Annotation of rpl/lapack/lapack/zlanhp.f, revision 1.8
1.8 ! bertrand 1: *> \brief \b ZLANHP
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download ZLANHP + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlanhp.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlanhp.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlanhp.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * DOUBLE PRECISION FUNCTION ZLANHP( NORM, UPLO, N, AP, WORK )
! 22: *
! 23: * .. Scalar Arguments ..
! 24: * CHARACTER NORM, UPLO
! 25: * INTEGER N
! 26: * ..
! 27: * .. Array Arguments ..
! 28: * DOUBLE PRECISION WORK( * )
! 29: * COMPLEX*16 AP( * )
! 30: * ..
! 31: *
! 32: *
! 33: *> \par Purpose:
! 34: * =============
! 35: *>
! 36: *> \verbatim
! 37: *>
! 38: *> ZLANHP returns the value of the one norm, or the Frobenius norm, or
! 39: *> the infinity norm, or the element of largest absolute value of a
! 40: *> complex hermitian matrix A, supplied in packed form.
! 41: *> \endverbatim
! 42: *>
! 43: *> \return ZLANHP
! 44: *> \verbatim
! 45: *>
! 46: *> ZLANHP = ( max(abs(A(i,j))), NORM = 'M' or 'm'
! 47: *> (
! 48: *> ( norm1(A), NORM = '1', 'O' or 'o'
! 49: *> (
! 50: *> ( normI(A), NORM = 'I' or 'i'
! 51: *> (
! 52: *> ( normF(A), NORM = 'F', 'f', 'E' or 'e'
! 53: *>
! 54: *> where norm1 denotes the one norm of a matrix (maximum column sum),
! 55: *> normI denotes the infinity norm of a matrix (maximum row sum) and
! 56: *> normF denotes the Frobenius norm of a matrix (square root of sum of
! 57: *> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
! 58: *> \endverbatim
! 59: *
! 60: * Arguments:
! 61: * ==========
! 62: *
! 63: *> \param[in] NORM
! 64: *> \verbatim
! 65: *> NORM is CHARACTER*1
! 66: *> Specifies the value to be returned in ZLANHP as described
! 67: *> above.
! 68: *> \endverbatim
! 69: *>
! 70: *> \param[in] UPLO
! 71: *> \verbatim
! 72: *> UPLO is CHARACTER*1
! 73: *> Specifies whether the upper or lower triangular part of the
! 74: *> hermitian matrix A is supplied.
! 75: *> = 'U': Upper triangular part of A is supplied
! 76: *> = 'L': Lower triangular part of A is supplied
! 77: *> \endverbatim
! 78: *>
! 79: *> \param[in] N
! 80: *> \verbatim
! 81: *> N is INTEGER
! 82: *> The order of the matrix A. N >= 0. When N = 0, ZLANHP is
! 83: *> set to zero.
! 84: *> \endverbatim
! 85: *>
! 86: *> \param[in] AP
! 87: *> \verbatim
! 88: *> AP is COMPLEX*16 array, dimension (N*(N+1)/2)
! 89: *> The upper or lower triangle of the hermitian matrix A, packed
! 90: *> columnwise in a linear array. The j-th column of A is stored
! 91: *> in the array AP as follows:
! 92: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
! 93: *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
! 94: *> Note that the imaginary parts of the diagonal elements need
! 95: *> not be set and are assumed to be zero.
! 96: *> \endverbatim
! 97: *>
! 98: *> \param[out] WORK
! 99: *> \verbatim
! 100: *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
! 101: *> where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
! 102: *> WORK is not referenced.
! 103: *> \endverbatim
! 104: *
! 105: * Authors:
! 106: * ========
! 107: *
! 108: *> \author Univ. of Tennessee
! 109: *> \author Univ. of California Berkeley
! 110: *> \author Univ. of Colorado Denver
! 111: *> \author NAG Ltd.
! 112: *
! 113: *> \date November 2011
! 114: *
! 115: *> \ingroup complex16OTHERauxiliary
! 116: *
! 117: * =====================================================================
1.1 bertrand 118: DOUBLE PRECISION FUNCTION ZLANHP( NORM, UPLO, N, AP, WORK )
119: *
1.8 ! bertrand 120: * -- LAPACK auxiliary routine (version 3.4.0) --
1.1 bertrand 121: * -- LAPACK is a software package provided by Univ. of Tennessee, --
122: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.8 ! bertrand 123: * November 2011
1.1 bertrand 124: *
125: * .. Scalar Arguments ..
126: CHARACTER NORM, UPLO
127: INTEGER N
128: * ..
129: * .. Array Arguments ..
130: DOUBLE PRECISION WORK( * )
131: COMPLEX*16 AP( * )
132: * ..
133: *
134: * =====================================================================
135: *
136: * .. Parameters ..
137: DOUBLE PRECISION ONE, ZERO
138: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
139: * ..
140: * .. Local Scalars ..
141: INTEGER I, J, K
142: DOUBLE PRECISION ABSA, SCALE, SUM, VALUE
143: * ..
144: * .. External Functions ..
145: LOGICAL LSAME
146: EXTERNAL LSAME
147: * ..
148: * .. External Subroutines ..
149: EXTERNAL ZLASSQ
150: * ..
151: * .. Intrinsic Functions ..
152: INTRINSIC ABS, DBLE, MAX, SQRT
153: * ..
154: * .. Executable Statements ..
155: *
156: IF( N.EQ.0 ) THEN
157: VALUE = ZERO
158: ELSE IF( LSAME( NORM, 'M' ) ) THEN
159: *
160: * Find max(abs(A(i,j))).
161: *
162: VALUE = ZERO
163: IF( LSAME( UPLO, 'U' ) ) THEN
164: K = 0
165: DO 20 J = 1, N
166: DO 10 I = K + 1, K + J - 1
167: VALUE = MAX( VALUE, ABS( AP( I ) ) )
168: 10 CONTINUE
169: K = K + J
170: VALUE = MAX( VALUE, ABS( DBLE( AP( K ) ) ) )
171: 20 CONTINUE
172: ELSE
173: K = 1
174: DO 40 J = 1, N
175: VALUE = MAX( VALUE, ABS( DBLE( AP( K ) ) ) )
176: DO 30 I = K + 1, K + N - J
177: VALUE = MAX( VALUE, ABS( AP( I ) ) )
178: 30 CONTINUE
179: K = K + N - J + 1
180: 40 CONTINUE
181: END IF
182: ELSE IF( ( LSAME( NORM, 'I' ) ) .OR. ( LSAME( NORM, 'O' ) ) .OR.
183: $ ( NORM.EQ.'1' ) ) THEN
184: *
185: * Find normI(A) ( = norm1(A), since A is hermitian).
186: *
187: VALUE = ZERO
188: K = 1
189: IF( LSAME( UPLO, 'U' ) ) THEN
190: DO 60 J = 1, N
191: SUM = ZERO
192: DO 50 I = 1, J - 1
193: ABSA = ABS( AP( K ) )
194: SUM = SUM + ABSA
195: WORK( I ) = WORK( I ) + ABSA
196: K = K + 1
197: 50 CONTINUE
198: WORK( J ) = SUM + ABS( DBLE( AP( K ) ) )
199: K = K + 1
200: 60 CONTINUE
201: DO 70 I = 1, N
202: VALUE = MAX( VALUE, WORK( I ) )
203: 70 CONTINUE
204: ELSE
205: DO 80 I = 1, N
206: WORK( I ) = ZERO
207: 80 CONTINUE
208: DO 100 J = 1, N
209: SUM = WORK( J ) + ABS( DBLE( AP( K ) ) )
210: K = K + 1
211: DO 90 I = J + 1, N
212: ABSA = ABS( AP( K ) )
213: SUM = SUM + ABSA
214: WORK( I ) = WORK( I ) + ABSA
215: K = K + 1
216: 90 CONTINUE
217: VALUE = MAX( VALUE, SUM )
218: 100 CONTINUE
219: END IF
220: ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
221: *
222: * Find normF(A).
223: *
224: SCALE = ZERO
225: SUM = ONE
226: K = 2
227: IF( LSAME( UPLO, 'U' ) ) THEN
228: DO 110 J = 2, N
229: CALL ZLASSQ( J-1, AP( K ), 1, SCALE, SUM )
230: K = K + J
231: 110 CONTINUE
232: ELSE
233: DO 120 J = 1, N - 1
234: CALL ZLASSQ( N-J, AP( K ), 1, SCALE, SUM )
235: K = K + N - J + 1
236: 120 CONTINUE
237: END IF
238: SUM = 2*SUM
239: K = 1
240: DO 130 I = 1, N
241: IF( DBLE( AP( K ) ).NE.ZERO ) THEN
242: ABSA = ABS( DBLE( AP( K ) ) )
243: IF( SCALE.LT.ABSA ) THEN
244: SUM = ONE + SUM*( SCALE / ABSA )**2
245: SCALE = ABSA
246: ELSE
247: SUM = SUM + ( ABSA / SCALE )**2
248: END IF
249: END IF
250: IF( LSAME( UPLO, 'U' ) ) THEN
251: K = K + I + 1
252: ELSE
253: K = K + N - I + 1
254: END IF
255: 130 CONTINUE
256: VALUE = SCALE*SQRT( SUM )
257: END IF
258: *
259: ZLANHP = VALUE
260: RETURN
261: *
262: * End of ZLANHP
263: *
264: END
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