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/* zpbtrf.f -- translated by f2c (version 20061008).
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 "f2c.h"
#include "blaswrap.h"
/* Table of constant values */
static doublecomplex c_b1 = {1.,0.};
static integer c__1 = 1;
static integer c_n1 = -1;
static doublereal c_b21 = -1.;
static doublereal c_b22 = 1.;
static integer c__33 = 33;
/* Subroutine */ int zpbtrf_(char *uplo, integer *n, integer *kd,
doublecomplex *ab, integer *ldab, integer *info)
{
/* System generated locals */
integer ab_dim1, ab_offset, i__1, i__2, i__3, i__4, i__5, i__6;
doublecomplex z__1;
/* Local variables */
integer i__, j, i2, i3, ib, nb, ii, jj;
doublecomplex work[1056] /* was [33][32] */;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int zgemm_(char *, char *, integer *, integer *,
integer *, doublecomplex *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *), zherk_(char *, char *, integer *,
integer *, doublereal *, doublecomplex *, integer *, doublereal *,
doublecomplex *, integer *), ztrsm_(char *, char
*, char *, char *, integer *, integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *), zpbtf2_(char *, integer *, integer *,
doublecomplex *, integer *, integer *), zpotf2_(char *,
integer *, doublecomplex *, integer *, integer *),
xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *);
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZPBTRF computes the Cholesky factorization of a complex Hermitian */
/* positive definite band matrix A. */
/* The factorization has the form */
/* A = U**H * U, if UPLO = 'U', or */
/* A = L * L**H, if UPLO = 'L', */
/* where U is an upper triangular matrix and L is lower triangular. */
/* Arguments */
/* ========= */
/* UPLO (input) CHARACTER*1 */
/* = 'U': Upper triangle of A is stored; */
/* = 'L': Lower triangle of A is stored. */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* KD (input) INTEGER */
/* The number of superdiagonals of the matrix A if UPLO = 'U', */
/* or the number of subdiagonals if UPLO = 'L'. KD >= 0. */
/* AB (input/output) COMPLEX*16 array, dimension (LDAB,N) */
/* On entry, the upper or lower triangle of the Hermitian band */
/* matrix A, stored in the first KD+1 rows of the array. The */
/* j-th column of A is stored in the j-th column of the array AB */
/* as follows: */
/* if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; */
/* if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). */
/* On exit, if INFO = 0, the triangular factor U or L from the */
/* Cholesky factorization A = U**H*U or A = L*L**H of the band */
/* matrix A, in the same storage format as A. */
/* LDAB (input) INTEGER */
/* The leading dimension of the array AB. LDAB >= KD+1. */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* > 0: if INFO = i, the leading minor of order i is not */
/* positive definite, and the factorization could not be */
/* completed. */
/* Further Details */
/* =============== */
/* The band storage scheme is illustrated by the following example, when */
/* N = 6, KD = 2, and UPLO = 'U': */
/* On entry: On exit: */
/* * * a13 a24 a35 a46 * * u13 u24 u35 u46 */
/* * a12 a23 a34 a45 a56 * u12 u23 u34 u45 u56 */
/* a11 a22 a33 a44 a55 a66 u11 u22 u33 u44 u55 u66 */
/* Similarly, if UPLO = 'L' the format of A is as follows: */
/* On entry: On exit: */
/* a11 a22 a33 a44 a55 a66 l11 l22 l33 l44 l55 l66 */
/* a21 a32 a43 a54 a65 * l21 l32 l43 l54 l65 * */
/* a31 a42 a53 a64 * * l31 l42 l53 l64 * * */
/* Array elements marked * are not used by the routine. */
/* Contributed by */
/* Peter Mayes and Giuseppe Radicati, IBM ECSEC, Rome, March 23, 1989 */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
ab_dim1 = *ldab;
ab_offset = 1 + ab_dim1;
ab -= ab_offset;
/* Function Body */
*info = 0;
if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*kd < 0) {
*info = -3;
} else if (*ldab < *kd + 1) {
*info = -5;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZPBTRF", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/* Determine the block size for this environment */
nb = ilaenv_(&c__1, "ZPBTRF", uplo, n, kd, &c_n1, &c_n1);
/* The block size must not exceed the semi-bandwidth KD, and must not */
/* exceed the limit set by the size of the local array WORK. */
nb = min(nb,32);
if (nb <= 1 || nb > *kd) {
/* Use unblocked code */
zpbtf2_(uplo, n, kd, &ab[ab_offset], ldab, info);
} else {
/* Use blocked code */
if (lsame_(uplo, "U")) {
/* Compute the Cholesky factorization of a Hermitian band */
/* matrix, given the upper triangle of the matrix in band */
/* storage. */
/* Zero the upper triangle of the work array. */
i__1 = nb;
for (j = 1; j <= i__1; ++j) {
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * 33 - 34;
work[i__3].r = 0., work[i__3].i = 0.;
/* L10: */
}
/* L20: */
}
/* Process the band matrix one diagonal block at a time. */
i__1 = *n;
i__2 = nb;
for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
/* Computing MIN */
i__3 = nb, i__4 = *n - i__ + 1;
ib = min(i__3,i__4);
/* Factorize the diagonal block */
i__3 = *ldab - 1;
zpotf2_(uplo, &ib, &ab[*kd + 1 + i__ * ab_dim1], &i__3, &ii);
if (ii != 0) {
*info = i__ + ii - 1;
goto L150;
}
if (i__ + ib <= *n) {
/* Update the relevant part of the trailing submatrix. */
/* If A11 denotes the diagonal block which has just been */
/* factorized, then we need to update the remaining */
/* blocks in the diagram: */
/* A11 A12 A13 */
/* A22 A23 */
/* A33 */
/* The numbers of rows and columns in the partitioning */
/* are IB, I2, I3 respectively. The blocks A12, A22 and */
/* A23 are empty if IB = KD. The upper triangle of A13 */
/* lies outside the band. */
/* Computing MIN */
i__3 = *kd - ib, i__4 = *n - i__ - ib + 1;
i2 = min(i__3,i__4);
/* Computing MIN */
i__3 = ib, i__4 = *n - i__ - *kd + 1;
i3 = min(i__3,i__4);
if (i2 > 0) {
/* Update A12 */
i__3 = *ldab - 1;
i__4 = *ldab - 1;
ztrsm_("Left", "Upper", "Conjugate transpose", "Non-"
"unit", &ib, &i2, &c_b1, &ab[*kd + 1 + i__ *
ab_dim1], &i__3, &ab[*kd + 1 - ib + (i__ + ib)
* ab_dim1], &i__4);
/* Update A22 */
i__3 = *ldab - 1;
i__4 = *ldab - 1;
zherk_("Upper", "Conjugate transpose", &i2, &ib, &
c_b21, &ab[*kd + 1 - ib + (i__ + ib) *
ab_dim1], &i__3, &c_b22, &ab[*kd + 1 + (i__ +
ib) * ab_dim1], &i__4);
}
if (i3 > 0) {
/* Copy the lower triangle of A13 into the work array. */
i__3 = i3;
for (jj = 1; jj <= i__3; ++jj) {
i__4 = ib;
for (ii = jj; ii <= i__4; ++ii) {
i__5 = ii + jj * 33 - 34;
i__6 = ii - jj + 1 + (jj + i__ + *kd - 1) *
ab_dim1;
work[i__5].r = ab[i__6].r, work[i__5].i = ab[
i__6].i;
/* L30: */
}
/* L40: */
}
/* Update A13 (in the work array). */
i__3 = *ldab - 1;
ztrsm_("Left", "Upper", "Conjugate transpose", "Non-"
"unit", &ib, &i3, &c_b1, &ab[*kd + 1 + i__ *
ab_dim1], &i__3, work, &c__33);
/* Update A23 */
if (i2 > 0) {
z__1.r = -1., z__1.i = -0.;
i__3 = *ldab - 1;
i__4 = *ldab - 1;
zgemm_("Conjugate transpose", "No transpose", &i2,
&i3, &ib, &z__1, &ab[*kd + 1 - ib + (i__
+ ib) * ab_dim1], &i__3, work, &c__33, &
c_b1, &ab[ib + 1 + (i__ + *kd) * ab_dim1],
&i__4);
}
/* Update A33 */
i__3 = *ldab - 1;
zherk_("Upper", "Conjugate transpose", &i3, &ib, &
c_b21, work, &c__33, &c_b22, &ab[*kd + 1 + (
i__ + *kd) * ab_dim1], &i__3);
/* Copy the lower triangle of A13 back into place. */
i__3 = i3;
for (jj = 1; jj <= i__3; ++jj) {
i__4 = ib;
for (ii = jj; ii <= i__4; ++ii) {
i__5 = ii - jj + 1 + (jj + i__ + *kd - 1) *
ab_dim1;
i__6 = ii + jj * 33 - 34;
ab[i__5].r = work[i__6].r, ab[i__5].i = work[
i__6].i;
/* L50: */
}
/* L60: */
}
}
}
/* L70: */
}
} else {
/* Compute the Cholesky factorization of a Hermitian band */
/* matrix, given the lower triangle of the matrix in band */
/* storage. */
/* Zero the lower triangle of the work array. */
i__2 = nb;
for (j = 1; j <= i__2; ++j) {
i__1 = nb;
for (i__ = j + 1; i__ <= i__1; ++i__) {
i__3 = i__ + j * 33 - 34;
work[i__3].r = 0., work[i__3].i = 0.;
/* L80: */
}
/* L90: */
}
/* Process the band matrix one diagonal block at a time. */
i__2 = *n;
i__1 = nb;
for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += i__1) {
/* Computing MIN */
i__3 = nb, i__4 = *n - i__ + 1;
ib = min(i__3,i__4);
/* Factorize the diagonal block */
i__3 = *ldab - 1;
zpotf2_(uplo, &ib, &ab[i__ * ab_dim1 + 1], &i__3, &ii);
if (ii != 0) {
*info = i__ + ii - 1;
goto L150;
}
if (i__ + ib <= *n) {
/* Update the relevant part of the trailing submatrix. */
/* If A11 denotes the diagonal block which has just been */
/* factorized, then we need to update the remaining */
/* blocks in the diagram: */
/* A11 */
/* A21 A22 */
/* A31 A32 A33 */
/* The numbers of rows and columns in the partitioning */
/* are IB, I2, I3 respectively. The blocks A21, A22 and */
/* A32 are empty if IB = KD. The lower triangle of A31 */
/* lies outside the band. */
/* Computing MIN */
i__3 = *kd - ib, i__4 = *n - i__ - ib + 1;
i2 = min(i__3,i__4);
/* Computing MIN */
i__3 = ib, i__4 = *n - i__ - *kd + 1;
i3 = min(i__3,i__4);
if (i2 > 0) {
/* Update A21 */
i__3 = *ldab - 1;
i__4 = *ldab - 1;
ztrsm_("Right", "Lower", "Conjugate transpose", "Non"
"-unit", &i2, &ib, &c_b1, &ab[i__ * ab_dim1 +
1], &i__3, &ab[ib + 1 + i__ * ab_dim1], &i__4);
/* Update A22 */
i__3 = *ldab - 1;
i__4 = *ldab - 1;
zherk_("Lower", "No transpose", &i2, &ib, &c_b21, &ab[
ib + 1 + i__ * ab_dim1], &i__3, &c_b22, &ab[(
i__ + ib) * ab_dim1 + 1], &i__4);
}
if (i3 > 0) {
/* Copy the upper triangle of A31 into the work array. */
i__3 = ib;
for (jj = 1; jj <= i__3; ++jj) {
i__4 = min(jj,i3);
for (ii = 1; ii <= i__4; ++ii) {
i__5 = ii + jj * 33 - 34;
i__6 = *kd + 1 - jj + ii + (jj + i__ - 1) *
ab_dim1;
work[i__5].r = ab[i__6].r, work[i__5].i = ab[
i__6].i;
/* L100: */
}
/* L110: */
}
/* Update A31 (in the work array). */
i__3 = *ldab - 1;
ztrsm_("Right", "Lower", "Conjugate transpose", "Non"
"-unit", &i3, &ib, &c_b1, &ab[i__ * ab_dim1 +
1], &i__3, work, &c__33);
/* Update A32 */
if (i2 > 0) {
z__1.r = -1., z__1.i = -0.;
i__3 = *ldab - 1;
i__4 = *ldab - 1;
zgemm_("No transpose", "Conjugate transpose", &i3,
&i2, &ib, &z__1, work, &c__33, &ab[ib +
1 + i__ * ab_dim1], &i__3, &c_b1, &ab[*kd
+ 1 - ib + (i__ + ib) * ab_dim1], &i__4);
}
/* Update A33 */
i__3 = *ldab - 1;
zherk_("Lower", "No transpose", &i3, &ib, &c_b21,
work, &c__33, &c_b22, &ab[(i__ + *kd) *
ab_dim1 + 1], &i__3);
/* Copy the upper triangle of A31 back into place. */
i__3 = ib;
for (jj = 1; jj <= i__3; ++jj) {
i__4 = min(jj,i3);
for (ii = 1; ii <= i__4; ++ii) {
i__5 = *kd + 1 - jj + ii + (jj + i__ - 1) *
ab_dim1;
i__6 = ii + jj * 33 - 34;
ab[i__5].r = work[i__6].r, ab[i__5].i = work[
i__6].i;
/* L120: */
}
/* L130: */
}
}
}
/* L140: */
}
}
}
return 0;
L150:
return 0;
/* End of ZPBTRF */
} /* zpbtrf_ */
|
