/* zpftri.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 doublereal c_b12 = 1.;
/* Subroutine */ int zpftri_(char *transr, char *uplo, integer *n,
doublecomplex *a, integer *info)
{
/* System generated locals */
integer i__1, i__2;
/* Local variables */
integer k, n1, n2;
logical normaltransr;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int zherk_(char *, char *, integer *, integer *,
doublereal *, doublecomplex *, integer *, doublereal *,
doublecomplex *, integer *);
logical lower;
extern /* Subroutine */ int ztrmm_(char *, char *, char *, char *,
integer *, integer *, doublecomplex *, doublecomplex *, integer *,
doublecomplex *, integer *),
xerbla_(char *, integer *);
logical nisodd;
extern /* Subroutine */ int zlauum_(char *, integer *, doublecomplex *,
integer *, integer *), ztftri_(char *, char *, char *,
integer *, doublecomplex *, integer *);
/* -- LAPACK routine (version 3.2) -- */
/* -- Contributed by Fred Gustavson of the IBM Watson Research Center -- */
/* -- November 2008 -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* .. Scalar Arguments .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZPFTRI computes the inverse of a complex Hermitian positive definite */
/* matrix A using the Cholesky factorization A = U**H*U or A = L*L**H */
/* computed by ZPFTRF. */
/* Arguments */
/* ========= */
/* TRANSR (input) CHARACTER */
/* = 'N': The Normal TRANSR of RFP A is stored; */
/* = 'C': The Conjugate-transpose TRANSR of RFP A is stored. */
/* UPLO (input) CHARACTER */
/* = '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. */
/* A (input/output) COMPLEX*16 array, dimension ( N*(N+1)/2 ); */
/* On entry, the Hermitian matrix A in RFP format. RFP format is */
/* described by TRANSR, UPLO, and N as follows: If TRANSR = 'N' */
/* then RFP A is (0:N,0:k-1) when N is even; k=N/2. RFP A is */
/* (0:N-1,0:k) when N is odd; k=N/2. IF TRANSR = 'C' then RFP is */
/* the Conjugate-transpose of RFP A as defined when */
/* TRANSR = 'N'. The contents of RFP A are defined by UPLO as */
/* follows: If UPLO = 'U' the RFP A contains the nt elements of */
/* upper packed A. If UPLO = 'L' the RFP A contains the elements */
/* of lower packed A. The LDA of RFP A is (N+1)/2 when TRANSR = */
/* 'C'. When TRANSR is 'N' the LDA is N+1 when N is even and N */
/* is odd. See the Note below for more details. */
/* On exit, the Hermitian inverse of the original matrix, in the */
/* same storage format. */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* > 0: if INFO = i, the (i,i) element of the factor U or L is */
/* zero, and the inverse could not be computed. */
/* Note: */
/* ===== */
/* 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 */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
*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;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZPFTRI", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/* Invert the triangular Cholesky factor U or L. */
ztftri_(transr, uplo, "N", n, a, info);
if (*info > 0) {
return 0;
}
/* If N is odd, set NISODD = .TRUE. */
/* If N is even, set K = N/2 and NISODD = .FALSE. */
if (*n % 2 == 0) {
k = *n / 2;
nisodd = FALSE_;
} else {
nisodd = TRUE_;
}
/* Set N1 and N2 depending on LOWER */
if (lower) {
n2 = *n / 2;
n1 = *n - n2;
} else {
n1 = *n / 2;
n2 = *n - n1;
}
/* Start execution of triangular matrix multiply: inv(U)*inv(U)^C or */
/* inv(L)^C*inv(L). There are eight cases. */
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) */
zlauum_("L", &n1, a, n, info);
zherk_("L", "C", &n1, &n2, &c_b12, &a[n1], n, &c_b12, a, n);
ztrmm_("L", "U", "N", "N", &n2, &n1, &c_b1, &a[*n], n, &a[n1],
n);
zlauum_("U", &n2, &a[*n], n, info);
} 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) */
zlauum_("L", &n1, &a[n2], n, info);
zherk_("L", "N", &n1, &n2, &c_b12, a, n, &c_b12, &a[n2], n);
ztrmm_("R", "U", "C", "N", &n1, &n2, &c_b1, &a[n1], n, a, n);
zlauum_("U", &n2, &a[n1], n, info);
}
} else {
/* N is odd and TRANSR = 'C' */
if (lower) {
/* SRPA for LOWER, TRANSPOSE, and N is odd */
/* T1 -> a(0), T2 -> a(1), S -> a(0+N1*N1) */
zlauum_("U", &n1, a, &n1, info);
zherk_("U", "N", &n1, &n2, &c_b12, &a[n1 * n1], &n1, &c_b12,
a, &n1);
ztrmm_("R", "L", "N", "N", &n1, &n2, &c_b1, &a[1], &n1, &a[n1
* n1], &n1);
zlauum_("L", &n2, &a[1], &n1, info);
} else {
/* SRPA for UPPER, TRANSPOSE, and N is odd */
/* T1 -> a(0+N2*N2), T2 -> a(0+N1*N2), S -> a(0) */
zlauum_("U", &n1, &a[n2 * n2], &n2, info);
zherk_("U", "C", &n1, &n2, &c_b12, a, &n2, &c_b12, &a[n2 * n2]
, &n2);
ztrmm_("L", "L", "C", "N", &n2, &n1, &c_b1, &a[n1 * n2], &n2,
a, &n2);
zlauum_("L", &n2, &a[n1 * n2], &n2, info);
}
}
} 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) */
i__1 = *n + 1;
zlauum_("L", &k, &a[1], &i__1, info);
i__1 = *n + 1;
i__2 = *n + 1;
zherk_("L", "C", &k, &k, &c_b12, &a[k + 1], &i__1, &c_b12, &a[
1], &i__2);
i__1 = *n + 1;
i__2 = *n + 1;
ztrmm_("L", "U", "N", "N", &k, &k, &c_b1, a, &i__1, &a[k + 1],
&i__2);
i__1 = *n + 1;
zlauum_("U", &k, a, &i__1, info);
} 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) */
i__1 = *n + 1;
zlauum_("L", &k, &a[k + 1], &i__1, info);
i__1 = *n + 1;
i__2 = *n + 1;
zherk_("L", "N", &k, &k, &c_b12, a, &i__1, &c_b12, &a[k + 1],
&i__2);
i__1 = *n + 1;
i__2 = *n + 1;
ztrmm_("R", "U", "C", "N", &k, &k, &c_b1, &a[k], &i__1, a, &
i__2);
i__1 = *n + 1;
zlauum_("U", &k, &a[k], &i__1, info);
}
} else {
/* N is even and TRANSR = 'C' */
if (lower) {
/* SRPA for LOWER, TRANSPOSE, and N is even (see paper) */
/* T1 -> B(0,1), T2 -> B(0,0), S -> B(0,k+1), */
/* T1 -> a(0+k), T2 -> a(0+0), S -> a(0+k*(k+1)); lda=k */
zlauum_("U", &k, &a[k], &k, info);
zherk_("U", "N", &k, &k, &c_b12, &a[k * (k + 1)], &k, &c_b12,
&a[k], &k);
ztrmm_("R", "L", "N", "N", &k, &k, &c_b1, a, &k, &a[k * (k +
1)], &k);
zlauum_("L", &k, a, &k, info);
} else {
/* SRPA for UPPER, TRANSPOSE, and N is even (see paper) */
/* T1 -> B(0,k+1), T2 -> B(0,k), S -> B(0,0), */
/* T1 -> a(0+k*(k+1)), T2 -> a(0+k*k), S -> a(0+0)); lda=k */
zlauum_("U", &k, &a[k * (k + 1)], &k, info);
zherk_("U", "C", &k, &k, &c_b12, a, &k, &c_b12, &a[k * (k + 1)
], &k);
ztrmm_("L", "L", "C", "N", &k, &k, &c_b1, &a[k * k], &k, a, &
k);
zlauum_("L", &k, &a[k * k], &k, info);
}
}
}
return 0;
/* End of ZPFTRI */
} /* zpftri_ */
