int
f2c_cgerc(integer* M, integer* N,
complex* alpha,
complex* X, integer* incX,
complex* Y, integer* incY,
complex* A, integer* lda)
{
cgerc_(M, N, alpha,
X, incX, Y, incY, A, lda);
return 0;
}
/* Subroutine */ int clarz_(char *side, integer *m, integer *n, integer *l,
complex *v, integer *incv, complex *tau, complex *c__, integer *ldc,
complex *work)
{
/* System generated locals */
integer c_dim1, c_offset;
complex q__1;
/* Local variables */
extern /* Subroutine */ int cgerc_(integer *, integer *, complex *,
complex *, integer *, complex *, integer *, complex *, integer *),
cgemv_(char *, integer *, integer *, complex *, complex *,
integer *, complex *, integer *, complex *, complex *, integer *);
extern logical lsame_(char *, char *);
extern /* Subroutine */ int cgeru_(integer *, integer *, complex *,
complex *, integer *, complex *, integer *, complex *, integer *),
ccopy_(integer *, complex *, integer *, complex *, integer *),
caxpy_(integer *, complex *, complex *, integer *, complex *,
integer *), clacgv_(integer *, complex *, integer *);
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CLARZ applies a complex elementary reflector H to a complex */
/* M-by-N matrix C, from either the left or the right. H is represented */
/* in the form */
/* H = I - tau * v * v' */
/* where tau is a complex scalar and v is a complex vector. */
/* If tau = 0, then H is taken to be the unit matrix. */
/* To apply H' (the conjugate transpose of H), supply conjg(tau) instead */
/* tau. */
/* H is a product of k elementary reflectors as returned by CTZRZF. */
/* Arguments */
/* ========= */
/* SIDE (input) CHARACTER*1 */
/* = 'L': form H * C */
/* = 'R': form C * H */
/* M (input) INTEGER */
/* The number of rows of the matrix C. */
/* N (input) INTEGER */
/* The number of columns of the matrix C. */
/* L (input) INTEGER */
/* The number of entries of the vector V containing */
/* the meaningful part of the Householder vectors. */
/* If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0. */
/* V (input) COMPLEX array, dimension (1+(L-1)*abs(INCV)) */
/* The vector v in the representation of H as returned by */
/* CTZRZF. V is not used if TAU = 0. */
/* INCV (input) INTEGER */
/* The increment between elements of v. INCV <> 0. */
/* TAU (input) COMPLEX */
/* The value tau in the representation of H. */
/* C (input/output) COMPLEX array, dimension (LDC,N) */
/* On entry, the M-by-N matrix C. */
/* On exit, C is overwritten by the matrix H * C if SIDE = 'L', */
/* or C * H if SIDE = 'R'. */
/* LDC (input) INTEGER */
/* The leading dimension of the array C. LDC >= max(1,M). */
/* WORK (workspace) COMPLEX array, dimension */
/* (N) if SIDE = 'L' */
/* or (M) if SIDE = 'R' */
/* Further Details */
/* =============== */
/* Based on contributions by */
/* A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
--v;
c_dim1 = *ldc;
c_offset = 1 + c_dim1;
c__ -= c_offset;
--work;
/* Function Body */
if (lsame_(side, "L")) {
/* Form H * C */
if (tau->r != 0.f || tau->i != 0.f) {
/* w( 1:n ) = conjg( C( 1, 1:n ) ) */
ccopy_(n, &c__[c_offset], ldc, &work[1], &c__1);
clacgv_(n, &work[1], &c__1);
/* w( 1:n ) = conjg( w( 1:n ) + C( m-l+1:m, 1:n )' * v( 1:l ) ) */
cgemv_("Conjugate transpose", l, n, &c_b1, &c__[*m - *l + 1 +
c_dim1], ldc, &v[1], incv, &c_b1, &work[1], &c__1);
clacgv_(n, &work[1], &c__1);
/* C( 1, 1:n ) = C( 1, 1:n ) - tau * w( 1:n ) */
q__1.r = -tau->r, q__1.i = -tau->i;
caxpy_(n, &q__1, &work[1], &c__1, &c__[c_offset], ldc);
/* C( m-l+1:m, 1:n ) = C( m-l+1:m, 1:n ) - ... */
/* tau * v( 1:l ) * conjg( w( 1:n )' ) */
q__1.r = -tau->r, q__1.i = -tau->i;
cgeru_(l, n, &q__1, &v[1], incv, &work[1], &c__1, &c__[*m - *l +
1 + c_dim1], ldc);
}
} else {
/* Form C * H */
if (tau->r != 0.f || tau->i != 0.f) {
/* w( 1:m ) = C( 1:m, 1 ) */
ccopy_(m, &c__[c_offset], &c__1, &work[1], &c__1);
/* w( 1:m ) = w( 1:m ) + C( 1:m, n-l+1:n, 1:n ) * v( 1:l ) */
cgemv_("No transpose", m, l, &c_b1, &c__[(*n - *l + 1) * c_dim1 +
1], ldc, &v[1], incv, &c_b1, &work[1], &c__1);
/* C( 1:m, 1 ) = C( 1:m, 1 ) - tau * w( 1:m ) */
q__1.r = -tau->r, q__1.i = -tau->i;
caxpy_(m, &q__1, &work[1], &c__1, &c__[c_offset], &c__1);
/* C( 1:m, n-l+1:n ) = C( 1:m, n-l+1:n ) - ... */
/* tau * w( 1:m ) * v( 1:l )' */
q__1.r = -tau->r, q__1.i = -tau->i;
cgerc_(m, l, &q__1, &work[1], &c__1, &v[1], incv, &c__[(*n - *l +
1) * c_dim1 + 1], ldc);
}
}
return 0;
/* End of CLARZ */
} /* clarz_ */
/* Subroutine */ int clarf_(char *side, integer *m, integer *n, complex *v,
integer *incv, complex *tau, complex *c__, integer *ldc, complex *
work)
{
/* System generated locals */
integer c_dim1, c_offset, i__1;
complex q__1;
/* Local variables */
integer i__;
logical applyleft;
integer lastc, lastv;
/* -- LAPACK auxiliary routine (version 3.2) -- */
/* November 2006 */
/* Purpose */
/* ======= */
/* CLARF applies a complex elementary reflector H to a complex M-by-N */
/* matrix C, from either the left or the right. H is represented in the */
/* form */
/* H = I - tau * v * v' */
/* where tau is a complex scalar and v is a complex vector. */
/* If tau = 0, then H is taken to be the unit matrix. */
/* To apply H' (the conjugate transpose of H), supply conjg(tau) instead */
/* tau. */
/* Arguments */
/* ========= */
/* SIDE (input) CHARACTER*1 */
/* = 'L': form H * C */
/* = 'R': form C * H */
/* M (input) INTEGER */
/* The number of rows of the matrix C. */
/* N (input) INTEGER */
/* The number of columns of the matrix C. */
/* V (input) COMPLEX array, dimension */
/* (1 + (M-1)*abs(INCV)) if SIDE = 'L' */
/* or (1 + (N-1)*abs(INCV)) if SIDE = 'R' */
/* The vector v in the representation of H. V is not used if */
/* TAU = 0. */
/* INCV (input) INTEGER */
/* The increment between elements of v. INCV <> 0. */
/* TAU (input) COMPLEX */
/* The value tau in the representation of H. */
/* C (input/output) COMPLEX array, dimension (LDC,N) */
/* On entry, the M-by-N matrix C. */
/* On exit, C is overwritten by the matrix H * C if SIDE = 'L', */
/* or C * H if SIDE = 'R'. */
/* LDC (input) INTEGER */
/* The leading dimension of the array C. LDC >= max(1,M). */
/* WORK (workspace) COMPLEX array, dimension */
/* (N) if SIDE = 'L' */
/* or (M) if SIDE = 'R' */
/* ===================================================================== */
/* Parameter adjustments */
--v;
c_dim1 = *ldc;
c_offset = 1 + c_dim1;
c__ -= c_offset;
--work;
/* Function Body */
applyleft = lsame_(side, "L");
lastv = 0;
lastc = 0;
if (tau->r != 0.f || tau->i != 0.f) {
/* Set up variables for scanning V. LASTV begins pointing to the end */
/* of V. */
if (applyleft) {
lastv = *m;
} else {
lastv = *n;
}
if (*incv > 0) {
i__ = (lastv - 1) * *incv + 1;
} else {
i__ = 1;
}
/* Look for the last non-zero row in V. */
for(;;) { /* while(complicated condition) */
i__1 = i__;
if (!(lastv > 0 && (v[i__1].r == 0.f && v[i__1].i == 0.f)))
break;
--lastv;
i__ -= *incv;
}
if (applyleft) {
/* Scan for the last non-zero column in C(1:lastv,:). */
lastc = ilaclc_(&lastv, n, &c__[c_offset], ldc);
} else {
/* Scan for the last non-zero row in C(:,1:lastv). */
lastc = ilaclr_(m, &lastv, &c__[c_offset], ldc);
}
}
/* Note that lastc.eq.0 renders the BLAS operations null; no special */
/* case is needed at this level. */
if (applyleft) {
/* Form H * C */
if (lastv > 0) {
/* w(1:lastc,1) := C(1:lastv,1:lastc)' * v(1:lastv,1) */
cgemv_("Conjugate transpose", &lastv, &lastc, &c_b1, &c__[
c_offset], ldc, &v[1], incv, &c_b2, &work[1], &c__1);
q__1.r = -tau->r, q__1.i = -tau->i;
cgerc_(&lastv, &lastc, &q__1, &v[1], incv, &work[1], &c__1, &c__[
c_offset], ldc);
}
} else {
/* Form C * H */
if (lastv > 0) {
/* w(1:lastc,1) := C(1:lastc,1:lastv) * v(1:lastv,1) */
cgemv_("No transpose", &lastc, &lastv, &c_b1, &c__[c_offset], ldc,
&v[1], incv, &c_b2, &work[1], &c__1);
q__1.r = -tau->r, q__1.i = -tau->i;
cgerc_(&lastc, &lastv, &q__1, &work[1], &c__1, &v[1], incv, &c__[
c_offset], ldc);
}
}
return 0;
/* End of CLARF */
} /* clarf_ */
void
cgerc(int m, int n, complex *alpha, complex *x, int incx, complex *y, int incy, complex *a, int lda)
{
cgerc_( &m, &n, alpha, x, &incx, y, &incy, a, &lda);
}
/* Subroutine */ int clagsy_(integer *n, integer *k, real *d, complex *a,
integer *lda, integer *iseed, complex *work, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5, i__6, i__7, i__8,
i__9;
doublereal d__1;
complex q__1, q__2, q__3, q__4;
/* Builtin functions */
double c_abs(complex *);
void c_div(complex *, complex *, complex *);
/* Local variables */
static integer i, j;
extern /* Subroutine */ int cgerc_(integer *, integer *, complex *,
complex *, integer *, complex *, integer *, complex *, integer *);
static complex alpha;
extern /* Subroutine */ int cscal_(integer *, complex *, complex *,
integer *);
extern /* Complex */ VOID cdotc_(complex *, integer *, complex *, integer
*, complex *, integer *);
extern /* Subroutine */ int cgemv_(char *, integer *, integer *, complex *
, complex *, integer *, complex *, integer *, complex *, complex *
, integer *), caxpy_(integer *, complex *, complex *,
integer *, complex *, integer *), csymv_(char *, integer *,
complex *, complex *, integer *, complex *, integer *, complex *,
complex *, integer *);
extern real scnrm2_(integer *, complex *, integer *);
static integer ii, jj;
static complex wa, wb;
extern /* Subroutine */ int clacgv_(integer *, complex *, integer *);
static real wn;
extern /* Subroutine */ int xerbla_(char *, integer *), clarnv_(
integer *, integer *, integer *, complex *);
static complex tau;
/* -- LAPACK auxiliary test 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
=======
CLAGSY generates a complex symmetric matrix A, by pre- and post-
multiplying a real diagonal matrix D with a random unitary matrix:
A = U*D*U**T. The semi-bandwidth may then be reduced to k by
additional unitary transformations.
Arguments
=========
N (input) INTEGER
The order of the matrix A. N >= 0.
K (input) INTEGER
The number of nonzero subdiagonals within the band of A.
0 <= K <= N-1.
D (input) REAL array, dimension (N)
The diagonal elements of the diagonal matrix D.
A (output) COMPLEX array, dimension (LDA,N)
The generated n by n symmetric matrix A (the full matrix is
stored).
LDA (input) INTEGER
The leading dimension of the array A. LDA >= N.
ISEED (input/output) INTEGER array, dimension (4)
On entry, the seed of the random number generator; the array
elements must be between 0 and 4095, and ISEED(4) must be
odd.
On exit, the seed is updated.
WORK (workspace) COMPLEX array, dimension (2*N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
=====================================================================
Test the input arguments
Parameter adjustments */
--d;
a_dim1 = *lda;
a_offset = a_dim1 + 1;
a -= a_offset;
--iseed;
--work;
/* Function Body */
*info = 0;
if (*n < 0) {
*info = -1;
} else if (*k < 0 || *k > *n - 1) {
*info = -2;
} else if (*lda < max(1,*n)) {
*info = -5;
}
if (*info < 0) {
i__1 = -(*info);
xerbla_("CLAGSY", &i__1);
return 0;
}
/* initialize lower triangle of A to diagonal matrix */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i = j + 1; i <= i__2; ++i) {
i__3 = i + j * a_dim1;
a[i__3].r = 0.f, a[i__3].i = 0.f;
/* L10: */
}
/* L20: */
}
i__1 = *n;
for (i = 1; i <= i__1; ++i) {
i__2 = i + i * a_dim1;
i__3 = i;
a[i__2].r = d[i__3], a[i__2].i = 0.f;
/* L30: */
}
/* Generate lower triangle of symmetric matrix */
for (i = *n - 1; i >= 1; --i) {
/* generate random reflection */
i__1 = *n - i + 1;
clarnv_(&c__3, &iseed[1], &i__1, &work[1]);
i__1 = *n - i + 1;
wn = scnrm2_(&i__1, &work[1], &c__1);
d__1 = wn / c_abs(&work[1]);
q__1.r = d__1 * work[1].r, q__1.i = d__1 * work[1].i;
wa.r = q__1.r, wa.i = q__1.i;
if (wn == 0.f) {
tau.r = 0.f, tau.i = 0.f;
} else {
q__1.r = work[1].r + wa.r, q__1.i = work[1].i + wa.i;
wb.r = q__1.r, wb.i = q__1.i;
i__1 = *n - i;
c_div(&q__1, &c_b2, &wb);
cscal_(&i__1, &q__1, &work[2], &c__1);
work[1].r = 1.f, work[1].i = 0.f;
c_div(&q__1, &wb, &wa);
d__1 = q__1.r;
tau.r = d__1, tau.i = 0.f;
}
/* apply random reflection to A(i:n,i:n) from the left
and the right
compute y := tau * A * conjg(u) */
i__1 = *n - i + 1;
clacgv_(&i__1, &work[1], &c__1);
i__1 = *n - i + 1;
csymv_("Lower", &i__1, &tau, &a[i + i * a_dim1], lda, &work[1], &c__1,
&c_b1, &work[*n + 1], &c__1);
i__1 = *n - i + 1;
clacgv_(&i__1, &work[1], &c__1);
/* compute v := y - 1/2 * tau * ( u, y ) * u */
q__3.r = -.5f, q__3.i = 0.f;
q__2.r = q__3.r * tau.r - q__3.i * tau.i, q__2.i = q__3.r * tau.i +
q__3.i * tau.r;
i__1 = *n - i + 1;
cdotc_(&q__4, &i__1, &work[1], &c__1, &work[*n + 1], &c__1);
q__1.r = q__2.r * q__4.r - q__2.i * q__4.i, q__1.i = q__2.r * q__4.i
+ q__2.i * q__4.r;
alpha.r = q__1.r, alpha.i = q__1.i;
i__1 = *n - i + 1;
caxpy_(&i__1, &alpha, &work[1], &c__1, &work[*n + 1], &c__1);
/* apply the transformation as a rank-2 update to A(i:n,i:n)
CALL CSYR2( 'Lower', N-I+1, -ONE, WORK, 1, WORK( N+1 ), 1,
$ A( I, I ), LDA ) */
i__1 = *n;
for (jj = i; jj <= i__1; ++jj) {
i__2 = *n;
for (ii = jj; ii <= i__2; ++ii) {
i__3 = ii + jj * a_dim1;
i__4 = ii + jj * a_dim1;
i__5 = ii - i + 1;
i__6 = *n + jj - i + 1;
q__3.r = work[i__5].r * work[i__6].r - work[i__5].i * work[
i__6].i, q__3.i = work[i__5].r * work[i__6].i + work[
i__5].i * work[i__6].r;
q__2.r = a[i__4].r - q__3.r, q__2.i = a[i__4].i - q__3.i;
i__7 = *n + ii - i + 1;
i__8 = jj - i + 1;
q__4.r = work[i__7].r * work[i__8].r - work[i__7].i * work[
i__8].i, q__4.i = work[i__7].r * work[i__8].i + work[
i__7].i * work[i__8].r;
q__1.r = q__2.r - q__4.r, q__1.i = q__2.i - q__4.i;
a[i__3].r = q__1.r, a[i__3].i = q__1.i;
/* L40: */
}
/* L50: */
}
/* L60: */
}
/* Reduce number of subdiagonals to K */
i__1 = *n - 1 - *k;
for (i = 1; i <= i__1; ++i) {
/* generate reflection to annihilate A(k+i+1:n,i) */
i__2 = *n - *k - i + 1;
wn = scnrm2_(&i__2, &a[*k + i + i * a_dim1], &c__1);
d__1 = wn / c_abs(&a[*k + i + i * a_dim1]);
i__2 = *k + i + i * a_dim1;
q__1.r = d__1 * a[i__2].r, q__1.i = d__1 * a[i__2].i;
wa.r = q__1.r, wa.i = q__1.i;
if (wn == 0.f) {
tau.r = 0.f, tau.i = 0.f;
} else {
i__2 = *k + i + i * a_dim1;
q__1.r = a[i__2].r + wa.r, q__1.i = a[i__2].i + wa.i;
wb.r = q__1.r, wb.i = q__1.i;
i__2 = *n - *k - i;
c_div(&q__1, &c_b2, &wb);
cscal_(&i__2, &q__1, &a[*k + i + 1 + i * a_dim1], &c__1);
i__2 = *k + i + i * a_dim1;
a[i__2].r = 1.f, a[i__2].i = 0.f;
c_div(&q__1, &wb, &wa);
d__1 = q__1.r;
tau.r = d__1, tau.i = 0.f;
}
/* apply reflection to A(k+i:n,i+1:k+i-1) from the left */
i__2 = *n - *k - i + 1;
i__3 = *k - 1;
cgemv_("Conjugate transpose", &i__2, &i__3, &c_b2, &a[*k + i + (i + 1)
* a_dim1], lda, &a[*k + i + i * a_dim1], &c__1, &c_b1, &work[
1], &c__1);
i__2 = *n - *k - i + 1;
i__3 = *k - 1;
q__1.r = -(doublereal)tau.r, q__1.i = -(doublereal)tau.i;
cgerc_(&i__2, &i__3, &q__1, &a[*k + i + i * a_dim1], &c__1, &work[1],
&c__1, &a[*k + i + (i + 1) * a_dim1], lda);
/* apply reflection to A(k+i:n,k+i:n) from the left and the rig
ht
compute y := tau * A * conjg(u) */
i__2 = *n - *k - i + 1;
clacgv_(&i__2, &a[*k + i + i * a_dim1], &c__1);
i__2 = *n - *k - i + 1;
csymv_("Lower", &i__2, &tau, &a[*k + i + (*k + i) * a_dim1], lda, &a[*
k + i + i * a_dim1], &c__1, &c_b1, &work[1], &c__1);
i__2 = *n - *k - i + 1;
clacgv_(&i__2, &a[*k + i + i * a_dim1], &c__1);
/* compute v := y - 1/2 * tau * ( u, y ) * u */
q__3.r = -.5f, q__3.i = 0.f;
q__2.r = q__3.r * tau.r - q__3.i * tau.i, q__2.i = q__3.r * tau.i +
q__3.i * tau.r;
i__2 = *n - *k - i + 1;
cdotc_(&q__4, &i__2, &a[*k + i + i * a_dim1], &c__1, &work[1], &c__1);
q__1.r = q__2.r * q__4.r - q__2.i * q__4.i, q__1.i = q__2.r * q__4.i
+ q__2.i * q__4.r;
alpha.r = q__1.r, alpha.i = q__1.i;
i__2 = *n - *k - i + 1;
caxpy_(&i__2, &alpha, &a[*k + i + i * a_dim1], &c__1, &work[1], &c__1)
;
/* apply symmetric rank-2 update to A(k+i:n,k+i:n)
CALL CSYR2( 'Lower', N-K-I+1, -ONE, A( K+I, I ), 1, WORK, 1,
$ A( K+I, K+I ), LDA ) */
i__2 = *n;
for (jj = *k + i; jj <= i__2; ++jj) {
i__3 = *n;
for (ii = jj; ii <= i__3; ++ii) {
i__4 = ii + jj * a_dim1;
i__5 = ii + jj * a_dim1;
i__6 = ii + i * a_dim1;
i__7 = jj - *k - i + 1;
q__3.r = a[i__6].r * work[i__7].r - a[i__6].i * work[i__7].i,
q__3.i = a[i__6].r * work[i__7].i + a[i__6].i * work[
i__7].r;
q__2.r = a[i__5].r - q__3.r, q__2.i = a[i__5].i - q__3.i;
i__8 = ii - *k - i + 1;
i__9 = jj + i * a_dim1;
q__4.r = work[i__8].r * a[i__9].r - work[i__8].i * a[i__9].i,
q__4.i = work[i__8].r * a[i__9].i + work[i__8].i * a[
i__9].r;
q__1.r = q__2.r - q__4.r, q__1.i = q__2.i - q__4.i;
a[i__4].r = q__1.r, a[i__4].i = q__1.i;
/* L70: */
}
/* L80: */
}
i__2 = *k + i + i * a_dim1;
q__1.r = -(doublereal)wa.r, q__1.i = -(doublereal)wa.i;
a[i__2].r = q__1.r, a[i__2].i = q__1.i;
i__2 = *n;
for (j = *k + i + 1; j <= i__2; ++j) {
i__3 = j + i * a_dim1;
a[i__3].r = 0.f, a[i__3].i = 0.f;
/* L90: */
}
/* L100: */
}
/* Store full symmetric matrix */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i = j + 1; i <= i__2; ++i) {
i__3 = j + i * a_dim1;
i__4 = i + j * a_dim1;
a[i__3].r = a[i__4].r, a[i__3].i = a[i__4].i;
/* L110: */
}
/* L120: */
}
return 0;
/* End of CLAGSY */
} /* clagsy_ */
/* Subroutine */ int clarge_(integer *n, complex *a, integer *lda, integer *
iseed, complex *work, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1;
real r__1;
complex q__1;
/* Builtin functions */
double c_abs(complex *);
void c_div(complex *, complex *, complex *);
/* Local variables */
static integer i__;
extern /* Subroutine */ int cgerc_(integer *, integer *, complex *,
complex *, integer *, complex *, integer *, complex *, integer *),
cscal_(integer *, complex *, complex *, integer *), cgemv_(char *
, integer *, integer *, complex *, complex *, integer *, complex *
, integer *, complex *, complex *, integer *);
extern doublereal scnrm2_(integer *, complex *, integer *);
static complex wa, wb;
static real wn;
extern /* Subroutine */ int xerbla_(char *, integer *), clarnv_(
integer *, integer *, integer *, complex *);
static complex tau;
#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)]
/* -- LAPACK auxiliary test routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
September 30, 1994
Purpose
=======
CLARGE pre- and post-multiplies a complex general n by n matrix A
with a random unitary matrix: A = U*D*U'.
Arguments
=========
N (input) INTEGER
The order of the matrix A. N >= 0.
A (input/output) COMPLEX array, dimension (LDA,N)
On entry, the original n by n matrix A.
On exit, A is overwritten by U*A*U' for some random
unitary matrix U.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= N.
ISEED (input/output) INTEGER array, dimension (4)
On entry, the seed of the random number generator; the array
elements must be between 0 and 4095, and ISEED(4) must be
odd.
On exit, the seed is updated.
WORK (workspace) COMPLEX array, dimension (2*N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
=====================================================================
Test the input arguments
Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--iseed;
--work;
/* Function Body */
*info = 0;
if (*n < 0) {
*info = -1;
} else if (*lda < max(1,*n)) {
*info = -3;
}
if (*info < 0) {
i__1 = -(*info);
xerbla_("CLARGE", &i__1);
return 0;
}
/* pre- and post-multiply A by random unitary matrix */
for (i__ = *n; i__ >= 1; --i__) {
/* generate random reflection */
i__1 = *n - i__ + 1;
clarnv_(&c__3, &iseed[1], &i__1, &work[1]);
i__1 = *n - i__ + 1;
wn = scnrm2_(&i__1, &work[1], &c__1);
r__1 = wn / c_abs(&work[1]);
q__1.r = r__1 * work[1].r, q__1.i = r__1 * work[1].i;
wa.r = q__1.r, wa.i = q__1.i;
if (wn == 0.f) {
tau.r = 0.f, tau.i = 0.f;
} else {
q__1.r = work[1].r + wa.r, q__1.i = work[1].i + wa.i;
wb.r = q__1.r, wb.i = q__1.i;
i__1 = *n - i__;
c_div(&q__1, &c_b2, &wb);
cscal_(&i__1, &q__1, &work[2], &c__1);
work[1].r = 1.f, work[1].i = 0.f;
c_div(&q__1, &wb, &wa);
r__1 = q__1.r;
tau.r = r__1, tau.i = 0.f;
}
/* multiply A(i:n,1:n) by random reflection from the left */
i__1 = *n - i__ + 1;
cgemv_("Conjugate transpose", &i__1, n, &c_b2, &a_ref(i__, 1), lda, &
work[1], &c__1, &c_b1, &work[*n + 1], &c__1);
i__1 = *n - i__ + 1;
q__1.r = -tau.r, q__1.i = -tau.i;
cgerc_(&i__1, n, &q__1, &work[1], &c__1, &work[*n + 1], &c__1, &a_ref(
i__, 1), lda);
/* multiply A(1:n,i:n) by random reflection from the right */
i__1 = *n - i__ + 1;
cgemv_("No transpose", n, &i__1, &c_b2, &a_ref(1, i__), lda, &work[1],
&c__1, &c_b1, &work[*n + 1], &c__1);
i__1 = *n - i__ + 1;
q__1.r = -tau.r, q__1.i = -tau.i;
cgerc_(n, &i__1, &q__1, &work[*n + 1], &c__1, &work[1], &c__1, &a_ref(
1, i__), lda);
/* L10: */
}
return 0;
/* End of CLARGE */
} /* clarge_ */
/* Subroutine */ int clagsy_(integer *n, integer *k, real *d__, complex *a,
integer *lda, integer *iseed, complex *work, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5, i__6, i__7, i__8,
i__9;
real r__1;
complex q__1, q__2, q__3, q__4;
/* Local variables */
integer i__, j, ii, jj;
complex wa, wb;
real wn;
complex tau;
complex alpha;
/* -- LAPACK auxiliary test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CLAGSY generates a complex symmetric matrix A, by pre- and post- */
/* multiplying a real diagonal matrix D with a random unitary matrix: */
/* A = U*D*U**T. The semi-bandwidth may then be reduced to k by */
/* additional unitary transformations. */
/* Arguments */
/* ========= */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* K (input) INTEGER */
/* The number of nonzero subdiagonals within the band of A. */
/* 0 <= K <= N-1. */
/* D (input) REAL array, dimension (N) */
/* The diagonal elements of the diagonal matrix D. */
/* A (output) COMPLEX array, dimension (LDA,N) */
/* The generated n by n symmetric matrix A (the full matrix is */
/* stored). */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= N. */
/* ISEED (input/output) INTEGER array, dimension (4) */
/* On entry, the seed of the random number generator; the array */
/* elements must be between 0 and 4095, and ISEED(4) must be */
/* odd. */
/* On exit, the seed is updated. */
/* WORK (workspace) COMPLEX array, dimension (2*N) */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input arguments */
/* Parameter adjustments */
--d__;
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--iseed;
--work;
/* Function Body */
*info = 0;
if (*n < 0) {
*info = -1;
} else if (*k < 0 || *k > *n - 1) {
*info = -2;
} else if (*lda < max(1,*n)) {
*info = -5;
}
if (*info < 0) {
i__1 = -(*info);
xerbla_("CLAGSY", &i__1);
return 0;
}
/* initialize lower triangle of A to diagonal matrix */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
a[i__3].r = 0.f, a[i__3].i = 0.f;
/* L10: */
}
/* L20: */
}
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__ + i__ * a_dim1;
i__3 = i__;
a[i__2].r = d__[i__3], a[i__2].i = 0.f;
/* L30: */
}
/* Generate lower triangle of symmetric matrix */
for (i__ = *n - 1; i__ >= 1; --i__) {
/* generate random reflection */
i__1 = *n - i__ + 1;
clarnv_(&c__3, &iseed[1], &i__1, &work[1]);
i__1 = *n - i__ + 1;
wn = scnrm2_(&i__1, &work[1], &c__1);
r__1 = wn / c_abs(&work[1]);
q__1.r = r__1 * work[1].r, q__1.i = r__1 * work[1].i;
wa.r = q__1.r, wa.i = q__1.i;
if (wn == 0.f) {
tau.r = 0.f, tau.i = 0.f;
} else {
q__1.r = work[1].r + wa.r, q__1.i = work[1].i + wa.i;
wb.r = q__1.r, wb.i = q__1.i;
i__1 = *n - i__;
c_div(&q__1, &c_b2, &wb);
cscal_(&i__1, &q__1, &work[2], &c__1);
work[1].r = 1.f, work[1].i = 0.f;
c_div(&q__1, &wb, &wa);
r__1 = q__1.r;
tau.r = r__1, tau.i = 0.f;
}
/* apply random reflection to A(i:n,i:n) from the left */
/* and the right */
/* compute y := tau * A * conjg(u) */
i__1 = *n - i__ + 1;
clacgv_(&i__1, &work[1], &c__1);
i__1 = *n - i__ + 1;
csymv_("Lower", &i__1, &tau, &a[i__ + i__ * a_dim1], lda, &work[1], &
c__1, &c_b1, &work[*n + 1], &c__1);
i__1 = *n - i__ + 1;
clacgv_(&i__1, &work[1], &c__1);
/* compute v := y - 1/2 * tau * ( u, y ) * u */
q__3.r = -.5f, q__3.i = -0.f;
q__2.r = q__3.r * tau.r - q__3.i * tau.i, q__2.i = q__3.r * tau.i +
q__3.i * tau.r;
i__1 = *n - i__ + 1;
cdotc_(&q__4, &i__1, &work[1], &c__1, &work[*n + 1], &c__1);
q__1.r = q__2.r * q__4.r - q__2.i * q__4.i, q__1.i = q__2.r * q__4.i
+ q__2.i * q__4.r;
alpha.r = q__1.r, alpha.i = q__1.i;
i__1 = *n - i__ + 1;
caxpy_(&i__1, &alpha, &work[1], &c__1, &work[*n + 1], &c__1);
/* apply the transformation as a rank-2 update to A(i:n,i:n) */
/* CALL CSYR2( 'Lower', N-I+1, -ONE, WORK, 1, WORK( N+1 ), 1, */
/* $ A( I, I ), LDA ) */
i__1 = *n;
for (jj = i__; jj <= i__1; ++jj) {
i__2 = *n;
for (ii = jj; ii <= i__2; ++ii) {
i__3 = ii + jj * a_dim1;
i__4 = ii + jj * a_dim1;
i__5 = ii - i__ + 1;
i__6 = *n + jj - i__ + 1;
q__3.r = work[i__5].r * work[i__6].r - work[i__5].i * work[
i__6].i, q__3.i = work[i__5].r * work[i__6].i + work[
i__5].i * work[i__6].r;
q__2.r = a[i__4].r - q__3.r, q__2.i = a[i__4].i - q__3.i;
i__7 = *n + ii - i__ + 1;
i__8 = jj - i__ + 1;
q__4.r = work[i__7].r * work[i__8].r - work[i__7].i * work[
i__8].i, q__4.i = work[i__7].r * work[i__8].i + work[
i__7].i * work[i__8].r;
q__1.r = q__2.r - q__4.r, q__1.i = q__2.i - q__4.i;
a[i__3].r = q__1.r, a[i__3].i = q__1.i;
/* L40: */
}
/* L50: */
}
/* L60: */
}
/* Reduce number of subdiagonals to K */
i__1 = *n - 1 - *k;
for (i__ = 1; i__ <= i__1; ++i__) {
/* generate reflection to annihilate A(k+i+1:n,i) */
i__2 = *n - *k - i__ + 1;
wn = scnrm2_(&i__2, &a[*k + i__ + i__ * a_dim1], &c__1);
r__1 = wn / c_abs(&a[*k + i__ + i__ * a_dim1]);
i__2 = *k + i__ + i__ * a_dim1;
q__1.r = r__1 * a[i__2].r, q__1.i = r__1 * a[i__2].i;
wa.r = q__1.r, wa.i = q__1.i;
if (wn == 0.f) {
tau.r = 0.f, tau.i = 0.f;
} else {
i__2 = *k + i__ + i__ * a_dim1;
q__1.r = a[i__2].r + wa.r, q__1.i = a[i__2].i + wa.i;
wb.r = q__1.r, wb.i = q__1.i;
i__2 = *n - *k - i__;
c_div(&q__1, &c_b2, &wb);
cscal_(&i__2, &q__1, &a[*k + i__ + 1 + i__ * a_dim1], &c__1);
i__2 = *k + i__ + i__ * a_dim1;
a[i__2].r = 1.f, a[i__2].i = 0.f;
c_div(&q__1, &wb, &wa);
r__1 = q__1.r;
tau.r = r__1, tau.i = 0.f;
}
/* apply reflection to A(k+i:n,i+1:k+i-1) from the left */
i__2 = *n - *k - i__ + 1;
i__3 = *k - 1;
cgemv_("Conjugate transpose", &i__2, &i__3, &c_b2, &a[*k + i__ + (i__
+ 1) * a_dim1], lda, &a[*k + i__ + i__ * a_dim1], &c__1, &
c_b1, &work[1], &c__1);
i__2 = *n - *k - i__ + 1;
i__3 = *k - 1;
q__1.r = -tau.r, q__1.i = -tau.i;
cgerc_(&i__2, &i__3, &q__1, &a[*k + i__ + i__ * a_dim1], &c__1, &work[
1], &c__1, &a[*k + i__ + (i__ + 1) * a_dim1], lda);
/* apply reflection to A(k+i:n,k+i:n) from the left and the right */
/* compute y := tau * A * conjg(u) */
i__2 = *n - *k - i__ + 1;
clacgv_(&i__2, &a[*k + i__ + i__ * a_dim1], &c__1);
i__2 = *n - *k - i__ + 1;
csymv_("Lower", &i__2, &tau, &a[*k + i__ + (*k + i__) * a_dim1], lda,
&a[*k + i__ + i__ * a_dim1], &c__1, &c_b1, &work[1], &c__1);
i__2 = *n - *k - i__ + 1;
clacgv_(&i__2, &a[*k + i__ + i__ * a_dim1], &c__1);
/* compute v := y - 1/2 * tau * ( u, y ) * u */
q__3.r = -.5f, q__3.i = -0.f;
q__2.r = q__3.r * tau.r - q__3.i * tau.i, q__2.i = q__3.r * tau.i +
q__3.i * tau.r;
i__2 = *n - *k - i__ + 1;
cdotc_(&q__4, &i__2, &a[*k + i__ + i__ * a_dim1], &c__1, &work[1], &
c__1);
q__1.r = q__2.r * q__4.r - q__2.i * q__4.i, q__1.i = q__2.r * q__4.i
+ q__2.i * q__4.r;
alpha.r = q__1.r, alpha.i = q__1.i;
i__2 = *n - *k - i__ + 1;
caxpy_(&i__2, &alpha, &a[*k + i__ + i__ * a_dim1], &c__1, &work[1], &
c__1);
/* apply symmetric rank-2 update to A(k+i:n,k+i:n) */
/* CALL CSYR2( 'Lower', N-K-I+1, -ONE, A( K+I, I ), 1, WORK, 1, */
/* $ A( K+I, K+I ), LDA ) */
i__2 = *n;
for (jj = *k + i__; jj <= i__2; ++jj) {
i__3 = *n;
for (ii = jj; ii <= i__3; ++ii) {
i__4 = ii + jj * a_dim1;
i__5 = ii + jj * a_dim1;
i__6 = ii + i__ * a_dim1;
i__7 = jj - *k - i__ + 1;
q__3.r = a[i__6].r * work[i__7].r - a[i__6].i * work[i__7].i,
q__3.i = a[i__6].r * work[i__7].i + a[i__6].i * work[
i__7].r;
q__2.r = a[i__5].r - q__3.r, q__2.i = a[i__5].i - q__3.i;
i__8 = ii - *k - i__ + 1;
i__9 = jj + i__ * a_dim1;
q__4.r = work[i__8].r * a[i__9].r - work[i__8].i * a[i__9].i,
q__4.i = work[i__8].r * a[i__9].i + work[i__8].i * a[
i__9].r;
q__1.r = q__2.r - q__4.r, q__1.i = q__2.i - q__4.i;
a[i__4].r = q__1.r, a[i__4].i = q__1.i;
/* L70: */
}
/* L80: */
}
i__2 = *k + i__ + i__ * a_dim1;
q__1.r = -wa.r, q__1.i = -wa.i;
a[i__2].r = q__1.r, a[i__2].i = q__1.i;
i__2 = *n;
for (j = *k + i__ + 1; j <= i__2; ++j) {
i__3 = j + i__ * a_dim1;
a[i__3].r = 0.f, a[i__3].i = 0.f;
/* L90: */
}
/* L100: */
}
/* Store full symmetric matrix */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
i__3 = j + i__ * a_dim1;
i__4 = i__ + j * a_dim1;
a[i__3].r = a[i__4].r, a[i__3].i = a[i__4].i;
/* L110: */
}
/* L120: */
}
return 0;
/* End of CLAGSY */
} /* clagsy_ */
/* Subroutine */ int claror_(char *side, char *init, integer *m, integer *n,
complex *a, integer *lda, integer *iseed, complex *x, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3;
complex q__1, q__2;
/* Builtin functions */
double c_abs(complex *);
void r_cnjg(complex *, complex *);
/* Local variables */
static integer kbeg, jcol;
static real xabs;
static integer irow, j;
extern /* Subroutine */ int cgerc_(integer *, integer *, complex *,
complex *, integer *, complex *, integer *, complex *, integer *),
cscal_(integer *, complex *, complex *, integer *);
extern logical lsame_(char *, char *);
extern /* Subroutine */ int cgemv_(char *, integer *, integer *, complex *
, complex *, integer *, complex *, integer *, complex *, complex *
, integer *);
static complex csign;
static integer ixfrm, itype, nxfrm;
static real xnorm;
extern real scnrm2_(integer *, complex *, integer *);
extern /* Subroutine */ int clacgv_(integer *, complex *, integer *);
extern /* Complex */ VOID clarnd_(complex *, integer *, integer *);
extern /* Subroutine */ int claset_(char *, integer *, integer *, complex
*, complex *, complex *, integer *), xerbla_(char *,
integer *);
static real factor;
static complex xnorms;
/* -- LAPACK auxiliary test 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
=======
CLAROR pre- or post-multiplies an M by N matrix A by a random
unitary matrix U, overwriting A. A may optionally be
initialized to the identity matrix before multiplying by U.
U is generated using the method of G.W. Stewart
( SIAM J. Numer. Anal. 17, 1980, pp. 403-409 ).
(BLAS-2 version)
Arguments
=========
SIDE - CHARACTER*1
SIDE specifies whether A is multiplied on the left or right
by U.
SIDE = 'L' Multiply A on the left (premultiply) by U
SIDE = 'R' Multiply A on the right (postmultiply) by U*
SIDE = 'C' Multiply A on the left by U and the right by U*
SIDE = 'T' Multiply A on the left by U and the right by U'
Not modified.
INIT - CHARACTER*1
INIT specifies whether or not A should be initialized to
the identity matrix.
INIT = 'I' Initialize A to (a section of) the
identity matrix before applying U.
INIT = 'N' No initialization. Apply U to the
input matrix A.
INIT = 'I' may be used to generate square (i.e., unitary)
or rectangular orthogonal matrices (orthogonality being
in the sense of CDOTC):
For square matrices, M=N, and SIDE many be either 'L' or
'R'; the rows will be orthogonal to each other, as will the
columns.
For rectangular matrices where M < N, SIDE = 'R' will
produce a dense matrix whose rows will be orthogonal and
whose columns will not, while SIDE = 'L' will produce a
matrix whose rows will be orthogonal, and whose first M
columns will be orthogonal, the remaining columns being
zero.
For matrices where M > N, just use the previous
explaination, interchanging 'L' and 'R' and "rows" and
"columns".
Not modified.
M - INTEGER
Number of rows of A. Not modified.
N - INTEGER
Number of columns of A. Not modified.
A - COMPLEX array, dimension ( LDA, N )
Input and output array. Overwritten by U A ( if SIDE = 'L' )
or by A U ( if SIDE = 'R' )
or by U A U* ( if SIDE = 'C')
or by U A U' ( if SIDE = 'T') on exit.
LDA - INTEGER
Leading dimension of A. Must be at least MAX ( 1, M ).
Not modified.
ISEED - INTEGER array, dimension ( 4 )
On entry ISEED specifies the seed of the random number
generator. The array elements should be between 0 and 4095;
if not they will be reduced mod 4096. Also, ISEED(4) must
be odd. The random number generator uses a linear
congruential sequence limited to small integers, and so
should produce machine independent random numbers. The
values of ISEED are changed on exit, and can be used in the
next call to CLAROR to continue the same random number
sequence.
Modified.
X - COMPLEX array, dimension ( 3*MAX( M, N ) )
Workspace. Of length:
2*M + N if SIDE = 'L',
2*N + M if SIDE = 'R',
3*N if SIDE = 'C' or 'T'.
Modified.
INFO - INTEGER
An error flag. It is set to:
0 if no error.
1 if CLARND returned a bad random number (installation
problem)
-1 if SIDE is not L, R, C, or T.
-3 if M is negative.
-4 if N is negative or if SIDE is C or T and N is not equal
to M.
-6 if LDA is less than M.
=====================================================================
Parameter adjustments */
a_dim1 = *lda;
a_offset = a_dim1 + 1;
a -= a_offset;
--iseed;
--x;
/* Function Body */
if (*n == 0 || *m == 0) {
return 0;
}
itype = 0;
if (lsame_(side, "L")) {
itype = 1;
} else if (lsame_(side, "R")) {
itype = 2;
} else if (lsame_(side, "C")) {
itype = 3;
} else if (lsame_(side, "T")) {
itype = 4;
}
/* Check for argument errors. */
*info = 0;
if (itype == 0) {
*info = -1;
} else if (*m < 0) {
*info = -3;
} else if (*n < 0 || itype == 3 && *n != *m) {
*info = -4;
} else if (*lda < *m) {
*info = -6;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CLAROR", &i__1);
return 0;
}
if (itype == 1) {
nxfrm = *m;
} else {
nxfrm = *n;
}
/* Initialize A to the identity matrix if desired */
if (lsame_(init, "I")) {
claset_("Full", m, n, &c_b1, &c_b2, &a[a_offset], lda);
}
/* If no rotation possible, still multiply by
a random complex number from the circle |x| = 1
2) Compute Rotation by computing Householder
Transformations H(2), H(3), ..., H(n). Note that the
order in which they are computed is irrelevant. */
i__1 = nxfrm;
for (j = 1; j <= i__1; ++j) {
i__2 = j;
x[i__2].r = 0.f, x[i__2].i = 0.f;
/* L40: */
}
i__1 = nxfrm;
for (ixfrm = 2; ixfrm <= i__1; ++ixfrm) {
kbeg = nxfrm - ixfrm + 1;
/* Generate independent normal( 0, 1 ) random numbers */
i__2 = nxfrm;
for (j = kbeg; j <= i__2; ++j) {
i__3 = j;
clarnd_(&q__1, &c__3, &iseed[1]);
x[i__3].r = q__1.r, x[i__3].i = q__1.i;
/* L50: */
}
/* Generate a Householder transformation from the random vector
X */
xnorm = scnrm2_(&ixfrm, &x[kbeg], &c__1);
xabs = c_abs(&x[kbeg]);
if (xabs != 0.f) {
i__2 = kbeg;
q__1.r = x[i__2].r / xabs, q__1.i = x[i__2].i / xabs;
csign.r = q__1.r, csign.i = q__1.i;
} else {
csign.r = 1.f, csign.i = 0.f;
}
q__1.r = xnorm * csign.r, q__1.i = xnorm * csign.i;
xnorms.r = q__1.r, xnorms.i = q__1.i;
i__2 = nxfrm + kbeg;
q__1.r = -(doublereal)csign.r, q__1.i = -(doublereal)csign.i;
x[i__2].r = q__1.r, x[i__2].i = q__1.i;
factor = xnorm * (xnorm + xabs);
if (dabs(factor) < 1e-20f) {
*info = 1;
i__2 = -(*info);
xerbla_("CLAROR", &i__2);
return 0;
} else {
factor = 1.f / factor;
}
i__2 = kbeg;
i__3 = kbeg;
q__1.r = x[i__3].r + xnorms.r, q__1.i = x[i__3].i + xnorms.i;
x[i__2].r = q__1.r, x[i__2].i = q__1.i;
/* Apply Householder transformation to A */
if (itype == 1 || itype == 3 || itype == 4) {
/* Apply H(k) on the left of A */
cgemv_("C", &ixfrm, n, &c_b2, &a[kbeg + a_dim1], lda, &x[kbeg], &
c__1, &c_b1, &x[(nxfrm << 1) + 1], &c__1);
q__2.r = factor, q__2.i = 0.f;
q__1.r = -(doublereal)q__2.r, q__1.i = -(doublereal)q__2.i;
cgerc_(&ixfrm, n, &q__1, &x[kbeg], &c__1, &x[(nxfrm << 1) + 1], &
c__1, &a[kbeg + a_dim1], lda);
}
if (itype >= 2 && itype <= 4) {
/* Apply H(k)* (or H(k)') on the right of A */
if (itype == 4) {
clacgv_(&ixfrm, &x[kbeg], &c__1);
}
cgemv_("N", m, &ixfrm, &c_b2, &a[kbeg * a_dim1 + 1], lda, &x[kbeg]
, &c__1, &c_b1, &x[(nxfrm << 1) + 1], &c__1);
q__2.r = factor, q__2.i = 0.f;
q__1.r = -(doublereal)q__2.r, q__1.i = -(doublereal)q__2.i;
cgerc_(m, &ixfrm, &q__1, &x[(nxfrm << 1) + 1], &c__1, &x[kbeg], &
c__1, &a[kbeg * a_dim1 + 1], lda);
}
/* L60: */
}
clarnd_(&q__1, &c__3, &iseed[1]);
x[1].r = q__1.r, x[1].i = q__1.i;
xabs = c_abs(&x[1]);
if (xabs != 0.f) {
q__1.r = x[1].r / xabs, q__1.i = x[1].i / xabs;
csign.r = q__1.r, csign.i = q__1.i;
} else {
csign.r = 1.f, csign.i = 0.f;
}
i__1 = nxfrm << 1;
x[i__1].r = csign.r, x[i__1].i = csign.i;
/* Scale the matrix A by D. */
if (itype == 1 || itype == 3 || itype == 4) {
i__1 = *m;
for (irow = 1; irow <= i__1; ++irow) {
r_cnjg(&q__1, &x[nxfrm + irow]);
cscal_(n, &q__1, &a[irow + a_dim1], lda);
/* L70: */
}
}
if (itype == 2 || itype == 3) {
i__1 = *n;
for (jcol = 1; jcol <= i__1; ++jcol) {
cscal_(m, &x[nxfrm + jcol], &a[jcol * a_dim1 + 1], &c__1);
/* L80: */
}
}
if (itype == 4) {
i__1 = *n;
for (jcol = 1; jcol <= i__1; ++jcol) {
r_cnjg(&q__1, &x[nxfrm + jcol]);
cscal_(m, &q__1, &a[jcol * a_dim1 + 1], &c__1);
/* L90: */
}
}
return 0;
/* End of CLAROR */
} /* claror_ */
/* Subroutine */ int clatzm_(char *side, integer *m, integer *n, complex *v,
integer *incv, complex *tau, complex *c1, complex *c2, integer *ldc,
complex *work)
{
/* -- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
September 30, 1994
Purpose
=======
This routine is deprecated and has been replaced by routine CUNMRZ.
CLATZM applies a Householder matrix generated by CTZRQF to a matrix.
Let P = I - tau*u*u', u = ( 1 ),
( v )
where v is an (m-1) vector if SIDE = 'L', or a (n-1) vector if
SIDE = 'R'.
If SIDE equals 'L', let
C = [ C1 ] 1
[ C2 ] m-1
n
Then C is overwritten by P*C.
If SIDE equals 'R', let
C = [ C1, C2 ] m
1 n-1
Then C is overwritten by C*P.
Arguments
=========
SIDE (input) CHARACTER*1
= 'L': form P * C
= 'R': form C * P
M (input) INTEGER
The number of rows of the matrix C.
N (input) INTEGER
The number of columns of the matrix C.
V (input) COMPLEX array, dimension
(1 + (M-1)*abs(INCV)) if SIDE = 'L'
(1 + (N-1)*abs(INCV)) if SIDE = 'R'
The vector v in the representation of P. V is not used
if TAU = 0.
INCV (input) INTEGER
The increment between elements of v. INCV <> 0
TAU (input) COMPLEX
The value tau in the representation of P.
C1 (input/output) COMPLEX array, dimension
(LDC,N) if SIDE = 'L'
(M,1) if SIDE = 'R'
On entry, the n-vector C1 if SIDE = 'L', or the m-vector C1
if SIDE = 'R'.
On exit, the first row of P*C if SIDE = 'L', or the first
column of C*P if SIDE = 'R'.
C2 (input/output) COMPLEX array, dimension
(LDC, N) if SIDE = 'L'
(LDC, N-1) if SIDE = 'R'
On entry, the (m - 1) x n matrix C2 if SIDE = 'L', or the
m x (n - 1) matrix C2 if SIDE = 'R'.
On exit, rows 2:m of P*C if SIDE = 'L', or columns 2:m of C*P
if SIDE = 'R'.
LDC (input) INTEGER
The leading dimension of the arrays C1 and C2.
LDC >= max(1,M).
WORK (workspace) COMPLEX array, dimension
(N) if SIDE = 'L'
(M) if SIDE = 'R'
=====================================================================
Parameter adjustments */
/* Table of constant values */
static complex c_b1 = {1.f,0.f};
static integer c__1 = 1;
/* System generated locals */
integer c1_dim1, c1_offset, c2_dim1, c2_offset, i__1;
complex q__1;
/* Local variables */
extern /* Subroutine */ int cgerc_(integer *, integer *, complex *,
complex *, integer *, complex *, integer *, complex *, integer *),
cgemv_(char *, integer *, integer *, complex *, complex *,
integer *, complex *, integer *, complex *, complex *, integer *);
extern logical lsame_(char *, char *);
extern /* Subroutine */ int cgeru_(integer *, integer *, complex *,
complex *, integer *, complex *, integer *, complex *, integer *),
ccopy_(integer *, complex *, integer *, complex *, integer *),
caxpy_(integer *, complex *, complex *, integer *, complex *,
integer *), clacgv_(integer *, complex *, integer *);
--v;
c2_dim1 = *ldc;
c2_offset = 1 + c2_dim1 * 1;
c2 -= c2_offset;
c1_dim1 = *ldc;
c1_offset = 1 + c1_dim1 * 1;
c1 -= c1_offset;
--work;
/* Function Body */
if (min(*m,*n) == 0 || tau->r == 0.f && tau->i == 0.f) {
return 0;
}
if (lsame_(side, "L")) {
/* w := conjg( C1 + v' * C2 ) */
ccopy_(n, &c1[c1_offset], ldc, &work[1], &c__1);
clacgv_(n, &work[1], &c__1);
i__1 = *m - 1;
cgemv_("Conjugate transpose", &i__1, n, &c_b1, &c2[c2_offset], ldc, &
v[1], incv, &c_b1, &work[1], &c__1);
/* [ C1 ] := [ C1 ] - tau* [ 1 ] * w'
[ C2 ] [ C2 ] [ v ] */
clacgv_(n, &work[1], &c__1);
q__1.r = -tau->r, q__1.i = -tau->i;
caxpy_(n, &q__1, &work[1], &c__1, &c1[c1_offset], ldc);
i__1 = *m - 1;
q__1.r = -tau->r, q__1.i = -tau->i;
cgeru_(&i__1, n, &q__1, &v[1], incv, &work[1], &c__1, &c2[c2_offset],
ldc);
} else if (lsame_(side, "R")) {
/* w := C1 + C2 * v */
ccopy_(m, &c1[c1_offset], &c__1, &work[1], &c__1);
i__1 = *n - 1;
cgemv_("No transpose", m, &i__1, &c_b1, &c2[c2_offset], ldc, &v[1],
incv, &c_b1, &work[1], &c__1);
/* [ C1, C2 ] := [ C1, C2 ] - tau* w * [ 1 , v'] */
q__1.r = -tau->r, q__1.i = -tau->i;
caxpy_(m, &q__1, &work[1], &c__1, &c1[c1_offset], &c__1);
i__1 = *n - 1;
q__1.r = -tau->r, q__1.i = -tau->i;
cgerc_(m, &i__1, &q__1, &work[1], &c__1, &v[1], incv, &c2[c2_offset],
ldc);
}
return 0;
/* End of CLATZM */
} /* clatzm_ */
/* Subroutine */ int clagge_(integer *m, integer *n, integer *kl, integer *ku,
real *d__, complex *a, integer *lda, integer *iseed, complex *work,
integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3;
real r__1;
complex q__1;
/* Local variables */
integer i__, j;
complex wa, wb;
real wn;
complex tau;
/* -- LAPACK auxiliary test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CLAGGE generates a complex general m by n matrix A, by pre- and post- */
/* multiplying a real diagonal matrix D with random unitary matrices: */
/* A = U*D*V. The lower and upper bandwidths may then be reduced to */
/* kl and ku by additional unitary transformations. */
/* 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. */
/* KL (input) INTEGER */
/* The number of nonzero subdiagonals within the band of A. */
/* 0 <= KL <= M-1. */
/* KU (input) INTEGER */
/* The number of nonzero superdiagonals within the band of A. */
/* 0 <= KU <= N-1. */
/* D (input) REAL array, dimension (min(M,N)) */
/* The diagonal elements of the diagonal matrix D. */
/* A (output) COMPLEX array, dimension (LDA,N) */
/* The generated m by n matrix A. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= M. */
/* ISEED (input/output) INTEGER array, dimension (4) */
/* On entry, the seed of the random number generator; the array */
/* elements must be between 0 and 4095, and ISEED(4) must be */
/* odd. */
/* On exit, the seed is updated. */
/* WORK (workspace) COMPLEX array, dimension (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 arguments */
/* Parameter adjustments */
--d__;
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--iseed;
--work;
/* Function Body */
*info = 0;
if (*m < 0) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*kl < 0 || *kl > *m - 1) {
*info = -3;
} else if (*ku < 0 || *ku > *n - 1) {
*info = -4;
} else if (*lda < max(1,*m)) {
*info = -7;
}
if (*info < 0) {
i__1 = -(*info);
xerbla_("CLAGGE", &i__1);
return 0;
}
/* initialize A to diagonal matrix */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
a[i__3].r = 0.f, a[i__3].i = 0.f;
/* L10: */
}
/* L20: */
}
i__1 = min(*m,*n);
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__ + i__ * a_dim1;
i__3 = i__;
a[i__2].r = d__[i__3], a[i__2].i = 0.f;
/* L30: */
}
/* pre- and post-multiply A by random unitary matrices */
for (i__ = min(*m,*n); i__ >= 1; --i__) {
if (i__ < *m) {
/* generate random reflection */
i__1 = *m - i__ + 1;
clarnv_(&c__3, &iseed[1], &i__1, &work[1]);
i__1 = *m - i__ + 1;
wn = scnrm2_(&i__1, &work[1], &c__1);
r__1 = wn / c_abs(&work[1]);
q__1.r = r__1 * work[1].r, q__1.i = r__1 * work[1].i;
wa.r = q__1.r, wa.i = q__1.i;
if (wn == 0.f) {
tau.r = 0.f, tau.i = 0.f;
} else {
q__1.r = work[1].r + wa.r, q__1.i = work[1].i + wa.i;
wb.r = q__1.r, wb.i = q__1.i;
i__1 = *m - i__;
c_div(&q__1, &c_b2, &wb);
cscal_(&i__1, &q__1, &work[2], &c__1);
work[1].r = 1.f, work[1].i = 0.f;
c_div(&q__1, &wb, &wa);
r__1 = q__1.r;
tau.r = r__1, tau.i = 0.f;
}
/* multiply A(i:m,i:n) by random reflection from the left */
i__1 = *m - i__ + 1;
i__2 = *n - i__ + 1;
cgemv_("Conjugate transpose", &i__1, &i__2, &c_b2, &a[i__ + i__ *
a_dim1], lda, &work[1], &c__1, &c_b1, &work[*m + 1], &
c__1);
i__1 = *m - i__ + 1;
i__2 = *n - i__ + 1;
q__1.r = -tau.r, q__1.i = -tau.i;
cgerc_(&i__1, &i__2, &q__1, &work[1], &c__1, &work[*m + 1], &c__1,
&a[i__ + i__ * a_dim1], lda);
}
if (i__ < *n) {
/* generate random reflection */
i__1 = *n - i__ + 1;
clarnv_(&c__3, &iseed[1], &i__1, &work[1]);
i__1 = *n - i__ + 1;
wn = scnrm2_(&i__1, &work[1], &c__1);
r__1 = wn / c_abs(&work[1]);
q__1.r = r__1 * work[1].r, q__1.i = r__1 * work[1].i;
wa.r = q__1.r, wa.i = q__1.i;
if (wn == 0.f) {
tau.r = 0.f, tau.i = 0.f;
} else {
q__1.r = work[1].r + wa.r, q__1.i = work[1].i + wa.i;
wb.r = q__1.r, wb.i = q__1.i;
i__1 = *n - i__;
c_div(&q__1, &c_b2, &wb);
cscal_(&i__1, &q__1, &work[2], &c__1);
work[1].r = 1.f, work[1].i = 0.f;
c_div(&q__1, &wb, &wa);
r__1 = q__1.r;
tau.r = r__1, tau.i = 0.f;
}
/* multiply A(i:m,i:n) by random reflection from the right */
i__1 = *m - i__ + 1;
i__2 = *n - i__ + 1;
cgemv_("No transpose", &i__1, &i__2, &c_b2, &a[i__ + i__ * a_dim1]
, lda, &work[1], &c__1, &c_b1, &work[*n + 1], &c__1);
i__1 = *m - i__ + 1;
i__2 = *n - i__ + 1;
q__1.r = -tau.r, q__1.i = -tau.i;
cgerc_(&i__1, &i__2, &q__1, &work[*n + 1], &c__1, &work[1], &c__1,
&a[i__ + i__ * a_dim1], lda);
}
/* L40: */
}
/* Reduce number of subdiagonals to KL and number of superdiagonals */
/* to KU */
/* Computing MAX */
i__2 = *m - 1 - *kl, i__3 = *n - 1 - *ku;
i__1 = max(i__2,i__3);
for (i__ = 1; i__ <= i__1; ++i__) {
if (*kl <= *ku) {
/* annihilate subdiagonal elements first (necessary if KL = 0) */
/* Computing MIN */
i__2 = *m - 1 - *kl;
if (i__ <= min(i__2,*n)) {
/* generate reflection to annihilate A(kl+i+1:m,i) */
i__2 = *m - *kl - i__ + 1;
wn = scnrm2_(&i__2, &a[*kl + i__ + i__ * a_dim1], &c__1);
r__1 = wn / c_abs(&a[*kl + i__ + i__ * a_dim1]);
i__2 = *kl + i__ + i__ * a_dim1;
q__1.r = r__1 * a[i__2].r, q__1.i = r__1 * a[i__2].i;
wa.r = q__1.r, wa.i = q__1.i;
if (wn == 0.f) {
tau.r = 0.f, tau.i = 0.f;
} else {
i__2 = *kl + i__ + i__ * a_dim1;
q__1.r = a[i__2].r + wa.r, q__1.i = a[i__2].i + wa.i;
wb.r = q__1.r, wb.i = q__1.i;
i__2 = *m - *kl - i__;
c_div(&q__1, &c_b2, &wb);
cscal_(&i__2, &q__1, &a[*kl + i__ + 1 + i__ * a_dim1], &
c__1);
i__2 = *kl + i__ + i__ * a_dim1;
a[i__2].r = 1.f, a[i__2].i = 0.f;
c_div(&q__1, &wb, &wa);
r__1 = q__1.r;
tau.r = r__1, tau.i = 0.f;
}
/* apply reflection to A(kl+i:m,i+1:n) from the left */
i__2 = *m - *kl - i__ + 1;
i__3 = *n - i__;
cgemv_("Conjugate transpose", &i__2, &i__3, &c_b2, &a[*kl +
i__ + (i__ + 1) * a_dim1], lda, &a[*kl + i__ + i__ *
a_dim1], &c__1, &c_b1, &work[1], &c__1);
i__2 = *m - *kl - i__ + 1;
i__3 = *n - i__;
q__1.r = -tau.r, q__1.i = -tau.i;
cgerc_(&i__2, &i__3, &q__1, &a[*kl + i__ + i__ * a_dim1], &
c__1, &work[1], &c__1, &a[*kl + i__ + (i__ + 1) *
a_dim1], lda);
i__2 = *kl + i__ + i__ * a_dim1;
q__1.r = -wa.r, q__1.i = -wa.i;
a[i__2].r = q__1.r, a[i__2].i = q__1.i;
}
/* Computing MIN */
i__2 = *n - 1 - *ku;
if (i__ <= min(i__2,*m)) {
/* generate reflection to annihilate A(i,ku+i+1:n) */
i__2 = *n - *ku - i__ + 1;
wn = scnrm2_(&i__2, &a[i__ + (*ku + i__) * a_dim1], lda);
r__1 = wn / c_abs(&a[i__ + (*ku + i__) * a_dim1]);
i__2 = i__ + (*ku + i__) * a_dim1;
q__1.r = r__1 * a[i__2].r, q__1.i = r__1 * a[i__2].i;
wa.r = q__1.r, wa.i = q__1.i;
if (wn == 0.f) {
tau.r = 0.f, tau.i = 0.f;
} else {
i__2 = i__ + (*ku + i__) * a_dim1;
q__1.r = a[i__2].r + wa.r, q__1.i = a[i__2].i + wa.i;
wb.r = q__1.r, wb.i = q__1.i;
i__2 = *n - *ku - i__;
c_div(&q__1, &c_b2, &wb);
cscal_(&i__2, &q__1, &a[i__ + (*ku + i__ + 1) * a_dim1],
lda);
i__2 = i__ + (*ku + i__) * a_dim1;
a[i__2].r = 1.f, a[i__2].i = 0.f;
c_div(&q__1, &wb, &wa);
r__1 = q__1.r;
tau.r = r__1, tau.i = 0.f;
}
/* apply reflection to A(i+1:m,ku+i:n) from the right */
i__2 = *n - *ku - i__ + 1;
clacgv_(&i__2, &a[i__ + (*ku + i__) * a_dim1], lda);
i__2 = *m - i__;
i__3 = *n - *ku - i__ + 1;
cgemv_("No transpose", &i__2, &i__3, &c_b2, &a[i__ + 1 + (*ku
+ i__) * a_dim1], lda, &a[i__ + (*ku + i__) * a_dim1],
lda, &c_b1, &work[1], &c__1);
i__2 = *m - i__;
i__3 = *n - *ku - i__ + 1;
q__1.r = -tau.r, q__1.i = -tau.i;
cgerc_(&i__2, &i__3, &q__1, &work[1], &c__1, &a[i__ + (*ku +
i__) * a_dim1], lda, &a[i__ + 1 + (*ku + i__) *
a_dim1], lda);
i__2 = i__ + (*ku + i__) * a_dim1;
q__1.r = -wa.r, q__1.i = -wa.i;
a[i__2].r = q__1.r, a[i__2].i = q__1.i;
}
} else {
/* annihilate superdiagonal elements first (necessary if */
/* KU = 0) */
/* Computing MIN */
i__2 = *n - 1 - *ku;
if (i__ <= min(i__2,*m)) {
/* generate reflection to annihilate A(i,ku+i+1:n) */
i__2 = *n - *ku - i__ + 1;
wn = scnrm2_(&i__2, &a[i__ + (*ku + i__) * a_dim1], lda);
r__1 = wn / c_abs(&a[i__ + (*ku + i__) * a_dim1]);
i__2 = i__ + (*ku + i__) * a_dim1;
q__1.r = r__1 * a[i__2].r, q__1.i = r__1 * a[i__2].i;
wa.r = q__1.r, wa.i = q__1.i;
if (wn == 0.f) {
tau.r = 0.f, tau.i = 0.f;
} else {
i__2 = i__ + (*ku + i__) * a_dim1;
q__1.r = a[i__2].r + wa.r, q__1.i = a[i__2].i + wa.i;
wb.r = q__1.r, wb.i = q__1.i;
i__2 = *n - *ku - i__;
c_div(&q__1, &c_b2, &wb);
cscal_(&i__2, &q__1, &a[i__ + (*ku + i__ + 1) * a_dim1],
lda);
i__2 = i__ + (*ku + i__) * a_dim1;
a[i__2].r = 1.f, a[i__2].i = 0.f;
c_div(&q__1, &wb, &wa);
r__1 = q__1.r;
tau.r = r__1, tau.i = 0.f;
}
/* apply reflection to A(i+1:m,ku+i:n) from the right */
i__2 = *n - *ku - i__ + 1;
clacgv_(&i__2, &a[i__ + (*ku + i__) * a_dim1], lda);
i__2 = *m - i__;
i__3 = *n - *ku - i__ + 1;
cgemv_("No transpose", &i__2, &i__3, &c_b2, &a[i__ + 1 + (*ku
+ i__) * a_dim1], lda, &a[i__ + (*ku + i__) * a_dim1],
lda, &c_b1, &work[1], &c__1);
i__2 = *m - i__;
i__3 = *n - *ku - i__ + 1;
q__1.r = -tau.r, q__1.i = -tau.i;
cgerc_(&i__2, &i__3, &q__1, &work[1], &c__1, &a[i__ + (*ku +
i__) * a_dim1], lda, &a[i__ + 1 + (*ku + i__) *
a_dim1], lda);
i__2 = i__ + (*ku + i__) * a_dim1;
q__1.r = -wa.r, q__1.i = -wa.i;
a[i__2].r = q__1.r, a[i__2].i = q__1.i;
}
/* Computing MIN */
i__2 = *m - 1 - *kl;
if (i__ <= min(i__2,*n)) {
/* generate reflection to annihilate A(kl+i+1:m,i) */
i__2 = *m - *kl - i__ + 1;
wn = scnrm2_(&i__2, &a[*kl + i__ + i__ * a_dim1], &c__1);
r__1 = wn / c_abs(&a[*kl + i__ + i__ * a_dim1]);
i__2 = *kl + i__ + i__ * a_dim1;
q__1.r = r__1 * a[i__2].r, q__1.i = r__1 * a[i__2].i;
wa.r = q__1.r, wa.i = q__1.i;
if (wn == 0.f) {
tau.r = 0.f, tau.i = 0.f;
} else {
i__2 = *kl + i__ + i__ * a_dim1;
q__1.r = a[i__2].r + wa.r, q__1.i = a[i__2].i + wa.i;
wb.r = q__1.r, wb.i = q__1.i;
i__2 = *m - *kl - i__;
c_div(&q__1, &c_b2, &wb);
cscal_(&i__2, &q__1, &a[*kl + i__ + 1 + i__ * a_dim1], &
c__1);
i__2 = *kl + i__ + i__ * a_dim1;
a[i__2].r = 1.f, a[i__2].i = 0.f;
c_div(&q__1, &wb, &wa);
r__1 = q__1.r;
tau.r = r__1, tau.i = 0.f;
}
/* apply reflection to A(kl+i:m,i+1:n) from the left */
i__2 = *m - *kl - i__ + 1;
i__3 = *n - i__;
cgemv_("Conjugate transpose", &i__2, &i__3, &c_b2, &a[*kl +
i__ + (i__ + 1) * a_dim1], lda, &a[*kl + i__ + i__ *
a_dim1], &c__1, &c_b1, &work[1], &c__1);
i__2 = *m - *kl - i__ + 1;
i__3 = *n - i__;
q__1.r = -tau.r, q__1.i = -tau.i;
cgerc_(&i__2, &i__3, &q__1, &a[*kl + i__ + i__ * a_dim1], &
c__1, &work[1], &c__1, &a[*kl + i__ + (i__ + 1) *
a_dim1], lda);
i__2 = *kl + i__ + i__ * a_dim1;
q__1.r = -wa.r, q__1.i = -wa.i;
a[i__2].r = q__1.r, a[i__2].i = q__1.i;
}
}
i__2 = *m;
for (j = *kl + i__ + 1; j <= i__2; ++j) {
i__3 = j + i__ * a_dim1;
a[i__3].r = 0.f, a[i__3].i = 0.f;
/* L50: */
}
i__2 = *n;
for (j = *ku + i__ + 1; j <= i__2; ++j) {
i__3 = i__ + j * a_dim1;
a[i__3].r = 0.f, a[i__3].i = 0.f;
/* L60: */
}
/* L70: */
}
return 0;
/* End of CLAGGE */
} /* clagge_ */
/* Subroutine */ int clatme_(integer *n, char *dist, integer *iseed, complex *
d__, integer *mode, real *cond, complex *dmax__, char *ei, char *
rsign, char *upper, char *sim, real *ds, integer *modes, real *conds,
integer *kl, integer *ku, real *anorm, complex *a, integer *lda,
complex *work, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2;
real r__1, r__2;
complex q__1, q__2;
/* Builtin functions */
double c_abs(complex *);
void r_cnjg(complex *, complex *);
/* Local variables */
integer i__, j, ic, jc, ir, jcr;
complex tau;
logical bads;
integer isim;
real temp;
extern /* Subroutine */ int cgerc_(integer *, integer *, complex *,
complex *, integer *, complex *, integer *, complex *, integer *);
complex alpha;
extern /* Subroutine */ int cscal_(integer *, complex *, complex *,
integer *);
extern logical lsame_(char *, char *);
extern /* Subroutine */ int cgemv_(char *, integer *, integer *, complex *
, complex *, integer *, complex *, integer *, complex *, complex *
, integer *);
integer iinfo;
real tempa[1];
integer icols, idist;
extern /* Subroutine */ int ccopy_(integer *, complex *, integer *,
complex *, integer *);
integer irows;
extern /* Subroutine */ int clatm1_(integer *, real *, integer *, integer
*, integer *, complex *, integer *, integer *), slatm1_(integer *,
real *, integer *, integer *, integer *, real *, integer *,
integer *);
extern doublereal clange_(char *, integer *, integer *, complex *,
integer *, real *);
extern /* Subroutine */ int clarge_(integer *, complex *, integer *,
integer *, complex *, integer *), clarfg_(integer *, complex *,
complex *, integer *, complex *), clacgv_(integer *, complex *,
integer *);
extern /* Complex */ VOID clarnd_(complex *, integer *, integer *);
real ralpha;
extern /* Subroutine */ int csscal_(integer *, real *, complex *, integer
*), claset_(char *, integer *, integer *, complex *, complex *,
complex *, integer *), xerbla_(char *, integer *),
clarnv_(integer *, integer *, integer *, complex *);
integer irsign, iupper;
complex xnorms;
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CLATME generates random non-symmetric square matrices with */
/* specified eigenvalues for testing LAPACK programs. */
/* CLATME operates by applying the following sequence of */
/* operations: */
/* 1. Set the diagonal to D, where D may be input or */
/* computed according to MODE, COND, DMAX, and RSIGN */
/* as described below. */
/* 2. If UPPER='T', the upper triangle of A is set to random values */
/* out of distribution DIST. */
/* 3. If SIM='T', A is multiplied on the left by a random matrix */
/* X, whose singular values are specified by DS, MODES, and */
/* CONDS, and on the right by X inverse. */
/* 4. If KL < N-1, the lower bandwidth is reduced to KL using */
/* Householder transformations. If KU < N-1, the upper */
/* bandwidth is reduced to KU. */
/* 5. If ANORM is not negative, the matrix is scaled to have */
/* maximum-element-norm ANORM. */
/* (Note: since the matrix cannot be reduced beyond Hessenberg form, */
/* no packing options are available.) */
/* Arguments */
/* ========= */
/* N - INTEGER */
/* The number of columns (or rows) of A. Not modified. */
/* DIST - CHARACTER*1 */
/* On entry, DIST specifies the type of distribution to be used */
/* to generate the random eigen-/singular values, and on the */
/* upper triangle (see UPPER). */
/* 'U' => UNIFORM( 0, 1 ) ( 'U' for uniform ) */
/* 'S' => UNIFORM( -1, 1 ) ( 'S' for symmetric ) */
/* 'N' => NORMAL( 0, 1 ) ( 'N' for normal ) */
/* 'D' => uniform on the complex disc |z| < 1. */
/* Not modified. */
/* ISEED - INTEGER array, dimension ( 4 ) */
/* On entry ISEED specifies the seed of the random number */
/* generator. They should lie between 0 and 4095 inclusive, */
/* and ISEED(4) should be odd. The random number generator */
/* uses a linear congruential sequence limited to small */
/* integers, and so should produce machine independent */
/* random numbers. The values of ISEED are changed on */
/* exit, and can be used in the next call to CLATME */
/* to continue the same random number sequence. */
/* Changed on exit. */
/* D - COMPLEX array, dimension ( N ) */
/* This array is used to specify the eigenvalues of A. If */
/* MODE=0, then D is assumed to contain the eigenvalues */
/* otherwise they will be computed according to MODE, COND, */
/* DMAX, and RSIGN and placed in D. */
/* Modified if MODE is nonzero. */
/* MODE - INTEGER */
/* On entry this describes how the eigenvalues are to */
/* be specified: */
/* MODE = 0 means use D as input */
/* MODE = 1 sets D(1)=1 and D(2:N)=1.0/COND */
/* MODE = 2 sets D(1:N-1)=1 and D(N)=1.0/COND */
/* MODE = 3 sets D(I)=COND**(-(I-1)/(N-1)) */
/* MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND) */
/* MODE = 5 sets D to random numbers in the range */
/* ( 1/COND , 1 ) such that their logarithms */
/* are uniformly distributed. */
/* MODE = 6 set D to random numbers from same distribution */
/* as the rest of the matrix. */
/* MODE < 0 has the same meaning as ABS(MODE), except that */
/* the order of the elements of D is reversed. */
/* Thus if MODE is between 1 and 4, D has entries ranging */
/* from 1 to 1/COND, if between -1 and -4, D has entries */
/* ranging from 1/COND to 1, */
/* Not modified. */
/* COND - REAL */
/* On entry, this is used as described under MODE above. */
/* If used, it must be >= 1. Not modified. */
/* DMAX - COMPLEX */
/* If MODE is neither -6, 0 nor 6, the contents of D, as */
/* computed according to MODE and COND, will be scaled by */
/* DMAX / max(abs(D(i))). Note that DMAX need not be */
/* positive or real: if DMAX is negative or complex (or zero), */
/* D will be scaled by a negative or complex number (or zero). */
/* If RSIGN='F' then the largest (absolute) eigenvalue will be */
/* equal to DMAX. */
/* Not modified. */
/* EI - CHARACTER*1 (ignored) */
/* Not modified. */
/* RSIGN - CHARACTER*1 */
/* If MODE is not 0, 6, or -6, and RSIGN='T', then the */
/* elements of D, as computed according to MODE and COND, will */
/* be multiplied by a random complex number from the unit */
/* circle |z| = 1. If RSIGN='F', they will not be. RSIGN may */
/* only have the values 'T' or 'F'. */
/* Not modified. */
/* UPPER - CHARACTER*1 */
/* If UPPER='T', then the elements of A above the diagonal */
/* will be set to random numbers out of DIST. If UPPER='F', */
/* they will not. UPPER may only have the values 'T' or 'F'. */
/* Not modified. */
/* SIM - CHARACTER*1 */
/* If SIM='T', then A will be operated on by a "similarity */
/* transform", i.e., multiplied on the left by a matrix X and */
/* on the right by X inverse. X = U S V, where U and V are */
/* random unitary matrices and S is a (diagonal) matrix of */
/* singular values specified by DS, MODES, and CONDS. If */
/* SIM='F', then A will not be transformed. */
/* Not modified. */
/* DS - REAL array, dimension ( N ) */
/* This array is used to specify the singular values of X, */
/* in the same way that D specifies the eigenvalues of A. */
/* If MODE=0, the DS contains the singular values, which */
/* may not be zero. */
/* Modified if MODE is nonzero. */
/* MODES - INTEGER */
/* CONDS - REAL */
/* Similar to MODE and COND, but for specifying the diagonal */
/* of S. MODES=-6 and +6 are not allowed (since they would */
/* result in randomly ill-conditioned eigenvalues.) */
/* KL - INTEGER */
/* This specifies the lower bandwidth of the matrix. KL=1 */
/* specifies upper Hessenberg form. If KL is at least N-1, */
/* then A will have full lower bandwidth. */
/* Not modified. */
/* KU - INTEGER */
/* This specifies the upper bandwidth of the matrix. KU=1 */
/* specifies lower Hessenberg form. If KU is at least N-1, */
/* then A will have full upper bandwidth; if KU and KL */
/* are both at least N-1, then A will be dense. Only one of */
/* KU and KL may be less than N-1. */
/* Not modified. */
/* ANORM - REAL */
/* If ANORM is not negative, then A will be scaled by a non- */
/* negative real number to make the maximum-element-norm of A */
/* to be ANORM. */
/* Not modified. */
/* A - COMPLEX array, dimension ( LDA, N ) */
/* On exit A is the desired test matrix. */
/* Modified. */
/* LDA - INTEGER */
/* LDA specifies the first dimension of A as declared in the */
/* calling program. LDA must be at least M. */
/* Not modified. */
/* WORK - COMPLEX array, dimension ( 3*N ) */
/* Workspace. */
/* Modified. */
/* INFO - INTEGER */
/* Error code. On exit, INFO will be set to one of the */
/* following values: */
/* 0 => normal return */
/* -1 => N negative */
/* -2 => DIST illegal string */
/* -5 => MODE not in range -6 to 6 */
/* -6 => COND less than 1.0, and MODE neither -6, 0 nor 6 */
/* -9 => RSIGN is not 'T' or 'F' */
/* -10 => UPPER is not 'T' or 'F' */
/* -11 => SIM is not 'T' or 'F' */
/* -12 => MODES=0 and DS has a zero singular value. */
/* -13 => MODES is not in the range -5 to 5. */
/* -14 => MODES is nonzero and CONDS is less than 1. */
/* -15 => KL is less than 1. */
/* -16 => KU is less than 1, or KL and KU are both less than */
/* N-1. */
/* -19 => LDA is less than M. */
/* 1 => Error return from CLATM1 (computing D) */
/* 2 => Cannot scale to DMAX (max. eigenvalue is 0) */
/* 3 => Error return from SLATM1 (computing DS) */
/* 4 => Error return from CLARGE */
/* 5 => Zero singular value from SLATM1. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* 1) Decode and Test the input parameters. */
/* Initialize flags & seed. */
/* Parameter adjustments */
--iseed;
--d__;
--ds;
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--work;
/* Function Body */
*info = 0;
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/* Decode DIST */
if (lsame_(dist, "U")) {
idist = 1;
} else if (lsame_(dist, "S")) {
idist = 2;
} else if (lsame_(dist, "N")) {
idist = 3;
} else if (lsame_(dist, "D")) {
idist = 4;
} else {
idist = -1;
}
/* Decode RSIGN */
if (lsame_(rsign, "T")) {
irsign = 1;
} else if (lsame_(rsign, "F")) {
irsign = 0;
} else {
irsign = -1;
}
/* Decode UPPER */
if (lsame_(upper, "T")) {
iupper = 1;
} else if (lsame_(upper, "F")) {
iupper = 0;
} else {
iupper = -1;
}
/* Decode SIM */
if (lsame_(sim, "T")) {
isim = 1;
} else if (lsame_(sim, "F")) {
isim = 0;
} else {
isim = -1;
}
/* Check DS, if MODES=0 and ISIM=1 */
bads = FALSE_;
if (*modes == 0 && isim == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (ds[j] == 0.f) {
bads = TRUE_;
}
/* L10: */
}
}
/* Set INFO if an error */
if (*n < 0) {
*info = -1;
} else if (idist == -1) {
*info = -2;
} else if (abs(*mode) > 6) {
*info = -5;
} else if (*mode != 0 && abs(*mode) != 6 && *cond < 1.f) {
*info = -6;
} else if (irsign == -1) {
*info = -9;
} else if (iupper == -1) {
*info = -10;
} else if (isim == -1) {
*info = -11;
} else if (bads) {
*info = -12;
} else if (isim == 1 && abs(*modes) > 5) {
*info = -13;
} else if (isim == 1 && *modes != 0 && *conds < 1.f) {
*info = -14;
} else if (*kl < 1) {
*info = -15;
} else if (*ku < 1 || *ku < *n - 1 && *kl < *n - 1) {
*info = -16;
} else if (*lda < max(1,*n)) {
*info = -19;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CLATME", &i__1);
return 0;
}
/* Initialize random number generator */
for (i__ = 1; i__ <= 4; ++i__) {
iseed[i__] = (i__1 = iseed[i__], abs(i__1)) % 4096;
/* L20: */
}
if (iseed[4] % 2 != 1) {
++iseed[4];
}
/* 2) Set up diagonal of A */
/* Compute D according to COND and MODE */
clatm1_(mode, cond, &irsign, &idist, &iseed[1], &d__[1], n, &iinfo);
if (iinfo != 0) {
*info = 1;
return 0;
}
if (*mode != 0 && abs(*mode) != 6) {
/* Scale by DMAX */
temp = c_abs(&d__[1]);
i__1 = *n;
for (i__ = 2; i__ <= i__1; ++i__) {
/* Computing MAX */
r__1 = temp, r__2 = c_abs(&d__[i__]);
temp = dmax(r__1,r__2);
/* L30: */
}
if (temp > 0.f) {
q__1.r = dmax__->r / temp, q__1.i = dmax__->i / temp;
alpha.r = q__1.r, alpha.i = q__1.i;
} else {
*info = 2;
return 0;
}
cscal_(n, &alpha, &d__[1], &c__1);
}
claset_("Full", n, n, &c_b1, &c_b1, &a[a_offset], lda);
i__1 = *lda + 1;
ccopy_(n, &d__[1], &c__1, &a[a_offset], &i__1);
/* 3) If UPPER='T', set upper triangle of A to random numbers. */
if (iupper != 0) {
i__1 = *n;
for (jc = 2; jc <= i__1; ++jc) {
i__2 = jc - 1;
clarnv_(&idist, &iseed[1], &i__2, &a[jc * a_dim1 + 1]);
/* L40: */
}
}
/* 4) If SIM='T', apply similarity transformation. */
/* -1 */
/* Transform is X A X , where X = U S V, thus */
/* it is U S V A V' (1/S) U' */
if (isim != 0) {
/* Compute S (singular values of the eigenvector matrix) */
/* according to CONDS and MODES */
slatm1_(modes, conds, &c__0, &c__0, &iseed[1], &ds[1], n, &iinfo);
if (iinfo != 0) {
*info = 3;
return 0;
}
/* Multiply by V and V' */
clarge_(n, &a[a_offset], lda, &iseed[1], &work[1], &iinfo);
if (iinfo != 0) {
*info = 4;
return 0;
}
/* Multiply by S and (1/S) */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
csscal_(n, &ds[j], &a[j + a_dim1], lda);
if (ds[j] != 0.f) {
r__1 = 1.f / ds[j];
csscal_(n, &r__1, &a[j * a_dim1 + 1], &c__1);
} else {
*info = 5;
return 0;
}
/* L50: */
}
/* Multiply by U and U' */
clarge_(n, &a[a_offset], lda, &iseed[1], &work[1], &iinfo);
if (iinfo != 0) {
*info = 4;
return 0;
}
}
/* 5) Reduce the bandwidth. */
if (*kl < *n - 1) {
/* Reduce bandwidth -- kill column */
i__1 = *n - 1;
for (jcr = *kl + 1; jcr <= i__1; ++jcr) {
ic = jcr - *kl;
irows = *n + 1 - jcr;
icols = *n + *kl - jcr;
ccopy_(&irows, &a[jcr + ic * a_dim1], &c__1, &work[1], &c__1);
xnorms.r = work[1].r, xnorms.i = work[1].i;
clarfg_(&irows, &xnorms, &work[2], &c__1, &tau);
r_cnjg(&q__1, &tau);
tau.r = q__1.r, tau.i = q__1.i;
work[1].r = 1.f, work[1].i = 0.f;
clarnd_(&q__1, &c__5, &iseed[1]);
alpha.r = q__1.r, alpha.i = q__1.i;
cgemv_("C", &irows, &icols, &c_b2, &a[jcr + (ic + 1) * a_dim1],
lda, &work[1], &c__1, &c_b1, &work[irows + 1], &c__1);
q__1.r = -tau.r, q__1.i = -tau.i;
cgerc_(&irows, &icols, &q__1, &work[1], &c__1, &work[irows + 1], &
c__1, &a[jcr + (ic + 1) * a_dim1], lda);
cgemv_("N", n, &irows, &c_b2, &a[jcr * a_dim1 + 1], lda, &work[1],
&c__1, &c_b1, &work[irows + 1], &c__1);
r_cnjg(&q__2, &tau);
q__1.r = -q__2.r, q__1.i = -q__2.i;
cgerc_(n, &irows, &q__1, &work[irows + 1], &c__1, &work[1], &c__1,
&a[jcr * a_dim1 + 1], lda);
i__2 = jcr + ic * a_dim1;
a[i__2].r = xnorms.r, a[i__2].i = xnorms.i;
i__2 = irows - 1;
claset_("Full", &i__2, &c__1, &c_b1, &c_b1, &a[jcr + 1 + ic *
a_dim1], lda);
i__2 = icols + 1;
cscal_(&i__2, &alpha, &a[jcr + ic * a_dim1], lda);
r_cnjg(&q__1, &alpha);
cscal_(n, &q__1, &a[jcr * a_dim1 + 1], &c__1);
/* L60: */
}
} else if (*ku < *n - 1) {
/* Reduce upper bandwidth -- kill a row at a time. */
i__1 = *n - 1;
for (jcr = *ku + 1; jcr <= i__1; ++jcr) {
ir = jcr - *ku;
irows = *n + *ku - jcr;
icols = *n + 1 - jcr;
ccopy_(&icols, &a[ir + jcr * a_dim1], lda, &work[1], &c__1);
xnorms.r = work[1].r, xnorms.i = work[1].i;
clarfg_(&icols, &xnorms, &work[2], &c__1, &tau);
r_cnjg(&q__1, &tau);
tau.r = q__1.r, tau.i = q__1.i;
work[1].r = 1.f, work[1].i = 0.f;
i__2 = icols - 1;
clacgv_(&i__2, &work[2], &c__1);
clarnd_(&q__1, &c__5, &iseed[1]);
alpha.r = q__1.r, alpha.i = q__1.i;
cgemv_("N", &irows, &icols, &c_b2, &a[ir + 1 + jcr * a_dim1], lda,
&work[1], &c__1, &c_b1, &work[icols + 1], &c__1);
q__1.r = -tau.r, q__1.i = -tau.i;
cgerc_(&irows, &icols, &q__1, &work[icols + 1], &c__1, &work[1], &
c__1, &a[ir + 1 + jcr * a_dim1], lda);
cgemv_("C", &icols, n, &c_b2, &a[jcr + a_dim1], lda, &work[1], &
c__1, &c_b1, &work[icols + 1], &c__1);
r_cnjg(&q__2, &tau);
q__1.r = -q__2.r, q__1.i = -q__2.i;
cgerc_(&icols, n, &q__1, &work[1], &c__1, &work[icols + 1], &c__1,
&a[jcr + a_dim1], lda);
i__2 = ir + jcr * a_dim1;
a[i__2].r = xnorms.r, a[i__2].i = xnorms.i;
i__2 = icols - 1;
claset_("Full", &c__1, &i__2, &c_b1, &c_b1, &a[ir + (jcr + 1) *
a_dim1], lda);
i__2 = irows + 1;
cscal_(&i__2, &alpha, &a[ir + jcr * a_dim1], &c__1);
r_cnjg(&q__1, &alpha);
cscal_(n, &q__1, &a[jcr + a_dim1], lda);
/* L70: */
}
}
/* Scale the matrix to have norm ANORM */
if (*anorm >= 0.f) {
temp = clange_("M", n, n, &a[a_offset], lda, tempa);
if (temp > 0.f) {
ralpha = *anorm / temp;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
csscal_(n, &ralpha, &a[j * a_dim1 + 1], &c__1);
/* L80: */
}
}
}
return 0;
/* End of CLATME */
} /* clatme_ */
/* Subroutine */ int clarf_(char *side, integer *m, integer *n, complex *v,
integer *incv, complex *tau, complex *c__, integer *ldc, complex *
work)
{
/* System generated locals */
integer c_dim1, c_offset;
complex q__1;
/* Local variables */
extern /* Subroutine */ int cgerc_(integer *, integer *, complex *,
complex *, integer *, complex *, integer *, complex *, integer *),
cgemv_(char *, integer *, integer *, complex *, complex *,
integer *, complex *, integer *, complex *, complex *, integer *);
extern logical lsame_(char *, char *);
/* -- LAPACK auxiliary routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CLARF applies a complex elementary reflector H to a complex M-by-N */
/* matrix C, from either the left or the right. H is represented in the */
/* form */
/* H = I - tau * v * v' */
/* where tau is a complex scalar and v is a complex vector. */
/* If tau = 0, then H is taken to be the unit matrix. */
/* To apply H' (the conjugate transpose of H), supply conjg(tau) instead */
/* tau. */
/* Arguments */
/* ========= */
/* SIDE (input) CHARACTER*1 */
/* = 'L': form H * C */
/* = 'R': form C * H */
/* M (input) INTEGER */
/* The number of rows of the matrix C. */
/* N (input) INTEGER */
/* The number of columns of the matrix C. */
/* V (input) COMPLEX array, dimension */
/* (1 + (M-1)*abs(INCV)) if SIDE = 'L' */
/* or (1 + (N-1)*abs(INCV)) if SIDE = 'R' */
/* The vector v in the representation of H. V is not used if */
/* TAU = 0. */
/* INCV (input) INTEGER */
/* The increment between elements of v. INCV <> 0. */
/* TAU (input) COMPLEX */
/* The value tau in the representation of H. */
/* C (input/output) COMPLEX array, dimension (LDC,N) */
/* On entry, the M-by-N matrix C. */
/* On exit, C is overwritten by the matrix H * C if SIDE = 'L', */
/* or C * H if SIDE = 'R'. */
/* LDC (input) INTEGER */
/* The leading dimension of the array C. LDC >= max(1,M). */
/* WORK (workspace) COMPLEX array, dimension */
/* (N) if SIDE = 'L' */
/* or (M) if SIDE = 'R' */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
--v;
c_dim1 = *ldc;
c_offset = 1 + c_dim1;
c__ -= c_offset;
--work;
/* Function Body */
if (lsame_(side, "L")) {
/* Form H * C */
if (tau->r != 0.f || tau->i != 0.f) {
/* w := C' * v */
cgemv_("Conjugate transpose", m, n, &c_b1, &c__[c_offset], ldc, &
v[1], incv, &c_b2, &work[1], &c__1);
/* C := C - v * w' */
q__1.r = -tau->r, q__1.i = -tau->i;
cgerc_(m, n, &q__1, &v[1], incv, &work[1], &c__1, &c__[c_offset],
ldc);
}
} else {
/* Form C * H */
if (tau->r != 0.f || tau->i != 0.f) {
/* w := C * v */
cgemv_("No transpose", m, n, &c_b1, &c__[c_offset], ldc, &v[1],
incv, &c_b2, &work[1], &c__1);
/* C := C - w * v' */
q__1.r = -tau->r, q__1.i = -tau->i;
cgerc_(m, n, &q__1, &work[1], &c__1, &v[1], incv, &c__[c_offset],
ldc);
}
}
return 0;
/* End of CLARF */
} /* clarf_ */
/* Subroutine */ int clagge_slu(integer *m, integer *n, integer *kl, integer *ku,
real *d, complex *a, integer *lda, integer *iseed, complex *work,
integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3;
doublereal d__1;
complex q__1;
/* Builtin functions */
double c_abs(complex *);
void c_div(complex *, complex *, complex *);
/* Local variables */
static integer i, j;
extern /* Subroutine */ int cgerc_(integer *, integer *, complex *,
complex *, integer *, complex *, integer *, complex *, integer *),
cscal_(integer *, complex *, complex *, integer *), cgemv_(char *
, integer *, integer *, complex *, complex *, integer *, complex *
, integer *, complex *, complex *, integer *);
extern real scnrm2_(integer *, complex *, integer *);
static complex wa, wb;
extern /* Subroutine */ int clacgv_slu(integer *, complex *, integer *);
static real wn;
extern /* Subroutine */ int clarnv_slu(integer *, integer *, integer *, complex *);
extern int input_error(char *, int *);
static complex tau;
/* -- LAPACK auxiliary test 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
=======
CLAGGE generates a complex general m by n matrix A, by pre- and post-
multiplying a real diagonal matrix D with random unitary matrices:
A = U*D*V. The lower and upper bandwidths may then be reduced to
kl and ku by additional unitary transformations.
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.
KL (input) INTEGER
The number of nonzero subdiagonals within the band of A.
0 <= KL <= M-1.
KU (input) INTEGER
The number of nonzero superdiagonals within the band of A.
0 <= KU <= N-1.
D (input) REAL array, dimension (min(M,N))
The diagonal elements of the diagonal matrix D.
A (output) COMPLEX array, dimension (LDA,N)
The generated m by n matrix A.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= M.
ISEED (input/output) INTEGER array, dimension (4)
On entry, the seed of the random number generator; the array
elements must be between 0 and 4095, and ISEED(4) must be
odd.
On exit, the seed is updated.
WORK (workspace) COMPLEX array, dimension (M+N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
=====================================================================
Test the input arguments
Parameter adjustments */
--d;
a_dim1 = *lda;
a_offset = a_dim1 + 1;
a -= a_offset;
--iseed;
--work;
/* Function Body */
*info = 0;
if (*m < 0) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*kl < 0 || *kl > *m - 1) {
*info = -3;
} else if (*ku < 0 || *ku > *n - 1) {
*info = -4;
} else if (*lda < max(1,*m)) {
*info = -7;
}
if (*info < 0) {
i__1 = -(*info);
input_error("CLAGGE", &i__1);
return 0;
}
/* initialize A to diagonal matrix */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i = 1; i <= i__2; ++i) {
i__3 = i + j * a_dim1;
a[i__3].r = 0.f, a[i__3].i = 0.f;
/* L10: */
}
/* L20: */
}
i__1 = min(*m,*n);
for (i = 1; i <= i__1; ++i) {
i__2 = i + i * a_dim1;
i__3 = i;
a[i__2].r = d[i__3], a[i__2].i = 0.f;
/* L30: */
}
/* pre- and post-multiply A by random unitary matrices */
for (i = min(*m,*n); i >= 1; --i) {
if (i < *m) {
/* generate random reflection */
i__1 = *m - i + 1;
clarnv_slu(&c__3, &iseed[1], &i__1, &work[1]);
i__1 = *m - i + 1;
wn = scnrm2_(&i__1, &work[1], &c__1);
d__1 = wn / c_abs(&work[1]);
q__1.r = d__1 * work[1].r, q__1.i = d__1 * work[1].i;
wa.r = q__1.r, wa.i = q__1.i;
if (wn == 0.f) {
tau.r = 0.f, tau.i = 0.f;
} else {
q__1.r = work[1].r + wa.r, q__1.i = work[1].i + wa.i;
wb.r = q__1.r, wb.i = q__1.i;
i__1 = *m - i;
c_div(&q__1, &c_b2, &wb);
cscal_(&i__1, &q__1, &work[2], &c__1);
work[1].r = 1.f, work[1].i = 0.f;
c_div(&q__1, &wb, &wa);
d__1 = q__1.r;
tau.r = d__1, tau.i = 0.f;
}
/* multiply A(i:m,i:n) by random reflection from the lef
t */
i__1 = *m - i + 1;
i__2 = *n - i + 1;
cgemv_("Conjugate transpose", &i__1, &i__2, &c_b2, &a[i + i *
a_dim1], lda, &work[1], &c__1, &c_b1, &work[*m + 1], &
c__1);
i__1 = *m - i + 1;
i__2 = *n - i + 1;
q__1.r = -(doublereal)tau.r, q__1.i = -(doublereal)tau.i;
cgerc_(&i__1, &i__2, &q__1, &work[1], &c__1, &work[*m + 1], &c__1,
&a[i + i * a_dim1], lda);
}
if (i < *n) {
/* generate random reflection */
i__1 = *n - i + 1;
clarnv_slu(&c__3, &iseed[1], &i__1, &work[1]);
i__1 = *n - i + 1;
wn = scnrm2_(&i__1, &work[1], &c__1);
d__1 = wn / c_abs(&work[1]);
q__1.r = d__1 * work[1].r, q__1.i = d__1 * work[1].i;
wa.r = q__1.r, wa.i = q__1.i;
if (wn == 0.f) {
tau.r = 0.f, tau.i = 0.f;
} else {
q__1.r = work[1].r + wa.r, q__1.i = work[1].i + wa.i;
wb.r = q__1.r, wb.i = q__1.i;
i__1 = *n - i;
c_div(&q__1, &c_b2, &wb);
cscal_(&i__1, &q__1, &work[2], &c__1);
work[1].r = 1.f, work[1].i = 0.f;
c_div(&q__1, &wb, &wa);
d__1 = q__1.r;
tau.r = d__1, tau.i = 0.f;
}
/* multiply A(i:m,i:n) by random reflection from the rig
ht */
i__1 = *m - i + 1;
i__2 = *n - i + 1;
cgemv_("No transpose", &i__1, &i__2, &c_b2, &a[i + i * a_dim1],
lda, &work[1], &c__1, &c_b1, &work[*n + 1], &c__1);
i__1 = *m - i + 1;
i__2 = *n - i + 1;
q__1.r = -(doublereal)tau.r, q__1.i = -(doublereal)tau.i;
cgerc_(&i__1, &i__2, &q__1, &work[*n + 1], &c__1, &work[1], &c__1,
&a[i + i * a_dim1], lda);
}
/* L40: */
}
/* Reduce number of subdiagonals to KL and number of superdiagonals
to KU
Computing MAX */
i__2 = *m - 1 - *kl, i__3 = *n - 1 - *ku;
i__1 = max(i__2,i__3);
for (i = 1; i <= i__1; ++i) {
if (*kl <= *ku) {
/* annihilate subdiagonal elements first (necessary if K
L = 0)
Computing MIN */
i__2 = *m - 1 - *kl;
if (i <= min(i__2,*n)) {
/* generate reflection to annihilate A(kl+i+1:m,i
) */
i__2 = *m - *kl - i + 1;
wn = scnrm2_(&i__2, &a[*kl + i + i * a_dim1], &c__1);
d__1 = wn / c_abs(&a[*kl + i + i * a_dim1]);
i__2 = *kl + i + i * a_dim1;
q__1.r = d__1 * a[i__2].r, q__1.i = d__1 * a[i__2].i;
wa.r = q__1.r, wa.i = q__1.i;
if (wn == 0.f) {
tau.r = 0.f, tau.i = 0.f;
} else {
i__2 = *kl + i + i * a_dim1;
q__1.r = a[i__2].r + wa.r, q__1.i = a[i__2].i + wa.i;
wb.r = q__1.r, wb.i = q__1.i;
i__2 = *m - *kl - i;
c_div(&q__1, &c_b2, &wb);
cscal_(&i__2, &q__1, &a[*kl + i + 1 + i * a_dim1], &c__1);
i__2 = *kl + i + i * a_dim1;
a[i__2].r = 1.f, a[i__2].i = 0.f;
c_div(&q__1, &wb, &wa);
d__1 = q__1.r;
tau.r = d__1, tau.i = 0.f;
}
/* apply reflection to A(kl+i:m,i+1:n) from the l
eft */
i__2 = *m - *kl - i + 1;
i__3 = *n - i;
cgemv_("Conjugate transpose", &i__2, &i__3, &c_b2, &a[*kl + i
+ (i + 1) * a_dim1], lda, &a[*kl + i + i * a_dim1], &
c__1, &c_b1, &work[1], &c__1);
i__2 = *m - *kl - i + 1;
i__3 = *n - i;
q__1.r = -(doublereal)tau.r, q__1.i = -(doublereal)tau.i;
cgerc_(&i__2, &i__3, &q__1, &a[*kl + i + i * a_dim1], &c__1, &
work[1], &c__1, &a[*kl + i + (i + 1) * a_dim1], lda);
i__2 = *kl + i + i * a_dim1;
q__1.r = -(doublereal)wa.r, q__1.i = -(doublereal)wa.i;
a[i__2].r = q__1.r, a[i__2].i = q__1.i;
}
/* Computing MIN */
i__2 = *n - 1 - *ku;
if (i <= min(i__2,*m)) {
/* generate reflection to annihilate A(i,ku+i+1:n
) */
i__2 = *n - *ku - i + 1;
wn = scnrm2_(&i__2, &a[i + (*ku + i) * a_dim1], lda);
d__1 = wn / c_abs(&a[i + (*ku + i) * a_dim1]);
i__2 = i + (*ku + i) * a_dim1;
q__1.r = d__1 * a[i__2].r, q__1.i = d__1 * a[i__2].i;
wa.r = q__1.r, wa.i = q__1.i;
if (wn == 0.f) {
tau.r = 0.f, tau.i = 0.f;
} else {
i__2 = i + (*ku + i) * a_dim1;
q__1.r = a[i__2].r + wa.r, q__1.i = a[i__2].i + wa.i;
wb.r = q__1.r, wb.i = q__1.i;
i__2 = *n - *ku - i;
c_div(&q__1, &c_b2, &wb);
cscal_(&i__2, &q__1, &a[i + (*ku + i + 1) * a_dim1], lda);
i__2 = i + (*ku + i) * a_dim1;
a[i__2].r = 1.f, a[i__2].i = 0.f;
c_div(&q__1, &wb, &wa);
d__1 = q__1.r;
tau.r = d__1, tau.i = 0.f;
}
/* apply reflection to A(i+1:m,ku+i:n) from the r
ight */
i__2 = *n - *ku - i + 1;
clacgv_slu(&i__2, &a[i + (*ku + i) * a_dim1], lda);
i__2 = *m - i;
i__3 = *n - *ku - i + 1;
cgemv_("No transpose", &i__2, &i__3, &c_b2, &a[i + 1 + (*ku +
i) * a_dim1], lda, &a[i + (*ku + i) * a_dim1], lda, &
c_b1, &work[1], &c__1);
i__2 = *m - i;
i__3 = *n - *ku - i + 1;
q__1.r = -(doublereal)tau.r, q__1.i = -(doublereal)tau.i;
cgerc_(&i__2, &i__3, &q__1, &work[1], &c__1, &a[i + (*ku + i)
* a_dim1], lda, &a[i + 1 + (*ku + i) * a_dim1], lda);
i__2 = i + (*ku + i) * a_dim1;
q__1.r = -(doublereal)wa.r, q__1.i = -(doublereal)wa.i;
a[i__2].r = q__1.r, a[i__2].i = q__1.i;
}
} else {
/* annihilate superdiagonal elements first (necessary if
KU = 0)
Computing MIN */
i__2 = *n - 1 - *ku;
if (i <= min(i__2,*m)) {
/* generate reflection to annihilate A(i,ku+i+1:n
) */
i__2 = *n - *ku - i + 1;
wn = scnrm2_(&i__2, &a[i + (*ku + i) * a_dim1], lda);
d__1 = wn / c_abs(&a[i + (*ku + i) * a_dim1]);
i__2 = i + (*ku + i) * a_dim1;
q__1.r = d__1 * a[i__2].r, q__1.i = d__1 * a[i__2].i;
wa.r = q__1.r, wa.i = q__1.i;
if (wn == 0.f) {
tau.r = 0.f, tau.i = 0.f;
} else {
i__2 = i + (*ku + i) * a_dim1;
q__1.r = a[i__2].r + wa.r, q__1.i = a[i__2].i + wa.i;
wb.r = q__1.r, wb.i = q__1.i;
i__2 = *n - *ku - i;
c_div(&q__1, &c_b2, &wb);
cscal_(&i__2, &q__1, &a[i + (*ku + i + 1) * a_dim1], lda);
i__2 = i + (*ku + i) * a_dim1;
a[i__2].r = 1.f, a[i__2].i = 0.f;
c_div(&q__1, &wb, &wa);
d__1 = q__1.r;
tau.r = d__1, tau.i = 0.f;
}
/* apply reflection to A(i+1:m,ku+i:n) from the r
ight */
i__2 = *n - *ku - i + 1;
clacgv_slu(&i__2, &a[i + (*ku + i) * a_dim1], lda);
i__2 = *m - i;
i__3 = *n - *ku - i + 1;
cgemv_("No transpose", &i__2, &i__3, &c_b2, &a[i + 1 + (*ku +
i) * a_dim1], lda, &a[i + (*ku + i) * a_dim1], lda, &
c_b1, &work[1], &c__1);
i__2 = *m - i;
i__3 = *n - *ku - i + 1;
q__1.r = -(doublereal)tau.r, q__1.i = -(doublereal)tau.i;
cgerc_(&i__2, &i__3, &q__1, &work[1], &c__1, &a[i + (*ku + i)
* a_dim1], lda, &a[i + 1 + (*ku + i) * a_dim1], lda);
i__2 = i + (*ku + i) * a_dim1;
q__1.r = -(doublereal)wa.r, q__1.i = -(doublereal)wa.i;
a[i__2].r = q__1.r, a[i__2].i = q__1.i;
}
/* Computing MIN */
i__2 = *m - 1 - *kl;
if (i <= min(i__2,*n)) {
/* generate reflection to annihilate A(kl+i+1:m,i
) */
i__2 = *m - *kl - i + 1;
wn = scnrm2_(&i__2, &a[*kl + i + i * a_dim1], &c__1);
d__1 = wn / c_abs(&a[*kl + i + i * a_dim1]);
i__2 = *kl + i + i * a_dim1;
q__1.r = d__1 * a[i__2].r, q__1.i = d__1 * a[i__2].i;
wa.r = q__1.r, wa.i = q__1.i;
if (wn == 0.f) {
tau.r = 0.f, tau.i = 0.f;
} else {
i__2 = *kl + i + i * a_dim1;
q__1.r = a[i__2].r + wa.r, q__1.i = a[i__2].i + wa.i;
wb.r = q__1.r, wb.i = q__1.i;
i__2 = *m - *kl - i;
c_div(&q__1, &c_b2, &wb);
cscal_(&i__2, &q__1, &a[*kl + i + 1 + i * a_dim1], &c__1);
i__2 = *kl + i + i * a_dim1;
a[i__2].r = 1.f, a[i__2].i = 0.f;
c_div(&q__1, &wb, &wa);
d__1 = q__1.r;
tau.r = d__1, tau.i = 0.f;
}
/* apply reflection to A(kl+i:m,i+1:n) from the l
eft */
i__2 = *m - *kl - i + 1;
i__3 = *n - i;
cgemv_("Conjugate transpose", &i__2, &i__3, &c_b2, &a[*kl + i
+ (i + 1) * a_dim1], lda, &a[*kl + i + i * a_dim1], &
c__1, &c_b1, &work[1], &c__1);
i__2 = *m - *kl - i + 1;
i__3 = *n - i;
q__1.r = -(doublereal)tau.r, q__1.i = -(doublereal)tau.i;
cgerc_(&i__2, &i__3, &q__1, &a[*kl + i + i * a_dim1], &c__1, &
work[1], &c__1, &a[*kl + i + (i + 1) * a_dim1], lda);
i__2 = *kl + i + i * a_dim1;
q__1.r = -(doublereal)wa.r, q__1.i = -(doublereal)wa.i;
a[i__2].r = q__1.r, a[i__2].i = q__1.i;
}
}
i__2 = *m;
for (j = *kl + i + 1; j <= i__2; ++j) {
i__3 = j + i * a_dim1;
a[i__3].r = 0.f, a[i__3].i = 0.f;
/* L50: */
}
i__2 = *n;
for (j = *ku + i + 1; j <= i__2; ++j) {
i__3 = i + j * a_dim1;
a[i__3].r = 0.f, a[i__3].i = 0.f;
/* L60: */
}
/* L70: */
}
return 0;
/* End of CLAGGE */
} /* clagge_slu */
/* Subroutine */ int clarge_(integer *n, complex *a, integer *lda, integer *
iseed, complex *work, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1;
real r__1;
complex q__1;
/* Builtin functions */
double c_abs(complex *);
void c_div(complex *, complex *, complex *);
/* Local variables */
integer i__;
complex wa, wb;
real wn;
complex tau;
extern /* Subroutine */ int cgerc_(integer *, integer *, complex *,
complex *, integer *, complex *, integer *, complex *, integer *),
cscal_(integer *, complex *, complex *, integer *), cgemv_(char *
, integer *, integer *, complex *, complex *, integer *, complex *
, integer *, complex *, complex *, integer *);
extern doublereal scnrm2_(integer *, complex *, integer *);
extern /* Subroutine */ int xerbla_(char *, integer *), clarnv_(
integer *, integer *, integer *, complex *);
/* -- LAPACK auxiliary test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CLARGE pre- and post-multiplies a complex general n by n matrix A */
/* with a random unitary matrix: A = U*D*U'. */
/* Arguments */
/* ========= */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* A (input/output) COMPLEX array, dimension (LDA,N) */
/* On entry, the original n by n matrix A. */
/* On exit, A is overwritten by U*A*U' for some random */
/* unitary matrix U. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= N. */
/* ISEED (input/output) INTEGER array, dimension (4) */
/* On entry, the seed of the random number generator; the array */
/* elements must be between 0 and 4095, and ISEED(4) must be */
/* odd. */
/* On exit, the seed is updated. */
/* WORK (workspace) COMPLEX array, dimension (2*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 arguments */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--iseed;
--work;
/* Function Body */
*info = 0;
if (*n < 0) {
*info = -1;
} else if (*lda < max(1,*n)) {
*info = -3;
}
if (*info < 0) {
i__1 = -(*info);
xerbla_("CLARGE", &i__1);
return 0;
}
/* pre- and post-multiply A by random unitary matrix */
for (i__ = *n; i__ >= 1; --i__) {
/* generate random reflection */
i__1 = *n - i__ + 1;
clarnv_(&c__3, &iseed[1], &i__1, &work[1]);
i__1 = *n - i__ + 1;
wn = scnrm2_(&i__1, &work[1], &c__1);
r__1 = wn / c_abs(&work[1]);
q__1.r = r__1 * work[1].r, q__1.i = r__1 * work[1].i;
wa.r = q__1.r, wa.i = q__1.i;
if (wn == 0.f) {
tau.r = 0.f, tau.i = 0.f;
} else {
q__1.r = work[1].r + wa.r, q__1.i = work[1].i + wa.i;
wb.r = q__1.r, wb.i = q__1.i;
i__1 = *n - i__;
c_div(&q__1, &c_b2, &wb);
cscal_(&i__1, &q__1, &work[2], &c__1);
work[1].r = 1.f, work[1].i = 0.f;
c_div(&q__1, &wb, &wa);
r__1 = q__1.r;
tau.r = r__1, tau.i = 0.f;
}
/* multiply A(i:n,1:n) by random reflection from the left */
i__1 = *n - i__ + 1;
cgemv_("Conjugate transpose", &i__1, n, &c_b2, &a[i__ + a_dim1], lda,
&work[1], &c__1, &c_b1, &work[*n + 1], &c__1);
i__1 = *n - i__ + 1;
q__1.r = -tau.r, q__1.i = -tau.i;
cgerc_(&i__1, n, &q__1, &work[1], &c__1, &work[*n + 1], &c__1, &a[i__
+ a_dim1], lda);
/* multiply A(1:n,i:n) by random reflection from the right */
i__1 = *n - i__ + 1;
cgemv_("No transpose", n, &i__1, &c_b2, &a[i__ * a_dim1 + 1], lda, &
work[1], &c__1, &c_b1, &work[*n + 1], &c__1);
i__1 = *n - i__ + 1;
q__1.r = -tau.r, q__1.i = -tau.i;
cgerc_(n, &i__1, &q__1, &work[*n + 1], &c__1, &work[1], &c__1, &a[i__
* a_dim1 + 1], lda);
/* L10: */
}
return 0;
/* End of CLARGE */
} /* clarge_ */
/* Subroutine */
int cgeqrt2_(integer *m, integer *n, complex *a, integer * lda, complex *t, integer *ldt, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, t_dim1, t_offset, i__1, i__2, i__3;
complex q__1, q__2;
/* Builtin functions */
void r_cnjg(complex *, complex *);
/* Local variables */
integer i__, k;
complex aii;
extern /* Subroutine */
int cgerc_(integer *, integer *, complex *, complex *, integer *, complex *, integer *, complex *, integer *);
complex alpha;
extern /* Subroutine */
int cgemv_(char *, integer *, integer *, complex * , complex *, integer *, complex *, integer *, complex *, complex * , integer *), ctrmv_(char *, char *, char *, integer *, complex *, integer *, complex *, integer *), clarfg_(integer *, complex *, complex *, integer *, complex *), xerbla_(char *, 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 .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input arguments */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
t_dim1 = *ldt;
t_offset = 1 + t_dim1;
t -= t_offset;
/* Function Body */
*info = 0;
if (*m < 0)
{
*info = -1;
}
else if (*n < 0)
{
*info = -2;
}
else if (*lda < max(1,*m))
{
*info = -4;
}
else if (*ldt < max(1,*n))
{
*info = -6;
}
if (*info != 0)
{
i__1 = -(*info);
xerbla_("CGEQRT2", &i__1);
return 0;
}
k = min(*m,*n);
i__1 = k;
for (i__ = 1;
i__ <= i__1;
++i__)
{
/* Generate elem. refl. H(i) to annihilate A(i+1:m,i), tau(I) -> T(I,1) */
i__2 = *m - i__ + 1;
/* Computing MIN */
i__3 = i__ + 1;
clarfg_(&i__2, &a[i__ + i__ * a_dim1], &a[min(i__3,*m) + i__ * a_dim1] , &c__1, &t[i__ + t_dim1]);
if (i__ < *n)
{
/* Apply H(i) to A(I:M,I+1:N) from the left */
i__2 = i__ + i__ * a_dim1;
aii.r = a[i__2].r;
aii.i = a[i__2].i; // , expr subst
i__2 = i__ + i__ * a_dim1;
a[i__2].r = 1.f;
a[i__2].i = 0.f; // , expr subst
/* W(1:N-I) := A(I:M,I+1:N)**H * A(I:M,I) [W = T(:,N)] */
i__2 = *m - i__ + 1;
i__3 = *n - i__;
cgemv_("C", &i__2, &i__3, &c_b1, &a[i__ + (i__ + 1) * a_dim1], lda, &a[i__ + i__ * a_dim1], &c__1, &c_b2, &t[*n * t_dim1 + 1], &c__1);
/* A(I:M,I+1:N) = A(I:m,I+1:N) + alpha*A(I:M,I)*W(1:N-1)**H */
r_cnjg(&q__2, &t[i__ + t_dim1]);
q__1.r = -q__2.r;
q__1.i = -q__2.i; // , expr subst
alpha.r = q__1.r;
alpha.i = q__1.i; // , expr subst
i__2 = *m - i__ + 1;
i__3 = *n - i__;
cgerc_(&i__2, &i__3, &alpha, &a[i__ + i__ * a_dim1], &c__1, &t[*n * t_dim1 + 1], &c__1, &a[i__ + (i__ + 1) * a_dim1], lda);
i__2 = i__ + i__ * a_dim1;
a[i__2].r = aii.r;
a[i__2].i = aii.i; // , expr subst
}
}
i__1 = *n;
for (i__ = 2;
i__ <= i__1;
++i__)
{
i__2 = i__ + i__ * a_dim1;
aii.r = a[i__2].r;
aii.i = a[i__2].i; // , expr subst
i__2 = i__ + i__ * a_dim1;
a[i__2].r = 1.f;
a[i__2].i = 0.f; // , expr subst
/* T(1:I-1,I) := alpha * A(I:M,1:I-1)**H * A(I:M,I) */
i__2 = i__ + t_dim1;
q__1.r = -t[i__2].r;
q__1.i = -t[i__2].i; // , expr subst
alpha.r = q__1.r;
alpha.i = q__1.i; // , expr subst
i__2 = *m - i__ + 1;
i__3 = i__ - 1;
cgemv_("C", &i__2, &i__3, &alpha, &a[i__ + a_dim1], lda, &a[i__ + i__ * a_dim1], &c__1, &c_b2, &t[i__ * t_dim1 + 1], &c__1);
i__2 = i__ + i__ * a_dim1;
a[i__2].r = aii.r;
a[i__2].i = aii.i; // , expr subst
/* T(1:I-1,I) := T(1:I-1,1:I-1) * T(1:I-1,I) */
i__2 = i__ - 1;
ctrmv_("U", "N", "N", &i__2, &t[t_offset], ldt, &t[i__ * t_dim1 + 1], &c__1);
/* T(I,I) = tau(I) */
i__2 = i__ + i__ * t_dim1;
i__3 = i__ + t_dim1;
t[i__2].r = t[i__3].r;
t[i__2].i = t[i__3].i; // , expr subst
i__2 = i__ + t_dim1;
t[i__2].r = 0.f;
t[i__2].i = 0.f; // , expr subst
}
/* End of CGEQRT2 */
return 0;
}
