Annotation of rpl/lapack/lapack/zunbdb5.f, revision 1.1
1.1 ! bertrand 1: *> \brief \b ZUNBDB5
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download ZUNBDB5 + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zunbdb5.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zunbdb5.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zunbdb5.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE ZUNBDB5( M1, M2, N, X1, INCX1, X2, INCX2, Q1, LDQ1, Q2,
! 22: * LDQ2, WORK, LWORK, INFO )
! 23: *
! 24: * .. Scalar Arguments ..
! 25: * INTEGER INCX1, INCX2, INFO, LDQ1, LDQ2, LWORK, M1, M2,
! 26: * $ N
! 27: * ..
! 28: * .. Array Arguments ..
! 29: * COMPLEX*16 Q1(LDQ1,*), Q2(LDQ2,*), WORK(*), X1(*), X2(*)
! 30: * ..
! 31: *
! 32: *
! 33: *> \par Purpose:
! 34: *> =============
! 35: *>
! 36: *>\verbatim
! 37: *>
! 38: *> ZUNBDB5 orthogonalizes the column vector
! 39: *> X = [ X1 ]
! 40: *> [ X2 ]
! 41: *> with respect to the columns of
! 42: *> Q = [ Q1 ] .
! 43: *> [ Q2 ]
! 44: *> The columns of Q must be orthonormal.
! 45: *>
! 46: *> If the projection is zero according to Kahan's "twice is enough"
! 47: *> criterion, then some other vector from the orthogonal complement
! 48: *> is returned. This vector is chosen in an arbitrary but deterministic
! 49: *> way.
! 50: *>
! 51: *>\endverbatim
! 52: *
! 53: * Arguments:
! 54: * ==========
! 55: *
! 56: *> \param[in] M1
! 57: *> \verbatim
! 58: *> M1 is INTEGER
! 59: *> The dimension of X1 and the number of rows in Q1. 0 <= M1.
! 60: *> \endverbatim
! 61: *>
! 62: *> \param[in] M2
! 63: *> \verbatim
! 64: *> M2 is INTEGER
! 65: *> The dimension of X2 and the number of rows in Q2. 0 <= M2.
! 66: *> \endverbatim
! 67: *>
! 68: *> \param[in] N
! 69: *> \verbatim
! 70: *> N is INTEGER
! 71: *> The number of columns in Q1 and Q2. 0 <= N.
! 72: *> \endverbatim
! 73: *>
! 74: *> \param[in,out] X1
! 75: *> \verbatim
! 76: *> X1 is COMPLEX*16 array, dimension (M1)
! 77: *> On entry, the top part of the vector to be orthogonalized.
! 78: *> On exit, the top part of the projected vector.
! 79: *> \endverbatim
! 80: *>
! 81: *> \param[in] INCX1
! 82: *> \verbatim
! 83: *> INCX1 is INTEGER
! 84: *> Increment for entries of X1.
! 85: *> \endverbatim
! 86: *>
! 87: *> \param[in,out] X2
! 88: *> \verbatim
! 89: *> X2 is COMPLEX*16 array, dimension (M2)
! 90: *> On entry, the bottom part of the vector to be
! 91: *> orthogonalized. On exit, the bottom part of the projected
! 92: *> vector.
! 93: *> \endverbatim
! 94: *>
! 95: *> \param[in] INCX2
! 96: *> \verbatim
! 97: *> INCX2 is INTEGER
! 98: *> Increment for entries of X2.
! 99: *> \endverbatim
! 100: *>
! 101: *> \param[in] Q1
! 102: *> \verbatim
! 103: *> Q1 is COMPLEX*16 array, dimension (LDQ1, N)
! 104: *> The top part of the orthonormal basis matrix.
! 105: *> \endverbatim
! 106: *>
! 107: *> \param[in] LDQ1
! 108: *> \verbatim
! 109: *> LDQ1 is INTEGER
! 110: *> The leading dimension of Q1. LDQ1 >= M1.
! 111: *> \endverbatim
! 112: *>
! 113: *> \param[in] Q2
! 114: *> \verbatim
! 115: *> Q2 is COMPLEX*16 array, dimension (LDQ2, N)
! 116: *> The bottom part of the orthonormal basis matrix.
! 117: *> \endverbatim
! 118: *>
! 119: *> \param[in] LDQ2
! 120: *> \verbatim
! 121: *> LDQ2 is INTEGER
! 122: *> The leading dimension of Q2. LDQ2 >= M2.
! 123: *> \endverbatim
! 124: *>
! 125: *> \param[out] WORK
! 126: *> \verbatim
! 127: *> WORK is COMPLEX*16 array, dimension (LWORK)
! 128: *> \endverbatim
! 129: *>
! 130: *> \param[in] LWORK
! 131: *> \verbatim
! 132: *> LWORK is INTEGER
! 133: *> The dimension of the array WORK. LWORK >= N.
! 134: *> \endverbatim
! 135: *>
! 136: *> \param[out] INFO
! 137: *> \verbatim
! 138: *> INFO is INTEGER
! 139: *> = 0: successful exit.
! 140: *> < 0: if INFO = -i, the i-th argument had an illegal value.
! 141: *> \endverbatim
! 142: *
! 143: * Authors:
! 144: * ========
! 145: *
! 146: *> \author Univ. of Tennessee
! 147: *> \author Univ. of California Berkeley
! 148: *> \author Univ. of Colorado Denver
! 149: *> \author NAG Ltd.
! 150: *
! 151: *> \date July 2012
! 152: *
! 153: *> \ingroup complex16OTHERcomputational
! 154: *
! 155: * =====================================================================
! 156: SUBROUTINE ZUNBDB5( M1, M2, N, X1, INCX1, X2, INCX2, Q1, LDQ1, Q2,
! 157: $ LDQ2, WORK, LWORK, INFO )
! 158: *
! 159: * -- LAPACK computational routine (version 3.5.0) --
! 160: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 161: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 162: * July 2012
! 163: *
! 164: * .. Scalar Arguments ..
! 165: INTEGER INCX1, INCX2, INFO, LDQ1, LDQ2, LWORK, M1, M2,
! 166: $ N
! 167: * ..
! 168: * .. Array Arguments ..
! 169: COMPLEX*16 Q1(LDQ1,*), Q2(LDQ2,*), WORK(*), X1(*), X2(*)
! 170: * ..
! 171: *
! 172: * =====================================================================
! 173: *
! 174: * .. Parameters ..
! 175: COMPLEX*16 ONE, ZERO
! 176: PARAMETER ( ONE = (1.0D0,0.0D0), ZERO = (0.0D0,0.0D0) )
! 177: * ..
! 178: * .. Local Scalars ..
! 179: INTEGER CHILDINFO, I, J
! 180: * ..
! 181: * .. External Subroutines ..
! 182: EXTERNAL ZUNBDB6, XERBLA
! 183: * ..
! 184: * .. External Functions ..
! 185: DOUBLE PRECISION DZNRM2
! 186: EXTERNAL DZNRM2
! 187: * ..
! 188: * .. Intrinsic Function ..
! 189: INTRINSIC MAX
! 190: * ..
! 191: * .. Executable Statements ..
! 192: *
! 193: * Test input arguments
! 194: *
! 195: INFO = 0
! 196: IF( M1 .LT. 0 ) THEN
! 197: INFO = -1
! 198: ELSE IF( M2 .LT. 0 ) THEN
! 199: INFO = -2
! 200: ELSE IF( N .LT. 0 ) THEN
! 201: INFO = -3
! 202: ELSE IF( INCX1 .LT. 1 ) THEN
! 203: INFO = -5
! 204: ELSE IF( INCX2 .LT. 1 ) THEN
! 205: INFO = -7
! 206: ELSE IF( LDQ1 .LT. MAX( 1, M1 ) ) THEN
! 207: INFO = -9
! 208: ELSE IF( LDQ2 .LT. MAX( 1, M2 ) ) THEN
! 209: INFO = -11
! 210: ELSE IF( LWORK .LT. N ) THEN
! 211: INFO = -13
! 212: END IF
! 213: *
! 214: IF( INFO .NE. 0 ) THEN
! 215: CALL XERBLA( 'ZUNBDB5', -INFO )
! 216: RETURN
! 217: END IF
! 218: *
! 219: * Project X onto the orthogonal complement of Q
! 220: *
! 221: CALL ZUNBDB6( M1, M2, N, X1, INCX1, X2, INCX2, Q1, LDQ1, Q2, LDQ2,
! 222: $ WORK, LWORK, CHILDINFO )
! 223: *
! 224: * If the projection is nonzero, then return
! 225: *
! 226: IF( DZNRM2(M1,X1,INCX1) .NE. ZERO
! 227: $ .OR. DZNRM2(M2,X2,INCX2) .NE. ZERO ) THEN
! 228: RETURN
! 229: END IF
! 230: *
! 231: * Project each standard basis vector e_1,...,e_M1 in turn, stopping
! 232: * when a nonzero projection is found
! 233: *
! 234: DO I = 1, M1
! 235: DO J = 1, M1
! 236: X1(J) = ZERO
! 237: END DO
! 238: X1(I) = ONE
! 239: DO J = 1, M2
! 240: X2(J) = ZERO
! 241: END DO
! 242: CALL ZUNBDB6( M1, M2, N, X1, INCX1, X2, INCX2, Q1, LDQ1, Q2,
! 243: $ LDQ2, WORK, LWORK, CHILDINFO )
! 244: IF( DZNRM2(M1,X1,INCX1) .NE. ZERO
! 245: $ .OR. DZNRM2(M2,X2,INCX2) .NE. ZERO ) THEN
! 246: RETURN
! 247: END IF
! 248: END DO
! 249: *
! 250: * Project each standard basis vector e_(M1+1),...,e_(M1+M2) in turn,
! 251: * stopping when a nonzero projection is found
! 252: *
! 253: DO I = 1, M2
! 254: DO J = 1, M1
! 255: X1(J) = ZERO
! 256: END DO
! 257: DO J = 1, M2
! 258: X2(J) = ZERO
! 259: END DO
! 260: X2(I) = ONE
! 261: CALL ZUNBDB6( M1, M2, N, X1, INCX1, X2, INCX2, Q1, LDQ1, Q2,
! 262: $ LDQ2, WORK, LWORK, CHILDINFO )
! 263: IF( DZNRM2(M1,X1,INCX1) .NE. ZERO
! 264: $ .OR. DZNRM2(M2,X2,INCX2) .NE. ZERO ) THEN
! 265: RETURN
! 266: END IF
! 267: END DO
! 268: *
! 269: RETURN
! 270: *
! 271: * End of ZUNBDB5
! 272: *
! 273: END
! 274:
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