# 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) SPBSTF Function/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 = -i, 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. Author Generated automatically by Doxygen for LAPACK from the source code. Version 3.4.2 Tue 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 A SYNOPSIS
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 = -i, 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. 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. LAPACK version 3.0 15 June 2000 DPBSTF(l)
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