int cgehrd_(int *n, int *ilo, int *ihi, complex *
a, int *lda, complex *tau, complex *work, int *lwork, int
*info)
{
/* System generated locals */
int a_dim1, a_offset, i__1, i__2, i__3, i__4;
complex q__1;
/* Local variables */
int i__, j;
complex t[4160] /* was [65][64] */;
int ib;
complex ei;
int nb, nh, nx, iws;
extern int cgemm_(char *, char *, int *, int *,
int *, complex *, complex *, int *, complex *, int *,
complex *, complex *, int *);
int nbmin, iinfo;
extern int ctrmm_(char *, char *, char *, char *,
int *, int *, complex *, complex *, int *, complex *,
int *), caxpy_(int *,
complex *, complex *, int *, complex *, int *), cgehd2_(
int *, int *, int *, complex *, int *, complex *,
complex *, int *), clahr2_(int *, int *, int *,
complex *, int *, complex *, complex *, int *, complex *,
int *), clarfb_(char *, char *, char *, char *, int *,
int *, int *, complex *, int *, complex *, int *,
complex *, int *, complex *, int *), xerbla_(char *, int *);
extern int ilaenv_(int *, char *, char *, int *, int *,
int *, int *);
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 */
/* ======= */
/* CGEHRD reduces a complex general matrix A to upper Hessenberg form H by */
/* an unitary similarity transformation: Q' * A * Q = H . */
/* Arguments */
/* ========= */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* ILO (input) INTEGER */
/* IHI (input) INTEGER */
/* It is assumed that A is already upper triangular in rows */
/* and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally */
/* set by a previous call to CGEBAL; otherwise they should be */
/* set to 1 and N respectively. See Further Details. */
/* 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0. */
/* A (input/output) COMPLEX array, dimension (LDA,N) */
/* On entry, the N-by-N general matrix to be reduced. */
/* On exit, the upper triangle and the first subdiagonal of A */
/* are overwritten with the upper Hessenberg matrix H, and the */
/* elements below the first subdiagonal, 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,N). */
/* TAU (output) COMPLEX array, dimension (N-1) */
/* The scalar factors of the elementary reflectors (see Further */
/* Details). Elements 1:ILO-1 and IHI:N-1 of TAU are set to */
/* zero. */
/* WORK (workspace/output) COMPLEX array, dimension (LWORK) */
/* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
/* LWORK (input) INTEGER */
/* The length 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 (ihi-ilo) elementary */
/* reflectors */
/* Q = H(ilo) H(ilo+1) . . . H(ihi-1). */
/* 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) = 0, v(i+1) = 1 and v(ihi+1:n) = 0; v(i+2:ihi) is stored on */
/* exit in A(i+2:ihi,i), and tau in TAU(i). */
/* The contents of A are illustrated by the following example, with */
/* n = 7, ilo = 2 and ihi = 6: */
/* on entry, on exit, */
/* ( a a a a a a a ) ( a a h h h h a ) */
/* ( a a a a a a ) ( a h h h h a ) */
/* ( a a a a a a ) ( h h h h h h ) */
/* ( a a a a a a ) ( v2 h h h h h ) */
/* ( a a a a a a ) ( v2 v3 h h h h ) */
/* ( a a a a a a ) ( v2 v3 v4 h h h ) */
/* ( a ) ( a ) */
/* where a denotes an element of the original matrix A, h denotes a */
/* modified element of the upper Hessenberg matrix H, and vi denotes an */
/* element of the vector defining H(i). */
/* This file is a slight modification of LAPACK-3.0's CGEHRD */
/* subroutine incorporating improvements proposed by Quintana-Orti and */
/* Van de Geijn (2005). */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--tau;
--work;
/* Function Body */
*info = 0;
/* Computing MIN */
i__1 = 64, i__2 = ilaenv_(&c__1, "CGEHRD", " ", n, ilo, ihi, &c_n1);
nb = MIN(i__1,i__2);
lwkopt = *n * nb;
work[1].r = (float) lwkopt, work[1].i = 0.f;
lquery = *lwork == -1;
if (*n < 0) {
*info = -1;
} else if (*ilo < 1 || *ilo > MAX(1,*n)) {
*info = -2;
} else if (*ihi < MIN(*ilo,*n) || *ihi > *n) {
*info = -3;
} else if (*lda < MAX(1,*n)) {
*info = -5;
} else if (*lwork < MAX(1,*n) && ! lquery) {
*info = -8;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CGEHRD", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Set elements 1:ILO-1 and IHI:N-1 of TAU to zero */
i__1 = *ilo - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
tau[i__2].r = 0.f, tau[i__2].i = 0.f;
/* L10: */
}
i__1 = *n - 1;
for (i__ = MAX(1,*ihi); i__ <= i__1; ++i__) {
i__2 = i__;
tau[i__2].r = 0.f, tau[i__2].i = 0.f;
/* L20: */
}
/* Quick return if possible */
nh = *ihi - *ilo + 1;
if (nh <= 1) {
work[1].r = 1.f, work[1].i = 0.f;
return 0;
}
/* Determine the block size */
/* Computing MIN */
i__1 = 64, i__2 = ilaenv_(&c__1, "CGEHRD", " ", n, ilo, ihi, &c_n1);
nb = MIN(i__1,i__2);
nbmin = 2;
iws = 1;
if (nb > 1 && nb < nh) {
/* Determine when to cross over from blocked to unblocked code */
/* (last block is always handled by unblocked code) */
/* Computing MAX */
i__1 = nb, i__2 = ilaenv_(&c__3, "CGEHRD", " ", n, ilo, ihi, &c_n1);
nx = MAX(i__1,i__2);
if (nx < nh) {
/* Determine if workspace is large enough for blocked code */
iws = *n * nb;
if (*lwork < iws) {
/* Not enough workspace to use optimal NB: determine the */
/* minimum value of NB, and reduce NB or force use of */
/* unblocked code */
/* Computing MAX */
i__1 = 2, i__2 = ilaenv_(&c__2, "CGEHRD", " ", n, ilo, ihi, &
c_n1);
nbmin = MAX(i__1,i__2);
if (*lwork >= *n * nbmin) {
nb = *lwork / *n;
} else {
nb = 1;
}
}
}
}
ldwork = *n;
if (nb < nbmin || nb >= nh) {
/* Use unblocked code below */
i__ = *ilo;
} else {
/* Use blocked code */
i__1 = *ihi - 1 - nx;
i__2 = nb;
for (i__ = *ilo; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
/* Computing MIN */
i__3 = nb, i__4 = *ihi - i__;
ib = MIN(i__3,i__4);
/* Reduce columns i:i+ib-1 to Hessenberg form, returning the */
/* matrices V and T of the block reflector H = I - V*T*V' */
/* which performs the reduction, and also the matrix Y = A*V*T */
clahr2_(ihi, &i__, &ib, &a[i__ * a_dim1 + 1], lda, &tau[i__], t, &
c__65, &work[1], &ldwork);
/* Apply the block reflector H to A(1:ihi,i+ib:ihi) from the */
/* right, computing A := A - Y * V'. V(i+ib,ib-1) must be set */
/* to 1 */
i__3 = i__ + ib + (i__ + ib - 1) * a_dim1;
ei.r = a[i__3].r, ei.i = a[i__3].i;
i__3 = i__ + ib + (i__ + ib - 1) * a_dim1;
a[i__3].r = 1.f, a[i__3].i = 0.f;
i__3 = *ihi - i__ - ib + 1;
q__1.r = -1.f, q__1.i = -0.f;
cgemm_("No transpose", "Conjugate transpose", ihi, &i__3, &ib, &
q__1, &work[1], &ldwork, &a[i__ + ib + i__ * a_dim1], lda,
&c_b2, &a[(i__ + ib) * a_dim1 + 1], lda);
i__3 = i__ + ib + (i__ + ib - 1) * a_dim1;
a[i__3].r = ei.r, a[i__3].i = ei.i;
/* Apply the block reflector H to A(1:i,i+1:i+ib-1) from the */
/* right */
i__3 = ib - 1;
ctrmm_("Right", "Lower", "Conjugate transpose", "Unit", &i__, &
i__3, &c_b2, &a[i__ + 1 + i__ * a_dim1], lda, &work[1], &
ldwork);
i__3 = ib - 2;
for (j = 0; j <= i__3; ++j) {
q__1.r = -1.f, q__1.i = -0.f;
caxpy_(&i__, &q__1, &work[ldwork * j + 1], &c__1, &a[(i__ + j
+ 1) * a_dim1 + 1], &c__1);
/* L30: */
}
/* Apply the block reflector H to A(i+1:ihi,i+ib:n) from the */
/* left */
i__3 = *ihi - i__;
i__4 = *n - i__ - ib + 1;
clarfb_("Left", "Conjugate transpose", "Forward", "Columnwise", &
i__3, &i__4, &ib, &a[i__ + 1 + i__ * a_dim1], lda, t, &
c__65, &a[i__ + 1 + (i__ + ib) * a_dim1], lda, &work[1], &
ldwork);
/* L40: */
}
}
/* Use unblocked code to reduce the rest of the matrix */
cgehd2_(n, &i__, ihi, &a[a_offset], lda, &tau[1], &work[1], &iinfo);
work[1].r = (float) iws, work[1].i = 0.f;
return 0;
/* End of CGEHRD */
} /* cgehrd_ */
/* Subroutine */
int cgehrd_(integer *n, integer *ilo, integer *ihi, complex * a, integer *lda, complex *tau, complex *work, integer *lwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
complex q__1;
/* Local variables */
integer i__, j;
complex t[4160] /* was [65][64] */
;
integer ib;
complex ei;
integer nb, nh, nx, iws;
extern /* Subroutine */
int cgemm_(char *, char *, integer *, integer *, integer *, complex *, complex *, integer *, complex *, integer *, complex *, complex *, integer *);
integer nbmin, iinfo;
extern /* Subroutine */
int ctrmm_(char *, char *, char *, char *, integer *, integer *, complex *, complex *, integer *, complex *, integer *), caxpy_(integer *, complex *, complex *, integer *, complex *, integer *), cgehd2_( integer *, integer *, integer *, complex *, integer *, complex *, complex *, integer *), clahr2_(integer *, integer *, integer *, complex *, integer *, complex *, complex *, integer *, complex *, integer *), clarfb_(char *, char *, char *, char *, integer *, integer *, integer *, complex *, integer *, complex *, integer *, complex *, integer *, complex *, integer *), xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *);
integer ldwork, lwkopt;
logical lquery;
/* -- LAPACK computational routine (version 3.4.0) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* November 2011 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--tau;
--work;
/* Function Body */
*info = 0;
/* Computing MIN */
i__1 = 64;
i__2 = ilaenv_(&c__1, "CGEHRD", " ", n, ilo, ihi, &c_n1); // , expr subst
nb = min(i__1,i__2);
lwkopt = *n * nb;
work[1].r = (real) lwkopt;
work[1].i = 0.f; // , expr subst
lquery = *lwork == -1;
if (*n < 0)
{
*info = -1;
}
else if (*ilo < 1 || *ilo > max(1,*n))
{
*info = -2;
}
else if (*ihi < min(*ilo,*n) || *ihi > *n)
{
*info = -3;
}
else if (*lda < max(1,*n))
{
*info = -5;
}
else if (*lwork < max(1,*n) && ! lquery)
{
*info = -8;
}
if (*info != 0)
{
i__1 = -(*info);
xerbla_("CGEHRD", &i__1);
return 0;
}
else if (lquery)
{
return 0;
}
/* Set elements 1:ILO-1 and IHI:N-1 of TAU to zero */
i__1 = *ilo - 1;
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: */
}
i__1 = *n - 1;
for (i__ = max(1,*ihi);
i__ <= i__1;
++i__)
{
i__2 = i__;
tau[i__2].r = 0.f;
tau[i__2].i = 0.f; // , expr subst
/* L20: */
}
/* Quick return if possible */
nh = *ihi - *ilo + 1;
if (nh <= 1)
{
work[1].r = 1.f;
work[1].i = 0.f; // , expr subst
return 0;
}
/* Determine the block size */
/* Computing MIN */
i__1 = 64;
i__2 = ilaenv_(&c__1, "CGEHRD", " ", n, ilo, ihi, &c_n1); // , expr subst
nb = min(i__1,i__2);
nbmin = 2;
iws = 1;
if (nb > 1 && nb < nh)
{
/* Determine when to cross over from blocked to unblocked code */
/* (last block is always handled by unblocked code) */
/* Computing MAX */
i__1 = nb;
i__2 = ilaenv_(&c__3, "CGEHRD", " ", n, ilo, ihi, &c_n1); // , expr subst
nx = max(i__1,i__2);
if (nx < nh)
{
/* Determine if workspace is large enough for blocked code */
iws = *n * nb;
if (*lwork < iws)
{
/* Not enough workspace to use optimal NB: determine the */
/* minimum value of NB, and reduce NB or force use of */
/* unblocked code */
/* Computing MAX */
i__1 = 2;
i__2 = ilaenv_(&c__2, "CGEHRD", " ", n, ilo, ihi, & c_n1); // , expr subst
nbmin = max(i__1,i__2);
if (*lwork >= *n * nbmin)
{
nb = *lwork / *n;
}
else
{
nb = 1;
}
}
}
}
ldwork = *n;
if (nb < nbmin || nb >= nh)
{
/* Use unblocked code below */
i__ = *ilo;
}
else
{
/* Use blocked code */
i__1 = *ihi - 1 - nx;
i__2 = nb;
for (i__ = *ilo;
i__2 < 0 ? i__ >= i__1 : i__ <= i__1;
i__ += i__2)
{
/* Computing MIN */
i__3 = nb;
i__4 = *ihi - i__; // , expr subst
ib = min(i__3,i__4);
/* Reduce columns i:i+ib-1 to Hessenberg form, returning the */
/* matrices V and T of the block reflector H = I - V*T*V**H */
/* which performs the reduction, and also the matrix Y = A*V*T */
clahr2_(ihi, &i__, &ib, &a[i__ * a_dim1 + 1], lda, &tau[i__], t, & c__65, &work[1], &ldwork);
/* Apply the block reflector H to A(1:ihi,i+ib:ihi) from the */
/* right, computing A := A - Y * V**H. V(i+ib,ib-1) must be set */
/* to 1 */
i__3 = i__ + ib + (i__ + ib - 1) * a_dim1;
ei.r = a[i__3].r;
ei.i = a[i__3].i; // , expr subst
i__3 = i__ + ib + (i__ + ib - 1) * a_dim1;
a[i__3].r = 1.f;
a[i__3].i = 0.f; // , expr subst
i__3 = *ihi - i__ - ib + 1;
q__1.r = -1.f;
q__1.i = -0.f; // , expr subst
cgemm_("No transpose", "Conjugate transpose", ihi, &i__3, &ib, & q__1, &work[1], &ldwork, &a[i__ + ib + i__ * a_dim1], lda, &c_b2, &a[(i__ + ib) * a_dim1 + 1], lda);
i__3 = i__ + ib + (i__ + ib - 1) * a_dim1;
a[i__3].r = ei.r;
a[i__3].i = ei.i; // , expr subst
/* Apply the block reflector H to A(1:i,i+1:i+ib-1) from the */
/* right */
i__3 = ib - 1;
ctrmm_("Right", "Lower", "Conjugate transpose", "Unit", &i__, & i__3, &c_b2, &a[i__ + 1 + i__ * a_dim1], lda, &work[1], & ldwork);
i__3 = ib - 2;
for (j = 0;
j <= i__3;
++j)
{
q__1.r = -1.f;
q__1.i = -0.f; // , expr subst
caxpy_(&i__, &q__1, &work[ldwork * j + 1], &c__1, &a[(i__ + j + 1) * a_dim1 + 1], &c__1);
/* L30: */
}
/* Apply the block reflector H to A(i+1:ihi,i+ib:n) from the */
/* left */
i__3 = *ihi - i__;
i__4 = *n - i__ - ib + 1;
clarfb_("Left", "Conjugate transpose", "Forward", "Columnwise", & i__3, &i__4, &ib, &a[i__ + 1 + i__ * a_dim1], lda, t, & c__65, &a[i__ + 1 + (i__ + ib) * a_dim1], lda, &work[1], & ldwork);
/* L40: */
}
}
/* Use unblocked code to reduce the rest of the matrix */
cgehd2_(n, &i__, ihi, &a[a_offset], lda, &tau[1], &work[1], &iinfo);
work[1].r = (real) iws;
work[1].i = 0.f; // , expr subst
return 0;
/* End of CGEHRD */
}
