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

spbstf.f(3) LAPACK spbstf.f(3)NAME

spbstf.f-SYNOPSIS

Functions/Subroutines subroutine spbstf (UPLO, N, KD, AB, LDAB, INFO) SPBSTFFunction/Subroutine Documentation subroutine spbstf (characterUPLO, integerN, integerKD, real, dimension( ldab, * )AB, integerLDAB, integerINFO) SPBSTF Purpose: SPBSTF computes a split Cholesky factorization of a real symmetric positive definite band matrix A. This routine is designed to be used in conjunction with SSBGST. The factorization has the form A = S**T*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 REAL array, dimension (LDAB,N) On entry, the upper or lower triangle of the symmetric 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**T*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 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. Definition at line 153 of file spbstf.f.-iAuthorGenerated automatically by Doxygen for LAPACK from the source code.Version 3.4.2Tue Sep 25 2012 spbstf.f(3)

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DPBSTF(l)) DPBSTF(l)NAME

DPBSTF - compute a split Cholesky factorization of a real symmetric positive definite band matrix ASYNOPSIS

SUBROUTINE DPBSTF( UPLO, N, KD, AB, LDAB, INFO ) CHARACTER UPLO INTEGER INFO, KD, LDAB, N DOUBLE PRECISION AB( LDAB, * )PURPOSE

DPBSTF computes a split Cholesky factorization of a real symmetric positive definite band matrix A. This routine is designed to be used in conjunction with DSBGST. The factorization has the form A = S**T*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) DOUBLE PRECISION array, dimension (LDAB,N) On entry, the upper or lower triangle of the symmetric 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**T*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.LAPACK version 3.015 June 2000 DPBSTF(l)