#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int zpbtf2_(char *uplo, integer *n, integer *kd, doublecomplex *ab, integer *ldab, integer *info) { /* -- LAPACK routine (version 3.1) -- Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. November 2006 Purpose ======= ZPBTF2 computes the Cholesky factorization of a complex Hermitian positive definite band matrix A. The factorization has the form A = U' * U , if UPLO = 'U', or A = L * L', if UPLO = 'L', where U is an upper triangular matrix, U' is the conjugate transpose of U, and L is lower triangular. This is the unblocked version of the algorithm, calling Level 2 BLAS. Arguments ========= UPLO (input) CHARACTER*1 Specifies whether the upper or lower triangular part of the Hermitian matrix A is stored: = 'U': Upper triangular = 'L': Lower triangular N (input) INTEGER The order of the matrix A. N >= 0. KD (input) INTEGER The number of super-diagonals of the matrix A if UPLO = 'U', or the number of sub-diagonals 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'*U or A = L*L' 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 = -k, the k-th argument had an illegal value > 0: if INFO = k, the leading minor of order k 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. ===================================================================== Test the input parameters. Parameter adjustments */ /* Table of constant values */ static doublereal c_b8 = -1.; static integer c__1 = 1; /* System generated locals */ integer ab_dim1, ab_offset, i__1, i__2, i__3; doublereal d__1; /* Builtin functions */ double sqrt(doublereal); /* Local variables */ static integer j, kn; static doublereal ajj; static integer kld; extern /* Subroutine */ int zher_(char *, integer *, doublereal *, doublecomplex *, integer *, doublecomplex *, integer *); extern logical lsame_(char *, char *); static logical upper; extern /* Subroutine */ int xerbla_(char *, integer *), zdscal_( integer *, doublereal *, doublecomplex *, integer *), zlacgv_( integer *, doublecomplex *, integer *); ab_dim1 = *ldab; ab_offset = 1 + ab_dim1; ab -= ab_offset; /* Function Body */ *info = 0; upper = lsame_(uplo, "U"); if (! upper && ! 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_("ZPBTF2", &i__1); return 0; } /* Quick return if possible */ if (*n == 0) { return 0; } /* Computing MAX */ i__1 = 1, i__2 = *ldab - 1; kld = max(i__1,i__2); if (upper) { /* Compute the Cholesky factorization A = U'*U. */ i__1 = *n; for (j = 1; j <= i__1; ++j) { /* Compute U(J,J) and test for non-positive-definiteness. */ i__2 = *kd + 1 + j * ab_dim1; ajj = ab[i__2].r; if (ajj <= 0.) { i__2 = *kd + 1 + j * ab_dim1; ab[i__2].r = ajj, ab[i__2].i = 0.; goto L30; } ajj = sqrt(ajj); i__2 = *kd + 1 + j * ab_dim1; ab[i__2].r = ajj, ab[i__2].i = 0.; /* Compute elements J+1:J+KN of row J and update the trailing submatrix within the band. Computing MIN */ i__2 = *kd, i__3 = *n - j; kn = min(i__2,i__3); if (kn > 0) { d__1 = 1. / ajj; zdscal_(&kn, &d__1, &ab[*kd + (j + 1) * ab_dim1], &kld); zlacgv_(&kn, &ab[*kd + (j + 1) * ab_dim1], &kld); zher_("Upper", &kn, &c_b8, &ab[*kd + (j + 1) * ab_dim1], &kld, &ab[*kd + 1 + (j + 1) * ab_dim1], &kld); zlacgv_(&kn, &ab[*kd + (j + 1) * ab_dim1], &kld); } /* L10: */ } } else { /* Compute the Cholesky factorization A = L*L'. */ i__1 = *n; for (j = 1; j <= i__1; ++j) { /* Compute L(J,J) and test for non-positive-definiteness. */ i__2 = j * ab_dim1 + 1; ajj = ab[i__2].r; if (ajj <= 0.) { i__2 = j * ab_dim1 + 1; ab[i__2].r = ajj, ab[i__2].i = 0.; goto L30; } ajj = sqrt(ajj); i__2 = j * ab_dim1 + 1; ab[i__2].r = ajj, ab[i__2].i = 0.; /* Compute elements J+1:J+KN of column J and update the trailing submatrix within the band. Computing MIN */ i__2 = *kd, i__3 = *n - j; kn = min(i__2,i__3); if (kn > 0) { d__1 = 1. / ajj; zdscal_(&kn, &d__1, &ab[j * ab_dim1 + 2], &c__1); zher_("Lower", &kn, &c_b8, &ab[j * ab_dim1 + 2], &c__1, &ab[( j + 1) * ab_dim1 + 1], &kld); } /* L20: */ } } return 0; L30: *info = j; return 0; /* End of ZPBTF2 */ } /* zpbtf2_ */