1*> \brief <b> SPBSV computes the solution to system of linear equations A * X = B for OTHER matrices</b> 2* 3* =========== DOCUMENTATION =========== 4* 5* Online html documentation available at 6* http://www.netlib.org/lapack/explore-html/ 7* 8*> \htmlonly 9*> Download SPBSV + dependencies 10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/spbsv.f"> 11*> [TGZ]</a> 12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/spbsv.f"> 13*> [ZIP]</a> 14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/spbsv.f"> 15*> [TXT]</a> 16*> \endhtmlonly 17* 18* Definition: 19* =========== 20* 21* SUBROUTINE SPBSV( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO ) 22* 23* .. Scalar Arguments .. 24* CHARACTER UPLO 25* INTEGER INFO, KD, LDAB, LDB, N, NRHS 26* .. 27* .. Array Arguments .. 28* REAL AB( LDAB, * ), B( LDB, * ) 29* .. 30* 31* 32*> \par Purpose: 33* ============= 34*> 35*> \verbatim 36*> 37*> SPBSV computes the solution to a real system of linear equations 38*> A * X = B, 39*> where A is an N-by-N symmetric positive definite band matrix and X 40*> and B are N-by-NRHS matrices. 41*> 42*> The Cholesky decomposition is used to factor A as 43*> A = U**T * U, if UPLO = 'U', or 44*> A = L * L**T, if UPLO = 'L', 45*> where U is an upper triangular band matrix, and L is a lower 46*> triangular band matrix, with the same number of superdiagonals or 47*> subdiagonals as A. The factored form of A is then used to solve the 48*> system of equations A * X = B. 49*> \endverbatim 50* 51* Arguments: 52* ========== 53* 54*> \param[in] UPLO 55*> \verbatim 56*> UPLO is CHARACTER*1 57*> = 'U': Upper triangle of A is stored; 58*> = 'L': Lower triangle of A is stored. 59*> \endverbatim 60*> 61*> \param[in] N 62*> \verbatim 63*> N is INTEGER 64*> The number of linear equations, i.e., the order of the 65*> matrix A. N >= 0. 66*> \endverbatim 67*> 68*> \param[in] KD 69*> \verbatim 70*> KD is INTEGER 71*> The number of superdiagonals of the matrix A if UPLO = 'U', 72*> or the number of subdiagonals if UPLO = 'L'. KD >= 0. 73*> \endverbatim 74*> 75*> \param[in] NRHS 76*> \verbatim 77*> NRHS is INTEGER 78*> The number of right hand sides, i.e., the number of columns 79*> of the matrix B. NRHS >= 0. 80*> \endverbatim 81*> 82*> \param[in,out] AB 83*> \verbatim 84*> AB is REAL array, dimension (LDAB,N) 85*> On entry, the upper or lower triangle of the symmetric band 86*> matrix A, stored in the first KD+1 rows of the array. The 87*> j-th column of A is stored in the j-th column of the array AB 88*> as follows: 89*> if UPLO = 'U', AB(KD+1+i-j,j) = A(i,j) for max(1,j-KD)<=i<=j; 90*> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(N,j+KD). 91*> See below for further details. 92*> 93*> On exit, if INFO = 0, the triangular factor U or L from the 94*> Cholesky factorization A = U**T*U or A = L*L**T of the band 95*> matrix A, in the same storage format as A. 96*> \endverbatim 97*> 98*> \param[in] LDAB 99*> \verbatim 100*> LDAB is INTEGER 101*> The leading dimension of the array AB. LDAB >= KD+1. 102*> \endverbatim 103*> 104*> \param[in,out] B 105*> \verbatim 106*> B is REAL array, dimension (LDB,NRHS) 107*> On entry, the N-by-NRHS right hand side matrix B. 108*> On exit, if INFO = 0, the N-by-NRHS solution matrix X. 109*> \endverbatim 110*> 111*> \param[in] LDB 112*> \verbatim 113*> LDB is INTEGER 114*> The leading dimension of the array B. LDB >= max(1,N). 115*> \endverbatim 116*> 117*> \param[out] INFO 118*> \verbatim 119*> INFO is INTEGER 120*> = 0: successful exit 121*> < 0: if INFO = -i, the i-th argument had an illegal value 122*> > 0: if INFO = i, the leading minor of order i of A is not 123*> positive definite, so the factorization could not be 124*> completed, and the solution has not been computed. 125*> \endverbatim 126* 127* Authors: 128* ======== 129* 130*> \author Univ. of Tennessee 131*> \author Univ. of California Berkeley 132*> \author Univ. of Colorado Denver 133*> \author NAG Ltd. 134* 135*> \ingroup realOTHERsolve 136* 137*> \par Further Details: 138* ===================== 139*> 140*> \verbatim 141*> 142*> The band storage scheme is illustrated by the following example, when 143*> N = 6, KD = 2, and UPLO = 'U': 144*> 145*> On entry: On exit: 146*> 147*> * * a13 a24 a35 a46 * * u13 u24 u35 u46 148*> * a12 a23 a34 a45 a56 * u12 u23 u34 u45 u56 149*> a11 a22 a33 a44 a55 a66 u11 u22 u33 u44 u55 u66 150*> 151*> Similarly, if UPLO = 'L' the format of A is as follows: 152*> 153*> On entry: On exit: 154*> 155*> a11 a22 a33 a44 a55 a66 l11 l22 l33 l44 l55 l66 156*> a21 a32 a43 a54 a65 * l21 l32 l43 l54 l65 * 157*> a31 a42 a53 a64 * * l31 l42 l53 l64 * * 158*> 159*> Array elements marked * are not used by the routine. 160*> \endverbatim 161*> 162* ===================================================================== 163 SUBROUTINE SPBSV( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO ) 164* 165* -- LAPACK driver routine -- 166* -- LAPACK is a software package provided by Univ. of Tennessee, -- 167* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 168* 169* .. Scalar Arguments .. 170 CHARACTER UPLO 171 INTEGER INFO, KD, LDAB, LDB, N, NRHS 172* .. 173* .. Array Arguments .. 174 REAL AB( LDAB, * ), B( LDB, * ) 175* .. 176* 177* ===================================================================== 178* 179* .. External Functions .. 180 LOGICAL LSAME 181 EXTERNAL LSAME 182* .. 183* .. External Subroutines .. 184 EXTERNAL SPBTRF, SPBTRS, XERBLA 185* .. 186* .. Intrinsic Functions .. 187 INTRINSIC MAX 188* .. 189* .. Executable Statements .. 190* 191* Test the input parameters. 192* 193 INFO = 0 194 IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN 195 INFO = -1 196 ELSE IF( N.LT.0 ) THEN 197 INFO = -2 198 ELSE IF( KD.LT.0 ) THEN 199 INFO = -3 200 ELSE IF( NRHS.LT.0 ) THEN 201 INFO = -4 202 ELSE IF( LDAB.LT.KD+1 ) THEN 203 INFO = -6 204 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN 205 INFO = -8 206 END IF 207 IF( INFO.NE.0 ) THEN 208 CALL XERBLA( 'SPBSV ', -INFO ) 209 RETURN 210 END IF 211* 212* Compute the Cholesky factorization A = U**T*U or A = L*L**T. 213* 214 CALL SPBTRF( UPLO, N, KD, AB, LDAB, INFO ) 215 IF( INFO.EQ.0 ) THEN 216* 217* Solve the system A*X = B, overwriting B with X. 218* 219 CALL SPBTRS( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO ) 220* 221 END IF 222 RETURN 223* 224* End of SPBSV 225* 226 END 227