Annotation of rpl/lapack/lapack/zsptrs.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZSPTRS( UPLO, N, NRHS, AP, 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, LDB, N, NRHS
! 11: * ..
! 12: * .. Array Arguments ..
! 13: INTEGER IPIV( * )
! 14: COMPLEX*16 AP( * ), B( LDB, * )
! 15: * ..
! 16: *
! 17: * Purpose
! 18: * =======
! 19: *
! 20: * ZSPTRS solves a system of linear equations A*X = B with a complex
! 21: * symmetric matrix A stored in packed format using the factorization
! 22: * A = U*D*U**T or A = L*D*L**T computed by ZSPTRF.
! 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: * AP (input) COMPLEX*16 array, dimension (N*(N+1)/2)
! 41: * The block diagonal matrix D and the multipliers used to
! 42: * obtain the factor U or L as computed by ZSPTRF, stored as a
! 43: * packed triangular matrix.
! 44: *
! 45: * IPIV (input) INTEGER array, dimension (N)
! 46: * Details of the interchanges and the block structure of D
! 47: * as determined by ZSPTRF.
! 48: *
! 49: * B (input/output) COMPLEX*16 array, dimension (LDB,NRHS)
! 50: * On entry, the right hand side matrix B.
! 51: * On exit, the solution matrix X.
! 52: *
! 53: * LDB (input) INTEGER
! 54: * The leading dimension of the array B. LDB >= max(1,N).
! 55: *
! 56: * INFO (output) INTEGER
! 57: * = 0: successful exit
! 58: * < 0: if INFO = -i, the i-th argument had an illegal value
! 59: *
! 60: * =====================================================================
! 61: *
! 62: * .. Parameters ..
! 63: COMPLEX*16 ONE
! 64: PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) )
! 65: * ..
! 66: * .. Local Scalars ..
! 67: LOGICAL UPPER
! 68: INTEGER J, K, KC, KP
! 69: COMPLEX*16 AK, AKM1, AKM1K, BK, BKM1, DENOM
! 70: * ..
! 71: * .. External Functions ..
! 72: LOGICAL LSAME
! 73: EXTERNAL LSAME
! 74: * ..
! 75: * .. External Subroutines ..
! 76: EXTERNAL XERBLA, ZGEMV, ZGERU, ZSCAL, ZSWAP
! 77: * ..
! 78: * .. Intrinsic Functions ..
! 79: INTRINSIC MAX
! 80: * ..
! 81: * .. Executable Statements ..
! 82: *
! 83: INFO = 0
! 84: UPPER = LSAME( UPLO, 'U' )
! 85: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
! 86: INFO = -1
! 87: ELSE IF( N.LT.0 ) THEN
! 88: INFO = -2
! 89: ELSE IF( NRHS.LT.0 ) THEN
! 90: INFO = -3
! 91: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
! 92: INFO = -7
! 93: END IF
! 94: IF( INFO.NE.0 ) THEN
! 95: CALL XERBLA( 'ZSPTRS', -INFO )
! 96: RETURN
! 97: END IF
! 98: *
! 99: * Quick return if possible
! 100: *
! 101: IF( N.EQ.0 .OR. NRHS.EQ.0 )
! 102: $ RETURN
! 103: *
! 104: IF( UPPER ) THEN
! 105: *
! 106: * Solve A*X = B, where A = U*D*U'.
! 107: *
! 108: * First solve U*D*X = B, overwriting B with X.
! 109: *
! 110: * K is the main loop index, decreasing from N to 1 in steps of
! 111: * 1 or 2, depending on the size of the diagonal blocks.
! 112: *
! 113: K = N
! 114: KC = N*( N+1 ) / 2 + 1
! 115: 10 CONTINUE
! 116: *
! 117: * If K < 1, exit from loop.
! 118: *
! 119: IF( K.LT.1 )
! 120: $ GO TO 30
! 121: *
! 122: KC = KC - K
! 123: IF( IPIV( K ).GT.0 ) THEN
! 124: *
! 125: * 1 x 1 diagonal block
! 126: *
! 127: * Interchange rows K and IPIV(K).
! 128: *
! 129: KP = IPIV( K )
! 130: IF( KP.NE.K )
! 131: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
! 132: *
! 133: * Multiply by inv(U(K)), where U(K) is the transformation
! 134: * stored in column K of A.
! 135: *
! 136: CALL ZGERU( K-1, NRHS, -ONE, AP( KC ), 1, B( K, 1 ), LDB,
! 137: $ B( 1, 1 ), LDB )
! 138: *
! 139: * Multiply by the inverse of the diagonal block.
! 140: *
! 141: CALL ZSCAL( NRHS, ONE / AP( KC+K-1 ), B( K, 1 ), LDB )
! 142: K = K - 1
! 143: ELSE
! 144: *
! 145: * 2 x 2 diagonal block
! 146: *
! 147: * Interchange rows K-1 and -IPIV(K).
! 148: *
! 149: KP = -IPIV( K )
! 150: IF( KP.NE.K-1 )
! 151: $ CALL ZSWAP( NRHS, B( K-1, 1 ), LDB, B( KP, 1 ), LDB )
! 152: *
! 153: * Multiply by inv(U(K)), where U(K) is the transformation
! 154: * stored in columns K-1 and K of A.
! 155: *
! 156: CALL ZGERU( K-2, NRHS, -ONE, AP( KC ), 1, B( K, 1 ), LDB,
! 157: $ B( 1, 1 ), LDB )
! 158: CALL ZGERU( K-2, NRHS, -ONE, AP( KC-( K-1 ) ), 1,
! 159: $ B( K-1, 1 ), LDB, B( 1, 1 ), LDB )
! 160: *
! 161: * Multiply by the inverse of the diagonal block.
! 162: *
! 163: AKM1K = AP( KC+K-2 )
! 164: AKM1 = AP( KC-1 ) / AKM1K
! 165: AK = AP( KC+K-1 ) / AKM1K
! 166: DENOM = AKM1*AK - ONE
! 167: DO 20 J = 1, NRHS
! 168: BKM1 = B( K-1, J ) / AKM1K
! 169: BK = B( K, J ) / AKM1K
! 170: B( K-1, J ) = ( AK*BKM1-BK ) / DENOM
! 171: B( K, J ) = ( AKM1*BK-BKM1 ) / DENOM
! 172: 20 CONTINUE
! 173: KC = KC - K + 1
! 174: K = K - 2
! 175: END IF
! 176: *
! 177: GO TO 10
! 178: 30 CONTINUE
! 179: *
! 180: * Next solve U'*X = B, overwriting B with X.
! 181: *
! 182: * K is the main loop index, increasing from 1 to N in steps of
! 183: * 1 or 2, depending on the size of the diagonal blocks.
! 184: *
! 185: K = 1
! 186: KC = 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 ZGEMV( 'Transpose', K-1, NRHS, -ONE, B, LDB, AP( KC ),
! 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 ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
! 209: KC = KC + K
! 210: K = K + 1
! 211: ELSE
! 212: *
! 213: * 2 x 2 diagonal block
! 214: *
! 215: * Multiply by inv(U'(K+1)), where U(K+1) is the transformation
! 216: * stored in columns K and K+1 of A.
! 217: *
! 218: CALL ZGEMV( 'Transpose', K-1, NRHS, -ONE, B, LDB, AP( KC ),
! 219: $ 1, ONE, B( K, 1 ), LDB )
! 220: CALL ZGEMV( 'Transpose', K-1, NRHS, -ONE, B, LDB,
! 221: $ AP( KC+K ), 1, ONE, B( K+1, 1 ), LDB )
! 222: *
! 223: * Interchange rows K and -IPIV(K).
! 224: *
! 225: KP = -IPIV( K )
! 226: IF( KP.NE.K )
! 227: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
! 228: KC = KC + 2*K + 1
! 229: K = K + 2
! 230: END IF
! 231: *
! 232: GO TO 40
! 233: 50 CONTINUE
! 234: *
! 235: ELSE
! 236: *
! 237: * Solve A*X = B, where A = L*D*L'.
! 238: *
! 239: * First solve L*D*X = B, overwriting B with X.
! 240: *
! 241: * K is the main loop index, increasing from 1 to N in steps of
! 242: * 1 or 2, depending on the size of the diagonal blocks.
! 243: *
! 244: K = 1
! 245: KC = 1
! 246: 60 CONTINUE
! 247: *
! 248: * If K > N, exit from loop.
! 249: *
! 250: IF( K.GT.N )
! 251: $ GO TO 80
! 252: *
! 253: IF( IPIV( K ).GT.0 ) THEN
! 254: *
! 255: * 1 x 1 diagonal block
! 256: *
! 257: * Interchange rows K and IPIV(K).
! 258: *
! 259: KP = IPIV( K )
! 260: IF( KP.NE.K )
! 261: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
! 262: *
! 263: * Multiply by inv(L(K)), where L(K) is the transformation
! 264: * stored in column K of A.
! 265: *
! 266: IF( K.LT.N )
! 267: $ CALL ZGERU( N-K, NRHS, -ONE, AP( KC+1 ), 1, B( K, 1 ),
! 268: $ LDB, B( K+1, 1 ), LDB )
! 269: *
! 270: * Multiply by the inverse of the diagonal block.
! 271: *
! 272: CALL ZSCAL( NRHS, ONE / AP( KC ), B( K, 1 ), LDB )
! 273: KC = KC + N - K + 1
! 274: K = K + 1
! 275: ELSE
! 276: *
! 277: * 2 x 2 diagonal block
! 278: *
! 279: * Interchange rows K+1 and -IPIV(K).
! 280: *
! 281: KP = -IPIV( K )
! 282: IF( KP.NE.K+1 )
! 283: $ CALL ZSWAP( NRHS, B( K+1, 1 ), LDB, B( KP, 1 ), LDB )
! 284: *
! 285: * Multiply by inv(L(K)), where L(K) is the transformation
! 286: * stored in columns K and K+1 of A.
! 287: *
! 288: IF( K.LT.N-1 ) THEN
! 289: CALL ZGERU( N-K-1, NRHS, -ONE, AP( KC+2 ), 1, B( K, 1 ),
! 290: $ LDB, B( K+2, 1 ), LDB )
! 291: CALL ZGERU( N-K-1, NRHS, -ONE, AP( KC+N-K+2 ), 1,
! 292: $ B( K+1, 1 ), LDB, B( K+2, 1 ), LDB )
! 293: END IF
! 294: *
! 295: * Multiply by the inverse of the diagonal block.
! 296: *
! 297: AKM1K = AP( KC+1 )
! 298: AKM1 = AP( KC ) / AKM1K
! 299: AK = AP( KC+N-K+1 ) / AKM1K
! 300: DENOM = AKM1*AK - ONE
! 301: DO 70 J = 1, NRHS
! 302: BKM1 = B( K, J ) / AKM1K
! 303: BK = B( K+1, J ) / AKM1K
! 304: B( K, J ) = ( AK*BKM1-BK ) / DENOM
! 305: B( K+1, J ) = ( AKM1*BK-BKM1 ) / DENOM
! 306: 70 CONTINUE
! 307: KC = KC + 2*( N-K ) + 1
! 308: K = K + 2
! 309: END IF
! 310: *
! 311: GO TO 60
! 312: 80 CONTINUE
! 313: *
! 314: * Next solve L'*X = B, overwriting B with X.
! 315: *
! 316: * K is the main loop index, decreasing from N to 1 in steps of
! 317: * 1 or 2, depending on the size of the diagonal blocks.
! 318: *
! 319: K = N
! 320: KC = N*( N+1 ) / 2 + 1
! 321: 90 CONTINUE
! 322: *
! 323: * If K < 1, exit from loop.
! 324: *
! 325: IF( K.LT.1 )
! 326: $ GO TO 100
! 327: *
! 328: KC = KC - ( N-K+1 )
! 329: IF( IPIV( K ).GT.0 ) THEN
! 330: *
! 331: * 1 x 1 diagonal block
! 332: *
! 333: * Multiply by inv(L'(K)), where L(K) is the transformation
! 334: * stored in column K of A.
! 335: *
! 336: IF( K.LT.N )
! 337: $ CALL ZGEMV( 'Transpose', N-K, NRHS, -ONE, B( K+1, 1 ),
! 338: $ LDB, AP( KC+1 ), 1, ONE, B( K, 1 ), LDB )
! 339: *
! 340: * Interchange rows K and IPIV(K).
! 341: *
! 342: KP = IPIV( K )
! 343: IF( KP.NE.K )
! 344: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
! 345: K = K - 1
! 346: ELSE
! 347: *
! 348: * 2 x 2 diagonal block
! 349: *
! 350: * Multiply by inv(L'(K-1)), where L(K-1) is the transformation
! 351: * stored in columns K-1 and K of A.
! 352: *
! 353: IF( K.LT.N ) THEN
! 354: CALL ZGEMV( 'Transpose', N-K, NRHS, -ONE, B( K+1, 1 ),
! 355: $ LDB, AP( KC+1 ), 1, ONE, B( K, 1 ), LDB )
! 356: CALL ZGEMV( 'Transpose', N-K, NRHS, -ONE, B( K+1, 1 ),
! 357: $ LDB, AP( KC-( N-K ) ), 1, ONE, B( K-1, 1 ),
! 358: $ LDB )
! 359: END IF
! 360: *
! 361: * Interchange rows K and -IPIV(K).
! 362: *
! 363: KP = -IPIV( K )
! 364: IF( KP.NE.K )
! 365: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
! 366: KC = KC - ( N-K+2 )
! 367: K = K - 2
! 368: END IF
! 369: *
! 370: GO TO 90
! 371: 100 CONTINUE
! 372: END IF
! 373: *
! 374: RETURN
! 375: *
! 376: * End of ZSPTRS
! 377: *
! 378: END
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