Annotation of rpl/lapack/lapack/zhetrs2.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZHETRS2( UPLO, N, NRHS, A, LDA, IPIV, B, LDB,
! 2: $ WORK, INFO )
! 3: *
! 4: * -- LAPACK PROTOTYPE routine (version 3.3.0) --
! 5: *
! 6: * -- Written by Julie Langou of the Univ. of TN --
! 7: * November 2010
! 8: *
! 9: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 10: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 11: *
! 12: * .. Scalar Arguments ..
! 13: CHARACTER UPLO
! 14: INTEGER INFO, LDA, LDB, N, NRHS
! 15: * ..
! 16: * .. Array Arguments ..
! 17: INTEGER IPIV( * )
! 18: DOUBLE COMPLEX A( LDA, * ), B( LDB, * ), WORK( * )
! 19: * ..
! 20: *
! 21: * Purpose
! 22: * =======
! 23: *
! 24: * ZHETRS2 solves a system of linear equations A*X = B with a real
! 25: * Hermitian matrix A using the factorization A = U*D*U**T or
! 26: * A = L*D*L**T computed by ZSYTRF and converted by ZSYCONV.
! 27: *
! 28: * Arguments
! 29: * =========
! 30: *
! 31: * UPLO (input) CHARACTER*1
! 32: * Specifies whether the details of the factorization are stored
! 33: * as an upper or lower triangular matrix.
! 34: * = 'U': Upper triangular, form is A = U*D*U**H;
! 35: * = 'L': Lower triangular, form is A = L*D*L**H.
! 36: *
! 37: * N (input) INTEGER
! 38: * The order of the matrix A. N >= 0.
! 39: *
! 40: * NRHS (input) INTEGER
! 41: * The number of right hand sides, i.e., the number of columns
! 42: * of the matrix B. NRHS >= 0.
! 43: *
! 44: * A (input) DOUBLE COMPLEX array, dimension (LDA,N)
! 45: * The block diagonal matrix D and the multipliers used to
! 46: * obtain the factor U or L as computed by ZHETRF.
! 47: *
! 48: * LDA (input) INTEGER
! 49: * The leading dimension of the array A. LDA >= max(1,N).
! 50: *
! 51: * IPIV (input) INTEGER array, dimension (N)
! 52: * Details of the interchanges and the block structure of D
! 53: * as determined by ZHETRF.
! 54: *
! 55: * B (input/output) DOUBLE COMPLEX array, dimension (LDB,NRHS)
! 56: * On entry, the right hand side matrix B.
! 57: * On exit, the solution matrix X.
! 58: *
! 59: * LDB (input) INTEGER
! 60: * The leading dimension of the array B. LDB >= max(1,N).
! 61: *
! 62: * WORK (workspace) REAL array, dimension (N)
! 63: *
! 64: * INFO (output) INTEGER
! 65: * = 0: successful exit
! 66: * < 0: if INFO = -i, the i-th argument had an illegal value
! 67: *
! 68: * =====================================================================
! 69: *
! 70: * .. Parameters ..
! 71: DOUBLE COMPLEX ONE
! 72: PARAMETER ( ONE = (1.0D+0,0.0D+0) )
! 73: * ..
! 74: * .. Local Scalars ..
! 75: LOGICAL UPPER
! 76: INTEGER I, IINFO, J, K, KP
! 77: DOUBLE PRECISION S
! 78: DOUBLE COMPLEX AK, AKM1, AKM1K, BK, BKM1, DENOM
! 79: * ..
! 80: * .. External Functions ..
! 81: LOGICAL LSAME
! 82: EXTERNAL LSAME
! 83: * ..
! 84: * .. External Subroutines ..
! 85: EXTERNAL ZLACGV, ZSCAL, ZSYCONV, ZSWAP, ZTRSM, XERBLA
! 86: * ..
! 87: * .. Intrinsic Functions ..
! 88: INTRINSIC DBLE, DCONJG, MAX
! 89: * ..
! 90: * .. Executable Statements ..
! 91: *
! 92: INFO = 0
! 93: UPPER = LSAME( UPLO, 'U' )
! 94: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
! 95: INFO = -1
! 96: ELSE IF( N.LT.0 ) THEN
! 97: INFO = -2
! 98: ELSE IF( NRHS.LT.0 ) THEN
! 99: INFO = -3
! 100: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
! 101: INFO = -5
! 102: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
! 103: INFO = -8
! 104: END IF
! 105: IF( INFO.NE.0 ) THEN
! 106: CALL XERBLA( 'ZHETRS2', -INFO )
! 107: RETURN
! 108: END IF
! 109: *
! 110: * Quick return if possible
! 111: *
! 112: IF( N.EQ.0 .OR. NRHS.EQ.0 )
! 113: $ RETURN
! 114: *
! 115: * Convert A
! 116: *
! 117: CALL ZSYCONV( UPLO, 'C', N, A, LDA, IPIV, WORK, IINFO )
! 118: *
! 119: IF( UPPER ) THEN
! 120: *
! 121: * Solve A*X = B, where A = U*D*U'.
! 122: *
! 123: * P' * B
! 124: K=N
! 125: DO WHILE ( K .GE. 1 )
! 126: IF( IPIV( K ).GT.0 ) THEN
! 127: * 1 x 1 diagonal block
! 128: * Interchange rows K and IPIV(K).
! 129: KP = IPIV( K )
! 130: IF( KP.NE.K )
! 131: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
! 132: K=K-1
! 133: ELSE
! 134: * 2 x 2 diagonal block
! 135: * Interchange rows K-1 and -IPIV(K).
! 136: KP = -IPIV( K )
! 137: IF( KP.EQ.-IPIV( K-1 ) )
! 138: $ CALL ZSWAP( NRHS, B( K-1, 1 ), LDB, B( KP, 1 ), LDB )
! 139: K=K-2
! 140: END IF
! 141: END DO
! 142: *
! 143: * Compute (U \P' * B) -> B [ (U \P' * B) ]
! 144: *
! 145: CALL ZTRSM('L','U','N','U',N,NRHS,ONE,A,N,B,N)
! 146: *
! 147: * Compute D \ B -> B [ D \ (U \P' * B) ]
! 148: *
! 149: I=N
! 150: DO WHILE ( I .GE. 1 )
! 151: IF( IPIV(I) .GT. 0 ) THEN
! 152: S = DBLE( ONE ) / DBLE( A( I, I ) )
! 153: CALL ZDSCAL( NRHS, S, B( I, 1 ), LDB )
! 154: ELSEIF ( I .GT. 1) THEN
! 155: IF ( IPIV(I-1) .EQ. IPIV(I) ) THEN
! 156: AKM1K = WORK(I)
! 157: AKM1 = A( I-1, I-1 ) / AKM1K
! 158: AK = A( I, I ) / DCONJG( AKM1K )
! 159: DENOM = AKM1*AK - ONE
! 160: DO 15 J = 1, NRHS
! 161: BKM1 = B( I-1, J ) / AKM1K
! 162: BK = B( I, J ) / DCONJG( AKM1K )
! 163: B( I-1, J ) = ( AK*BKM1-BK ) / DENOM
! 164: B( I, J ) = ( AKM1*BK-BKM1 ) / DENOM
! 165: 15 CONTINUE
! 166: I = I - 1
! 167: ENDIF
! 168: ENDIF
! 169: I = I - 1
! 170: END DO
! 171: *
! 172: * Compute (U' \ B) -> B [ U' \ (D \ (U \P' * B) ) ]
! 173: *
! 174: CALL ZTRSM('L','U','C','U',N,NRHS,ONE,A,N,B,N)
! 175: *
! 176: * P * B [ P * (U' \ (D \ (U \P' * B) )) ]
! 177: *
! 178: K=1
! 179: DO WHILE ( K .LE. N )
! 180: IF( IPIV( K ).GT.0 ) THEN
! 181: * 1 x 1 diagonal block
! 182: * Interchange rows K and IPIV(K).
! 183: KP = IPIV( K )
! 184: IF( KP.NE.K )
! 185: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
! 186: K=K+1
! 187: ELSE
! 188: * 2 x 2 diagonal block
! 189: * Interchange rows K-1 and -IPIV(K).
! 190: KP = -IPIV( K )
! 191: IF( K .LT. N .AND. KP.EQ.-IPIV( K+1 ) )
! 192: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
! 193: K=K+2
! 194: ENDIF
! 195: END DO
! 196: *
! 197: ELSE
! 198: *
! 199: * Solve A*X = B, where A = L*D*L'.
! 200: *
! 201: * P' * B
! 202: K=1
! 203: DO WHILE ( K .LE. N )
! 204: IF( IPIV( K ).GT.0 ) THEN
! 205: * 1 x 1 diagonal block
! 206: * Interchange rows K and IPIV(K).
! 207: KP = IPIV( K )
! 208: IF( KP.NE.K )
! 209: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
! 210: K=K+1
! 211: ELSE
! 212: * 2 x 2 diagonal block
! 213: * Interchange rows K and -IPIV(K+1).
! 214: KP = -IPIV( K+1 )
! 215: IF( KP.EQ.-IPIV( K ) )
! 216: $ CALL ZSWAP( NRHS, B( K+1, 1 ), LDB, B( KP, 1 ), LDB )
! 217: K=K+2
! 218: ENDIF
! 219: END DO
! 220: *
! 221: * Compute (L \P' * B) -> B [ (L \P' * B) ]
! 222: *
! 223: CALL ZTRSM('L','L','N','U',N,NRHS,ONE,A,N,B,N)
! 224: *
! 225: * Compute D \ B -> B [ D \ (L \P' * B) ]
! 226: *
! 227: I=1
! 228: DO WHILE ( I .LE. N )
! 229: IF( IPIV(I) .GT. 0 ) THEN
! 230: S = DBLE( ONE ) / DBLE( A( I, I ) )
! 231: CALL ZDSCAL( NRHS, S, B( I, 1 ), LDB )
! 232: ELSE
! 233: AKM1K = WORK(I)
! 234: AKM1 = A( I, I ) / DCONJG( AKM1K )
! 235: AK = A( I+1, I+1 ) / AKM1K
! 236: DENOM = AKM1*AK - ONE
! 237: DO 25 J = 1, NRHS
! 238: BKM1 = B( I, J ) / DCONJG( AKM1K )
! 239: BK = B( I+1, J ) / AKM1K
! 240: B( I, J ) = ( AK*BKM1-BK ) / DENOM
! 241: B( I+1, J ) = ( AKM1*BK-BKM1 ) / DENOM
! 242: 25 CONTINUE
! 243: I = I + 1
! 244: ENDIF
! 245: I = I + 1
! 246: END DO
! 247: *
! 248: * Compute (L' \ B) -> B [ L' \ (D \ (L \P' * B) ) ]
! 249: *
! 250: CALL ZTRSM('L','L','C','U',N,NRHS,ONE,A,N,B,N)
! 251: *
! 252: * P * B [ P * (L' \ (D \ (L \P' * B) )) ]
! 253: *
! 254: K=N
! 255: DO WHILE ( K .GE. 1 )
! 256: IF( IPIV( K ).GT.0 ) THEN
! 257: * 1 x 1 diagonal block
! 258: * Interchange rows K and IPIV(K).
! 259: KP = IPIV( K )
! 260: IF( KP.NE.K )
! 261: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
! 262: K=K-1
! 263: ELSE
! 264: * 2 x 2 diagonal block
! 265: * Interchange rows K-1 and -IPIV(K).
! 266: KP = -IPIV( K )
! 267: IF( K.GT.1 .AND. KP.EQ.-IPIV( K-1 ) )
! 268: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
! 269: K=K-2
! 270: ENDIF
! 271: END DO
! 272: *
! 273: END IF
! 274: *
! 275: * Revert A
! 276: *
! 277: CALL ZSYCONV( UPLO, 'R', N, A, LDA, IPIV, WORK, IINFO )
! 278: *
! 279: RETURN
! 280: *
! 281: * End of ZHETRS2
! 282: *
! 283: END
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