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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 DLARHS( PATH, XTYPE, UPLO, TRANS, M, N, KL, KU, NRHS, 00002 $ A, LDA, X, LDX, B, LDB, ISEED, INFO ) 00003 * 00004 * -- LAPACK test routine (version 3.1) -- 00005 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. 00006 * November 2006 00007 * 00008 * .. Scalar Arguments .. 00009 CHARACTER TRANS, UPLO, XTYPE 00010 CHARACTER*3 PATH 00011 INTEGER INFO, KL, KU, LDA, LDB, LDX, M, N, NRHS 00012 * .. 00013 * .. Array Arguments .. 00014 INTEGER ISEED( 4 ) 00015 DOUBLE PRECISION A( LDA, * ), B( LDB, * ), X( LDX, * ) 00016 * .. 00017 * 00018 * Purpose 00019 * ======= 00020 * 00021 * DLARHS chooses a set of NRHS random solution vectors and sets 00022 * up the right hand sides for the linear system 00023 * op( A ) * X = B, 00024 * where op( A ) may be A or A' (transpose of A). 00025 * 00026 * Arguments 00027 * ========= 00028 * 00029 * PATH (input) CHARACTER*3 00030 * The type of the real matrix A. PATH may be given in any 00031 * combination of upper and lower case. Valid types include 00032 * xGE: General m x n matrix 00033 * xGB: General banded matrix 00034 * xPO: Symmetric positive definite, 2-D storage 00035 * xPP: Symmetric positive definite packed 00036 * xPB: Symmetric positive definite banded 00037 * xSY: Symmetric indefinite, 2-D storage 00038 * xSP: Symmetric indefinite packed 00039 * xSB: Symmetric indefinite banded 00040 * xTR: Triangular 00041 * xTP: Triangular packed 00042 * xTB: Triangular banded 00043 * xQR: General m x n matrix 00044 * xLQ: General m x n matrix 00045 * xQL: General m x n matrix 00046 * xRQ: General m x n matrix 00047 * where the leading character indicates the precision. 00048 * 00049 * XTYPE (input) CHARACTER*1 00050 * Specifies how the exact solution X will be determined: 00051 * = 'N': New solution; generate a random X. 00052 * = 'C': Computed; use value of X on entry. 00053 * 00054 * UPLO (input) CHARACTER*1 00055 * Specifies whether the upper or lower triangular part of the 00056 * matrix A is stored, if A is symmetric. 00057 * = 'U': Upper triangular 00058 * = 'L': Lower triangular 00059 * 00060 * TRANS (input) CHARACTER*1 00061 * Specifies the operation applied to the matrix A. 00062 * = 'N': System is A * x = b 00063 * = 'T': System is A'* x = b 00064 * = 'C': System is A'* x = b 00065 * 00066 * M (input) INTEGER 00067 * The number or rows of the matrix A. M >= 0. 00068 * 00069 * N (input) INTEGER 00070 * The number of columns of the matrix A. N >= 0. 00071 * 00072 * KL (input) INTEGER 00073 * Used only if A is a band matrix; specifies the number of 00074 * subdiagonals of A if A is a general band matrix or if A is 00075 * symmetric or triangular and UPLO = 'L'; specifies the number 00076 * of superdiagonals of A if A is symmetric or triangular and 00077 * UPLO = 'U'. 0 <= KL <= M-1. 00078 * 00079 * KU (input) INTEGER 00080 * Used only if A is a general band matrix or if A is 00081 * triangular. 00082 * 00083 * If PATH = xGB, specifies the number of superdiagonals of A, 00084 * and 0 <= KU <= N-1. 00085 * 00086 * If PATH = xTR, xTP, or xTB, specifies whether or not the 00087 * matrix has unit diagonal: 00088 * = 1: matrix has non-unit diagonal (default) 00089 * = 2: matrix has unit diagonal 00090 * 00091 * NRHS (input) INTEGER 00092 * The number of right hand side vectors in the system A*X = B. 00093 * 00094 * A (input) DOUBLE PRECISION array, dimension (LDA,N) 00095 * The test matrix whose type is given by PATH. 00096 * 00097 * LDA (input) INTEGER 00098 * The leading dimension of the array A. 00099 * If PATH = xGB, LDA >= KL+KU+1. 00100 * If PATH = xPB, xSB, xHB, or xTB, LDA >= KL+1. 00101 * Otherwise, LDA >= max(1,M). 00102 * 00103 * X (input or output) DOUBLE PRECISION array, dimension(LDX,NRHS) 00104 * On entry, if XTYPE = 'C' (for 'Computed'), then X contains 00105 * the exact solution to the system of linear equations. 00106 * On exit, if XTYPE = 'N' (for 'New'), then X is initialized 00107 * with random values. 00108 * 00109 * LDX (input) INTEGER 00110 * The leading dimension of the array X. If TRANS = 'N', 00111 * LDX >= max(1,N); if TRANS = 'T', LDX >= max(1,M). 00112 * 00113 * B (output) DOUBLE PRECISION array, dimension (LDB,NRHS) 00114 * The right hand side vector(s) for the system of equations, 00115 * computed from B = op(A) * X, where op(A) is determined by 00116 * TRANS. 00117 * 00118 * LDB (input) INTEGER 00119 * The leading dimension of the array B. If TRANS = 'N', 00120 * LDB >= max(1,M); if TRANS = 'T', LDB >= max(1,N). 00121 * 00122 * ISEED (input/output) INTEGER array, dimension (4) 00123 * The seed vector for the random number generator (used in 00124 * DLATMS). Modified on exit. 00125 * 00126 * INFO (output) INTEGER 00127 * = 0: successful exit 00128 * < 0: if INFO = -i, the i-th argument had an illegal value 00129 * 00130 * ===================================================================== 00131 * 00132 * .. Parameters .. 00133 DOUBLE PRECISION ONE, ZERO 00134 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) 00135 * .. 00136 * .. Local Scalars .. 00137 LOGICAL BAND, GEN, NOTRAN, QRS, SYM, TRAN, TRI 00138 CHARACTER C1, DIAG 00139 CHARACTER*2 C2 00140 INTEGER J, MB, NX 00141 * .. 00142 * .. External Functions .. 00143 LOGICAL LSAME, LSAMEN 00144 EXTERNAL LSAME, LSAMEN 00145 * .. 00146 * .. External Subroutines .. 00147 EXTERNAL DGBMV, DGEMM, DLACPY, DLARNV, DSBMV, DSPMV, 00148 $ DSYMM, DTBMV, DTPMV, DTRMM, XERBLA 00149 * .. 00150 * .. Intrinsic Functions .. 00151 INTRINSIC MAX 00152 * .. 00153 * .. Executable Statements .. 00154 * 00155 * Test the input parameters. 00156 * 00157 INFO = 0 00158 C1 = PATH( 1: 1 ) 00159 C2 = PATH( 2: 3 ) 00160 TRAN = LSAME( TRANS, 'T' ) .OR. LSAME( TRANS, 'C' ) 00161 NOTRAN = .NOT.TRAN 00162 GEN = LSAME( PATH( 2: 2 ), 'G' ) 00163 QRS = LSAME( PATH( 2: 2 ), 'Q' ) .OR. LSAME( PATH( 3: 3 ), 'Q' ) 00164 SYM = LSAME( PATH( 2: 2 ), 'P' ) .OR. LSAME( PATH( 2: 2 ), 'S' ) 00165 TRI = LSAME( PATH( 2: 2 ), 'T' ) 00166 BAND = LSAME( PATH( 3: 3 ), 'B' ) 00167 IF( .NOT.LSAME( C1, 'Double precision' ) ) THEN 00168 INFO = -1 00169 ELSE IF( .NOT.( LSAME( XTYPE, 'N' ) .OR. LSAME( XTYPE, 'C' ) ) ) 00170 $ THEN 00171 INFO = -2 00172 ELSE IF( ( SYM .OR. TRI ) .AND. .NOT. 00173 $ ( LSAME( UPLO, 'U' ) .OR. LSAME( UPLO, 'L' ) ) ) THEN 00174 INFO = -3 00175 ELSE IF( ( GEN .OR. QRS ) .AND. .NOT. 00176 $ ( TRAN .OR. LSAME( TRANS, 'N' ) ) ) THEN 00177 INFO = -4 00178 ELSE IF( M.LT.0 ) THEN 00179 INFO = -5 00180 ELSE IF( N.LT.0 ) THEN 00181 INFO = -6 00182 ELSE IF( BAND .AND. KL.LT.0 ) THEN 00183 INFO = -7 00184 ELSE IF( BAND .AND. KU.LT.0 ) THEN 00185 INFO = -8 00186 ELSE IF( NRHS.LT.0 ) THEN 00187 INFO = -9 00188 ELSE IF( ( .NOT.BAND .AND. LDA.LT.MAX( 1, M ) ) .OR. 00189 $ ( BAND .AND. ( SYM .OR. TRI ) .AND. LDA.LT.KL+1 ) .OR. 00190 $ ( BAND .AND. GEN .AND. LDA.LT.KL+KU+1 ) ) THEN 00191 INFO = -11 00192 ELSE IF( ( NOTRAN .AND. LDX.LT.MAX( 1, N ) ) .OR. 00193 $ ( TRAN .AND. LDX.LT.MAX( 1, M ) ) ) THEN 00194 INFO = -13 00195 ELSE IF( ( NOTRAN .AND. LDB.LT.MAX( 1, M ) ) .OR. 00196 $ ( TRAN .AND. LDB.LT.MAX( 1, N ) ) ) THEN 00197 INFO = -15 00198 END IF 00199 IF( INFO.NE.0 ) THEN 00200 CALL XERBLA( 'DLARHS', -INFO ) 00201 RETURN 00202 END IF 00203 * 00204 * Initialize X to NRHS random vectors unless XTYPE = 'C'. 00205 * 00206 IF( TRAN ) THEN 00207 NX = M 00208 MB = N 00209 ELSE 00210 NX = N 00211 MB = M 00212 END IF 00213 IF( .NOT.LSAME( XTYPE, 'C' ) ) THEN 00214 DO 10 J = 1, NRHS 00215 CALL DLARNV( 2, ISEED, N, X( 1, J ) ) 00216 10 CONTINUE 00217 END IF 00218 * 00219 * Multiply X by op( A ) using an appropriate 00220 * matrix multiply routine. 00221 * 00222 IF( LSAMEN( 2, C2, 'GE' ) .OR. LSAMEN( 2, C2, 'QR' ) .OR. 00223 $ LSAMEN( 2, C2, 'LQ' ) .OR. LSAMEN( 2, C2, 'QL' ) .OR. 00224 $ LSAMEN( 2, C2, 'RQ' ) ) THEN 00225 * 00226 * General matrix 00227 * 00228 CALL DGEMM( TRANS, 'N', MB, NRHS, NX, ONE, A, LDA, X, LDX, 00229 $ ZERO, B, LDB ) 00230 * 00231 ELSE IF( LSAMEN( 2, C2, 'PO' ) .OR. LSAMEN( 2, C2, 'SY' ) ) THEN 00232 * 00233 * Symmetric matrix, 2-D storage 00234 * 00235 CALL DSYMM( 'Left', UPLO, N, NRHS, ONE, A, LDA, X, LDX, ZERO, 00236 $ B, LDB ) 00237 * 00238 ELSE IF( LSAMEN( 2, C2, 'GB' ) ) THEN 00239 * 00240 * General matrix, band storage 00241 * 00242 DO 20 J = 1, NRHS 00243 CALL DGBMV( TRANS, MB, NX, KL, KU, ONE, A, LDA, X( 1, J ), 00244 $ 1, ZERO, B( 1, J ), 1 ) 00245 20 CONTINUE 00246 * 00247 ELSE IF( LSAMEN( 2, C2, 'PB' ) ) THEN 00248 * 00249 * Symmetric matrix, band storage 00250 * 00251 DO 30 J = 1, NRHS 00252 CALL DSBMV( UPLO, N, KL, ONE, A, LDA, X( 1, J ), 1, ZERO, 00253 $ B( 1, J ), 1 ) 00254 30 CONTINUE 00255 * 00256 ELSE IF( LSAMEN( 2, C2, 'PP' ) .OR. LSAMEN( 2, C2, 'SP' ) ) THEN 00257 * 00258 * Symmetric matrix, packed storage 00259 * 00260 DO 40 J = 1, NRHS 00261 CALL DSPMV( UPLO, N, ONE, A, X( 1, J ), 1, ZERO, B( 1, J ), 00262 $ 1 ) 00263 40 CONTINUE 00264 * 00265 ELSE IF( LSAMEN( 2, C2, 'TR' ) ) THEN 00266 * 00267 * Triangular matrix. Note that for triangular matrices, 00268 * KU = 1 => non-unit triangular 00269 * KU = 2 => unit triangular 00270 * 00271 CALL DLACPY( 'Full', N, NRHS, X, LDX, B, LDB ) 00272 IF( KU.EQ.2 ) THEN 00273 DIAG = 'U' 00274 ELSE 00275 DIAG = 'N' 00276 END IF 00277 CALL DTRMM( 'Left', UPLO, TRANS, DIAG, N, NRHS, ONE, A, LDA, B, 00278 $ LDB ) 00279 * 00280 ELSE IF( LSAMEN( 2, C2, 'TP' ) ) THEN 00281 * 00282 * Triangular matrix, packed storage 00283 * 00284 CALL DLACPY( 'Full', N, NRHS, X, LDX, B, LDB ) 00285 IF( KU.EQ.2 ) THEN 00286 DIAG = 'U' 00287 ELSE 00288 DIAG = 'N' 00289 END IF 00290 DO 50 J = 1, NRHS 00291 CALL DTPMV( UPLO, TRANS, DIAG, N, A, B( 1, J ), 1 ) 00292 50 CONTINUE 00293 * 00294 ELSE IF( LSAMEN( 2, C2, 'TB' ) ) THEN 00295 * 00296 * Triangular matrix, banded storage 00297 * 00298 CALL DLACPY( 'Full', N, NRHS, X, LDX, B, LDB ) 00299 IF( KU.EQ.2 ) THEN 00300 DIAG = 'U' 00301 ELSE 00302 DIAG = 'N' 00303 END IF 00304 DO 60 J = 1, NRHS 00305 CALL DTBMV( UPLO, TRANS, DIAG, N, KL, A, LDA, B( 1, J ), 1 ) 00306 60 CONTINUE 00307 * 00308 ELSE 00309 * 00310 * If PATH is none of the above, return with an error code. 00311 * 00312 INFO = -1 00313 CALL XERBLA( 'DLARHS', -INFO ) 00314 END IF 00315 * 00316 RETURN 00317 * 00318 * End of DLARHS 00319 * 00320 END
1.7.3 
