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LAPACK 3.3.1
Linear Algebra PACKage
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LAPACK 3.3.1
Linear Algebra PACKage
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00001 SUBROUTINE SGBTF2( M, N, KL, KU, AB, LDAB, IPIV, INFO ) 00002 * 00003 * -- LAPACK routine (version 3.2) -- 00004 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00005 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00006 * November 2006 00007 * 00008 * .. Scalar Arguments .. 00009 INTEGER INFO, KL, KU, LDAB, M, N 00010 * .. 00011 * .. Array Arguments .. 00012 INTEGER IPIV( * ) 00013 REAL AB( LDAB, * ) 00014 * .. 00015 * 00016 * Purpose 00017 * ======= 00018 * 00019 * SGBTF2 computes an LU factorization of a real m-by-n band matrix A 00020 * using partial pivoting with row interchanges. 00021 * 00022 * This is the unblocked version of the algorithm, calling Level 2 BLAS. 00023 * 00024 * Arguments 00025 * ========= 00026 * 00027 * M (input) INTEGER 00028 * The number of rows of the matrix A. M >= 0. 00029 * 00030 * N (input) INTEGER 00031 * The number of columns of the matrix A. N >= 0. 00032 * 00033 * KL (input) INTEGER 00034 * The number of subdiagonals within the band of A. KL >= 0. 00035 * 00036 * KU (input) INTEGER 00037 * The number of superdiagonals within the band of A. KU >= 0. 00038 * 00039 * AB (input/output) REAL array, dimension (LDAB,N) 00040 * On entry, the matrix A in band storage, in rows KL+1 to 00041 * 2*KL+KU+1; rows 1 to KL of the array need not be set. 00042 * The j-th column of A is stored in the j-th column of the 00043 * array AB as follows: 00044 * AB(kl+ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl) 00045 * 00046 * On exit, details of the factorization: U is stored as an 00047 * upper triangular band matrix with KL+KU superdiagonals in 00048 * rows 1 to KL+KU+1, and the multipliers used during the 00049 * factorization are stored in rows KL+KU+2 to 2*KL+KU+1. 00050 * See below for further details. 00051 * 00052 * LDAB (input) INTEGER 00053 * The leading dimension of the array AB. LDAB >= 2*KL+KU+1. 00054 * 00055 * IPIV (output) INTEGER array, dimension (min(M,N)) 00056 * The pivot indices; for 1 <= i <= min(M,N), row i of the 00057 * matrix was interchanged with row IPIV(i). 00058 * 00059 * INFO (output) INTEGER 00060 * = 0: successful exit 00061 * < 0: if INFO = -i, the i-th argument had an illegal value 00062 * > 0: if INFO = +i, U(i,i) is exactly zero. The factorization 00063 * has been completed, but the factor U is exactly 00064 * singular, and division by zero will occur if it is used 00065 * to solve a system of equations. 00066 * 00067 * Further Details 00068 * =============== 00069 * 00070 * The band storage scheme is illustrated by the following example, when 00071 * M = N = 6, KL = 2, KU = 1: 00072 * 00073 * On entry: On exit: 00074 * 00075 * * * * + + + * * * u14 u25 u36 00076 * * * + + + + * * u13 u24 u35 u46 00077 * * a12 a23 a34 a45 a56 * u12 u23 u34 u45 u56 00078 * a11 a22 a33 a44 a55 a66 u11 u22 u33 u44 u55 u66 00079 * a21 a32 a43 a54 a65 * m21 m32 m43 m54 m65 * 00080 * a31 a42 a53 a64 * * m31 m42 m53 m64 * * 00081 * 00082 * Array elements marked * are not used by the routine; elements marked 00083 * + need not be set on entry, but are required by the routine to store 00084 * elements of U, because of fill-in resulting from the row 00085 * interchanges. 00086 * 00087 * ===================================================================== 00088 * 00089 * .. Parameters .. 00090 REAL ONE, ZERO 00091 PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) 00092 * .. 00093 * .. Local Scalars .. 00094 INTEGER I, J, JP, JU, KM, KV 00095 * .. 00096 * .. External Functions .. 00097 INTEGER ISAMAX 00098 EXTERNAL ISAMAX 00099 * .. 00100 * .. External Subroutines .. 00101 EXTERNAL SGER, SSCAL, SSWAP, XERBLA 00102 * .. 00103 * .. Intrinsic Functions .. 00104 INTRINSIC MAX, MIN 00105 * .. 00106 * .. Executable Statements .. 00107 * 00108 * KV is the number of superdiagonals in the factor U, allowing for 00109 * fill-in. 00110 * 00111 KV = KU + KL 00112 * 00113 * Test the input parameters. 00114 * 00115 INFO = 0 00116 IF( M.LT.0 ) THEN 00117 INFO = -1 00118 ELSE IF( N.LT.0 ) THEN 00119 INFO = -2 00120 ELSE IF( KL.LT.0 ) THEN 00121 INFO = -3 00122 ELSE IF( KU.LT.0 ) THEN 00123 INFO = -4 00124 ELSE IF( LDAB.LT.KL+KV+1 ) THEN 00125 INFO = -6 00126 END IF 00127 IF( INFO.NE.0 ) THEN 00128 CALL XERBLA( 'SGBTF2', -INFO ) 00129 RETURN 00130 END IF 00131 * 00132 * Quick return if possible 00133 * 00134 IF( M.EQ.0 .OR. N.EQ.0 ) 00135 $ RETURN 00136 * 00137 * Gaussian elimination with partial pivoting 00138 * 00139 * Set fill-in elements in columns KU+2 to KV to zero. 00140 * 00141 DO 20 J = KU + 2, MIN( KV, N ) 00142 DO 10 I = KV - J + 2, KL 00143 AB( I, J ) = ZERO 00144 10 CONTINUE 00145 20 CONTINUE 00146 * 00147 * JU is the index of the last column affected by the current stage 00148 * of the factorization. 00149 * 00150 JU = 1 00151 * 00152 DO 40 J = 1, MIN( M, N ) 00153 * 00154 * Set fill-in elements in column J+KV to zero. 00155 * 00156 IF( J+KV.LE.N ) THEN 00157 DO 30 I = 1, KL 00158 AB( I, J+KV ) = ZERO 00159 30 CONTINUE 00160 END IF 00161 * 00162 * Find pivot and test for singularity. KM is the number of 00163 * subdiagonal elements in the current column. 00164 * 00165 KM = MIN( KL, M-J ) 00166 JP = ISAMAX( KM+1, AB( KV+1, J ), 1 ) 00167 IPIV( J ) = JP + J - 1 00168 IF( AB( KV+JP, J ).NE.ZERO ) THEN 00169 JU = MAX( JU, MIN( J+KU+JP-1, N ) ) 00170 * 00171 * Apply interchange to columns J to JU. 00172 * 00173 IF( JP.NE.1 ) 00174 $ CALL SSWAP( JU-J+1, AB( KV+JP, J ), LDAB-1, 00175 $ AB( KV+1, J ), LDAB-1 ) 00176 * 00177 IF( KM.GT.0 ) THEN 00178 * 00179 * Compute multipliers. 00180 * 00181 CALL SSCAL( KM, ONE / AB( KV+1, J ), AB( KV+2, J ), 1 ) 00182 * 00183 * Update trailing submatrix within the band. 00184 * 00185 IF( JU.GT.J ) 00186 $ CALL SGER( KM, JU-J, -ONE, AB( KV+2, J ), 1, 00187 $ AB( KV, J+1 ), LDAB-1, AB( KV+1, J+1 ), 00188 $ LDAB-1 ) 00189 END IF 00190 ELSE 00191 * 00192 * If pivot is zero, set INFO to the index of the pivot 00193 * unless a zero pivot has already been found. 00194 * 00195 IF( INFO.EQ.0 ) 00196 $ INFO = J 00197 END IF 00198 40 CONTINUE 00199 RETURN 00200 * 00201 * End of SGBTF2 00202 * 00203 END
1.7.3 
