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|
/* ../netlib/ctfttr.f -- translated by f2c (version 20100827). You must link the resulting object file with libf2c: on Microsoft Windows system, link with libf2c.lib;
on Linux or Unix systems, link with .../path/to/libf2c.a -lm or, if you install libf2c.a in a standard place, with -lf2c -lm -- in that order, at the end of the command line, as in cc *.o -lf2c -lm Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., http://www.netlib.org/f2c/libf2c.zip */
#include "FLA_f2c.h" /* > \brief \b CTFTTR copies a triangular matrix from the rectangular full packed format (TF) to the standard full format (TR). */
/* =========== DOCUMENTATION =========== */
/* Online html documentation available at */
/* http://www.netlib.org/lapack/explore-html/ */
/* > \htmlonly */
/* > Download CTFTTR + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ctfttr. f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ctfttr. f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ctfttr. f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */
/* Definition: */
/* =========== */
/* SUBROUTINE CTFTTR( TRANSR, UPLO, N, ARF, A, LDA, INFO ) */
/* .. Scalar Arguments .. */
/* CHARACTER TRANSR, UPLO */
/* INTEGER INFO, N, LDA */
/* .. */
/* .. Array Arguments .. */
/* COMPLEX A( 0: LDA-1, 0: * ), ARF( 0: * ) */
/* .. */
/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > CTFTTR copies a triangular matrix A from rectangular full packed */
/* > format (TF) to standard full format (TR). */
/* > \endverbatim */
/* Arguments: */
/* ========== */
/* > \param[in] TRANSR */
/* > \verbatim */
/* > TRANSR is CHARACTER*1 */
/* > = 'N': ARF is in Normal format;
*/
/* > = 'C': ARF is in Conjugate-transpose format;
*/
/* > \endverbatim */
/* > */
/* > \param[in] UPLO */
/* > \verbatim */
/* > UPLO is CHARACTER*1 */
/* > = 'U': A is upper triangular;
*/
/* > = 'L': A is lower triangular. */
/* > \endverbatim */
/* > */
/* > \param[in] N */
/* > \verbatim */
/* > N is INTEGER */
/* > The order of the matrix A. N >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in] ARF */
/* > \verbatim */
/* > ARF is COMPLEX array, dimension ( N*(N+1)/2 ), */
/* > On entry, the upper or lower triangular matrix A stored in */
/* > RFP format. For a further discussion see Notes below. */
/* > \endverbatim */
/* > */
/* > \param[out] A */
/* > \verbatim */
/* > A is COMPLEX array, dimension ( LDA, N ) */
/* > On exit, the triangular matrix A. If UPLO = 'U', the */
/* > leading N-by-N upper triangular part of the array A contains */
/* > the upper triangular matrix, and the strictly lower */
/* > triangular part of A is not referenced. If UPLO = 'L', the */
/* > leading N-by-N lower triangular part of the array A contains */
/* > the lower triangular matrix, and the strictly upper */
/* > triangular part of A is not referenced. */
/* > \endverbatim */
/* > */
/* > \param[in] LDA */
/* > \verbatim */
/* > LDA is INTEGER */
/* > The leading dimension of the array A. LDA >= max(1,N). */
/* > \endverbatim */
/* > */
/* > \param[out] INFO */
/* > \verbatim */
/* > INFO is INTEGER */
/* > = 0: successful exit */
/* > < 0: if INFO = -i, the i-th argument had an illegal value */
/* > \endverbatim */
/* Authors: */
/* ======== */
/* > \author Univ. of Tennessee */
/* > \author Univ. of California Berkeley */
/* > \author Univ. of Colorado Denver */
/* > \author NAG Ltd. */
/* > \date September 2012 */
/* > \ingroup complexOTHERcomputational */
/* > \par Further Details: */
/* ===================== */
/* > */
/* > \verbatim */
/* > */
/* > We first consider Standard Packed Format when N is even. */
/* > We give an example where N = 6. */
/* > */
/* > AP is Upper AP is Lower */
/* > */
/* > 00 01 02 03 04 05 00 */
/* > 11 12 13 14 15 10 11 */
/* > 22 23 24 25 20 21 22 */
/* > 33 34 35 30 31 32 33 */
/* > 44 45 40 41 42 43 44 */
/* > 55 50 51 52 53 54 55 */
/* > */
/* > */
/* > Let TRANSR = 'N'. RFP holds AP as follows: */
/* > For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last */
/* > three columns of AP upper. The lower triangle A(4:6,0:2) consists of */
/* > conjugate-transpose of the first three columns of AP upper. */
/* > For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first */
/* > three columns of AP lower. The upper triangle A(0:2,0:2) consists of */
/* > conjugate-transpose of the last three columns of AP lower. */
/* > To denote conjugate we place -- above the element. This covers the */
/* > case N even and TRANSR = 'N'. */
/* > */
/* > RFP A RFP A */
/* > */
/* > -- -- -- */
/* > 03 04 05 33 43 53 */
/* > -- -- */
/* > 13 14 15 00 44 54 */
/* > -- */
/* > 23 24 25 10 11 55 */
/* > */
/* > 33 34 35 20 21 22 */
/* > -- */
/* > 00 44 45 30 31 32 */
/* > -- -- */
/* > 01 11 55 40 41 42 */
/* > -- -- -- */
/* > 02 12 22 50 51 52 */
/* > */
/* > Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate- */
/* > transpose of RFP A above. One therefore gets: */
/* > */
/* > */
/* > RFP A RFP A */
/* > */
/* > -- -- -- -- -- -- -- -- -- -- */
/* > 03 13 23 33 00 01 02 33 00 10 20 30 40 50 */
/* > -- -- -- -- -- -- -- -- -- -- */
/* > 04 14 24 34 44 11 12 43 44 11 21 31 41 51 */
/* > -- -- -- -- -- -- -- -- -- -- */
/* > 05 15 25 35 45 55 22 53 54 55 22 32 42 52 */
/* > */
/* > */
/* > We next consider Standard Packed Format when N is odd. */
/* > We give an example where N = 5. */
/* > */
/* > AP is Upper AP is Lower */
/* > */
/* > 00 01 02 03 04 00 */
/* > 11 12 13 14 10 11 */
/* > 22 23 24 20 21 22 */
/* > 33 34 30 31 32 33 */
/* > 44 40 41 42 43 44 */
/* > */
/* > */
/* > Let TRANSR = 'N'. RFP holds AP as follows: */
/* > For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last */
/* > three columns of AP upper. The lower triangle A(3:4,0:1) consists of */
/* > conjugate-transpose of the first two columns of AP upper. */
/* > For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first */
/* > three columns of AP lower. The upper triangle A(0:1,1:2) consists of */
/* > conjugate-transpose of the last two columns of AP lower. */
/* > To denote conjugate we place -- above the element. This covers the */
/* > case N odd and TRANSR = 'N'. */
/* > */
/* > RFP A RFP A */
/* > */
/* > -- -- */
/* > 02 03 04 00 33 43 */
/* > -- */
/* > 12 13 14 10 11 44 */
/* > */
/* > 22 23 24 20 21 22 */
/* > -- */
/* > 00 33 34 30 31 32 */
/* > -- -- */
/* > 01 11 44 40 41 42 */
/* > */
/* > Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate- */
/* > transpose of RFP A above. One therefore gets: */
/* > */
/* > */
/* > RFP A RFP A */
/* > */
/* > -- -- -- -- -- -- -- -- -- */
/* > 02 12 22 00 01 00 10 20 30 40 50 */
/* > -- -- -- -- -- -- -- -- -- */
/* > 03 13 23 33 11 33 11 21 31 41 51 */
/* > -- -- -- -- -- -- -- -- -- */
/* > 04 14 24 34 44 43 44 22 32 42 52 */
/* > \endverbatim */
/* > */
/* ===================================================================== */
/* Subroutine */
int ctfttr_(char *transr, char *uplo, integer *n, complex * arf, complex *a, integer *lda, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
complex q__1;
/* Builtin functions */
void r_cnjg(complex *, complex *);
/* Local variables */
integer i__, j, k, l, n1, n2, ij, nt, nx2, np1x2;
logical normaltransr;
extern logical lsame_(char *, char *);
logical lower;
extern /* Subroutine */
int xerbla_(char *, integer *);
logical nisodd;
/* -- 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 Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
a_dim1 = *lda - 1 - 0 + 1;
a_offset = 0 + a_dim1 * 0;
a -= a_offset;
/* Function Body */
*info = 0;
normaltransr = lsame_(transr, "N");
lower = lsame_(uplo, "L");
if (! normaltransr && ! lsame_(transr, "C"))
{
*info = -1;
}
else if (! lower && ! lsame_(uplo, "U"))
{
*info = -2;
}
else if (*n < 0)
{
*info = -3;
}
else if (*lda < max(1,*n))
{
*info = -6;
}
if (*info != 0)
{
i__1 = -(*info);
xerbla_("CTFTTR", &i__1);
return 0;
}
/* Quick return if possible */
if (*n <= 1)
{
if (*n == 1)
{
if (normaltransr)
{
a[0].r = arf[0].r;
a[0].i = arf[0].i; // , expr subst
}
else
{
r_cnjg(&q__1, arf);
a[0].r = q__1.r;
a[0].i = q__1.i; // , expr subst
}
}
return 0;
}
/* Size of array ARF(1:2,0:nt-1) */
nt = *n * (*n + 1) / 2;
/* set N1 and N2 depending on LOWER: for N even N1=N2=K */
if (lower)
{
n2 = *n / 2;
n1 = *n - n2;
}
else
{
n1 = *n / 2;
n2 = *n - n1;
}
/* If N is odd, set NISODD = .TRUE., LDA=N+1 and A is (N+1)--by--K2. */
/* If N is even, set K = N/2 and NISODD = .FALSE., LDA=N and A is */
/* N--by--(N+1)/2. */
if (*n % 2 == 0)
{
k = *n / 2;
nisodd = FALSE_;
if (! lower)
{
np1x2 = *n + *n + 2;
}
}
else
{
nisodd = TRUE_;
if (! lower)
{
nx2 = *n + *n;
}
}
if (nisodd)
{
/* N is odd */
if (normaltransr)
{
/* N is odd and TRANSR = 'N' */
if (lower)
{
/* SRPA for LOWER, NORMAL and N is odd ( a(0:n-1,0:n1-1) ) */
/* T1 -> a(0,0), T2 -> a(0,1), S -> a(n1,0) */
/* T1 -> a(0), T2 -> a(n), S -> a(n1);
lda=n */
ij = 0;
i__1 = n2;
for (j = 0;
j <= i__1;
++j)
{
i__2 = n2 + j;
for (i__ = n1;
i__ <= i__2;
++i__)
{
i__3 = n2 + j + i__ * a_dim1;
r_cnjg(&q__1, &arf[ij]);
a[i__3].r = q__1.r;
a[i__3].i = q__1.i; // , expr subst
++ij;
}
i__2 = *n - 1;
for (i__ = j;
i__ <= i__2;
++i__)
{
i__3 = i__ + j * a_dim1;
i__4 = ij;
a[i__3].r = arf[i__4].r;
a[i__3].i = arf[i__4].i; // , expr subst
++ij;
}
}
}
else
{
/* SRPA for UPPER, NORMAL and N is odd ( a(0:n-1,0:n2-1) */
/* T1 -> a(n1+1,0), T2 -> a(n1,0), S -> a(0,0) */
/* T1 -> a(n2), T2 -> a(n1), S -> a(0);
lda=n */
ij = nt - *n;
i__1 = n1;
for (j = *n - 1;
j >= i__1;
--j)
{
i__2 = j;
for (i__ = 0;
i__ <= i__2;
++i__)
{
i__3 = i__ + j * a_dim1;
i__4 = ij;
a[i__3].r = arf[i__4].r;
a[i__3].i = arf[i__4].i; // , expr subst
++ij;
}
i__2 = n1 - 1;
for (l = j - n1;
l <= i__2;
++l)
{
i__3 = j - n1 + l * a_dim1;
r_cnjg(&q__1, &arf[ij]);
a[i__3].r = q__1.r;
a[i__3].i = q__1.i; // , expr subst
++ij;
}
ij -= nx2;
}
}
}
else
{
/* N is odd and TRANSR = 'C' */
if (lower)
{
/* SRPA for LOWER, TRANSPOSE and N is odd */
/* T1 -> A(0,0) , T2 -> A(1,0) , S -> A(0,n1) */
/* T1 -> A(0+0) , T2 -> A(1+0) , S -> A(0+n1*n1);
lda=n1 */
ij = 0;
i__1 = n2 - 1;
for (j = 0;
j <= i__1;
++j)
{
i__2 = j;
for (i__ = 0;
i__ <= i__2;
++i__)
{
i__3 = j + i__ * a_dim1;
r_cnjg(&q__1, &arf[ij]);
a[i__3].r = q__1.r;
a[i__3].i = q__1.i; // , expr subst
++ij;
}
i__2 = *n - 1;
for (i__ = n1 + j;
i__ <= i__2;
++i__)
{
i__3 = i__ + (n1 + j) * a_dim1;
i__4 = ij;
a[i__3].r = arf[i__4].r;
a[i__3].i = arf[i__4].i; // , expr subst
++ij;
}
}
i__1 = *n - 1;
for (j = n2;
j <= i__1;
++j)
{
i__2 = n1 - 1;
for (i__ = 0;
i__ <= i__2;
++i__)
{
i__3 = j + i__ * a_dim1;
r_cnjg(&q__1, &arf[ij]);
a[i__3].r = q__1.r;
a[i__3].i = q__1.i; // , expr subst
++ij;
}
}
}
else
{
/* SRPA for UPPER, TRANSPOSE and N is odd */
/* T1 -> A(0,n1+1), T2 -> A(0,n1), S -> A(0,0) */
/* T1 -> A(n2*n2), T2 -> A(n1*n2), S -> A(0);
lda = n2 */
ij = 0;
i__1 = n1;
for (j = 0;
j <= i__1;
++j)
{
i__2 = *n - 1;
for (i__ = n1;
i__ <= i__2;
++i__)
{
i__3 = j + i__ * a_dim1;
r_cnjg(&q__1, &arf[ij]);
a[i__3].r = q__1.r;
a[i__3].i = q__1.i; // , expr subst
++ij;
}
}
i__1 = n1 - 1;
for (j = 0;
j <= i__1;
++j)
{
i__2 = j;
for (i__ = 0;
i__ <= i__2;
++i__)
{
i__3 = i__ + j * a_dim1;
i__4 = ij;
a[i__3].r = arf[i__4].r;
a[i__3].i = arf[i__4].i; // , expr subst
++ij;
}
i__2 = *n - 1;
for (l = n2 + j;
l <= i__2;
++l)
{
i__3 = n2 + j + l * a_dim1;
r_cnjg(&q__1, &arf[ij]);
a[i__3].r = q__1.r;
a[i__3].i = q__1.i; // , expr subst
++ij;
}
}
}
}
}
else
{
/* N is even */
if (normaltransr)
{
/* N is even and TRANSR = 'N' */
if (lower)
{
/* SRPA for LOWER, NORMAL, and N is even ( a(0:n,0:k-1) ) */
/* T1 -> a(1,0), T2 -> a(0,0), S -> a(k+1,0) */
/* T1 -> a(1), T2 -> a(0), S -> a(k+1);
lda=n+1 */
ij = 0;
i__1 = k - 1;
for (j = 0;
j <= i__1;
++j)
{
i__2 = k + j;
for (i__ = k;
i__ <= i__2;
++i__)
{
i__3 = k + j + i__ * a_dim1;
r_cnjg(&q__1, &arf[ij]);
a[i__3].r = q__1.r;
a[i__3].i = q__1.i; // , expr subst
++ij;
}
i__2 = *n - 1;
for (i__ = j;
i__ <= i__2;
++i__)
{
i__3 = i__ + j * a_dim1;
i__4 = ij;
a[i__3].r = arf[i__4].r;
a[i__3].i = arf[i__4].i; // , expr subst
++ij;
}
}
}
else
{
/* SRPA for UPPER, NORMAL, and N is even ( a(0:n,0:k-1) ) */
/* T1 -> a(k+1,0) , T2 -> a(k,0), S -> a(0,0) */
/* T1 -> a(k+1), T2 -> a(k), S -> a(0);
lda=n+1 */
ij = nt - *n - 1;
i__1 = k;
for (j = *n - 1;
j >= i__1;
--j)
{
i__2 = j;
for (i__ = 0;
i__ <= i__2;
++i__)
{
i__3 = i__ + j * a_dim1;
i__4 = ij;
a[i__3].r = arf[i__4].r;
a[i__3].i = arf[i__4].i; // , expr subst
++ij;
}
i__2 = k - 1;
for (l = j - k;
l <= i__2;
++l)
{
i__3 = j - k + l * a_dim1;
r_cnjg(&q__1, &arf[ij]);
a[i__3].r = q__1.r;
a[i__3].i = q__1.i; // , expr subst
++ij;
}
ij -= np1x2;
}
}
}
else
{
/* N is even and TRANSR = 'C' */
if (lower)
{
/* SRPA for LOWER, TRANSPOSE and N is even (see paper, A=B) */
/* T1 -> A(0,1) , T2 -> A(0,0) , S -> A(0,k+1) : */
/* T1 -> A(0+k) , T2 -> A(0+0) , S -> A(0+k*(k+1));
lda=k */
ij = 0;
j = k;
i__1 = *n - 1;
for (i__ = k;
i__ <= i__1;
++i__)
{
i__2 = i__ + j * a_dim1;
i__3 = ij;
a[i__2].r = arf[i__3].r;
a[i__2].i = arf[i__3].i; // , expr subst
++ij;
}
i__1 = k - 2;
for (j = 0;
j <= i__1;
++j)
{
i__2 = j;
for (i__ = 0;
i__ <= i__2;
++i__)
{
i__3 = j + i__ * a_dim1;
r_cnjg(&q__1, &arf[ij]);
a[i__3].r = q__1.r;
a[i__3].i = q__1.i; // , expr subst
++ij;
}
i__2 = *n - 1;
for (i__ = k + 1 + j;
i__ <= i__2;
++i__)
{
i__3 = i__ + (k + 1 + j) * a_dim1;
i__4 = ij;
a[i__3].r = arf[i__4].r;
a[i__3].i = arf[i__4].i; // , expr subst
++ij;
}
}
i__1 = *n - 1;
for (j = k - 1;
j <= i__1;
++j)
{
i__2 = k - 1;
for (i__ = 0;
i__ <= i__2;
++i__)
{
i__3 = j + i__ * a_dim1;
r_cnjg(&q__1, &arf[ij]);
a[i__3].r = q__1.r;
a[i__3].i = q__1.i; // , expr subst
++ij;
}
}
}
else
{
/* SRPA for UPPER, TRANSPOSE and N is even (see paper, A=B) */
/* T1 -> A(0,k+1) , T2 -> A(0,k) , S -> A(0,0) */
/* T1 -> A(0+k*(k+1)) , T2 -> A(0+k*k) , S -> A(0+0));
lda=k */
ij = 0;
i__1 = k;
for (j = 0;
j <= i__1;
++j)
{
i__2 = *n - 1;
for (i__ = k;
i__ <= i__2;
++i__)
{
i__3 = j + i__ * a_dim1;
r_cnjg(&q__1, &arf[ij]);
a[i__3].r = q__1.r;
a[i__3].i = q__1.i; // , expr subst
++ij;
}
}
i__1 = k - 2;
for (j = 0;
j <= i__1;
++j)
{
i__2 = j;
for (i__ = 0;
i__ <= i__2;
++i__)
{
i__3 = i__ + j * a_dim1;
i__4 = ij;
a[i__3].r = arf[i__4].r;
a[i__3].i = arf[i__4].i; // , expr subst
++ij;
}
i__2 = *n - 1;
for (l = k + 1 + j;
l <= i__2;
++l)
{
i__3 = k + 1 + j + l * a_dim1;
r_cnjg(&q__1, &arf[ij]);
a[i__3].r = q__1.r;
a[i__3].i = q__1.i; // , expr subst
++ij;
}
}
/* Note that here J = K-1 */
i__1 = j;
for (i__ = 0;
i__ <= i__1;
++i__)
{
i__2 = i__ + j * a_dim1;
i__3 = ij;
a[i__2].r = arf[i__3].r;
a[i__2].i = arf[i__3].i; // , expr subst
++ij;
}
}
}
}
return 0;
/* End of CTFTTR */
}
/* ctfttr_ */
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