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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 SLASD0( N, SQRE, D, E, U, LDU, VT, LDVT, SMLSIZ, IWORK, 00002 $ WORK, INFO ) 00003 * 00004 * -- LAPACK auxiliary routine (version 3.2.2) -- 00005 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00006 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00007 * June 2010 00008 * 00009 * .. Scalar Arguments .. 00010 INTEGER INFO, LDU, LDVT, N, SMLSIZ, SQRE 00011 * .. 00012 * .. Array Arguments .. 00013 INTEGER IWORK( * ) 00014 REAL D( * ), E( * ), U( LDU, * ), VT( LDVT, * ), 00015 $ WORK( * ) 00016 * .. 00017 * 00018 * Purpose 00019 * ======= 00020 * 00021 * Using a divide and conquer approach, SLASD0 computes the singular 00022 * value decomposition (SVD) of a real upper bidiagonal N-by-M 00023 * matrix B with diagonal D and offdiagonal E, where M = N + SQRE. 00024 * The algorithm computes orthogonal matrices U and VT such that 00025 * B = U * S * VT. The singular values S are overwritten on D. 00026 * 00027 * A related subroutine, SLASDA, computes only the singular values, 00028 * and optionally, the singular vectors in compact form. 00029 * 00030 * Arguments 00031 * ========= 00032 * 00033 * N (input) INTEGER 00034 * On entry, the row dimension of the upper bidiagonal matrix. 00035 * This is also the dimension of the main diagonal array D. 00036 * 00037 * SQRE (input) INTEGER 00038 * Specifies the column dimension of the bidiagonal matrix. 00039 * = 0: The bidiagonal matrix has column dimension M = N; 00040 * = 1: The bidiagonal matrix has column dimension M = N+1; 00041 * 00042 * D (input/output) REAL array, dimension (N) 00043 * On entry D contains the main diagonal of the bidiagonal 00044 * matrix. 00045 * On exit D, if INFO = 0, contains its singular values. 00046 * 00047 * E (input) REAL array, dimension (M-1) 00048 * Contains the subdiagonal entries of the bidiagonal matrix. 00049 * On exit, E has been destroyed. 00050 * 00051 * U (output) REAL array, dimension at least (LDQ, N) 00052 * On exit, U contains the left singular vectors. 00053 * 00054 * LDU (input) INTEGER 00055 * On entry, leading dimension of U. 00056 * 00057 * VT (output) REAL array, dimension at least (LDVT, M) 00058 * On exit, VT**T contains the right singular vectors. 00059 * 00060 * LDVT (input) INTEGER 00061 * On entry, leading dimension of VT. 00062 * 00063 * SMLSIZ (input) INTEGER 00064 * On entry, maximum size of the subproblems at the 00065 * bottom of the computation tree. 00066 * 00067 * IWORK (workspace) INTEGER array, dimension (8*N) 00068 * 00069 * WORK (workspace) REAL array, dimension (3*M**2+2*M) 00070 * 00071 * INFO (output) INTEGER 00072 * = 0: successful exit. 00073 * < 0: if INFO = -i, the i-th argument had an illegal value. 00074 * > 0: if INFO = 1, a singular value did not converge 00075 * 00076 * Further Details 00077 * =============== 00078 * 00079 * Based on contributions by 00080 * Ming Gu and Huan Ren, Computer Science Division, University of 00081 * California at Berkeley, USA 00082 * 00083 * ===================================================================== 00084 * 00085 * .. Local Scalars .. 00086 INTEGER I, I1, IC, IDXQ, IDXQC, IM1, INODE, ITEMP, IWK, 00087 $ J, LF, LL, LVL, M, NCC, ND, NDB1, NDIML, NDIMR, 00088 $ NL, NLF, NLP1, NLVL, NR, NRF, NRP1, SQREI 00089 REAL ALPHA, BETA 00090 * .. 00091 * .. External Subroutines .. 00092 EXTERNAL SLASD1, SLASDQ, SLASDT, XERBLA 00093 * .. 00094 * .. Executable Statements .. 00095 * 00096 * Test the input parameters. 00097 * 00098 INFO = 0 00099 * 00100 IF( N.LT.0 ) THEN 00101 INFO = -1 00102 ELSE IF( ( SQRE.LT.0 ) .OR. ( SQRE.GT.1 ) ) THEN 00103 INFO = -2 00104 END IF 00105 * 00106 M = N + SQRE 00107 * 00108 IF( LDU.LT.N ) THEN 00109 INFO = -6 00110 ELSE IF( LDVT.LT.M ) THEN 00111 INFO = -8 00112 ELSE IF( SMLSIZ.LT.3 ) THEN 00113 INFO = -9 00114 END IF 00115 IF( INFO.NE.0 ) THEN 00116 CALL XERBLA( 'SLASD0', -INFO ) 00117 RETURN 00118 END IF 00119 * 00120 * If the input matrix is too small, call SLASDQ to find the SVD. 00121 * 00122 IF( N.LE.SMLSIZ ) THEN 00123 CALL SLASDQ( 'U', SQRE, N, M, N, 0, D, E, VT, LDVT, U, LDU, U, 00124 $ LDU, WORK, INFO ) 00125 RETURN 00126 END IF 00127 * 00128 * Set up the computation tree. 00129 * 00130 INODE = 1 00131 NDIML = INODE + N 00132 NDIMR = NDIML + N 00133 IDXQ = NDIMR + N 00134 IWK = IDXQ + N 00135 CALL SLASDT( N, NLVL, ND, IWORK( INODE ), IWORK( NDIML ), 00136 $ IWORK( NDIMR ), SMLSIZ ) 00137 * 00138 * For the nodes on bottom level of the tree, solve 00139 * their subproblems by SLASDQ. 00140 * 00141 NDB1 = ( ND+1 ) / 2 00142 NCC = 0 00143 DO 30 I = NDB1, ND 00144 * 00145 * IC : center row of each node 00146 * NL : number of rows of left subproblem 00147 * NR : number of rows of right subproblem 00148 * NLF: starting row of the left subproblem 00149 * NRF: starting row of the right subproblem 00150 * 00151 I1 = I - 1 00152 IC = IWORK( INODE+I1 ) 00153 NL = IWORK( NDIML+I1 ) 00154 NLP1 = NL + 1 00155 NR = IWORK( NDIMR+I1 ) 00156 NRP1 = NR + 1 00157 NLF = IC - NL 00158 NRF = IC + 1 00159 SQREI = 1 00160 CALL SLASDQ( 'U', SQREI, NL, NLP1, NL, NCC, D( NLF ), E( NLF ), 00161 $ VT( NLF, NLF ), LDVT, U( NLF, NLF ), LDU, 00162 $ U( NLF, NLF ), LDU, WORK, INFO ) 00163 IF( INFO.NE.0 ) THEN 00164 RETURN 00165 END IF 00166 ITEMP = IDXQ + NLF - 2 00167 DO 10 J = 1, NL 00168 IWORK( ITEMP+J ) = J 00169 10 CONTINUE 00170 IF( I.EQ.ND ) THEN 00171 SQREI = SQRE 00172 ELSE 00173 SQREI = 1 00174 END IF 00175 NRP1 = NR + SQREI 00176 CALL SLASDQ( 'U', SQREI, NR, NRP1, NR, NCC, D( NRF ), E( NRF ), 00177 $ VT( NRF, NRF ), LDVT, U( NRF, NRF ), LDU, 00178 $ U( NRF, NRF ), LDU, WORK, INFO ) 00179 IF( INFO.NE.0 ) THEN 00180 RETURN 00181 END IF 00182 ITEMP = IDXQ + IC 00183 DO 20 J = 1, NR 00184 IWORK( ITEMP+J-1 ) = J 00185 20 CONTINUE 00186 30 CONTINUE 00187 * 00188 * Now conquer each subproblem bottom-up. 00189 * 00190 DO 50 LVL = NLVL, 1, -1 00191 * 00192 * Find the first node LF and last node LL on the 00193 * current level LVL. 00194 * 00195 IF( LVL.EQ.1 ) THEN 00196 LF = 1 00197 LL = 1 00198 ELSE 00199 LF = 2**( LVL-1 ) 00200 LL = 2*LF - 1 00201 END IF 00202 DO 40 I = LF, LL 00203 IM1 = I - 1 00204 IC = IWORK( INODE+IM1 ) 00205 NL = IWORK( NDIML+IM1 ) 00206 NR = IWORK( NDIMR+IM1 ) 00207 NLF = IC - NL 00208 IF( ( SQRE.EQ.0 ) .AND. ( I.EQ.LL ) ) THEN 00209 SQREI = SQRE 00210 ELSE 00211 SQREI = 1 00212 END IF 00213 IDXQC = IDXQ + NLF - 1 00214 ALPHA = D( IC ) 00215 BETA = E( IC ) 00216 CALL SLASD1( NL, NR, SQREI, D( NLF ), ALPHA, BETA, 00217 $ U( NLF, NLF ), LDU, VT( NLF, NLF ), LDVT, 00218 $ IWORK( IDXQC ), IWORK( IWK ), WORK, INFO ) 00219 IF( INFO.NE.0 ) THEN 00220 RETURN 00221 END IF 00222 40 CONTINUE 00223 50 CONTINUE 00224 * 00225 RETURN 00226 * 00227 * End of SLASD0 00228 * 00229 END
1.7.3 
