Annotation of rpl/lapack/lapack/zsytrs2.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZSYTRS2( UPLO, N, NRHS, A, LDA, IPIV, B, LDB,
! 2: $ WORK, INFO )
! 3: *
! 4: * -- LAPACK PROTOTYPE routine (version 3.2.2) --
! 5: *
! 6: * -- Written by Julie Langou of the Univ. of TN --
! 7: * May 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: * ZSYTRS2 solves a system of linear equations A*X = B with a real
! 25: * symmetric 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**T;
! 35: * = 'L': Lower triangular, form is A = L*D*L**T.
! 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 ZSYTRF.
! 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 ZSYTRF.
! 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 COMPLEX AK, AKM1, AKM1K, BK, BKM1, DENOM
! 78: * ..
! 79: * .. External Functions ..
! 80: LOGICAL LSAME
! 81: EXTERNAL LSAME
! 82: * ..
! 83: * .. External Subroutines ..
! 84: EXTERNAL ZSCAL, ZSYCONV, ZSWAP, ZTRSM, XERBLA
! 85: * ..
! 86: * .. Intrinsic Functions ..
! 87: INTRINSIC MAX
! 88: * ..
! 89: * .. Executable Statements ..
! 90: *
! 91: INFO = 0
! 92: UPPER = LSAME( UPLO, 'U' )
! 93: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
! 94: INFO = -1
! 95: ELSE IF( N.LT.0 ) THEN
! 96: INFO = -2
! 97: ELSE IF( NRHS.LT.0 ) THEN
! 98: INFO = -3
! 99: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
! 100: INFO = -5
! 101: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
! 102: INFO = -8
! 103: END IF
! 104: IF( INFO.NE.0 ) THEN
! 105: CALL XERBLA( 'ZSYTRS2', -INFO )
! 106: RETURN
! 107: END IF
! 108: *
! 109: * Quick return if possible
! 110: *
! 111: IF( N.EQ.0 .OR. NRHS.EQ.0 )
! 112: $ RETURN
! 113: *
! 114: * Convert A
! 115: *
! 116: CALL ZSYCONV( UPLO, 'C', N, A, LDA, IPIV, WORK, IINFO )
! 117: *
! 118: IF( UPPER ) THEN
! 119: *
! 120: * Solve A*X = B, where A = U*D*U'.
! 121: *
! 122: * P' * B
! 123: K=N
! 124: DO WHILE ( K .GE. 1 )
! 125: IF( IPIV( K ).GT.0 ) THEN
! 126: * 1 x 1 diagonal block
! 127: * Interchange rows K and IPIV(K).
! 128: KP = IPIV( K )
! 129: IF( KP.NE.K )
! 130: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
! 131: K=K-1
! 132: ELSE
! 133: * 2 x 2 diagonal block
! 134: * Interchange rows K-1 and -IPIV(K).
! 135: KP = -IPIV( K )
! 136: IF( KP.EQ.-IPIV( K-1 ) )
! 137: $ CALL ZSWAP( NRHS, B( K-1, 1 ), LDB, B( KP, 1 ), LDB )
! 138: K=K-2
! 139: END IF
! 140: END DO
! 141: *
! 142: * Compute (U \P' * B) -> B [ (U \P' * B) ]
! 143: *
! 144: CALL ZTRSM('L','U','N','U',N,NRHS,ONE,A,N,B,N)
! 145: *
! 146: * Compute D \ B -> B [ D \ (U \P' * B) ]
! 147: *
! 148: I=N
! 149: DO WHILE ( I .GE. 1 )
! 150: IF( IPIV(I) .GT. 0 ) THEN
! 151: CALL ZSCAL( NRHS, ONE / A( I, I ), B( I, 1 ), N )
! 152: ELSEIF ( I .GT. 1) THEN
! 153: IF ( IPIV(I-1) .EQ. IPIV(I) ) THEN
! 154: AKM1K = WORK(I)
! 155: AKM1 = A( I-1, I-1 ) / AKM1K
! 156: AK = A( I, I ) / AKM1K
! 157: DENOM = AKM1*AK - ONE
! 158: DO 15 J = 1, NRHS
! 159: BKM1 = B( I-1, J ) / AKM1K
! 160: BK = B( I, J ) / AKM1K
! 161: B( I-1, J ) = ( AK*BKM1-BK ) / DENOM
! 162: B( I, J ) = ( AKM1*BK-BKM1 ) / DENOM
! 163: 15 CONTINUE
! 164: I = I - 1
! 165: ENDIF
! 166: ENDIF
! 167: I = I - 1
! 168: END DO
! 169: *
! 170: * Compute (U' \ B) -> B [ U' \ (D \ (U \P' * B) ) ]
! 171: *
! 172: CALL ZTRSM('L','U','T','U',N,NRHS,ONE,A,N,B,N)
! 173: *
! 174: * P * B [ P * (U' \ (D \ (U \P' * B) )) ]
! 175: *
! 176: K=1
! 177: DO WHILE ( K .LE. N )
! 178: IF( IPIV( K ).GT.0 ) THEN
! 179: * 1 x 1 diagonal block
! 180: * Interchange rows K and IPIV(K).
! 181: KP = IPIV( K )
! 182: IF( KP.NE.K )
! 183: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
! 184: K=K+1
! 185: ELSE
! 186: * 2 x 2 diagonal block
! 187: * Interchange rows K-1 and -IPIV(K).
! 188: KP = -IPIV( K )
! 189: IF( K .LT. N .AND. KP.EQ.-IPIV( K+1 ) )
! 190: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
! 191: K=K+2
! 192: ENDIF
! 193: END DO
! 194: *
! 195: ELSE
! 196: *
! 197: * Solve A*X = B, where A = L*D*L'.
! 198: *
! 199: * P' * B
! 200: K=1
! 201: DO WHILE ( K .LE. N )
! 202: IF( IPIV( K ).GT.0 ) THEN
! 203: * 1 x 1 diagonal block
! 204: * Interchange rows K and IPIV(K).
! 205: KP = IPIV( K )
! 206: IF( KP.NE.K )
! 207: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
! 208: K=K+1
! 209: ELSE
! 210: * 2 x 2 diagonal block
! 211: * Interchange rows K and -IPIV(K+1).
! 212: KP = -IPIV( K+1 )
! 213: IF( KP.EQ.-IPIV( K ) )
! 214: $ CALL ZSWAP( NRHS, B( K+1, 1 ), LDB, B( KP, 1 ), LDB )
! 215: K=K+2
! 216: ENDIF
! 217: END DO
! 218: *
! 219: * Compute (L \P' * B) -> B [ (L \P' * B) ]
! 220: *
! 221: CALL ZTRSM('L','L','N','U',N,NRHS,ONE,A,N,B,N)
! 222: *
! 223: * Compute D \ B -> B [ D \ (L \P' * B) ]
! 224: *
! 225: I=1
! 226: DO WHILE ( I .LE. N )
! 227: IF( IPIV(I) .GT. 0 ) THEN
! 228: CALL ZSCAL( NRHS, ONE / A( I, I ), B( I, 1 ), N )
! 229: ELSE
! 230: AKM1K = WORK(I)
! 231: AKM1 = A( I, I ) / AKM1K
! 232: AK = A( I+1, I+1 ) / AKM1K
! 233: DENOM = AKM1*AK - ONE
! 234: DO 25 J = 1, NRHS
! 235: BKM1 = B( I, J ) / AKM1K
! 236: BK = B( I+1, J ) / AKM1K
! 237: B( I, J ) = ( AK*BKM1-BK ) / DENOM
! 238: B( I+1, J ) = ( AKM1*BK-BKM1 ) / DENOM
! 239: 25 CONTINUE
! 240: I = I + 1
! 241: ENDIF
! 242: I = I + 1
! 243: END DO
! 244: *
! 245: * Compute (L' \ B) -> B [ L' \ (D \ (L \P' * B) ) ]
! 246: *
! 247: CALL ZTRSM('L','L','T','U',N,NRHS,ONE,A,N,B,N)
! 248: *
! 249: * P * B [ P * (L' \ (D \ (L \P' * B) )) ]
! 250: *
! 251: K=N
! 252: DO WHILE ( K .GE. 1 )
! 253: IF( IPIV( K ).GT.0 ) THEN
! 254: * 1 x 1 diagonal block
! 255: * Interchange rows K and IPIV(K).
! 256: KP = IPIV( K )
! 257: IF( KP.NE.K )
! 258: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
! 259: K=K-1
! 260: ELSE
! 261: * 2 x 2 diagonal block
! 262: * Interchange rows K-1 and -IPIV(K).
! 263: KP = -IPIV( K )
! 264: IF( K.GT.1 .AND. KP.EQ.-IPIV( K-1 ) )
! 265: $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
! 266: K=K-2
! 267: ENDIF
! 268: END DO
! 269: *
! 270: END IF
! 271: *
! 272: * Revert A
! 273: *
! 274: CALL ZSYCONV( UPLO, 'R', N, A, LDA, IPIV, WORK, IINFO )
! 275: *
! 276: RETURN
! 277: *
! 278: * End of ZSYTRS2
! 279: *
! 280: END
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