Annotation of rpl/lapack/lapack/zlagtm.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZLAGTM( TRANS, N, NRHS, ALPHA, DL, D, DU, X, LDX, BETA,
! 2: $ B, LDB )
! 3: *
! 4: * -- LAPACK auxiliary routine (version 3.2) --
! 5: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 6: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 7: * November 2006
! 8: *
! 9: * .. Scalar Arguments ..
! 10: CHARACTER TRANS
! 11: INTEGER LDB, LDX, N, NRHS
! 12: DOUBLE PRECISION ALPHA, BETA
! 13: * ..
! 14: * .. Array Arguments ..
! 15: COMPLEX*16 B( LDB, * ), D( * ), DL( * ), DU( * ),
! 16: $ X( LDX, * )
! 17: * ..
! 18: *
! 19: * Purpose
! 20: * =======
! 21: *
! 22: * ZLAGTM performs a matrix-vector product of the form
! 23: *
! 24: * B := alpha * A * X + beta * B
! 25: *
! 26: * where A is a tridiagonal matrix of order N, B and X are N by NRHS
! 27: * matrices, and alpha and beta are real scalars, each of which may be
! 28: * 0., 1., or -1.
! 29: *
! 30: * Arguments
! 31: * =========
! 32: *
! 33: * TRANS (input) CHARACTER*1
! 34: * Specifies the operation applied to A.
! 35: * = 'N': No transpose, B := alpha * A * X + beta * B
! 36: * = 'T': Transpose, B := alpha * A**T * X + beta * B
! 37: * = 'C': Conjugate transpose, B := alpha * A**H * X + beta * B
! 38: *
! 39: * N (input) INTEGER
! 40: * The order of the matrix A. N >= 0.
! 41: *
! 42: * NRHS (input) INTEGER
! 43: * The number of right hand sides, i.e., the number of columns
! 44: * of the matrices X and B.
! 45: *
! 46: * ALPHA (input) DOUBLE PRECISION
! 47: * The scalar alpha. ALPHA must be 0., 1., or -1.; otherwise,
! 48: * it is assumed to be 0.
! 49: *
! 50: * DL (input) COMPLEX*16 array, dimension (N-1)
! 51: * The (n-1) sub-diagonal elements of T.
! 52: *
! 53: * D (input) COMPLEX*16 array, dimension (N)
! 54: * The diagonal elements of T.
! 55: *
! 56: * DU (input) COMPLEX*16 array, dimension (N-1)
! 57: * The (n-1) super-diagonal elements of T.
! 58: *
! 59: * X (input) COMPLEX*16 array, dimension (LDX,NRHS)
! 60: * The N by NRHS matrix X.
! 61: * LDX (input) INTEGER
! 62: * The leading dimension of the array X. LDX >= max(N,1).
! 63: *
! 64: * BETA (input) DOUBLE PRECISION
! 65: * The scalar beta. BETA must be 0., 1., or -1.; otherwise,
! 66: * it is assumed to be 1.
! 67: *
! 68: * B (input/output) COMPLEX*16 array, dimension (LDB,NRHS)
! 69: * On entry, the N by NRHS matrix B.
! 70: * On exit, B is overwritten by the matrix expression
! 71: * B := alpha * A * X + beta * B.
! 72: *
! 73: * LDB (input) INTEGER
! 74: * The leading dimension of the array B. LDB >= max(N,1).
! 75: *
! 76: * =====================================================================
! 77: *
! 78: * .. Parameters ..
! 79: DOUBLE PRECISION ONE, ZERO
! 80: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
! 81: * ..
! 82: * .. Local Scalars ..
! 83: INTEGER I, J
! 84: * ..
! 85: * .. External Functions ..
! 86: LOGICAL LSAME
! 87: EXTERNAL LSAME
! 88: * ..
! 89: * .. Intrinsic Functions ..
! 90: INTRINSIC DCONJG
! 91: * ..
! 92: * .. Executable Statements ..
! 93: *
! 94: IF( N.EQ.0 )
! 95: $ RETURN
! 96: *
! 97: * Multiply B by BETA if BETA.NE.1.
! 98: *
! 99: IF( BETA.EQ.ZERO ) THEN
! 100: DO 20 J = 1, NRHS
! 101: DO 10 I = 1, N
! 102: B( I, J ) = ZERO
! 103: 10 CONTINUE
! 104: 20 CONTINUE
! 105: ELSE IF( BETA.EQ.-ONE ) THEN
! 106: DO 40 J = 1, NRHS
! 107: DO 30 I = 1, N
! 108: B( I, J ) = -B( I, J )
! 109: 30 CONTINUE
! 110: 40 CONTINUE
! 111: END IF
! 112: *
! 113: IF( ALPHA.EQ.ONE ) THEN
! 114: IF( LSAME( TRANS, 'N' ) ) THEN
! 115: *
! 116: * Compute B := B + A*X
! 117: *
! 118: DO 60 J = 1, NRHS
! 119: IF( N.EQ.1 ) THEN
! 120: B( 1, J ) = B( 1, J ) + D( 1 )*X( 1, J )
! 121: ELSE
! 122: B( 1, J ) = B( 1, J ) + D( 1 )*X( 1, J ) +
! 123: $ DU( 1 )*X( 2, J )
! 124: B( N, J ) = B( N, J ) + DL( N-1 )*X( N-1, J ) +
! 125: $ D( N )*X( N, J )
! 126: DO 50 I = 2, N - 1
! 127: B( I, J ) = B( I, J ) + DL( I-1 )*X( I-1, J ) +
! 128: $ D( I )*X( I, J ) + DU( I )*X( I+1, J )
! 129: 50 CONTINUE
! 130: END IF
! 131: 60 CONTINUE
! 132: ELSE IF( LSAME( TRANS, 'T' ) ) THEN
! 133: *
! 134: * Compute B := B + A**T * X
! 135: *
! 136: DO 80 J = 1, NRHS
! 137: IF( N.EQ.1 ) THEN
! 138: B( 1, J ) = B( 1, J ) + D( 1 )*X( 1, J )
! 139: ELSE
! 140: B( 1, J ) = B( 1, J ) + D( 1 )*X( 1, J ) +
! 141: $ DL( 1 )*X( 2, J )
! 142: B( N, J ) = B( N, J ) + DU( N-1 )*X( N-1, J ) +
! 143: $ D( N )*X( N, J )
! 144: DO 70 I = 2, N - 1
! 145: B( I, J ) = B( I, J ) + DU( I-1 )*X( I-1, J ) +
! 146: $ D( I )*X( I, J ) + DL( I )*X( I+1, J )
! 147: 70 CONTINUE
! 148: END IF
! 149: 80 CONTINUE
! 150: ELSE IF( LSAME( TRANS, 'C' ) ) THEN
! 151: *
! 152: * Compute B := B + A**H * X
! 153: *
! 154: DO 100 J = 1, NRHS
! 155: IF( N.EQ.1 ) THEN
! 156: B( 1, J ) = B( 1, J ) + DCONJG( D( 1 ) )*X( 1, J )
! 157: ELSE
! 158: B( 1, J ) = B( 1, J ) + DCONJG( D( 1 ) )*X( 1, J ) +
! 159: $ DCONJG( DL( 1 ) )*X( 2, J )
! 160: B( N, J ) = B( N, J ) + DCONJG( DU( N-1 ) )*
! 161: $ X( N-1, J ) + DCONJG( D( N ) )*X( N, J )
! 162: DO 90 I = 2, N - 1
! 163: B( I, J ) = B( I, J ) + DCONJG( DU( I-1 ) )*
! 164: $ X( I-1, J ) + DCONJG( D( I ) )*
! 165: $ X( I, J ) + DCONJG( DL( I ) )*
! 166: $ X( I+1, J )
! 167: 90 CONTINUE
! 168: END IF
! 169: 100 CONTINUE
! 170: END IF
! 171: ELSE IF( ALPHA.EQ.-ONE ) THEN
! 172: IF( LSAME( TRANS, 'N' ) ) THEN
! 173: *
! 174: * Compute B := B - A*X
! 175: *
! 176: DO 120 J = 1, NRHS
! 177: IF( N.EQ.1 ) THEN
! 178: B( 1, J ) = B( 1, J ) - D( 1 )*X( 1, J )
! 179: ELSE
! 180: B( 1, J ) = B( 1, J ) - D( 1 )*X( 1, J ) -
! 181: $ DU( 1 )*X( 2, J )
! 182: B( N, J ) = B( N, J ) - DL( N-1 )*X( N-1, J ) -
! 183: $ D( N )*X( N, J )
! 184: DO 110 I = 2, N - 1
! 185: B( I, J ) = B( I, J ) - DL( I-1 )*X( I-1, J ) -
! 186: $ D( I )*X( I, J ) - DU( I )*X( I+1, J )
! 187: 110 CONTINUE
! 188: END IF
! 189: 120 CONTINUE
! 190: ELSE IF( LSAME( TRANS, 'T' ) ) THEN
! 191: *
! 192: * Compute B := B - A'*X
! 193: *
! 194: DO 140 J = 1, NRHS
! 195: IF( N.EQ.1 ) THEN
! 196: B( 1, J ) = B( 1, J ) - D( 1 )*X( 1, J )
! 197: ELSE
! 198: B( 1, J ) = B( 1, J ) - D( 1 )*X( 1, J ) -
! 199: $ DL( 1 )*X( 2, J )
! 200: B( N, J ) = B( N, J ) - DU( N-1 )*X( N-1, J ) -
! 201: $ D( N )*X( N, J )
! 202: DO 130 I = 2, N - 1
! 203: B( I, J ) = B( I, J ) - DU( I-1 )*X( I-1, J ) -
! 204: $ D( I )*X( I, J ) - DL( I )*X( I+1, J )
! 205: 130 CONTINUE
! 206: END IF
! 207: 140 CONTINUE
! 208: ELSE IF( LSAME( TRANS, 'C' ) ) THEN
! 209: *
! 210: * Compute B := B - A'*X
! 211: *
! 212: DO 160 J = 1, NRHS
! 213: IF( N.EQ.1 ) THEN
! 214: B( 1, J ) = B( 1, J ) - DCONJG( D( 1 ) )*X( 1, J )
! 215: ELSE
! 216: B( 1, J ) = B( 1, J ) - DCONJG( D( 1 ) )*X( 1, J ) -
! 217: $ DCONJG( DL( 1 ) )*X( 2, J )
! 218: B( N, J ) = B( N, J ) - DCONJG( DU( N-1 ) )*
! 219: $ X( N-1, J ) - DCONJG( D( N ) )*X( N, J )
! 220: DO 150 I = 2, N - 1
! 221: B( I, J ) = B( I, J ) - DCONJG( DU( I-1 ) )*
! 222: $ X( I-1, J ) - DCONJG( D( I ) )*
! 223: $ X( I, J ) - DCONJG( DL( I ) )*
! 224: $ X( I+1, J )
! 225: 150 CONTINUE
! 226: END IF
! 227: 160 CONTINUE
! 228: END IF
! 229: END IF
! 230: RETURN
! 231: *
! 232: * End of ZLAGTM
! 233: *
! 234: END
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