Annotation of rpl/lapack/lapack/zgtts2.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZGTTS2( ITRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB )
! 2: *
! 3: * -- LAPACK auxiliary 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: INTEGER ITRANS, LDB, N, NRHS
! 10: * ..
! 11: * .. Array Arguments ..
! 12: INTEGER IPIV( * )
! 13: COMPLEX*16 B( LDB, * ), D( * ), DL( * ), DU( * ), DU2( * )
! 14: * ..
! 15: *
! 16: * Purpose
! 17: * =======
! 18: *
! 19: * ZGTTS2 solves one of the systems of equations
! 20: * A * X = B, A**T * X = B, or A**H * X = B,
! 21: * with a tridiagonal matrix A using the LU factorization computed
! 22: * by ZGTTRF.
! 23: *
! 24: * Arguments
! 25: * =========
! 26: *
! 27: * ITRANS (input) INTEGER
! 28: * Specifies the form of the system of equations.
! 29: * = 0: A * X = B (No transpose)
! 30: * = 1: A**T * X = B (Transpose)
! 31: * = 2: A**H * X = B (Conjugate transpose)
! 32: *
! 33: * N (input) INTEGER
! 34: * The order of the matrix A.
! 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: * DL (input) COMPLEX*16 array, dimension (N-1)
! 41: * The (n-1) multipliers that define the matrix L from the
! 42: * LU factorization of A.
! 43: *
! 44: * D (input) COMPLEX*16 array, dimension (N)
! 45: * The n diagonal elements of the upper triangular matrix U from
! 46: * the LU factorization of A.
! 47: *
! 48: * DU (input) COMPLEX*16 array, dimension (N-1)
! 49: * The (n-1) elements of the first super-diagonal of U.
! 50: *
! 51: * DU2 (input) COMPLEX*16 array, dimension (N-2)
! 52: * The (n-2) elements of the second super-diagonal of U.
! 53: *
! 54: * IPIV (input) INTEGER array, dimension (N)
! 55: * The pivot indices; for 1 <= i <= n, row i of the matrix was
! 56: * interchanged with row IPIV(i). IPIV(i) will always be either
! 57: * i or i+1; IPIV(i) = i indicates a row interchange was not
! 58: * required.
! 59: *
! 60: * B (input/output) COMPLEX*16 array, dimension (LDB,NRHS)
! 61: * On entry, the matrix of right hand side vectors B.
! 62: * On exit, B is overwritten by the solution vectors X.
! 63: *
! 64: * LDB (input) INTEGER
! 65: * The leading dimension of the array B. LDB >= max(1,N).
! 66: *
! 67: * =====================================================================
! 68: *
! 69: * .. Local Scalars ..
! 70: INTEGER I, J
! 71: COMPLEX*16 TEMP
! 72: * ..
! 73: * .. Intrinsic Functions ..
! 74: INTRINSIC DCONJG
! 75: * ..
! 76: * .. Executable Statements ..
! 77: *
! 78: * Quick return if possible
! 79: *
! 80: IF( N.EQ.0 .OR. NRHS.EQ.0 )
! 81: $ RETURN
! 82: *
! 83: IF( ITRANS.EQ.0 ) THEN
! 84: *
! 85: * Solve A*X = B using the LU factorization of A,
! 86: * overwriting each right hand side vector with its solution.
! 87: *
! 88: IF( NRHS.LE.1 ) THEN
! 89: J = 1
! 90: 10 CONTINUE
! 91: *
! 92: * Solve L*x = b.
! 93: *
! 94: DO 20 I = 1, N - 1
! 95: IF( IPIV( I ).EQ.I ) THEN
! 96: B( I+1, J ) = B( I+1, J ) - DL( I )*B( I, J )
! 97: ELSE
! 98: TEMP = B( I, J )
! 99: B( I, J ) = B( I+1, J )
! 100: B( I+1, J ) = TEMP - DL( I )*B( I, J )
! 101: END IF
! 102: 20 CONTINUE
! 103: *
! 104: * Solve U*x = b.
! 105: *
! 106: B( N, J ) = B( N, J ) / D( N )
! 107: IF( N.GT.1 )
! 108: $ B( N-1, J ) = ( B( N-1, J )-DU( N-1 )*B( N, J ) ) /
! 109: $ D( N-1 )
! 110: DO 30 I = N - 2, 1, -1
! 111: B( I, J ) = ( B( I, J )-DU( I )*B( I+1, J )-DU2( I )*
! 112: $ B( I+2, J ) ) / D( I )
! 113: 30 CONTINUE
! 114: IF( J.LT.NRHS ) THEN
! 115: J = J + 1
! 116: GO TO 10
! 117: END IF
! 118: ELSE
! 119: DO 60 J = 1, NRHS
! 120: *
! 121: * Solve L*x = b.
! 122: *
! 123: DO 40 I = 1, N - 1
! 124: IF( IPIV( I ).EQ.I ) THEN
! 125: B( I+1, J ) = B( I+1, J ) - DL( I )*B( I, J )
! 126: ELSE
! 127: TEMP = B( I, J )
! 128: B( I, J ) = B( I+1, J )
! 129: B( I+1, J ) = TEMP - DL( I )*B( I, J )
! 130: END IF
! 131: 40 CONTINUE
! 132: *
! 133: * Solve U*x = b.
! 134: *
! 135: B( N, J ) = B( N, J ) / D( N )
! 136: IF( N.GT.1 )
! 137: $ B( N-1, J ) = ( B( N-1, J )-DU( N-1 )*B( N, J ) ) /
! 138: $ D( N-1 )
! 139: DO 50 I = N - 2, 1, -1
! 140: B( I, J ) = ( B( I, J )-DU( I )*B( I+1, J )-DU2( I )*
! 141: $ B( I+2, J ) ) / D( I )
! 142: 50 CONTINUE
! 143: 60 CONTINUE
! 144: END IF
! 145: ELSE IF( ITRANS.EQ.1 ) THEN
! 146: *
! 147: * Solve A**T * X = B.
! 148: *
! 149: IF( NRHS.LE.1 ) THEN
! 150: J = 1
! 151: 70 CONTINUE
! 152: *
! 153: * Solve U**T * x = b.
! 154: *
! 155: B( 1, J ) = B( 1, J ) / D( 1 )
! 156: IF( N.GT.1 )
! 157: $ B( 2, J ) = ( B( 2, J )-DU( 1 )*B( 1, J ) ) / D( 2 )
! 158: DO 80 I = 3, N
! 159: B( I, J ) = ( B( I, J )-DU( I-1 )*B( I-1, J )-DU2( I-2 )*
! 160: $ B( I-2, J ) ) / D( I )
! 161: 80 CONTINUE
! 162: *
! 163: * Solve L**T * x = b.
! 164: *
! 165: DO 90 I = N - 1, 1, -1
! 166: IF( IPIV( I ).EQ.I ) THEN
! 167: B( I, J ) = B( I, J ) - DL( I )*B( I+1, J )
! 168: ELSE
! 169: TEMP = B( I+1, J )
! 170: B( I+1, J ) = B( I, J ) - DL( I )*TEMP
! 171: B( I, J ) = TEMP
! 172: END IF
! 173: 90 CONTINUE
! 174: IF( J.LT.NRHS ) THEN
! 175: J = J + 1
! 176: GO TO 70
! 177: END IF
! 178: ELSE
! 179: DO 120 J = 1, NRHS
! 180: *
! 181: * Solve U**T * x = b.
! 182: *
! 183: B( 1, J ) = B( 1, J ) / D( 1 )
! 184: IF( N.GT.1 )
! 185: $ B( 2, J ) = ( B( 2, J )-DU( 1 )*B( 1, J ) ) / D( 2 )
! 186: DO 100 I = 3, N
! 187: B( I, J ) = ( B( I, J )-DU( I-1 )*B( I-1, J )-
! 188: $ DU2( I-2 )*B( I-2, J ) ) / D( I )
! 189: 100 CONTINUE
! 190: *
! 191: * Solve L**T * x = b.
! 192: *
! 193: DO 110 I = N - 1, 1, -1
! 194: IF( IPIV( I ).EQ.I ) THEN
! 195: B( I, J ) = B( I, J ) - DL( I )*B( I+1, J )
! 196: ELSE
! 197: TEMP = B( I+1, J )
! 198: B( I+1, J ) = B( I, J ) - DL( I )*TEMP
! 199: B( I, J ) = TEMP
! 200: END IF
! 201: 110 CONTINUE
! 202: 120 CONTINUE
! 203: END IF
! 204: ELSE
! 205: *
! 206: * Solve A**H * X = B.
! 207: *
! 208: IF( NRHS.LE.1 ) THEN
! 209: J = 1
! 210: 130 CONTINUE
! 211: *
! 212: * Solve U**H * x = b.
! 213: *
! 214: B( 1, J ) = B( 1, J ) / DCONJG( D( 1 ) )
! 215: IF( N.GT.1 )
! 216: $ B( 2, J ) = ( B( 2, J )-DCONJG( DU( 1 ) )*B( 1, J ) ) /
! 217: $ DCONJG( D( 2 ) )
! 218: DO 140 I = 3, N
! 219: B( I, J ) = ( B( I, J )-DCONJG( DU( I-1 ) )*B( I-1, J )-
! 220: $ DCONJG( DU2( I-2 ) )*B( I-2, J ) ) /
! 221: $ DCONJG( D( I ) )
! 222: 140 CONTINUE
! 223: *
! 224: * Solve L**H * x = b.
! 225: *
! 226: DO 150 I = N - 1, 1, -1
! 227: IF( IPIV( I ).EQ.I ) THEN
! 228: B( I, J ) = B( I, J ) - DCONJG( DL( I ) )*B( I+1, J )
! 229: ELSE
! 230: TEMP = B( I+1, J )
! 231: B( I+1, J ) = B( I, J ) - DCONJG( DL( I ) )*TEMP
! 232: B( I, J ) = TEMP
! 233: END IF
! 234: 150 CONTINUE
! 235: IF( J.LT.NRHS ) THEN
! 236: J = J + 1
! 237: GO TO 130
! 238: END IF
! 239: ELSE
! 240: DO 180 J = 1, NRHS
! 241: *
! 242: * Solve U**H * x = b.
! 243: *
! 244: B( 1, J ) = B( 1, J ) / DCONJG( D( 1 ) )
! 245: IF( N.GT.1 )
! 246: $ B( 2, J ) = ( B( 2, J )-DCONJG( DU( 1 ) )*B( 1, J ) )
! 247: $ / DCONJG( D( 2 ) )
! 248: DO 160 I = 3, N
! 249: B( I, J ) = ( B( I, J )-DCONJG( DU( I-1 ) )*
! 250: $ B( I-1, J )-DCONJG( DU2( I-2 ) )*
! 251: $ B( I-2, J ) ) / DCONJG( D( I ) )
! 252: 160 CONTINUE
! 253: *
! 254: * Solve L**H * x = b.
! 255: *
! 256: DO 170 I = N - 1, 1, -1
! 257: IF( IPIV( I ).EQ.I ) THEN
! 258: B( I, J ) = B( I, J ) - DCONJG( DL( I ) )*
! 259: $ B( I+1, J )
! 260: ELSE
! 261: TEMP = B( I+1, J )
! 262: B( I+1, J ) = B( I, J ) - DCONJG( DL( I ) )*TEMP
! 263: B( I, J ) = TEMP
! 264: END IF
! 265: 170 CONTINUE
! 266: 180 CONTINUE
! 267: END IF
! 268: END IF
! 269: *
! 270: * End of ZGTTS2
! 271: *
! 272: END
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