Annotation of rpl/lapack/lapack/zhetrs.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZHETRS( 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: COMPLEX*16 A( LDA, * ), B( LDB, * )
! 15: * ..
! 16: *
! 17: * Purpose
! 18: * =======
! 19: *
! 20: * ZHETRS solves a system of linear equations A*X = B with a complex
! 21: * Hermitian matrix A using the factorization A = U*D*U**H or
! 22: * A = L*D*L**H computed by ZHETRF.
! 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**H;
! 31: * = 'L': Lower triangular, form is A = L*D*L**H.
! 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) COMPLEX*16 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 ZHETRF.
! 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 ZHETRF.
! 50: *
! 51: * B (input/output) COMPLEX*16 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: COMPLEX*16 ONE
! 66: PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) )
! 67: * ..
! 68: * .. Local Scalars ..
! 69: LOGICAL UPPER
! 70: INTEGER J, K, KP
! 71: DOUBLE PRECISION S
! 72: COMPLEX*16 AK, AKM1, AKM1K, BK, BKM1, DENOM
! 73: * ..
! 74: * .. External Functions ..
! 75: LOGICAL LSAME
! 76: EXTERNAL LSAME
! 77: * ..
! 78: * .. External Subroutines ..
! 79: EXTERNAL XERBLA, ZDSCAL, ZGEMV, ZGERU, ZLACGV, ZSWAP
! 80: * ..
! 81: * .. Intrinsic Functions ..
! 82: INTRINSIC DBLE, DCONJG, MAX
! 83: * ..
! 84: * .. Executable Statements ..
! 85: *
! 86: INFO = 0
! 87: UPPER = LSAME( UPLO, 'U' )
! 88: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
! 89: INFO = -1
! 90: ELSE IF( N.LT.0 ) THEN
! 91: INFO = -2
! 92: ELSE IF( NRHS.LT.0 ) THEN
! 93: INFO = -3
! 94: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
! 95: INFO = -5
! 96: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
! 97: INFO = -8
! 98: END IF
! 99: IF( INFO.NE.0 ) THEN
! 100: CALL XERBLA( 'ZHETRS', -INFO )
! 101: RETURN
! 102: END IF
! 103: *
! 104: * Quick return if possible
! 105: *
! 106: IF( N.EQ.0 .OR. NRHS.EQ.0 )
! 107: $ RETURN
! 108: *
! 109: IF( UPPER ) THEN
! 110: *
! 111: * Solve A*X = B, where A = U*D*U'.
! 112: *
! 113: * First solve U*D*X = B, overwriting B with X.
! 114: *
! 115: * K is the main loop index, decreasing from N to 1 in steps of
! 116: * 1 or 2, depending on the size of the diagonal blocks.
! 117: *
! 118: K = N
! 119: 10 CONTINUE
! 120: *
! 121: * If K < 1, exit from loop.
! 122: *
! 123: IF( K.LT.1 )
! 124: $ GO TO 30
! 125: *
! 126: IF( IPIV( K ).GT.0 ) THEN
! 127: *
! 128: * 1 x 1 diagonal block
! 129: *
! 130: * Interchange rows K and IPIV(K).
! 131: *
! 132: KP = IPIV( K )
! 133: IF( KP.NE.K )
! 134: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
! 135: *
! 136: * Multiply by inv(U(K)), where U(K) is the transformation
! 137: * stored in column K of A.
! 138: *
! 139: CALL ZGERU( K-1, NRHS, -ONE, A( 1, K ), 1, B( K, 1 ), LDB,
! 140: $ B( 1, 1 ), LDB )
! 141: *
! 142: * Multiply by the inverse of the diagonal block.
! 143: *
! 144: S = DBLE( ONE ) / DBLE( A( K, K ) )
! 145: CALL ZDSCAL( NRHS, S, B( K, 1 ), LDB )
! 146: K = K - 1
! 147: ELSE
! 148: *
! 149: * 2 x 2 diagonal block
! 150: *
! 151: * Interchange rows K-1 and -IPIV(K).
! 152: *
! 153: KP = -IPIV( K )
! 154: IF( KP.NE.K-1 )
! 155: $ CALL ZSWAP( NRHS, B( K-1, 1 ), LDB, B( KP, 1 ), LDB )
! 156: *
! 157: * Multiply by inv(U(K)), where U(K) is the transformation
! 158: * stored in columns K-1 and K of A.
! 159: *
! 160: CALL ZGERU( K-2, NRHS, -ONE, A( 1, K ), 1, B( K, 1 ), LDB,
! 161: $ B( 1, 1 ), LDB )
! 162: CALL ZGERU( K-2, NRHS, -ONE, A( 1, K-1 ), 1, B( K-1, 1 ),
! 163: $ LDB, B( 1, 1 ), LDB )
! 164: *
! 165: * Multiply by the inverse of the diagonal block.
! 166: *
! 167: AKM1K = A( K-1, K )
! 168: AKM1 = A( K-1, K-1 ) / AKM1K
! 169: AK = A( K, K ) / DCONJG( AKM1K )
! 170: DENOM = AKM1*AK - ONE
! 171: DO 20 J = 1, NRHS
! 172: BKM1 = B( K-1, J ) / AKM1K
! 173: BK = B( K, J ) / DCONJG( AKM1K )
! 174: B( K-1, J ) = ( AK*BKM1-BK ) / DENOM
! 175: B( K, J ) = ( AKM1*BK-BKM1 ) / DENOM
! 176: 20 CONTINUE
! 177: K = K - 2
! 178: END IF
! 179: *
! 180: GO TO 10
! 181: 30 CONTINUE
! 182: *
! 183: * Next solve U'*X = B, overwriting B with X.
! 184: *
! 185: * K is the main loop index, increasing from 1 to N in steps of
! 186: * 1 or 2, depending on the size of the diagonal blocks.
! 187: *
! 188: K = 1
! 189: 40 CONTINUE
! 190: *
! 191: * If K > N, exit from loop.
! 192: *
! 193: IF( K.GT.N )
! 194: $ GO TO 50
! 195: *
! 196: IF( IPIV( K ).GT.0 ) THEN
! 197: *
! 198: * 1 x 1 diagonal block
! 199: *
! 200: * Multiply by inv(U'(K)), where U(K) is the transformation
! 201: * stored in column K of A.
! 202: *
! 203: IF( K.GT.1 ) THEN
! 204: CALL ZLACGV( NRHS, B( K, 1 ), LDB )
! 205: CALL ZGEMV( 'Conjugate transpose', K-1, NRHS, -ONE, B,
! 206: $ LDB, A( 1, K ), 1, ONE, B( K, 1 ), LDB )
! 207: CALL ZLACGV( NRHS, B( K, 1 ), LDB )
! 208: END IF
! 209: *
! 210: * Interchange rows K and IPIV(K).
! 211: *
! 212: KP = IPIV( K )
! 213: IF( KP.NE.K )
! 214: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
! 215: K = K + 1
! 216: ELSE
! 217: *
! 218: * 2 x 2 diagonal block
! 219: *
! 220: * Multiply by inv(U'(K+1)), where U(K+1) is the transformation
! 221: * stored in columns K and K+1 of A.
! 222: *
! 223: IF( K.GT.1 ) THEN
! 224: CALL ZLACGV( NRHS, B( K, 1 ), LDB )
! 225: CALL ZGEMV( 'Conjugate transpose', K-1, NRHS, -ONE, B,
! 226: $ LDB, A( 1, K ), 1, ONE, B( K, 1 ), LDB )
! 227: CALL ZLACGV( NRHS, B( K, 1 ), LDB )
! 228: *
! 229: CALL ZLACGV( NRHS, B( K+1, 1 ), LDB )
! 230: CALL ZGEMV( 'Conjugate transpose', K-1, NRHS, -ONE, B,
! 231: $ LDB, A( 1, K+1 ), 1, ONE, B( K+1, 1 ), LDB )
! 232: CALL ZLACGV( NRHS, B( K+1, 1 ), LDB )
! 233: END IF
! 234: *
! 235: * Interchange rows K and -IPIV(K).
! 236: *
! 237: KP = -IPIV( K )
! 238: IF( KP.NE.K )
! 239: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
! 240: K = K + 2
! 241: END IF
! 242: *
! 243: GO TO 40
! 244: 50 CONTINUE
! 245: *
! 246: ELSE
! 247: *
! 248: * Solve A*X = B, where A = L*D*L'.
! 249: *
! 250: * First solve L*D*X = B, overwriting B with X.
! 251: *
! 252: * K is the main loop index, increasing from 1 to N in steps of
! 253: * 1 or 2, depending on the size of the diagonal blocks.
! 254: *
! 255: K = 1
! 256: 60 CONTINUE
! 257: *
! 258: * If K > N, exit from loop.
! 259: *
! 260: IF( K.GT.N )
! 261: $ GO TO 80
! 262: *
! 263: IF( IPIV( K ).GT.0 ) THEN
! 264: *
! 265: * 1 x 1 diagonal block
! 266: *
! 267: * Interchange rows K and IPIV(K).
! 268: *
! 269: KP = IPIV( K )
! 270: IF( KP.NE.K )
! 271: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
! 272: *
! 273: * Multiply by inv(L(K)), where L(K) is the transformation
! 274: * stored in column K of A.
! 275: *
! 276: IF( K.LT.N )
! 277: $ CALL ZGERU( N-K, NRHS, -ONE, A( K+1, K ), 1, B( K, 1 ),
! 278: $ LDB, B( K+1, 1 ), LDB )
! 279: *
! 280: * Multiply by the inverse of the diagonal block.
! 281: *
! 282: S = DBLE( ONE ) / DBLE( A( K, K ) )
! 283: CALL ZDSCAL( NRHS, S, B( K, 1 ), LDB )
! 284: K = K + 1
! 285: ELSE
! 286: *
! 287: * 2 x 2 diagonal block
! 288: *
! 289: * Interchange rows K+1 and -IPIV(K).
! 290: *
! 291: KP = -IPIV( K )
! 292: IF( KP.NE.K+1 )
! 293: $ CALL ZSWAP( NRHS, B( K+1, 1 ), LDB, B( KP, 1 ), LDB )
! 294: *
! 295: * Multiply by inv(L(K)), where L(K) is the transformation
! 296: * stored in columns K and K+1 of A.
! 297: *
! 298: IF( K.LT.N-1 ) THEN
! 299: CALL ZGERU( N-K-1, NRHS, -ONE, A( K+2, K ), 1, B( K, 1 ),
! 300: $ LDB, B( K+2, 1 ), LDB )
! 301: CALL ZGERU( N-K-1, NRHS, -ONE, A( K+2, K+1 ), 1,
! 302: $ B( K+1, 1 ), LDB, B( K+2, 1 ), LDB )
! 303: END IF
! 304: *
! 305: * Multiply by the inverse of the diagonal block.
! 306: *
! 307: AKM1K = A( K+1, K )
! 308: AKM1 = A( K, K ) / DCONJG( AKM1K )
! 309: AK = A( K+1, K+1 ) / AKM1K
! 310: DENOM = AKM1*AK - ONE
! 311: DO 70 J = 1, NRHS
! 312: BKM1 = B( K, J ) / DCONJG( AKM1K )
! 313: BK = B( K+1, J ) / AKM1K
! 314: B( K, J ) = ( AK*BKM1-BK ) / DENOM
! 315: B( K+1, J ) = ( AKM1*BK-BKM1 ) / DENOM
! 316: 70 CONTINUE
! 317: K = K + 2
! 318: END IF
! 319: *
! 320: GO TO 60
! 321: 80 CONTINUE
! 322: *
! 323: * Next solve L'*X = B, overwriting B with X.
! 324: *
! 325: * K is the main loop index, decreasing from N to 1 in steps of
! 326: * 1 or 2, depending on the size of the diagonal blocks.
! 327: *
! 328: K = N
! 329: 90 CONTINUE
! 330: *
! 331: * If K < 1, exit from loop.
! 332: *
! 333: IF( K.LT.1 )
! 334: $ GO TO 100
! 335: *
! 336: IF( IPIV( K ).GT.0 ) THEN
! 337: *
! 338: * 1 x 1 diagonal block
! 339: *
! 340: * Multiply by inv(L'(K)), where L(K) is the transformation
! 341: * stored in column K of A.
! 342: *
! 343: IF( K.LT.N ) THEN
! 344: CALL ZLACGV( NRHS, B( K, 1 ), LDB )
! 345: CALL ZGEMV( 'Conjugate transpose', N-K, NRHS, -ONE,
! 346: $ B( K+1, 1 ), LDB, A( K+1, K ), 1, ONE,
! 347: $ B( K, 1 ), LDB )
! 348: CALL ZLACGV( NRHS, B( K, 1 ), LDB )
! 349: END IF
! 350: *
! 351: * Interchange rows K and IPIV(K).
! 352: *
! 353: KP = IPIV( K )
! 354: IF( KP.NE.K )
! 355: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
! 356: K = K - 1
! 357: ELSE
! 358: *
! 359: * 2 x 2 diagonal block
! 360: *
! 361: * Multiply by inv(L'(K-1)), where L(K-1) is the transformation
! 362: * stored in columns K-1 and K of A.
! 363: *
! 364: IF( K.LT.N ) THEN
! 365: CALL ZLACGV( NRHS, B( K, 1 ), LDB )
! 366: CALL ZGEMV( 'Conjugate transpose', N-K, NRHS, -ONE,
! 367: $ B( K+1, 1 ), LDB, A( K+1, K ), 1, ONE,
! 368: $ B( K, 1 ), LDB )
! 369: CALL ZLACGV( NRHS, B( K, 1 ), LDB )
! 370: *
! 371: CALL ZLACGV( NRHS, B( K-1, 1 ), LDB )
! 372: CALL ZGEMV( 'Conjugate transpose', N-K, NRHS, -ONE,
! 373: $ B( K+1, 1 ), LDB, A( K+1, K-1 ), 1, ONE,
! 374: $ B( K-1, 1 ), LDB )
! 375: CALL ZLACGV( NRHS, B( K-1, 1 ), LDB )
! 376: END IF
! 377: *
! 378: * Interchange rows K and -IPIV(K).
! 379: *
! 380: KP = -IPIV( K )
! 381: IF( KP.NE.K )
! 382: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
! 383: K = K - 2
! 384: END IF
! 385: *
! 386: GO TO 90
! 387: 100 CONTINUE
! 388: END IF
! 389: *
! 390: RETURN
! 391: *
! 392: * End of ZHETRS
! 393: *
! 394: END
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