Annotation of rpl/lapack/lapack/dsytrs.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE DSYTRS( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO )
! 2: *
! 3: * -- LAPACK routine (version 3.2) --
! 4: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 5: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 6: * November 2006
! 7: *
! 8: * .. Scalar Arguments ..
! 9: CHARACTER UPLO
! 10: INTEGER INFO, LDA, LDB, N, NRHS
! 11: * ..
! 12: * .. Array Arguments ..
! 13: INTEGER IPIV( * )
! 14: DOUBLE PRECISION A( LDA, * ), B( LDB, * )
! 15: * ..
! 16: *
! 17: * Purpose
! 18: * =======
! 19: *
! 20: * DSYTRS solves a system of linear equations A*X = B with a real
! 21: * symmetric matrix A using the factorization A = U*D*U**T or
! 22: * A = L*D*L**T computed by DSYTRF.
! 23: *
! 24: * Arguments
! 25: * =========
! 26: *
! 27: * UPLO (input) CHARACTER*1
! 28: * Specifies whether the details of the factorization are stored
! 29: * as an upper or lower triangular matrix.
! 30: * = 'U': Upper triangular, form is A = U*D*U**T;
! 31: * = 'L': Lower triangular, form is A = L*D*L**T.
! 32: *
! 33: * N (input) INTEGER
! 34: * The order of the matrix A. N >= 0.
! 35: *
! 36: * NRHS (input) INTEGER
! 37: * The number of right hand sides, i.e., the number of columns
! 38: * of the matrix B. NRHS >= 0.
! 39: *
! 40: * A (input) DOUBLE PRECISION array, dimension (LDA,N)
! 41: * The block diagonal matrix D and the multipliers used to
! 42: * obtain the factor U or L as computed by DSYTRF.
! 43: *
! 44: * LDA (input) INTEGER
! 45: * The leading dimension of the array A. LDA >= max(1,N).
! 46: *
! 47: * IPIV (input) INTEGER array, dimension (N)
! 48: * Details of the interchanges and the block structure of D
! 49: * as determined by DSYTRF.
! 50: *
! 51: * B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
! 52: * On entry, the right hand side matrix B.
! 53: * On exit, the solution matrix X.
! 54: *
! 55: * LDB (input) INTEGER
! 56: * The leading dimension of the array B. LDB >= max(1,N).
! 57: *
! 58: * INFO (output) INTEGER
! 59: * = 0: successful exit
! 60: * < 0: if INFO = -i, the i-th argument had an illegal value
! 61: *
! 62: * =====================================================================
! 63: *
! 64: * .. Parameters ..
! 65: DOUBLE PRECISION ONE
! 66: PARAMETER ( ONE = 1.0D+0 )
! 67: * ..
! 68: * .. Local Scalars ..
! 69: LOGICAL UPPER
! 70: INTEGER J, K, KP
! 71: DOUBLE PRECISION AK, AKM1, AKM1K, BK, BKM1, DENOM
! 72: * ..
! 73: * .. External Functions ..
! 74: LOGICAL LSAME
! 75: EXTERNAL LSAME
! 76: * ..
! 77: * .. External Subroutines ..
! 78: EXTERNAL DGEMV, DGER, DSCAL, DSWAP, XERBLA
! 79: * ..
! 80: * .. Intrinsic Functions ..
! 81: INTRINSIC MAX
! 82: * ..
! 83: * .. Executable Statements ..
! 84: *
! 85: INFO = 0
! 86: UPPER = LSAME( UPLO, 'U' )
! 87: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
! 88: INFO = -1
! 89: ELSE IF( N.LT.0 ) THEN
! 90: INFO = -2
! 91: ELSE IF( NRHS.LT.0 ) THEN
! 92: INFO = -3
! 93: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
! 94: INFO = -5
! 95: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
! 96: INFO = -8
! 97: END IF
! 98: IF( INFO.NE.0 ) THEN
! 99: CALL XERBLA( 'DSYTRS', -INFO )
! 100: RETURN
! 101: END IF
! 102: *
! 103: * Quick return if possible
! 104: *
! 105: IF( N.EQ.0 .OR. NRHS.EQ.0 )
! 106: $ RETURN
! 107: *
! 108: IF( UPPER ) THEN
! 109: *
! 110: * Solve A*X = B, where A = U*D*U'.
! 111: *
! 112: * First solve U*D*X = B, overwriting B with X.
! 113: *
! 114: * K is the main loop index, decreasing from N to 1 in steps of
! 115: * 1 or 2, depending on the size of the diagonal blocks.
! 116: *
! 117: K = N
! 118: 10 CONTINUE
! 119: *
! 120: * If K < 1, exit from loop.
! 121: *
! 122: IF( K.LT.1 )
! 123: $ GO TO 30
! 124: *
! 125: IF( IPIV( K ).GT.0 ) THEN
! 126: *
! 127: * 1 x 1 diagonal block
! 128: *
! 129: * Interchange rows K and IPIV(K).
! 130: *
! 131: KP = IPIV( K )
! 132: IF( KP.NE.K )
! 133: $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
! 134: *
! 135: * Multiply by inv(U(K)), where U(K) is the transformation
! 136: * stored in column K of A.
! 137: *
! 138: CALL DGER( K-1, NRHS, -ONE, A( 1, K ), 1, B( K, 1 ), LDB,
! 139: $ B( 1, 1 ), LDB )
! 140: *
! 141: * Multiply by the inverse of the diagonal block.
! 142: *
! 143: CALL DSCAL( NRHS, ONE / A( K, K ), B( K, 1 ), LDB )
! 144: K = K - 1
! 145: ELSE
! 146: *
! 147: * 2 x 2 diagonal block
! 148: *
! 149: * Interchange rows K-1 and -IPIV(K).
! 150: *
! 151: KP = -IPIV( K )
! 152: IF( KP.NE.K-1 )
! 153: $ CALL DSWAP( NRHS, B( K-1, 1 ), LDB, B( KP, 1 ), LDB )
! 154: *
! 155: * Multiply by inv(U(K)), where U(K) is the transformation
! 156: * stored in columns K-1 and K of A.
! 157: *
! 158: CALL DGER( K-2, NRHS, -ONE, A( 1, K ), 1, B( K, 1 ), LDB,
! 159: $ B( 1, 1 ), LDB )
! 160: CALL DGER( K-2, NRHS, -ONE, A( 1, K-1 ), 1, B( K-1, 1 ),
! 161: $ LDB, B( 1, 1 ), LDB )
! 162: *
! 163: * Multiply by the inverse of the diagonal block.
! 164: *
! 165: AKM1K = A( K-1, K )
! 166: AKM1 = A( K-1, K-1 ) / AKM1K
! 167: AK = A( K, K ) / AKM1K
! 168: DENOM = AKM1*AK - ONE
! 169: DO 20 J = 1, NRHS
! 170: BKM1 = B( K-1, J ) / AKM1K
! 171: BK = B( K, J ) / AKM1K
! 172: B( K-1, J ) = ( AK*BKM1-BK ) / DENOM
! 173: B( K, J ) = ( AKM1*BK-BKM1 ) / DENOM
! 174: 20 CONTINUE
! 175: K = K - 2
! 176: END IF
! 177: *
! 178: GO TO 10
! 179: 30 CONTINUE
! 180: *
! 181: * Next solve U'*X = B, overwriting B with X.
! 182: *
! 183: * K is the main loop index, increasing from 1 to N in steps of
! 184: * 1 or 2, depending on the size of the diagonal blocks.
! 185: *
! 186: K = 1
! 187: 40 CONTINUE
! 188: *
! 189: * If K > N, exit from loop.
! 190: *
! 191: IF( K.GT.N )
! 192: $ GO TO 50
! 193: *
! 194: IF( IPIV( K ).GT.0 ) THEN
! 195: *
! 196: * 1 x 1 diagonal block
! 197: *
! 198: * Multiply by inv(U'(K)), where U(K) is the transformation
! 199: * stored in column K of A.
! 200: *
! 201: CALL DGEMV( 'Transpose', K-1, NRHS, -ONE, B, LDB, A( 1, K ),
! 202: $ 1, ONE, B( K, 1 ), LDB )
! 203: *
! 204: * Interchange rows K and IPIV(K).
! 205: *
! 206: KP = IPIV( K )
! 207: IF( KP.NE.K )
! 208: $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
! 209: K = K + 1
! 210: ELSE
! 211: *
! 212: * 2 x 2 diagonal block
! 213: *
! 214: * Multiply by inv(U'(K+1)), where U(K+1) is the transformation
! 215: * stored in columns K and K+1 of A.
! 216: *
! 217: CALL DGEMV( 'Transpose', K-1, NRHS, -ONE, B, LDB, A( 1, K ),
! 218: $ 1, ONE, B( K, 1 ), LDB )
! 219: CALL DGEMV( 'Transpose', K-1, NRHS, -ONE, B, LDB,
! 220: $ A( 1, K+1 ), 1, ONE, B( K+1, 1 ), LDB )
! 221: *
! 222: * Interchange rows K and -IPIV(K).
! 223: *
! 224: KP = -IPIV( K )
! 225: IF( KP.NE.K )
! 226: $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
! 227: K = K + 2
! 228: END IF
! 229: *
! 230: GO TO 40
! 231: 50 CONTINUE
! 232: *
! 233: ELSE
! 234: *
! 235: * Solve A*X = B, where A = L*D*L'.
! 236: *
! 237: * First solve L*D*X = B, overwriting B with X.
! 238: *
! 239: * K is the main loop index, increasing from 1 to N in steps of
! 240: * 1 or 2, depending on the size of the diagonal blocks.
! 241: *
! 242: K = 1
! 243: 60 CONTINUE
! 244: *
! 245: * If K > N, exit from loop.
! 246: *
! 247: IF( K.GT.N )
! 248: $ GO TO 80
! 249: *
! 250: IF( IPIV( K ).GT.0 ) THEN
! 251: *
! 252: * 1 x 1 diagonal block
! 253: *
! 254: * Interchange rows K and IPIV(K).
! 255: *
! 256: KP = IPIV( K )
! 257: IF( KP.NE.K )
! 258: $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
! 259: *
! 260: * Multiply by inv(L(K)), where L(K) is the transformation
! 261: * stored in column K of A.
! 262: *
! 263: IF( K.LT.N )
! 264: $ CALL DGER( N-K, NRHS, -ONE, A( K+1, K ), 1, B( K, 1 ),
! 265: $ LDB, B( K+1, 1 ), LDB )
! 266: *
! 267: * Multiply by the inverse of the diagonal block.
! 268: *
! 269: CALL DSCAL( NRHS, ONE / A( K, K ), B( K, 1 ), LDB )
! 270: K = K + 1
! 271: ELSE
! 272: *
! 273: * 2 x 2 diagonal block
! 274: *
! 275: * Interchange rows K+1 and -IPIV(K).
! 276: *
! 277: KP = -IPIV( K )
! 278: IF( KP.NE.K+1 )
! 279: $ CALL DSWAP( NRHS, B( K+1, 1 ), LDB, B( KP, 1 ), LDB )
! 280: *
! 281: * Multiply by inv(L(K)), where L(K) is the transformation
! 282: * stored in columns K and K+1 of A.
! 283: *
! 284: IF( K.LT.N-1 ) THEN
! 285: CALL DGER( N-K-1, NRHS, -ONE, A( K+2, K ), 1, B( K, 1 ),
! 286: $ LDB, B( K+2, 1 ), LDB )
! 287: CALL DGER( N-K-1, NRHS, -ONE, A( K+2, K+1 ), 1,
! 288: $ B( K+1, 1 ), LDB, B( K+2, 1 ), LDB )
! 289: END IF
! 290: *
! 291: * Multiply by the inverse of the diagonal block.
! 292: *
! 293: AKM1K = A( K+1, K )
! 294: AKM1 = A( K, K ) / AKM1K
! 295: AK = A( K+1, K+1 ) / AKM1K
! 296: DENOM = AKM1*AK - ONE
! 297: DO 70 J = 1, NRHS
! 298: BKM1 = B( K, J ) / AKM1K
! 299: BK = B( K+1, J ) / AKM1K
! 300: B( K, J ) = ( AK*BKM1-BK ) / DENOM
! 301: B( K+1, J ) = ( AKM1*BK-BKM1 ) / DENOM
! 302: 70 CONTINUE
! 303: K = K + 2
! 304: END IF
! 305: *
! 306: GO TO 60
! 307: 80 CONTINUE
! 308: *
! 309: * Next solve L'*X = B, overwriting B with X.
! 310: *
! 311: * K is the main loop index, decreasing from N to 1 in steps of
! 312: * 1 or 2, depending on the size of the diagonal blocks.
! 313: *
! 314: K = N
! 315: 90 CONTINUE
! 316: *
! 317: * If K < 1, exit from loop.
! 318: *
! 319: IF( K.LT.1 )
! 320: $ GO TO 100
! 321: *
! 322: IF( IPIV( K ).GT.0 ) THEN
! 323: *
! 324: * 1 x 1 diagonal block
! 325: *
! 326: * Multiply by inv(L'(K)), where L(K) is the transformation
! 327: * stored in column K of A.
! 328: *
! 329: IF( K.LT.N )
! 330: $ CALL DGEMV( 'Transpose', N-K, NRHS, -ONE, B( K+1, 1 ),
! 331: $ LDB, A( K+1, K ), 1, ONE, B( K, 1 ), LDB )
! 332: *
! 333: * Interchange rows K and IPIV(K).
! 334: *
! 335: KP = IPIV( K )
! 336: IF( KP.NE.K )
! 337: $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
! 338: K = K - 1
! 339: ELSE
! 340: *
! 341: * 2 x 2 diagonal block
! 342: *
! 343: * Multiply by inv(L'(K-1)), where L(K-1) is the transformation
! 344: * stored in columns K-1 and K of A.
! 345: *
! 346: IF( K.LT.N ) THEN
! 347: CALL DGEMV( 'Transpose', N-K, NRHS, -ONE, B( K+1, 1 ),
! 348: $ LDB, A( K+1, K ), 1, ONE, B( K, 1 ), LDB )
! 349: CALL DGEMV( 'Transpose', N-K, NRHS, -ONE, B( K+1, 1 ),
! 350: $ LDB, A( K+1, K-1 ), 1, ONE, B( K-1, 1 ),
! 351: $ LDB )
! 352: END IF
! 353: *
! 354: * Interchange rows K and -IPIV(K).
! 355: *
! 356: KP = -IPIV( K )
! 357: IF( KP.NE.K )
! 358: $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
! 359: K = K - 2
! 360: END IF
! 361: *
! 362: GO TO 90
! 363: 100 CONTINUE
! 364: END IF
! 365: *
! 366: RETURN
! 367: *
! 368: * End of DSYTRS
! 369: *
! 370: END
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