Annotation of rpl/lapack/lapack/zhptrs.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZHPTRS( 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: * ZHPTRS solves a system of linear equations A*X = B with a complex
! 21: * Hermitian matrix A stored in packed format using the factorization
! 22: * A = U*D*U**H or A = L*D*L**H computed by ZHPTRF.
! 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: * 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 ZHPTRF, 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 ZHPTRF.
! 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: DOUBLE PRECISION S
! 70: COMPLEX*16 AK, AKM1, AKM1K, BK, BKM1, DENOM
! 71: * ..
! 72: * .. External Functions ..
! 73: LOGICAL LSAME
! 74: EXTERNAL LSAME
! 75: * ..
! 76: * .. External Subroutines ..
! 77: EXTERNAL XERBLA, ZDSCAL, ZGEMV, ZGERU, ZLACGV, ZSWAP
! 78: * ..
! 79: * .. Intrinsic Functions ..
! 80: INTRINSIC DBLE, DCONJG, MAX
! 81: * ..
! 82: * .. Executable Statements ..
! 83: *
! 84: INFO = 0
! 85: UPPER = LSAME( UPLO, 'U' )
! 86: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
! 87: INFO = -1
! 88: ELSE IF( N.LT.0 ) THEN
! 89: INFO = -2
! 90: ELSE IF( NRHS.LT.0 ) THEN
! 91: INFO = -3
! 92: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
! 93: INFO = -7
! 94: END IF
! 95: IF( INFO.NE.0 ) THEN
! 96: CALL XERBLA( 'ZHPTRS', -INFO )
! 97: RETURN
! 98: END IF
! 99: *
! 100: * Quick return if possible
! 101: *
! 102: IF( N.EQ.0 .OR. NRHS.EQ.0 )
! 103: $ RETURN
! 104: *
! 105: IF( UPPER ) THEN
! 106: *
! 107: * Solve A*X = B, where A = U*D*U'.
! 108: *
! 109: * First solve U*D*X = B, overwriting B with X.
! 110: *
! 111: * K is the main loop index, decreasing from N to 1 in steps of
! 112: * 1 or 2, depending on the size of the diagonal blocks.
! 113: *
! 114: K = N
! 115: KC = N*( N+1 ) / 2 + 1
! 116: 10 CONTINUE
! 117: *
! 118: * If K < 1, exit from loop.
! 119: *
! 120: IF( K.LT.1 )
! 121: $ GO TO 30
! 122: *
! 123: KC = KC - K
! 124: IF( IPIV( K ).GT.0 ) THEN
! 125: *
! 126: * 1 x 1 diagonal block
! 127: *
! 128: * Interchange rows K and IPIV(K).
! 129: *
! 130: KP = IPIV( K )
! 131: IF( KP.NE.K )
! 132: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
! 133: *
! 134: * Multiply by inv(U(K)), where U(K) is the transformation
! 135: * stored in column K of A.
! 136: *
! 137: CALL ZGERU( K-1, NRHS, -ONE, AP( KC ), 1, B( K, 1 ), LDB,
! 138: $ B( 1, 1 ), LDB )
! 139: *
! 140: * Multiply by the inverse of the diagonal block.
! 141: *
! 142: S = DBLE( ONE ) / DBLE( AP( KC+K-1 ) )
! 143: CALL ZDSCAL( NRHS, S, 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 ZSWAP( 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 ZGERU( K-2, NRHS, -ONE, AP( KC ), 1, B( K, 1 ), LDB,
! 159: $ B( 1, 1 ), LDB )
! 160: CALL ZGERU( K-2, NRHS, -ONE, AP( KC-( K-1 ) ), 1,
! 161: $ B( K-1, 1 ), LDB, B( 1, 1 ), LDB )
! 162: *
! 163: * Multiply by the inverse of the diagonal block.
! 164: *
! 165: AKM1K = AP( KC+K-2 )
! 166: AKM1 = AP( KC-1 ) / AKM1K
! 167: AK = AP( KC+K-1 ) / DCONJG( AKM1K )
! 168: DENOM = AKM1*AK - ONE
! 169: DO 20 J = 1, NRHS
! 170: BKM1 = B( K-1, J ) / AKM1K
! 171: BK = B( K, J ) / DCONJG( AKM1K )
! 172: B( K-1, J ) = ( AK*BKM1-BK ) / DENOM
! 173: B( K, J ) = ( AKM1*BK-BKM1 ) / DENOM
! 174: 20 CONTINUE
! 175: KC = KC - K + 1
! 176: K = K - 2
! 177: END IF
! 178: *
! 179: GO TO 10
! 180: 30 CONTINUE
! 181: *
! 182: * Next solve U'*X = B, overwriting B with X.
! 183: *
! 184: * K is the main loop index, increasing from 1 to N in steps of
! 185: * 1 or 2, depending on the size of the diagonal blocks.
! 186: *
! 187: K = 1
! 188: KC = 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, AP( KC ), 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: KC = KC + K
! 216: K = K + 1
! 217: ELSE
! 218: *
! 219: * 2 x 2 diagonal block
! 220: *
! 221: * Multiply by inv(U'(K+1)), where U(K+1) is the transformation
! 222: * stored in columns K and K+1 of A.
! 223: *
! 224: IF( K.GT.1 ) THEN
! 225: CALL ZLACGV( NRHS, B( K, 1 ), LDB )
! 226: CALL ZGEMV( 'Conjugate transpose', K-1, NRHS, -ONE, B,
! 227: $ LDB, AP( KC ), 1, ONE, B( K, 1 ), LDB )
! 228: CALL ZLACGV( NRHS, B( K, 1 ), LDB )
! 229: *
! 230: CALL ZLACGV( NRHS, B( K+1, 1 ), LDB )
! 231: CALL ZGEMV( 'Conjugate transpose', K-1, NRHS, -ONE, B,
! 232: $ LDB, AP( KC+K ), 1, ONE, B( K+1, 1 ), LDB )
! 233: CALL ZLACGV( NRHS, B( K+1, 1 ), LDB )
! 234: END IF
! 235: *
! 236: * Interchange rows K and -IPIV(K).
! 237: *
! 238: KP = -IPIV( K )
! 239: IF( KP.NE.K )
! 240: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
! 241: KC = KC + 2*K + 1
! 242: K = K + 2
! 243: END IF
! 244: *
! 245: GO TO 40
! 246: 50 CONTINUE
! 247: *
! 248: ELSE
! 249: *
! 250: * Solve A*X = B, where A = L*D*L'.
! 251: *
! 252: * First solve L*D*X = B, overwriting B with X.
! 253: *
! 254: * K is the main loop index, increasing from 1 to N in steps of
! 255: * 1 or 2, depending on the size of the diagonal blocks.
! 256: *
! 257: K = 1
! 258: KC = 1
! 259: 60 CONTINUE
! 260: *
! 261: * If K > N, exit from loop.
! 262: *
! 263: IF( K.GT.N )
! 264: $ GO TO 80
! 265: *
! 266: IF( IPIV( K ).GT.0 ) THEN
! 267: *
! 268: * 1 x 1 diagonal block
! 269: *
! 270: * Interchange rows K and IPIV(K).
! 271: *
! 272: KP = IPIV( K )
! 273: IF( KP.NE.K )
! 274: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
! 275: *
! 276: * Multiply by inv(L(K)), where L(K) is the transformation
! 277: * stored in column K of A.
! 278: *
! 279: IF( K.LT.N )
! 280: $ CALL ZGERU( N-K, NRHS, -ONE, AP( KC+1 ), 1, B( K, 1 ),
! 281: $ LDB, B( K+1, 1 ), LDB )
! 282: *
! 283: * Multiply by the inverse of the diagonal block.
! 284: *
! 285: S = DBLE( ONE ) / DBLE( AP( KC ) )
! 286: CALL ZDSCAL( NRHS, S, B( K, 1 ), LDB )
! 287: KC = KC + N - K + 1
! 288: K = K + 1
! 289: ELSE
! 290: *
! 291: * 2 x 2 diagonal block
! 292: *
! 293: * Interchange rows K+1 and -IPIV(K).
! 294: *
! 295: KP = -IPIV( K )
! 296: IF( KP.NE.K+1 )
! 297: $ CALL ZSWAP( NRHS, B( K+1, 1 ), LDB, B( KP, 1 ), LDB )
! 298: *
! 299: * Multiply by inv(L(K)), where L(K) is the transformation
! 300: * stored in columns K and K+1 of A.
! 301: *
! 302: IF( K.LT.N-1 ) THEN
! 303: CALL ZGERU( N-K-1, NRHS, -ONE, AP( KC+2 ), 1, B( K, 1 ),
! 304: $ LDB, B( K+2, 1 ), LDB )
! 305: CALL ZGERU( N-K-1, NRHS, -ONE, AP( KC+N-K+2 ), 1,
! 306: $ B( K+1, 1 ), LDB, B( K+2, 1 ), LDB )
! 307: END IF
! 308: *
! 309: * Multiply by the inverse of the diagonal block.
! 310: *
! 311: AKM1K = AP( KC+1 )
! 312: AKM1 = AP( KC ) / DCONJG( AKM1K )
! 313: AK = AP( KC+N-K+1 ) / AKM1K
! 314: DENOM = AKM1*AK - ONE
! 315: DO 70 J = 1, NRHS
! 316: BKM1 = B( K, J ) / DCONJG( AKM1K )
! 317: BK = B( K+1, J ) / AKM1K
! 318: B( K, J ) = ( AK*BKM1-BK ) / DENOM
! 319: B( K+1, J ) = ( AKM1*BK-BKM1 ) / DENOM
! 320: 70 CONTINUE
! 321: KC = KC + 2*( N-K ) + 1
! 322: K = K + 2
! 323: END IF
! 324: *
! 325: GO TO 60
! 326: 80 CONTINUE
! 327: *
! 328: * Next solve L'*X = B, overwriting B with X.
! 329: *
! 330: * K is the main loop index, decreasing from N to 1 in steps of
! 331: * 1 or 2, depending on the size of the diagonal blocks.
! 332: *
! 333: K = N
! 334: KC = N*( N+1 ) / 2 + 1
! 335: 90 CONTINUE
! 336: *
! 337: * If K < 1, exit from loop.
! 338: *
! 339: IF( K.LT.1 )
! 340: $ GO TO 100
! 341: *
! 342: KC = KC - ( N-K+1 )
! 343: IF( IPIV( K ).GT.0 ) THEN
! 344: *
! 345: * 1 x 1 diagonal block
! 346: *
! 347: * Multiply by inv(L'(K)), where L(K) is the transformation
! 348: * stored in column K of A.
! 349: *
! 350: IF( K.LT.N ) THEN
! 351: CALL ZLACGV( NRHS, B( K, 1 ), LDB )
! 352: CALL ZGEMV( 'Conjugate transpose', N-K, NRHS, -ONE,
! 353: $ B( K+1, 1 ), LDB, AP( KC+1 ), 1, ONE,
! 354: $ B( K, 1 ), LDB )
! 355: CALL ZLACGV( NRHS, B( K, 1 ), LDB )
! 356: END IF
! 357: *
! 358: * Interchange rows K and IPIV(K).
! 359: *
! 360: KP = IPIV( K )
! 361: IF( KP.NE.K )
! 362: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
! 363: K = K - 1
! 364: ELSE
! 365: *
! 366: * 2 x 2 diagonal block
! 367: *
! 368: * Multiply by inv(L'(K-1)), where L(K-1) is the transformation
! 369: * stored in columns K-1 and K of A.
! 370: *
! 371: IF( K.LT.N ) THEN
! 372: CALL ZLACGV( NRHS, B( K, 1 ), LDB )
! 373: CALL ZGEMV( 'Conjugate transpose', N-K, NRHS, -ONE,
! 374: $ B( K+1, 1 ), LDB, AP( KC+1 ), 1, ONE,
! 375: $ B( K, 1 ), LDB )
! 376: CALL ZLACGV( NRHS, B( K, 1 ), LDB )
! 377: *
! 378: CALL ZLACGV( NRHS, B( K-1, 1 ), LDB )
! 379: CALL ZGEMV( 'Conjugate transpose', N-K, NRHS, -ONE,
! 380: $ B( K+1, 1 ), LDB, AP( KC-( N-K ) ), 1, ONE,
! 381: $ B( K-1, 1 ), LDB )
! 382: CALL ZLACGV( NRHS, B( K-1, 1 ), LDB )
! 383: END IF
! 384: *
! 385: * Interchange rows K and -IPIV(K).
! 386: *
! 387: KP = -IPIV( K )
! 388: IF( KP.NE.K )
! 389: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
! 390: KC = KC - ( N-K+2 )
! 391: K = K - 2
! 392: END IF
! 393: *
! 394: GO TO 90
! 395: 100 CONTINUE
! 396: END IF
! 397: *
! 398: RETURN
! 399: *
! 400: * End of ZHPTRS
! 401: *
! 402: END
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