Annotation of rpl/lapack/lapack/zungtr.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZUNGTR( UPLO, N, A, LDA, TAU, WORK, LWORK, 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, LDA, LWORK, N
! 11: * ..
! 12: * .. Array Arguments ..
! 13: COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
! 14: * ..
! 15: *
! 16: * Purpose
! 17: * =======
! 18: *
! 19: * ZUNGTR generates a complex unitary matrix Q which is defined as the
! 20: * product of n-1 elementary reflectors of order N, as returned by
! 21: * ZHETRD:
! 22: *
! 23: * if UPLO = 'U', Q = H(n-1) . . . H(2) H(1),
! 24: *
! 25: * if UPLO = 'L', Q = H(1) H(2) . . . H(n-1).
! 26: *
! 27: * Arguments
! 28: * =========
! 29: *
! 30: * UPLO (input) CHARACTER*1
! 31: * = 'U': Upper triangle of A contains elementary reflectors
! 32: * from ZHETRD;
! 33: * = 'L': Lower triangle of A contains elementary reflectors
! 34: * from ZHETRD.
! 35: *
! 36: * N (input) INTEGER
! 37: * The order of the matrix Q. N >= 0.
! 38: *
! 39: * A (input/output) COMPLEX*16 array, dimension (LDA,N)
! 40: * On entry, the vectors which define the elementary reflectors,
! 41: * as returned by ZHETRD.
! 42: * On exit, the N-by-N unitary matrix Q.
! 43: *
! 44: * LDA (input) INTEGER
! 45: * The leading dimension of the array A. LDA >= N.
! 46: *
! 47: * TAU (input) COMPLEX*16 array, dimension (N-1)
! 48: * TAU(i) must contain the scalar factor of the elementary
! 49: * reflector H(i), as returned by ZHETRD.
! 50: *
! 51: * WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
! 52: * On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
! 53: *
! 54: * LWORK (input) INTEGER
! 55: * The dimension of the array WORK. LWORK >= N-1.
! 56: * For optimum performance LWORK >= (N-1)*NB, where NB is
! 57: * the optimal blocksize.
! 58: *
! 59: * If LWORK = -1, then a workspace query is assumed; the routine
! 60: * only calculates the optimal size of the WORK array, returns
! 61: * this value as the first entry of the WORK array, and no error
! 62: * message related to LWORK is issued by XERBLA.
! 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: COMPLEX*16 ZERO, ONE
! 72: PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ),
! 73: $ ONE = ( 1.0D+0, 0.0D+0 ) )
! 74: * ..
! 75: * .. Local Scalars ..
! 76: LOGICAL LQUERY, UPPER
! 77: INTEGER I, IINFO, J, LWKOPT, NB
! 78: * ..
! 79: * .. External Functions ..
! 80: LOGICAL LSAME
! 81: INTEGER ILAENV
! 82: EXTERNAL LSAME, ILAENV
! 83: * ..
! 84: * .. External Subroutines ..
! 85: EXTERNAL XERBLA, ZUNGQL, ZUNGQR
! 86: * ..
! 87: * .. Intrinsic Functions ..
! 88: INTRINSIC MAX
! 89: * ..
! 90: * .. Executable Statements ..
! 91: *
! 92: * Test the input arguments
! 93: *
! 94: INFO = 0
! 95: LQUERY = ( LWORK.EQ.-1 )
! 96: UPPER = LSAME( UPLO, 'U' )
! 97: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
! 98: INFO = -1
! 99: ELSE IF( N.LT.0 ) THEN
! 100: INFO = -2
! 101: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
! 102: INFO = -4
! 103: ELSE IF( LWORK.LT.MAX( 1, N-1 ) .AND. .NOT.LQUERY ) THEN
! 104: INFO = -7
! 105: END IF
! 106: *
! 107: IF( INFO.EQ.0 ) THEN
! 108: IF( UPPER ) THEN
! 109: NB = ILAENV( 1, 'ZUNGQL', ' ', N-1, N-1, N-1, -1 )
! 110: ELSE
! 111: NB = ILAENV( 1, 'ZUNGQR', ' ', N-1, N-1, N-1, -1 )
! 112: END IF
! 113: LWKOPT = MAX( 1, N-1 )*NB
! 114: WORK( 1 ) = LWKOPT
! 115: END IF
! 116: *
! 117: IF( INFO.NE.0 ) THEN
! 118: CALL XERBLA( 'ZUNGTR', -INFO )
! 119: RETURN
! 120: ELSE IF( LQUERY ) THEN
! 121: RETURN
! 122: END IF
! 123: *
! 124: * Quick return if possible
! 125: *
! 126: IF( N.EQ.0 ) THEN
! 127: WORK( 1 ) = 1
! 128: RETURN
! 129: END IF
! 130: *
! 131: IF( UPPER ) THEN
! 132: *
! 133: * Q was determined by a call to ZHETRD with UPLO = 'U'
! 134: *
! 135: * Shift the vectors which define the elementary reflectors one
! 136: * column to the left, and set the last row and column of Q to
! 137: * those of the unit matrix
! 138: *
! 139: DO 20 J = 1, N - 1
! 140: DO 10 I = 1, J - 1
! 141: A( I, J ) = A( I, J+1 )
! 142: 10 CONTINUE
! 143: A( N, J ) = ZERO
! 144: 20 CONTINUE
! 145: DO 30 I = 1, N - 1
! 146: A( I, N ) = ZERO
! 147: 30 CONTINUE
! 148: A( N, N ) = ONE
! 149: *
! 150: * Generate Q(1:n-1,1:n-1)
! 151: *
! 152: CALL ZUNGQL( N-1, N-1, N-1, A, LDA, TAU, WORK, LWORK, IINFO )
! 153: *
! 154: ELSE
! 155: *
! 156: * Q was determined by a call to ZHETRD with UPLO = 'L'.
! 157: *
! 158: * Shift the vectors which define the elementary reflectors one
! 159: * column to the right, and set the first row and column of Q to
! 160: * those of the unit matrix
! 161: *
! 162: DO 50 J = N, 2, -1
! 163: A( 1, J ) = ZERO
! 164: DO 40 I = J + 1, N
! 165: A( I, J ) = A( I, J-1 )
! 166: 40 CONTINUE
! 167: 50 CONTINUE
! 168: A( 1, 1 ) = ONE
! 169: DO 60 I = 2, N
! 170: A( I, 1 ) = ZERO
! 171: 60 CONTINUE
! 172: IF( N.GT.1 ) THEN
! 173: *
! 174: * Generate Q(2:n,2:n)
! 175: *
! 176: CALL ZUNGQR( N-1, N-1, N-1, A( 2, 2 ), LDA, TAU, WORK,
! 177: $ LWORK, IINFO )
! 178: END IF
! 179: END IF
! 180: WORK( 1 ) = LWKOPT
! 181: RETURN
! 182: *
! 183: * End of ZUNGTR
! 184: *
! 185: END
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