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 >= lmax(1,N). */
/* For optimum performance LWORK >= N*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 has an illegal value */
/* ===================================================================== */
/* .. 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;
nb = ilaenv_(&c__1, "ZUNGQR", " ", m, n, k, &c_n1);
lwkopt = lmax(1,*n) * nb;
work[1].r = (doublereal) lwkopt, work[1].i = 0.;
lquery = *lwork == -1;
if (*m < 0) {
*info = -1;
} else if (*n < 0 || *n > *m) {
*info = -2;
} else if (*k < 0 || *k > *n) {
*info = -3;
} else if (*lda < lmax(1,*m)) {
*info = -5;
} else if (*lwork < lmax(1,*n) && ! lquery) {
*info = -8;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZUNGQR", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*n <= 0) {
work[1].r = 1., work[1].i = 0.;
return 0;
}
nbmin = 2;
nx = 0;
iws = *n;
if (nb > 1 && nb < *k) {
/* Determine when to cross over from blocked to unblocked code. */
/* Computing MAX */
i__1 = 0, i__2 = ilaenv_(&c__3, "ZUNGQR", " ", m, n, k, &c_n1);
nx = lmax(i__1,i__2);
if (nx < *k) {
/* Determine if workspace is large enough for blocked code. */
ldwork = *n;
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, "ZUNGQR", " ", m, n, k, &c_n1);
nbmin = lmax(i__1,i__2);
}
}
}
if (nb >= nbmin && nb < *k && nx < *k) {
/* Use blocked code after the last block. */
/* The first kk columns are handled by the block method. */
ki = (*k - nx - 1) / nb * nb;
/* Computing MIN */
i__1 = *k, i__2 = ki + nb;
kk = lmin(i__1,i__2);
/* Set A(1:kk,kk+1:n) to zero. */
i__1 = *n;
for (j = kk + 1; j <= i__1; ++j) {
i__2 = kk;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
a[i__3].r = 0., a[i__3].i = 0.;
/* L10: */
}
/* L20: */
}
} else {
kk = 0;
}
/* Use unblocked code for the last or only block. */
if (kk < *n) {
i__1 = *m - kk;
i__2 = *n - kk;
i__3 = *k - kk;
zung2r_(&i__1, &i__2, &i__3, &a[kk + 1 + (kk + 1) * a_dim1], lda, &
tau[kk + 1], &work[1], &iinfo);
}
if (kk > 0) {
/* Use blocked code */
i__1 = -nb;
for (i__ = ki + 1; i__1 < 0 ? i__ >= 1 : i__ <= 1; i__ += i__1) {
/* Computing MIN */
i__2 = nb, i__3 = *k - i__ + 1;
ib = lmin(i__2,i__3);
if (i__ + ib <= *n) {
/* Form the triangular factor of the block reflector */
/* H = H(i) H(i+1) . . . H(i+ib-1) */
i__2 = *m - i__ + 1;
zlarft_("Forward", "Columnwise", &i__2, &ib, &a[i__ + i__ *
a_dim1], lda, &tau[i__], &work[1], &ldwork);
/* Apply H to A(i:m,i+ib:n) from the left */
i__2 = *m - i__ + 1;
i__3 = *n - i__ - ib + 1;
zlarfb_("Left", "No transpose", "Forward", "Columnwise", &
i__2, &i__3, &ib, &a[i__ + i__ * a_dim1], lda, &work[
1], &ldwork, &a[i__ + (i__ + ib) * a_dim1], lda, &
work[ib + 1], &ldwork);
}
/* Apply H to rows i:m of current block */
i__2 = *m - i__ + 1;
zung2r_(&i__2, &ib, &ib, &a[i__ + i__ * a_dim1], lda, &tau[i__], &
work[1], &iinfo);
/* Set rows 1:i-1 of current block to zero */
i__2 = i__ + ib - 1;
for (j = i__; j <= i__2; ++j) {
i__3 = i__ - 1;
for (l = 1; l <= i__3; ++l) {
i__4 = l + j * a_dim1;
a[i__4].r = 0., a[i__4].i = 0.;
/* L30: */
}
/* L40: */
}
/* L50: */
}
}
work[1].r = (doublereal) iws, work[1].i = 0.;
return 0;
/* End of ZUNGQR */
} /* zungqr_ */
/* Subroutine */ int zungqr_(integer *m, integer *n, integer *k,
doublecomplex *a, integer *lda, doublecomplex *tau, 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
=======
ZUNGQR generates an M-by-N complex matrix Q with orthonormal columns,
which is defined as the first N columns of a product of K elementary
reflectors of order M
Q = H(1) H(2) . . . H(k)
as returned by ZGEQRF.
Arguments
=========
M (input) INTEGER
The number of rows of the matrix Q. M >= 0.
N (input) INTEGER
The number of columns of the matrix Q. M >= N >= 0.
K (input) INTEGER
The number of elementary reflectors whose product defines the
matrix Q. N >= K >= 0.
A (input/output) COMPLEX*16 array, dimension (LDA,N)
On entry, the i-th column must contain the vector which
defines the elementary reflector H(i), for i = 1,2,...,k, as
returned by ZGEQRF in the first k columns of its array
argument A.
On exit, the M-by-N matrix Q.
LDA (input) INTEGER
The first dimension of the array A. LDA >= max(1,M).
TAU (input) COMPLEX*16 array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by ZGEQRF.
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. LWORK >= max(1,N).
For optimum performance LWORK >= N*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 has 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__3 = 3;
static integer c__2 = 2;
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
/* Local variables */
static integer i__, j, l, nbmin, iinfo, ib, nb, ki, kk;
extern /* Subroutine */ int zung2r_(integer *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *);
static integer nx;
extern /* Subroutine */ int xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
extern /* Subroutine */ int zlarfb_(char *, char *, char *, char *,
integer *, integer *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *);
static integer ldwork;
extern /* Subroutine */ int zlarft_(char *, char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *);
static integer lwkopt;
static logical lquery;
static integer iws;
#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 */
*info = 0;
nb = ilaenv_(&c__1, "ZUNGQR", " ", m, n, k, &c_n1, (ftnlen)6, (ftnlen)1);
lwkopt = max(1,*n) * nb;
work[1].r = (doublereal) lwkopt, work[1].i = 0.;
lquery = *lwork == -1;
if (*m < 0) {
*info = -1;
} else if (*n < 0 || *n > *m) {
*info = -2;
} else if (*k < 0 || *k > *n) {
*info = -3;
} else if (*lda < max(1,*m)) {
*info = -5;
} else if (*lwork < max(1,*n) && ! lquery) {
*info = -8;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZUNGQR", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*n <= 0) {
work[1].r = 1., work[1].i = 0.;
return 0;
}
nbmin = 2;
nx = 0;
iws = *n;
if (nb > 1 && nb < *k) {
/* Determine when to cross over from blocked to unblocked code.
Computing MAX */
i__1 = 0, i__2 = ilaenv_(&c__3, "ZUNGQR", " ", m, n, k, &c_n1, (
ftnlen)6, (ftnlen)1);
nx = max(i__1,i__2);
if (nx < *k) {
/* Determine if workspace is large enough for blocked code. */
ldwork = *n;
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, "ZUNGQR", " ", m, n, k, &c_n1,
(ftnlen)6, (ftnlen)1);
nbmin = max(i__1,i__2);
}
}
}
if (nb >= nbmin && nb < *k && nx < *k) {
/* Use blocked code after the last block.
The first kk columns are handled by the block method. */
ki = (*k - nx - 1) / nb * nb;
/* Computing MIN */
i__1 = *k, i__2 = ki + nb;
kk = min(i__1,i__2);
/* Set A(1:kk,kk+1:n) to zero. */
i__1 = *n;
for (j = kk + 1; j <= i__1; ++j) {
i__2 = kk;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = a_subscr(i__, j);
a[i__3].r = 0., a[i__3].i = 0.;
/* L10: */
}
/* L20: */
}
} else {
kk = 0;
}
/* Use unblocked code for the last or only block. */
if (kk < *n) {
i__1 = *m - kk;
i__2 = *n - kk;
i__3 = *k - kk;
zung2r_(&i__1, &i__2, &i__3, &a_ref(kk + 1, kk + 1), lda, &tau[kk + 1]
, &work[1], &iinfo);
}
if (kk > 0) {
/* Use blocked code */
i__1 = -nb;
for (i__ = ki + 1; i__1 < 0 ? i__ >= 1 : i__ <= 1; i__ += i__1) {
/* Computing MIN */
i__2 = nb, i__3 = *k - i__ + 1;
ib = min(i__2,i__3);
if (i__ + ib <= *n) {
/* Form the triangular factor of the block reflector
H = H(i) H(i+1) . . . H(i+ib-1) */
i__2 = *m - i__ + 1;
zlarft_("Forward", "Columnwise", &i__2, &ib, &a_ref(i__, i__),
lda, &tau[i__], &work[1], &ldwork);
/* Apply H to A(i:m,i+ib:n) from the left */
i__2 = *m - i__ + 1;
i__3 = *n - i__ - ib + 1;
zlarfb_("Left", "No transpose", "Forward", "Columnwise", &
i__2, &i__3, &ib, &a_ref(i__, i__), lda, &work[1], &
ldwork, &a_ref(i__, i__ + ib), lda, &work[ib + 1], &
ldwork);
}
/* Apply H to rows i:m of current block */
i__2 = *m - i__ + 1;
zung2r_(&i__2, &ib, &ib, &a_ref(i__, i__), lda, &tau[i__], &work[
1], &iinfo);
/* Set rows 1:i-1 of current block to zero */
i__2 = i__ + ib - 1;
for (j = i__; j <= i__2; ++j) {
i__3 = i__ - 1;
for (l = 1; l <= i__3; ++l) {
i__4 = a_subscr(l, j);
a[i__4].r = 0., a[i__4].i = 0.;
/* L30: */
}
/* L40: */
}
/* L50: */
}
}
work[1].r = (doublereal) iws, work[1].i = 0.;
return 0;
/* End of ZUNGQR */
} /* zungqr_ */