# zpbstf.f(3) [centos man page]

zpbstf.f(3) LAPACK zpbstf.f(3)NAME

zpbstf.f-SYNOPSIS

Functions/Subroutines subroutine zpbstf (UPLO, N, KD, AB, LDAB, INFO) ZPBSTFFunction/Subroutine Documentation subroutine zpbstf (characterUPLO, integerN, integerKD, complex*16, dimension( ldab, * )AB, integerLDAB, integerINFO) ZPBSTF Purpose: ZPBSTF computes a split Cholesky factorization of a complex Hermitian positive definite band matrix A. This routine is designed to be used in conjunction with ZHBGST. The factorization has the form A = S**H*S where S is a band matrix of the same bandwidth as A and the following structure: S = ( U ) ( M L ) where U is upper triangular of order m = (n+kd)/2, and L is lower triangular of order n-m. Parameters: UPLO UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. N N is INTEGER The order of the matrix A. N >= 0. KD KD is INTEGER The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KD >= 0. AB AB is 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 factor S from the split Cholesky factorization A = S**H*S. See Further Details. LDAB LDAB is INTEGER The leading dimension of the array AB. LDAB >= KD+1. INFO INFO is INTEGER = 0: successful exit < 0: if INFO =, the i-th argument had an illegal value > 0: if INFO = i, the factorization could not be completed, because the updated element a(i,i) was negative; the matrix A is not positive definite. Author: Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Date: November 2011 Further Details: The band storage scheme is illustrated by the following example, when N = 7, KD = 2: S = ( s11 s12 s13 ) ( s22 s23 s24 ) ( s33 s34 ) ( s44 ) ( s53 s54 s55 ) ( s64 s65 s66 ) ( s75 s76 s77 ) If UPLO = 'U', the array AB holds: on entry: on exit: * * a13 a24 a35 a46 a57 * * s13 s24 s53**H s64**H s75**H * a12 a23 a34 a45 a56 a67 * s12 s23 s34 s54**H s65**H s76**H a11 a22 a33 a44 a55 a66 a77 s11 s22 s33 s44 s55 s66 s77 If UPLO = 'L', the array AB holds: on entry: on exit: a11 a22 a33 a44 a55 a66 a77 s11 s22 s33 s44 s55 s66 s77 a21 a32 a43 a54 a65 a76 * s12**H s23**H s34**H s54 s65 s76 * a31 a42 a53 a64 a64 * * s13**H s24**H s53 s64 s75 * * Array elements marked * are not used by the routine; s12**H denotes conjg(s12); the diagonal elements of S are real. Definition at line 154 of file zpbstf.f.-iAuthorGenerated automatically by Doxygen for LAPACK from the source code.Version 3.4.2Tue Sep 25 2012 zpbstf.f(3)

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ZPBSTF(l)) ZPBSTF(l)NAME

ZPBSTF - compute a split Cholesky factorization of a complex Hermitian positive definite band matrix ASYNOPSIS

SUBROUTINE ZPBSTF( UPLO, N, KD, AB, LDAB, INFO ) CHARACTER UPLO INTEGER INFO, KD, LDAB, N COMPLEX*16 AB( LDAB, * )PURPOSE

ZPBSTF computes a split Cholesky factorization of a complex Hermitian positive definite band matrix A. This routine is designed to be used in conjunction with ZHBGST. The factorization has the form A = S**H*S where S is a band matrix of the same bandwidth as A and the following structure: S = ( U ) ( M L ) where U is upper triangular of order m = (n+kd)/2, and L is lower triangular of order n-m.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 factor S from the split Cholesky factorization A = S**H*S. See Further Details. LDAB (input) INTEGER The leading dimension of the array AB. LDAB >= KD+1. INFO (output) INTEGER = 0: successful exit < 0: if INFO =, the i-th argument had an illegal value > 0: if INFO = i, the factorization could not be completed, because the updated element a(i,i) was negative; the matrix A is not positive definite.-iFURTHER DETAILS

The band storage scheme is illustrated by the following example, when N = 7, KD = 2: S = ( s11 s12 s13 ) ( s22 s23 s24 ) ( s33 s34 ) ( s44 ) ( s53 s54 s55 ) ( s64 s65 s66 ) ( s75 s76 s77 ) If UPLO = 'U', the array AB holds: on entry: on exit: * * a13 a24 a35 a46 a57 * * s13 s24 s53' s64' s75' * a12 a23 a34 a45 a56 a67 * s12 s23 s34 s54' s65' s76' a11 a22 a33 a44 a55 a66 a77 s11 s22 s33 s44 s55 s66 s77 If UPLO = 'L', the array AB holds: on entry: on exit: a11 a22 a33 a44 a55 a66 a77 s11 s22 s33 s44 s55 s66 s77 a21 a32 a43 a54 a65 a76 * s12' s23' s34' s54 s65 s76 * a31 a42 a53 a64 a64 * * s13' s24' s53 s64 s75 * * Array elements marked * are not used by the routine; s12' denotes conjg(s12); the diagonal elements of S are real.LAPACK version 3.015 June 2000 ZPBSTF(l)