Programmer Guide/Command Reference/EVAL/complex arithmetic - Revision history

Toni: /* multiplication and division (element-wise) */

2012-05-02T09:15:48Z

multiplication and division (element-wise)

← Older revision		Revision as of 11:15, 2 May 2012
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	:;<code>''rc'' = '''cmul'''(''xc'', ''yc'')</code>: Multiply ''xc'' and ''yc'' element by element.		:;<code>''rc'' = '''cmul'''(''xc'', ''yc'')</code>: Multiply ''xc'' and ''yc'' element by element.
	::<code>''rc''<sub>i,j</sub> = ''xc''<sub>i,j</sub> * ''yc''<sub>i,j</sub></code>		::<code>''rc''<sub>i,j</sub> = ''xc''<sub>i,j</sub> * ''yc''<sub>i,j</sub></code>
			:;<code>''rc'' = '''cdiv'''(''xc'')</code>: Compute the inverse of each element of ''xc''.
			::<code>''rc''<sub>i,j</sub> = 1 / ''xc''<sub>i,j</sub></code>
	:;<code>''rc'' = '''cdiv'''(''xc'', ''n'')</code>: Divide each element of ''xc'' by the complex number ''n''.		:;<code>''rc'' = '''cdiv'''(''xc'', ''n'')</code>: Divide each element of ''xc'' by the complex number ''n''.
	::<code>''rc''<sub>i,j</sub> = ''xc''<sub>i,j</sub> / ''n''</code>		::<code>''rc''<sub>i,j</sub> = ''xc''<sub>i,j</sub> / ''n''</code>

Toni: /* multiplication and division (element-wise) */

2012-05-02T09:00:25Z

multiplication and division (element-wise)

← Older revision		Revision as of 11:00, 2 May 2012
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	:;<code>''rc'' = '''cmul'''(''xc'', ''yc'')</code>: Multiply ''xc'' and ''yc'' element by element.		:;<code>''rc'' = '''cmul'''(''xc'', ''yc'')</code>: Multiply ''xc'' and ''yc'' element by element.
	::<code>''rc''<sub>i,j</sub> = ''xc''<sub>i,j</sub> * ''yc''<sub>i,j</sub></code>		::<code>''rc''<sub>i,j</sub> = ''xc''<sub>i,j</sub> * ''yc''<sub>i,j</sub></code>
			:;<code>''rc'' = '''cdiv'''(''xc'', ''n'')</code>: Divide each element of ''xc'' by the complex number ''n''.
			::<code>''rc''<sub>i,j</sub> = ''xc''<sub>i,j</sub> / ''n''</code>
			:;<code>''rc'' = '''cdiv'''(''xc'', ''yc'')</code>: Divide ''xc'' by ''yc'' element by element.
			::<code>''rc''<sub>i,j</sub> = ''xc''<sub>i,j</sub> / ''yc''<sub>i,j</sub></code>

	==special functions==		==special functions==

Toni: /* multiplication (element-wise) */

2012-05-02T08:53:52Z

multiplication (element-wise)

← Older revision		Revision as of 10:53, 2 May 2012
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	:;<code>''rc'' = '''cset'''(''x'', ''y'')</code>: Combine elements of ''x'' (real part or length) and ''y'' (imaginary part or phase) to complex numbers.		:;<code>''rc'' = '''cset'''(''x'', ''y'')</code>: Combine elements of ''x'' (real part or length) and ''y'' (imaginary part or phase) to complex numbers.

	==multiplication (element-wise)==		==multiplication and division (element-wise)==
	:{\|class="keinrahmen"		:{\|class="keinrahmen"
	\|''xc'' \|\|... any complex type (re,im)		\|''xc'' \|\|... any complex type (re,im)

Toni at 08:53, 2 May 2012

2012-05-02T08:53:23Z

← Older revision		Revision as of 10:53, 2 May 2012
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	The package consists of the following functions:		The package consists of the following functions:
	:[[#complex → complex\|cr2p, cp2r, conj]], [[#complex → real\|cr2len, cr2phi, cget]], [[#real → complex\|cset, conj]], [[#multiplication (element-wise)\|cmul]], [[#special functions\|ctrn, cdot, cmulv]]		:[[#complex → complex\|cr2p, cp2r, conj]], [[#complex → real\|cr2len, cr2phi, cget]], [[#real → complex\|cset, conj]], [[#multiplication and division (element-wise)\|cmul, cdiv]], [[#special functions\|ctrn, cdot, cmulv]]

	==complex numerical objects==		==complex numerical objects==

Christian at 18:25, 21 April 2011

2011-04-21T18:25:35Z

← Older revision		Revision as of 20:25, 21 April 2011
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	\|''v''[2*i+1,j] = \|\| ''im''<sub>i,j</sub> or ''phi''<sub>i,j</sub>		\|''v''[2*i+1,j] = \|\| ''im''<sub>i,j</sub> or ''phi''<sub>i,j</sub>
	\|}		\|}
	:* In general a numerical object containing '''N x M''' complex numbers (N>=1, M>=1), consists of 2N rows and M columns, because each complex number uses two cells of a row.		:* In general a numerical object containing '''N x M''' complex numbers (N≥1, M≥1), consists of 2N rows and M columns, because each complex number uses two cells of a row.
	:* If a numerical object containing '''N x M''' complex numbers, is converted element-wise to real, the resulting object consists of '''N x M''' real numbers.		:* If a numerical object containing '''N x M''' complex numbers, is converted element-wise to real, the resulting object consists of '''N x M''' real numbers.

193.171.195.48 at 09:26, 21 April 2011

2011-04-21T09:26:50Z

← Older revision		Revision as of 11:26, 21 April 2011
Line 3:		Line 3:

	The package consists of the following functions:		The package consists of the following functions:
	:[[#complex->complex\|cr2p, cp2r, conj]], [[#complex->real\|cr2len, cr2phi, cget]], [[#real->complex\|cset, conj]], [[#multiplication (element-wise)\|cmul]], [[#special functions\|ctrn, cdot, cmulv]]		:[[#complex → complex\|cr2p, cp2r, conj]], [[#complex → real\|cr2len, cr2phi, cget]], [[#real → complex\|cset, conj]], [[#multiplication (element-wise)\|cmul]], [[#special functions\|ctrn, cdot, cmulv]]

	==complex numerical objects==		==complex numerical objects==

193.171.195.48 at 09:25, 21 April 2011

2011-04-21T09:25:01Z

← Older revision		Revision as of 11:25, 21 April 2011
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	:[[#complex->complex\|cr2p, cp2r, conj]], [[#complex->real\|cr2len, cr2phi, cget]], [[#real->complex\|cset, conj]], [[#multiplication (element-wise)\|cmul]], [[#special functions\|ctrn, cdot, cmulv]]		:[[#complex->complex\|cr2p, cp2r, conj]], [[#complex->real\|cr2len, cr2phi, cget]], [[#real->complex\|cset, conj]], [[#multiplication (element-wise)\|cmul]], [[#special functions\|ctrn, cdot, cmulv]]

	===complex numerical objects===		==complex numerical objects==
	:* A complex number or complex scalar is a numerical object ''v'' with 2 rows and 1 column (a vector):		:* A complex number or complex scalar is a numerical object ''v'' with 2 rows and 1 column (a vector):
	::{\|class="keinrahmen"		::{\|class="keinrahmen"
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	:* If a numerical object containing '''N x M''' complex numbers, is converted element-wise to real, the resulting object consists of '''N x M''' real numbers.		:* If a numerical object containing '''N x M''' complex numbers, is converted element-wise to real, the resulting object consists of '''N x M''' real numbers.

	===complex → complex===		==complex → complex==
	:{\|class="keinrahmen"		:{\|class="keinrahmen"
	\|''xc'' \|\|... any complex type		\|''xc'' \|\|... any complex type
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	:;<code>''rc'' = '''conj'''(''xc'')</code>: Conjugate ''xc''; ''xc'' must be in cartesian format.		:;<code>''rc'' = '''conj'''(''xc'')</code>: Conjugate ''xc''; ''xc'' must be in cartesian format.

	===complex → real===		==complex → real==
	:{\|class="keinrahmen"		:{\|class="keinrahmen"
	\|''xc'' \|\|... any complex type		\|''xc'' \|\|... any complex type
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	:;<code>''r'' = '''cget'''(''xc'', 1)</code>: Get imaginary part or phase of ''xc'' (depends on format of ''xc'').		:;<code>''r'' = '''cget'''(''xc'', 1)</code>: Get imaginary part or phase of ''xc'' (depends on format of ''xc'').

	===real → complex===		==real → complex==
	:{\|class="keinrahmen"		:{\|class="keinrahmen"
	\|''x'' \|\|... any real type		\|''x'' \|\|... any real type
Line 61:		Line 61:
	:;<code>''rc'' = '''cset'''(''x'', ''y'')</code>: Combine elements of ''x'' (real part or length) and ''y'' (imaginary part or phase) to complex numbers.		:;<code>''rc'' = '''cset'''(''x'', ''y'')</code>: Combine elements of ''x'' (real part or length) and ''y'' (imaginary part or phase) to complex numbers.

	===multiplication (element-wise)===		==multiplication (element-wise)==
	:{\|class="keinrahmen"		:{\|class="keinrahmen"
	\|''xc'' \|\|... any complex type (re,im)		\|''xc'' \|\|... any complex type (re,im)
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	::<code>''rc''<sub>i,j</sub> = ''xc''<sub>i,j</sub> * ''yc''<sub>i,j</sub></code>		::<code>''rc''<sub>i,j</sub> = ''xc''<sub>i,j</sub> * ''yc''<sub>i,j</sub></code>

	===special functions===		==special functions==
	:;<code>''rc''<sub>matrix</sub> = '''ctrn'''(''xc''<sub>matrix</sub>)</code>: Transposed the complex matrix ''xc''.		:;<code>''rc''<sub>matrix</sub> = '''ctrn'''(''xc''<sub>matrix</sub>)</code>: Transposed the complex matrix ''xc''.
	::<code>''rc''<sub>i,j</sub> = ''xc''<sub>j,i</sub></code>		::<code>''rc''<sub>i,j</sub> = ''xc''<sub>j,i</sub></code>
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	:;<code>''rc''<sub>matrix</sub> = '''cmulv'''(''xc''<sub>matrix</sub>, ''yc''<sub>matrix</sub>)</code>: Compute the product of the complex '''NxM''' matrix ''xc'' and the complex '''MxL''' matrix ''yc''. The result is the complex NxL matrix ''rc''.		:;<code>''rc''<sub>matrix</sub> = '''cmulv'''(''xc''<sub>matrix</sub>, ''yc''<sub>matrix</sub>)</code>: Compute the product of the complex '''NxM''' matrix ''xc'' and the complex '''MxL''' matrix ''yc''. The result is the complex NxL matrix ''rc''.
	::<code>''rc''<sub>i,k</sub> = sum<sub>j=0..M-1</sub> (''xc''<sub>i,j</sub> * ''yc''<sub>j,i</sub>) , i=0..N-1 and k=0..L-1</code>		::<code>''rc''<sub>i,k</sub> = sum<sub>j=0..M-1</sub> (''xc''<sub>i,j</sub> * ''yc''<sub>j,i</sub>) , i=0..N-1 and k=0..L-1</code>
	===See also===		==See also==
	:[[../#complex numbers\|complex numbers]], [[../vvset\|vvset]], [[../vvget\|vvget]], [[../vv\|vv]], [[../fft\|fft]], [[../dft\|dft]]		:[[../#complex numbers\|complex numbers]], [[../vvset\|vvset]], [[../vvget\|vvget]], [[../vv\|vv]], [[../fft\|fft]], [[../dft\|dft]]

	[[../#Functions\|<function list>]]		[[../#Functions\|<function list>]]

193.171.195.48 at 09:24, 21 April 2011

2011-04-21T09:24:11Z

← Older revision		Revision as of 11:24, 21 April 2011
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	:[[#complex->complex\|cr2p, cp2r, conj]], [[#complex->real\|cr2len, cr2phi, cget]], [[#real->complex\|cset, conj]], [[#multiplication (element-wise)\|cmul]], [[#special functions\|ctrn, cdot, cmulv]]		:[[#complex->complex\|cr2p, cp2r, conj]], [[#complex->real\|cr2len, cr2phi, cget]], [[#real->complex\|cset, conj]], [[#multiplication (element-wise)\|cmul]], [[#special functions\|ctrn, cdot, cmulv]]

	====complex numerical objects====		===complex numerical objects===
	:* A complex number or complex scalar is a numerical object ''v'' with 2 rows and 1 column (a vector):		:* A complex number or complex scalar is a numerical object ''v'' with 2 rows and 1 column (a vector):
	::{\|class="keinrahmen"		::{\|class="keinrahmen"
Line 30:		Line 30:
	:* If a numerical object containing '''N x M''' complex numbers, is converted element-wise to real, the resulting object consists of '''N x M''' real numbers.		:* If a numerical object containing '''N x M''' complex numbers, is converted element-wise to real, the resulting object consists of '''N x M''' real numbers.

	====complex → complex====		===complex → complex===
	:{\|class="keinrahmen"		:{\|class="keinrahmen"
	\|''xc'' \|\|... any complex type		\|''xc'' \|\|... any complex type
Line 40:		Line 40:
	:;<code>''rc'' = '''conj'''(''xc'')</code>: Conjugate ''xc''; ''xc'' must be in cartesian format.		:;<code>''rc'' = '''conj'''(''xc'')</code>: Conjugate ''xc''; ''xc'' must be in cartesian format.

	====complex → real====		===complex → real===
	:{\|class="keinrahmen"		:{\|class="keinrahmen"
	\|''xc'' \|\|... any complex type		\|''xc'' \|\|... any complex type
Line 51:		Line 51:
	:;<code>''r'' = '''cget'''(''xc'', 1)</code>: Get imaginary part or phase of ''xc'' (depends on format of ''xc'').		:;<code>''r'' = '''cget'''(''xc'', 1)</code>: Get imaginary part or phase of ''xc'' (depends on format of ''xc'').

	====real → complex====		===real → complex===
	:{\|class="keinrahmen"		:{\|class="keinrahmen"
	\|''x'' \|\|... any real type		\|''x'' \|\|... any real type
Line 61:		Line 61:
	:;<code>''rc'' = '''cset'''(''x'', ''y'')</code>: Combine elements of ''x'' (real part or length) and ''y'' (imaginary part or phase) to complex numbers.		:;<code>''rc'' = '''cset'''(''x'', ''y'')</code>: Combine elements of ''x'' (real part or length) and ''y'' (imaginary part or phase) to complex numbers.

	====multiplication (element-wise)====		===multiplication (element-wise)===
	:{\|class="keinrahmen"		:{\|class="keinrahmen"
	\|''xc'' \|\|... any complex type (re,im)		\|''xc'' \|\|... any complex type (re,im)
Line 77:		Line 77:
	::<code>''rc''<sub>i,j</sub> = ''xc''<sub>i,j</sub> * ''yc''<sub>i,j</sub></code>		::<code>''rc''<sub>i,j</sub> = ''xc''<sub>i,j</sub> * ''yc''<sub>i,j</sub></code>

	====special functions====		===special functions===
	:;<code>''rc''<sub>matrix</sub> = '''ctrn'''(''xc''<sub>matrix</sub>)</code>: Transposed the complex matrix ''xc''.		:;<code>''rc''<sub>matrix</sub> = '''ctrn'''(''xc''<sub>matrix</sub>)</code>: Transposed the complex matrix ''xc''.
	::<code>''rc''<sub>i,j</sub> = ''xc''<sub>j,i</sub></code>		::<code>''rc''<sub>i,j</sub> = ''xc''<sub>j,i</sub></code>
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	:;<code>''rc''<sub>matrix</sub> = '''cmulv'''(''xc''<sub>matrix</sub>, ''yc''<sub>matrix</sub>)</code>: Compute the product of the complex '''NxM''' matrix ''xc'' and the complex '''MxL''' matrix ''yc''. The result is the complex NxL matrix ''rc''.		:;<code>''rc''<sub>matrix</sub> = '''cmulv'''(''xc''<sub>matrix</sub>, ''yc''<sub>matrix</sub>)</code>: Compute the product of the complex '''NxM''' matrix ''xc'' and the complex '''MxL''' matrix ''yc''. The result is the complex NxL matrix ''rc''.
	::<code>''rc''<sub>i,k</sub> = sum<sub>j=0..M-1</sub> (''xc''<sub>i,j</sub> * ''yc''<sub>j,i</sub>) , i=0..N-1 and k=0..L-1</code>		::<code>''rc''<sub>i,k</sub> = sum<sub>j=0..M-1</sub> (''xc''<sub>i,j</sub> * ''yc''<sub>j,i</sub>) , i=0..N-1 and k=0..L-1</code>
	====See also====		===See also===
	:[[../#complex numbers\|complex numbers]], [[../vvset\|vvset]], [[../vvget\|vvget]], [[../vv\|vv]], [[../fft\|fft]], [[../dft\|dft]]		:[[../#complex numbers\|complex numbers]], [[../vvset\|vvset]], [[../vvget\|vvget]], [[../vv\|vv]], [[../fft\|fft]], [[../dft\|dft]]

	[[../#Functions\|<function list>]]		[[../#Functions\|<function list>]]

193.171.195.48 at 09:22, 21 April 2011

2011-04-21T09:22:54Z

← Older revision		Revision as of 11:22, 21 April 2011
Line 91:		Line 91:
	::<code>''rc''<sub>i,k</sub> = sum<sub>j=0..M-1</sub> (''xc''<sub>i,j</sub> * ''yc''<sub>j,i</sub>) , i=0..N-1 and k=0..L-1</code>		::<code>''rc''<sub>i,k</sub> = sum<sub>j=0..M-1</sub> (''xc''<sub>i,j</sub> * ''yc''<sub>j,i</sub>) , i=0..N-1 and k=0..L-1</code>
	====See also====		====See also====
	:[[~~Programmer_Guide~~/~~Command_Reference/EVAL~~#complex numbers\|complex numbers]], [[~~Programmer_Guide/Command_Reference/EVAL~~/vvset\|vvset]], [[~~Programmer_Guide/Command_Reference/EVAL~~/vvget\|vvget]], [[~~Programmer_Guide/Command_Reference/EVAL~~/vv\|vv]], [[~~Programmer_Guide/Command_Reference/EVAL~~/fft\|fft]], [[~~Programmer_Guide/Command_Reference/EVAL~~/dft\|dft]]		:[[../#complex numbers\|complex numbers]], [[../vvset\|vvset]], [[../vvget\|vvget]], [[../vv\|vv]], [[../fft\|fft]], [[../dft\|dft]]

	[[~~Programmer_Guide~~/~~Command_Reference/EVAL~~#Functions\|<function list>]]		[[../#Functions\|<function list>]]

Toni: /* See also */

2011-04-20T09:28:22Z

← Older revision		Revision as of 11:28, 20 April 2011
Line 91:		Line 91:
	::<code>''rc''<sub>i,k</sub> = sum<sub>j=0..M-1</sub> (''xc''<sub>i,j</sub> * ''yc''<sub>j,i</sub>) , i=0..N-1 and k=0..L-1</code>		::<code>''rc''<sub>i,k</sub> = sum<sub>j=0..M-1</sub> (''xc''<sub>i,j</sub> * ''yc''<sub>j,i</sub>) , i=0..N-1 and k=0..L-1</code>
	====See also====		====See also====
	[[Programmer_Guide/Command_Reference/EVAL#complex numbers\|complex numbers]], [[Programmer_Guide/Command_Reference/EVAL/vvset\|vvset]], [[Programmer_Guide/Command_Reference/EVAL/vvget\|vvget]], [[Programmer_Guide/Command_Reference/EVAL/vv\|vv]], [[Programmer_Guide/Command_Reference/EVAL/fft\|fft]], [[Programmer_Guide/Command_Reference/EVAL/dft\|dft]]		:[[Programmer_Guide/Command_Reference/EVAL#complex numbers\|complex numbers]], [[Programmer_Guide/Command_Reference/EVAL/vvset\|vvset]], [[Programmer_Guide/Command_Reference/EVAL/vvget\|vvget]], [[Programmer_Guide/Command_Reference/EVAL/vv\|vv]], [[Programmer_Guide/Command_Reference/EVAL/fft\|fft]], [[Programmer_Guide/Command_Reference/EVAL/dft\|dft]]

	[[Programmer_Guide/Command_Reference/EVAL#Functions\|<function list>]]		[[Programmer_Guide/Command_Reference/EVAL#Functions\|<function list>]]